TSTP Solution File: SWW343+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW343+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:55 EDT 2023
% Result : Theorem 51.10s 50.80s
% Output : CNFRefutation 51.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW343+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 20:07:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 50.50/50.63 %-------------------------------------------
% 50.50/50.63 % File :CSE---1.6
% 50.50/50.63 % Problem :theBenchmark
% 50.50/50.63 % Transform :cnf
% 50.50/50.63 % Format :tptp:raw
% 50.50/50.64 % Command :java -jar mcs_scs.jar %d %s
% 50.50/50.64
% 50.50/50.64 % Result :Theorem 47.330000s
% 50.50/50.64 % Output :CNFRefutation 47.330000s
% 50.50/50.64 %-------------------------------------------
% 50.50/50.64 %------------------------------------------------------------------------------
% 50.50/50.64 % File : SWW343+1 : TPTP v8.1.2. Released v5.2.0.
% 50.50/50.64 % Domain : Software Verification
% 50.50/50.64 % Problem : Hoare's Logic with Procedures 435205, 5000 axioms selected
% 50.50/50.64 % Version : Especial.
% 50.50/50.64 % English :
% 50.50/50.64
% 50.50/50.64 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 50.50/50.64 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 50.50/50.64 % Source : [Bla11]
% 50.50/50.64 % Names : hoare_435205.5000.p [Bla11]
% 50.50/50.64
% 50.50/50.64 % Status : ContradictoryAxioms
% 50.50/50.64 % Rating : 0.58 v8.1.0, 0.64 v7.5.0, 0.59 v7.4.0, 0.73 v7.3.0, 0.69 v7.1.0, 0.70 v7.0.0, 0.77 v6.4.0, 0.69 v6.3.0, 0.71 v6.2.0, 0.80 v6.1.0, 0.83 v6.0.0, 0.74 v5.5.0, 0.78 v5.4.0, 0.89 v5.3.0, 0.93 v5.2.0
% 50.50/50.64 % Syntax : Number of formulae : 5209 (1692 unt; 0 def)
% 50.50/50.64 % Number of atoms : 12623 (4520 equ)
% 50.50/50.64 % Maximal formula atoms : 13 ( 2 avg)
% 50.50/50.64 % Number of connectives : 8504 (1090 ~; 158 |; 716 &)
% 50.50/50.64 % ( 883 <=>;5657 =>; 0 <=; 0 <~>)
% 50.50/50.64 % Maximal formula depth : 22 ( 6 avg)
% 50.50/50.64 % Maximal term depth : 19 ( 2 avg)
% 50.50/50.64 % Number of predicates : 142 ( 141 usr; 1 prp; 0-7 aty)
% 50.50/50.64 % Number of functors : 394 ( 394 usr; 67 con; 0-7 aty)
% 50.50/50.64 % Number of variables : 16611 (16479 !; 132 ?)
% 50.50/50.64 % SPC : FOF_CAX_RFO_SEQ
% 50.50/50.64
% 50.50/50.64 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 50.50/50.64 % 2011-03-01 12:13:08
% 50.50/50.64 %------------------------------------------------------------------------------
% 50.50/50.64 %----Relevant facts (4983)
% 50.50/50.64 fof(fact_ext,axiom,
% 50.50/50.64 ! [V_g_2,V_f_2] :
% 50.50/50.64 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 50.50/50.64 => V_f_2 = V_g_2 ) ).
% 50.50/50.64
% 50.50/50.64 fof(fact_triple__valid__Suc,axiom,
% 50.50/50.64 ! [V_t,V_n,T_a] :
% 50.50/50.64 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 50.50/50.64 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 50.50/50.64
% 50.50/50.64 fof(fact_evaln_OBody,axiom,
% 50.50/50.64 ! [V_s1,V_n,V_s0,V_pn] :
% 50.50/50.64 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
% 50.50/50.64 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ).
% 50.50/50.64
% 50.50/50.64 fof(fact_evaln_Oequations_I9_J,axiom,
% 50.50/50.64 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 50.50/50.64 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
% 50.50/50.64 <=> 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) ) ).
% 50.50/50.64
% 50.50/50.64 fof(fact_evaln_OCall,axiom,
% 50.50/50.64 ! [V_X_2,V_s1_2,V_n_2,V_a_2,V_s0_2,V_pn_2] :
% 50.50/50.64 ( 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)
% 50.50/50.64 => 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))) ) ).
% 50.50/50.64
% 50.50/50.64 fof(fact_evaln_Oequations_I10_J,axiom,
% 50.50/50.64 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a6_2] :
% 50.50/50.64 ( 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)))
% 50.50/50.64 <=> ? [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 & 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) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln__Suc,axiom,
% 50.50/50.65 ! [V_s_H,V_n,V_s,V_c] :
% 50.50/50.65 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
% 50.50/50.65 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_Body__triple__valid__Suc,axiom,
% 50.50/50.65 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_b] :
% 50.50/50.65 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
% 50.50/50.65 <=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln__elim__cases_I7_J,axiom,
% 50.50/50.65 ! [V_s1_2,V_n_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 50.50/50.65 ( 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)
% 50.50/50.65 => ~ ! [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 => ~ 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) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln__elim__cases_I6_J,axiom,
% 50.50/50.65 ! [V_s1,V_n,V_s,V_P] :
% 50.50/50.65 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
% 50.50/50.65 => ~ ! [B_n] :
% 50.50/50.65 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 50.50/50.65 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc_OCall,axiom,
% 50.50/50.65 ! [V_X_2,V_s1_2,V_a_2,V_s0_2,V_pn_2] :
% 50.50/50.65 ( 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))
% 50.50/50.65 => 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)))) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc_Oequations_I10_J,axiom,
% 50.50/50.65 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_a5_2] :
% 50.50/50.65 ( 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))))
% 50.50/50.65 <=> ? [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 & 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)) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln_OLocal,axiom,
% 50.50/50.65 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
% 50.50/50.65 ( c_Natural_Oevaln(V_c_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)
% 50.50/50.65 => c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_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))) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc_OBody,axiom,
% 50.50/50.65 ! [V_s1,V_s0,V_pn] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 50.50/50.65 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc__elim__cases_I6_J,axiom,
% 50.50/50.65 ! [V_s1,V_s,V_P] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 50.50/50.65 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc_OLocal,axiom,
% 50.50/50.65 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_c_2] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_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))
% 50.50/50.65 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_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)))) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_triple_Oinject,axiom,
% 50.50/50.65 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 50.50/50.65 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
% 50.50/50.65 <=> ( V_fun1_2 = V_fun1_H_2
% 50.50/50.65 & V_com_2 = V_com_H_2
% 50.50/50.65 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com__det,axiom,
% 50.50/50.65 ! [V_u,V_t,V_s,V_c] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 50.50/50.65 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 50.50/50.65 => V_u = V_t ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln__evalc,axiom,
% 50.50/50.65 ! [V_t,V_n,V_s,V_c] :
% 50.50/50.65 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 50.50/50.65 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_eval__eq,axiom,
% 50.50/50.65 ! [V_t_2,V_s_2,V_c_2] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
% 50.50/50.65 <=> ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc_Oequations_I3_J,axiom,
% 50.50/50.65 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 50.50/50.65 ( 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))))
% 50.50/50.65 <=> ? [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 & 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)) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_triple__valid__def2,axiom,
% 50.50/50.65 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_b] :
% 50.50/50.65 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2))
% 50.50/50.65 <=> ! [B_Z,B_s] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 50.50/50.65 => ! [B_s_H] :
% 50.50/50.65 ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
% 50.50/50.65 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc_Oequations_I9_J,axiom,
% 50.50/50.65 ! [V_a3_2,V_a2_2,V_a1_2] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 50.50/50.65 <=> 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)) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln_Oequations_I3_J,axiom,
% 50.50/50.65 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] :
% 50.50/50.65 ( 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)))
% 50.50/50.65 <=> ? [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 & 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) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc__elim__cases_I7_J,axiom,
% 50.50/50.65 ! [V_s1_2,V_s_2,V_a_2,V_P_2,V_X_2] :
% 50.50/50.65 ( 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))
% 50.50/50.65 => ~ ! [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 => ~ 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)) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc__elim__cases_I3_J,axiom,
% 50.50/50.65 ! [V_t_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)),V_s_2),V_t_2))
% 50.50/50.65 => ~ ! [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_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)) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln__elim__cases_I3_J,axiom,
% 50.50/50.65 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_a_2,V_Y_2] :
% 50.50/50.65 ( c_Natural_Oevaln(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2),V_s_2,V_n_2,V_t_2)
% 50.50/50.65 => ~ ! [B_s1] :
% 50.50/50.65 ( 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))
% 50.50/50.65 => ~ c_Natural_Oevaln(V_c_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) ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I43_J,axiom,
% 50.50/50.65 ! [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) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I42_J,axiom,
% 50.50/50.65 ! [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) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I40_J,axiom,
% 50.50/50.65 ! [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) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I63_J,axiom,
% 50.50/50.65 ! [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) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I41_J,axiom,
% 50.50/50.65 ! [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) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I62_J,axiom,
% 50.50/50.65 ! [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) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_triple_Orecs,axiom,
% 50.50/50.65 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_triple_Osimps_I2_J,axiom,
% 50.50/50.65 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I7_J,axiom,
% 50.50/50.65 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 50.50/50.65 ( 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)
% 50.50/50.65 <=> ( V_vname_2 = V_vname_H_2
% 50.50/50.65 & V_pname_2 = V_pname_H_2
% 50.50/50.65 & V_fun_2 = V_fun_H_2 ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I6_J,axiom,
% 50.50/50.65 ! [V_pname_H_2,V_pname_2] :
% 50.50/50.65 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 50.50/50.65 <=> V_pname_2 = V_pname_H_2 ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_vname_Osimps_I2_J,axiom,
% 50.50/50.65 ! [V_loc_H_2,V_loc_2] :
% 50.50/50.65 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2)
% 50.50/50.65 <=> V_loc_2 = V_loc_H_2 ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_com_Osimps_I2_J,axiom,
% 50.50/50.65 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 50.50/50.65 ( 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)
% 50.50/50.65 <=> ( V_loc_2 = V_loc_H_2
% 50.50/50.65 & V_fun_2 = V_fun_H_2
% 50.50/50.65 & V_com_2 = V_com_H_2 ) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_vname_Orecs_I2_J,axiom,
% 50.50/50.65 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_vname_Osimps_I6_J,axiom,
% 50.50/50.65 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_Body__triple__valid__0,axiom,
% 50.50/50.65 ! [V_Q_2,V_pn_2,V_P_2,T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc_OAssign,axiom,
% 50.50/50.65 ! [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)))) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evalc__elim__cases_I2_J,axiom,
% 50.50/50.65 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 50.50/50.65 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 50.50/50.65 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln_OAssign,axiom,
% 50.50/50.65 ! [V_n_2,V_s_2,V_a_2,V_X_2] : 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))) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_evaln__elim__cases_I2_J,axiom,
% 50.50/50.65 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 50.50/50.65 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2)
% 50.50/50.65 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_n__not__Suc__n,axiom,
% 50.50/50.65 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_Suc__n__not__n,axiom,
% 50.50/50.65 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 50.50/50.65
% 50.50/50.65 fof(fact_nat_Oinject,axiom,
% 50.50/50.65 ! [V_nat_H_2,V_nat_2] :
% 50.50/50.65 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 50.50/50.65 <=> V_nat_2 = V_nat_H_2 ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_Suc__inject,axiom,
% 50.50/50.65 ! [V_y,V_x] :
% 50.50/50.65 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 50.50/50.65 => V_x = V_y ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_WTs__elim__cases_I8_J,axiom,
% 50.50/50.65 ! [V_a_2,V_P_2,V_X_2] :
% 50.50/50.65 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
% 50.50/50.65 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ).
% 50.50/50.65
% 50.50/50.65 fof(fact_WTs__elim__cases_I3_J,axiom,
% 50.50/50.65 ! [V_c_2,V_a_2,V_Y_2] :
% 50.50/50.65 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
% 50.50/50.66 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osimps_I1_J,axiom,
% 50.50/50.66 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 50.50/50.66 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 50.50/50.66 <=> ( V_vname_2 = V_vname_H_2
% 50.50/50.66 & V_fun_2 = V_fun_H_2 ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_Oequations_I2_J,axiom,
% 50.50/50.66 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_OAssign,axiom,
% 50.50/50.66 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_Suc__neq__Zero,axiom,
% 50.50/50.66 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_Zero__neq__Suc,axiom,
% 50.50/50.66 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat_Osimps_I3_J,axiom,
% 50.50/50.66 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_Suc__not__Zero,axiom,
% 50.50/50.66 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat_Osimps_I2_J,axiom,
% 50.50/50.66 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_Zero__not__Suc,axiom,
% 50.50/50.66 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_Oequations_I3_J,axiom,
% 50.50/50.66 ! [V_a1_2,V_a3_2,V_a2_2] :
% 50.50/50.66 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 50.50/50.66 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_OLocal,axiom,
% 50.50/50.66 ! [V_a_2,V_Y_2,V_c_2] :
% 50.50/50.66 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 50.50/50.66 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osimps_I30_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osimps_I31_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osimps_I32_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osimps_I22_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osimps_I33_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osimps_I23_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_Oequations_I8_J,axiom,
% 50.50/50.66 ! [V_a3_2,V_a1_2,V_a2_2] :
% 50.50/50.66 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 50.50/50.66 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_OCall,axiom,
% 50.50/50.66 ! [V_a_2,V_X_2,V_pn_2] :
% 50.50/50.66 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 50.50/50.66 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_evaln_Oequations_I2_J,axiom,
% 50.50/50.66 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : 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))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_evalc_Oequations_I2_J,axiom,
% 50.50/50.66 ! [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)))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_triple_Osize_I1_J,axiom,
% 50.50/50.66 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osize_I2_J,axiom,
% 50.50/50.66 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_triple_Osize_I2_J,axiom,
% 50.50/50.66 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osize_I4_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osimps_I5_J,axiom,
% 50.50/50.66 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Orecs_I1_J,axiom,
% 50.50/50.66 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I8_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I2_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I7_J,axiom,
% 50.50/50.66 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I16_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I10_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I15_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osimps_I1_J,axiom,
% 50.50/50.66 ! [V_glb_H_2,V_glb_2] :
% 50.50/50.66 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2)
% 50.50/50.66 <=> V_glb_2 = V_glb_H_2 ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osize_I3_J,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osize_I1_J,axiom,
% 50.50/50.66 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osimps_I3_J,axiom,
% 50.50/50.66 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_vname_Osimps_I4_J,axiom,
% 50.50/50.66 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I11_J,axiom,
% 50.50/50.66 ! [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))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I3_J,axiom,
% 50.50/50.66 ! [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))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_OBody,axiom,
% 50.50/50.66 ! [V_pn] :
% 50.50/50.66 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 50.50/50.66 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_WT_Oequations_I7_J,axiom,
% 50.50/50.66 ! [V_a_2] :
% 50.50/50.66 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 50.50/50.66 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_zero__reorient,axiom,
% 50.50/50.66 ! [V_x_2,T_b] :
% 50.50/50.66 ( class_Groups_Ozero(T_b)
% 50.50/50.66 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 50.50/50.66 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 50.50/50.66 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 50.50/50.66 ( class_Rings_Osemiring__1(T_b)
% 50.50/50.66 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I9_J,axiom,
% 50.50/50.66 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_com_Osize_I1_J,axiom,
% 50.50/50.66 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 50.50/50.66 ! [V_i_2,V_inc_2,T_b] :
% 50.50/50.66 ( class_Rings_Osemiring__1(T_b)
% 50.50/50.66 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_evalc__evaln,axiom,
% 50.50/50.66 ! [V_t,V_s,V_c] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 50.50/50.66 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_zero__less__Suc,axiom,
% 50.50/50.66 ! [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))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_less__zeroE,axiom,
% 50.50/50.66 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_Suc__mono,axiom,
% 50.50/50.66 ! [V_n,V_m] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_lessI,axiom,
% 50.50/50.66 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_evaln__elim__cases_I1_J,axiom,
% 50.50/50.66 ! [V_t,V_n,V_s] :
% 50.50/50.66 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
% 50.50/50.66 => V_t = V_s ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_evaln_OSkip,axiom,
% 50.50/50.66 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_evalc_OSkip,axiom,
% 50.50/50.66 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_evalc__elim__cases_I1_J,axiom,
% 50.50/50.66 ! [V_t,V_s] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 50.50/50.66 => V_t = V_s ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 50.50/50.66 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Oab__semigroup__add(T_a)
% 50.50/50.66 => 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)) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__left__cancel,axiom,
% 50.50/50.66 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.66 ( class_Groups_Ocancel__semigroup__add(T_b)
% 50.50/50.66 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
% 50.50/50.66 <=> V_b_2 = V_c_2 ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__right__cancel,axiom,
% 50.50/50.66 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 50.50/50.66 ( class_Groups_Ocancel__semigroup__add(T_b)
% 50.50/50.66 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
% 50.50/50.66 <=> V_b_2 = V_c_2 ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__less__cancel__right,axiom,
% 50.50/50.66 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 50.50/50.66 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 50.50/50.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__less__cancel__left,axiom,
% 50.50/50.66 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.66 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 50.50/50.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__strict__right__mono,axiom,
% 50.50/50.66 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.66 => 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))) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__strict__left__mono,axiom,
% 50.50/50.66 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.66 => 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))) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__strict__mono,axiom,
% 50.50/50.66 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 50.50/50.66 => 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))) ) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__left__imp__eq,axiom,
% 50.50/50.66 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Ocancel__semigroup__add(T_a)
% 50.50/50.66 => ( 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)
% 50.50/50.66 => V_b = V_c ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__imp__eq,axiom,
% 50.50/50.66 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 50.50/50.66 => ( 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)
% 50.50/50.66 => V_b = V_c ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__right__imp__eq,axiom,
% 50.50/50.66 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.66 ( class_Groups_Ocancel__semigroup__add(T_a)
% 50.50/50.66 => ( 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)
% 50.50/50.66 => V_b = V_c ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__less__imp__less__right,axiom,
% 50.50/50.66 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 50.50/50.66 => ( 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)))
% 50.50/50.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__less__imp__less__left,axiom,
% 50.50/50.66 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.66 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 50.50/50.66 => ( 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)))
% 50.50/50.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__less__cases,axiom,
% 50.50/50.66 ! [V_P_2,V_n_2,V_m_2] :
% 50.50/50.66 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.66 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 50.50/50.66 => ( ( V_m_2 = V_n_2
% 50.50/50.66 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 50.50/50.66 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 50.50/50.66 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 50.50/50.66 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__lessD1,axiom,
% 50.50/50.66 ! [V_k,V_j,V_i] :
% 50.50/50.66 ( 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))
% 50.50/50.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_less__add__eq__less,axiom,
% 50.50/50.66 ! [V_n,V_m,V_l,V_k] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 50.50/50.66 => ( 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)
% 50.50/50.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__less__mono,axiom,
% 50.50/50.66 ! [V_l,V_k,V_j,V_i] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 50.50/50.66 => 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))) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__less__mono1,axiom,
% 50.50/50.66 ! [V_k,V_j,V_i] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.66 => 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))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_trans__less__add2,axiom,
% 50.50/50.66 ! [V_m,V_j,V_i] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.66 => 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))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_trans__less__add1,axiom,
% 50.50/50.66 ! [V_m,V_j,V_i] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.66 => 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))) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_less__not__refl3,axiom,
% 50.50/50.66 ! [V_t,V_s] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 50.50/50.66 => V_s != V_t ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_less__not__refl2,axiom,
% 50.50/50.66 ! [V_m,V_n] :
% 50.50/50.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 50.50/50.66 => V_m != V_n ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_less__irrefl__nat,axiom,
% 50.50/50.66 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__neg__neg,axiom,
% 50.50/50.66 ! [V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.66 => 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))) ) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_add__pos__pos,axiom,
% 50.50/50.66 ! [V_b,V_a,T_a] :
% 50.50/50.66 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.66 => 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))) ) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_linorder__neqE__nat,axiom,
% 50.50/50.66 ! [V_y,V_x] :
% 50.50/50.66 ( V_x != V_y
% 50.50/50.66 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 50.50/50.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__add__left__cancel__less,axiom,
% 50.50/50.66 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.66 ( 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)))
% 50.50/50.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__add__right__cancel,axiom,
% 50.50/50.66 ! [V_n_2,V_k_2,V_m_2] :
% 50.50/50.66 ( 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)
% 50.50/50.66 <=> V_m_2 = V_n_2 ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__add__left__cancel,axiom,
% 50.50/50.66 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.66 ( 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)
% 50.50/50.66 <=> V_m_2 = V_n_2 ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__add__assoc,axiom,
% 50.50/50.66 ! [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)) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 50.50/50.66 ! [V_a_2,T_b] :
% 50.50/50.66 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__add__left__commute,axiom,
% 50.50/50.66 ! [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)) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__add__commute,axiom,
% 50.50/50.66 ! [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) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 50.50/50.66 ! [V_a_2,T_b] :
% 50.50/50.66 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 50.50/50.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_nat__neq__iff,axiom,
% 50.50/50.66 ! [V_n_2,V_m_2] :
% 50.50/50.66 ( V_m_2 != V_n_2
% 50.50/50.66 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.66 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_not__add__less2,axiom,
% 50.50/50.66 ! [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)) ).
% 50.50/50.66
% 50.50/50.66 fof(fact_not__add__less1,axiom,
% 50.50/50.66 ! [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)) ).
% 50.50/50.66
% 50.50/50.67 fof(fact_less__not__refl,axiom,
% 50.50/50.67 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__gr__0,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( 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)))
% 50.50/50.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 50.50/50.67 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__add__Suc1,axiom,
% 50.50/50.67 ! [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)))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__add__Suc2,axiom,
% 50.50/50.67 ! [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)))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__iff__Suc__add,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.67 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__0__left,axiom,
% 50.50/50.67 ! [V_a,T_a] :
% 50.50/50.67 ( class_Groups_Omonoid__add(T_a)
% 50.50/50.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__0,axiom,
% 50.50/50.67 ! [V_a,T_a] :
% 50.50/50.67 ( class_Groups_Ocomm__monoid__add(T_a)
% 50.50/50.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_double__zero__sym,axiom,
% 50.50/50.67 ! [V_a_2,T_b] :
% 50.50/50.67 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.67 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 50.50/50.67 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__0__right,axiom,
% 50.50/50.67 ! [V_a,T_a] :
% 50.50/50.67 ( class_Groups_Omonoid__add(T_a)
% 50.50/50.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add_Ocomm__neutral,axiom,
% 50.50/50.67 ! [V_a,T_a] :
% 50.50/50.67 ( class_Groups_Ocomm__monoid__add(T_a)
% 50.50/50.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_plus__nat_Oadd__0,axiom,
% 50.50/50.67 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 50.50/50.67
% 50.50/50.67 fof(fact_Nat_Oadd__0__right,axiom,
% 50.50/50.67 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__is__0,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.67 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.67 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__eq__self__zero,axiom,
% 50.50/50.67 ! [V_n,V_m] :
% 50.50/50.67 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 50.50/50.67 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__Suc__shift,axiom,
% 50.50/50.67 ! [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)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__Suc,axiom,
% 50.50/50.67 ! [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)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__Suc__right,axiom,
% 50.50/50.67 ! [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)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_not__less0,axiom,
% 50.50/50.67 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_neq0__conv,axiom,
% 50.50/50.67 ! [V_n_2] :
% 50.50/50.67 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__nat__zero__code,axiom,
% 50.50/50.67 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_gr__implies__not0,axiom,
% 50.50/50.67 ! [V_n,V_m] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.67 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_gr0I,axiom,
% 50.50/50.67 ! [V_n] :
% 50.50/50.67 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_Suc__less__SucD,axiom,
% 50.50/50.67 ! [V_n,V_m] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_Suc__lessD,axiom,
% 50.50/50.67 ! [V_n,V_m] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__SucE,axiom,
% 50.50/50.67 ! [V_n,V_m] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 50.50/50.67 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.67 => V_m = V_n ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__trans__Suc,axiom,
% 50.50/50.67 ! [V_k,V_j,V_i] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_Suc__lessI,axiom,
% 50.50/50.67 ! [V_n,V_m] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.67 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__SucI,axiom,
% 50.50/50.67 ! [V_n,V_m] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__antisym,axiom,
% 50.50/50.67 ! [V_m,V_n] :
% 50.50/50.67 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 50.50/50.67 => V_m = V_n ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_not__less__less__Suc__eq,axiom,
% 50.50/50.67 ! [V_m_2,V_n_2] :
% 50.50/50.67 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 50.50/50.67 <=> V_n_2 = V_m_2 ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_Suc__less__eq,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( 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)))
% 50.50/50.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__Suc__eq,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 50.50/50.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.67 | V_m_2 = V_n_2 ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_not__less__eq,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_Oequations_I1_J,axiom,
% 50.50/50.67 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_Oequations_I1_J,axiom,
% 50.50/50.67 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT_Oequations_I1_J,axiom,
% 50.50/50.67 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT_OSkip,axiom,
% 50.50/50.67 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I19_J,axiom,
% 50.50/50.67 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I18_J,axiom,
% 50.50/50.67 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I9_J,axiom,
% 50.50/50.67 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I8_J,axiom,
% 50.50/50.67 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I20_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I10_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I21_J,axiom,
% 50.50/50.67 ! [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 ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I11_J,axiom,
% 50.50/50.67 ! [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 ).
% 50.50/50.67
% 50.50/50.67 fof(fact_one__is__add,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( 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)
% 50.50/50.67 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.50/50.67 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.50/50.67 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.67 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__is__1,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( 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))
% 50.50/50.67 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.50/50.67 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.50/50.67 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.67 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_gr0__conv__Suc,axiom,
% 50.50/50.67 ! [V_n_2] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 50.50/50.67 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__Suc0,axiom,
% 50.50/50.67 ! [V_n_2] :
% 50.50/50.67 ( 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))))
% 50.50/50.67 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_less__Suc__eq__0__disj,axiom,
% 50.50/50.67 ! [V_n_2,V_m_2] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 50.50/50.67 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.67 | ? [B_j] :
% 50.50/50.67 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT__bodiesD,axiom,
% 50.50/50.67 ! [V_b,V_pn] :
% 50.50/50.67 ( c_Com_OWT__bodies
% 50.50/50.67 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 50.50/50.67 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_pos__add__strict,axiom,
% 50.50/50.67 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.67 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 50.50/50.67 => 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))) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_even__less__0__iff,axiom,
% 50.50/50.67 ! [V_a_2,T_b] :
% 50.50/50.67 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WTs__elim__cases_I7_J,axiom,
% 50.50/50.67 ! [V_P] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 50.50/50.67 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_the_Osimps,axiom,
% 50.50/50.67 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osimps_I2_J,axiom,
% 50.50/50.67 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osimps_I3_J,axiom,
% 50.50/50.67 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_not__Some__eq,axiom,
% 50.50/50.67 ! [T_b,V_x_2] :
% 50.50/50.67 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 50.50/50.67 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_not__None__eq,axiom,
% 50.50/50.67 ! [T_b,V_x_2] :
% 50.50/50.67 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 50.50/50.67 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osize_I2_J,axiom,
% 50.50/50.67 ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_termination__basic__simps_I1_J,axiom,
% 50.50/50.67 ! [V_z,V_y,V_x] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 50.50/50.67 => 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))) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_linorder__neqE__linordered__idom,axiom,
% 50.50/50.67 ! [V_y,V_x,T_a] :
% 50.50/50.67 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.67 => ( V_x != V_y
% 50.50/50.67 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osize_I1_J,axiom,
% 50.50/50.67 ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Oinject,axiom,
% 50.50/50.67 ! [V_a_H_2,V_a_2,T_b] :
% 50.50/50.67 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 50.50/50.67 <=> V_a_2 = V_a_H_2 ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_double__eq__0__iff,axiom,
% 50.50/50.67 ! [V_a_2,T_b] :
% 50.50/50.67 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.67 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.67 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_termination__basic__simps_I2_J,axiom,
% 50.50/50.67 ! [V_y,V_z,V_x] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 50.50/50.67 => 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))) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_nat_Osize_I2_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_nat_Osize_I4_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osize_I4_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osize_I3_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_add__0__iff,axiom,
% 50.50/50.67 ! [V_a_2,V_b_2,T_b] :
% 50.50/50.67 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 50.50/50.67 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 50.50/50.67 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 50.50/50.67 ! [V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 50.50/50.67 ! [V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osize_I12_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osize_I4_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osize_I13_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osize_I5_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln__elim__cases_I5_J,axiom,
% 50.50/50.67 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 50.50/50.67 ( 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)
% 50.50/50.67 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
% 50.50/50.67 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_OIfTrue,axiom,
% 50.50/50.67 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 50.50/50.67 ( hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
% 50.50/50.67 => 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) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_OIfFalse,axiom,
% 50.50/50.67 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 50.50/50.67 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
% 50.50/50.67 => 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) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_OIfFalse,axiom,
% 50.50/50.67 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 50.50/50.67 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 50.50/50.67 => 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)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_OIfTrue,axiom,
% 50.50/50.67 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 50.50/50.67 ( hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 50.50/50.67 => 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)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc__elim__cases_I5_J,axiom,
% 50.50/50.67 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 50.50/50.67 ( 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))
% 50.50/50.67 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 50.50/50.67 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_OSemi,axiom,
% 50.50/50.67 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 50.50/50.67 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
% 50.50/50.67 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
% 50.50/50.67 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_OSemi,axiom,
% 50.50/50.67 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WTs__elim__cases_I5_J,axiom,
% 50.50/50.67 ! [V_c2_2,V_c1_2,V_b_2] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 50.50/50.67 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 50.50/50.67 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WTs__elim__cases_I4_J,axiom,
% 50.50/50.67 ! [V_c2,V_c1] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 50.50/50.67 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 50.50/50.67 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I4_J,axiom,
% 50.50/50.67 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 50.50/50.67 ( 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)
% 50.50/50.67 <=> ( V_fun_2 = V_fun_H_2
% 50.50/50.67 & V_com1_2 = V_com1_H_2
% 50.50/50.67 & V_com2_2 = V_com2_H_2 ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I3_J,axiom,
% 50.50/50.67 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 50.50/50.67 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 50.50/50.67 <=> ( V_com1_2 = V_com1_H_2
% 50.50/50.67 & V_com2_2 = V_com2_H_2 ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I45_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I44_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_nat__size,axiom,
% 50.50/50.67 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_Oequations_I6_J,axiom,
% 50.50/50.67 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 50.50/50.67 ( 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)
% 50.50/50.67 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) )
% 50.50/50.67 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_Oequations_I5_J,axiom,
% 50.50/50.67 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 50.50/50.67 ( 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)
% 50.50/50.67 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) )
% 50.50/50.67 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_Oequations_I5_J,axiom,
% 50.50/50.67 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 50.50/50.67 ( 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))
% 50.50/50.67 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 50.50/50.67 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_Oequations_I6_J,axiom,
% 50.50/50.67 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 50.50/50.67 ( 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))
% 50.50/50.67 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 50.50/50.67 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT_OIf,axiom,
% 50.50/50.67 ! [V_b_2,V_c1_2,V_c0_2] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 50.50/50.67 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 50.50/50.67 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT_Oequations_I5_J,axiom,
% 50.50/50.67 ! [V_a2_2,V_a1_2,V_a3_2] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 50.50/50.67 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 50.50/50.67 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I54_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I55_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_Oequations_I4_J,axiom,
% 50.50/50.67 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 50.50/50.67 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
% 50.50/50.67 <=> ? [B_s1] :
% 50.50/50.67 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1)
% 50.50/50.67 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_Oequations_I4_J,axiom,
% 50.50/50.67 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 50.50/50.67 <=> ? [B_s1] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT_OSemi,axiom,
% 50.50/50.67 ! [V_c1,V_c0] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 50.50/50.67 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 50.50/50.67 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT_Oequations_I4_J,axiom,
% 50.50/50.67 ! [V_a2_2,V_a1_2] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 50.50/50.67 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 50.50/50.67 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I48_J,axiom,
% 50.50/50.67 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I49_J,axiom,
% 50.50/50.67 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I27_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I26_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I57_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I56_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I37_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I36_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I15_J,axiom,
% 50.50/50.67 ! [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 ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I14_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I25_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I24_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I50_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I35_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I51_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I34_J,axiom,
% 50.50/50.67 ! [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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I13_J,axiom,
% 50.50/50.67 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I12_J,axiom,
% 50.50/50.67 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_nat_Osize_I3_J,axiom,
% 50.50/50.67 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) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 50.50/50.67 ! [V_c,V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => 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) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 50.50/50.67 ! [V_d,V_c,V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => 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)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 50.50/50.67 ! [V_d,V_c,V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => 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) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 50.50/50.67 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => 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)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 50.50/50.67 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => 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) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 50.50/50.67 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.67 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.67 => 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)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_nat_Osize_I1_J,axiom,
% 50.50/50.67 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Orecs_I2_J,axiom,
% 50.50/50.67 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osimps_I5_J,axiom,
% 50.50/50.67 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Orecs_I1_J,axiom,
% 50.50/50.67 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 50.50/50.67
% 50.50/50.67 fof(fact_option_Osimps_I4_J,axiom,
% 50.50/50.67 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 50.50/50.67
% 50.50/50.67 fof(fact_bool_Osize_I1_J,axiom,
% 50.50/50.67 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_bool_Osize_I2_J,axiom,
% 50.50/50.67 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osize_I6_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osize_I14_J,axiom,
% 50.50/50.67 ! [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))) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_is__none__code_I2_J,axiom,
% 50.50/50.67 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_is__none__code_I1_J,axiom,
% 50.50/50.67 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_is__none__def,axiom,
% 50.50/50.67 ! [V_x_2,T_b] :
% 50.50/50.67 ( c_Option_Ois__none(T_b,V_x_2)
% 50.50/50.67 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_OWhileFalse,axiom,
% 50.50/50.67 ! [V_n_2,V_c_2,V_s_2,V_b_2] :
% 50.50/50.67 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_OWhileTrue,axiom,
% 50.50/50.67 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
% 50.50/50.67 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 50.50/50.67 => ( c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2)
% 50.50/50.67 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2)
% 50.50/50.67 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_OWhileTrue,axiom,
% 50.50/50.67 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
% 50.50/50.67 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
% 50.50/50.67 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_OWhileFalse,axiom,
% 50.50/50.67 ! [V_c_2,V_s_2,V_b_2] :
% 50.50/50.67 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 50.50/50.67 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WTs__elim__cases_I6_J,axiom,
% 50.50/50.67 ! [V_c_2,V_b_2] :
% 50.50/50.67 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
% 50.50/50.67 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_com_Osimps_I5_J,axiom,
% 50.50/50.67 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 50.50/50.67 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 50.50/50.67 <=> ( V_fun_2 = V_fun_H_2
% 50.50/50.67 & V_com_2 = V_com_H_2 ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_Oequations_I7_J,axiom,
% 50.50/50.67 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 50.50/50.67 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
% 50.50/50.67 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 => ? [B_s1] :
% 50.50/50.67 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 50.50/50.67 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evaln_Oequations_I8_J,axiom,
% 50.50/50.67 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 50.50/50.67 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
% 50.50/50.67 <=> ( ( V_a6_2 = V_a2_2
% 50.50/50.67 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 50.50/50.67 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & ? [B_s1] :
% 50.50/50.67 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 50.50/50.67 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_Oequations_I8_J,axiom,
% 50.50/50.67 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 50.50/50.67 <=> ( ( V_a5_2 = V_a2_2
% 50.50/50.67 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 50.50/50.67 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 & ? [B_s1] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_evalc_Oequations_I7_J,axiom,
% 50.50/50.67 ! [V_a2_2,V_a3_2,V_a1_2] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 50.50/50.67 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 50.50/50.67 => ? [B_s1] :
% 50.50/50.67 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 50.50/50.67 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 50.50/50.67
% 50.50/50.67 fof(fact_WT_Oequations_I6_J,axiom,
% 50.50/50.68 ! [V_a1_2,V_a2_2] :
% 50.50/50.68 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 50.50/50.68 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_While,axiom,
% 50.50/50.68 ! [V_b_2,V_c_2] :
% 50.50/50.68 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 50.50/50.68 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I59_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I58_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I53_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I52_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I28_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I29_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I38_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I61_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I39_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I60_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I46_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I47_J,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I16_J,axiom,
% 50.50/50.68 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_com_Osimps_I17_J,axiom,
% 50.50/50.68 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__0__less__iff,axiom,
% 50.50/50.68 ! [V_n_2,T_b] :
% 50.50/50.68 ( class_Rings_Olinordered__semidom(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_bool_Osize_I4_J,axiom,
% 50.50/50.68 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_bool_Osize_I3_J,axiom,
% 50.50/50.68 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_less__imp__Suc__add,axiom,
% 50.50/50.68 ! [V_n,V_m] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.68 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_less__imp__add__positive,axiom,
% 50.50/50.68 ! [V_j,V_i] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.68 => ? [B_k] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k))
% 50.50/50.68 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_gr0__implies__Suc,axiom,
% 50.50/50.68 ! [V_n] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.68 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_evalc__elim__cases_I4_J,axiom,
% 50.50/50.68 ! [V_t,V_s,V_c2,V_c1] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 50.50/50.68 => ~ ! [B_s1] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
% 50.50/50.68 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_lift__Suc__mono__less__iff,axiom,
% 50.50/50.68 ! [V_m_2,V_n_2,V_f_2,T_b] :
% 50.50/50.68 ( class_Orderings_Oorder(T_b)
% 50.50/50.68 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_lift__Suc__mono__less,axiom,
% 50.50/50.68 ! [V_n_H_2,V_n_2,V_f_2,T_b] :
% 50.50/50.68 ( class_Orderings_Oorder(T_b)
% 50.50/50.68 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_evaln__elim__cases_I4_J,axiom,
% 50.50/50.68 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 50.50/50.68 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t)
% 50.50/50.68 => ~ ! [B_s1] :
% 50.50/50.68 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1)
% 50.50/50.68 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__eq__iff,axiom,
% 50.50/50.68 ! [V_n_2,V_m_2,T_b] :
% 50.50/50.68 ( class_Nat_Osemiring__char__0(T_b)
% 50.50/50.68 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
% 50.50/50.68 <=> V_m_2 = V_n_2 ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_int__eq__0__conv,axiom,
% 50.50/50.68 ! [V_n_2] :
% 50.50/50.68 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.68 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_int__0,axiom,
% 50.50/50.68 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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zless__iff__Suc__zadd,axiom,
% 50.50/50.68 ! [V_z_2,V_w_2] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 50.50/50.68 <=> ? [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))) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zless__int,axiom,
% 50.50/50.68 ! [V_n_2,V_m_2] :
% 50.50/50.68 ( 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)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__int__left,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__int,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zero__less__int__conv,axiom,
% 50.50/50.68 ! [V_n_2] :
% 50.50/50.68 ( 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)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__less__0__iff,axiom,
% 50.50/50.68 ! [V_m,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.68 => ~ 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))) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__0,axiom,
% 50.50/50.68 ! [T_a] :
% 50.50/50.68 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__less__imp__less,axiom,
% 50.50/50.68 ! [V_n,V_m,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.68 => ( 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)))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_less__imp__of__nat__less,axiom,
% 50.50/50.68 ! [V_n,V_m,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.68 => 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))) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__less__iff,axiom,
% 50.50/50.68 ! [V_n_2,V_m_2,T_b] :
% 50.50/50.68 ( class_Rings_Olinordered__semidom(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__add,axiom,
% 50.50/50.68 ! [V_n,V_m,T_a] :
% 50.50/50.68 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 50.50/50.68 ! [V_y_2,V_x_2] :
% 50.50/50.68 ( 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)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 50.50/50.68 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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__irrefl,axiom,
% 50.50/50.68 ! [V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Opreorder(T_a)
% 50.50/50.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_linorder__neq__iff,axiom,
% 50.50/50.68 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.68 ( class_Orderings_Olinorder(T_b)
% 50.50/50.68 => ( V_x_2 != V_y_2
% 50.50/50.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.68 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_not__less__iff__gr__or__eq,axiom,
% 50.50/50.68 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.68 ( class_Orderings_Olinorder(T_b)
% 50.50/50.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 50.50/50.68 | V_x_2 = V_y_2 ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_linorder__less__linear,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Olinorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 | V_x = V_y
% 50.50/50.68 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_linorder__antisym__conv3,axiom,
% 50.50/50.68 ! [V_x_2,V_y_2,T_b] :
% 50.50/50.68 ( class_Orderings_Olinorder(T_b)
% 50.50/50.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 50.50/50.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.68 <=> V_x_2 = V_y_2 ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_linorder__neqE,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Olinorder(T_a)
% 50.50/50.68 => ( V_x != V_y
% 50.50/50.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_less__imp__neq,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Oorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => V_x != V_y ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_int__less__0__conv,axiom,
% 50.50/50.68 ! [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))) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_int__int__eq,axiom,
% 50.50/50.68 ! [V_n_2,V_m_2] :
% 50.50/50.68 ( 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)
% 50.50/50.68 <=> V_m_2 = V_n_2 ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 50.50/50.68 ! [V_y_2,V_x_2] :
% 50.50/50.68 ( 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)
% 50.50/50.68 <=> V_x_2 = V_y_2 ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__0,axiom,
% 50.50/50.68 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__0__right,axiom,
% 50.50/50.68 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__strict__right__mono,axiom,
% 50.50/50.68 ! [V_k,V_j,V_i] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 50.50/50.68 => 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))) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__assoc,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__left__commute,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zless__linear,axiom,
% 50.50/50.68 ! [V_y,V_x] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 50.50/50.68 | V_x = V_y
% 50.50/50.68 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__commute,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_linorder__cases,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Olinorder(T_a)
% 50.50/50.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => ( V_x != V_y
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__asym,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Opreorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_xt1_I10_J,axiom,
% 50.50/50.68 ! [V_z,V_x,V_y,T_a] :
% 50.50/50.68 ( class_Orderings_Oorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__trans,axiom,
% 50.50/50.68 ! [V_z,V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Opreorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_xt1_I2_J,axiom,
% 50.50/50.68 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.68 ( class_Orderings_Oorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 50.50/50.68 => ( V_b = V_c
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_ord__less__eq__trans,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Orderings_Oord(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.68 => ( V_b = V_c
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_xt1_I1_J,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Orderings_Oorder(T_a)
% 50.50/50.68 => ( V_a = V_b
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_ord__eq__less__trans,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Orderings_Oord(T_a)
% 50.50/50.68 => ( V_a = V_b
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_xt1_I9_J,axiom,
% 50.50/50.68 ! [V_a,V_b,T_a] :
% 50.50/50.68 ( class_Orderings_Oorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 50.50/50.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__asym_H,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Orderings_Opreorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__imp__not__eq2,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Oorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => V_y != V_x ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__imp__not__eq,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Oorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => V_x != V_y ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__imp__not__less,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Opreorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_order__less__not__sym,axiom,
% 50.50/50.68 ! [V_y,V_x,T_a] :
% 50.50/50.68 ( class_Orderings_Opreorder(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zero__less__imp__eq__int,axiom,
% 50.50/50.68 ! [V_k] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 50.50/50.68 => ? [B_n] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 50.50/50.68 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__0__less__iff,axiom,
% 50.50/50.68 ! [V_z_2,T_b] :
% 50.50/50.68 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__less__0__iff,axiom,
% 50.50/50.68 ! [V_z_2,T_b] :
% 50.50/50.68 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zmult__zless__mono2__lemma,axiom,
% 50.50/50.68 ! [V_k,V_j,V_i] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 50.50/50.68 => 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))) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_negative__zless__0,axiom,
% 50.50/50.68 ! [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))) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_split__nat,axiom,
% 50.50/50.68 ! [V_i_2,V_P_2] :
% 50.50/50.68 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 50.50/50.68 <=> ( ! [B_n] :
% 50.50/50.68 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 50.50/50.68 => hBOOL(hAPP(V_P_2,B_n)) )
% 50.50/50.68 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.68 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zero__less__nat__eq,axiom,
% 50.50/50.68 ! [V_z_2] :
% 50.50/50.68 ( 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)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_negative__zless,axiom,
% 50.50/50.68 ! [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))) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_int__Suc,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_odd__less__0,axiom,
% 50.50/50.68 ! [V_z_2] :
% 50.50/50.68 ( 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)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_less__1__mult,axiom,
% 50.50/50.68 ! [V_n,V_m,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 50.50/50.68 ! [V_m,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 50.50/50.68 ! [V_a,V_m,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 50.50/50.68 ! [V_m,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_square__eq__iff,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Rings_Oidom(T_b)
% 50.50/50.68 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
% 50.50/50.68 <=> ( V_a_2 = V_b_2
% 50.50/50.68 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zmult__assoc,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_square__eq__1__iff,axiom,
% 50.50/50.68 ! [V_x_2,T_b] :
% 50.50/50.68 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 50.50/50.68 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 50.50/50.68 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 50.50/50.68 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__mult__minus,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Oring(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__eq__iff,axiom,
% 50.50/50.68 ! [V_z_2,V_w_2,T_b] :
% 50.50/50.68 ( class_Int_Oring__char__0(T_b)
% 50.50/50.68 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 50.50/50.68 <=> V_w_2 = V_z_2 ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__mult__commute,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Oring(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zmult__zminus,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zmult__commute,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zmult__1__right,axiom,
% 50.50/50.68 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zmult__1,axiom,
% 50.50/50.68 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__mult,axiom,
% 50.50/50.68 ! [V_z,V_w,T_a] :
% 50.50/50.68 ( class_Rings_Oring__1(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__mult__left,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Oring(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__mult__right,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Oring(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__minus,axiom,
% 50.50/50.68 ! [V_z,T_a] :
% 50.50/50.68 ( class_Rings_Oring__1(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zminus__zminus,axiom,
% 50.50/50.68 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__1,axiom,
% 50.50/50.68 ! [T_a] :
% 50.50/50.68 ( class_Rings_Oring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Groups_Oab__semigroup__mult(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__equal__iff__equal,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_b)
% 50.50/50.68 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 50.50/50.68 <=> V_a_2 = V_b_2 ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__equation__iff,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_b)
% 50.50/50.68 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 50.50/50.68 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_equation__minus__iff,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_b)
% 50.50/50.68 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 50.50/50.68 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult_Ocomm__neutral,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ocomm__monoid__mult(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__1__right,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_one__reorient,axiom,
% 50.50/50.68 ! [V_x_2,T_b] :
% 50.50/50.68 ( class_Groups_Oone(T_b)
% 50.50/50.68 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 50.50/50.68 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__1,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ocomm__monoid__mult(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__1__left,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__minus,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 50.50/50.68 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 50.50/50.68 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 50.50/50.68 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 50.50/50.68 ! [V_rx,V_ly,V_lx,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 50.50/50.68 ! [V_rx,V_ly,V_lx,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 50.50/50.68 ! [V_ry,V_rx,V_lx,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 50.50/50.68 ! [V_ry,V_rx,V_lx,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 50.50/50.68 ! [V_x,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__ring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__mult,axiom,
% 50.50/50.68 ! [V_n,V_m,T_a] :
% 50.50/50.68 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__nat__1,axiom,
% 50.50/50.68 ! [T_a] :
% 50.50/50.68 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__of__nat,axiom,
% 50.50/50.68 ! [V_k,T_a] :
% 50.50/50.68 ( class_Rings_Oring__1(T_a)
% 50.50/50.68 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.68 => 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)))) )
% 50.50/50.68 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.68 => 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)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_nat__zminus__int,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_nat__1,axiom,
% 50.50/50.68 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_pos__zmult__eq__1__iff,axiom,
% 50.50/50.68 ! [V_n_2,V_m_2] :
% 50.50/50.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 50.50/50.68 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 50.50/50.68 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 50.50/50.68 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__zero,axiom,
% 50.50/50.68 ! [T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__0__equal__iff__equal,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_b)
% 50.50/50.68 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 50.50/50.68 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_equal__neg__zero,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.68 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 50.50/50.68 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__equal__0__iff__equal,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_b)
% 50.50/50.68 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.68 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__equal__zero,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.68 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 50.50/50.68 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_less__minus__iff,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__less__iff,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__less__iff__less,axiom,
% 50.50/50.68 ! [V_a_2,V_b_2,T_b] :
% 50.50/50.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__add__distrib,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Groups_Oab__group__add(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__add,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => 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)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_add__minus__cancel,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => 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 ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__add__cancel,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => 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 ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__zero__left,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Rings_Omult__zero(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__zero__right,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Rings_Omult__zero(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__eq__0__iff,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Rings_Oring__no__zero__divisors(T_b)
% 50.50/50.68 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.68 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.68 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_no__zero__divisors,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ono__zero__divisors(T_a)
% 50.50/50.68 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.68 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_divisors__zero,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ono__zero__divisors(T_a)
% 50.50/50.68 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.68 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.68 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_one__neq__zero,axiom,
% 50.50/50.68 ! [T_a] :
% 50.50/50.68 ( class_Rings_Ozero__neq__one(T_a)
% 50.50/50.68 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zero__neq__one,axiom,
% 50.50/50.68 ! [T_a] :
% 50.50/50.68 ( class_Rings_Ozero__neq__one(T_a)
% 50.50/50.68 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zminus__0,axiom,
% 50.50/50.68 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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_nat__int,axiom,
% 50.50/50.68 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 50.50/50.68 ! [V_z,V_y,V_x,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_crossproduct__noteq,axiom,
% 50.50/50.68 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 50.50/50.68 => ( ( V_a_2 != V_b_2
% 50.50/50.68 & V_c_2 != V_d_2 )
% 50.50/50.68 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 50.50/50.68 ! [V_b,V_m,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_crossproduct__eq,axiom,
% 50.50/50.68 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 50.50/50.68 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 50.50/50.68 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
% 50.50/50.68 <=> ( V_w_2 = V_x_2
% 50.50/50.68 | V_y_2 = V_z_2 ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__semiring__class_Odistrib,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Ocomm__semiring(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_combine__common__factor,axiom,
% 50.50/50.68 ! [V_c,V_b,V_e,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Osemiring(T_a)
% 50.50/50.68 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zminus__zadd__distrib,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__zmult__distrib2,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zadd__zmult__distrib,axiom,
% 50.50/50.68 ! [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)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_int__0__neq__1,axiom,
% 50.50/50.68 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_of__int__int__eq,axiom,
% 50.50/50.68 ! [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) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_one__less__nat__eq,axiom,
% 50.50/50.68 ! [V_z_2] :
% 50.50/50.68 ( 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)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__less__nonneg,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__less__0__iff__less,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_neg__0__less__iff__less,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_less__minus__self__iff,axiom,
% 50.50/50.68 ! [V_a_2,T_b] :
% 50.50/50.68 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_minus__unique,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.68 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_ab__left__minus,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Oab__group__add(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_left__minus,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_b)
% 50.50/50.68 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 50.50/50.68 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_right__minus,axiom,
% 50.50/50.68 ! [V_a,T_a] :
% 50.50/50.68 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.68 => 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) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_nat__0,axiom,
% 50.50/50.68 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 50.50/50.68 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__strict__left__mono__neg,axiom,
% 50.50/50.68 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__ring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__strict__right__mono__neg,axiom,
% 50.50/50.68 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__ring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_comm__mult__strict__left__mono,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__strict__left__mono,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__strict__right__mono,axiom,
% 50.50/50.68 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__neg__neg,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__ring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__neg__pos,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__less__cancel__left__neg,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.68 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 50.50/50.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zero__less__mult__pos2,axiom,
% 50.50/50.68 ! [V_a,V_b,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( 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)))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_zero__less__mult__pos,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( 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)))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__pos__neg2,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__pos__neg,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__pos__pos,axiom,
% 50.50/50.68 ! [V_b,V_a,T_a] :
% 50.50/50.68 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.68 => 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))) ) ) ) ).
% 50.50/50.68
% 50.50/50.68 fof(fact_mult__less__cancel__left__pos,axiom,
% 50.50/50.68 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.68 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__less__cancel__left__disj,axiom,
% 50.50/50.69 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 50.50/50.69 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 50.50/50.69 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__less__cancel__right__disj,axiom,
% 50.50/50.69 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 50.50/50.69 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 50.50/50.69 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_not__square__less__zero,axiom,
% 50.50/50.69 ! [V_a,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__ring(T_a)
% 50.50/50.69 => ~ 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__less__one,axiom,
% 50.50/50.69 ! [T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_not__one__less__zero,axiom,
% 50.50/50.69 ! [T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__scale__eq__noteq,axiom,
% 50.50/50.69 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 50.50/50.69 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 50.50/50.69 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.69 => ( ( V_a = V_b
% 50.50/50.69 & V_c != V_d )
% 50.50/50.69 => 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)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sum__squares__eq__zero__iff,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.69 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.69 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.69 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_less__add__one,axiom,
% 50.50/50.69 ! [V_a,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zadd__zminus__inverse2,axiom,
% 50.50/50.69 ! [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) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_negative__eq__positive,axiom,
% 50.50/50.69 ! [V_m_2,V_n_2] :
% 50.50/50.69 ( 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)
% 50.50/50.69 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.69 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_not__int__zless__negative,axiom,
% 50.50/50.69 ! [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)))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zmult__zless__mono2,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_int__0__less__1,axiom,
% 50.50/50.69 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))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_odd__nonzero,axiom,
% 50.50/50.69 ! [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) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zless__add1__eq,axiom,
% 50.50/50.69 ! [V_z_2,V_w_2] :
% 50.50/50.69 ( 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))))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 50.50/50.69 | V_w_2 = V_z_2 ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__0,axiom,
% 50.50/50.69 ! [T_a] :
% 50.50/50.69 ( class_Rings_Oring__1(T_a)
% 50.50/50.69 => 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) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__0__eq__iff,axiom,
% 50.50/50.69 ! [V_z_2,T_b] :
% 50.50/50.69 ( class_Int_Oring__char__0(T_b)
% 50.50/50.69 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 50.50/50.69 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__eq__0__iff,axiom,
% 50.50/50.69 ! [V_z_2,T_b] :
% 50.50/50.69 ( class_Int_Oring__char__0(T_b)
% 50.50/50.69 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.69 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__less__iff,axiom,
% 50.50/50.69 ! [V_z_2,V_w_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__add,axiom,
% 50.50/50.69 ! [V_z,V_w,T_a] :
% 50.50/50.69 ( class_Rings_Oring__1(T_a)
% 50.50/50.69 => 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)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__of__nat__eq,axiom,
% 50.50/50.69 ! [V_n,T_a] :
% 50.50/50.69 ( class_Rings_Oring__1(T_a)
% 50.50/50.69 => 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) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zless__nat__conj,axiom,
% 50.50/50.69 ! [V_z_2,V_w_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mono__iff,axiom,
% 50.50/50.69 ! [V_w_2,V_z_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 50.50/50.69 => ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zless__nat__eq__int__zless,axiom,
% 50.50/50.69 ! [V_z_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 50.50/50.69 <=> 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)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_not__sum__squares__lt__zero,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__ring(T_a)
% 50.50/50.69 => ~ 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sum__squares__gt__zero__iff,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
% 50.50/50.69 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.69 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__less__two,axiom,
% 50.50/50.69 ! [T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => 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)))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__nat__Suc,axiom,
% 50.50/50.69 ! [V_m,T_a] :
% 50.50/50.69 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.69 => 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)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_int__Suc0__eq__1,axiom,
% 50.50/50.69 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) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__aux__def,axiom,
% 50.50/50.69 ! [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) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_negD,axiom,
% 50.50/50.69 ! [V_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.69 => ? [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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn__if,axiom,
% 50.50/50.69 ! [V_x,T_a] :
% 50.50/50.69 ( class_Groups_Osgn__if(T_a)
% 50.50/50.69 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 50.50/50.69 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.69 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 50.50/50.69 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn__neg,axiom,
% 50.50/50.69 ! [V_a,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn__1__neg,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.69 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zsgn__def,axiom,
% 50.50/50.69 ! [V_i] :
% 50.50/50.69 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 50.50/50.69 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.69 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 50.50/50.69 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 50.50/50.69 => 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)) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 50.50/50.69 ! [V_z] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.69 => 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)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__less__iff,axiom,
% 50.50/50.69 ! [V_m_2,V_w_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 50.50/50.69 <=> 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_convex__bound__lt,axiom,
% 50.50/50.69 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 50.50/50.69 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 50.50/50.69 => 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)) ) ) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn__pos,axiom,
% 50.50/50.69 ! [V_a,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__refl,axiom,
% 50.50/50.69 ! [V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Opreorder(T_a)
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le0,axiom,
% 50.50/50.69 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_negative__zle,axiom,
% 50.50/50.69 ! [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))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__le__mono,axiom,
% 50.50/50.69 ! [V_l,V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__le__mono2,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__le__mono1,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mult__assoc,axiom,
% 50.50/50.69 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mult__eq__1__iff,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 50.50/50.69 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 50.50/50.69 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mult__commute,axiom,
% 50.50/50.69 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mult__1__right,axiom,
% 50.50/50.69 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__1__eq__mult__iff,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 50.50/50.69 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 50.50/50.69 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mult__1,axiom,
% 50.50/50.69 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__cube,axiom,
% 50.50/50.69 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__square,axiom,
% 50.50/50.69 ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__eq__self__implies__10,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 50.50/50.69 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 50.50/50.69 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zle__refl,axiom,
% 50.50/50.69 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn__sgn,axiom,
% 50.50/50.69 ! [V_a,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.69 => 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) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zle__linear,axiom,
% 50.50/50.69 ! [V_w,V_z] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 50.50/50.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zle__trans,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zle__antisym,axiom,
% 50.50/50.69 ! [V_w,V_z] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 50.50/50.69 => V_z = V_w ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__fun__def,axiom,
% 50.50/50.69 ! [V_g_2,V_f_2,T_b,T_c] :
% 50.50/50.69 ( class_Orderings_Oord(T_c)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 50.50/50.69 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_linorder__linear,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__eq__iff,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Oorder(T_b)
% 50.50/50.69 => ( V_x_2 = V_y_2
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__eq__refl,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Opreorder(T_a)
% 50.50/50.69 => ( V_x = V_y
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__funD,axiom,
% 50.50/50.69 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 50.50/50.69 ( class_Orderings_Oord(T_c)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__antisym__conv,axiom,
% 50.50/50.69 ! [V_x_2,V_y_2,T_b] :
% 50.50/50.69 ( class_Orderings_Oorder(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> V_x_2 = V_y_2 ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_ord__eq__le__trans,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Orderings_Oord(T_a)
% 50.50/50.69 => ( V_a = V_b
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I3_J,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( V_a = V_b
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_ord__le__eq__trans,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Orderings_Oord(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( V_b = V_c
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I4_J,axiom,
% 50.50/50.69 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 50.50/50.69 => ( V_b = V_c
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__antisym,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.50/50.69 => V_x = V_y ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__trans,axiom,
% 50.50/50.69 ! [V_z,V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Opreorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I5_J,axiom,
% 50.50/50.69 ! [V_x,V_y,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 => V_x = V_y ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I6_J,axiom,
% 50.50/50.69 ! [V_z,V_x,V_y,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__funE,axiom,
% 50.50/50.69 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 50.50/50.69 ( class_Orderings_Oord(T_c)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_linorder__le__cases,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_a)
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__mult__le__cancel1,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__nat__le__iff,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zle__int,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__le__iff,axiom,
% 50.50/50.69 ! [V_z_2,V_w_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_one__le__mult__iff,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> ( 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))
% 50.50/50.69 & 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)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__le__cancel1,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__le__cancel2,axiom,
% 50.50/50.69 ! [V_n_2,V_k_2,V_m_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 50.50/50.69 => ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I8_J,axiom,
% 50.50/50.69 ! [V_z,V_x,V_y,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__le__less__trans,axiom,
% 50.50/50.69 ! [V_z,V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Opreorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I7_J,axiom,
% 50.50/50.69 ! [V_z,V_x,V_y,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__less__le__trans,axiom,
% 50.50/50.69 ! [V_z,V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Opreorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I11_J,axiom,
% 50.50/50.69 ! [V_a,V_b,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 50.50/50.69 => ( V_a != V_b
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__le__neq__trans,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( V_a != V_b
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__le__imp__less__or__eq,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.69 | V_x = V_y ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_linorder__antisym__conv2,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> V_x_2 = V_y_2 ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__less__imp__le,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Opreorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_leD,axiom,
% 50.50/50.69 ! [V_x,V_y,T_a] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.50/50.69 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_xt1_I12_J,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( V_a != V_b
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__neq__le__trans,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Orderings_Oorder(T_a)
% 50.50/50.69 => ( V_a != V_b
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_linorder__antisym__conv1,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_b)
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> V_x_2 = V_y_2 ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_not__leE,axiom,
% 50.50/50.69 ! [V_x,V_y,T_a] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_a)
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_leI,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_a)
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__le__less,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Oorder(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.69 | V_x_2 = V_y_2 ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_less__le__not__le,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Opreorder(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_order__less__le,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Oorder(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 & V_x_2 != V_y_2 ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_linorder__le__less__linear,axiom,
% 50.50/50.69 ! [V_y,V_x,T_a] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_linorder__not__le,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_b)
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_linorder__not__less,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Orderings_Olinorder(T_b)
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__le__imp__le__left,axiom,
% 50.50/50.69 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 50.50/50.69 => ( 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)))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__le__imp__le__right,axiom,
% 50.50/50.69 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 50.50/50.69 => ( 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)))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__mono,axiom,
% 50.50/50.69 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__left__mono,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__right__mono,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__le__cancel__left,axiom,
% 50.50/50.69 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__le__cancel__right,axiom,
% 50.50/50.69 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__cancel2,axiom,
% 50.50/50.69 ! [V_n_2,V_k_2,V_m_2] :
% 50.50/50.69 ( 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)
% 50.50/50.69 <=> ( V_m_2 = V_n_2
% 50.50/50.69 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__cancel1,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.69 ( 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)
% 50.50/50.69 <=> ( V_m_2 = V_n_2
% 50.50/50.69 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__is__0,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.69 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.69 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__0__right,axiom,
% 50.50/50.69 ! [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) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__0,axiom,
% 50.50/50.69 ! [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) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__mult__cancel1,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.69 ( 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)
% 50.50/50.69 <=> V_m_2 = V_n_2 ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__0__eq,axiom,
% 50.50/50.69 ! [V_n_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 50.50/50.69 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 50.50/50.69 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__minus__iff,axiom,
% 50.50/50.69 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_minus__le__iff,axiom,
% 50.50/50.69 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_neg__le__iff__le,axiom,
% 50.50/50.69 ! [V_a_2,V_b_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__imp__neg__le,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__ab__group__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__mult__distrib2,axiom,
% 50.50/50.69 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__mult__distrib,axiom,
% 50.50/50.69 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__n__not__le__n,axiom,
% 50.50/50.69 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_not__less__eq__eq,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__Suc__eq,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__le__mono,axiom,
% 50.50/50.69 ! [V_m_2,V_n_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__SucI,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__SucE,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 50.50/50.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__leD,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 50.50/50.69 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))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_termination__basic__simps_I5_J,axiom,
% 50.50/50.69 ! [V_y,V_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__less__le,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 & V_m_2 != V_n_2 ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__eq__less__or__eq,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 | V_m_2 = V_n_2 ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_less__imp__le__nat,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__neq__implies__less,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 => ( V_m != V_n
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_less__or__eq__imp__le,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 | V_m = V_n )
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_termination__basic__simps_I4_J,axiom,
% 50.50/50.69 ! [V_y,V_z,V_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_termination__basic__simps_I3_J,axiom,
% 50.50/50.69 ! [V_z,V_y,V_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__add2,axiom,
% 50.50/50.69 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__add1,axiom,
% 50.50/50.69 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__iff__add,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__add__left__cancel__le,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_trans__le__add1,axiom,
% 50.50/50.69 ! [V_m,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_trans__le__add2,axiom,
% 50.50/50.69 ! [V_m,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__le__mono1,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__le__mono,axiom,
% 50.50/50.69 ! [V_l,V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__leD2,axiom,
% 50.50/50.69 ! [V_n,V_k,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__leD1,axiom,
% 50.50/50.69 ! [V_n,V_k,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__leE,axiom,
% 50.50/50.69 ! [V_n,V_k,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 50.50/50.69 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zless__le,axiom,
% 50.50/50.69 ! [V_w_2,V_z_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 50.50/50.69 & V_z_2 != V_w_2 ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zadd__left__mono,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 50.50/50.69 => 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_evaln__nonstrict,axiom,
% 50.50/50.69 ! [V_m,V_t,V_n,V_s,V_c] :
% 50.50/50.69 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.69 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__le__eq__zle,axiom,
% 50.50/50.69 ! [V_z_2,V_w_2] :
% 50.50/50.69 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 50.50/50.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 50.50/50.69 => ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mult__distrib,axiom,
% 50.50/50.69 ! [V_z_H,V_z] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.69 => 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)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 50.50/50.69 ! [V_y,V_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.69 => 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)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__0__le__iff,axiom,
% 50.50/50.69 ! [V_z_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__int__le__0__iff,axiom,
% 50.50/50.69 ! [V_z_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn__0__0,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.69 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.69 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn0,axiom,
% 50.50/50.69 ! [T_a] :
% 50.50/50.69 ( class_Groups_Osgn__if(T_a)
% 50.50/50.69 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_sgn__times,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.69 => 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)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__mult__distrib__neg,axiom,
% 50.50/50.69 ! [V_z_H,V_z] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.69 => 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__nonneg__nonneg,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__nonneg__eq__0__iff,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 50.50/50.69 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.69 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.69 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__increasing,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__increasing2,axiom,
% 50.50/50.69 ! [V_a,V_b,V_c,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__nonpos__nonpos,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_split__mult__neg__le,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__cancel__semiring(T_a)
% 50.50/50.69 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 50.50/50.69 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_split__mult__pos__le,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__ring(T_a)
% 50.50/50.69 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 50.50/50.69 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__mono,axiom,
% 50.50/50.69 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.69 => 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))) ) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__mono_H,axiom,
% 50.50/50.69 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.69 => 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))) ) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__left__mono__neg,axiom,
% 50.50/50.69 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__ring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__right__mono__neg,axiom,
% 50.50/50.69 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__ring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_comm__mult__left__mono,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__comm__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__left__mono,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__right__mono,axiom,
% 50.50/50.69 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__nonpos__nonpos,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__ring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__nonpos__nonneg,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__cancel__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__nonneg__nonpos2,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__cancel__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__nonneg__nonpos,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__cancel__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__nonneg__nonneg,axiom,
% 50.50/50.69 ! [V_b,V_a,T_a] :
% 50.50/50.69 ( class_Rings_Oordered__cancel__semiring(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__le__0__iff,axiom,
% 50.50/50.69 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 50.50/50.69 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__le__mult__iff,axiom,
% 50.50/50.69 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.69 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
% 50.50/50.69 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 50.50/50.69 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__le__square,axiom,
% 50.50/50.69 ! [V_a,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__ring(T_a)
% 50.50/50.69 => 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__le__less__mono,axiom,
% 50.50/50.69 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_add__less__le__mono,axiom,
% 50.50/50.69 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.69 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 50.50/50.69 => 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))) ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__le__one,axiom,
% 50.50/50.69 ! [T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_not__one__le__zero,axiom,
% 50.50/50.69 ! [T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => ~ 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_neg__0__le__iff__le,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__minus__self__iff,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_neg__le__0__iff__le,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_minus__le__self__iff,axiom,
% 50.50/50.69 ! [V_a_2,T_b] :
% 50.50/50.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__eq__1__iff,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( 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))
% 50.50/50.69 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.50/50.69 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_of__nat__0__le__iff,axiom,
% 50.50/50.69 ! [V_n,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__le__imp__of__nat,axiom,
% 50.50/50.69 ! [V_m,T_a] :
% 50.50/50.69 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.69 => 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))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__less__mono2,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__less__mono1,axiom,
% 50.50/50.69 ! [V_k,V_j,V_i] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__less__cancel2,axiom,
% 50.50/50.69 ! [V_n_2,V_k_2,V_m_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__less__cancel1,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_nat__0__less__mult__iff,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 50.50/50.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__mult__less__cancel1,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.69 ( 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)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__Suc,axiom,
% 50.50/50.69 ! [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)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_mult__Suc__right,axiom,
% 50.50/50.69 ! [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)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_One__nat__def,axiom,
% 50.50/50.69 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__le__lessD,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__less__Suc__eq,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 50.50/50.69 <=> V_n_2 = V_m_2 ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__leI,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_le__imp__less__Suc,axiom,
% 50.50/50.69 ! [V_n,V_m] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__le__eq,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_less__Suc__eq__le,axiom,
% 50.50/50.69 ! [V_n_2,V_m_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_less__eq__Suc__le,axiom,
% 50.50/50.69 ! [V_m_2,V_n_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 50.50/50.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__eq__plus1,axiom,
% 50.50/50.69 ! [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)) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Suc__eq__plus1__left,axiom,
% 50.50/50.69 ! [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) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 50.50/50.69 ! [V_y,V_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zero__zle__int,axiom,
% 50.50/50.69 ! [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))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 50.50/50.69 ! [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))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 50.50/50.69 ! [V_P_2] :
% 50.50/50.69 ( ? [B_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 50.50/50.69 & hBOOL(hAPP(V_P_2,B_x)) )
% 50.50/50.69 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 50.50/50.69 ! [V_P_2] :
% 50.50/50.69 ( ! [B_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 50.50/50.69 => hBOOL(hAPP(V_P_2,B_x)) )
% 50.50/50.69 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 50.50/50.69 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))) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_eq__nat__nat__iff,axiom,
% 50.50/50.69 ! [V_z_H_2,V_z_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 50.50/50.69 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 50.50/50.69 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_ex__nat,axiom,
% 50.50/50.69 ! [V_P_2] :
% 50.50/50.69 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 50.50/50.69 <=> ? [B_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 50.50/50.69 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_all__nat,axiom,
% 50.50/50.69 ! [V_P_2] :
% 50.50/50.69 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 50.50/50.69 <=> ! [B_x] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 50.50/50.69 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 50.50/50.69 ! [V_y_2,V_x_2] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 50.50/50.69 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 50.50/50.69 <=> V_x_2 = V_y_2 ) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_zadd__zless__mono,axiom,
% 50.50/50.69 ! [V_z,V_z_H,V_w,V_w_H] :
% 50.50/50.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 50.50/50.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 50.50/50.69 => 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))) ) ) ).
% 50.50/50.69
% 50.50/50.69 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => 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))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmult__int,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__mult,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zle__iff__zadd,axiom,
% 50.50/50.70 ! [V_z_2,V_w_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 50.50/50.70 <=> ? [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)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__1,axiom,
% 50.50/50.70 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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 50.50/50.70 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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 50.50/50.70 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_add__pos__nonneg,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_add__nonneg__pos,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_add__strict__increasing,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_add__strict__increasing2,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_add__neg__nonpos,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_add__nonpos__neg,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__le__cancel__left__pos,axiom,
% 50.50/50.70 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__le__cancel__left__neg,axiom,
% 50.50/50.70 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__strict__mono,axiom,
% 50.50/50.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__strict__mono_H,axiom,
% 50.50/50.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__less__le__imp__less,axiom,
% 50.50/50.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__le__less__imp__less,axiom,
% 50.50/50.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__right__less__imp__less,axiom,
% 50.50/50.70 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__less__imp__less__right,axiom,
% 50.50/50.70 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__left__less__imp__less,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__less__imp__less__left,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__right__le__imp__le,axiom,
% 50.50/50.70 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__left__le__imp__le,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_sum__squares__le__zero__iff,axiom,
% 50.50/50.70 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.70 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.70 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_sum__squares__ge__zero,axiom,
% 50.50/50.70 ! [V_y,V_x,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__ring(T_a)
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__left__le__one__le,axiom,
% 50.50/50.70 ! [V_y,V_x,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__right__le__one__le,axiom,
% 50.50/50.70 ! [V_y,V_x,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_sgn__greater,axiom,
% 50.50/50.70 ! [V_a_2,T_b] :
% 50.50/50.70 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_sgn__less,axiom,
% 50.50/50.70 ! [V_a_2,T_b] :
% 50.50/50.70 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_one__less__mult,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_n__less__n__mult__m,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_n__less__m__mult__n,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__le__0__conv,axiom,
% 50.50/50.70 ! [V_n_2] :
% 50.50/50.70 ( 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)))
% 50.50/50.70 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__0__iff,axiom,
% 50.50/50.70 ! [V_i_2] :
% 50.50/50.70 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__le__0,axiom,
% 50.50/50.70 ! [V_z] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__one__le__iff__zero__less,axiom,
% 50.50/50.70 ! [V_z_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__0__le,axiom,
% 50.50/50.70 ! [V_z] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.70 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__eq__iff,axiom,
% 50.50/50.70 ! [V_z_2,V_m_2] :
% 50.50/50.70 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 50.50/50.70 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__nat__eq,axiom,
% 50.50/50.70 ! [V_z] :
% 50.50/50.70 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.70 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 50.50/50.70 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.70 => 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) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zless__imp__add1__zle,axiom,
% 50.50/50.70 ! [V_z,V_w] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 50.50/50.70 => 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)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_add1__zle__eq,axiom,
% 50.50/50.70 ! [V_z_2,V_w_2] :
% 50.50/50.70 ( 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))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zle__add1__eq__le,axiom,
% 50.50/50.70 ! [V_z_2,V_w_2] :
% 50.50/50.70 ( 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))))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__zle__neg,axiom,
% 50.50/50.70 ! [V_m_2,V_n_2] :
% 50.50/50.70 ( 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))))
% 50.50/50.70 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_negative__zle__0,axiom,
% 50.50/50.70 ! [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))) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_convex__bound__le,axiom,
% 50.50/50.70 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 50.50/50.70 ( class_Rings_Olinordered__semiring__1(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 50.50/50.70 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 50.50/50.70 ! [V_y_2,V_x_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 50.50/50.70 => ( 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)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__less__eq__zless,axiom,
% 50.50/50.70 ! [V_z_2,V_w_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 50.50/50.70 => ( 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)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__eq__iff,axiom,
% 50.50/50.70 ! [V_m_2,V_w_2] :
% 50.50/50.70 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 50.50/50.70 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 50.50/50.70 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 50.50/50.70 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 50.50/50.70 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__eq__iff2,axiom,
% 50.50/50.70 ! [V_w_2,V_m_2] :
% 50.50/50.70 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 50.50/50.70 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 50.50/50.70 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 50.50/50.70 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 50.50/50.70 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => 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)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__add__distrib,axiom,
% 50.50/50.70 ! [V_z_H,V_z] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 50.50/50.70 => 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)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_le__imp__0__less,axiom,
% 50.50/50.70 ! [V_z] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.70 => 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))) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_not__zle__0__negative,axiom,
% 50.50/50.70 ! [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))))) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_of__nat__nat,axiom,
% 50.50/50.70 ! [V_z,T_a] :
% 50.50/50.70 ( class_Rings_Oring__1(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.70 => 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) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_sgn__1__pos,axiom,
% 50.50/50.70 ! [V_a_2,T_b] :
% 50.50/50.70 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.70 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_self__quotient__aux2,axiom,
% 50.50/50.70 ! [V_q,V_r,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.70 => ( 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))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_self__quotient__aux1,axiom,
% 50.50/50.70 ! [V_q,V_r,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.70 => ( 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))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_q__pos__lemma,axiom,
% 50.50/50.70 ! [V_r_H,V_q_H,V_b_H] :
% 50.50/50.70 ( 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)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_q__neg__lemma,axiom,
% 50.50/50.70 ! [V_r_H,V_q_H,V_b_H] :
% 50.50/50.70 ( 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)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_unique__quotient__lemma,axiom,
% 50.50/50.70 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 50.50/50.70 ( 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)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__mono2__lemma,axiom,
% 50.50/50.70 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 50.50/50.70 ( 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)
% 50.50/50.70 => ( 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)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_unique__quotient__lemma__neg,axiom,
% 50.50/50.70 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 50.50/50.70 ( 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)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 50.50/50.70 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 50.50/50.70 ( 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)
% 50.50/50.70 => ( 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)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__mult__le__cancel1,axiom,
% 50.50/50.70 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_le__refl,axiom,
% 50.50/50.70 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__le__linear,axiom,
% 50.50/50.70 ! [V_n,V_m] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.70 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_eq__imp__le,axiom,
% 50.50/50.70 ! [V_n,V_m] :
% 50.50/50.70 ( V_m = V_n
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_le__trans,axiom,
% 50.50/50.70 ! [V_k,V_j,V_i] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_le__antisym,axiom,
% 50.50/50.70 ! [V_n,V_m] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.70 => V_m = V_n ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_less__fun__def,axiom,
% 50.50/50.70 ! [V_g_2,V_f_2,T_b,T_c] :
% 50.50/50.70 ( class_Orderings_Oord(T_c)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 50.50/50.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 50.50/50.70 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 50.50/50.70 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.70 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 50.50/50.70 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 | V_m_2 = V_n_2 ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_left__add__mult__distrib,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__mult__less__cancel1,axiom,
% 50.50/50.70 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__mult__eq__cancel1,axiom,
% 50.50/50.70 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.50/50.70 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 50.50/50.70 <=> V_m_2 = V_n_2 ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_transfer__morphism__nat__int,axiom,
% 50.50/50.70 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))) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_compl__le__compl__iff,axiom,
% 50.50/50.70 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.70 ( class_Lattices_Oboolean__algebra(T_b)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_compl__mono,axiom,
% 50.50/50.70 ! [V_y,V_x,T_a] :
% 50.50/50.70 ( class_Lattices_Oboolean__algebra(T_a)
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.70 => 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))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_ex__least__nat__less,axiom,
% 50.50/50.70 ! [V_n_2,V_P_2] :
% 50.50/50.70 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 50.50/50.70 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 50.50/50.70 => ? [B_k] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 50.50/50.70 & ! [B_i] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 50.50/50.70 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 50.50/50.70 & 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)))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_divmod__int__rel__mod__eq,axiom,
% 50.50/50.70 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 50.50/50.70 ( 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)
% 50.50/50.70 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 50.50/50.70 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 50.50/50.70 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmult2__lemma__aux2,axiom,
% 50.50/50.70 ! [V_q,V_r,V_b,V_c] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => 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))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmult2__lemma__aux1,axiom,
% 50.50/50.70 ! [V_q,V_r,V_b,V_c] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => 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))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmult2__lemma__aux4,axiom,
% 50.50/50.70 ! [V_q,V_b,V_r,V_c] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 50.50/50.70 => 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))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mod__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__0,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__by__0,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__self,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__add__self2,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__add__self1,axiom,
% 50.50/50.70 ! [V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__add__right__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__add__left__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__add__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__simps_I2_J,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__simps_I1_J,axiom,
% 50.50/50.70 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__add__cong,axiom,
% 50.50/50.70 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 50.50/50.70 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 50.50/50.70 => 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) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__right__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__left__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__mult1,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__mult2,axiom,
% 50.50/50.70 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__simps_I4_J,axiom,
% 50.50/50.70 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__cong,axiom,
% 50.50/50.70 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 50.50/50.70 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 50.50/50.70 => 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) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__minus__eq,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Oring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__minus__cong,axiom,
% 50.50/50.70 ! [V_a_H,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Oring__div(T_a)
% 50.50/50.70 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 50.50/50.70 => 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) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__self,axiom,
% 50.50/50.70 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zero,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__simps_I3_J,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zmult1__eq,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zminus__zmod,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zminus__zminus,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zminus2,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__self2__is__0,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__self1__is__0,axiom,
% 50.50/50.70 ! [V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__self2,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__self1,axiom,
% 50.50/50.70 ! [V_b,V_c,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__by__1,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__le__nonneg__dividend,axiom,
% 50.50/50.70 ! [V_k,V_m] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 50.50/50.70 => 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)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => 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))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_pos__mod__bound,axiom,
% 50.50/50.70 ! [V_a,V_b] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.70 => 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)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_neg__mod__bound,axiom,
% 50.50/50.70 ! [V_a,V_b] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => 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))) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__eq__0__iff,axiom,
% 50.50/50.70 ! [V_d_2,V_m_2] :
% 50.50/50.70 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zminus2__not__zero,axiom,
% 50.50/50.70 ! [V_l,V_k] :
% 50.50/50.70 ( 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)
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zminus1__not__zero,axiom,
% 50.50/50.70 ! [V_l,V_k] :
% 50.50/50.70 ( 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)
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_pos__mod__sign,axiom,
% 50.50/50.70 ! [V_a,V_b] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.70 => 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))) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_pos__mod__conj,axiom,
% 50.50/50.70 ! [V_a,V_b] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.70 => ( 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)))
% 50.50/50.70 & 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)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__pos__pos__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_neg__mod__sign,axiom,
% 50.50/50.70 ! [V_a,V_b] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => 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))) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_neg__mod__conj,axiom,
% 50.50/50.70 ! [V_a,V_b] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( 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)))
% 50.50/50.70 & 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))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__neg__neg__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__left__idem,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mult__idem,axiom,
% 50.50/50.70 ! [V_x,T_a] :
% 50.50/50.70 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_times_Oidem,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_compl__eq__compl__iff,axiom,
% 50.50/50.70 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.70 ( class_Lattices_Oboolean__algebra(T_b)
% 50.50/50.70 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 50.50/50.70 <=> V_x_2 = V_y_2 ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_uminus__apply,axiom,
% 50.50/50.70 ! [V_x_2,V_A_2,T_c,T_b] :
% 50.50/50.70 ( class_Groups_Ouminus(T_b)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_double__compl,axiom,
% 50.50/50.70 ! [V_x,T_a] :
% 50.50/50.70 ( class_Lattices_Oboolean__algebra(T_a)
% 50.50/50.70 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__pos__neg__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.70 => ( 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)))
% 50.50/50.70 => 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) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__zmod,axiom,
% 50.50/50.70 ! [V_k_2,V_n_2,V_P_2] :
% 50.50/50.70 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 50.50/50.70 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 50.50/50.70 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 50.50/50.70 => ! [B_i,B_j] :
% 50.50/50.70 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 50.50/50.70 & 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) )
% 50.50/50.70 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 50.50/50.70 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ! [B_i,B_j] :
% 50.50/50.70 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 & 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) )
% 50.50/50.70 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmult2__lemma__aux3,axiom,
% 50.50/50.70 ! [V_q,V_b,V_r,V_c] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 50.50/50.70 => 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))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_z3mod__def,axiom,
% 50.50/50.70 ! [V_k,V_l] :
% 50.50/50.70 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 50.50/50.70 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 50.50/50.70 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 50.50/50.70 => 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)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__pos__lemma,axiom,
% 50.50/50.70 ! [V_n_2,V_P_2,V_k_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 50.50/50.70 <=> ! [B_i,B_j] :
% 50.50/50.70 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 50.50/50.70 & 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) )
% 50.50/50.70 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__neg__lemma,axiom,
% 50.50/50.70 ! [V_n_2,V_P_2,V_k_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 50.50/50.70 <=> ! [B_i,B_j] :
% 50.50/50.70 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 & 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) )
% 50.50/50.70 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zmult2__eq,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => 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))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__zdiv,axiom,
% 50.50/50.70 ! [V_k_2,V_n_2,V_P_2] :
% 50.50/50.70 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 50.50/50.70 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.50/50.70 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 50.50/50.70 => ! [B_i] :
% 50.50/50.70 ( ? [B_j] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 50.50/50.70 & 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) )
% 50.50/50.70 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 50.50/50.70 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ! [B_i] :
% 50.50/50.70 ( ? [B_j] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 & 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) )
% 50.50/50.70 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_divmod__int__rel__div__eq,axiom,
% 50.50/50.70 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 50.50/50.70 ( 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)
% 50.50/50.70 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 50.50/50.70 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 50.50/50.70 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__div_H,axiom,
% 50.50/50.70 ! [V_n_2,V_m_2,V_P_2] :
% 50.50/50.70 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 50.50/50.70 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 50.50/50.70 | ? [B_q] :
% 50.50/50.70 ( 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))
% 50.50/50.70 & 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))))
% 50.50/50.70 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__add1__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 50.50/50.70 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__int,axiom,
% 50.50/50.70 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult2__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult1__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__le__mono,axiom,
% 50.50/50.70 ! [V_k,V_n,V_m] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__le__dividend,axiom,
% 50.50/50.70 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zero,axiom,
% 50.50/50.70 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult2__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__less,axiom,
% 50.50/50.70 ! [V_n,V_m] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__less__eq__dividend,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__distrib,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__distrib2,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zminus2,axiom,
% 50.50/50.70 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zminus__zminus,axiom,
% 50.50/50.70 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__0,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__by__0,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__by__1,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__div__distrib,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__1,axiom,
% 50.50/50.70 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__less,axiom,
% 50.50/50.70 ! [V_n,V_m] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__mult__div__cancel__disj,axiom,
% 50.50/50.70 ! [V_n,V_m,V_k] :
% 50.50/50.70 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.50/50.70 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__1,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__Suc,axiom,
% 50.50/50.70 ! [V_n,V_m] :
% 50.50/50.70 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 50.50/50.70 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.50/50.70 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 50.50/50.70 => 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)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__less__divisor,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.70 => 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)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__neg__pos__less0,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 50.50/50.70 ! [V_a_2,V_b_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 50.50/50.70 ! [V_a_2,V_b_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__self,axiom,
% 50.50/50.70 ! [V_a] :
% 50.50/50.70 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__eq__0__iff,axiom,
% 50.50/50.70 ! [V_d_2,V_m_2] :
% 50.50/50.70 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_DIVISION__BY__ZERO,axiom,
% 50.50/50.70 ! [V_a] :
% 50.50/50.70 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zdiv__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__self3,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zadd1__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__int,axiom,
% 50.50/50.70 ! [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)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__mult1,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__mult2,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__self1__is__id,axiom,
% 50.50/50.70 ! [V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__self2__is__id,axiom,
% 50.50/50.70 ! [V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__mult1__if,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 50.50/50.70 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__self,axiom,
% 50.50/50.70 ! [V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__div__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__le__mono2,axiom,
% 50.50/50.70 ! [V_k,V_n,V_m] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__mult__div__cancel1,axiom,
% 50.50/50.70 ! [V_n,V_m,V_k] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__self1__is__m,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__self__is__m,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__less__dividend,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__mono1__neg,axiom,
% 50.50/50.70 ! [V_b,V_a_H,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__mono1,axiom,
% 50.50/50.70 ! [V_b,V_a_H,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__neg__neg__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__mono2__neg,axiom,
% 50.50/50.70 ! [V_b,V_b_H,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__nonpos__pos__le0,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 50.50/50.70 ! [V_a_2,V_b_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__pos__pos__trivial,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__nonneg__neg__le0,axiom,
% 50.50/50.70 ! [V_b,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__mono2,axiom,
% 50.50/50.70 ! [V_b,V_b_H,V_a] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 50.50/50.70 ! [V_b_2,V_a_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 50.50/50.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 50.50/50.70 ! [V_i_2,V_k_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 50.50/50.70 ! [V_a_2,V_b_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 50.50/50.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__eq__0__iff,axiom,
% 50.50/50.70 ! [V_k_2,V_i_2] :
% 50.50/50.70 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 50.50/50.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__le__divisor,axiom,
% 50.50/50.70 ! [V_m,V_n] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.70 => 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)) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_int__div__less__self,axiom,
% 50.50/50.70 ! [V_k,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 50.50/50.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zmult2__eq,axiom,
% 50.50/50.70 ! [V_b,V_a,V_c] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__mult__self4,axiom,
% 50.50/50.70 ! [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) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zmod__equality2,axiom,
% 50.50/50.70 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zmod__equality,axiom,
% 50.50/50.70 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zdiv__zmult1__eq,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_zmod__zdiv__equality,axiom,
% 50.50/50.70 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__self1,axiom,
% 50.50/50.70 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mult__self2,axiom,
% 50.50/50.70 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__add__self1,axiom,
% 50.50/50.70 ! [V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__add__self2,axiom,
% 50.50/50.70 ! [V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mod__equality,axiom,
% 50.50/50.70 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_div__mod__equality2,axiom,
% 50.50/50.70 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__div__equality,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__div__equality2,axiom,
% 50.50/50.70 ! [V_a,V_b,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 50.50/50.70 ! [V_b,V_a,T_a] :
% 50.50/50.70 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__div,axiom,
% 50.50/50.70 ! [V_k_2,V_n_2,V_P_2] :
% 50.50/50.70 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 50.50/50.70 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 50.50/50.70 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 => ! [B_i,B_j] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 50.50/50.70 => ( 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)
% 50.50/50.70 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_mod__lemma,axiom,
% 50.50/50.70 ! [V_q,V_b,V_r,V_c] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 50.50/50.70 => 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))) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__mod,axiom,
% 50.50/50.70 ! [V_k_2,V_n_2,V_P_2] :
% 50.50/50.70 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 50.50/50.70 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 50.50/50.70 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.70 => ! [B_i,B_j] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 50.50/50.70 => ( 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)
% 50.50/50.70 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Suc__times__mod__eq,axiom,
% 50.50/50.70 ! [V_m,V_k] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 50.50/50.70 => 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) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_nat__mod__distrib,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => 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)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 50.50/50.70 ! [V_y,V_x] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.70 => 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)) ) ) ).
% 50.50/50.70
% 50.50/50.70 fof(fact_split__div__lemma,axiom,
% 50.50/50.70 ! [V_m_2,V_q_2,V_n_2] :
% 50.50/50.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 50.50/50.70 => ( ( 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))
% 50.50/50.71 & 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)))) )
% 50.50/50.71 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_z3div__def,axiom,
% 50.50/50.71 ! [V_k,V_l] :
% 50.50/50.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 50.50/50.71 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 50.50/50.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 50.50/50.71 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiv__zminus1__eq__if,axiom,
% 50.50/50.71 ! [V_a,V_b] :
% 50.50/50.71 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 50.50/50.71 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiv__zminus2__eq__if,axiom,
% 50.50/50.71 ! [V_a,V_b] :
% 50.50/50.71 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 50.50/50.71 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__div__geq,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__div__decomp,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Divides_Osemiring__div(T_a)
% 50.50/50.71 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 50.50/50.71 ! [V_y,V_x] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_incr__mult__lemma,axiom,
% 50.50/50.71 ! [V_k_2,V_P_2,V_d_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 50.50/50.71 => ( ! [B_x] :
% 50.50/50.71 ( hBOOL(hAPP(V_P_2,B_x))
% 50.50/50.71 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 50.50/50.71 => ! [B_x] :
% 50.50/50.71 ( hBOOL(hAPP(V_P_2,B_x))
% 50.50/50.71 => 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)))) ) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_field__le__mult__one__interval,axiom,
% 50.50/50.71 ! [V_y,V_x,T_a] :
% 50.50/50.71 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 50.50/50.71 => ( ! [B_z] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) )
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__eq__diff__eq,axiom,
% 50.50/50.71 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oab__group__add(T_b)
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 50.50/50.71 => ( V_a_2 = V_b_2
% 50.50/50.71 <=> V_c_2 = V_d_2 ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__commute,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_of__int__diff,axiom,
% 50.50/50.71 ! [V_z,V_w,T_a] :
% 50.50/50.71 ( class_Rings_Oring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_minus__apply,axiom,
% 50.50/50.71 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 50.50/50.71 ( class_Groups_Ominus(T_b)
% 50.50/50.71 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_of__nat__diff,axiom,
% 50.50/50.71 ! [V_m,V_n,T_a] :
% 50.50/50.71 ( class_Rings_Oring__1(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiff__int,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__eq__diff__less__eq,axiom,
% 50.50/50.71 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_right__minus__eq,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_b)
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.71 <=> V_a_2 = V_b_2 ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_eq__iff__diff__eq__0,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oab__group__add(T_b)
% 50.50/50.71 => ( V_a_2 = V_b_2
% 50.50/50.71 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__self,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__0__right,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__eq__diff__less,axiom,
% 50.50/50.71 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__diff__cancel,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__add__cancel,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_minus__diff__eq,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oab__group__add(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__diff__right__eq,axiom,
% 50.50/50.71 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.71 ( class_Divides_Oring__div(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__diff__left__eq,axiom,
% 50.50/50.71 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.71 ( class_Divides_Oring__div(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__diff__eq,axiom,
% 50.50/50.71 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.71 ( class_Divides_Oring__div(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__diff__cong,axiom,
% 50.50/50.71 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 50.50/50.71 ( class_Divides_Oring__div(T_a)
% 50.50/50.71 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 50.50/50.71 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 50.50/50.71 => 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) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diffs0__imp__equal,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 => V_m = V_n ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__self__eq__0,axiom,
% 50.50/50.71 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_minus__nat_Odiff__0,axiom,
% 50.50/50.71 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__0__eq__0,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__Suc__Suc,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Suc__diff__diff,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__imp__diff__less,axiom,
% 50.50/50.71 ! [V_n,V_k,V_j] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__less__mono2,axiom,
% 50.50/50.71 ! [V_l,V_n,V_m] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 50.50/50.71 => 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))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__if,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 50.50/50.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => 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) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__geq,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__add__inverse2,axiom,
% 50.50/50.71 ! [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 ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__add__inverse,axiom,
% 50.50/50.71 ! [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 ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__diff__left,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__cancel,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__cancel2,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__diff__iff,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Nat_Odiff__diff__eq,axiom,
% 50.50/50.71 ! [V_n,V_m,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 50.50/50.71 => 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) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_eq__diff__iff,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 50.50/50.71 => ( 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)
% 50.50/50.71 <=> V_m_2 = V_n_2 ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__diff__cancel,axiom,
% 50.50/50.71 ! [V_n,V_i] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__le__mono,axiom,
% 50.50/50.71 ! [V_l,V_n,V_m] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__le__mono2,axiom,
% 50.50/50.71 ! [V_l,V_n,V_m] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__le__self,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__mod__geq,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiff__zmult__distrib2,axiom,
% 50.50/50.71 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiff__zmult__distrib,axiom,
% 50.50/50.71 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__mult__distrib,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__mult__distrib2,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiff__zmod__right,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiff__zmod__left,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__diff__distrib,axiom,
% 50.50/50.71 ! [V_z,V_z_H] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zdiff__int__split,axiom,
% 50.50/50.71 ! [V_y_2,V_x_2,V_P_2] :
% 50.50/50.71 ( 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))))
% 50.50/50.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 50.50/50.71 => 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)))) )
% 50.50/50.71 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 50.50/50.71 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__iff__diff__le__0,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__iff__diff__less__0,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_eq__add__iff2,axiom,
% 50.50/50.71 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Rings_Oring(T_b)
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 50.50/50.71 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_eq__add__iff1,axiom,
% 50.50/50.71 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Rings_Oring(T_b)
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 50.50/50.71 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__0,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__minus__eq__add,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_ab__diff__minus,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oab__group__add(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__def,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Ogroup__add(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 50.50/50.71 ! [V_y,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__ring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__bin__lemma,axiom,
% 50.50/50.71 ! [V_l_2,V_k_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__less,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zero__less__diff,axiom,
% 50.50/50.71 ! [V_m_2,V_n_2] :
% 50.50/50.71 ( 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)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__less__Suc,axiom,
% 50.50/50.71 ! [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))) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__add__0,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__is__0__eq,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2] :
% 50.50/50.71 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__is__0__eq_H,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__diff__conv,axiom,
% 50.50/50.71 ! [V_k_2,V_j_2,V_i_2] :
% 50.50/50.71 ( 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)))
% 50.50/50.71 <=> 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__diff__inverse,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Suc__diff__le,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__diff__iff,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_k_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__less__mono,axiom,
% 50.50/50.71 ! [V_c,V_b,V_a] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 50.50/50.71 => 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))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__add__assoc2,axiom,
% 50.50/50.71 ! [V_i,V_j,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__diff__assoc2,axiom,
% 50.50/50.71 ! [V_i,V_j,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__add__assoc,axiom,
% 50.50/50.71 ! [V_i,V_j,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__imp__diff__is__add,axiom,
% 50.50/50.71 ! [V_k_2,V_j_2,V_i_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 50.50/50.71 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 50.50/50.71 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__add__diff__inverse2,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__diff__conv2,axiom,
% 50.50/50.71 ! [V_i_2,V_j_2,V_k_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 <=> 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__diff__assoc,axiom,
% 50.50/50.71 ! [V_i,V_j,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__add__diff__inverse,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__add__diff,axiom,
% 50.50/50.71 ! [V_m,V_n,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__diff__conv,axiom,
% 50.50/50.71 ! [V_i_2,V_k_2,V_j_2] :
% 50.50/50.71 ( 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))
% 50.50/50.71 <=> 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__diff__right,axiom,
% 50.50/50.71 ! [V_i,V_j,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__int__def,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__int__def__symmetric,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__Suc__1,axiom,
% 50.50/50.71 ! [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 ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_div__mod__equality_H,axiom,
% 50.50/50.71 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mult__div__cancel,axiom,
% 50.50/50.71 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Divides_Omod__div__equality_H,axiom,
% 50.50/50.71 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_tsub__eq,axiom,
% 50.50/50.71 ! [V_x,V_y] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 50.50/50.71 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 50.50/50.71 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__add__iff2,axiom,
% 50.50/50.71 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Rings_Oordered__ring(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__add__iff1,axiom,
% 50.50/50.71 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Rings_Oordered__ring(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__add__iff1,axiom,
% 50.50/50.71 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Rings_Oordered__ring(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__add__iff2,axiom,
% 50.50/50.71 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Rings_Oordered__ring(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__Suc__less,axiom,
% 50.50/50.71 ! [V_i,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Suc__pred,axiom,
% 50.50/50.71 ! [V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__diff__split__asm,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,V_P_2] :
% 50.50/50.71 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 50.50/50.71 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 50.50/50.71 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 50.50/50.71 | ? [B_d] :
% 50.50/50.71 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 50.50/50.71 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__diff__split,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,V_P_2] :
% 50.50/50.71 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 50.50/50.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 50.50/50.71 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 50.50/50.71 & ! [B_d] :
% 50.50/50.71 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 50.50/50.71 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zle__diff1__eq,axiom,
% 50.50/50.71 ! [V_z_2,V_w_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__Suc__diff__eq1,axiom,
% 50.50/50.71 ! [V_m,V_j,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__Suc__diff__eq2,axiom,
% 50.50/50.71 ! [V_m,V_j,V_k] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__le__add__iff1,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 <=> 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__diff__add__eq1,axiom,
% 50.50/50.71 ! [V_n,V_m,V_u,V_i,V_j] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__eq__add__iff1,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 50.50/50.71 => ( 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)
% 50.50/50.71 <=> 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 ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__le__add__iff2,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 <=> 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))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__diff__add__eq2,axiom,
% 50.50/50.71 ! [V_n,V_m,V_u,V_j,V_i] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__eq__add__iff2,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 50.50/50.71 => ( 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)
% 50.50/50.71 <=> 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) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zmod__zminus2__eq__if,axiom,
% 50.50/50.71 ! [V_b,V_a] :
% 50.50/50.71 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => 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) )
% 50.50/50.71 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => 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) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zmod__zminus1__eq__if,axiom,
% 50.50/50.71 ! [V_b,V_a] :
% 50.50/50.71 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => 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) )
% 50.50/50.71 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zmod__zdiv__equality_H,axiom,
% 50.50/50.71 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zmult__div__cancel,axiom,
% 50.50/50.71 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_tsub__def,axiom,
% 50.50/50.71 ! [V_x,V_y] :
% 50.50/50.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 50.50/50.71 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 50.50/50.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 50.50/50.71 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Suc__pred_H,axiom,
% 50.50/50.71 ! [V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Suc__diff__1,axiom,
% 50.50/50.71 ! [V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__less__add__iff2,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 <=> 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))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__less__add__iff1,axiom,
% 50.50/50.71 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 <=> 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__eq__if,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 50.50/50.71 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_div__if,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.50/50.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_div__geq,axiom,
% 50.50/50.71 ! [V_m,V_n] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mult__eq__if,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.50/50.71 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_int__power__div__base,axiom,
% 50.50/50.71 ! [V_k,V_m] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 50.50/50.71 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_decr__mult__lemma,axiom,
% 50.50/50.71 ! [V_k_2,V_P_2,V_d_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 50.50/50.71 => ( ! [B_x] :
% 50.50/50.71 ( hBOOL(hAPP(V_P_2,B_x))
% 50.50/50.71 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 50.50/50.71 => ! [B_x] :
% 50.50/50.71 ( hBOOL(hAPP(V_P_2,B_x))
% 50.50/50.71 => 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)))) ) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_incr__lemma,axiom,
% 50.50/50.71 ! [V_x,V_z,V_d] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 50.50/50.71 => 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)))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_decr__lemma,axiom,
% 50.50/50.71 ! [V_z,V_x,V_d] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__mod__eq__lemma,axiom,
% 50.50/50.71 ! [V_y,V_n,V_x] :
% 50.50/50.71 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 50.50/50.71 => ? [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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mod__induct__0,axiom,
% 50.50/50.71 ! [V_i_2,V_P_2,V_p_2] :
% 50.50/50.71 ( ! [B_i] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 50.50/50.71 => ( hBOOL(hAPP(V_P_2,B_i))
% 50.50/50.71 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 50.50/50.71 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 50.50/50.71 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_expand__Suc,axiom,
% 50.50/50.71 ! [V_v] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
% 50.50/50.71 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_field__le__epsilon,axiom,
% 50.50/50.71 ! [V_y,V_x,T_a] :
% 50.50/50.71 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.71 => ( ! [B_e] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_of__int__power,axiom,
% 50.50/50.71 ! [V_n,V_z,T_a] :
% 50.50/50.71 ( class_Rings_Oring__1(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_of__int__number__of__eq,axiom,
% 50.50/50.71 ! [V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_eq__number__of,axiom,
% 50.50/50.71 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.71 & class_Int_Oring__char__0(T_b) )
% 50.50/50.71 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 50.50/50.71 <=> V_x_2 = V_y_2 ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_number__of__reorient,axiom,
% 50.50/50.71 ! [V_x_2,V_w_2,T_b] :
% 50.50/50.71 ( class_Int_Onumber(T_b)
% 50.50/50.71 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 50.50/50.71 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__idempotent,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zero__le__zpower__abs,axiom,
% 50.50/50.71 ! [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))) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__le__D1,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__ge__self,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__zero,axiom,
% 50.50/50.71 ! [T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__eq__0,axiom,
% 50.50/50.71 ! [V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 50.50/50.71 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.71 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__add__abs,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__mult__self,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__mult,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__minus__commute,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__one,axiom,
% 50.50/50.71 ! [T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__minus__cancel,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 50.50/50.71 ! [V_q,V_y,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__of__nat,axiom,
% 50.50/50.71 ! [V_n,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__int__eq,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 50.50/50.71 ! [V_q,V_p,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zpower__zpower,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 50.50/50.71 ! [V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zpower__zmod,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_of__nat__number__of__lemma,axiom,
% 50.50/50.71 ! [V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) )
% 50.50/50.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_number__of__eq,axiom,
% 50.50/50.71 ! [V_k,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__number__of,axiom,
% 50.50/50.71 ! [V_x,T_a] :
% 50.50/50.71 ( ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 & class_Rings_Olinordered__idom(T_a) )
% 50.50/50.71 => ( ( 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)))
% 50.50/50.71 => 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)) )
% 50.50/50.71 & ( ~ 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)))
% 50.50/50.71 => 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) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zero__less__zpower__abs__iff,axiom,
% 50.50/50.71 ! [V_n_2,V_x_2] :
% 50.50/50.71 ( 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)))
% 50.50/50.71 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.50/50.71 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__of__nonneg,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__le__zero__iff,axiom,
% 50.50/50.71 ! [V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.71 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__ge__zero,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__of__pos,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zero__less__abs__iff,axiom,
% 50.50/50.71 ! [V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
% 50.50/50.71 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__not__less__zero,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ~ 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__triangle__ineq,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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)))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__mult__less,axiom,
% 50.50/50.71 ! [V_d,V_b,V_c,V_a,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 50.50/50.71 => 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))) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__triangle__ineq2__sym,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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)))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__triangle__ineq2,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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)))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__triangle__ineq3,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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)))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__ge__minus__self,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__le__iff,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 50.50/50.71 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 50.50/50.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__leI,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__le__D2,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__less__iff,axiom,
% 50.50/50.71 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 50.50/50.71 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 50.50/50.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__number__of__eq__not__less,axiom,
% 50.50/50.71 ! [V_w_2,V_v_2,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber(T_b)
% 50.50/50.71 & class_Orderings_Olinorder(T_b) )
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.71 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_left__distrib__number__of,axiom,
% 50.50/50.71 ! [V_v,V_b,V_a,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber(T_b)
% 50.50/50.71 & class_Rings_Osemiring(T_b) )
% 50.50/50.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_right__distrib__number__of,axiom,
% 50.50/50.71 ! [V_c,V_b,V_v,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber(T_b)
% 50.50/50.71 & class_Rings_Osemiring(T_b) )
% 50.50/50.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 50.50/50.71 ! [V_q,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 50.50/50.71 ! [V_q,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 50.50/50.71 ! [V_q,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_left__diff__distrib__number__of,axiom,
% 50.50/50.71 ! [V_v,V_b,V_a,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber(T_b)
% 50.50/50.71 & class_Rings_Oring(T_b) )
% 50.50/50.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_right__diff__distrib__number__of,axiom,
% 50.50/50.71 ! [V_c,V_b,V_v,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber(T_b)
% 50.50/50.71 & class_Rings_Oring(T_b) )
% 50.50/50.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_le__number__of,axiom,
% 50.50/50.71 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.71 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 50.50/50.71 ! [V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 50.50/50.71 ! [V_q,V_p,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__number__of,axiom,
% 50.50/50.71 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.71 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.71 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_number__of__add,axiom,
% 50.50/50.71 ! [V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__number__of__eq,axiom,
% 50.50/50.71 ! [V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__number__of__left,axiom,
% 50.50/50.71 ! [V_z,V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 50.50/50.71 ! [V_n,V_x] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mult__number__of__left,axiom,
% 50.50/50.71 ! [V_z,V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_arith__simps_I32_J,axiom,
% 50.50/50.71 ! [V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_number__of__mult,axiom,
% 50.50/50.71 ! [V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__zmult__eq__1,axiom,
% 50.50/50.71 ! [V_n,V_m] :
% 50.50/50.71 ( 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)
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_number__of__diff,axiom,
% 50.50/50.71 ! [V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zpower__zadd__distrib,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_number__of__minus,axiom,
% 50.50/50.71 ! [V_w,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_arith__simps_I30_J,axiom,
% 50.50/50.71 ! [V_w,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_mult__sgn__abs,axiom,
% 50.50/50.71 ! [V_x,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => 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 ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__sgn,axiom,
% 50.50/50.71 ! [V_k,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => 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)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__mult__pos,axiom,
% 50.50/50.71 ! [V_y,V_x,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__eq__mult,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Rings_Oordered__ring__abs(T_a)
% 50.50/50.71 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.71 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 50.50/50.71 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.71 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 50.50/50.71 => 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)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__diff__triangle__ineq,axiom,
% 50.50/50.71 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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))))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__triangle__ineq4,axiom,
% 50.50/50.71 ! [V_b,V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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)))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__of__nonpos,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__minus__le__zero,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__of__neg,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_abs__if,axiom,
% 50.50/50.71 ! [V_a,T_a] :
% 50.50/50.71 ( class_Groups_Oabs__if(T_a)
% 50.50/50.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 50.50/50.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zabs__less__one__iff,axiom,
% 50.50/50.71 ! [V_z_2] :
% 50.50/50.71 ( 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)))
% 50.50/50.71 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__number__of__diff1,axiom,
% 50.50/50.71 ! [V_c,V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zabs__def,axiom,
% 50.50/50.71 ! [V_i] :
% 50.50/50.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 50.50/50.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.71 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_minus__number__of__mult,axiom,
% 50.50/50.71 ! [V_z,V_w,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => 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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__abs__mult__distrib,axiom,
% 50.50/50.71 ! [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))) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_diff__number__of__eq,axiom,
% 50.50/50.71 ! [V_w,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_add__number__of__diff2,axiom,
% 50.50/50.71 ! [V_w,V_c,V_v,T_a] :
% 50.50/50.71 ( class_Int_Onumber__ring(T_a)
% 50.50/50.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),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) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_power__strict__mono,axiom,
% 50.50/50.71 ! [V_n,V_b,V_a,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => 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))) ) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_one__less__power,axiom,
% 50.50/50.71 ! [V_n,V_a,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.71 => 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))) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_power__increasing__iff,axiom,
% 50.50/50.71 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 50.50/50.71 ( class_Rings_Olinordered__semidom(T_b)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_power__le__imp__le__exp,axiom,
% 50.50/50.71 ! [V_n,V_m,V_a,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_power__decreasing,axiom,
% 50.50/50.71 ! [V_a,V_N,V_n,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 50.50/50.71 => 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))) ) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_power__strict__decreasing,axiom,
% 50.50/50.71 ! [V_a,V_N,V_n,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 50.50/50.71 => 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))) ) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_power__Suc__less__one,axiom,
% 50.50/50.71 ! [V_n,V_a,T_a] :
% 50.50/50.71 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 50.50/50.71 => 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))) ) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_number__of__is__id,axiom,
% 50.50/50.71 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__eq__number__of__int__code,axiom,
% 50.50/50.71 ! [V_l_2,V_k_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_less__number__of__int__code,axiom,
% 50.50/50.71 ! [V_l_2,V_k_2] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 50.50/50.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_plus__numeral__code_I9_J,axiom,
% 50.50/50.71 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_times__numeral__code_I5_J,axiom,
% 50.50/50.71 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_minus__numeral__code_I5_J,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 50.50/50.71 ! [V_m_2,V_x_2] :
% 50.50/50.71 ( 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))
% 50.50/50.71 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.71 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_power__Suc__0,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__zero__less__power__iff,axiom,
% 50.50/50.71 ! [V_n_2,V_x_2] :
% 50.50/50.71 ( 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)))
% 50.50/50.71 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 50.50/50.71 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__power__less__imp__less,axiom,
% 50.50/50.71 ! [V_n,V_m,V_i] :
% 50.50/50.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 50.50/50.71 => ( 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)))
% 50.50/50.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_int__number__of__def,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__one__le__power,axiom,
% 50.50/50.71 ! [V_n,V_i] :
% 50.50/50.71 ( 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))
% 50.50/50.71 => 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))) ) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__number__of,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_nat__number__of__def,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 50.50/50.71 ! [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)) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_int__power,axiom,
% 50.50/50.71 ! [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) ).
% 50.50/50.71
% 50.50/50.71 fof(fact_zpower__int,axiom,
% 50.50/50.72 ! [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)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_minus__numeral__code_I6_J,axiom,
% 50.50/50.72 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__eq__if,axiom,
% 50.50/50.72 ! [V_p,V_m] :
% 50.50/50.72 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.72 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 50.50/50.72 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.72 => 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)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_int__eq__iff__number__of,axiom,
% 50.50/50.72 ! [V_v_2,V_m_2] :
% 50.50/50.72 ( 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)
% 50.50/50.72 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 50.50/50.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__power__eq,axiom,
% 50.50/50.72 ! [V_n,V_z] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 50.50/50.72 ! [V_n,V_x] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_field__power__not__zero,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 50.50/50.72 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__commutes,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__mult__distrib,axiom,
% 50.50/50.72 ! [V_n,V_b,V_a,T_a] :
% 50.50/50.72 ( class_Groups_Ocomm__monoid__mult(T_a)
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__one,axiom,
% 50.50/50.72 ! [V_n,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_of__nat__power,axiom,
% 50.50/50.72 ! [V_n,V_m,T_a] :
% 50.50/50.72 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__mult,axiom,
% 50.50/50.72 ! [V_n,V_m,V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_one__div__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__abs,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__one__right,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__le__power,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.72 => 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))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__mono,axiom,
% 50.50/50.72 ! [V_n,V_b,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.72 => 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))) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__less__power,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.72 => 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))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__eq__0__iff,axiom,
% 50.50/50.72 ! [V_n_2,V_a_2,T_b] :
% 50.50/50.72 ( ( class_Power_Opower(T_b)
% 50.50/50.72 & class_Rings_Omult__zero(T_b)
% 50.50/50.72 & class_Rings_Ono__zero__divisors(T_b)
% 50.50/50.72 & class_Rings_Ozero__neq__one(T_b) )
% 50.50/50.72 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.72 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.72 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_one__le__power,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.72 => 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))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__0__Suc,axiom,
% 50.50/50.72 ! [V_n,T_a] :
% 50.50/50.72 ( ( class_Power_Opower(T_a)
% 50.50/50.72 & class_Rings_Osemiring__0(T_a) )
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__inject__exp,axiom,
% 50.50/50.72 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_b)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 50.50/50.72 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
% 50.50/50.72 <=> V_m_2 = V_n_2 ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__Suc2,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__Suc,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Power_Opower(T_a)
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__0,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Power_Opower(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__add,axiom,
% 50.50/50.72 ! [V_n,V_m,V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_abs__power__minus,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__less__imp__less__base,axiom,
% 50.50/50.72 ! [V_b,V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( 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)))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__inject__base,axiom,
% 50.50/50.72 ! [V_b,V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( 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))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.72 => V_a = V_b ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__le__imp__le__base,axiom,
% 50.50/50.72 ! [V_b,V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( 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))))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__gt1__lemma,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.72 => 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)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__less__power__Suc,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.72 => 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)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__0__left,axiom,
% 50.50/50.72 ! [V_n,T_a] :
% 50.50/50.72 ( ( class_Power_Opower(T_a)
% 50.50/50.72 & class_Rings_Osemiring__0(T_a) )
% 50.50/50.72 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.72 => 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) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__gt1,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.72 => 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)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__strict__increasing,axiom,
% 50.50/50.72 ! [V_a,V_N,V_n,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.72 => 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))) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__less__imp__less__exp,axiom,
% 50.50/50.72 ! [V_n,V_m,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.72 => ( 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)))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__strict__increasing__iff,axiom,
% 50.50/50.72 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_b)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__le__power__abs,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.72 => 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))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__increasing,axiom,
% 50.50/50.72 ! [V_a,V_N,V_n,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 50.50/50.72 => 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))) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__minus,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Oring__1(T_a)
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__Suc__less,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 50.50/50.72 => 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))) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__eq__imp__eq__base,axiom,
% 50.50/50.72 ! [V_b,V_n,V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( 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)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.72 => V_a = V_b ) ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_one__mod__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 50.50/50.72 => 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)) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 50.50/50.72 => 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))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__power__power,axiom,
% 50.50/50.72 ! [T_b] :
% 50.50/50.72 ( class_Power_Opower(T_b)
% 50.50/50.72 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_div__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mod__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 50.50/50.72 => 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))) ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__nat__number__of,axiom,
% 50.50/50.72 ! [V_n,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__nat__number__of__number__of,axiom,
% 50.50/50.72 ! [V_w,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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)) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zmod__minus1,axiom,
% 50.50/50.72 ! [V_b] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__number__of__Min,axiom,
% 50.50/50.72 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I24_J,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I7_J,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__neg__0,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__neg__int,axiom,
% 50.50/50.72 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__neg__1,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_bin__less__0__simps_I2_J,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Int_OMin__def,axiom,
% 50.50/50.72 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__Min,axiom,
% 50.50/50.72 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__neg__eq__ge__0,axiom,
% 50.50/50.72 ! [V_x_2] :
% 50.50/50.72 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__def,axiom,
% 50.50/50.72 ! [V_Z_2] :
% 50.50/50.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__nat,axiom,
% 50.50/50.72 ! [V_z] :
% 50.50/50.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 50.50/50.72 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__neg__nat,axiom,
% 50.50/50.72 ! [V_z] :
% 50.50/50.72 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 50.50/50.72 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__minus1,axiom,
% 50.50/50.72 ! [V_z,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__minus1__right,axiom,
% 50.50/50.72 ! [V_z,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of__Min,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_arith__simps_I31_J,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_abs__minus__one,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_a) )
% 50.50/50.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zmod__minus1__right,axiom,
% 50.50/50.72 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 50.50/50.72 ! [V_n,V_m] :
% 50.50/50.72 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 50.50/50.72 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 50.50/50.72 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zmult__eq__1__iff,axiom,
% 50.50/50.72 ! [V_n_2,V_m_2] :
% 50.50/50.72 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 50.50/50.72 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 50.50/50.72 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 50.50/50.72 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 50.50/50.72 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power_Opower_Opower__0,axiom,
% 50.50/50.72 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power_Opower_Opower__Suc,axiom,
% 50.50/50.72 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_of__int__m1,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zdiv__minus1__right,axiom,
% 50.50/50.72 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__imp__number__of__eq__0,axiom,
% 50.50/50.72 ! [V_v] :
% 50.50/50.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__zminus__int,axiom,
% 50.50/50.72 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_abs__power__minus__one,axiom,
% 50.50/50.72 ! [V_n,T_a] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_a) )
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_div__eq__minus1,axiom,
% 50.50/50.72 ! [V_b] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.50/50.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H_2,V_v_2] :
% 50.50/50.72 ( 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)
% 50.50/50.72 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 50.50/50.72 => 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))) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 50.50/50.72 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 50.50/50.72 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__number__of__add__left,axiom,
% 50.50/50.72 ! [V_k,V_v_H,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 50.50/50.72 => 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) ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_int__nat__number__of,axiom,
% 50.50/50.72 ! [V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_of__nat__number__of__eq,axiom,
% 50.50/50.72 ! [V_v,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_div__pos__neg__trivial,axiom,
% 50.50/50.72 ! [V_b,V_a] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__nat__number__of__add,axiom,
% 50.50/50.72 ! [V_n,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__nat__number__of,axiom,
% 50.50/50.72 ! [V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 50.50/50.72 => 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)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat0__intermed__int__val,axiom,
% 50.50/50.72 ! [V_k_2,V_f_2,V_n_2] :
% 50.50/50.72 ( ! [B_i] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 50.50/50.72 => ? [B_i] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 50.50/50.72 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_int__val__lemma,axiom,
% 50.50/50.72 ! [V_k_2,V_f_2,V_n_2] :
% 50.50/50.72 ( ! [B_i] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 50.50/50.72 => ? [B_i] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 50.50/50.72 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__number__of__eq,axiom,
% 50.50/50.72 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 50.50/50.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__number__of__pred__iff__0,axiom,
% 50.50/50.72 ! [V_v_2] :
% 50.50/50.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 50.50/50.72 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__number__of__mult__left,axiom,
% 50.50/50.72 ! [V_k,V_v_H,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_succ__Min,axiom,
% 50.50/50.72 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pred__Pls,axiom,
% 50.50/50.72 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 50.50/50.72
% 50.50/50.72 fof(fact_succ__pred,axiom,
% 50.50/50.72 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 50.50/50.72
% 50.50/50.72 fof(fact_iszero__Numeral0,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Pls__def,axiom,
% 50.50/50.72 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I19_J,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I2_J,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Pls__right,axiom,
% 50.50/50.72 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Pls,axiom,
% 50.50/50.72 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__Pls,axiom,
% 50.50/50.72 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I1_J,axiom,
% 50.50/50.72 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 50.50/50.72
% 50.50/50.72 fof(fact_minus__Pls,axiom,
% 50.50/50.72 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I40_J,axiom,
% 50.50/50.72 c_Int_OMin != c_Int_OPls ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I37_J,axiom,
% 50.50/50.72 c_Int_OPls != c_Int_OMin ).
% 50.50/50.72
% 50.50/50.72 fof(fact_iszero__def,axiom,
% 50.50/50.72 ! [V_z_2,T_b] :
% 50.50/50.72 ( class_Rings_Osemiring__1(T_b)
% 50.50/50.72 => ( c_Int_Oiszero(T_b,V_z_2)
% 50.50/50.72 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_iszero__0,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.72 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__iszero__1,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.72 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of__Pls,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_semiring__norm_I112_J,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__numeral__0__right,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => 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 ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__numeral__0,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => 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 ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_bin__less__0__simps_I1_J,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__number__of__Pls,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_semiring__norm_I113_J,axiom,
% 50.50/50.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__is__num__zero,axiom,
% 50.50/50.72 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__diff__number__of,axiom,
% 50.50/50.72 ! [V_m,V_v] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 50.50/50.72 => 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))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I23_J,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I20_J,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I3_J,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I6_J,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__number__of__Pls__Min,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__neg__number__of__Pls,axiom,
% 50.50/50.72 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__special_I3_J,axiom,
% 50.50/50.72 ! [V_x_2,T_b] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__special_I1_J,axiom,
% 50.50/50.72 ! [V_y_2,T_b] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 50.50/50.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__1__add__number__of,axiom,
% 50.50/50.72 ! [V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__number__of__add__1,axiom,
% 50.50/50.72 ! [V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_le__iff__pred__less,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pred__def,axiom,
% 50.50/50.72 ! [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)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Min,axiom,
% 50.50/50.72 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Min__right,axiom,
% 50.50/50.72 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__number__of__diff__1,axiom,
% 50.50/50.72 ! [V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__number__of__0,axiom,
% 50.50/50.72 ! [V_v_2] :
% 50.50/50.72 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__0__number__of,axiom,
% 50.50/50.72 ! [V_v_2] :
% 50.50/50.72 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of2,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H_2,V_v_2] :
% 50.50/50.72 ( 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)))
% 50.50/50.72 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 50.50/50.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_le__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H_2,V_v_2] :
% 50.50/50.72 ( 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)))
% 50.50/50.72 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_succ__def,axiom,
% 50.50/50.72 ! [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)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I2_J,axiom,
% 50.50/50.72 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nonzero__number__of__Min,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_le__special_I3_J,axiom,
% 50.50/50.72 ! [V_x_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_le__special_I1_J,axiom,
% 50.50/50.72 ! [V_y_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__special_I1_J,axiom,
% 50.50/50.72 ! [V_y_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__special_I3_J,axiom,
% 50.50/50.72 ! [V_x_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__0__number__of,axiom,
% 50.50/50.72 ! [V_v_2] :
% 50.50/50.72 ( 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)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 50.50/50.72 => 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)) ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of__succ,axiom,
% 50.50/50.72 ! [V_k,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of__pred,axiom,
% 50.50/50.72 ! [V_w,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__nat__number__of,axiom,
% 50.50/50.72 ! [V_v_H,V_v] :
% 50.50/50.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 50.50/50.72 => 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)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__special_I2_J,axiom,
% 50.50/50.72 ! [V_y_2,T_b] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 50.50/50.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_eq__special_I4_J,axiom,
% 50.50/50.72 ! [V_x_2,T_b] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 50.50/50.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__special_I1_J,axiom,
% 50.50/50.72 ! [V_w,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__special_I2_J,axiom,
% 50.50/50.72 ! [V_v,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 50.50/50.72 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__div__eq__add3__div,axiom,
% 50.50/50.72 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_div__Suc__eq__div__add3,axiom,
% 50.50/50.72 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I51_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 50.50/50.72 <=> V_k_2 = V_l_2 ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__eq__int__code_I16_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I34_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I17_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__int__code_I16_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I46_J,axiom,
% 50.50/50.72 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I39_J,axiom,
% 50.50/50.72 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I47_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 50.50/50.72 <=> V_k_2 = c_Int_OMin ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I43_J,axiom,
% 50.50/50.72 ! [V_l_2] :
% 50.50/50.72 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 50.50/50.72 <=> c_Int_OMin = V_l_2 ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Bit1__Min,axiom,
% 50.50/50.72 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 50.50/50.72
% 50.50/50.72 fof(fact_bin__less__0__simps_I4_J,axiom,
% 50.50/50.72 ! [V_w_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I22_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I12_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Bit1__def,axiom,
% 50.50/50.72 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I30_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I26_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I9_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I13_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__number__of__Bit1,axiom,
% 50.50/50.72 ! [V_w_2] :
% 50.50/50.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 50.50/50.72 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_minus__Bit1,axiom,
% 50.50/50.72 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_iszero__number__of__Bit1,axiom,
% 50.50/50.72 ! [V_w,T_a] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 & class_Int_Oring__char__0(T_a) )
% 50.50/50.72 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_succ__Pls,axiom,
% 50.50/50.72 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of__Bit1,axiom,
% 50.50/50.72 ! [V_w,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__numeral__1,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__numeral__1__right,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_numeral__1__eq__1,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_semiring__norm_I110_J,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I29_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I5_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_one__is__num__one,axiom,
% 50.50/50.72 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__numeral__1__eq__1,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Numeral1__eq1__nat,axiom,
% 50.50/50.72 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I4_J,axiom,
% 50.50/50.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_minus__Min,axiom,
% 50.50/50.72 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_not__iszero__Numeral1,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_numeral__1__eq__Suc__0,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_numeral__3__eq__3,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power3__eq__cube,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc3__eq__add__3,axiom,
% 50.50/50.72 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 50.50/50.72 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)))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_le__special_I2_J,axiom,
% 50.50/50.72 ! [V_y_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_le__special_I4_J,axiom,
% 50.50/50.72 ! [V_x_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__special_I4_J,axiom,
% 50.50/50.72 ! [V_x_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__special_I2_J,axiom,
% 50.50/50.72 ! [V_y_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Rings_Olinordered__idom(T_b) )
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__special_I3_J,axiom,
% 50.50/50.72 ! [V_v,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__special_I2_J,axiom,
% 50.50/50.72 ! [V_w,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 50.50/50.72 ! [V_m,V_n] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
% 50.50/50.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 50.50/50.72 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 50.50/50.72 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 50.50/50.72 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__zmod__mult__2,axiom,
% 50.50/50.72 ! [V_b,V_a] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zmod__number__of__Bit1,axiom,
% 50.50/50.72 ! [V_v,V_w] :
% 50.50/50.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 50.50/50.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 50.50/50.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 50.50/50.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__zdiv__mult__2,axiom,
% 50.50/50.72 ! [V_b,V_a] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pos__zdiv__mult__2,axiom,
% 50.50/50.72 ! [V_b,V_a] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pos__zmod__mult__2,axiom,
% 50.50/50.72 ! [V_b,V_a] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.50/50.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_of__nat__double,axiom,
% 50.50/50.72 ! [V_x,T_a] :
% 50.50/50.72 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 50.50/50.72 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I48_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 50.50/50.72 <=> V_k_2 = V_l_2 ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I31_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__eq__int__code_I13_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__int__code_I13_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I14_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Bit0__Pls,axiom,
% 50.50/50.72 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I38_J,axiom,
% 50.50/50.72 ! [V_l_2] :
% 50.50/50.72 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 50.50/50.72 <=> c_Int_OPls = V_l_2 ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I44_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 50.50/50.72 <=> V_k_2 = c_Int_OPls ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I49_J,axiom,
% 50.50/50.72 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I50_J,axiom,
% 50.50/50.72 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Bit0__Bit0,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Bit0__def,axiom,
% 50.50/50.72 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__Bit0,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I7_J,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_minus__Bit0,axiom,
% 50.50/50.72 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I42_J,axiom,
% 50.50/50.72 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I45_J,axiom,
% 50.50/50.72 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 50.50/50.72
% 50.50/50.72 fof(fact_bin__less__0__simps_I3_J,axiom,
% 50.50/50.72 ! [V_w_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I21_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I27_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I32_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__eq__int__code_I14_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I10_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I4_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__int__code_I15_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I16_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Bit0__Bit1,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Bit1__Bit0,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I3_J,axiom,
% 50.50/50.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I9_J,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I10_J,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I28_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I8_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zdiv__number__of__Bit0,axiom,
% 50.50/50.72 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_neg__number__of__Bit0,axiom,
% 50.50/50.72 ! [V_w_2] :
% 50.50/50.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 50.50/50.72 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pred__Bit0,axiom,
% 50.50/50.72 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pred__Bit1,axiom,
% 50.50/50.72 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_pred__Min,axiom,
% 50.50/50.72 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_iszero__number__of__Bit0,axiom,
% 50.50/50.72 ! [V_w_2,T_b] :
% 50.50/50.72 ( ( class_Int_Onumber__ring(T_b)
% 50.50/50.72 & class_Int_Oring__char__0(T_b) )
% 50.50/50.72 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 50.50/50.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_succ__Bit1,axiom,
% 50.50/50.72 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_succ__Bit0,axiom,
% 50.50/50.72 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of__Bit0,axiom,
% 50.50/50.72 ! [V_w,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I15_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__int__code_I14_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I33_J,axiom,
% 50.50/50.72 ! [V_l_2,V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__eq__int__code_I15_J,axiom,
% 50.50/50.72 ! [V_k2_2,V_k1_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__Bit1,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I25_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_rel__simps_I11_J,axiom,
% 50.50/50.72 ! [V_k_2] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 50.50/50.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I5_J,axiom,
% 50.50/50.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I6_J,axiom,
% 50.50/50.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_diff__bin__simps_I8_J,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__Bit1__Bit1,axiom,
% 50.50/50.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_double__number__of__Bit0,axiom,
% 50.50/50.72 ! [V_w,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_number__of1,axiom,
% 50.50/50.72 ! [V_n] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n))))
% 50.50/50.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__2__right,axiom,
% 50.50/50.72 ! [V_z,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mult__2,axiom,
% 50.50/50.72 ! [V_z,T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_one__add__one__is__two,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Int_Onumber__ring(T_a)
% 50.50/50.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__eq__power2,axiom,
% 50.50/50.72 ! [V_a_2,T_b] :
% 50.50/50.72 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 50.50/50.72 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__power2,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_numeral__2__eq__2,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_semiring__norm_I115_J,axiom,
% 50.50/50.72 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 50.50/50.72 ! [V_x,T_a] :
% 50.50/50.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.72 => 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)))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__eq__square,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 50.50/50.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__2__eq__Suc,axiom,
% 50.50/50.72 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__2__eq__Suc_H,axiom,
% 50.50/50.72 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_one__power2,axiom,
% 50.50/50.72 ! [T_a] :
% 50.50/50.72 ( class_Rings_Osemiring__1(T_a)
% 50.50/50.72 => 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) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__minus,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Rings_Oring__1(T_a)
% 50.50/50.72 => 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)))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__mult__2,axiom,
% 50.50/50.72 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__mult__2__right,axiom,
% 50.50/50.72 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power__even__eq,axiom,
% 50.50/50.72 ! [V_n,V_a,T_a] :
% 50.50/50.72 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.72 => 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)))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 50.50/50.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 50.50/50.72 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)))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_abs__power2,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.72 => 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)))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__abs,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.72 => 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)))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__1__add__1,axiom,
% 50.50/50.72 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_mod2__Suc__Suc,axiom,
% 50.50/50.72 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_div2__Suc__Suc,axiom,
% 50.50/50.72 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zmod__number__of__Bit0,axiom,
% 50.50/50.72 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_add__self__div__2,axiom,
% 50.50/50.72 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__eq__imp__eq,axiom,
% 50.50/50.72 ! [V_y,V_x,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( 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))))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.72 => V_x = V_y ) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__le__imp__le,axiom,
% 50.50/50.72 ! [V_y,V_x,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.72 => ( 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))))))
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__le__power2,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.72 => 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)))))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_zero__less__power2,axiom,
% 50.50/50.72 ! [V_a_2,T_b] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 50.50/50.72 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__less__0,axiom,
% 50.50/50.72 ! [V_a,T_a] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.72 => ~ 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))) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_sum__power2__eq__zero__iff,axiom,
% 50.50/50.72 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.72 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.72 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.72 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.72 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__eq__square__number__of,axiom,
% 50.50/50.72 ! [V_w,T_b] :
% 50.50/50.72 ( ( class_Groups_Omonoid__mult(T_b)
% 50.50/50.72 & class_Int_Onumber(T_b) )
% 50.50/50.72 => 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)) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_less__2__cases,axiom,
% 50.50/50.72 ! [V_n] :
% 50.50/50.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 50.50/50.72 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.50/50.72 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_nat__2,axiom,
% 50.50/50.72 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))) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_power2__eq__1__iff,axiom,
% 50.50/50.72 ! [V_a_2,T_b] :
% 50.50/50.72 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 50.50/50.72 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
% 50.50/50.72 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 50.50/50.72 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 50.50/50.72
% 50.50/50.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 50.50/50.73 ! [V_n,V_x,T_a] :
% 50.50/50.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__minus__even,axiom,
% 50.50/50.73 ! [V_n,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Oring__1(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power2__less__imp__less,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Rings_Olinordered__semidom(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_sum__power2__ge__zero,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_sum__power2__le__zero__iff,axiom,
% 50.50/50.73 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.73 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_not__sum__power2__lt__zero,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.73 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_sum__power2__gt__zero__iff,axiom,
% 50.50/50.73 ! [V_y_2,V_x_2,T_b] :
% 50.50/50.73 ( class_Rings_Olinordered__idom(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
% 50.50/50.73 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power2__sum,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Int_Onumber__ring(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_zero__le__even__power_H,axiom,
% 50.50/50.73 ! [V_n,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 50.50/50.73 ! [V_n,V_x,T_a] :
% 50.50/50.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__odd__eq,axiom,
% 50.50/50.73 ! [V_n,V_a,T_a] :
% 50.50/50.73 ( class_Groups_Omonoid__mult(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__minus1__even,axiom,
% 50.50/50.73 ! [V_n,T_a] :
% 50.50/50.73 ( class_Rings_Oring__1(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_zdiv__number__of__Bit1,axiom,
% 50.50/50.73 ! [V_v,V_w] :
% 50.50/50.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 50.50/50.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 50.50/50.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_mod2__gr__0,axiom,
% 50.50/50.73 ! [V_m_2] :
% 50.50/50.73 ( 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))))))
% 50.50/50.73 <=> 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_div__2__gt__zero,axiom,
% 50.50/50.73 ! [V_n] :
% 50.50/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power2__diff,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Int_Onumber__ring(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 50.50/50.73 ! [V_n,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_odd__power__less__zero,axiom,
% 50.50/50.73 ! [V_n,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Olinordered__idom(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__minus1__odd,axiom,
% 50.50/50.73 ! [V_n,T_a] :
% 50.50/50.73 ( class_Rings_Oring__1(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__m1__even,axiom,
% 50.50/50.73 ! [V_n,T_a] :
% 50.50/50.73 ( class_Int_Onumber__ring(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__m1__odd,axiom,
% 50.50/50.73 ! [V_n,T_a] :
% 50.50/50.73 ( class_Int_Onumber__ring(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 50.50/50.73 ! [V_n] :
% 50.50/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_int__of__code,axiom,
% 50.50/50.73 ! [V_k] :
% 50.50/50.73 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.50/50.73 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 50.50/50.73 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.50/50.73 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.50/50.73 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
% 50.50/50.73 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.50/50.73 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_one__code__numeral__code,axiom,
% 50.50/50.73 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)) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_half__gt__zero__iff,axiom,
% 50.50/50.73 ! [V_r_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber__ring(T_b) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_half__gt__zero,axiom,
% 50.50/50.73 ! [V_r,T_a] :
% 50.50/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 50.50/50.73 & class_Int_Onumber__ring(T_a) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 50.50/50.73 => 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)))))) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 50.50/50.73 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_nat__intermed__int__val,axiom,
% 50.50/50.73 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 50.50/50.73 ( ! [B_i] :
% 50.50/50.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 50.50/50.73 => 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))) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 50.50/50.73 => ? [B_i] :
% 50.50/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 50.50/50.73 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_code__numeral__zero__minus__one,axiom,
% 50.50/50.73 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) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__zero__left,axiom,
% 50.50/50.73 ! [V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__zero,axiom,
% 50.50/50.73 ! [V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 50.50/50.73 => 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_add__divide__distrib,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => 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)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_times__divide__eq__right,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_times__divide__times__eq,axiom,
% 50.50/50.73 ! [V_w,V_z,V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => 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)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_diff__divide__distrib,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => 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)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__1,axiom,
% 50.50/50.73 ! [V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_minus__divide__left,axiom,
% 50.50/50.73 ! [V_b,V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_minus__divide__right,axiom,
% 50.50/50.73 ! [V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => 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)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_minus__divide__divide,axiom,
% 50.50/50.73 ! [V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__divide,axiom,
% 50.50/50.73 ! [V_n,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_abs__divide,axiom,
% 50.50/50.73 ! [V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 50.50/50.73 => 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)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 50.50/50.73 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 50.50/50.73 ! [V_y,V_x] :
% 50.50/50.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 50.50/50.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 50.50/50.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 50.50/50.73 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 50.50/50.73 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 50.50/50.73 ! [V_y,V_x] :
% 50.50/50.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 50.50/50.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 50.50/50.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 50.50/50.73 ! [V_y,V_x] :
% 50.50/50.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 50.50/50.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 50.50/50.73 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 50.50/50.73 ! [V_y,V_x] :
% 50.50/50.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 50.50/50.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 50.50/50.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 50.50/50.73 ! [V_n,V_x] :
% 50.50/50.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 50.50/50.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__right__mono__neg,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__right__mono,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__le__0__iff,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 50.50/50.73 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_zero__le__divide__iff,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 50.50/50.73 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__strict__right__mono__neg,axiom,
% 50.50/50.73 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__strict__right__mono,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__neg__neg,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__neg__pos,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__pos__neg,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__pos__pos,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__less__0__iff,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 50.50/50.73 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_zero__less__divide__iff,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 50.50/50.73 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_nonzero__eq__divide__eq,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_b)
% 50.50/50.73 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 50.50/50.73 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_nonzero__divide__eq__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_b)
% 50.50/50.73 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 50.50/50.73 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__eq__imp,axiom,
% 50.50/50.73 ! [V_a,V_b,V_c,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 50.50/50.73 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_eq__divide__imp,axiom,
% 50.50/50.73 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 50.50/50.73 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_frac__eq__eq,axiom,
% 50.50/50.73 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 50.50/50.73 ( class_Fields_Ofield(T_b)
% 50.50/50.73 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
% 50.50/50.73 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_mult__divide__mult__cancel__left,axiom,
% 50.50/50.73 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_mult__divide__mult__cancel__right,axiom,
% 50.50/50.73 ! [V_b,V_a,V_c,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__eq__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_b)
% 50.50/50.73 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 50.50/50.73 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 50.50/50.73 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_eq__divide__eq,axiom,
% 50.50/50.73 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_b)
% 50.50/50.73 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 50.50/50.73 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 50.50/50.73 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__self__if,axiom,
% 50.50/50.73 ! [V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 50.50/50.73 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 50.50/50.73 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__self,axiom,
% 50.50/50.73 ! [V_a,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_right__inverse__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_b_2,T_b] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_b)
% 50.50/50.73 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 50.50/50.73 <=> V_a_2 = V_b_2 ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_nonzero__minus__divide__right,axiom,
% 50.50/50.73 ! [V_a,V_b,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_nonzero__minus__divide__divide,axiom,
% 50.50/50.73 ! [V_a,V_b,T_a] :
% 50.50/50.73 ( class_Rings_Odivision__ring(T_a)
% 50.50/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_nonzero__power__divide,axiom,
% 50.50/50.73 ! [V_n,V_a,V_b,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_nonzero__abs__divide,axiom,
% 50.50/50.73 ! [V_a,V_b,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__one__over,axiom,
% 50.50/50.73 ! [V_n,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 50.50/50.73 ! [V_y,V_x] :
% 50.50/50.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 50.50/50.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 50.50/50.73 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__nonpos__neg,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__nonpos__pos,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_frac__le,axiom,
% 50.50/50.73 ! [V_z,V_w,V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 50.50/50.73 => 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))) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_frac__less,axiom,
% 50.50/50.73 ! [V_z,V_w,V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 50.50/50.73 => 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))) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_frac__less2,axiom,
% 50.50/50.73 ! [V_z,V_w,V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 50.50/50.73 => 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))) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__nonneg__neg,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__nonneg__pos,axiom,
% 50.50/50.73 ! [V_y,V_x,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__strict__left__mono__neg,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => ( 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)))
% 50.50/50.73 => 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))) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__strict__left__mono,axiom,
% 50.50/50.73 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.73 => ( 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)))
% 50.50/50.73 => 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))) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_neg__divide__less__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_neg__less__divide__eq,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_mult__imp__less__div__pos,axiom,
% 50.50/50.73 ! [V_x,V_z,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => ( 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))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_mult__imp__div__pos__less,axiom,
% 50.50/50.73 ! [V_z,V_x,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => ( 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)))
% 50.50/50.73 => 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)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_pos__divide__less__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_pos__less__divide__eq,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__less__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_less__divide__eq,axiom,
% 50.50/50.73 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_is__nat__def,axiom,
% 50.50/50.73 ! [V_x_2] :
% 50.50/50.73 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_add__frac__eq,axiom,
% 50.50/50.73 ! [V_w,V_x,V_z,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__add__eq__iff,axiom,
% 50.50/50.73 ! [V_y,V_x,V_z,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_add__frac__num,axiom,
% 50.50/50.73 ! [V_z,V_x,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_add__divide__eq__iff,axiom,
% 50.50/50.73 ! [V_y,V_x,V_z,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_add__num__frac,axiom,
% 50.50/50.73 ! [V_x,V_z,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_diff__divide__eq__iff,axiom,
% 50.50/50.73 ! [V_y,V_x,V_z,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__diff__eq__iff,axiom,
% 50.50/50.73 ! [V_y,V_x,V_z,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_diff__frac__eq,axiom,
% 50.50/50.73 ! [V_w,V_x,V_z,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => 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)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_eq__divide__eq__number__of1,axiom,
% 50.50/50.73 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
% 50.50/50.73 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 )
% 50.50/50.73 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_eq__divide__eq__number__of,axiom,
% 50.50/50.73 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 50.50/50.73 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 )
% 50.50/50.73 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__eq__eq__number__of,axiom,
% 50.50/50.73 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 50.50/50.73 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) )
% 50.50/50.73 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__eq__eq__number__of1,axiom,
% 50.50/50.73 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
% 50.50/50.73 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
% 50.50/50.73 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.50/50.73 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_less__half__sum,axiom,
% 50.50/50.73 ! [V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.73 => 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))))) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_gt__half__sum,axiom,
% 50.50/50.73 ! [V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 50.50/50.73 => 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)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__Numeral0,axiom,
% 50.50/50.73 ! [V_x,T_a] :
% 50.50/50.73 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 & class_Int_Onumber__ring(T_a) )
% 50.50/50.73 => 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_abs__div__pos,axiom,
% 50.50/50.73 ! [V_x,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => 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)) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__Numeral1,axiom,
% 50.50/50.73 ! [V_x,T_a] :
% 50.50/50.73 ( ( class_Fields_Ofield(T_a)
% 50.50/50.73 & class_Int_Onumber__ring(T_a) )
% 50.50/50.73 => 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 ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__numeral__1,axiom,
% 50.50/50.73 ! [V_a,T_a] :
% 50.50/50.73 ( ( class_Fields_Ofield(T_a)
% 50.50/50.73 & class_Int_Onumber__ring(T_a) )
% 50.50/50.73 => 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 ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__minus1,axiom,
% 50.50/50.73 ! [V_x,T_a] :
% 50.50/50.73 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 & class_Int_Onumber__ring(T_a) )
% 50.50/50.73 => 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) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_zero__code__numeral__code,axiom,
% 50.50/50.73 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) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_le__divide__eq,axiom,
% 50.50/50.73 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__le__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_pos__le__divide__eq,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_pos__divide__le__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_mult__imp__div__pos__le,axiom,
% 50.50/50.73 ! [V_z,V_x,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => ( 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)))
% 50.50/50.73 => 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)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_mult__imp__le__div__pos,axiom,
% 50.50/50.73 ! [V_x,V_z,V_y,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 50.50/50.73 => ( 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))
% 50.50/50.73 => 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))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_neg__le__divide__eq,axiom,
% 50.50/50.73 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_neg__divide__le__eq,axiom,
% 50.50/50.73 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_b)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 50.50/50.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__left__mono,axiom,
% 50.50/50.73 ! [V_c,V_a,V_b,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 50.50/50.73 => ( 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)))
% 50.50/50.73 => 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))) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__left__mono__neg,axiom,
% 50.50/50.73 ! [V_c,V_b,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 50.50/50.73 => ( 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)))
% 50.50/50.73 => 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))) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_less__divide__eq__number__of1,axiom,
% 50.50/50.73 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_less__divide__eq__number__of,axiom,
% 50.50/50.73 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__less__eq__number__of,axiom,
% 50.50/50.73 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_divide__less__eq__number__of1,axiom,
% 50.50/50.73 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_power__diff,axiom,
% 50.50/50.73 ! [V_m,V_n,V_a,T_a] :
% 50.50/50.73 ( class_Fields_Ofield(T_a)
% 50.50/50.73 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.50/50.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_minus1__divide,axiom,
% 50.50/50.73 ! [V_x,T_a] :
% 50.50/50.73 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 50.50/50.73 & class_Int_Onumber__ring(T_a) )
% 50.50/50.73 => 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)) ) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 50.50/50.73 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 50.50/50.73
% 50.50/50.73 fof(fact_le__divide__eq__number__of1,axiom,
% 50.50/50.73 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 50.50/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.50/50.73 & class_Int_Onumber(T_b) )
% 50.50/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 50.50/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.50/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.50/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 50.50/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_le__divide__eq__number__of,axiom,
% 50.63/50.73 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 50.63/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.63/50.73 & class_Int_Onumber(T_b) )
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 50.63/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.63/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_divide__le__eq__number__of,axiom,
% 50.63/50.73 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 50.63/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.63/50.73 & class_Int_Onumber(T_b) )
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.63/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 50.63/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_divide__le__eq__number__of1,axiom,
% 50.63/50.73 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 50.63/50.73 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 50.63/50.73 & class_Int_Onumber(T_b) )
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 50.63/50.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 50.63/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_nat__of__aux__code,axiom,
% 50.63/50.73 ! [V_n,V_i] :
% 50.63/50.73 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.73 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 50.63/50.73 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.73 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_code__numeral_Osize_I1_J,axiom,
% 50.63/50.73 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_code__numeral_Osize_I3_J,axiom,
% 50.63/50.73 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 50.63/50.73 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 50.63/50.73
% 50.63/50.73 fof(fact_log_Osimps,axiom,
% 50.63/50.73 ! [V_i,V_b] :
% 50.63/50.73 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 50.63/50.73 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 50.63/50.73 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 50.63/50.73 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 50.63/50.73 ! [V_w] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( ( 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))))
% 50.63/50.73 => 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))) )
% 50.63/50.73 & ( ~ 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))))
% 50.63/50.73 => 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)))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg__div__mod,axiom,
% 50.63/50.73 ! [V_l,V_k] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 50.63/50.73 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg__minus1,axiom,
% 50.63/50.73 ! [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))) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg_Osimps,axiom,
% 50.63/50.73 ! [V_b,V_a] :
% 50.63/50.73 ( ( ( 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)))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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)) )
% 50.63/50.73 & ( ~ ( 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)))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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))) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg__eqn__number__of,axiom,
% 50.63/50.73 ! [V_w,V_v] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( ( 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))))
% 50.63/50.73 => 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))) )
% 50.63/50.73 & ( ~ 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))))
% 50.63/50.73 => 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)))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg__eqn,axiom,
% 50.63/50.73 ! [V_a,V_b] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.73 => ( ( 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)))
% 50.63/50.73 => 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)) )
% 50.63/50.73 & ( ~ 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)))
% 50.63/50.73 => 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))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_minus__shift__def,axiom,
% 50.63/50.73 ! [V_r,V_l,V_k] :
% 50.63/50.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 50.63/50.73 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 50.63/50.73 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_inc__shift__def,axiom,
% 50.63/50.73 ! [V_k,V_v] :
% 50.63/50.73 ( ( V_v = V_k
% 50.63/50.73 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 50.63/50.73 & ( V_v != V_k
% 50.63/50.73 => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 50.63/50.73 ! [V_w] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( ( 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)))
% 50.63/50.73 => 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)) )
% 50.63/50.73 & ( ~ 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)))
% 50.63/50.73 => 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)))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg_Osimps,axiom,
% 50.63/50.73 ! [V_b,V_a] :
% 50.63/50.73 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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) )
% 50.63/50.73 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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))) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg__eqn__number__of,axiom,
% 50.63/50.73 ! [V_w,V_v] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( ( 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)))
% 50.63/50.73 => 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)) )
% 50.63/50.73 & ( ~ 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)))
% 50.63/50.73 => 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)))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg__eqn,axiom,
% 50.63/50.73 ! [V_a,V_b] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 50.63/50.73 => 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) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 50.63/50.73 => 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))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg__0,axiom,
% 50.63/50.73 ! [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)) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg__div__mod,axiom,
% 50.63/50.73 ! [V_l,V_k] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 50.63/50.73 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg_Opsimps,axiom,
% 50.63/50.73 ! [V_b_2,V_a_2] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( ( ( 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)))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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)) )
% 50.63/50.73 & ( ~ ( 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)))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_pdivmod__posDivAlg,axiom,
% 50.63/50.73 ! [V_k,V_l] :
% 50.63/50.73 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => 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)) )
% 50.63/50.73 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => 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)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_pdivmod__def,axiom,
% 50.63/50.73 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_zmult2__lemma,axiom,
% 50.63/50.73 ! [V_c,V_r,V_q,V_b,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 50.63/50.73 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg_Opsimps,axiom,
% 50.63/50.73 ! [V_b_2,V_a_2] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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) )
% 50.63/50.73 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 50.63/50.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.73 => 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))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_zmult1__lemma,axiom,
% 50.63/50.73 ! [V_a,V_r,V_q,V_c,V_b] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_accp_Osimps,axiom,
% 50.63/50.73 ! [V_a_2,V_r_2,T_b] :
% 50.63/50.73 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 50.63/50.73 <=> ! [B_x] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 50.63/50.73 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_accp_Oequations,axiom,
% 50.63/50.73 ! [V_a_2,V_r_2,T_b] :
% 50.63/50.73 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 50.63/50.73 <=> ! [B_x] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 50.63/50.73 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_accp__downward,axiom,
% 50.63/50.73 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 50.63/50.73 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 50.63/50.73 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_accp__subset,axiom,
% 50.63/50.73 ! [V_R2_2,V_R1_2,T_b] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
% 50.63/50.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_divmod__int__rel__0,axiom,
% 50.63/50.73 ! [V_b] :
% 50.63/50.73 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => 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)))) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_self__remainder,axiom,
% 50.63/50.73 ! [V_r,V_q,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_unique__quotient,axiom,
% 50.63/50.73 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( 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)))
% 50.63/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => V_q = V_q_H ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_unique__remainder,axiom,
% 50.63/50.73 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( 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)))
% 50.63/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => V_r = V_r_H ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_self__quotient,axiom,
% 50.63/50.73 ! [V_r,V_q,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_divmod__int__rel__mod,axiom,
% 50.63/50.73 ! [V_r,V_q,V_b,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_divmod__int__rel__div,axiom,
% 50.63/50.73 ! [V_r,V_q,V_b,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_negDivAlg__correct,axiom,
% 50.63/50.73 ! [V_b,V_a] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.73 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_divmod__int__rel__div__mod,axiom,
% 50.63/50.73 ! [V_a,V_b] :
% 50.63/50.73 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_posDivAlg__correct,axiom,
% 50.63/50.73 ! [V_b,V_a] :
% 50.63/50.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.73 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_zadd1__lemma,axiom,
% 50.63/50.73 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => ( 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)))
% 50.63/50.73 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.73 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_zminus1__lemma,axiom,
% 50.63/50.73 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 50.63/50.73 ( 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)))
% 50.63/50.73 => 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))))) ) ).
% 50.63/50.73
% 50.63/50.73 fof(fact_divmod__int__relI,axiom,
% 50.63/50.73 ! [V_r,V_q,V_b,V_a] :
% 50.63/50.73 ( 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)
% 50.63/50.73 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 50.63/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 50.63/50.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 50.63/50.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 50.63/50.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_negDivAlg_Opinduct,axiom,
% 50.63/50.74 ! [V_P_2,V_a1_2,V_a0_2] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 50.63/50.74 => ( ! [B_a,B_b] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 50.63/50.74 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b)))
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.74 => 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))) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_posDivAlg_Opinduct,axiom,
% 50.63/50.74 ! [V_P_2,V_a1_2,V_a0_2] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 50.63/50.74 => ( ! [B_a,B_b] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 50.63/50.74 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 50.63/50.74 => 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))) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Osize_I4_J,axiom,
% 50.63/50.74 ! [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))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Osize_I2_J,axiom,
% 50.63/50.74 ! [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))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__int__def,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 50.63/50.74 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__pos__pos__1__number__of,axiom,
% 50.63/50.74 ! [V_w] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 50.63/50.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Oinject,axiom,
% 50.63/50.74 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 50.63/50.74 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 50.63/50.74 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__int__def,axiom,
% 50.63/50.74 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 50.63/50.74 ! [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) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 50.63/50.74 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__pos__neg,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 50.63/50.74 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_negateSnd__eq,axiom,
% 50.63/50.74 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__neg__neg,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__int__rel__neg,axiom,
% 50.63/50.74 ! [V_qr,V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr))
% 50.63/50.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Suc__code__numeral__minus__one,axiom,
% 50.63/50.74 ! [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 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__neg__pos,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__int__correct,axiom,
% 50.63/50.74 ! [V_a,V_b] :
% 50.63/50.74 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__pos__neg__1__number__of,axiom,
% 50.63/50.74 ! [V_w] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__pos__pos,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__int__mod__div,axiom,
% 50.63/50.74 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_equalityI,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.74 => V_A_2 = V_B_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__pos__neg__1__number__of,axiom,
% 50.63/50.74 ! [V_w] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__neg__neg,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_snd__eqD,axiom,
% 50.63/50.74 ! [V_a,V_y,V_x,T_a,T_b] :
% 50.63/50.74 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
% 50.63/50.74 => V_y = V_a ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_snd__conv,axiom,
% 50.63/50.74 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__pos__neg,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Pair__fst__snd__eq,axiom,
% 50.63/50.74 ! [T_c,T_b,V_t_2,V_s_2] :
% 50.63/50.74 ( V_s_2 = V_t_2
% 50.63/50.74 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 50.63/50.74 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_prod__eqI,axiom,
% 50.63/50.74 ! [V_q,V_p,T_b,T_a] :
% 50.63/50.74 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 50.63/50.74 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 50.63/50.74 => V_p = V_q ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_fst__conv,axiom,
% 50.63/50.74 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ).
% 50.63/50.74
% 50.63/50.74 fof(fact_fst__eqD,axiom,
% 50.63/50.74 ! [V_a,V_y,V_x,T_b,T_a] :
% 50.63/50.74 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
% 50.63/50.74 => V_x = V_a ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_surjective__pairing,axiom,
% 50.63/50.74 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_pair__collapse,axiom,
% 50.63/50.74 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__int__def,axiom,
% 50.63/50.74 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Pair__inject,axiom,
% 50.63/50.74 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 50.63/50.74 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H)
% 50.63/50.74 => ~ ( V_a = V_a_H
% 50.63/50.74 => V_b != V_b_H ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Pair__eq,axiom,
% 50.63/50.74 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.74 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
% 50.63/50.74 <=> ( V_a_2 = V_a_H_2
% 50.63/50.74 & V_b_2 = V_b_H_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__paired__All,axiom,
% 50.63/50.74 ! [T_c,T_b,V_P_2] :
% 50.63/50.74 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 50.63/50.74 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_psubset__eq,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 & V_A_2 != V_B_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_subset__iff__psubset__eq,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 | V_A_2 = V_B_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_psubset__imp__subset,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_psubset__subset__trans,axiom,
% 50.63/50.74 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_subset__psubset__trans,axiom,
% 50.63/50.74 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_subset__refl,axiom,
% 50.63/50.74 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_set__eq__subset,axiom,
% 50.63/50.74 ! [T_b,V_B_2,V_A_2] :
% 50.63/50.74 ( V_A_2 = V_B_2
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_equalityD1,axiom,
% 50.63/50.74 ! [T_b,V_B_2,V_A_2] :
% 50.63/50.74 ( V_A_2 = V_B_2
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_equalityD2,axiom,
% 50.63/50.74 ! [T_b,V_B_2,V_A_2] :
% 50.63/50.74 ( V_A_2 = V_B_2
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_subset__trans,axiom,
% 50.63/50.74 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_equalityE,axiom,
% 50.63/50.74 ! [T_b,V_B_2,V_A_2] :
% 50.63/50.74 ( V_A_2 = V_B_2
% 50.63/50.74 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Compl__subset__Compl__iff,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Compl__anti__mono,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Diff__subset,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Diff__mono,axiom,
% 50.63/50.74 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_double__diff,axiom,
% 50.63/50.74 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__neg__pos,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__pos__pos,axiom,
% 50.63/50.74 ! [V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 50.63/50.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__pos__pos__1__number__of,axiom,
% 50.63/50.74 ! [V_w] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 50.63/50.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_prod__size__simp,axiom,
% 50.63/50.74 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__mod__code__numeral__def,axiom,
% 50.63/50.74 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__step,axiom,
% 50.63/50.74 ! [V_m,V_n] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.63/50.74 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_conjI__realizer,axiom,
% 50.63/50.74 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 50.63/50.74 ( hBOOL(hAPP(V_P_2,V_p_2))
% 50.63/50.74 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 50.63/50.74 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 50.63/50.74 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_exI__realizer,axiom,
% 50.63/50.74 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__nat__def,axiom,
% 50.63/50.74 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_double__complement,axiom,
% 50.63/50.74 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Compl__eq__Compl__iff,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
% 50.63/50.74 <=> V_A_2 = V_B_2 ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_psubset__trans,axiom,
% 50.63/50.74 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Diff__idemp,axiom,
% 50.63/50.74 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__zero,axiom,
% 50.63/50.74 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__nat__def,axiom,
% 50.63/50.74 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__base,axiom,
% 50.63/50.74 ! [V_n,V_m] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.63/50.74 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__div__mod,axiom,
% 50.63/50.74 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 50.63/50.74 ! [V_c,V_r,V_q,V_b,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 50.63/50.74 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 50.63/50.74 ! [V_a,V_r,V_q,V_c,V_b] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 50.63/50.74 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 50.63/50.74 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
% 50.63/50.74 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 50.63/50.74 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_range,axiom,
% 50.63/50.74 ! [V_s,V_k] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__rel__def,axiom,
% 50.63/50.74 ! [V_qr_2,V_n_2,V_m_2] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 50.63/50.74 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))
% 50.63/50.74 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.63/50.74 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 50.63/50.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 50.63/50.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__rel__unique,axiom,
% 50.63/50.74 ! [V_qr_H,V_qr,V_n,V_m] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 50.63/50.74 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 50.63/50.74 => V_qr = V_qr_H ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 50.63/50.74 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__eq,axiom,
% 50.63/50.74 ! [V_qr,V_n,V_m] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 50.63/50.74 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_mod__eq,axiom,
% 50.63/50.74 ! [V_r,V_q,V_n,V_m] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 50.63/50.74 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_div__eq,axiom,
% 50.63/50.74 ! [V_r,V_q,V_n,V_m] :
% 50.63/50.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 50.63/50.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__rel,axiom,
% 50.63/50.74 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_prod_Orecs,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_adjust__eq,axiom,
% 50.63/50.74 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_iterate_Osimps,axiom,
% 50.63/50.74 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 50.63/50.74 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.74 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) )
% 50.63/50.74 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.74 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_subtract__code__numeral__def,axiom,
% 50.63/50.74 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_minus__code__numeral__code,axiom,
% 50.63/50.74 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_scomp__unfold,axiom,
% 50.63/50.74 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_scomp__scomp,axiom,
% 50.63/50.74 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_fun__Compl__def,axiom,
% 50.63/50.74 ! [V_x_2,V_A_2,T_c,T_b] :
% 50.63/50.74 ( class_Groups_Ouminus(T_b)
% 50.63/50.74 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_fun__diff__def,axiom,
% 50.63/50.74 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.74 ( class_Groups_Ominus(T_b)
% 50.63/50.74 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_less__eq__Suc__le__raw,axiom,
% 50.63/50.74 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__number__of__Bit0,axiom,
% 50.63/50.74 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_scomp__Pair,axiom,
% 50.63/50.74 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_power__number__of__even,axiom,
% 50.63/50.74 ! [V_w_2,V_z_2,T_b] :
% 50.63/50.74 ( class_Int_Onumber__ring(T_b)
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_zpower__number__of__even,axiom,
% 50.63/50.74 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Pair__scomp,axiom,
% 50.63/50.74 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_power__number__of__even__number__of,axiom,
% 50.63/50.74 ! [V_w_2,V_v_2,T_b] :
% 50.63/50.74 ( class_Int_Onumber__ring(T_b)
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_diff__nat__eq__if,axiom,
% 50.63/50.74 ! [V_z_2,V_z_H_2] :
% 50.63/50.74 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 50.63/50.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 50.63/50.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 50.63/50.74 ! [V_n_2,T_b] :
% 50.63/50.74 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.74 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_eq__number__of__Suc,axiom,
% 50.63/50.74 ! [V_n_2,V_v_2] :
% 50.63/50.74 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Suc__eq__number__of,axiom,
% 50.63/50.74 ! [V_v_2,V_n_2] :
% 50.63/50.74 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__number__of__Bit1,axiom,
% 50.63/50.74 ! [V_w_2] :
% 50.63/50.74 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_less__number__of__Suc,axiom,
% 50.63/50.74 ! [V_n_2,V_v_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_less__Suc__number__of,axiom,
% 50.63/50.74 ! [V_v_2,V_n_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_le__number__of__Suc,axiom,
% 50.63/50.74 ! [V_n_2,V_v_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_le__Suc__number__of,axiom,
% 50.63/50.74 ! [V_v_2,V_n_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_power__number__of__odd,axiom,
% 50.63/50.74 ! [V_z_2,V_w_2,T_b] :
% 50.63/50.74 ( class_Int_Onumber__ring(T_b)
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_zpower__number__of__odd,axiom,
% 50.63/50.74 ! [V_z_2,V_w_2] :
% 50.63/50.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_power__number__of__odd__number__of,axiom,
% 50.63/50.74 ! [V_v_2,V_w_2,T_b] :
% 50.63/50.74 ( class_Int_Onumber__ring(T_b)
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 50.63/50.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_diff__nat__number__of,axiom,
% 50.63/50.74 ! [V_v_2,V_v_H_2] :
% 50.63/50.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 50.63/50.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 50.63/50.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_of__int__num,axiom,
% 50.63/50.74 ! [V_k_2,T_b] :
% 50.63/50.74 ( class_Rings_Oring__1(T_b)
% 50.63/50.74 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 50.63/50.74 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__case__add__eq__if,axiom,
% 50.63/50.74 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_adjust__def,axiom,
% 50.63/50.74 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__case__number__of,axiom,
% 50.63/50.74 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__rec__add__eq__if,axiom,
% 50.63/50.74 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__twice,axiom,
% 50.63/50.74 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__weak__cong,axiom,
% 50.63/50.74 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 50.63/50.74 ( V_p_2 = V_q_2
% 50.63/50.74 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__conv,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_prod_Osimps_I2_J,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_scomp__apply,axiom,
% 50.63/50.74 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__eta,axiom,
% 50.63/50.74 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_fst__def,axiom,
% 50.63/50.74 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_snd__def,axiom,
% 50.63/50.74 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_scomp__def,axiom,
% 50.63/50.74 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__rec__0,axiom,
% 50.63/50.74 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__rec__Suc,axiom,
% 50.63/50.74 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__case__0,axiom,
% 50.63/50.74 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__case__Suc,axiom,
% 50.63/50.74 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_prod__case__beta,axiom,
% 50.63/50.74 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__beta,axiom,
% 50.63/50.74 ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__comp__eq,axiom,
% 50.63/50.74 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__def,axiom,
% 50.63/50.74 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 50.63/50.74 ! [V_n_2,V_m_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 50.63/50.74 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_diff__Suc,axiom,
% 50.63/50.74 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__int__rel__def,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__rec__number__of,axiom,
% 50.63/50.74 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__int__pdivmod,axiom,
% 50.63/50.74 ! [V_l_2,V_k_2] :
% 50.63/50.74 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 50.63/50.74 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 50.63/50.74 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__int__code,axiom,
% 50.63/50.74 ! [V_l_2,V_k_2] :
% 50.63/50.74 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 50.63/50.74 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 50.63/50.74 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_MGT__def,axiom,
% 50.63/50.74 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__Suc__number__of,axiom,
% 50.63/50.74 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__number__of__Suc,axiom,
% 50.63/50.74 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_prod__caseI,axiom,
% 50.63/50.74 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_splitI,axiom,
% 50.63/50.74 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_splitD,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__0R,axiom,
% 50.63/50.74 ! [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) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__0L,axiom,
% 50.63/50.74 ! [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) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__Suc__Suc,axiom,
% 50.63/50.74 ! [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)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__diff__distrib__left,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Groups_Oordered__ab__group__add(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__infE,axiom,
% 50.63/50.74 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( 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)))
% 50.63/50.74 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 50.63/50.74 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__mono,axiom,
% 50.63/50.74 ! [V_d,V_b,V_c,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 50.63/50.74 => 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))) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__greatest,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 50.63/50.74 => 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))) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__infI,axiom,
% 50.63/50.74 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 50.63/50.74 => 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))) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__absorb2,axiom,
% 50.63/50.74 ! [V_x,V_y,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__absorb1,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__infI2,axiom,
% 50.63/50.74 ! [V_a,V_x,V_b,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 50.63/50.74 => 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)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__infI1,axiom,
% 50.63/50.74 ! [V_b,V_x,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 50.63/50.74 => 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)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__inf__iff,axiom,
% 50.63/50.74 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.63/50.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__iff__inf,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.63/50.74 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__le2,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__le1,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__le__iff__disj,axiom,
% 50.63/50.74 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__assoc,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf_Oassoc,axiom,
% 50.63/50.74 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__left__commute,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 50.63/50.74 ! [V_c,V_a,V_b,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__left__idem,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 50.63/50.74 ! [V_b,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__commute,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf_Ocommute,axiom,
% 50.63/50.74 ! [V_b,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => 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) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf_Oidem,axiom,
% 50.63/50.74 ! [V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__add__distrib__left,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 50.63/50.74 => 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oless__infI1,axiom,
% 50.63/50.74 ! [V_b,V_x,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 50.63/50.74 => 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)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oless__infI2,axiom,
% 50.63/50.74 ! [V_a,V_x,V_b,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 50.63/50.74 => 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)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__less__iff__disj,axiom,
% 50.63/50.74 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__less__iff__conj,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 50.63/50.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__diff,axiom,
% 50.63/50.74 ! [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) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_splitD_H,axiom,
% 50.63/50.74 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_apsnd__conv,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_fst__apsnd,axiom,
% 50.63/50.74 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_apsnd__eq__conv,axiom,
% 50.63/50.74 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 50.63/50.74 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
% 50.63/50.74 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_snd__apsnd,axiom,
% 50.63/50.74 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__number__of,axiom,
% 50.63/50.74 ! [V_v,V_u,T_b] :
% 50.63/50.74 ( ( class_Int_Onumber(T_b)
% 50.63/50.74 & class_Orderings_Oord(T_b) )
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 50.63/50.74 => 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) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 50.63/50.74 => 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) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__Suc1,axiom,
% 50.63/50.74 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__Suc2,axiom,
% 50.63/50.74 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_negateSnd__def,axiom,
% 50.63/50.74 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__if,axiom,
% 50.63/50.74 ! [V_m_2,V_n_2] :
% 50.63/50.74 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 50.63/50.74 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
% 50.63/50.74 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 50.63/50.74 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__ord__min,axiom,
% 50.63/50.74 ! [T_b] :
% 50.63/50.74 ( class_Orderings_Oord(T_b)
% 50.63/50.74 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__number__of__Suc,axiom,
% 50.63/50.74 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__Suc__number__of,axiom,
% 50.63/50.74 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_apfst__apsnd,axiom,
% 50.63/50.74 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_apsnd__apfst,axiom,
% 50.63/50.74 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oless__supI1,axiom,
% 50.63/50.74 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oless__supI2,axiom,
% 50.63/50.74 ! [V_a,V_b,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__less__iff__conj,axiom,
% 50.63/50.74 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 50.63/50.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_less__max__iff__disj,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__add__distrib__left,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup_Oidem,axiom,
% 50.63/50.74 ! [V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup_Ocommute,axiom,
% 50.63/50.74 ! [V_b,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__commute,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 50.63/50.74 ! [V_b,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__left__idem,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 50.63/50.74 ! [V_c,V_a,V_b,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__left__commute,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup_Oassoc,axiom,
% 50.63/50.74 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__assoc,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_le__max__iff__disj,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 50.63/50.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_le__maxI1,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_le__maxI2,axiom,
% 50.63/50.74 ! [V_x,V_y,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__iff__sup,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.63/50.74 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__sup__iff,axiom,
% 50.63/50.74 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 50.63/50.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 50.63/50.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__supI1,axiom,
% 50.63/50.74 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__supI2,axiom,
% 50.63/50.74 ! [V_a,V_b,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__absorb2,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__absorb1,axiom,
% 50.63/50.74 ! [V_x,V_y,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__supI,axiom,
% 50.63/50.74 ! [V_b,V_x,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__least,axiom,
% 50.63/50.74 ! [V_z,V_x,V_y,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__mono,axiom,
% 50.63/50.74 ! [V_d,V_b,V_c,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Ole__supE,axiom,
% 50.63/50.74 ! [V_x,V_b,V_a,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
% 50.63/50.74 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 50.63/50.74 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__diff__distrib__left,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Groups_Oordered__ab__group__add(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__Suc__Suc,axiom,
% 50.63/50.74 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__0L,axiom,
% 50.63/50.74 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__0R,axiom,
% 50.63/50.74 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__inf__absorb,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 50.63/50.74 ! [V_x,V_z,V_y,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 50.63/50.74 ! [V_x,V_z,V_y,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_apfst__conv,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_apfst__eq__conv,axiom,
% 50.63/50.74 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 50.63/50.74 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
% 50.63/50.74 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_fst__apfst,axiom,
% 50.63/50.74 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_snd__apfst,axiom,
% 50.63/50.74 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__number__of,axiom,
% 50.63/50.74 ! [V_v,V_u,T_b] :
% 50.63/50.74 ( ( class_Int_Onumber(T_b)
% 50.63/50.74 & class_Orderings_Oord(T_b) )
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Odistrib__sup__le,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_min__max_Odistrib__inf__le,axiom,
% 50.63/50.74 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_minus__max__eq__min,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Groups_Olinordered__ab__group__add(T_a)
% 50.63/50.74 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_minus__min__eq__max,axiom,
% 50.63/50.74 ! [V_y,V_x,T_a] :
% 50.63/50.74 ( class_Groups_Olinordered__ab__group__add(T_a)
% 50.63/50.74 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__minus__add__max,axiom,
% 50.63/50.74 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_apsnd__apfst__commute,axiom,
% 50.63/50.74 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__Suc1,axiom,
% 50.63/50.74 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__Suc2,axiom,
% 50.63/50.74 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_dual__min,axiom,
% 50.63/50.74 ! [T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_max__ord__max,axiom,
% 50.63/50.74 ! [T_b] :
% 50.63/50.74 ( class_Orderings_Oord(T_b)
% 50.63/50.74 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_OFrac__def,axiom,
% 50.63/50.74 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_norm__frac_Osimps,axiom,
% 50.63/50.74 ! [V_a_2,V_b_2] :
% 50.63/50.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 50.63/50.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 50.63/50.74 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 50.63/50.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_norm__frac_Opsimps,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 50.63/50.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 50.63/50.74 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 50.63/50.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Min_Oidem,axiom,
% 50.63/50.74 ! [V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Max_Oidem,axiom,
% 50.63/50.74 ! [V_x,T_a] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_a)
% 50.63/50.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_dual__max,axiom,
% 50.63/50.74 ! [T_b] :
% 50.63/50.74 ( class_Orderings_Olinorder(T_b)
% 50.63/50.74 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 50.63/50.74 ! [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)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_norm__frac_Opinduct,axiom,
% 50.63/50.74 ! [V_P_2,V_a1_2,V_a0_2] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 50.63/50.74 => ( ! [B_a,B_b] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 50.63/50.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 50.63/50.74 => 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))) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 50.63/50.74 ! [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)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 50.63/50.74 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__gcd_Osimps,axiom,
% 50.63/50.74 ! [V_x,V_y] :
% 50.63/50.74 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 50.63/50.74 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 => 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)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 50.63/50.74 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oone__frac__def,axiom,
% 50.63/50.74 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 50.63/50.74 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__gcd_Opsimps,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
% 50.63/50.74 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 50.63/50.74 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Ofrac__def,axiom,
% 50.63/50.74 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_internal__split__def,axiom,
% 50.63/50.74 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_internal__split__conv,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_nat__gcd_Opinduct,axiom,
% 50.63/50.74 ! [V_P_2,V_a1_2,V_a0_2] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
% 50.63/50.74 => ( ! [B_x,B_y] :
% 50.63/50.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
% 50.63/50.74 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 50.63/50.74 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_transfer__morphism__int__nat,axiom,
% 50.63/50.74 c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_pair__box_Osize_I1_J,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_rev__predicate2D,axiom,
% 50.63/50.74 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_pair__box_Oinject,axiom,
% 50.63/50.74 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.74 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 50.63/50.74 <=> ( V_a_2 = V_a_H_2
% 50.63/50.74 & V_b_2 = V_b_H_2 ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_rev__predicate1D,axiom,
% 50.63/50.74 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 50.63/50.74 ( hBOOL(hAPP(V_P_2,V_x_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 50.63/50.74 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_predicate1D,axiom,
% 50.63/50.74 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 50.63/50.74 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 50.63/50.74 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_predicate2D,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 50.63/50.74 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 50.63/50.74 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 50.63/50.74 ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oof__frac__def,axiom,
% 50.63/50.74 ! [V_q,T_a,T_b] :
% 50.63/50.74 ( ( class_Rings_Oinverse(T_b)
% 50.63/50.74 & class_Rings_Oring__1(T_b) )
% 50.63/50.74 => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 50.63/50.74 ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 50.63/50.74 ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oless__frac__def,axiom,
% 50.63/50.74 ! [V_r_2,V_q_2,T_b] :
% 50.63/50.74 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 50.63/50.74 ! [V_r_2,V_q_2,T_b] :
% 50.63/50.74 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_pair__box_Osize_I2_J,axiom,
% 50.63/50.74 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_pair__box_Osimps_I2_J,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_pair__box_Orecs,axiom,
% 50.63/50.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_The__split,axiom,
% 50.63/50.74 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_split__paired__The,axiom,
% 50.63/50.74 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_The__split__eq,axiom,
% 50.63/50.74 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_divmod__nat__def,axiom,
% 50.63/50.74 ! [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)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_the__eq__trivial,axiom,
% 50.63/50.74 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_the__sym__eq__trivial,axiom,
% 50.63/50.74 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 50.63/50.74 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Random_Osimps,axiom,
% 50.63/50.74 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 50.63/50.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 50.63/50.74 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 50.63/50.74 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_exE__realizer,axiom,
% 50.63/50.74 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 50.63/50.74 => ( ! [B_x,B_y] :
% 50.63/50.74 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 50.63/50.74 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 50.63/50.74 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 50.63/50.74 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Random__Sequence_Oempty__def,axiom,
% 50.63/50.74 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Random__Sequence_Osingle__def,axiom,
% 50.63/50.74 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 50.63/50.74 ! [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))) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral__not__eq__zero,axiom,
% 50.63/50.74 ! [V_i_2] :
% 50.63/50.74 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.63/50.74 <=> 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)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_beyond__def,axiom,
% 50.63/50.74 ! [V_l,V_k] :
% 50.63/50.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 50.63/50.74 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 50.63/50.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 50.63/50.74 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 50.63/50.74 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 50.63/50.74 ! [V_m_2,V_n_2] :
% 50.63/50.74 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 50.63/50.74 <=> V_n_2 = V_m_2 ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_times__code__numeral__code,axiom,
% 50.63/50.74 ! [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)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_beyond__zero,axiom,
% 50.63/50.74 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_zero__code__numeral__def,axiom,
% 50.63/50.74 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_one__code__numeral__def,axiom,
% 50.63/50.74 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_less__code__numeral__code,axiom,
% 50.63/50.74 ! [V_m_2,V_n_2] :
% 50.63/50.74 ( 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)))
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_plus__code__numeral__code,axiom,
% 50.63/50.74 ! [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)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_less__eq__code__numeral__code,axiom,
% 50.63/50.74 ! [V_m_2,V_n_2] :
% 50.63/50.74 ( 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)))
% 50.63/50.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_subtract__code__numeral__code,axiom,
% 50.63/50.74 ! [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)) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_code__numeral__decr,axiom,
% 50.63/50.74 ! [V_k] :
% 50.63/50.74 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.63/50.74 => 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))) ) ).
% 50.63/50.74
% 50.63/50.74 fof(fact_pos__not__random__dseq__def,axiom,
% 50.63/50.74 ! [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)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_mod__code__numeral__def,axiom,
% 50.63/50.75 ! [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))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_times__code__numeral__def,axiom,
% 50.63/50.75 ! [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))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 50.63/50.75 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 50.63/50.75 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.75 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) )
% 50.63/50.75 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.75 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_code__numeral_Onat__of__inject,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 50.63/50.75 <=> V_x_2 = V_y_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 50.63/50.75 ! [V_l_2,V_k_2] :
% 50.63/50.75 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 50.63/50.75 <=> V_k_2 = V_l_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__of__inverse,axiom,
% 50.63/50.75 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 50.63/50.75
% 50.63/50.75 fof(fact_of__nat__nat__of,axiom,
% 50.63/50.75 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__of__of__nat,axiom,
% 50.63/50.75 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 50.63/50.75
% 50.63/50.75 fof(fact_less__code__numeral__def,axiom,
% 50.63/50.75 ! [V_m_2,V_n_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 50.63/50.75 <=> 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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__of__number,axiom,
% 50.63/50.75 ! [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) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_less__eq__code__numeral__def,axiom,
% 50.63/50.75 ! [V_m_2,V_n_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 50.63/50.75 <=> 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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__of__code,axiom,
% 50.63/50.75 ! [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)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__of__aux__def,axiom,
% 50.63/50.75 ! [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) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Suc__code__numeral__def,axiom,
% 50.63/50.75 ! [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))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_minus__code__numeral__def,axiom,
% 50.63/50.75 ! [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))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_plus__code__numeral__def,axiom,
% 50.63/50.75 ! [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))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_div__code__numeral__def,axiom,
% 50.63/50.75 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 50.63/50.75 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 50.63/50.75 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 50.63/50.75 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 50.63/50.75 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 50.63/50.75 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.75 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) )
% 50.63/50.75 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 50.63/50.75 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_curry__def,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_curryI,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 50.63/50.75 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_curryD,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 50.63/50.75 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_curryE,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 50.63/50.75 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_curry__conv,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_curry__split,axiom,
% 50.63/50.75 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ).
% 50.63/50.75
% 50.63/50.75 fof(fact_split__curry,axiom,
% 50.63/50.75 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pos__empty__def,axiom,
% 50.63/50.75 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 50.63/50.75 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pos__bind__def,axiom,
% 50.63/50.75 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 50.63/50.75 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_power__dvd__imp__le,axiom,
% 50.63/50.75 ! [V_n,V_m,V_i] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oorder__refl,axiom,
% 50.63/50.75 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__0__right,axiom,
% 50.63/50.75 ! [V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__1__left,axiom,
% 50.63/50.75 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__right,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__left,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvdI,axiom,
% 50.63/50.75 ! [V_k,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Odvd(T_a)
% 50.63/50.75 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_mult__dvd__mono,axiom,
% 50.63/50.75 ! [V_d,V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult,axiom,
% 50.63/50.75 ! [V_b,V_c,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult2,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__triv__right,axiom,
% 50.63/50.75 ! [V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__triv__left,axiom,
% 50.63/50.75 ! [V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__power__same,axiom,
% 50.63/50.75 ! [V_n,V_y,V_x,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_y),V_n))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_div__dvd__div,axiom,
% 50.63/50.75 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_one__dvd,axiom,
% 50.63/50.75 ! [V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__0__left,axiom,
% 50.63/50.75 ! [V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 50.63/50.75 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__trans,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__refl,axiom,
% 50.63/50.75 ! [V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__asym,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__trans,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__asym_H,axiom,
% 50.63/50.75 ! [V_b,V_a] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 50.63/50.75 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__le__trans,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 50.63/50.75 => ( V_b = V_c
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => V_y != V_x ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => V_x != V_y ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__imp__not__less,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__imp__le,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__not__sym,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__imp__neq,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 => V_x != V_y ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Ole__less__trans,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a] :
% 50.63/50.75 ( V_a = V_b
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oorder__trans,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oantisym,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 50.63/50.75 => V_x = V_y ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__antisym,axiom,
% 50.63/50.75 ! [V_n,V_m] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 50.63/50.75 => V_m = V_n ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 50.63/50.75 => ( V_b = V_c
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a] :
% 50.63/50.75 ( V_a = V_b
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Ole__neq__trans,axiom,
% 50.63/50.75 ! [V_b,V_a] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 50.63/50.75 => ( V_a != V_b
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 50.63/50.75 | V_x = V_y ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oantisym__conv,axiom,
% 50.63/50.75 ! [V_x_2,V_y_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 <=> V_x_2 = V_y_2 ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oeq__refl,axiom,
% 50.63/50.75 ! [V_y,V_x] :
% 50.63/50.75 ( V_x = V_y
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oneq__le__trans,axiom,
% 50.63/50.75 ! [V_b,V_a] :
% 50.63/50.75 ( V_a != V_b
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oless__le,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 50.63/50.75 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 & V_x_2 != V_y_2 ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Ole__less,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 50.63/50.75 | V_x_2 = V_y_2 ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Oeq__iff,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( V_x_2 = V_y_2
% 50.63/50.75 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__add,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mod__iff,axiom,
% 50.63/50.75 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_mod__mod__cancel,axiom,
% 50.63/50.75 ! [V_a,V_b,V_c,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 50.63/50.75 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mod,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mod__imp__dvd,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__minus__iff,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( class_Rings_Ocomm__ring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_minus__dvd__iff,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( class_Rings_Ocomm__ring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__diff,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__ring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__abs__iff,axiom,
% 50.63/50.75 ! [V_k_2,V_m_2,T_b] :
% 50.63/50.75 ( class_Rings_Olinordered__idom(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_abs__dvd__iff,axiom,
% 50.63/50.75 ! [V_k_2,V_m_2,T_b] :
% 50.63/50.75 ( class_Rings_Olinordered__idom(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__if__abs__eq,axiom,
% 50.63/50.75 ! [V_k,V_l,T_a] :
% 50.63/50.75 ( class_Rings_Olinordered__idom(T_a)
% 50.63/50.75 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__diff__nat,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__reduce,axiom,
% 50.63/50.75 ! [V_n_2,V_k_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__dvd__1__iff__1,axiom,
% 50.63/50.75 ! [V_m_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 50.63/50.75 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__cancel__right,axiom,
% 50.63/50.75 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Oidom(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 50.63/50.75 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.63/50.75 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__cancel__left,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 50.63/50.75 ( class_Rings_Oidom(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 50.63/50.75 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 50.63/50.75 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__eq__mod__eq__0,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 50.63/50.75 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__imp__mod__0,axiom,
% 50.63/50.75 ! [V_b,V_a,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_div__add,axiom,
% 50.63/50.75 ! [V_y,V_x,V_z,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 50.63/50.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_div__mult__div__if__dvd,axiom,
% 50.63/50.75 ! [V_w,V_z,V_x,V_y,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__div__mult,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__div__mult__self,axiom,
% 50.63/50.75 ! [V_b,V_a,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_div__mult__swap,axiom,
% 50.63/50.75 ! [V_a,V_b,V_c,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__div__cancel,axiom,
% 50.63/50.75 ! [V_b,V_a,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__neg__div,axiom,
% 50.63/50.75 ! [V_x,V_y,T_a] :
% 50.63/50.75 ( class_Divides_Oring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 50.63/50.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__div__neg,axiom,
% 50.63/50.75 ! [V_x,V_y,T_a] :
% 50.63/50.75 ( class_Divides_Oring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 50.63/50.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_le__imp__power__dvd,axiom,
% 50.63/50.75 ! [V_a,V_n,V_m,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__power__le,axiom,
% 50.63/50.75 ! [V_m,V_n,V_y,V_x,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_y),V_m))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_power__le__dvd,axiom,
% 50.63/50.75 ! [V_m,V_b,V_n,V_a,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_div__power,axiom,
% 50.63/50.75 ! [V_n,V_x,V_y,T_a] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 50.63/50.75 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(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_y),V_n)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__1__iff__1,axiom,
% 50.63/50.75 ! [V_m_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 50.63/50.75 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__dvd__not__less,axiom,
% 50.63/50.75 ! [V_n,V_m] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 50.63/50.75 ! [V_n_2,V_m_2,V_k_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 50.63/50.75 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.75 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__diffD,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__diffD1,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_unity__coeff__ex,axiom,
% 50.63/50.75 ! [V_l_2,V_P_2,T_b] :
% 50.63/50.75 ( ( class_Rings_Odvd(T_b)
% 50.63/50.75 & class_Rings_Osemiring__0(T_b) )
% 50.63/50.75 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 50.63/50.75 <=> ? [B_x] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))
% 50.63/50.75 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__period_I4_J,axiom,
% 50.63/50.75 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 50.63/50.75 ( ( class_Rings_Ocomm__ring(T_b)
% 50.63/50.75 & class_Rings_Odvd(T_b) )
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 50.63/50.75 => ! [B_x,B_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__period_I3_J,axiom,
% 50.63/50.75 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 50.63/50.75 ( ( class_Rings_Ocomm__ring(T_b)
% 50.63/50.75 & class_Rings_Odvd(T_b) )
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 50.63/50.75 => ! [B_x,B_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( ( class_Divides_Osemiring__div(T_b)
% 50.63/50.75 & class_Int_Onumber(T_b) )
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 50.63/50.75 <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__div__eq__mult,axiom,
% 50.63/50.75 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_b)
% 50.63/50.75 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 50.63/50.75 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 50.63/50.75 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__div__div__eq__mult,axiom,
% 50.63/50.75 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Divides_Osemiring__div(T_b)
% 50.63/50.75 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.63/50.75 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 50.63/50.75 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
% 50.63/50.75 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__imp__le,axiom,
% 50.63/50.75 ! [V_n,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__mult__dvd__cancel1,axiom,
% 50.63/50.75 ! [V_n_2,V_m_2,V_k_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__cancel,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__power,axiom,
% 50.63/50.75 ! [V_x,V_n,T_a] :
% 50.63/50.75 ( class_Rings_Ocomm__semiring__1(T_a)
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 50.63/50.75 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__cancel2,axiom,
% 50.63/50.75 ! [V_n_2,V_m_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))
% 50.63/50.75 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__mult__cancel1,axiom,
% 50.63/50.75 ! [V_n_2,V_m_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))
% 50.63/50.75 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_neg__bind__def,axiom,
% 50.63/50.75 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Ostrict__monoD,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 50.63/50.75 ( class_Orderings_Oorder(T_b)
% 50.63/50.75 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_OmonoD,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 50.63/50.75 ( class_Orderings_Oorder(T_b)
% 50.63/50.75 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 => 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))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_nat__dvd__iff,axiom,
% 50.63/50.75 ! [V_m_2,V_z_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
% 50.63/50.75 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) )
% 50.63/50.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 50.63/50.75 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_hoare__derivs_OCall,axiom,
% 50.63/50.75 ! [V_a_2,V_X_2,V_s_H_2,V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),tc_HOL_Obool))))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),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_b,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_b),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_b),tc_HOL_Obool)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_empty__subsetI,axiom,
% 50.63/50.75 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__zmod,axiom,
% 50.63/50.75 ! [V_n,V_m,V_f] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__zmod__imp__zdvd,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 50.63/50.75 ! [V_t_2,V_d_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 50.63/50.75 ! [V_t_2,V_d_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__zdiffD,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__insertI,axiom,
% 50.63/50.75 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__insertI2,axiom,
% 50.63/50.75 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__mono,axiom,
% 50.63/50.75 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_LoopF,axiom,
% 50.63/50.75 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_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_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Comp,axiom,
% 50.63/50.75 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 50.63/50.75 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_hoare__derivs_OSkip,axiom,
% 50.63/50.75 ! [V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 50.63/50.75 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Diff__insert,axiom,
% 50.63/50.75 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Diff__insert2,axiom,
% 50.63/50.75 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__Diff__single,axiom,
% 50.63/50.75 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_thin,axiom,
% 50.63/50.75 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_weaken,axiom,
% 50.63/50.75 ! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_asm,axiom,
% 50.63/50.75 ! [V_Ga_2,V_tsa_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_derivs__insertD,axiom,
% 50.63/50.75 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2))
% 50.63/50.75 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 50.63/50.75 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_hoare__derivs_Oinsert,axiom,
% 50.63/50.75 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 50.63/50.75 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_cut,axiom,
% 50.63/50.75 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 50.63/50.75 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 50.63/50.75 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_empty,axiom,
% 50.63/50.75 ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_bot__apply,axiom,
% 50.63/50.75 ! [V_x_2,T_c,T_b] :
% 50.63/50.75 ( class_Orderings_Obot(T_b)
% 50.63/50.75 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_empty__not__insert,axiom,
% 50.63/50.75 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__not__empty,axiom,
% 50.63/50.75 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__absorb2,axiom,
% 50.63/50.75 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__commute,axiom,
% 50.63/50.75 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_doubleton__eq__iff,axiom,
% 50.63/50.75 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.75 <=> ( ( V_a_2 = V_c_2
% 50.63/50.75 & V_b_2 = V_d_2 )
% 50.63/50.75 | ( V_a_2 = V_d_2
% 50.63/50.75 & V_b_2 = V_c_2 ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__code,axiom,
% 50.63/50.75 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 50.63/50.75 <=> ( V_y_2 = V_x_2
% 50.63/50.75 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_singleton__inject,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.75 => V_a_2 = V_b_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__singletonD,axiom,
% 50.63/50.75 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 50.63/50.75 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.75 | 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))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_bot__fun__def,axiom,
% 50.63/50.75 ! [V_x_2,T_c,T_b] :
% 50.63/50.75 ( class_Orderings_Obot(T_b)
% 50.63/50.75 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 50.63/50.75 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ass,axiom,
% 50.63/50.75 ! [V_a_2,V_X_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_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_b),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_b),tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__antisym__abs,axiom,
% 50.63/50.75 ! [V_b,V_a] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
% 50.63/50.75 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__empty,axiom,
% 50.63/50.75 ! [V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.75 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Diff__cancel,axiom,
% 50.63/50.75 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Diff__empty,axiom,
% 50.63/50.75 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 50.63/50.75
% 50.63/50.75 fof(fact_empty__Diff,axiom,
% 50.63/50.75 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_not__psubset__empty,axiom,
% 50.63/50.75 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_weak__Body,axiom,
% 50.63/50.75 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_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_b),tc_HOL_Obool))))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_BodyN,axiom,
% 50.63/50.75 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),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_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),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_b),tc_HOL_Obool))))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_bot__least,axiom,
% 50.63/50.75 ! [V_x,T_a] :
% 50.63/50.75 ( class_Orderings_Obot(T_a)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__antisym__nonneg,axiom,
% 50.63/50.75 ! [V_n,V_m] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 50.63/50.75 => V_m = V_n ) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__not__zless,axiom,
% 50.63/50.75 ! [V_n,V_m] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_hoare__derivs_OLocal,axiom,
% 50.63/50.75 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),tc_HOL_Obool))))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),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_b,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_b),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_c_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__mono,axiom,
% 50.63/50.75 ! [V_t_2,V_m_2,V_k_2] :
% 50.63/50.75 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__mult__cancel,axiom,
% 50.63/50.75 ! [V_n,V_m,V_k] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))
% 50.63/50.75 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__reduce,axiom,
% 50.63/50.75 ! [V_m_2,V_n_2,V_k_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__period,axiom,
% 50.63/50.75 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__int,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_transfer__int__nat__relations_I4_J,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__mult__div__cancel,axiom,
% 50.63/50.75 ! [V_m,V_n] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = V_m ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zmod__eq__dvd__iff,axiom,
% 50.63/50.75 ! [V_y_2,V_n_2,V_x_2] :
% 50.63/50.75 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd1__eq,axiom,
% 50.63/50.75 ! [V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 50.63/50.75 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_abs__div,axiom,
% 50.63/50.75 ! [V_x,V_y] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
% 50.63/50.75 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Ostrict__mono__mono,axiom,
% 50.63/50.75 ! [V_f_2,T_b] :
% 50.63/50.75 ( class_Orderings_Oorder(T_b)
% 50.63/50.75 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
% 50.63/50.75 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__Compl__self__eq,axiom,
% 50.63/50.75 ! [V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 50.63/50.75 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__imp__le,axiom,
% 50.63/50.75 ! [V_n,V_z] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2)))
% 50.63/50.75 <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__imp__le__int,axiom,
% 50.63/50.75 ! [V_d,V_i] :
% 50.63/50.75 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_transfer__nat__int__relations_I4_J,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_zdvd__mult__cancel1,axiom,
% 50.63/50.75 ! [V_n_2,V_m_2] :
% 50.63/50.75 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)),V_m_2))
% 50.63/50.75 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_int__dvd__iff,axiom,
% 50.63/50.75 ! [V_z_2,V_m_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd__int__iff,axiom,
% 50.63/50.75 ! [V_m_2,V_z_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_the__elem__def,axiom,
% 50.63/50.75 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_the__elem__eq,axiom,
% 50.63/50.75 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 50.63/50.75 ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_escape,axiom,
% 50.63/50.75 ! [V_Q_2,V_c_2,V_Ga_2,T_b,V_P_2] :
% 50.63/50.75 ( ! [B_Z,B_s] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_conseq1,axiom,
% 50.63/50.75 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 50.63/50.75 => ( ! [B_Z,B_s] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 50.63/50.75 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_bot__nat__def,axiom,
% 50.63/50.75 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_set__empty__eq,axiom,
% 50.63/50.75 ! [V_xo_2,T_b] :
% 50.63/50.75 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.75 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 50.63/50.75 ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_conseq2,axiom,
% 50.63/50.75 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.75 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 50.63/50.75 => ( ! [B_Z,B_s] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 50.63/50.75 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 50.63/50.75 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_psubset__insert__iff,axiom,
% 50.63/50.75 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 50.63/50.75 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 50.63/50.75 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 50.63/50.75 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_Ostrict__monoI,axiom,
% 50.63/50.75 ! [V_f_2,T_b] :
% 50.63/50.75 ( class_Orderings_Oorder(T_b)
% 50.63/50.75 => ( ! [B_x,B_y] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) )
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 50.63/50.75 => c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_dvd_OmonoI,axiom,
% 50.63/50.75 ! [V_f_2,T_b] :
% 50.63/50.75 ( class_Orderings_Oorder(T_b)
% 50.63/50.75 => ( ! [B_x,B_y] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 50.63/50.75 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_equalityCE,axiom,
% 50.63/50.75 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 50.63/50.75 ( V_A_2 = V_B_2
% 50.63/50.75 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 50.63/50.75 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_emptyE,axiom,
% 50.63/50.75 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insertE,axiom,
% 50.63/50.75 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 50.63/50.75 => ( V_a_2 != V_b_2
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insertCI,axiom,
% 50.63/50.75 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 50.63/50.75 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 50.63/50.75 => V_a_2 = V_b_2 )
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subsetD,axiom,
% 50.63/50.75 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_DiffE,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.75 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_DiffI,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_ComplI,axiom,
% 50.63/50.75 ! [V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_mem__splitI,axiom,
% 50.63/50.75 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insertI1,axiom,
% 50.63/50.75 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_all__not__in__conv,axiom,
% 50.63/50.75 ! [V_A_2,T_b] :
% 50.63/50.75 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.75 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_ex__in__conv,axiom,
% 50.63/50.75 ! [V_A_2,T_b] :
% 50.63/50.75 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.75 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_empty__iff,axiom,
% 50.63/50.75 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__iff,axiom,
% 50.63/50.75 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 50.63/50.75 <=> ( V_a_2 = V_b_2
% 50.63/50.75 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__ident,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 50.63/50.75 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 50.63/50.75 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
% 50.63/50.75 <=> V_A_2 = V_B_2 ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_equals0D,axiom,
% 50.63/50.75 ! [V_a_2,T_b,V_A_2] :
% 50.63/50.75 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insertI2,axiom,
% 50.63/50.75 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__absorb,axiom,
% 50.63/50.75 ! [V_A_2,V_a_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.75 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_set__mp,axiom,
% 50.63/50.75 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_set__rev__mp,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_in__mono,axiom,
% 50.63/50.75 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Compl__iff,axiom,
% 50.63/50.75 ! [V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 50.63/50.75 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_ComplD,axiom,
% 50.63/50.75 ! [V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_ComplE,axiom,
% 50.63/50.75 ! [V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Diff__iff,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.75 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_DiffD1,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_DiffD2,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_mem__def,axiom,
% 50.63/50.75 ! [V_A_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_eqset__imp__iff,axiom,
% 50.63/50.75 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 50.63/50.75 ( V_A_2 = V_B_2
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_eqelem__imp__iff,axiom,
% 50.63/50.75 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 50.63/50.75 ( V_x_2 = V_y_2
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_eq__mem__trans,axiom,
% 50.63/50.75 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 50.63/50.75 ( V_a_2 = V_b_2
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pred__equals__eq,axiom,
% 50.63/50.75 ! [V_S_2,V_R_2,T_b] :
% 50.63/50.75 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
% 50.63/50.75 <=> V_R_2 = V_S_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_eq__mem,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 50.63/50.75 <=> V_x_2 = V_y_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_psubsetD,axiom,
% 50.63/50.75 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_bot__empty__eq,axiom,
% 50.63/50.75 ! [V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pred__equals__eq2,axiom,
% 50.63/50.75 ! [V_S_2,V_R_2,T_c,T_b] :
% 50.63/50.75 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
% 50.63/50.75 <=> V_R_2 = V_S_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_bot__empty__eq2,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_c,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pred__subset__eq,axiom,
% 50.63/50.75 ! [V_S_2,V_R_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_singleton__iff,axiom,
% 50.63/50.75 ! [V_a_2,V_b_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 50.63/50.75 <=> V_b_2 = V_a_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_singletonE,axiom,
% 50.63/50.75 ! [V_a_2,V_b_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 50.63/50.75 => V_b_2 = V_a_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__subset,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
% 50.63/50.75 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 50.63/50.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__insert,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 50.63/50.75 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__Diff__if,axiom,
% 50.63/50.75 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
% 50.63/50.75 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__Diff1,axiom,
% 50.63/50.75 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_elem__set,axiom,
% 50.63/50.75 ! [V_xo_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 50.63/50.75 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pred__subset__eq2,axiom,
% 50.63/50.75 ! [V_S_2,V_R_2,T_c,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Diff__insert__absorb,axiom,
% 50.63/50.75 ! [V_A_2,V_x_2,T_b] :
% 50.63/50.75 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_insert__Diff,axiom,
% 50.63/50.75 ! [V_A_2,V_a_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.75 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_diff__single__insert,axiom,
% 50.63/50.75 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__insert__iff,axiom,
% 50.63/50.75 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 50.63/50.75 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 50.63/50.75 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_in__rel__def,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 50.63/50.75 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.75 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
% 50.63/50.75 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Nitpick_Orefl_H__def,axiom,
% 50.63/50.75 ! [V_r_2,T_b] :
% 50.63/50.75 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 50.63/50.75 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_flat__lub__def,axiom,
% 50.63/50.75 ! [V_b_2,V_A_2,T_b] :
% 50.63/50.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 50.63/50.75 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 50.63/50.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 50.63/50.75 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_bot2E,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_less__by__empty,axiom,
% 50.63/50.75 ! [V_B_2,T_b,V_A_2] :
% 50.63/50.75 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 50.63/50.75 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 50.63/50.75 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_in__measure,axiom,
% 50.63/50.75 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
% 50.63/50.75 <=> 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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_mlex__leq,axiom,
% 50.63/50.75 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 50.63/50.75 ( 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)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_mlex__less,axiom,
% 50.63/50.75 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 50.63/50.75 ( 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)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Nats__number__of,axiom,
% 50.63/50.75 ! [V_w_2,T_b] :
% 50.63/50.75 ( class_Int_Onumber__ring(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Nats__0,axiom,
% 50.63/50.75 ! [T_b] :
% 50.63/50.75 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Nats__add,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Nats__mult,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Nats__1,axiom,
% 50.63/50.75 ! [T_b] :
% 50.63/50.75 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_of__nat__in__Nats,axiom,
% 50.63/50.75 ! [V_n_2,T_b] :
% 50.63/50.75 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__odd__less__0,axiom,
% 50.63/50.75 ! [V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Olinordered__idom(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 50.63/50.75 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 50.63/50.75 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
% 50.63/50.75 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.75 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 50.63/50.75 | ? [B_x,B_y] :
% 50.63/50.75 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 50.63/50.75 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 50.63/50.75 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_in__lex__prod,axiom,
% 50.63/50.75 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
% 50.63/50.75 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
% 50.63/50.75 | ( V_a_2 = V_a_H_2
% 50.63/50.75 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pair__lessI2,axiom,
% 50.63/50.75 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 50.63/50.75 => 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)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__0,axiom,
% 50.63/50.75 ! [T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__add,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__mult,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__diff,axiom,
% 50.63/50.75 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__number__of,axiom,
% 50.63/50.75 ! [V_w_2,T_b] :
% 50.63/50.75 ( class_Int_Onumber__ring(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__1,axiom,
% 50.63/50.75 ! [T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__minus,axiom,
% 50.63/50.75 ! [V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__power,axiom,
% 50.63/50.75 ! [V_n_2,V_a_2,T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__of__nat,axiom,
% 50.63/50.75 ! [V_n_2,T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__of__int,axiom,
% 50.63/50.75 ! [V_z_2,T_b] :
% 50.63/50.75 ( class_Rings_Oring__1(T_b)
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__double__eq__0__iff,axiom,
% 50.63/50.75 ! [V_a_2,T_b] :
% 50.63/50.75 ( class_Int_Oring__char__0(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 50.63/50.75 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pair__lessI1,axiom,
% 50.63/50.75 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Ints__odd__nonzero,axiom,
% 50.63/50.75 ! [V_a_2,T_b] :
% 50.63/50.75 ( class_Int_Oring__char__0(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 50.63/50.75 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_same__fstI,axiom,
% 50.63/50.75 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 50.63/50.75 ( hBOOL(hAPP(V_P_2,V_x_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pair__leqI2,axiom,
% 50.63/50.75 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 50.63/50.75 => 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)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_smax__insertI,axiom,
% 50.63/50.75 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => 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)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_smin__insertI,axiom,
% 50.63/50.75 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => 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)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_smin__emptyI,axiom,
% 50.63/50.75 ! [V_X_2] :
% 50.63/50.75 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_pair__leqI1,axiom,
% 50.63/50.75 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_wmin__insertI,axiom,
% 50.63/50.75 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => 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)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_wmax__insertI,axiom,
% 50.63/50.75 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => ( 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))
% 50.63/50.75 => 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)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_wmin__emptyI,axiom,
% 50.63/50.75 ! [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)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_min__strict__def,axiom,
% 50.63/50.75 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_min__weak__def,axiom,
% 50.63/50.75 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)))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_max__rpair__set,axiom,
% 50.63/50.75 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)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_min__rpair__set,axiom,
% 50.63/50.75 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)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_less__than__iff,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2] :
% 50.63/50.75 ( 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))
% 50.63/50.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup1E,axiom,
% 50.63/50.75 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 50.63/50.75 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 50.63/50.75 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup1CI,axiom,
% 50.63/50.75 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 50.63/50.75 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 50.63/50.75 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 50.63/50.75 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_UnCI,axiom,
% 50.63/50.75 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 50.63/50.75 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_UnE,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__empty,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.75 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.75 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__empty__right,axiom,
% 50.63/50.75 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__empty__left,axiom,
% 50.63/50.75 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__eq__bot__iff,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( class_Lattices_Obounded__lattice__bot(T_b)
% 50.63/50.75 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 50.63/50.75 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 50.63/50.75 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__bot__right,axiom,
% 50.63/50.75 ! [V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Obounded__lattice__bot(T_a)
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__bot__left,axiom,
% 50.63/50.75 ! [V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Obounded__lattice__bot(T_a)
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__upper1,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__upper2,axiom,
% 50.63/50.75 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_subset__Un__eq,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__absorb1,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__absorb2,axiom,
% 50.63/50.75 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__least,axiom,
% 50.63/50.75 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__mono,axiom,
% 50.63/50.75 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 50.63/50.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 50.63/50.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__sup__ord_I3_J,axiom,
% 50.63/50.75 ! [V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Olattice(T_a)
% 50.63/50.75 => 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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__ge1,axiom,
% 50.63/50.75 ! [V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__sup__ord_I4_J,axiom,
% 50.63/50.75 ! [V_x,V_y,T_a] :
% 50.63/50.75 ( class_Lattices_Olattice(T_a)
% 50.63/50.75 => 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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__ge2,axiom,
% 50.63/50.75 ! [V_x,V_y,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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))) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_le__iff__sup,axiom,
% 50.63/50.75 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.63/50.75 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_le__sup__iff,axiom,
% 50.63/50.75 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_b)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
% 50.63/50.75 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 50.63/50.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_le__supI1,axiom,
% 50.63/50.75 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 50.63/50.75 => 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))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_le__supI2,axiom,
% 50.63/50.75 ! [V_a,V_b,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 50.63/50.75 => 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))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__absorb2,axiom,
% 50.63/50.75 ! [V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__absorb1,axiom,
% 50.63/50.75 ! [V_x,V_y,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_le__supI,axiom,
% 50.63/50.75 ! [V_b,V_x,V_a,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 50.63/50.75 => 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)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__least,axiom,
% 50.63/50.75 ! [V_z,V_x,V_y,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 50.63/50.75 => 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)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__mono,axiom,
% 50.63/50.75 ! [V_d,V_b,V_c,V_a,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 50.63/50.75 => 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))) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_le__supE,axiom,
% 50.63/50.75 ! [V_x,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( 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))
% 50.63/50.75 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 50.63/50.75 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__Diff__cancel,axiom,
% 50.63/50.75 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__Diff__cancel2,axiom,
% 50.63/50.75 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Un__Diff,axiom,
% 50.63/50.75 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__max,axiom,
% 50.63/50.75 ! [T_b] :
% 50.63/50.75 ( ( class_Lattices_Osemilattice__sup(T_b)
% 50.63/50.75 & class_Orderings_Olinorder(T_b) )
% 50.63/50.75 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_Sup__fin_Oidem,axiom,
% 50.63/50.75 ! [V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Olattice(T_a)
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_less__supI1,axiom,
% 50.63/50.75 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 50.63/50.75 => 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))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_less__supI2,axiom,
% 50.63/50.75 ! [V_a,V_b,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 50.63/50.75 => 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))) ) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup_Oidem,axiom,
% 50.63/50.75 ! [V_a,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__idem,axiom,
% 50.63/50.75 ! [V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup_Ocommute,axiom,
% 50.63/50.75 ! [V_b,V_a,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__sup__aci_I5_J,axiom,
% 50.63/50.75 ! [V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Olattice(T_a)
% 50.63/50.75 => 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) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__commute,axiom,
% 50.63/50.75 ! [V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup_Oleft__idem,axiom,
% 50.63/50.75 ! [V_b,V_a,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__sup__aci_I8_J,axiom,
% 50.63/50.75 ! [V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Olattice(T_a)
% 50.63/50.75 => 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) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__left__idem,axiom,
% 50.63/50.75 ! [V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup_Oleft__commute,axiom,
% 50.63/50.75 ! [V_c,V_a,V_b,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__sup__aci_I7_J,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Olattice(T_a)
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__left__commute,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup_Oassoc,axiom,
% 50.63/50.75 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_inf__sup__aci_I6_J,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Olattice(T_a)
% 50.63/50.75 => 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)) ) ).
% 50.63/50.75
% 50.63/50.75 fof(fact_sup__assoc,axiom,
% 50.63/50.75 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.75 ( class_Lattices_Osemilattice__sup(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__apply,axiom,
% 50.63/50.76 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__absorb,axiom,
% 50.63/50.76 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__commute,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__left__absorb,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__left__commute,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__assoc,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_bex__Un,axiom,
% 50.63/50.76 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( ? [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 & hBOOL(hAPP(V_P_2,B_x)) )
% 50.63/50.76 <=> ( ? [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.76 & hBOOL(hAPP(V_P_2,B_x)) )
% 50.63/50.76 | ? [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 50.63/50.76 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ball__Un,axiom,
% 50.63/50.76 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 => hBOOL(hAPP(V_P_2,B_x)) )
% 50.63/50.76 <=> ( ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(V_P_2,B_x)) )
% 50.63/50.76 & ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 50.63/50.76 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__fun__def,axiom,
% 50.63/50.76 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup1I1,axiom,
% 50.63/50.76 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 50.63/50.76 ( hBOOL(hAPP(V_A_2,V_x_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup1I2,axiom,
% 50.63/50.76 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 50.63/50.76 ( hBOOL(hAPP(V_B_2,V_x_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__insert__left,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__insert__right,axiom,
% 50.63/50.76 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__iff,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.76 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_UnI1,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_UnI2,axiom,
% 50.63/50.76 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__Un__eq,axiom,
% 50.63/50.76 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_insert__is__Un,axiom,
% 50.63/50.76 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__partition,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__subset__conv,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Compl__Diff__eq,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_pair__less__def,axiom,
% 50.63/50.76 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_max__weak__def,axiom,
% 50.63/50.76 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)))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_mlex__prod__def,axiom,
% 50.63/50.76 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_intrel__iff,axiom,
% 50.63/50.76 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 50.63/50.76 ( 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))
% 50.63/50.76 <=> 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_rp__inv__image__rp,axiom,
% 50.63/50.76 ! [V_f_2,T_c,V_P_2,T_b] :
% 50.63/50.76 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 50.63/50.76 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__nat__def,axiom,
% 50.63/50.76 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_rp__inv__image__def,axiom,
% 50.63/50.76 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__Un__eq2,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_max__strict__def,axiom,
% 50.63/50.76 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_max__ext__additive,axiom,
% 50.63/50.76 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_max__extp__max__ext__eq,axiom,
% 50.63/50.76 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 50.63/50.76 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_in__inv__image,axiom,
% 50.63/50.76 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Body1,axiom,
% 50.63/50.76 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),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_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),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))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 50.63/50.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(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_b),tc_HOL_Obool)))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_equiv__intrel__iff,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2] :
% 50.63/50.76 ( 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))))
% 50.63/50.76 <=> 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup2E,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 50.63/50.76 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup2CI,axiom,
% 50.63/50.76 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 50.63/50.76 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 50.63/50.76 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__eqI,axiom,
% 50.63/50.76 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 50.63/50.76 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Image__Un,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__Un,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup2I1,axiom,
% 50.63/50.76 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup2I2,axiom,
% 50.63/50.76 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_subset__image__iff,axiom,
% 50.63/50.76 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 50.63/50.76 <=> ? [B_AA] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 50.63/50.76 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__mono,axiom,
% 50.63/50.76 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__image,axiom,
% 50.63/50.76 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__iff,axiom,
% 50.63/50.76 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 50.63/50.76 <=> ? [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.76 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_imageI,axiom,
% 50.63/50.76 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_rev__image__eqI,axiom,
% 50.63/50.76 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__insert,axiom,
% 50.63/50.76 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Image__empty,axiom,
% 50.63/50.76 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_empty__is__image,axiom,
% 50.63/50.76 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
% 50.63/50.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__empty,axiom,
% 50.63/50.76 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__is__empty,axiom,
% 50.63/50.76 ! [V_A_2,V_f_2,T_b,T_c] :
% 50.63/50.76 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Image__mono,axiom,
% 50.63/50.76 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__Image,axiom,
% 50.63/50.76 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_insert__image,axiom,
% 50.63/50.76 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__diff__subset,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Image__iff,axiom,
% 50.63/50.76 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 50.63/50.76 <=> ? [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_rev__ImageI,axiom,
% 50.63/50.76 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__constant__conv,axiom,
% 50.63/50.76 ! [V_c_2,T_c,T_b,V_A_2] :
% 50.63/50.76 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.76 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__constant,axiom,
% 50.63/50.76 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Image__singleton__iff,axiom,
% 50.63/50.76 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_measure__def,axiom,
% 50.63/50.76 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_hoare__derivs_OBody,axiom,
% 50.63/50.76 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),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_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),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))
% 50.63/50.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Body__sound__lemma,axiom,
% 50.63/50.76 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 50.63/50.76 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_Ga_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),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_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),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))
% 50.63/50.76 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(tc_Com_Opname,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))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_of__int,axiom,
% 50.63/50.76 ! [V_j_2,V_i_2,T_b] :
% 50.63/50.76 ( class_Rings_Oring__1(T_b)
% 50.63/50.76 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_One__int__def,axiom,
% 50.63/50.76 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))))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_mult,axiom,
% 50.63/50.76 ! [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))))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_pair__imageI,axiom,
% 50.63/50.76 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 <=> 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))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 <=> 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))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( V_A_2 = V_B_2
% 50.63/50.76 <=> 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 50.63/50.76 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 50.63/50.76 ! [V_A_2,V_x_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 50.63/50.76 <=> 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))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 50.63/50.76 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))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 50.63/50.76 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_minus,axiom,
% 50.63/50.76 ! [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))))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Zero__int__def,axiom,
% 50.63/50.76 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))))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_int__def,axiom,
% 50.63/50.76 ! [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))))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_add,axiom,
% 50.63/50.76 ! [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))))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_nat,axiom,
% 50.63/50.76 ! [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) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_less,axiom,
% 50.63/50.76 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 50.63/50.76 ( 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)))))))
% 50.63/50.76 <=> 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))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_le,axiom,
% 50.63/50.76 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 50.63/50.76 ( 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)))))))
% 50.63/50.76 <=> 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))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_irrefl__def,axiom,
% 50.63/50.76 ! [V_r_2,T_b] :
% 50.63/50.76 ( c_Relation_Oirrefl(T_b,V_r_2)
% 50.63/50.76 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_eq__Abs__Integ,axiom,
% 50.63/50.76 ! [V_z_2] :
% 50.63/50.76 ~ ! [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))))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Field__insert,axiom,
% 50.63/50.76 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ImageE,axiom,
% 50.63/50.76 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 50.63/50.76 => ~ ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
% 50.63/50.76 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Field__empty,axiom,
% 50.63/50.76 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_mono__Field,axiom,
% 50.63/50.76 ! [V_s_2,V_r_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Field__Un,axiom,
% 50.63/50.76 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 50.63/50.76 ! [V_A_2,V_x_2] :
% 50.63/50.76 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 50.63/50.76 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.76 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_nat__set__def,axiom,
% 50.63/50.76 ! [V_S_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_S_2)
% 50.63/50.76 <=> ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 50.63/50.76 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.76 => ( V_A_2 = V_B_2
% 50.63/50.76 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 50.63/50.76 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 50.63/50.76 ! [V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_subset__equiv__class,axiom,
% 50.63/50.76 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_accp__acc__eq,axiom,
% 50.63/50.76 ! [V_x_2,V_r_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_wmax__emptyI,axiom,
% 50.63/50.76 ! [V_X_2] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_smax__emptyI,axiom,
% 50.63/50.76 ! [V_Y_2] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 50.63/50.76 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 50.63/50.76 => 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)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__Field,axiom,
% 50.63/50.76 ! [V_r_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_acc__subset,axiom,
% 50.63/50.76 ! [V_R2_2,V_R1_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_equiv__class__self,axiom,
% 50.63/50.76 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_acc_Osimps,axiom,
% 50.63/50.76 ! [V_r_2,V_a_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 50.63/50.76 <=> ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_acc__downward,axiom,
% 50.63/50.76 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_equiv__class__eq,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 50.63/50.76 => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_eq__equiv__class,axiom,
% 50.63/50.76 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 50.63/50.76 ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.76 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_eq__equiv__class__iff,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 50.63/50.76 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_equiv__class__eq__iff,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 50.63/50.76 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_equiv__class__subset,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__Diff,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__imageI,axiom,
% 50.63/50.76 ! [V_h_2,T_c,V_F_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite_OinsertI,axiom,
% 50.63/50.76 ! [V_a_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite_OemptyI,axiom,
% 50.63/50.76 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 50.63/50.76 ! [V_A_2] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 50.63/50.76 <=> 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))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 50.63/50.76 ! [V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 50.63/50.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Finite__Set_Ofinite(T_b)
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__code,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Finite__Set_Ofinite(T_b)
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite_Oequations_I1_J,axiom,
% 50.63/50.76 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__insert,axiom,
% 50.63/50.76 ! [V_A_2,V_a_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 50.63/50.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__subset,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_rev__finite__subset,axiom,
% 50.63/50.76 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__Un,axiom,
% 50.63/50.76 ! [V_Ga_2,V_F_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.76 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__UnI,axiom,
% 50.63/50.76 ! [V_Ga_2,V_F_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__Diff2,axiom,
% 50.63/50.76 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__surj,axiom,
% 50.63/50.76 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__Diff__insert,axiom,
% 50.63/50.76 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
% 50.63/50.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_in__finite__psubset,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__pointwise,axiom,
% 50.63/50.76 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 50.63/50.76 => ( ! [B_p] :
% 50.63/50.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
% 50.63/50.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
% 50.63/50.76 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
% 50.63/50.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__one_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__image__simple_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__image__simple_Oempty,axiom,
% 50.63/50.76 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.76 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__one_Osingleton,axiom,
% 50.63/50.76 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__image__simple_Oinsert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__one_Oinsert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__one_Oinsert__remove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 50.63/50.76 ! [V_N_2] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 50.63/50.76 <=> ? [B_m] :
% 50.63/50.76 ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__nat__set__iff__bounded,axiom,
% 50.63/50.76 ! [V_N_2] :
% 50.63/50.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 50.63/50.76 <=> ? [B_m] :
% 50.63/50.76 ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_eq__equiv__class__iff2,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 50.63/50.76 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_equiv__class__nondisjoint,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf1E,axiom,
% 50.63/50.76 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 50.63/50.76 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 50.63/50.76 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf1I,axiom,
% 50.63/50.76 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 50.63/50.76 ( hBOOL(hAPP(V_A_2,V_x_2))
% 50.63/50.76 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_IntI,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_IntE,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.76 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_finite__Int,axiom,
% 50.63/50.76 ! [V_Ga_2,V_F_2,T_b] :
% 50.63/50.76 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.76 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 50.63/50.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotient__disj,axiom,
% 50.63/50.76 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.76 => ( V_X_2 = V_Y_2
% 50.63/50.76 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotient__empty,axiom,
% 50.63/50.76 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotient__is__empty2,axiom,
% 50.63/50.76 ! [V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
% 50.63/50.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotient__is__empty,axiom,
% 50.63/50.76 ! [V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 50.63/50.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__Int__eq,axiom,
% 50.63/50.76 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__lower1,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__lower2,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__absorb2,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__absorb1,axiom,
% 50.63/50.76 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__greatest,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__mono,axiom,
% 50.63/50.76 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__ord_I1_J,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__le1,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__ord_I2_J,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__le2,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_le__iff__inf,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.63/50.76 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_le__inf__iff,axiom,
% 50.63/50.76 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_le__infI1,axiom,
% 50.63/50.76 ! [V_b,V_x,V_a,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 50.63/50.76 => 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)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_le__infI2,axiom,
% 50.63/50.76 ! [V_a,V_x,V_b,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 50.63/50.76 => 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)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__absorb1,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__absorb2,axiom,
% 50.63/50.76 ! [V_x,V_y,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_le__infI,axiom,
% 50.63/50.76 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 50.63/50.76 => 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))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__greatest,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 50.63/50.76 => 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))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__mono,axiom,
% 50.63/50.76 ! [V_d,V_b,V_c,V_a,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 50.63/50.76 => 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))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_le__infE,axiom,
% 50.63/50.76 ! [V_b,V_a,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( 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)))
% 50.63/50.76 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 50.63/50.76 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_less__infI1,axiom,
% 50.63/50.76 ! [V_b,V_x,V_a,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 50.63/50.76 => 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)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_less__infI2,axiom,
% 50.63/50.76 ! [V_a,V_x,V_b,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 50.63/50.76 => 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)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_insert__inter__insert,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__bot__left,axiom,
% 50.63/50.76 ! [V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Obounded__lattice__bot(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__bot__right,axiom,
% 50.63/50.76 ! [V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Obounded__lattice__bot(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__empty__left,axiom,
% 50.63/50.76 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__empty__right,axiom,
% 50.63/50.76 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_disjoint__iff__not__equal,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 <=> ! [B_x] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.76 => ! [B_xa] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 50.63/50.76 => B_x != B_xa ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_IntD2,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_IntD1,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__iff,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__Int__crazy,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__Int__distrib2,axiom,
% 50.63/50.76 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__Un__distrib2,axiom,
% 50.63/50.76 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__Int__distrib,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__Un__distrib,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__inf__distrib2,axiom,
% 50.63/50.76 ! [V_x,V_z,V_y,T_a] :
% 50.63/50.76 ( class_Lattices_Odistrib__lattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__distrib2,axiom,
% 50.63/50.76 ! [V_x,V_z,V_y,T_a] :
% 50.63/50.76 ( class_Lattices_Odistrib__lattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__inf__distrib1,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Odistrib__lattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__distrib1,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Odistrib__lattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__inf__absorb,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__absorb,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf1D2,axiom,
% 50.63/50.76 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 50.63/50.76 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf1D1,axiom,
% 50.63/50.76 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 50.63/50.76 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__Int2,axiom,
% 50.63/50.76 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__Int__distrib2,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__Diff,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__Int__distrib,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__min,axiom,
% 50.63/50.76 ! [T_b] :
% 50.63/50.76 ( ( class_Lattices_Osemilattice__inf(T_b)
% 50.63/50.76 & class_Orderings_Olinorder(T_b) )
% 50.63/50.76 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__fun__def,axiom,
% 50.63/50.76 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__assoc,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__left__commute,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__left__absorb,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__commute,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__absorb,axiom,
% 50.63/50.76 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__apply,axiom,
% 50.63/50.76 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__assoc,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__aci_I2_J,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf_Oassoc,axiom,
% 50.63/50.76 ! [V_c,V_b,V_a,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__left__commute,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__aci_I3_J,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf_Oleft__commute,axiom,
% 50.63/50.76 ! [V_c,V_a,V_b,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__left__idem,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__aci_I4_J,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf_Oleft__idem,axiom,
% 50.63/50.76 ! [V_b,V_a,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__commute,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__sup__aci_I1_J,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf_Ocommute,axiom,
% 50.63/50.76 ! [V_b,V_a,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__idem,axiom,
% 50.63/50.76 ! [V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf_Oidem,axiom,
% 50.63/50.76 ! [V_a,T_a] :
% 50.63/50.76 ( class_Lattices_Osemilattice__inf(T_a)
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Oidem,axiom,
% 50.63/50.76 ! [V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.76 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_distrib__inf__le,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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)))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_distrib__sup__le,axiom,
% 50.63/50.76 ! [V_z,V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Olattice(T_a)
% 50.63/50.76 => 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)))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_compl__inf__bot,axiom,
% 50.63/50.76 ! [V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__compl__bot,axiom,
% 50.63/50.76 ! [V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.76 => 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) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_diff__eq,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_compl__sup,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_compl__inf,axiom,
% 50.63/50.76 ! [V_y,V_x,T_a] :
% 50.63/50.76 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.76 => 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)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__insert__left__if1,axiom,
% 50.63/50.76 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__insert__right__if1,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__insert__left__if0,axiom,
% 50.63/50.76 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 50.63/50.76 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__insert__right__if0,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 50.63/50.76 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__insert__left,axiom,
% 50.63/50.76 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 50.63/50.76 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) )
% 50.63/50.76 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Int__insert__right,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 50.63/50.76 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 50.63/50.76 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_image__Int__subset,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__triv,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__disjoint,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__Int__assoc__eq,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Un__Diff__Int,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__Un,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__Int,axiom,
% 50.63/50.76 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Compl__disjoint2,axiom,
% 50.63/50.76 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Compl__disjoint,axiom,
% 50.63/50.76 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Image__Int__subset,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Compl__Un,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Compl__Int,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__Compl,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Diff__eq,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2] :
% 50.63/50.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_disjoint__eq__subset__Compl,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.76 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_singleton__quotient,axiom,
% 50.63/50.76 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__one_Ounion__inter,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => 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)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__one_Ounion__disjoint,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 50.63/50.76 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotientI,axiom,
% 50.63/50.76 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotient__eq__iff,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 50.63/50.76 => ( V_X_2 = V_Y_2
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotient__eqI,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 50.63/50.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 50.63/50.76 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 50.63/50.76 ! [V_k_2,V_l_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 50.63/50.76 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OlessThan__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_i_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OgreaterThan__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_i_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatMost__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_i_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__nat__def,axiom,
% 50.63/50.76 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__Int__eq2,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 50.63/50.76 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OgreaterThan__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OlessThan__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OatMost__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeast__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_i_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_quotientE,axiom,
% 50.63/50.76 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.76 => ~ ! [B_x] :
% 50.63/50.76 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.76 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 50.63/50.76 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 50.63/50.76 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf2E,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 50.63/50.76 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 50.63/50.76 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf2I,axiom,
% 50.63/50.76 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf2D2,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf2D1,axiom,
% 50.63/50.76 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2] :
% 50.63/50.76 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 50.63/50.76 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 50.63/50.76 ! [V_l_2,V_k_2] :
% 50.63/50.76 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 50.63/50.76 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2] :
% 50.63/50.76 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 50.63/50.76 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 50.63/50.76 ! [V_l_2,V_k_2] :
% 50.63/50.76 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 50.63/50.76 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 50.63/50.76 ! [V_a_2,V_b_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 50.63/50.76 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 50.63/50.76 ! [V_k_2,V_l_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 50.63/50.76 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OatLeast__iff,axiom,
% 50.63/50.76 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 50.63/50.76 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 50.63/50.76 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
% 50.63/50.76 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__le__Sup,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Osingleton,axiom,
% 50.63/50.76 ! [V_x_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Osingleton,axiom,
% 50.63/50.76 ! [V_x_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Osingleton,axiom,
% 50.63/50.76 ! [V_x_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max__ge,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max__in,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_sup__Inf__absorb,axiom,
% 50.63/50.76 ! [V_a_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Oin__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Oin__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_inf__Sup__absorb,axiom,
% 50.63/50.76 ! [V_a_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Oin__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2] :
% 50.63/50.76 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 50.63/50.76 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2] :
% 50.63/50.76 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 50.63/50.76 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 50.63/50.76 ! [V_a_2,V_b_2] :
% 50.63/50.76 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 50.63/50.76 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 50.63/50.76 ! [V_b_2,V_a_2] :
% 50.63/50.76 ( V_a_2 = V_b_2
% 50.63/50.76 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 50.63/50.76 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 50.63/50.76 ! [V_c_2,V_b_2,V_a_2] :
% 50.63/50.76 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 50.63/50.76 <=> ( V_a_2 = V_b_2
% 50.63/50.76 & V_b_2 = V_c_2 ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max__mono,axiom,
% 50.63/50.76 ! [V_N_2,V_M_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 50.63/50.76 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max__insert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Osubset__idem,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Osubset__idem,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Ounion__idem,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Osubset__idem,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Ounion__idem,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max__Un,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 50.63/50.76 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 50.63/50.76 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.76 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 50.63/50.76 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 50.63/50.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 50.63/50.76 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 50.63/50.76 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 50.63/50.76 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) )
% 50.63/50.76 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 50.63/50.76 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 50.63/50.76 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Oinsert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Oinsert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Oinsert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Ounion__inter,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Oinsert__remove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Ounion__inter,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Ounion__inter,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Ounion__disjoint,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Max_Oclosed,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Inf__fin_Oclosed,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Sup__fin_Oclosed,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Lattices_Olattice(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Osingleton,axiom,
% 50.63/50.76 ! [V_x_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min__le,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min__in,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Oin__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min__antimono,axiom,
% 50.63/50.76 ! [V_N_2,V_M_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 50.63/50.76 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min__insert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Osubset__idem,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min__Un,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Oinsert,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Oinsert__remove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Ounion__inter,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Ounion__disjoint,axiom,
% 50.63/50.76 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_minus__Max__eq__Min,axiom,
% 50.63/50.76 ! [V_S_2,T_b] :
% 50.63/50.76 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.76 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_minus__Min__eq__Max,axiom,
% 50.63/50.76 ! [V_S_2,T_b] :
% 50.63/50.76 ( class_Groups_Olinordered__ab__group__add(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.76 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_Min_Oclosed,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 50.63/50.76 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_folding__one_Oclosed,axiom,
% 50.63/50.76 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.76 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OInf__le__Sup,axiom,
% 50.63/50.76 ! [V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 50.63/50.76 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 50.63/50.76 ! [V_x_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 50.63/50.76 ! [V_x_2,T_b] :
% 50.63/50.76 ( class_Orderings_Olinorder(T_b)
% 50.63/50.76 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 50.63/50.76
% 50.63/50.76 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 50.63/50.77 ! [V_a_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 50.63/50.77 ! [V_a_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 50.63/50.77 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 50.63/50.77 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff__singleton__if,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff__singleton,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 50.63/50.77 ! [V_A_2] :
% 50.63/50.77 ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.77 => 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)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card_Oempty,axiom,
% 50.63/50.77 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__infinite,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__eq__0__iff,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.77 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__ge__0__finite,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 50.63/50.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__insert__le,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__seteq,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 50.63/50.77 => V_A_2 = V_B_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__mono,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__image__le,axiom,
% 50.63/50.77 ! [V_f_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_psubset__card__mono,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__insert__disjoint,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__insert__if,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__gt__0__iff,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 50.63/50.77 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card_Ounion__inter,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Un__Int,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff__subset,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff__subset__Int,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_diff__card__le__card__Diff,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__psubset,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__insert,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Un__disjoint,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff1__le,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card_Oinsert,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Suc__Diff1,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff1__less,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff2__less,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Diff__insert,axiom,
% 50.63/50.77 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card_Oinsert__remove,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card_Oremove,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card_Ounion__inter__neutral,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.77 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Suc__eq,axiom,
% 50.63/50.77 ! [V_k_2,V_A_2,T_b] :
% 50.63/50.77 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 50.63/50.77 <=> ? [B_b,B_B] :
% 50.63/50.77 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 50.63/50.77 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 50.63/50.77 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 50.63/50.77 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.77 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_equiv__imp__dvd__card,axiom,
% 50.63/50.77 ! [V_k_2,V_r_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Plus__conv__if,axiom,
% 50.63/50.77 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) )
% 50.63/50.77 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__Plus__iff,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 50.63/50.77 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__Plus,axiom,
% 50.63/50.77 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__PlusD_I1_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 50.63/50.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__PlusD_I2_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 50.63/50.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Plus,axiom,
% 50.63/50.77 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Plus__eq__empty__conv,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
% 50.63/50.77 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__greaterThanLessThan__int,axiom,
% 50.63/50.77 ! [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)))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__gen__delta,axiom,
% 50.63/50.77 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__greaterThanLessThan__int,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_b] :
% 50.63/50.77 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.77 & class_Groups_Ocomm__monoid__mult(T_b) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_of__int__setprod,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 50.63/50.77 & class_Rings_Oring__1(T_b) )
% 50.63/50.77 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_of__nat__setprod,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 50.63/50.77 & class_Rings_Osemiring__1(T_b) )
% 50.63/50.77 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_int__setprod,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__timesf,axiom,
% 50.63/50.77 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__1,axiom,
% 50.63/50.77 ! [V_A_2,T_c,T_b] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_abs__setprod,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( class_Fields_Olinordered__field(T_b)
% 50.63/50.77 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__zero,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Rings_Ocomm__semiring__1(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ? [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__zero__iff,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 50.63/50.77 & class_Rings_Ono__zero__divisors(T_c) )
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__empty,axiom,
% 50.63/50.77 ! [V_f_2,T_c,T_b] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Oempty,axiom,
% 50.63/50.77 ! [V_g_2,T_c,T_b] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__infinite,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Oinfinite,axiom,
% 50.63/50.77 ! [V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__eq__1__iff,axiom,
% 50.63/50.77 ! [V_f_2,V_F_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.77 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 50.63/50.77 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.77 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.77 & class_Groups_Ocomm__monoid__mult(T_b) )
% 50.63/50.77 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Odistrib,axiom,
% 50.63/50.77 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__dividef,axiom,
% 50.63/50.77 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Fields_Ofield__inverse__zero(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_dvd__setprod,axiom,
% 50.63/50.77 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Rings_Ocomm__semiring__1(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__pos__nat__iff,axiom,
% 50.63/50.77 ! [V_f_2,V_S_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 50.63/50.77 => 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))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__dvd__setprod__subset,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 50.63/50.77 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 & class_Rings_Odvd(T_c) )
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_greaterThanLessThan__empty,axiom,
% 50.63/50.77 ! [V_k_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 50.63/50.77 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.77 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__delta_H,axiom,
% 50.63/50.77 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__delta,axiom,
% 50.63/50.77 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__constant,axiom,
% 50.63/50.77 ! [V_y_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__insert,axiom,
% 50.63/50.77 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Oinsert,axiom,
% 50.63/50.77 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Ounion__inter,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__Un__Int,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Int__greaterThanLessThan,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Oinsert__remove,axiom,
% 50.63/50.77 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Ounion__disjoint,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__Un__disjoint,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Oremove,axiom,
% 50.63/50.77 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__diff1,axiom,
% 50.63/50.77 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Fields_Ofield(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 50.63/50.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__Un,axiom,
% 50.63/50.77 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Fields_Ofield(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__Un__one,axiom,
% 50.63/50.77 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 50.63/50.77 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__greaterThanLessThan,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__greaterThanLessThan,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.77 ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I4_J,axiom,
% 50.63/50.77 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_quotient__def,axiom,
% 50.63/50.77 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__greaterThanAtMost,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__greaterThanAtMost__int,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP1__I,axiom,
% 50.63/50.77 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP1__iff,axiom,
% 50.63/50.77 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Image__UN,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__UN,axiom,
% 50.63/50.77 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_greaterThanAtMost__empty,axiom,
% 50.63/50.77 ! [V_k_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 50.63/50.77 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 50.63/50.77 ! [V_l_2,V_k_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
% 50.63/50.77 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 50.63/50.77 ! [V_l_2,V_k_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I20_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I14_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__greaterThanAtMost,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Image__eq__UN,axiom,
% 50.63/50.77 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Int__greaterThanAtMost,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I10_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__greaterThanAtMost__int,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I16_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__I,axiom,
% 50.63/50.77 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__eq__UN,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__equiv__class2,axiom,
% 50.63/50.77 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 50.63/50.77 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 50.63/50.77 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ball__UN,axiom,
% 50.63/50.77 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.77 => hBOOL(hAPP(V_P_2,B_x)) )
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.77 => ! [B_xa] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 50.63/50.77 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP__commute,axiom,
% 50.63/50.77 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 50.63/50.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__UN__flatten,axiom,
% 50.63/50.77 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I9_J,axiom,
% 50.63/50.77 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I9_J,axiom,
% 50.63/50.77 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_congruent2D,axiom,
% 50.63/50.77 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
% 50.63/50.77 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP__le__iff,axiom,
% 50.63/50.77 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_less__SUP__iff,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 50.63/50.77 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 50.63/50.77 & class_Orderings_Olinorder(T_b) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__iff,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP__const,axiom,
% 50.63/50.77 ! [V_M_2,T_b,V_A_2,T_c] :
% 50.63/50.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 50.63/50.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UNION__empty__conv_I1_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.77 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.77 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__empty2,axiom,
% 50.63/50.77 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__constant,axiom,
% 50.63/50.77 ! [V_c_2,T_c,T_b,V_A_2] :
% 50.63/50.77 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.77 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UNION__empty__conv_I2_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.77 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__subset__iff,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I10_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__UN,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I10_J,axiom,
% 50.63/50.77 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__Un,axiom,
% 50.63/50.77 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__Un__distrib,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I5_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I4_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I5_J,axiom,
% 50.63/50.77 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Int__UN__distrib,axiom,
% 50.63/50.77 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I4_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Int__UN__distrib2,axiom,
% 50.63/50.77 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUPR__apply,axiom,
% 50.63/50.77 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 50.63/50.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 50.63/50.77 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I6_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I6_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP__subset,axiom,
% 50.63/50.77 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_le__SUPI,axiom,
% 50.63/50.77 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 50.63/50.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__insert__distrib,axiom,
% 50.63/50.77 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__upper,axiom,
% 50.63/50.77 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__absorb,axiom,
% 50.63/50.77 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I1_J,axiom,
% 50.63/50.77 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 50.63/50.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
% 50.63/50.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__singleton,axiom,
% 50.63/50.77 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I1_J,axiom,
% 50.63/50.77 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 50.63/50.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I2_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 50.63/50.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 50.63/50.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__extend__simps_I3_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 50.63/50.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 50.63/50.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I2_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 50.63/50.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__simps_I3_J,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 50.63/50.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__insert,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_congruent2__implies__congruent__UN,axiom,
% 50.63/50.77 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 50.63/50.77 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 50.63/50.77 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 50.63/50.77 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_minus__int__def,axiom,
% 50.63/50.77 ! [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))))))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__equiv__class,axiom,
% 50.63/50.77 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.77 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP2__I,axiom,
% 50.63/50.77 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Rep__Integ__inject,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2] :
% 50.63/50.77 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 50.63/50.77 <=> V_x_2 = V_y_2 ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Rep__Integ__inverse,axiom,
% 50.63/50.77 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 50.63/50.77
% 50.63/50.77 fof(fact_congruentD,axiom,
% 50.63/50.77 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
% 50.63/50.77 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_nat__def,axiom,
% 50.63/50.77 ! [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)))))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_congruent2__implies__congruent,axiom,
% 50.63/50.77 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 50.63/50.77 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__equiv__class__inject,axiom,
% 50.63/50.77 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.77 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 50.63/50.77 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 => ! [B_y] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 50.63/50.77 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
% 50.63/50.77 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__equiv__class__type2,axiom,
% 50.63/50.77 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 50.63/50.77 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 50.63/50.77 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
% 50.63/50.77 => ( ! [B_x1] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 50.63/50.77 => ! [B_x2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__equiv__class__type,axiom,
% 50.63/50.77 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 50.63/50.77 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.77 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SUP2__iff,axiom,
% 50.63/50.77 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Id__on__def,axiom,
% 50.63/50.77 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fold__Un__disjoint,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 50.63/50.77 ! [V_N_2,V_h_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fold__image__empty,axiom,
% 50.63/50.77 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Id__on__def_H,axiom,
% 50.63/50.77 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 50.63/50.77 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.77 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Id__on__empty,axiom,
% 50.63/50.77 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Image__Id__on,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fold__image__distrib,axiom,
% 50.63/50.77 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fold__image__insert,axiom,
% 50.63/50.77 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Oab__semigroup__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_OF__eq,axiom,
% 50.63/50.77 ! [V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod_Oeq__fold,axiom,
% 50.63/50.77 ! [V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Id__on__eqI,axiom,
% 50.63/50.77 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 50.63/50.77 ( V_a_2 = V_b_2
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Id__on__iff,axiom,
% 50.63/50.77 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
% 50.63/50.77 <=> ( V_x_2 = V_y_2
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fold__image__Un__Int,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__eq__fold__image,axiom,
% 50.63/50.77 ! [V_f_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__def,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card_Oeq__fold__g,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_comm__monoid__big_OF__eq,axiom,
% 50.63/50.77 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 50.63/50.77 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.77 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.77 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fold__image__Un__one,axiom,
% 50.63/50.77 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 50.63/50.77 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 50.63/50.77 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Id__onE,axiom,
% 50.63/50.77 ! [V_A_2,V_c_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 50.63/50.77 => ~ ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 50.63/50.77 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 50.63/50.77 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.77 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 50.63/50.77 ! [V_N_2,V_h_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Max_Ohom__commute,axiom,
% 50.63/50.77 ! [V_N_2,V_h_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Min_Ohom__commute,axiom,
% 50.63/50.77 ! [V_N_2,V_h_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Inf__fin_Ohom__commute,axiom,
% 50.63/50.77 ! [V_N_2,V_h_2,T_b] :
% 50.63/50.77 ( class_Lattices_Olattice(T_b)
% 50.63/50.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Sup__fin_Ohom__commute,axiom,
% 50.63/50.77 ! [V_N_2,V_h_2,T_b] :
% 50.63/50.77 ( class_Lattices_Olattice(T_b)
% 50.63/50.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__mono__one__right,axiom,
% 50.63/50.77 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 50.63/50.77 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_setprod__mono__one__left,axiom,
% 50.63/50.77 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 50.63/50.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 50.63/50.77 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 50.63/50.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__Pow,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__empty__induct,axiom,
% 50.63/50.77 ! [V_P_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 50.63/50.77 => ( ! [B_a,B_A] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 50.63/50.77 => ( hBOOL(hAPP(V_P_2,B_A))
% 50.63/50.77 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 50.63/50.77 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_PowI,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__top,axiom,
% 50.63/50.77 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__Pow__surj,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 50.63/50.77 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 50.63/50.77 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__mono,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Un__Pow__subset,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__Int__eq,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__insert,axiom,
% 50.63/50.77 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__Pow__iff,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 50.63/50.77 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__not__empty,axiom,
% 50.63/50.77 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__bottom,axiom,
% 50.63/50.77 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__Pow__mono,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_PowD,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__iff,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 50.63/50.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_UN__Pow__subset,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Pow__empty,axiom,
% 50.63/50.77 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Powp__Pow__eq,axiom,
% 50.63/50.77 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 50.63/50.77 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__quotient__disjoint,axiom,
% 50.63/50.77 ! [V_r_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I19_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__atLeastAtMost,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__atLeastAtMost__int,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__Suc__atLeastAtMost,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__add__atLeastAtMost,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__imageD,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 50.63/50.77 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 50.63/50.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__image,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 50.63/50.77 ! [V_n_2,V_m_2] :
% 50.63/50.77 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 50.63/50.77 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 50.63/50.77 => 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))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2] :
% 50.63/50.77 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 50.63/50.77 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastatMost__empty__iff2,axiom,
% 50.63/50.77 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
% 50.63/50.77 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastatMost__empty__iff,axiom,
% 50.63/50.77 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastatMost__empty,axiom,
% 50.63/50.77 ! [V_a_2,V_b_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 50.63/50.77 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastatMost__subset__iff,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 50.63/50.77 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 50.63/50.77 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastAtMost__singleton_H,axiom,
% 50.63/50.77 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( V_a_2 = V_b_2
% 50.63/50.77 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 50.63/50.77 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.77 <=> ( V_a_2 = V_b_2
% 50.63/50.77 & V_b_2 = V_c_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastAtMost__singleton,axiom,
% 50.63/50.77 ! [V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__uminus__atLeastAtMost,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.77 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__surj__inj,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
% 50.63/50.77 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_endo__inj__surj,axiom,
% 50.63/50.77 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
% 50.63/50.77 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_eq__card__imp__inj__on,axiom,
% 50.63/50.77 ! [V_f_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
% 50.63/50.77 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__iff__eq__card,axiom,
% 50.63/50.77 ! [V_f_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_pigeonhole,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
% 50.63/50.77 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 50.63/50.77 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__atLeastAtMost,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastAtMostSuc__conv,axiom,
% 50.63/50.77 ! [V_n_2,V_m_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 50.63/50.77 => 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)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Powp__mono,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__bij__eq,axiom,
% 50.63/50.77 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 50.63/50.77 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Int__atLeastAtMost,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastatMost__psubset__iff,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 50.63/50.77 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 50.63/50.77 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 50.63/50.77 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 50.63/50.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I22_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I16_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I13_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I12_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_simp__from__to,axiom,
% 50.63/50.77 ! [V_i_2,V_j_2] :
% 50.63/50.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 50.63/50.77 => 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)) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 50.63/50.77 => 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)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__inj__on__le,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__iff__card__le,axiom,
% 50.63/50.77 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.77 => ( ? [B_f] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) )
% 50.63/50.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_quotient__diff1,axiom,
% 50.63/50.77 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.77 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__atLeastAtMost__int,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I5_J,axiom,
% 50.63/50.77 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__Un,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 50.63/50.77 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__insert,axiom,
% 50.63/50.77 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 50.63/50.77 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__uminus,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.77 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__empty,axiom,
% 50.63/50.77 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__Suc,axiom,
% 50.63/50.77 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__Some,axiom,
% 50.63/50.77 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__add__nat,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_swap__inj__on,axiom,
% 50.63/50.77 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__def,axiom,
% 50.63/50.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.77 => ! [B_xa] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 50.63/50.77 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 50.63/50.77 => B_x = B_xa ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__ident,axiom,
% 50.63/50.77 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__id2,axiom,
% 50.63/50.77 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__onD,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 50.63/50.77 => V_x_2 = V_y_2 ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__iff,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 50.63/50.77 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 50.63/50.77 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__contraD,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => ( V_x_2 != V_y_2
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 50.63/50.77 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_subset__inj__on,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__Int,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 50.63/50.77 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__diff,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Cantors__paradox,axiom,
% 50.63/50.77 ! [V_A_2,T_b] :
% 50.63/50.77 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 50.63/50.77 <=> V_A_2 = V_B_2 ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__strict__subset,axiom,
% 50.63/50.77 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__image__Int,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__image__set__diff,axiom,
% 50.63/50.77 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_inj__on__iff__surj,axiom,
% 50.63/50.77 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 50.63/50.77 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 => ( ? [B_f] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) )
% 50.63/50.77 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_all__nat__less,axiom,
% 50.63/50.77 ! [V_P_2,V_n_2] :
% 50.63/50.77 ( ! [B_m] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 50.63/50.77 => hBOOL(hAPP(V_P_2,B_m)) )
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ex__nat__less,axiom,
% 50.63/50.77 ! [V_P_2,V_n_2] :
% 50.63/50.77 ( ? [B_m] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 50.63/50.77 & hBOOL(hAPP(V_P_2,B_m)) )
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I6_J,axiom,
% 50.63/50.77 ! [V_A_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 50.63/50.77 => 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)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I8_J,axiom,
% 50.63/50.77 ! [V_B_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 50.63/50.77 => 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))) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I3_J,axiom,
% 50.63/50.77 ! [V_B_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xa] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 50.63/50.77 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 50.63/50.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I4_J,axiom,
% 50.63/50.77 ! [V_A_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( B_x != V_t_2
% 50.63/50.77 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I4_J,axiom,
% 50.63/50.77 ! [V_B_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( B_x != V_t_2
% 50.63/50.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I7_J,axiom,
% 50.63/50.77 ! [V_B_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 50.63/50.77 => 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))) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I3_J,axiom,
% 50.63/50.77 ! [V_A_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( 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))
% 50.63/50.77 => ( ! [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xa] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 50.63/50.77 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 50.63/50.77 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I5_J,axiom,
% 50.63/50.77 ! [V_A_2,V_t_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 50.63/50.77 => 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)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I6_J,axiom,
% 50.63/50.77 ! [V_t_2,V_B_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 50.63/50.77 => 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)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I8_J,axiom,
% 50.63/50.77 ! [V_t_2,V_A_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 50.63/50.77 => 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))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_periodic__finite__ex,axiom,
% 50.63/50.77 ! [V_P_2,V_d_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 50.63/50.77 => ( ! [B_x,B_k] :
% 50.63/50.77 ( hBOOL(hAPP(V_P_2,B_x))
% 50.63/50.77 <=> 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)))) )
% 50.63/50.77 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I5_J,axiom,
% 50.63/50.77 ! [V_t_2,V_B_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 50.63/50.77 => 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)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I7_J,axiom,
% 50.63/50.77 ! [V_t_2,V_A_2,V_D_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 50.63/50.77 => 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))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 50.63/50.77 ! [V_x_2,V_y_2,V_c_2] :
% 50.63/50.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 50.63/50.77 => 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_c_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_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 50.63/50.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.77 => 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_c_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))) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 50.63/50.77 => 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_c_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)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I9_J,axiom,
% 50.63/50.77 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__atLeastLessThan,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__eq__iff,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 50.63/50.77 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 50.63/50.77 <=> ( V_a_2 = V_c_2
% 50.63/50.77 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 50.63/50.77 => V_a_2 = V_c_2 ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 50.63/50.77 => V_b_2 = V_d_2 ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_all__nat__less__eq,axiom,
% 50.63/50.77 ! [V_P_2,V_n_2] :
% 50.63/50.77 ( ! [B_m] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 50.63/50.77 => hBOOL(hAPP(V_P_2,B_m)) )
% 50.63/50.77 <=> ! [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ex__nat__less__eq,axiom,
% 50.63/50.77 ! [V_P_2,V_n_2] :
% 50.63/50.77 ( ? [B_m] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 50.63/50.77 & hBOOL(hAPP(V_P_2,B_m)) )
% 50.63/50.77 <=> ? [B_x] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan0,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__atLeastLessThan,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__Suc__atLeastLessThan,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__empty,axiom,
% 50.63/50.77 ! [V_a_2,V_b_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 50.63/50.77 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__empty__iff,axiom,
% 50.63/50.77 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.77 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 50.63/50.77 ! [V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
% 50.63/50.77 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__subset__iff,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 50.63/50.77 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 50.63/50.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I17_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__diff,axiom,
% 50.63/50.77 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 50.63/50.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I11_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__add__atLeastLessThan,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__singleton,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I21_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThan__add__Un,axiom,
% 50.63/50.77 ! [V_k_2,V_j_2,V_i_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 50.63/50.77 => 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))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I15_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_Int__atLeastLessThan,axiom,
% 50.63/50.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_subset__card__intvl__is__intvl,axiom,
% 50.63/50.77 ! [V_k_2,V_A_2] :
% 50.63/50.77 ( 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)))))
% 50.63/50.77 => 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))) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__int_I9_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Oorder(T_b)
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.77 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__uminus__atLeastLessThan,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.77 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThanSuc,axiom,
% 50.63/50.77 ! [V_n_2,V_m_2] :
% 50.63/50.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.77 => 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)) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.77 => 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)) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I15_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I6_J,axiom,
% 50.63/50.77 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I3_J,axiom,
% 50.63/50.77 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_ivl__disj__un_I18_J,axiom,
% 50.63/50.77 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 50.63/50.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I10_J,axiom,
% 50.63/50.77 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 50.63/50.77 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_bset_I10_J,axiom,
% 50.63/50.77 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 50.63/50.77 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_aset_I9_J,axiom,
% 50.63/50.77 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 50.63/50.77 => ! [B_x] :
% 50.63/50.77 ( ! [B_xa] :
% 50.63/50.77 ( 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)))
% 50.63/50.77 => ! [B_xb] :
% 50.63/50.77 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 50.63/50.77 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__atLeastLessThan__int,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_image__add__int__atLeastLessThan,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_card__atLeastLessThan__int,axiom,
% 50.63/50.77 ! [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)) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 50.63/50.77 ! [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) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 50.63/50.77 ! [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))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fun__upd__image,axiom,
% 50.63/50.77 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.77 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
% 50.63/50.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.77 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_the__inv__into__into,axiom,
% 50.63/50.77 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 50.63/50.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.77 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fun__upd__triv,axiom,
% 50.63/50.77 ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 50.63/50.77
% 50.63/50.77 fof(fact_finite__atMost,axiom,
% 50.63/50.77 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_atMost__eq__iff,axiom,
% 50.63/50.77 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.77 ( class_Orderings_Olinorder(T_b)
% 50.63/50.77 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 50.63/50.77 <=> V_x_2 = V_y_2 ) ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fun__upd__idem,axiom,
% 50.63/50.77 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 50.63/50.77 ( hAPP(V_f_2,V_x_2) = V_y_2
% 50.63/50.77 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 50.63/50.77
% 50.63/50.77 fof(fact_fun__upd__other,axiom,
% 50.63/50.77 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 50.63/50.77 ( V_z_2 != V_x_2
% 50.63/50.78 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__twist,axiom,
% 50.63/50.78 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 50.63/50.78 ( V_a_2 != V_c_2
% 50.63/50.78 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__apply,axiom,
% 50.63/50.78 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 50.63/50.78 ( ( V_z_2 = V_x_2
% 50.63/50.78 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 )
% 50.63/50.78 & ( V_z_2 != V_x_2
% 50.63/50.78 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__same,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__upd,axiom,
% 50.63/50.78 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__idem__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 50.63/50.78 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__def,axiom,
% 50.63/50.78 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 50.63/50.78 ( ( V_x_2 = V_a_2
% 50.63/50.78 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 )
% 50.63/50.78 & ( V_x_2 != V_a_2
% 50.63/50.78 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast0AtMost,axiom,
% 50.63/50.78 ! [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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__atMost,axiom,
% 50.63/50.78 ! [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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atMost__Suc,axiom,
% 50.63/50.78 ! [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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atMost__iff,axiom,
% 50.63/50.78 ! [V_k_2,V_i_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oord(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atMost__subset__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__le__add__shift,axiom,
% 50.63/50.78 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_the__inv__into__f__eq,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.78 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_the__inv__into__f__f,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__on__the__inv__into,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.78 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_the__inv__into__onto,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.78 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__on__fun__updI,axiom,
% 50.63/50.78 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 50.63/50.78 => c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_the__inv__into__def,axiom,
% 50.63/50.78 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atMost__0,axiom,
% 50.63/50.78 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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__atLeastAtMostL1,axiom,
% 50.63/50.78 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__atLeastAtMostR1,axiom,
% 50.63/50.78 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I9_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I3_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I1_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_f__the__inv__into__f,axiom,
% 50.63/50.78 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 50.63/50.78 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__le__eq__Un0,axiom,
% 50.63/50.78 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__upd__nonempty,axiom,
% 50.63/50.78 ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 50.63/50.78 ! [V_u_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 50.63/50.78 => 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))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__map__upd,axiom,
% 50.63/50.78 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__lessThan,axiom,
% 50.63/50.78 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__lessThan,axiom,
% 50.63/50.78 ! [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 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__eq__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 50.63/50.78 <=> V_x_2 = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast0LessThan,axiom,
% 50.63/50.78 ! [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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__0,axiom,
% 50.63/50.78 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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__Suc,axiom,
% 50.63/50.78 ! [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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__Suc__atMost,axiom,
% 50.63/50.78 ! [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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__iff,axiom,
% 50.63/50.78 ! [V_k_2,V_i_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oord(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__subset__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__strict__subset__iff,axiom,
% 50.63/50.78 ! [V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__upd__Some__unfold,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 50.63/50.78 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 50.63/50.78 <=> ( ( V_x_2 = V_a_2
% 50.63/50.78 & V_b_2 = V_y_2 )
% 50.63/50.78 | ( V_x_2 != V_a_2
% 50.63/50.78 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__upd__triv,axiom,
% 50.63/50.78 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 50.63/50.78 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 50.63/50.78 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__upd__eqD1,axiom,
% 50.63/50.78 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 50.63/50.78 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))
% 50.63/50.78 => V_x_2 = V_y_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_single__Diff__lessThan,axiom,
% 50.63/50.78 ! [V_k_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I8_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I4_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I2_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_empty__upd__none,axiom,
% 50.63/50.78 ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 50.63/50.78 ! [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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I2_J,axiom,
% 50.63/50.78 ! [V_u_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I10_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I7_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_arith__series__int,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ran__map__upd,axiom,
% 50.63/50.78 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 50.63/50.78 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 50.63/50.78 => c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__None__restrict,axiom,
% 50.63/50.78 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 50.63/50.78 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 50.63/50.78 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__abs,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__abs__ge__zero,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__in,axiom,
% 50.63/50.78 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__restrict,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__empty,axiom,
% 50.63/50.78 ! [V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Oempty,axiom,
% 50.63/50.78 ! [V_g_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__infinite,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Oinfinite,axiom,
% 50.63/50.78 ! [V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__negf,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Oab__group__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_of__int__setsum,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Rings_Oring__1(T_b)
% 50.63/50.78 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__commute,axiom,
% 50.63/50.78 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_of__nat__setsum,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.78 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__product,axiom,
% 50.63/50.78 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Rings_Osemiring__0(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__left__distrib,axiom,
% 50.63/50.78 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Rings_Osemiring__0(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__right__distrib,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 50.63/50.78 ( class_Rings_Osemiring__0(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__addf,axiom,
% 50.63/50.78 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__0,axiom,
% 50.63/50.78 ! [V_A_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_abs__setsum__abs,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 50.63/50.78 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__divide__distrib,axiom,
% 50.63/50.78 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Fields_Ofield(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__subtractf,axiom,
% 50.63/50.78 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Oab__group__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__map__empty,axiom,
% 50.63/50.78 ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Odistrib,axiom,
% 50.63/50.78 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 50.63/50.78 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 50.63/50.78 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 50.63/50.78 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 50.63/50.78 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__out,axiom,
% 50.63/50.78 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__map__insert,axiom,
% 50.63/50.78 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__add__nat__ivl,axiom,
% 50.63/50.78 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 50.63/50.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__diff__nat__ivl,axiom,
% 50.63/50.78 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Groups_Oab__group__add(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 50.63/50.78 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__delta,axiom,
% 50.63/50.78 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__delta_H,axiom,
% 50.63/50.78 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__map__def,axiom,
% 50.63/50.78 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__map__to__empty,axiom,
% 50.63/50.78 ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__constant,axiom,
% 50.63/50.78 ! [V_A_2,V_y_2,T_c,T_b] :
% 50.63/50.78 ( class_Rings_Osemiring__1(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__lessThan__Suc,axiom,
% 50.63/50.78 ! [V_n_2,V_f_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__atMost__Suc,axiom,
% 50.63/50.78 ! [V_n_2,V_f_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Oinsert,axiom,
% 50.63/50.78 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__insert,axiom,
% 50.63/50.78 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__Un__Int,axiom,
% 50.63/50.78 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__diff,axiom,
% 50.63/50.78 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Oab__group__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Oeq__fold,axiom,
% 50.63/50.78 ! [V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_OF__eq,axiom,
% 50.63/50.78 ! [V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 50.63/50.78 ! [V_k_2,V_f_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__head__upt__Suc,axiom,
% 50.63/50.78 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__head__Suc,axiom,
% 50.63/50.78 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__restrict__set,axiom,
% 50.63/50.78 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ranI,axiom,
% 50.63/50.78 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 50.63/50.78 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Oinsert__remove,axiom,
% 50.63/50.78 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__Un__disjoint,axiom,
% 50.63/50.78 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__Un,axiom,
% 50.63/50.78 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Oab__group__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__op__ivl__Suc,axiom,
% 50.63/50.78 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__cl__ivl__Suc,axiom,
% 50.63/50.78 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__head,axiom,
% 50.63/50.78 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__ub__add__nat,axiom,
% 50.63/50.78 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => ( 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))))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__restrict,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ran__empty,axiom,
% 50.63/50.78 ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__diff1_H,axiom,
% 50.63/50.78 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Oremove,axiom,
% 50.63/50.78 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__diff1__ring,axiom,
% 50.63/50.78 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Rings_Oring(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__diff1,axiom,
% 50.63/50.78 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Oab__group__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_geometric__sum,axiom,
% 50.63/50.78 ! [V_n_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Fields_Ofield(T_b)
% 50.63/50.78 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_gauss__sum,axiom,
% 50.63/50.78 ! [V_n_2,T_b] :
% 50.63/50.78 ( class_Rings_Ocomm__semiring__1(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__natinterval__difff,axiom,
% 50.63/50.78 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 50.63/50.78 ( class_Groups_Oab__group__add(T_b)
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__upd__restrict__conv,axiom,
% 50.63/50.78 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 50.63/50.78 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__fun__upd,axiom,
% 50.63/50.78 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 50.63/50.78 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 50.63/50.78 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__complement__singleton__eq,axiom,
% 50.63/50.78 ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_restrict__upd__same,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_arith__series__general,axiom,
% 50.63/50.78 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 50.63/50.78 ( class_Rings_Ocomm__semiring__1(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__mono2,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.78 => ( ! [B_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__bounded,axiom,
% 50.63/50.78 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 50.63/50.78 & class_Rings_Osemiring__1(T_c) )
% 50.63/50.78 => ( ! [B_i] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 50.63/50.78 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( 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)))
% 50.63/50.78 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__eq__0__iff,axiom,
% 50.63/50.78 ! [V_f_2,V_F_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.78 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.78 <=> ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 50.63/50.78 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__eq__setsum,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_int__setsum,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__eq__Suc0__iff,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.63/50.78 <=> ? [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.63/50.78 & ! [B_xa] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 50.63/50.78 => ( B_x != B_xa
% 50.63/50.78 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__eq__1__iff,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 50.63/50.78 <=> ? [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 50.63/50.78 & ! [B_xa] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 50.63/50.78 => ( B_x != B_xa
% 50.63/50.78 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 50.63/50.78 ! [V_k_2,V_f_2] :
% 50.63/50.78 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 50.63/50.78 => 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)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__diff__nat,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_b] :
% 50.63/50.78 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 & class_Groups_Ocomm__monoid__mult(T_b) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__diff1__nat,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__Un__nat,axiom,
% 50.63/50.78 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.78 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 & class_Groups_Ocomm__monoid__mult(T_b) )
% 50.63/50.78 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_arith__series__nat,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,T_b] :
% 50.63/50.78 ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__Un__zero,axiom,
% 50.63/50.78 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 50.63/50.78 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__mono3,axiom,
% 50.63/50.78 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 50.63/50.78 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__nonneg__0,axiom,
% 50.63/50.78 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 50.63/50.78 => ( ! [B_i] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 50.63/50.78 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 50.63/50.78 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__nonneg__leq__bound,axiom,
% 50.63/50.78 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 50.63/50.78 => ( ! [B_i] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 50.63/50.78 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_sum__diff__distrib,axiom,
% 50.63/50.78 ! [V_n_2,V_P_2,V_Q_2] :
% 50.63/50.78 ( ! [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)))
% 50.63/50.78 => 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)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__mono__zero__left,axiom,
% 50.63/50.78 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 50.63/50.78 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__mono__zero__right,axiom,
% 50.63/50.78 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 50.63/50.78 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => 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)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__one__idem_Oidem,axiom,
% 50.63/50.78 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 50.63/50.78 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__one__idem_Oin__idem,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 50.63/50.78 => 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) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__subset__induct,axiom,
% 50.63/50.78 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.78 => ( ! [B_a,B_F] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 50.63/50.78 => ( hBOOL(hAPP(V_P_2,B_F))
% 50.63/50.78 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 50.63/50.78 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__strict__mono,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atMost__Int__atLeast,axiom,
% 50.63/50.78 ! [V_n_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast__eq__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 50.63/50.78 <=> V_x_2 = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast__iff,axiom,
% 50.63/50.78 ! [V_k_2,V_i_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oord(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast__subset__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__atLeast,axiom,
% 50.63/50.78 ! [V_k_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__lessThan,axiom,
% 50.63/50.78 ! [V_k_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I14_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I8_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__atLeastAtMostR2,axiom,
% 50.63/50.78 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__atLeastAtMostL2,axiom,
% 50.63/50.78 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I6_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__uminus__atLeast,axiom,
% 50.63/50.78 ! [V_x_2,T_b] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__uminus__atMost,axiom,
% 50.63/50.78 ! [V_x_2,T_b] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast__Suc,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I12_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I13_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I1_J,axiom,
% 50.63/50.78 ! [V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast__Suc__greaterThan,axiom,
% 50.63/50.78 ! [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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_greaterThan__eq__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 50.63/50.78 <=> V_x_2 = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_greaterThan__iff,axiom,
% 50.63/50.78 ! [V_k_2,V_i_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oord(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_greaterThan__subset__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__greaterThan,axiom,
% 50.63/50.78 ! [V_k_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__atMost,axiom,
% 50.63/50.78 ! [V_k_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I7_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__un_I11_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__uminus__greaterThan,axiom,
% 50.63/50.78 ! [V_x_2,T_b] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__uminus__lessThan,axiom,
% 50.63/50.78 ! [V_x_2,T_b] :
% 50.63/50.78 ( class_Groups_Oordered__ab__group__add(T_b)
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ivl__disj__int_I5_J,axiom,
% 50.63/50.78 ! [V_u_2,V_l_2,T_b] :
% 50.63/50.78 ( class_Orderings_Oorder(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_greaterThan__Suc,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 & class_Groups_Ocomm__monoid__mult(T_b) )
% 50.63/50.78 => ( V_A_2 = V_B_2
% 50.63/50.78 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 50.63/50.78 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__eq__singleton__conv,axiom,
% 50.63/50.78 ! [V_x_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Map_Odom(T_b,T_c,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)))
% 50.63/50.78 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold__graph__permute__diff,axiom,
% 50.63/50.78 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 50.63/50.78 ( class_Groups_Oab__semigroup__mult(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_empty__fold__graphE,axiom,
% 50.63/50.78 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
% 50.63/50.78 => V_x_2 = V_z_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold__graph_OemptyI,axiom,
% 50.63/50.78 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 50.63/50.78 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__dom__body,axiom,
% 50.63/50.78 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold__graph__imp__finite,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_domIff,axiom,
% 50.63/50.78 ! [V_m_2,T_c,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 50.63/50.78 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_domI,axiom,
% 50.63/50.78 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 50.63/50.78 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_insert__dom,axiom,
% 50.63/50.78 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 50.63/50.78 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 50.63/50.78 => hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__restrict,axiom,
% 50.63/50.78 ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold__graph_OinsertI,axiom,
% 50.63/50.78 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 50.63/50.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__empty,axiom,
% 50.63/50.78 ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__eq__empty__conv,axiom,
% 50.63/50.78 ! [V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__minus,axiom,
% 50.63/50.78 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 50.63/50.78 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold__graph__insert__swap,axiom,
% 50.63/50.78 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 50.63/50.78 ( class_Groups_Oab__semigroup__mult(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Diff1__fold__graph,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__fun__upd,axiom,
% 50.63/50.78 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 50.63/50.78 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 50.63/50.78 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) )
% 50.63/50.78 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 50.63/50.78 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1Set_Ointros,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ran__restrictD,axiom,
% 50.63/50.78 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2))))
% 50.63/50.78 => ? [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 50.63/50.78 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_compl__unique,axiom,
% 50.63/50.78 ! [V_y,V_x,T_a] :
% 50.63/50.78 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 50.63/50.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 50.63/50.78 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UNIV__I,axiom,
% 50.63/50.78 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UNIV__option__conv,axiom,
% 50.63/50.78 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_range__composition,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__atMost__UNIV,axiom,
% 50.63/50.78 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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__int,axiom,
% 50.63/50.78 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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_injD,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 50.63/50.78 => V_x_2 = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__eq,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 50.63/50.78 <=> V_x_2 = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inf__eq__top__iff,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,T_b] :
% 50.63/50.78 ( class_Lattices_Obounded__lattice__top(T_b)
% 50.63/50.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 50.63/50.78 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 50.63/50.78 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inf__top__right,axiom,
% 50.63/50.78 ! [V_x,T_a] :
% 50.63/50.78 ( class_Lattices_Obounded__lattice__top(T_a)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inf__top__left,axiom,
% 50.63/50.78 ! [V_x,T_a] :
% 50.63/50.78 ( class_Lattices_Obounded__lattice__top(T_a)
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Prod__UNIV,axiom,
% 50.63/50.78 ! [T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__fun__UNIVD2,axiom,
% 50.63/50.78 ! [T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Plus__UNIV__iff,axiom,
% 50.63/50.78 ! [T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
% 50.63/50.78 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__option__UNIV,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
% 50.63/50.78 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_infinite__UNIV__nat,axiom,
% 50.63/50.78 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__UNIV,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Finite__Set_Ofinite(T_b)
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_infinite__UNIV__int,axiom,
% 50.63/50.78 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__UNIV__right,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__UNIV__left,axiom,
% 50.63/50.78 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Un__UNIV__left,axiom,
% 50.63/50.78 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Un__UNIV__right,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_subset__UNIV,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_top__greatest,axiom,
% 50.63/50.78 ! [V_x,T_a] :
% 50.63/50.78 ( class_Orderings_Otop(T_a)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_sup__top__right,axiom,
% 50.63/50.78 ! [V_x,T_a] :
% 50.63/50.78 ( class_Lattices_Obounded__lattice__top(T_a)
% 50.63/50.78 => 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) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_sup__top__left,axiom,
% 50.63/50.78 ! [V_x,T_a] :
% 50.63/50.78 ( class_Lattices_Obounded__lattice__top(T_a)
% 50.63/50.78 => 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) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_equiv__intrel,axiom,
% 50.63/50.78 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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_top__apply,axiom,
% 50.63/50.78 ! [V_x_2,T_c,T_b] :
% 50.63/50.78 ( class_Orderings_Otop(T_b)
% 50.63/50.78 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UNIV__not__empty,axiom,
% 50.63/50.78 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UNIV__Plus__UNIV,axiom,
% 50.63/50.78 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Pow__UNIV,axiom,
% 50.63/50.78 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__UNIV__unit,axiom,
% 50.63/50.78 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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__lessThan__UNIV,axiom,
% 50.63/50.78 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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1Set__nonempty,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 50.63/50.78 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_empty__fold1SetE,axiom,
% 50.63/50.78 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_range__eqI,axiom,
% 50.63/50.78 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 50.63/50.78 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rangeI,axiom,
% 50.63/50.78 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__atLeast__UNIV,axiom,
% 50.63/50.78 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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Diff__UNIV,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.78 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__image__eq__iff,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 50.63/50.78 <=> V_A_2 = V_B_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__UNIV__eq,axiom,
% 50.63/50.78 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__empty__eq,axiom,
% 50.63/50.78 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__compl,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 50.63/50.78 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__partition2,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__partition,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 50.63/50.78 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 50.63/50.78 <=> V_x_2 = V_y_2 ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SUP__UN__eq,axiom,
% 50.63/50.78 ! [V_x_2,V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__range__imageI,axiom,
% 50.63/50.78 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_nat__of,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_the__inv__f__f,axiom,
% 50.63/50.78 ! [V_x_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__fun__UNIVD1,axiom,
% 50.63/50.78 ! [T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 50.63/50.78 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__of__nat,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Nat_Osemiring__char__0(T_b)
% 50.63/50.78 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__const,axiom,
% 50.63/50.78 ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_atLeast__0,axiom,
% 50.63/50.78 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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__fun,axiom,
% 50.63/50.78 ! [T_d,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_compl__bot__eq,axiom,
% 50.63/50.78 ! [T_a] :
% 50.63/50.78 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.78 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_compl__top__eq,axiom,
% 50.63/50.78 ! [T_a] :
% 50.63/50.78 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.78 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_compl__sup__top,axiom,
% 50.63/50.78 ! [V_x,T_a] :
% 50.63/50.78 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.78 => 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) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_sup__compl__top,axiom,
% 50.63/50.78 ! [V_x,T_a] :
% 50.63/50.78 ( class_Lattices_Oboolean__algebra(T_a)
% 50.63/50.78 => 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) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__image__mem__iff,axiom,
% 50.63/50.78 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_range__ex1__eq,axiom,
% 50.63/50.78 ! [V_b_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 50.63/50.78 <=> ? [B_x] :
% 50.63/50.78 ( V_b_2 = hAPP(V_f_2,B_x)
% 50.63/50.78 & ! [B_y] :
% 50.63/50.78 ( V_b_2 = hAPP(V_f_2,B_y)
% 50.63/50.78 => B_y = B_x ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__UNIV__surj__inj,axiom,
% 50.63/50.78 ! [V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.78 => ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__UNIV__inj__surj,axiom,
% 50.63/50.78 ! [V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.78 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__image__subset__iff,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__Int,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__set__diff,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_surj__Compl__image__subset,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_b,T_c] :
% 50.63/50.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_of__nat__inverse,axiom,
% 50.63/50.78 ! [V_y_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 50.63/50.78 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1Set__sing,axiom,
% 50.63/50.78 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
% 50.63/50.78 <=> V_a_2 = V_b_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__range__updI,axiom,
% 50.63/50.78 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__UN__finite__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__singleton,axiom,
% 50.63/50.78 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__UNIV__card__ge__0,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__UNIV__bool,axiom,
% 50.63/50.78 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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__image__Compl__subset,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_greaterThan__0,axiom,
% 50.63/50.78 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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SUP__UN__eq2,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__finite2__subset,axiom,
% 50.63/50.78 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 50.63/50.78 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__finite2__eq,axiom,
% 50.63/50.78 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 50.63/50.78 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
% 50.63/50.78 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__finite__subset,axiom,
% 50.63/50.78 ! [V_C_2,V_A_2,T_b] :
% 50.63/50.78 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_top1I,axiom,
% 50.63/50.78 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Integ__def,axiom,
% 50.63/50.78 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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_iso__tuple__UNIV__I,axiom,
% 50.63/50.78 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_equivp__equiv,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 50.63/50.78 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_equivp__transp,axiom,
% 50.63/50.78 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_equivp__symp,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_equivp__reflp,axiom,
% 50.63/50.78 ! [V_x_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_equivp__def,axiom,
% 50.63/50.78 ! [V_R_2,T_b] :
% 50.63/50.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 50.63/50.78 <=> ! [B_x,B_y] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 50.63/50.78 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_identity__equivp,axiom,
% 50.63/50.78 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Rep__Integ,axiom,
% 50.63/50.78 ! [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)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition__Integ,axiom,
% 50.63/50.78 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) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__vimage__singleton,axiom,
% 50.63/50.78 ! [V_a_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 & class_Groups_Ocomm__monoid__mult(T_b) )
% 50.63/50.78 => ( V_A_2 = V_B_2
% 50.63/50.78 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 50.63/50.78 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimageI,axiom,
% 50.63/50.78 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 50.63/50.78 ( hAPP(V_f_2,V_a_2) = V_b_2
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__Diff,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__ident,axiom,
% 50.63/50.78 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__empty,axiom,
% 50.63/50.78 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__code,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 50.63/50.78 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__Compl,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimageI2,axiom,
% 50.63/50.78 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimageD,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__eq,axiom,
% 50.63/50.78 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__mono,axiom,
% 50.63/50.78 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__Un,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__Int,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__UN,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__UNIV,axiom,
% 50.63/50.78 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__vimage__subset,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_surj__image__vimage__eq,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_b,T_c] :
% 50.63/50.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__singleton__eq,axiom,
% 50.63/50.78 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 50.63/50.78 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__insert,axiom,
% 50.63/50.78 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__vimageD,axiom,
% 50.63/50.78 ! [V_F_2,V_h_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 50.63/50.78 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__subsetD,axiom,
% 50.63/50.78 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 50.63/50.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__vimage__eq,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__vimageI,axiom,
% 50.63/50.78 ! [V_h_2,T_c,V_F_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 50.63/50.78 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__vimage__image__eq,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__const,axiom,
% 50.63/50.78 ! [T_c,V_A_2,V_c_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.78 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.78 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__eq__UN,axiom,
% 50.63/50.78 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__subsetI,axiom,
% 50.63/50.78 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__if,axiom,
% 50.63/50.78 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 50.63/50.78 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 50.63/50.78 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 50.63/50.78 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 50.63/50.78 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 50.63/50.78 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition_ORep__range,axiom,
% 50.63/50.78 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 50.63/50.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 50.63/50.78 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition_OAbs__image,axiom,
% 50.63/50.78 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 50.63/50.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 50.63/50.78 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition_ORep,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 50.63/50.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition_ORep__inverse,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 50.63/50.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 50.63/50.78 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition_ORep__inject,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 50.63/50.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 50.63/50.78 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 50.63/50.78 <=> V_x_2 = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition__code__numeral,axiom,
% 50.63/50.78 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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition_OAbs__inject,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 50.63/50.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 50.63/50.78 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 50.63/50.78 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_type__definition_OAbs__inverse,axiom,
% 50.63/50.78 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 50.63/50.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 50.63/50.78 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_max__extp_Oequations,axiom,
% 50.63/50.78 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 50.63/50.78 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 50.63/50.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 50.63/50.78 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 & ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 50.63/50.78 => ? [B_xa] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 50.63/50.78 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_max__ext_Ointros,axiom,
% 50.63/50.78 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 50.63/50.78 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 50.63/50.78 => ? [B_xa] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 50.63/50.78 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_insert__fold1SetE,axiom,
% 50.63/50.78 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
% 50.63/50.78 => ~ ! [B_a,B_A] :
% 50.63/50.78 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1Set_Oequations,axiom,
% 50.63/50.78 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
% 50.63/50.78 <=> ? [B_a,B_A] :
% 50.63/50.78 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 50.63/50.78 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 50.63/50.78 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__split__eq__Sigma,axiom,
% 50.63/50.78 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__Un,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Groups_Oab__semigroup__mult(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SigmaI,axiom,
% 50.63/50.78 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Times__eq__cancel2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 50.63/50.78 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
% 50.63/50.78 <=> V_A_2 = V_B_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__empty1,axiom,
% 50.63/50.78 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__Diff__distrib2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Times__Diff__distrib1,axiom,
% 50.63/50.78 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__Diff__distrib1,axiom,
% 50.63/50.78 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__cartesian__product,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__cartesian__product,axiom,
% 50.63/50.78 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Times__empty,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.78 ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
% 50.63/50.78 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__empty2,axiom,
% 50.63/50.78 ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__Times__UNIV1,axiom,
% 50.63/50.78 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__Times__UNIV2,axiom,
% 50.63/50.78 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setprod__cartesian__product,axiom,
% 50.63/50.78 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__mult(T_b)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__Un__distrib1,axiom,
% 50.63/50.78 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Times__Un__distrib1,axiom,
% 50.63/50.78 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__Un__distrib2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_swap__product,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__singleton__def,axiom,
% 50.63/50.78 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 50.63/50.78 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 50.63/50.78 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__singleton,axiom,
% 50.63/50.78 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__cartesian__product,axiom,
% 50.63/50.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_equiv__type,axiom,
% 50.63/50.78 ! [V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__Int__distrib1,axiom,
% 50.63/50.78 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Times__Int__distrib1,axiom,
% 50.63/50.78 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__Int__distrib2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Id__on__subset__Times,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UNIV__Times__UNIV,axiom,
% 50.63/50.78 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_mem__Sigma__iff,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 50.63/50.78 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SigmaD1,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SigmaD2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SigmaE2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 50.63/50.78 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__one_Oeq__fold,axiom,
% 50.63/50.78 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__cartesian__product__singleton,axiom,
% 50.63/50.78 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Times__subset__cancel2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Image__subset,axiom,
% 50.63/50.78 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__cartesian__productD1,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__cartesian__productD2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fst__image__times,axiom,
% 50.63/50.78 ! [V_A_2,T_c,T_b,V_B_2] :
% 50.63/50.78 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.78 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_snd__image__times,axiom,
% 50.63/50.78 ! [V_B_2,T_c,T_b,V_A_2] :
% 50.63/50.78 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 50.63/50.78 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__def,axiom,
% 50.63/50.78 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sup__fin_OF__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Olattice(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Inf__fin_OF__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Olattice(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Min_OF__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Max_OF__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_insert__times__insert,axiom,
% 50.63/50.78 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__equiv__class,axiom,
% 50.63/50.78 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UN__Times__distrib,axiom,
% 50.63/50.78 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Sigma__def,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__belowI,axiom,
% 50.63/50.78 ! [V_a_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Osemilattice__inf(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__quotient,axiom,
% 50.63/50.78 ! [V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_below__fold1__iff,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Osemilattice__inf(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
% 50.63/50.78 <=> ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Ofold1__belowI,axiom,
% 50.63/50.78 ! [V_a_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__insert__idem,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__below__iff,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 50.63/50.78 <=> ? [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 50.63/50.78 <=> ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__Un2,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__strict__below__iff,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 50.63/50.78 <=> ? [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_strict__below__fold1__iff,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 50.63/50.78 <=> ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__insert,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Groups_Oab__semigroup__mult(T_b)
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__antimono,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_semilattice__big_OF__eq,axiom,
% 50.63/50.78 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 50.63/50.78 ! [V_A_2,V_I_2,T_c,T_b] :
% 50.63/50.78 ? [B_f] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))
% 50.63/50.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold__image__Sigma,axiom,
% 50.63/50.78 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 50.63/50.78 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setprod__Sigma,axiom,
% 50.63/50.78 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__Sigma,axiom,
% 50.63/50.78 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_d)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__SigmaI,axiom,
% 50.63/50.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 50.63/50.78 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fold1__in,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( class_Groups_Oab__semigroup__mult(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__SigmaI,axiom,
% 50.63/50.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( ! [B_a] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_hom__fold1__commute,axiom,
% 50.63/50.78 ! [V_N_2,V_h_2,T_b] :
% 50.63/50.78 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 50.63/50.78 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.78 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SigmaE,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 50.63/50.78 => ~ ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => ! [B_y] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 50.63/50.78 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair__surj,axiom,
% 50.63/50.78 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 50.63/50.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 50.63/50.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair__inj__on,axiom,
% 50.63/50.78 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 50.63/50.78 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 50.63/50.78 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair__imageI,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_snd__prod__fun,axiom,
% 50.63/50.78 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fst__map__pair,axiom,
% 50.63/50.78 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair__simp,axiom,
% 50.63/50.78 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair__ident,axiom,
% 50.63/50.78 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair__def,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair__surj__on,axiom,
% 50.63/50.78 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 50.63/50.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 50.63/50.78 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 50.63/50.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_prod__fun__imageE,axiom,
% 50.63/50.78 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 50.63/50.78 => ~ ! [B_x,B_y] :
% 50.63/50.78 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 50.63/50.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__on__def,axiom,
% 50.63/50.78 ! [V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 50.63/50.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 50.63/50.78 & ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setprod__pos__nat,axiom,
% 50.63/50.78 ! [V_f_2,V_S_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 50.63/50.78 => 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))) )
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__on__Id__on,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__on__empty,axiom,
% 50.63/50.78 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__on__Un,axiom,
% 50.63/50.78 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 50.63/50.78 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 50.63/50.78 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__on__Int,axiom,
% 50.63/50.78 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 50.63/50.78 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 50.63/50.78 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__onD2,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__onD1,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__onD,axiom,
% 50.63/50.78 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 50.63/50.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_refl__onI,axiom,
% 50.63/50.78 ! [V_A_2,V_r_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 50.63/50.78 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 50.63/50.78 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 50.63/50.78 => ( ! [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))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.78 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Rep__Integ__induct,axiom,
% 50.63/50.78 ! [V_P_2,V_y_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 50.63/50.78 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 50.63/50.78 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Rep__Integ__cases,axiom,
% 50.63/50.78 ! [V_y_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 50.63/50.78 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 50.63/50.78 => hAPP(V_g_2,B_x) = V_z_2 )
% 50.63/50.78 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__left__comm__idem__remove,axiom,
% 50.63/50.78 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__left__comm__idem__sup,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Lattices_Osemilattice__sup(T_b)
% 50.63/50.78 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__left__comm__idem__inf,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Lattices_Osemilattice__inf(T_b)
% 50.63/50.78 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 50.63/50.78 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 50.63/50.78 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 50.63/50.78 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 50.63/50.78 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 50.63/50.78 => 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) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__left__comm__idem,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 50.63/50.78 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fun__left__comm__idem__insert,axiom,
% 50.63/50.78 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__less__Suc2,axiom,
% 50.63/50.78 ! [V_i_2,V_M_2] :
% 50.63/50.78 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 50.63/50.78 => 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))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__less,axiom,
% 50.63/50.78 ! [V_i_2,V_M_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 50.63/50.78 => 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) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_card__less__Suc,axiom,
% 50.63/50.78 ! [V_i_2,V_M_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 50.63/50.78 => 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))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_CollectI,axiom,
% 50.63/50.78 ! [T_b,V_a_2,V_P_2] :
% 50.63/50.78 ( hBOOL(hAPP(V_P_2,V_a_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Collect__conjI,axiom,
% 50.63/50.78 ! [V_Q_2,V_P_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Collect__less__nat,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Collect__le__nat,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__split,axiom,
% 50.63/50.78 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_SetCompr__Sigma__eq,axiom,
% 50.63/50.78 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__neg__eq,axiom,
% 50.63/50.78 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__Collect__eq,axiom,
% 50.63/50.78 ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__mem__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_mem__Collect__eq,axiom,
% 50.63/50.78 ! [V_P_2,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_CollectD,axiom,
% 50.63/50.78 ! [V_P_2,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_CollectE,axiom,
% 50.63/50.78 ! [V_P_2,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Collect__disjI,axiom,
% 50.63/50.78 ! [V_Q_2,V_P_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
% 50.63/50.78 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_UNIV__def,axiom,
% 50.63/50.78 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_insert__Collect,axiom,
% 50.63/50.78 ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__conj__eq,axiom,
% 50.63/50.78 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__disj__eq,axiom,
% 50.63/50.78 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__def,axiom,
% 50.63/50.78 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_empty__def,axiom,
% 50.63/50.78 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_empty__Collect__eq,axiom,
% 50.63/50.78 ! [V_P_2,T_b] :
% 50.63/50.78 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 50.63/50.78 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__empty__eq,axiom,
% 50.63/50.78 ! [V_P_2,T_b] :
% 50.63/50.78 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_insert__compr__raw,axiom,
% 50.63/50.78 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_insert__compr,axiom,
% 50.63/50.78 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Un__def,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__Collect,axiom,
% 50.63/50.78 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
% 50.63/50.78 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 50.63/50.78 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Int__def,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__conv__if,axiom,
% 50.63/50.78 ! [T_b,V_a_2,V_P_2] :
% 50.63/50.78 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 50.63/50.78 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 50.63/50.78 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__conv__if2,axiom,
% 50.63/50.78 ! [T_b,V_a_2,V_P_2] :
% 50.63/50.78 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 50.63/50.78 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 50.63/50.78 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_singleton__conv,axiom,
% 50.63/50.78 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_singleton__conv2,axiom,
% 50.63/50.78 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_set__diff__eq,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Collect__not,axiom,
% 50.63/50.78 ! [V_P_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
% 50.63/50.78 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_insert__def,axiom,
% 50.63/50.78 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Compl__eq,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__def,axiom,
% 50.63/50.78 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Collect__imp__eq,axiom,
% 50.63/50.78 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__def,axiom,
% 50.63/50.78 ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__M__bounded__by__nat,axiom,
% 50.63/50.78 ! [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))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__setsum__restrict,axiom,
% 50.63/50.78 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_d)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_if__image__distrib,axiom,
% 50.63/50.78 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__if,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,V_P_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_nat__seg__image__imp__finite,axiom,
% 50.63/50.78 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 50.63/50.78 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__restrict__set_H,axiom,
% 50.63/50.78 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__image__gen,axiom,
% 50.63/50.78 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Image__singleton,axiom,
% 50.63/50.78 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__cases,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_dom__override__on,axiom,
% 50.63/50.78 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__multicount,axiom,
% 50.63/50.78 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 50.63/50.78 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Collect__subsets,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Pow__Compl,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Pow__def,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__image__set,axiom,
% 50.63/50.78 ! [V_f_2,T_c,V_P_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Collect__bounded__ex,axiom,
% 50.63/50.78 ! [V_Q_2,T_c,V_P_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
% 50.63/50.78 <=> ! [B_y] :
% 50.63/50.78 ( hBOOL(hAPP(V_P_2,B_y))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_override__on__apply__notin,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 50.63/50.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_override__on__apply__in,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_override__on__emptyset,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__graph,axiom,
% 50.63/50.78 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 50.63/50.78 ! [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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_override__on__def,axiom,
% 50.63/50.78 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 50.63/50.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) )
% 50.63/50.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 50.63/50.78 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__psubset__def,axiom,
% 50.63/50.78 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_ran__def,axiom,
% 50.63/50.78 ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,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_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inv__image__def,axiom,
% 50.63/50.78 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_add__Max__commute,axiom,
% 50.63/50.78 ! [V_k_2,V_N_2,T_b] :
% 50.63/50.78 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.78 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_add__Min__commute,axiom,
% 50.63/50.78 ! [V_k_2,V_N_2,T_b] :
% 50.63/50.78 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 50.63/50.78 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_sup__Inf2__distrib,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Odistrib__lattice(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_sup__Inf1__distrib,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Odistrib__lattice(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inf__Sup1__distrib,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Odistrib__lattice(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inf__Sup2__distrib,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Lattices_Odistrib__lattice(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 50.63/50.78 ! [V_x_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( class_Orderings_Olinorder(T_b)
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 50.63/50.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Nitpick_Oprod__def,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_int__ge__less__than2__def,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_int__ge__less__than__def,axiom,
% 50.63/50.78 ! [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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_reflp__def,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Predicate_Oreflp(T_b,V_r_2)
% 50.63/50.78 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_reflpE,axiom,
% 50.63/50.78 ! [V_x_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Predicate_Oreflp(T_b,V_r_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 50.63/50.78 ( class_Rings_Osemiring__0(T_d)
% 50.63/50.78 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
% 50.63/50.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__multicount__gen,axiom,
% 50.63/50.78 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 50.63/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 50.63/50.78 => ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 50.63/50.78 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_image__id,axiom,
% 50.63/50.78 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_vimage__id,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_of__int__eq__id,axiom,
% 50.63/50.78 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_apsnd__id,axiom,
% 50.63/50.78 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_apfst__id,axiom,
% 50.63/50.78 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_id__apply,axiom,
% 50.63/50.78 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 50.63/50.78
% 50.63/50.78 fof(fact_id__def,axiom,
% 50.63/50.78 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair_Oid,axiom,
% 50.63/50.78 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_map__pair_Oidentity,axiom,
% 50.63/50.78 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_inj__on__id,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_surj__id,axiom,
% 50.63/50.78 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_apsnd__def,axiom,
% 50.63/50.78 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_apfst__def,axiom,
% 50.63/50.78 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_split__Pair,axiom,
% 50.63/50.78 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setsum__reindex__id,axiom,
% 50.63/50.78 ! [V_B_2,V_f_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 50.63/50.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_setprod__reindex__id,axiom,
% 50.63/50.78 ! [V_B_2,V_f_2,T_b,T_c] :
% 50.63/50.78 ( class_Groups_Ocomm__monoid__mult(T_c)
% 50.63/50.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 50.63/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__conv__nat__seg__image,axiom,
% 50.63/50.78 ! [V_A_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 50.63/50.78 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__def,axiom,
% 50.63/50.78 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__compI,axiom,
% 50.63/50.78 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__empty2,axiom,
% 50.63/50.78 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__empty1,axiom,
% 50.63/50.78 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_O__assoc,axiom,
% 50.63/50.78 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__mono,axiom,
% 50.63/50.78 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__distrib,axiom,
% 50.63/50.78 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__distrib2,axiom,
% 50.63/50.78 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__UNION__distrib,axiom,
% 50.63/50.78 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__UNION__distrib2,axiom,
% 50.63/50.78 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_union__comp__emptyL,axiom,
% 50.63/50.78 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 50.63/50.78 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 50.63/50.78 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_union__comp__emptyR,axiom,
% 50.63/50.78 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 50.63/50.78 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 50.63/50.78 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 50.63/50.78 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_rel__comp__subset__Sigma,axiom,
% 50.63/50.78 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_max__ext__compat,axiom,
% 50.63/50.78 ! [V_S_2,V_R_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__ext__compat,axiom,
% 50.63/50.78 ! [V_S_2,V_R_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_pred__comp__rel__comp__eq,axiom,
% 50.63/50.78 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 50.63/50.78 ( c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2),V_x_2,V_y_2)
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_reduction__pairI,axiom,
% 50.63/50.78 ! [V_S_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_R_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 50.63/50.78 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__less__than,axiom,
% 50.63/50.78 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_pred__comp_Ointros,axiom,
% 50.63/50.78 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 50.63/50.78 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_c_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__empty,axiom,
% 50.63/50.78 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__inv__image,axiom,
% 50.63/50.78 ! [V_f_2,T_c,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__lex__prod,axiom,
% 50.63/50.78 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 50.63/50.78 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 50.63/50.78 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__measure,axiom,
% 50.63/50.78 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__comp__self,axiom,
% 50.63/50.78 ! [V_R_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_R_2)
% 50.63/50.78 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__int__ge__less__than,axiom,
% 50.63/50.78 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__not__refl,axiom,
% 50.63/50.78 ! [V_a_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__not__sym,axiom,
% 50.63/50.78 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 50.63/50.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__asym,axiom,
% 50.63/50.78 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 50.63/50.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__irrefl,axiom,
% 50.63/50.78 ! [V_a_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__mlex,axiom,
% 50.63/50.78 ! [V_f_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_R_2)
% 50.63/50.78 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__Int2,axiom,
% 50.63/50.78 ! [V_r_H_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__Int1,axiom,
% 50.63/50.78 ! [V_r_H_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__subset,axiom,
% 50.63/50.78 ! [V_p_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
% 50.63/50.78 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__pair__less,axiom,
% 50.63/50.78 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_max__ext__wf,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_pred__comp_Oequations,axiom,
% 50.63/50.78 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 50.63/50.78 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 50.63/50.78 <=> ? [B_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 50.63/50.78 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_min__ext__wf,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__finite__psubset,axiom,
% 50.63/50.78 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__acc__iff,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_acc__wfD,axiom,
% 50.63/50.78 ! [V_x_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__int__ge__less__than2,axiom,
% 50.63/50.78 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__less,axiom,
% 50.63/50.78 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)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__no__loop,axiom,
% 50.63/50.78 ! [V_R_2,T_b] :
% 50.63/50.78 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 50.63/50.78 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__union__merge,axiom,
% 50.63/50.78 ! [V_S_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 50.63/50.78 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 <=> ~ ? [B_f] :
% 50.63/50.78 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wfE__pf,axiom,
% 50.63/50.78 ! [V_A_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_R_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
% 50.63/50.78 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__union__compatible,axiom,
% 50.63/50.78 ! [V_S_2,V_R_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_R_2)
% 50.63/50.78 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 50.63/50.78 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf,axiom,
% 50.63/50.78 ! [T_b] :
% 50.63/50.78 ( class_Orderings_Owellorder(T_b)
% 50.63/50.78 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_reduction__pair__def,axiom,
% 50.63/50.78 ! [V_P_2,T_b] :
% 50.63/50.78 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 50.63/50.78 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))
% 50.63/50.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_reduction__pair__lemma,axiom,
% 50.63/50.78 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 50.63/50.78 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 50.63/50.78 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 50.63/50.78 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__map__pair__image,axiom,
% 50.63/50.78 ! [V_f_2,T_c,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 50.63/50.78 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__lenlex,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__if__measure,axiom,
% 50.63/50.78 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 50.63/50.78 ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(V_P_2,B_x))
% 50.63/50.78 => 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))) )
% 50.63/50.78 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_pred__nat__def,axiom,
% 50.63/50.78 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))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__lex,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__pred__nat,axiom,
% 50.63/50.78 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lex__def,axiom,
% 50.63/50.78 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__lexn,axiom,
% 50.63/50.78 ! [V_n_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_lexn_Osimps_I1_J,axiom,
% 50.63/50.78 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__same__fst,axiom,
% 50.63/50.78 ! [T_b,V_R_2,T_c,V_P_2] :
% 50.63/50.78 ( ! [B_x] :
% 50.63/50.78 ( hBOOL(hAPP(V_P_2,B_x))
% 50.63/50.78 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 50.63/50.78 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__Collect__split,axiom,
% 50.63/50.78 ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_RangeI,axiom,
% 50.63/50.78 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__Id__on,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__empty__iff,axiom,
% 50.63/50.78 ! [V_r_2,T_b,T_c] :
% 50.63/50.78 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__empty,axiom,
% 50.63/50.78 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__Un__eq,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Range,axiom,
% 50.63/50.78 ! [V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_snd__eq__Range,axiom,
% 50.63/50.78 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__iff,axiom,
% 50.63/50.78 ! [V_r_2,T_c,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 50.63/50.78 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__insert,axiom,
% 50.63/50.78 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__Int__subset,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Range__Diff__subset,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_RangeP__Range__eq,axiom,
% 50.63/50.78 ! [V_x_2,V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 50.63/50.78 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_RangeE,axiom,
% 50.63/50.78 ! [V_r_2,T_c,V_b_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 50.63/50.78 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_RangeP_Ointros,axiom,
% 50.63/50.78 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 50.63/50.78 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_RangeP_Oequations,axiom,
% 50.63/50.78 ! [V_a2_2,V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 50.63/50.78 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wf__Un,axiom,
% 50.63/50.78 ! [V_s_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 50.63/50.78 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 50.63/50.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wfP__def,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 50.63/50.78 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wfP__empty,axiom,
% 50.63/50.78 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_DomainI,axiom,
% 50.63/50.78 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wfP__accp__iff,axiom,
% 50.63/50.78 ! [V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 50.63/50.78 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_accp__wfPD,axiom,
% 50.63/50.78 ! [V_x_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 50.63/50.78 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__Id__on,axiom,
% 50.63/50.78 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 50.63/50.78
% 50.63/50.78 fof(fact_wfP__subset,axiom,
% 50.63/50.78 ! [V_p_2,V_r_2,T_b] :
% 50.63/50.78 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 50.63/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
% 50.63/50.78 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__empty__iff,axiom,
% 50.63/50.78 ! [V_r_2,T_c,T_b] :
% 50.63/50.78 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 50.63/50.78 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__empty,axiom,
% 50.63/50.78 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__mono,axiom,
% 50.63/50.78 ! [V_s_2,V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 50.63/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__Un__eq,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_finite__Domain,axiom,
% 50.63/50.78 ! [V_r_2,T_c,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 50.63/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_fst__eq__Domain,axiom,
% 50.63/50.78 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__iff,axiom,
% 50.63/50.78 ! [V_r_2,T_c,V_a_2,T_b] :
% 50.63/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 50.63/50.78 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__insert,axiom,
% 50.63/50.78 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__Int__subset,axiom,
% 50.63/50.78 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ).
% 50.63/50.78
% 50.63/50.78 fof(fact_Domain__Diff__subset,axiom,
% 51.10/50.78 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Field__def,axiom,
% 51.10/50.78 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_wf__in__rel,axiom,
% 51.10/50.78 ! [V_R_2,T_b] :
% 51.10/50.78 ( c_Wellfounded_Owf(T_b,V_R_2)
% 51.10/50.78 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_wfP__wf__eq,axiom,
% 51.10/50.78 ! [V_r_2,T_b] :
% 51.10/50.78 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
% 51.10/50.78 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Domain__Collect__split,axiom,
% 51.10/50.78 ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_DomainP__Domain__eq,axiom,
% 51.10/50.78 ! [V_x_2,V_r_2,T_c,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 51.10/50.78 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_DomainE,axiom,
% 51.10/50.78 ! [V_r_2,T_c,V_a_2,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 51.10/50.78 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_DomainP_Ointros,axiom,
% 51.10/50.78 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 51.10/50.78 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_DomainP_Oequations,axiom,
% 51.10/50.78 ! [V_a1_2,V_r_2,T_c,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 51.10/50.78 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_wfP__acyclicP,axiom,
% 51.10/50.78 ! [V_r_2,T_b] :
% 51.10/50.78 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 51.10/50.78 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_pigeonhole__infinite,axiom,
% 51.10/50.78 ! [V_f_2,T_c,V_A_2,T_b] :
% 51.10/50.78 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 51.10/50.78 => ? [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.78 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_wf__acyclic,axiom,
% 51.10/50.78 ! [V_r_2,T_b] :
% 51.10/50.78 ( c_Wellfounded_Owf(T_b,V_r_2)
% 51.10/50.78 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_acyclic__subset,axiom,
% 51.10/50.78 ! [V_r_2,V_s_2,T_b] :
% 51.10/50.78 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 51.10/50.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 51.10/50.78 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 51.10/50.78 ! [V_r_2,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 51.10/50.78 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 51.10/50.78 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_finite__acyclic__wf,axiom,
% 51.10/50.78 ! [V_r_2,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 51.10/50.78 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 51.10/50.78 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Nitpick_Owf_H__def,axiom,
% 51.10/50.78 ! [V_r_2,T_b] :
% 51.10/50.78 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 51.10/50.78 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 51.10/50.78 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 51.10/50.78 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_refl__on__def_H,axiom,
% 51.10/50.78 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 51.10/50.78 <=> ( ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 51.10/50.78 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) )
% 51.10/50.78 & ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_ball__empty,axiom,
% 51.10/50.78 ! [V_P_2,T_b,B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 51.10/50.78 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Powp__def,axiom,
% 51.10/50.78 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 51.10/50.78 <=> ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 51.10/50.78 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_congruent__def,axiom,
% 51.10/50.78 ! [V_f_2,V_r_2,T_c,T_b] :
% 51.10/50.78 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 51.10/50.78 <=> ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 51.10/50.78 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Abs__Integ__cases,axiom,
% 51.10/50.78 ! [V_x_2] :
% 51.10/50.78 ~ ! [B_y] :
% 51.10/50.78 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 51.10/50.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Abs__Integ__induct,axiom,
% 51.10/50.78 ! [V_x_2,V_P_2] :
% 51.10/50.78 ( ! [B_y] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 51.10/50.78 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 51.10/50.78 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_triples__valid__Suc,axiom,
% 51.10/50.78 ! [V_n_2,V_tsa_2,T_b] :
% 51.10/50.78 ( ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 51.10/50.78 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 51.10/50.78 => ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 51.10/50.78 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_hoare__valids__def,axiom,
% 51.10/50.78 ! [V_tsa_2,V_Ga_2,T_b] :
% 51.10/50.78 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
% 51.10/50.78 <=> ! [B_n] :
% 51.10/50.78 ( ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
% 51.10/50.78 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 51.10/50.78 => ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 51.10/50.78 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_finite__UN__I,axiom,
% 51.10/50.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.78 => ( ! [B_a] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 51.10/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 51.10/50.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_inj__on__diff__nat,axiom,
% 51.10/50.78 ! [V_k_2,V_N_2] :
% 51.10/50.78 ( ! [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 51.10/50.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 51.10/50.78 => 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) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_wfP__SUP,axiom,
% 51.10/50.78 ! [T_b,V_r_2,T_c] :
% 51.10/50.78 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 51.10/50.78 => ( ! [B_i,B_j] :
% 51.10/50.78 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 51.10/50.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 51.10/50.78 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_finite__map__freshness,axiom,
% 51.10/50.78 ! [V_f_2,T_c,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 51.10/50.78 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 51.10/50.78 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_mem__splitE,axiom,
% 51.10/50.78 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
% 51.10/50.78 => ~ ! [B_x,B_y] :
% 51.10/50.78 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 51.10/50.78 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_mem__splitI2,axiom,
% 51.10/50.78 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 51.10/50.78 ( ! [B_a,B_b] :
% 51.10/50.78 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 51.10/50.78 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 51.10/50.78 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_vimage__Times,axiom,
% 51.10/50.78 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_setsum__SucD,axiom,
% 51.10/50.78 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 51.10/50.78 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 51.10/50.78 => ? [B_x] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.78 & 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))) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__id,axiom,
% 51.10/50.78 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ).
% 51.10/50.78
% 51.10/50.78 fof(fact_id__o,axiom,
% 51.10/50.78 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__eq__id__dest,axiom,
% 51.10/50.78 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 51.10/50.78 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
% 51.10/50.78 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_image__compose,axiom,
% 51.10/50.78 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_comp__surj,axiom,
% 51.10/50.78 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 51.10/50.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.78 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 51.10/50.78 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_vimage__compose,axiom,
% 51.10/50.78 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_fun__upd__comp,axiom,
% 51.10/50.78 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_apfst__compose,axiom,
% 51.10/50.78 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_apsnd__compose,axiom,
% 51.10/50.78 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_comp__cong,axiom,
% 51.10/50.78 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
% 51.10/50.78 ( 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))
% 51.10/50.78 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__eq__elim,axiom,
% 51.10/50.78 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 51.10/50.78 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 51.10/50.78 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__eq__dest,axiom,
% 51.10/50.78 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 51.10/50.78 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 51.10/50.78 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__apply,axiom,
% 51.10/50.78 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__assoc,axiom,
% 51.10/50.78 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__def,axiom,
% 51.10/50.78 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_o__eq__dest__lhs,axiom,
% 51.10/50.78 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 51.10/50.78 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 51.10/50.78 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_K__record__comp,axiom,
% 51.10/50.78 ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 51.10/50.78
% 51.10/50.78 fof(fact_map__pair_Ocomp,axiom,
% 51.10/50.78 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_map__pair__compose,axiom,
% 51.10/50.78 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_map__pair_Ocompositionality,axiom,
% 51.10/50.78 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 51.10/50.78 ! [V_x_2,V_f_2,T_c,T_b] :
% 51.10/50.78 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 51.10/50.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_comp__inj__on__iff,axiom,
% 51.10/50.78 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 51.10/50.78 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 51.10/50.78 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_comp__inj__on,axiom,
% 51.10/50.78 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 51.10/50.78 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 51.10/50.78 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_inj__on__imageI,axiom,
% 51.10/50.78 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 51.10/50.78 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
% 51.10/50.78 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_inj__on__imageI2,axiom,
% 51.10/50.78 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 51.10/50.78 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
% 51.10/50.78 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_inj__comp,axiom,
% 51.10/50.78 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 51.10/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 51.10/50.78 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 51.10/50.78 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_setsum__reindex,axiom,
% 51.10/50.78 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 51.10/50.78 ( class_Groups_Ocomm__monoid__add(T_d)
% 51.10/50.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 51.10/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_setprod__reindex__cong,axiom,
% 51.10/50.78 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 51.10/50.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 51.10/50.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 51.10/50.78 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 51.10/50.78 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 51.10/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_setprod__reindex,axiom,
% 51.10/50.78 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 51.10/50.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 51.10/50.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 51.10/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_setsum_Oreindex,axiom,
% 51.10/50.78 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 51.10/50.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 51.10/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.78 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 51.10/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_setprod_Oreindex,axiom,
% 51.10/50.78 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 51.10/50.78 ( class_Groups_Ocomm__monoid__mult(T_c)
% 51.10/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.78 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 51.10/50.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_the__inv__into__comp,axiom,
% 51.10/50.78 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 51.10/50.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 51.10/50.78 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 51.10/50.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 51.10/50.78 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_fold__image__reindex,axiom,
% 51.10/50.78 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 51.10/50.78 ( class_Groups_Oab__semigroup__mult(T_d)
% 51.10/50.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.78 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 51.10/50.78 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Nitpick_Odenom__def,axiom,
% 51.10/50.78 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Nitpick_Onum__def,axiom,
% 51.10/50.78 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_UN__o,axiom,
% 51.10/50.78 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_snd__comp__map__pair,axiom,
% 51.10/50.78 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_fst__comp__map__pair,axiom,
% 51.10/50.78 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_split__comp,axiom,
% 51.10/50.78 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_number__of__code__numeral__def,axiom,
% 51.10/50.78 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) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_int__of__def,axiom,
% 51.10/50.78 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) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Loop__sound__lemma,axiom,
% 51.10/50.78 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 51.10/50.78 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 51.10/50.78 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,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_b),tc_HOL_Obool)))) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_hoare__derivs_OIf,axiom,
% 51.10/50.78 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 51.10/50.78 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 51.10/50.78 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_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_b),tc_HOL_Obool))))
% 51.10/50.78 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_peek__and__def,axiom,
% 51.10/50.78 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_b] :
% 51.10/50.78 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_p_2),V_Z_2),V_s_2))
% 51.10/50.78 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 51.10/50.78 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 51.10/50.78
% 51.10/50.78 fof(fact_Loop,axiom,
% 51.10/50.78 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 51.10/50.78 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 51.10/50.78 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,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_b),tc_HOL_Obool)))) ) ).
% 51.10/50.78
% 51.10/50.79 fof(fact_folding_Oremove,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image_Oreindex,axiom,
% 51.10/50.79 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 51.10/50.79 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 51.10/50.79 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ocommute__left__comp,axiom,
% 51.10/50.79 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ocommute__comp,axiom,
% 51.10/50.79 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 51.10/50.79 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image_Odistrib,axiom,
% 51.10/50.79 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 51.10/50.79 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ocommute__comp_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 51.10/50.79 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 51.10/50.79 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Oempty,axiom,
% 51.10/50.79 ! [V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image_Oeq__fold,axiom,
% 51.10/50.79 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 51.10/50.79 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Oinsert,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ounion__inter,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Oinsert__remove,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Ounion,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 51.10/50.79 => ( 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))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_setsum__reindex__nonzero,axiom,
% 51.10/50.79 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_d)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 51.10/50.79 => ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 51.10/50.79 => ( B_x != B_y
% 51.10/50.79 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 51.10/50.79 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 51.10/50.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Random__Sequence_Omap__def,axiom,
% 51.10/50.79 ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__idem_Ounion__idem,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__idem_Oidem__comp,axiom,
% 51.10/50.79 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 51.10/50.79 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__idem_Oinsert__idem,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_strong__setprod__reindex__cong,axiom,
% 51.10/50.79 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__mult(T_d)
% 51.10/50.79 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 51.10/50.79 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
% 51.10/50.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_neg__map__def,axiom,
% 51.10/50.79 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_neg__single__def,axiom,
% 51.10/50.79 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pos__map__def,axiom,
% 51.10/50.79 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 51.10/50.79 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pos__single__def,axiom,
% 51.10/50.79 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_New__DSequence_Opos__single__def,axiom,
% 51.10/50.79 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Osingle(T_a,V_x) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Eps__split,axiom,
% 51.10/50.79 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_exE__some,axiom,
% 51.10/50.79 ! [T_b,V_c_2,V_P_2] :
% 51.10/50.79 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 51.10/50.79 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 51.10/50.79 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_some__sym__eq__trivial,axiom,
% 51.10/50.79 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_some__eq__trivial,axiom,
% 51.10/50.79 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_some__eq__ex,axiom,
% 51.10/50.79 ! [T_b,V_P_2] :
% 51.10/50.79 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 51.10/50.79 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_someI__ex,axiom,
% 51.10/50.79 ! [T_b,V_P_2] :
% 51.10/50.79 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 51.10/50.79 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_tfl__some,axiom,
% 51.10/50.79 ! [T_b,B_P] :
% 51.10/50.79 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 51.10/50.79 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_someI,axiom,
% 51.10/50.79 ! [T_b,V_x_2,V_P_2] :
% 51.10/50.79 ( hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.79 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_split__paired__Eps,axiom,
% 51.10/50.79 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Eps__split__eq,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_wfI__pf,axiom,
% 51.10/50.79 ! [V_R_2,T_b] :
% 51.10/50.79 ( ! [B_A] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
% 51.10/50.79 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 51.10/50.79 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sigma__mono,axiom,
% 51.10/50.79 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_acc_OaccI,axiom,
% 51.10/50.79 ! [V_r_2,V_x_2,T_b] :
% 51.10/50.79 ( ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_not__acc__down,axiom,
% 51.10/50.79 ! [V_R_2,V_x_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 51.10/50.79 => ~ ! [B_z] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__image__1,axiom,
% 51.10/50.79 ! [V_f_2,V_S_2,T_b,T_c] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__mult(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 51.10/50.79 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 51.10/50.79 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_card_Oneutral,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 51.10/50.79 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_max__ext_Osimps,axiom,
% 51.10/50.79 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 51.10/50.79 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 51.10/50.79 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 51.10/50.79 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 & ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 51.10/50.79 => ? [B_xa] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__image__cong,axiom,
% 51.10/50.79 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( class_Groups_Oab__semigroup__mult(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 51.10/50.79 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_setprod__dvd__setprod__subset2,axiom,
% 51.10/50.79 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 51.10/50.79 ( class_Rings_Ocomm__semiring__1(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Max__eqI,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Min__eqI,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_wf__no__infinite__down__chainE,axiom,
% 51.10/50.79 ! [V_f_2,V_r_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 51.10/50.79 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_setsum__reindex__cong,axiom,
% 51.10/50.79 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_d)
% 51.10/50.79 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 51.10/50.79 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 51.10/50.79 => ( ! [B_a] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 51.10/50.79 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 51.10/50.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_setsum__ivl__cong,axiom,
% 51.10/50.79 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 51.10/50.79 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 51.10/50.79 & class_Orderings_Oord(T_b) )
% 51.10/50.79 => ( V_a_2 = V_c_2
% 51.10/50.79 => ( V_b_2 = V_d_2
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 51.10/50.79 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 51.10/50.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_less__eq,axiom,
% 51.10/50.79 ! [V_n_2,V_m_2] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__empty,axiom,
% 51.10/50.79 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__image__def,axiom,
% 51.10/50.79 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_wf__trancl,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 51.10/50.79 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding_Oeq__fold,axiom,
% 51.10/50.79 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__def,axiom,
% 51.10/50.79 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_union__fold__insert,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__sup__insert,axiom,
% 51.10/50.79 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Osemilattice__sup(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__inf__insert,axiom,
% 51.10/50.79 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Osemilattice__inf(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_less__than__def,axiom,
% 51.10/50.79 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_Ofold__inf__insert,axiom,
% 51.10/50.79 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_Ofold__sup__insert,axiom,
% 51.10/50.79 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_acyclic__def,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 51.10/50.79 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 51.10/50.79 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 51.10/50.79 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sup__SUPR__fold__sup,axiom,
% 51.10/50.79 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sup__le__fold__sup,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Osemilattice__sup(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__inf__le__inf,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Osemilattice__inf(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold1__eq__fold__idem,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Olattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Olattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_minus__fold__remove,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__one_Oeq__fold_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_SUPR__fold__sup,axiom,
% 51.10/50.79 ! [V_f_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold1__eq__fold,axiom,
% 51.10/50.79 ! [V_a_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Groups_Oab__semigroup__mult(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Olattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Olattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Min_Oeq__fold_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Max_Oeq__fold_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl_Or__into__trancl,axiom,
% 51.10/50.79 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__subset__Field2,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_r__into__trancl_H,axiom,
% 51.10/50.79 ! [V_r_2,V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__empty,axiom,
% 51.10/50.79 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__domain,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__range,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__trancl,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_r__r__into__trancl,axiom,
% 51.10/50.79 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
% 51.10/50.79 => ( 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_c_2)),V_R_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__into__trancl2,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 51.10/50.79 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => ( 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_c_2)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__trans,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__mono,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__unfold,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__subset__Sigma,axiom,
% 51.10/50.79 ! [V_A_2,V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__Int__subset,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 51.10/50.79 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 51.10/50.79 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 51.10/50.79 => V_y_2 = V_x_2 ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 51.10/50.79 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 51.10/50.79 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm,axiom,
% 51.10/50.79 ! [T_b] :
% 51.10/50.79 ( class_Groups_Oab__semigroup__mult(T_b)
% 51.10/50.79 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 51.10/50.79 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 51.10/50.79 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 51.10/50.79 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 51.10/50.79 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 51.10/50.79 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 51.10/50.79 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => ? [B_y_H] :
% 51.10/50.79 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 51.10/50.79 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__insert,axiom,
% 51.10/50.79 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_r__into__rtrancl,axiom,
% 51.10/50.79 ! [V_r_2,V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 51.10/50.79 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__into__rtrancl,axiom,
% 51.10/50.79 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Domain__rtrancl,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Range__rtrancl,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__idemp__self__comp,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_r__comp__rtrancl__eq,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_in__rtrancl__UnI,axiom,
% 51.10/50.79 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__Un__rtrancl,axiom,
% 51.10/50.79 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__mono,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__subset,axiom,
% 51.10/50.79 ! [V_S_2,V_R_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__subset__rtrancl,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__Un__subset,axiom,
% 51.10/50.79 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Image__closed__trancl,axiom,
% 51.10/50.79 ! [V_X_2,V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
% 51.10/50.79 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__idemp,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__trans,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( 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_c_2)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 51.10/50.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_refl__rtrancl,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__trancl__absorb,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__rtrancl__absorb,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__unfold__left,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__unfold__right,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__trancl__trancl,axiom,
% 51.10/50.79 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__rtrancl__trancl,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__into__trancl1,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( 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_c_2)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtranclD,axiom,
% 51.10/50.79 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 => ( V_a_2 = V_b_2
% 51.10/50.79 | ( V_a_2 != V_b_2
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__into__trancl2,axiom,
% 51.10/50.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 51.10/50.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__eq__or__trancl,axiom,
% 51.10/50.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 <=> ( V_x_2 = V_y_2
% 51.10/50.79 | ( V_x_2 != V_y_2
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Not__Domain__rtrancl,axiom,
% 51.10/50.79 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 <=> V_x_2 = V_y_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_acc__downwards,axiom,
% 51.10/50.79 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_acc__downwards__aux,axiom,
% 51.10/50.79 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_wf__insert,axiom,
% 51.10/50.79 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 51.10/50.79 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 51.10/50.79 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_acyclic__insert,axiom,
% 51.10/50.79 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 51.10/50.79 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 51.10/50.79 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pred__nat__trancl__eq__le,axiom,
% 51.10/50.79 ! [V_n_2,V_m_2] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__subset__Sigma__aux,axiom,
% 51.10/50.79 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 51.10/50.79 => ( V_a_2 = V_b_2
% 51.10/50.79 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_irrefl__tranclI,axiom,
% 51.10/50.79 ! [V_x_2,V_r_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INFI__fold__inf,axiom,
% 51.10/50.79 ! [V_f_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF2__E,axiom,
% 51.10/50.79 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF2__D,axiom,
% 51.10/50.79 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__D,axiom,
% 51.10/50.79 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__E,axiom,
% 51.10/50.79 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF1__D,axiom,
% 51.10/50.79 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF1__E,axiom,
% 51.10/50.79 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__INT,axiom,
% 51.10/50.79 ! [V_A_2,T_c,V_I_2,T_b] :
% 51.10/50.79 ( ? [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 51.10/50.79 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_wf__converse__trancl,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 51.10/50.79 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Range__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Domain__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Range__def,axiom,
% 51.10/50.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_vimage__INT,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_acyclic__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 51.10/50.79 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__constant,axiom,
% 51.10/50.79 ! [V_c_2,T_c,T_b,V_A_2] :
% 51.10/50.79 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 51.10/50.79 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__empty,axiom,
% 51.10/50.79 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF__const,axiom,
% 51.10/50.79 ! [V_M_2,T_b,V_A_2,T_c] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 51.10/50.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I1_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I2_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__rel__comp,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__Un,axiom,
% 51.10/50.79 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__insert,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_le__INF__iff,axiom,
% 51.10/50.79 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__insert__distrib,axiom,
% 51.10/50.79 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__lower,axiom,
% 51.10/50.79 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I5_J,axiom,
% 51.10/50.79 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I5_J,axiom,
% 51.10/50.79 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__Un,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__subset__iff,axiom,
% 51.10/50.79 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I7_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I6_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I7_J,axiom,
% 51.10/50.79 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Un__INT__distrib,axiom,
% 51.10/50.79 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I6_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Un__INT__distrib2,axiom,
% 51.10/50.79 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Image__INT__subset,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Pow__INT__eq,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__Id__on,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Field__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__INTER,axiom,
% 51.10/50.79 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__inv__image,axiom,
% 51.10/50.79 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF__commute,axiom,
% 51.10/50.79 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INFI__apply,axiom,
% 51.10/50.79 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__Int__distrib,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__Int,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b] :
% 51.10/50.79 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 51.10/50.79 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 51.10/50.79 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 51.10/50.79 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF__INT__eq2,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__iff,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__absorb,axiom,
% 51.10/50.79 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF__INT__eq,axiom,
% 51.10/50.79 ! [V_x_2,V_r_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF__less__iff,axiom,
% 51.10/50.79 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 51.10/50.79 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 & class_Orderings_Olinorder(T_b) )
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
% 51.10/50.79 <=> ? [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__iff,axiom,
% 51.10/50.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converseI,axiom,
% 51.10/50.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converseD,axiom,
% 51.10/50.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_refl__on__converse,axiom,
% 51.10/50.79 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.79 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 51.10/50.79 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I10_J,axiom,
% 51.10/50.79 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I10_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Compl__INT,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Compl__UN,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__UNION,axiom,
% 51.10/50.79 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I9_J,axiom,
% 51.10/50.79 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I9_J,axiom,
% 51.10/50.79 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_UN__simps_I7_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_UN__extend__simps_I7_J,axiom,
% 51.10/50.79 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Collect__ball__eq,axiom,
% 51.10/50.79 ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INFI__bool__eq,axiom,
% 51.10/50.79 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_equiv__comp__eq,axiom,
% 51.10/50.79 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.79 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 51.10/50.79 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF__subset,axiom,
% 51.10/50.79 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INTER__def,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I2_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I1_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I3_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I3_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I4_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__converseI,axiom,
% 51.10/50.79 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__converseD,axiom,
% 51.10/50.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__converseI,axiom,
% 51.10/50.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__converseD,axiom,
% 51.10/50.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Image__subset__eq,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF__leI,axiom,
% 51.10/50.79 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_refl__on__comp__subset,axiom,
% 51.10/50.79 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.79 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_comp__equivI,axiom,
% 51.10/50.79 ! [V_A_2,V_r_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
% 51.10/50.79 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 51.10/50.79 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__acyclic__wf__converse,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 51.10/50.79 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 51.10/50.79 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__greaterThan__UNIV,axiom,
% 51.10/50.79 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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I4_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 51.10/50.79 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 51.10/50.79 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__def,axiom,
% 51.10/50.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inf__INFI__fold__inf,axiom,
% 51.10/50.79 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sequence__trans,axiom,
% 51.10/50.79 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 51.10/50.79 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_reflcl__set__eq,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_IdI,axiom,
% 51.10/50.79 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF1__iff,axiom,
% 51.10/50.79 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INF2__iff,axiom,
% 51.10/50.79 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converse__Id,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Image__Id,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_R__O__Id,axiom,
% 51.10/50.79 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Id__O__R,axiom,
% 51.10/50.79 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pair__in__Id__conv,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
% 51.10/50.79 <=> V_a_2 = V_b_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Domain__Id,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__empty,axiom,
% 51.10/50.79 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Range__Id,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__reflcl__absorb,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__reflcl,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_refl__Id,axiom,
% 51.10/50.79 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__r__diff__Id,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pair__leq__def,axiom,
% 51.10/50.79 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))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__reflcl,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_reflcl__trancl,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__unfold,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_refl__reflcl,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Id__def,axiom,
% 51.10/50.79 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_irrefl__diff__Id,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__Int__subset,axiom,
% 51.10/50.79 ! [V_r_2,V_s_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Image__INT__eq,axiom,
% 51.10/50.79 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 51.10/50.79 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 51.10/50.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 51.10/50.79 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_image__INT,axiom,
% 51.10/50.79 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 51.10/50.79 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valued__Id,axiom,
% 51.10/50.79 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valued__rel__comp,axiom,
% 51.10/50.79 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 51.10/50.79 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 51.10/50.79 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 51.10/50.79 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valued__subset,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 51.10/50.79 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 51.10/50.79 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valued__Id__on,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valued__def,axiom,
% 51.10/50.79 ! [V_r_2,T_c,T_b] :
% 51.10/50.79 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 51.10/50.79 <=> ! [B_x,B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
% 51.10/50.79 => ! [B_z] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
% 51.10/50.79 => B_y = B_z ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valuedD,axiom,
% 51.10/50.79 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 51.10/50.79 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
% 51.10/50.79 => V_y_2 = V_z_2 ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valued__confluent,axiom,
% 51.10/50.79 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 51.10/50.79 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.79 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Image__Int__eq,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 51.10/50.79 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 51.10/50.79 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_total__on__diff__Id,axiom,
% 51.10/50.79 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.79 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 51.10/50.79 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 51.10/50.79 ! [V_R_2,V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_relpow_Osimps_I1_J,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_single__valued__rel__pow,axiom,
% 51.10/50.79 ! [V_n_2,V_R_2,T_b] :
% 51.10/50.79 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 51.10/50.79 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__imp__rtrancl,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__power,axiom,
% 51.10/50.79 ! [V_R_2,V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_comp__funpow,axiom,
% 51.10/50.79 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_wf__exp,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
% 51.10/50.79 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_funpow__mult,axiom,
% 51.10/50.79 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_funpow__swap1,axiom,
% 51.10/50.79 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_relpow_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__commute,axiom,
% 51.10/50.79 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__add,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__1,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_total__on__empty,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_total__on__converse,axiom,
% 51.10/50.79 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.79 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 51.10/50.79 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__0__E,axiom,
% 51.10/50.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 51.10/50.79 => V_x_2 = V_y_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__0__I,axiom,
% 51.10/50.79 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__Suc__I,axiom,
% 51.10/50.79 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__Suc__I2,axiom,
% 51.10/50.79 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_funpow_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_funpow__add,axiom,
% 51.10/50.79 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_funpow_Osimps_I1_J,axiom,
% 51.10/50.79 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_trancl__power,axiom,
% 51.10/50.79 ! [V_R_2,V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 51.10/50.79 <=> ? [B_n] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_total__on__def,axiom,
% 51.10/50.79 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.79 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => ! [B_xa] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 51.10/50.79 => ( B_x != B_xa
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
% 51.10/50.79 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_funpow__code__def,axiom,
% 51.10/50.79 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__E2,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 51.10/50.79 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => V_x_2 != V_z_2 )
% 51.10/50.79 => ~ ! [B_y,B_m] :
% 51.10/50.79 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__E,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 51.10/50.79 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => V_x_2 != V_z_2 )
% 51.10/50.79 => ~ ! [B_y,B_m] :
% 51.10/50.79 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__fold__inf,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__Inter,axiom,
% 51.10/50.79 ! [V_M_2,T_b] :
% 51.10/50.79 ( ? [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 51.10/50.79 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_InterE,axiom,
% 51.10/50.79 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_InterD,axiom,
% 51.10/50.79 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Un__Inter,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__insert,axiom,
% 51.10/50.79 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__lower,axiom,
% 51.10/50.79 ! [V_A_2,V_B_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__less__iff,axiom,
% 51.10/50.79 ! [V_a_2,V_S_2,T_b] :
% 51.10/50.79 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 & class_Orderings_Olinorder(T_b) )
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 51.10/50.79 <=> ? [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_le__Inf__iff,axiom,
% 51.10/50.79 ! [V_A_2,V_b_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__eq,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__empty,axiom,
% 51.10/50.79 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__anti__mono,axiom,
% 51.10/50.79 ! [V_A_2,V_B_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__UNIV,axiom,
% 51.10/50.79 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__lower,axiom,
% 51.10/50.79 ! [V_A_2,V_x_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__Un__distrib,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__singleton,axiom,
% 51.10/50.79 ! [V_a_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__empty,axiom,
% 51.10/50.79 ! [T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__UNIV,axiom,
% 51.10/50.79 ! [T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__insert,axiom,
% 51.10/50.79 ! [V_A_2,V_a_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__image__eq,axiom,
% 51.10/50.79 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INTER__eq__Inter__image,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Int__eq__Inter,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Int__Inter__image,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__Un__subset,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__binary,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inf__Inf__fold__inf,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__fin__Inf,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__Inf,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inf__Sup,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_UnionI,axiom,
% 51.10/50.79 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__def,axiom,
% 51.10/50.79 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Int__Union2,axiom,
% 51.10/50.79 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Int__Union,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_UN__simps_I8_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_UN__extend__simps_I8_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sigma__Union,axiom,
% 51.10/50.79 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_image__Union,axiom,
% 51.10/50.79 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Range__Union,axiom,
% 51.10/50.79 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Domain__Union,axiom,
% 51.10/50.79 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_vimage__Union,axiom,
% 51.10/50.79 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__extend__simps_I8_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_INT__simps_I8_J,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_subset__Pow__Union,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__UnionD,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__mono,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__disjoint,axiom,
% 51.10/50.79 ! [V_A_2,V_C_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__le__iff,axiom,
% 51.10/50.79 ! [V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__upper,axiom,
% 51.10/50.79 ! [V_A_2,V_B_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__Pow__eq,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_less__Sup__iff,axiom,
% 51.10/50.79 ! [V_S_2,V_a_2,T_b] :
% 51.10/50.79 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 & class_Orderings_Olinorder(T_b) )
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 51.10/50.79 <=> ? [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Field__Union,axiom,
% 51.10/50.79 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__empty,axiom,
% 51.10/50.79 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__quotient,axiom,
% 51.10/50.79 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.79 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__Un__distrib,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__UNIV,axiom,
% 51.10/50.79 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__insert,axiom,
% 51.10/50.79 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__image__eq,axiom,
% 51.10/50.79 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_UNION__eq__Union__image,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__upper,axiom,
% 51.10/50.79 ! [V_A_2,V_x_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__empty,axiom,
% 51.10/50.79 ! [T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__singleton,axiom,
% 51.10/50.79 ! [V_a_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__insert,axiom,
% 51.10/50.79 ! [V_A_2,V_a_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__UNIV,axiom,
% 51.10/50.79 ! [T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Un__eq__Union,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Un__Union__image,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__Int__subset,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__binary,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sup__Sup__fold__sup,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__fin__Sup,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Sup__fold__sup,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__on__Inter,axiom,
% 51.10/50.79 ! [V_f_2,T_c,T_b,V_S_2] :
% 51.10/50.79 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 51.10/50.79 => ( ! [B_A] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 51.10/50.79 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 51.10/50.79 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Inter__subset,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.79 ( ! [B_X] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 51.10/50.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Union__def,axiom,
% 51.10/50.79 ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__Union,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 51.10/50.79 => ( ! [B_M] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insert__partition,axiom,
% 51.10/50.79 ! [V_F_2,V_x_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 51.10/50.79 => ! [B_xa] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 51.10/50.79 => ( B_x != B_xa
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_card__partition,axiom,
% 51.10/50.79 ! [V_k_2,V_C_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 51.10/50.79 => ( ! [B_c] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 51.10/50.79 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 51.10/50.79 => ( ! [B_c1] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 51.10/50.79 => ! [B_c2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 51.10/50.79 => ( B_c1 != B_c2
% 51.10/50.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 51.10/50.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__on__INTER,axiom,
% 51.10/50.79 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 51.10/50.79 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => ( ! [B_i] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 51.10/50.79 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 51.10/50.79 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 51.10/50.79 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => ~ ! [B_y] :
% 51.10/50.79 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 51.10/50.79 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_acyclicI,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 51.10/50.79 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__Un__separatorE,axiom,
% 51.10/50.79 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 51.10/50.79 => ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
% 51.10/50.79 => B_x = B_y ) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 51.10/50.79 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 51.10/50.79 => ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
% 51.10/50.79 => B_y = B_x ) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__Suc__E,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 51.10/50.79 => ~ ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__Suc__E2,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 51.10/50.79 => ~ ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__pow__Suc__D2,axiom,
% 51.10/50.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 51.10/50.79 => ? [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_tranclD2,axiom,
% 51.10/50.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 51.10/50.79 => ? [B_z] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_tranclD,axiom,
% 51.10/50.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 51.10/50.79 => ? [B_z] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2))
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 51.10/50.79 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 51.10/50.79 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_InterI,axiom,
% 51.10/50.79 ! [V_A_2,V_C_2,T_b] :
% 51.10/50.79 ( ! [B_X] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inf__le__fold__inf,axiom,
% 51.10/50.79 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Osemilattice__inf(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fold__sup__le__sup,axiom,
% 51.10/50.79 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Lattices_Osemilattice__sup(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_IdE,axiom,
% 51.10/50.79 ! [V_p_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 51.10/50.79 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_wf__eq__minimal,axiom,
% 51.10/50.79 ! [V_r_2,T_b] :
% 51.10/50.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 51.10/50.79 <=> ! [B_Q] :
% 51.10/50.79 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 51.10/50.79 => ? [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 51.10/50.79 & ! [B_y] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_transfer__nat__int__set__cong,axiom,
% 51.10/50.79 ! [V_P_H_2,V_P_2] :
% 51.10/50.79 ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 51.10/50.79 => ( hBOOL(hAPP(V_P_2,B_x))
% 51.10/50.79 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 51.10/50.79 => 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_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 51.10/50.79 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 51.10/50.79 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 51.10/50.79 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 51.10/50.79 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 51.10/50.79 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 51.10/50.79 => 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) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Int__Collect__mono,axiom,
% 51.10/50.79 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 51.10/50.79 => ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(V_P_2,B_x))
% 51.10/50.79 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_UnionE,axiom,
% 51.10/50.79 ! [V_C_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 51.10/50.79 => ~ ! [B_X] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__upd__left,axiom,
% 51.10/50.79 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 51.10/50.79 => c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_rel__compE,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
% 51.10/50.79 => ~ ! [B_x,B_y,B_z] :
% 51.10/50.79 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__SomeD,axiom,
% 51.10/50.79 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 51.10/50.79 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 51.10/50.79 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__Some__iff,axiom,
% 51.10/50.79 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 51.10/50.79 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 51.10/50.79 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__def,axiom,
% 51.10/50.79 ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__empty,axiom,
% 51.10/50.79 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_empty__map__add,axiom,
% 51.10/50.79 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__None,axiom,
% 51.10/50.79 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__assoc,axiom,
% 51.10/50.79 ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__find__right,axiom,
% 51.10/50.79 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 51.10/50.79 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 51.10/50.79 => hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 51.10/50.79 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 51.10/50.79 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 51.10/50.79 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 51.10/50.79 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 51.10/50.79 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 51.10/50.79 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__upd,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_dom__map__add,axiom,
% 51.10/50.79 ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__on__map__add__dom,axiom,
% 51.10/50.79 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2))
% 51.10/50.79 <=> c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__comm,axiom,
% 51.10/50.79 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 => c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__range__map__of__map__add,axiom,
% 51.10/50.79 ! [V_l_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,c_Map_Omap__of(T_c,T_b,V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_converseE,axiom,
% 51.10/50.79 ! [V_r_2,V_yx_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 51.10/50.79 => ~ ! [B_x,B_y] :
% 51.10/50.79 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__dom__map__of,axiom,
% 51.10/50.79 ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_l_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__range__map__of,axiom,
% 51.10/50.79 ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__of(T_c,T_b,V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__map__of__foldr,axiom,
% 51.10/50.79 ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_full__small__int__def,axiom,
% 51.10/50.79 ! [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))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_small_H_Osimps,axiom,
% 51.10/50.79 ! [V_f_2,V_i_2,V_d_2] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 51.10/50.79 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_small_H_Opsimps,axiom,
% 51.10/50.79 ! [V_i_2,V_d_2,V_f_2] :
% 51.10/50.79 ( 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))))
% 51.10/50.79 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 51.10/50.79 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 51.10/50.79 => 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)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_small__int__def,axiom,
% 51.10/50.79 ! [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))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_small__prod__def,axiom,
% 51.10/50.79 ! [V_d_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( ( class_Smallcheck_Osmall(T_c)
% 51.10/50.79 & class_Smallcheck_Osmall(T_b) )
% 51.10/50.79 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,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_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_small_H_Opinduct,axiom,
% 51.10/50.79 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 51.10/50.79 ( 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))))
% 51.10/50.79 => ( ! [B_f,B_d,B_i] :
% 51.10/50.79 ( 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))))
% 51.10/50.79 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 51.10/50.79 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 51.10/50.79 => 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)))) ) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_body__def,axiom,
% 51.10/50.79 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__mapk__SomeI,axiom,
% 51.10/50.79 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 51.10/50.79 => ( hAPP(c_Map_Omap__of(T_b,T_d,V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2)
% 51.10/50.79 => hAPP(c_Map_Omap__of(T_c,T_d,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__def,axiom,
% 51.10/50.79 ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__mapI,axiom,
% 51.10/50.79 ! [V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 51.10/50.79 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__simps_I1_J,axiom,
% 51.10/50.79 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 51.10/50.79 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__Some__iff,axiom,
% 51.10/50.79 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 51.10/50.79 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
% 51.10/50.79 <=> ? [B_k_H] :
% 51.10/50.79 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 51.10/50.79 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__simps_I2_J,axiom,
% 51.10/50.79 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 51.10/50.79 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 51.10/50.79 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__injective,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 51.10/50.79 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 51.10/50.79 => V_xs_2 = V_ys_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__mapD,axiom,
% 51.10/50.79 ! [V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 51.10/50.79 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__map__eq__map,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 51.10/50.79 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 51.10/50.79 <=> V_xs_2 = V_ys_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__map,axiom,
% 51.10/50.79 ! [V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 51.10/50.79 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__ident,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_List_Omap_Oidentity,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_List_Omap_Oid,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__map,axiom,
% 51.10/50.79 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_List_Omap_Ocompositionality,axiom,
% 51.10/50.79 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__map,axiom,
% 51.10/50.79 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_List_Omap_Ocomp,axiom,
% 51.10/50.79 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_foldr__map,axiom,
% 51.10/50.79 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__empty_I1_J,axiom,
% 51.10/50.79 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__empty_I2_J,axiom,
% 51.10/50.79 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__comp__None__iff,axiom,
% 51.10/50.79 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 51.10/50.79 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 51.10/50.79 | ? [B_k_H] :
% 51.10/50.79 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 51.10/50.79 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__map,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_d,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),V_xs_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)),c_Map_Omap__of(T_b,T_d,V_xs_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__map__keys,axiom,
% 51.10/50.79 ! [V_m_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 51.10/50.79 => c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__set,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__map,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__eq__conv,axiom,
% 51.10/50.79 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 51.10/50.79 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Option_Omap_Ocomp,axiom,
% 51.10/50.79 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Option_Omap_Ocompositionality,axiom,
% 51.10/50.79 ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_option__map__comp,axiom,
% 51.10/50.79 ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Option_Omap_Oidentity,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Option_Omap_Oid,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_infinite__UNIV__listI,axiom,
% 51.10/50.79 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_dom__option__map,axiom,
% 51.10/50.79 ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_option__map__Some,axiom,
% 51.10/50.79 ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_option__map__eq__Some,axiom,
% 51.10/50.79 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 51.10/50.79 <=> ? [B_z] :
% 51.10/50.79 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 51.10/50.79 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_option__map__None,axiom,
% 51.10/50.79 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_option__map__is__None,axiom,
% 51.10/50.79 ! [V_opt_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_option__map__o__empty,axiom,
% 51.10/50.79 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_option__map__o__map__upd,axiom,
% 51.10/50.79 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : 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)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),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_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__inj__on,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 51.10/50.79 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
% 51.10/50.79 => V_xs_2 = V_ys_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__on__map__eq__map,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 51.10/50.79 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 51.10/50.79 <=> V_xs_2 = V_ys_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__fun__upd,axiom,
% 51.10/50.79 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_inj__on__mapI,axiom,
% 51.10/50.79 ! [V_A_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
% 51.10/50.79 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__eq__dom,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 51.10/50.79 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 51.10/50.79 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__is__SomeD,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__SomeD,axiom,
% 51.10/50.79 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_dom__map__of__conv__image__fst,axiom,
% 51.10/50.79 ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__eq__None__iff,axiom,
% 51.10/50.79 ! [V_x_2,V_xys_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 51.10/50.79 <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Option_Omap__def,axiom,
% 51.10/50.79 ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_WT__bodies__def,axiom,
% 51.10/50.79 ( c_Com_OWT__bodies
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__map__restrict,axiom,
% 51.10/50.79 ! [V_ks_2,V_f_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_ran__distinct,axiom,
% 51.10/50.79 ! [V_al_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2)))
% 51.10/50.79 => c_Map_Oran(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__map__of__compr,axiom,
% 51.10/50.79 ! [V_xs_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 51.10/50.79 => hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),c_Map_Omap__of(T_b,T_c,V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__map,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 51.10/50.79 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 51.10/50.79 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__inject__set,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 51.10/50.79 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2)))
% 51.10/50.79 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 51.10/50.79 <=> hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Some__eq__map__of__iff,axiom,
% 51.10/50.79 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 51.10/50.79 => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2)
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__eq__Some__iff,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 51.10/50.79 => ( hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2)
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__is__SomeI,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)))
% 51.10/50.79 => hAPP(c_Map_Omap__of(T_b,T_c,V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_greaterThanLessThan__upto,axiom,
% 51.10/50.79 ! [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)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_weak__map__of__SomeI,axiom,
% 51.10/50.79 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2)))
% 51.10/50.79 => ? [B_x] : hAPP(c_Map_Omap__of(T_b,T_c,V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_atLeastAtMost__upto,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__upto,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__upto,axiom,
% 51.10/50.79 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_atLeastLessThan__upto,axiom,
% 51.10/50.79 ! [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)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_greaterThanAtMost__upto,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nat__list__def,axiom,
% 51.10/50.79 ! [V_l_2] :
% 51.10/50.79 ( c_List_Onat__list(V_l_2)
% 51.10/50.79 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__remove1__eq,axiom,
% 51.10/50.79 ! [V_x_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_remove1__idem,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_notin__set__remove1,axiom,
% 51.10/50.79 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_in__set__remove1,axiom,
% 51.10/50.79 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 51.10/50.79 ( V_a_2 != V_b_2
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__remove1__subset,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_remove1__commute,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__remove1,axiom,
% 51.10/50.79 ! [V_x,V_xs,T_a] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sorted__list__of__set__remove,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__zip__map,axiom,
% 51.10/50.79 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2)) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__zipI2,axiom,
% 51.10/50.79 ! [V_xs,T_b,V_ys,T_a] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__zipI1,axiom,
% 51.10/50.79 ! [V_ys,T_b,V_xs,T_a] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__same__conv__map,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__map__fst__snd,axiom,
% 51.10/50.79 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__zip__map,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__zip__map2,axiom,
% 51.10/50.79 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__same,axiom,
% 51.10/50.79 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
% 51.10/50.79 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 & V_a_2 = V_b_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__zip__leftD,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__zip__rightD,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_in__set__zipE,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 51.10/50.79 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__map__map,axiom,
% 51.10/50.79 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__map1,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__map2,axiom,
% 51.10/50.79 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sorted__list__of__set__insert,axiom,
% 51.10/50.79 ! [V_x_2,V_A_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__zip__upd,axiom,
% 51.10/50.79 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 51.10/50.79 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 51.10/50.79 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 51.10/50.79 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2))
% 51.10/50.79 => c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__zip,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__insort,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_c)
% 51.10/50.79 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_neq__if__length__neq,axiom,
% 51.10/50.79 ! [V_ys,V_xs,T_a] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => V_xs != V_ys ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__insort,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_c)
% 51.10/50.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__left__comm,axiom,
% 51.10/50.79 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__key__left__comm,axiom,
% 51.10/50.79 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 51.10/50.79 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__left__comm__insort,axiom,
% 51.10/50.79 ! [T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexn__length,axiom,
% 51.10/50.79 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
% 51.10/50.79 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 51.10/50.79 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__map,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__eq__imp__length__eq,axiom,
% 51.10/50.79 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
% 51.10/50.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_remove1__insort,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_card__length,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_card__distinct,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__card,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__zip__inject,axiom,
% 51.10/50.79 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 51.10/50.79 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 51.10/50.79 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 51.10/50.79 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 51.10/50.79 => ( c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
% 51.10/50.79 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__fst__zip,axiom,
% 51.10/50.79 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__snd__zip,axiom,
% 51.10/50.79 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__insort,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
% 51.10/50.79 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__pos__if__in__set,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__eq__conv,axiom,
% 51.10/50.79 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 51.10/50.79 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2
% 51.10/50.79 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lenlex__conv,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lenlex__def,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__lists__length__eq,axiom,
% 51.10/50.79 ! [V_n_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__eq__iff__zip__eq,axiom,
% 51.10/50.79 ! [T_b,V_ys_2,V_xs_2] :
% 51.10/50.79 ( V_xs_2 = V_ys_2
% 51.10/50.79 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 51.10/50.79 & ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__zip__is__None,axiom,
% 51.10/50.79 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c)
% 51.10/50.79 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__zip__is__Some,axiom,
% 51.10/50.79 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 <=> ? [B_y] : hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__remove1,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_dom__map__of__zip,axiom,
% 51.10/50.79 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_finite__lists__length__le,axiom,
% 51.10/50.79 ! [V_n_2,V_A_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Nitpick_Ocard_H__def,axiom,
% 51.10/50.79 ! [V_A_2,T_b] :
% 51.10/50.79 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__iff__zip,axiom,
% 51.10/50.79 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 51.10/50.79 & ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__rtrancl__refl,axiom,
% 51.10/50.79 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__eq__len,axiom,
% 51.10/50.79 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__rtrancl__trans,axiom,
% 51.10/50.79 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__mono,axiom,
% 51.10/50.79 ! [V_s_2,V_r_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrelp__listrel__eq,axiom,
% 51.10/50.79 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 51.10/50.79 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
% 51.10/50.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexn_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_impossible__Cons,axiom,
% 51.10/50.79 ! [V_x,V_ys,V_xs,T_a] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__ConsD,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
% 51.10/50.79 => ( V_y_2 = V_x_2
% 51.10/50.79 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__Cons__Cons,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__subset__Cons,axiom,
% 51.10/50.79 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_foldr_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_not__Cons__self,axiom,
% 51.10/50.79 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_not__Cons__self2,axiom,
% 51.10/50.79 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list_Oinject,axiom,
% 51.10/50.79 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
% 51.10/50.79 <=> ( V_a_2 = V_a_H_2
% 51.10/50.79 & V_list_2 = V_list_H_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrelp_Oequations_I2_J,axiom,
% 51.10/50.79 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 51.10/50.79 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
% 51.10/50.79 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 51.10/50.79 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrelp_OCons,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 51.10/50.79 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 51.10/50.79 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_remove1_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_xs,T_a,V_y,V_x] :
% 51.10/50.79 ( ( V_x = V_y
% 51.10/50.79 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 51.10/50.79 & ( V_x != V_y
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__key_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( ( 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)))
% 51.10/50.79 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) )
% 51.10/50.79 & ( ~ 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)))
% 51.10/50.79 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 51.10/50.79 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__Cons__code_I2_J,axiom,
% 51.10/50.79 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 51.10/50.79 ( ( V_l = V_k
% 51.10/50.79 => 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) )
% 51.10/50.79 & ( V_l != V_k
% 51.10/50.79 => 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_Map_Omap__of(T_b,T_c,V_ps),V_k) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list_Osize_I4_J,axiom,
% 51.10/50.79 ! [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))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel_OCons,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_ps_2,V_p_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__of(T_b,T_c,V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Cons__in__lex,axiom,
% 51.10/50.79 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
% 51.10/50.79 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 51.10/50.79 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
% 51.10/50.79 | ( V_x_2 = V_y_2
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__Cons,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__Cons__def,axiom,
% 51.10/50.79 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__Cons2,axiom,
% 51.10/50.79 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 => ~ ! [B_x,B_xs] :
% 51.10/50.79 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__Cons1,axiom,
% 51.10/50.79 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 => ~ ! [B_y,B_ys] :
% 51.10/50.79 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__sublist,axiom,
% 51.10/50.79 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pick_Osimps,axiom,
% 51.10/50.79 ! [V_xs,V_x,T_a,V_i] :
% 51.10/50.79 ( ( 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)))
% 51.10/50.79 => 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) )
% 51.10/50.79 & ( ~ 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)))
% 51.10/50.79 => 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))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__sublistI,axiom,
% 51.10/50.79 ! [V_I_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_in__set__sublistD,axiom,
% 51.10/50.79 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_notin__set__sublistI,axiom,
% 51.10/50.79 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__sublist__subset,axiom,
% 51.10/50.79 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_select__weight__cons__zero,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pick__member,axiom,
% 51.10/50.79 ! [V_xs_2,T_b,V_i_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__simps_I2_J,axiom,
% 51.10/50.79 ! [V_xs,V_x,T_a] :
% 51.10/50.79 ( class_Groups_Omonoid__add(T_a)
% 51.10/50.79 => 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)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__subtractf,axiom,
% 51.10/50.79 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( class_Groups_Oab__group__add(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__addf,axiom,
% 51.10/50.79 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__const__mult,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 51.10/50.79 ( class_Rings_Osemiring__0(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__mult__const,axiom,
% 51.10/50.79 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( class_Rings_Osemiring__0(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__0,axiom,
% 51.10/50.79 ! [V_xs_2,T_c,T_b] :
% 51.10/50.79 ( class_Groups_Omonoid__add(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__abs,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_uminus__listsum__map,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( class_Groups_Oab__group__add(T_b)
% 51.10/50.79 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_select__weight__def,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 51.10/50.79 ! [V_f_2,V_xs_2,T_b,T_c] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 51.10/50.79 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 51.10/50.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 51.10/50.79 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__triv,axiom,
% 51.10/50.79 ! [V_xs_2,V_r_2,T_c,T_b] :
% 51.10/50.79 ( class_Rings_Osemiring__1(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__map__remove1,axiom,
% 51.10/50.79 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_select__weight__member,axiom,
% 51.10/50.79 ! [V_s_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 51.10/50.79 ! [V_f_2,V_A_2,T_b,T_c] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_c)
% 51.10/50.79 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.79 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__insert__insort__key,axiom,
% 51.10/50.79 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 51.10/50.79 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 51.10/50.79 ! [V_ns_2] :
% 51.10/50.79 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 <=> ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 51.10/50.79 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__insort__insert,axiom,
% 51.10/50.79 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_c)
% 51.10/50.79 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__insert__triv,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__insort__insert,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__insert__key__triv,axiom,
% 51.10/50.79 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 51.10/50.79 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__insert__insort,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexord__cons__cons,axiom,
% 51.10/50.79 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 51.10/50.79 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 51.10/50.79 | ( V_a_2 = V_b_2
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__zip,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__zip,axiom,
% 51.10/50.79 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => ( 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)))
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__map,axiom,
% 51.10/50.79 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_elem__le__listsum__nat,axiom,
% 51.10/50.79 ! [V_ns,V_k] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => 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))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth_Osimps,axiom,
% 51.10/50.79 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__Cons__0,axiom,
% 51.10/50.79 ! [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 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__Cons__Suc,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_all__set__conv__all__nth,axiom,
% 51.10/50.79 ! [V_P_2,V_xs_2,T_b] :
% 51.10/50.79 ( ! [B_x] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hBOOL(hAPP(V_P_2,B_x)) )
% 51.10/50.79 <=> ! [B_i] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__eq__iff__nth__eq,axiom,
% 51.10/50.79 ! [T_b,V_ys_2,V_xs_2] :
% 51.10/50.79 ( V_xs_2 = V_ys_2
% 51.10/50.79 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 51.10/50.79 & ! [B_i] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__conv__nth,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 <=> ! [B_i] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => ! [B_j] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => ( B_i != B_j
% 51.10/50.79 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__eq__iff__index__eq,axiom,
% 51.10/50.79 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
% 51.10/50.79 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__mem,axiom,
% 51.10/50.79 ! [V_xs_2,T_b,V_n_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_in__set__conv__nth,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 <=> ? [B_i] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__Cons_H,axiom,
% 51.10/50.79 ! [V_xs,V_x,T_a,V_n] :
% 51.10/50.79 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 51.10/50.79 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => 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))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__conv__nth,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__Cons__number__of,axiom,
% 51.10/50.79 ! [V_xs,V_x,T_a,V_v] :
% 51.10/50.79 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => 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 )
% 51.10/50.79 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => 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))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__setsum__nth,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__sublist,axiom,
% 51.10/50.79 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexord__lex,axiom,
% 51.10/50.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
% 51.10/50.79 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 51.10/50.79 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__iff__nth,axiom,
% 51.10/50.79 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 51.10/50.79 & ! [B_n] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_pick__same,axiom,
% 51.10/50.79 ! [V_xs_2,T_b,V_l_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_select__def,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexord__take__index__conv,axiom,
% 51.10/50.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 51.10/50.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))
% 51.10/50.79 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 )
% 51.10/50.79 | ? [B_i] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))))
% 51.10/50.79 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__take__subset__set__take,axiom,
% 51.10/50.79 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_in__set__takeD,axiom,
% 51.10/50.79 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__take,axiom,
% 51.10/50.79 ! [V_xs,T_a,V_n,V_i] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 51.10/50.79 => 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) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__take__subset,axiom,
% 51.10/50.79 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__all,axiom,
% 51.10/50.79 ! [V_n,V_xs,T_a] :
% 51.10/50.79 ( 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))
% 51.10/50.79 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__take,axiom,
% 51.10/50.79 ! [V_i,V_xs,T_a] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__take,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__zip,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__take,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__Suc__Cons,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sublist__upt__eq__take,axiom,
% 51.10/50.79 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__map,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__update__nat,axiom,
% 51.10/50.79 ! [V_n,V_ns,V_k] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => 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)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_select__weigth__select,axiom,
% 51.10/50.79 ! [T_b,V_xs_2] :
% 51.10/50.79 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.79 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__Nil2,axiom,
% 51.10/50.79 ! [V_r_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__Nil1,axiom,
% 51.10/50.79 ! [V_r_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.79 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__id,axiom,
% 51.10/50.79 ! [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 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__list__update__neq,axiom,
% 51.10/50.79 ! [V_x,V_xs,T_a,V_j,V_i] :
% 51.10/50.79 ( V_i != V_j
% 51.10/50.79 => 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) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__beyond,axiom,
% 51.10/50.79 ! [V_x,V_i,V_xs,T_a] :
% 51.10/50.79 ( 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))
% 51.10/50.79 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__eq__Nil,axiom,
% 51.10/50.79 ! [V_xs_2,V_n_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 51.10/50.79 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__0,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__Nil,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list_Osize_I3_J,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__0__conv,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__list__update,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__Cons,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Nil__is__map__conv,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.79 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map_Osimps_I1_J,axiom,
% 51.10/50.79 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__update,axiom,
% 51.10/50.79 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__is__Nil__conv,axiom,
% 51.10/50.79 ! [V_xs_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__update,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_update__zip,axiom,
% 51.10/50.79 ! [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))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sublist__nil,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sublist__empty,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__key_Osimps_I1_J,axiom,
% 51.10/50.79 ! [V_x_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_c)
% 51.10/50.79 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__code_I2_J,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__code_I3_J,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list_Osimps_I3_J,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list_Osimps_I2_J,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sorted__list__of__set__empty,axiom,
% 51.10/50.79 ! [T_b] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_b)
% 51.10/50.79 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip_Osimps_I1_J,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__Nil,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_upto__empty,axiom,
% 51.10/50.79 ! [V_i,V_j] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 51.10/50.79 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_foldr_Osimps_I1_J,axiom,
% 51.10/50.79 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__Cons__code_I1_J,axiom,
% 51.10/50.79 ! [V_k,T_a,T_b] : 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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of_Osimps_I1_J,axiom,
% 51.10/50.79 ! [V_x_1,T_b,T_a] : 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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__nonempty,axiom,
% 51.10/50.79 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update_Osimps_I1_J,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__code_I1_J,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__overwrite,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__swap,axiom,
% 51.10/50.79 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 51.10/50.79 ( V_i != V_i_H
% 51.10/50.79 => 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) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_remove1_Osimps_I1_J,axiom,
% 51.10/50.79 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct_Osimps_I1_J,axiom,
% 51.10/50.79 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_insort__not__Nil,axiom,
% 51.10/50.79 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 51.10/50.79 ( class_Orderings_Olinorder(T_c)
% 51.10/50.79 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrelp_ONil,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrelp_Oequations_I1_J,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 51.10/50.79 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__empty2,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__empty,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__simps_I1_J,axiom,
% 51.10/50.79 ! [T_a] :
% 51.10/50.79 ( class_Groups_Omonoid__add(T_a)
% 51.10/50.79 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__greater__0__conv,axiom,
% 51.10/50.79 ! [V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__update__subsetI,axiom,
% 51.10/50.79 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__1__Cons,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__update__subset__insert,axiom,
% 51.10/50.79 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__list__update,axiom,
% 51.10/50.79 ! [V_x,V_j,V_xs,T_a,V_i] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => ( ( V_i = V_j
% 51.10/50.79 => 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 )
% 51.10/50.79 & ( V_i != V_j
% 51.10/50.79 => 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) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__same__conv,axiom,
% 51.10/50.79 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 51.10/50.79 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__list__update__eq,axiom,
% 51.10/50.79 ! [V_x,V_xs,T_a,V_i] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => 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 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel_ONil,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexord__Nil__right,axiom,
% 51.10/50.79 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Nil__notin__lex,axiom,
% 51.10/50.79 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Nil2__notin__lex,axiom,
% 51.10/50.79 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__update__memI,axiom,
% 51.10/50.79 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_upto_Osimps,axiom,
% 51.10/50.79 ! [V_j,V_i] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 51.10/50.79 => 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)) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 51.10/50.79 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sublist__singleton,axiom,
% 51.10/50.79 ! [V_x_2,T_b,V_A_2] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 51.10/50.79 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 51.10/50.79 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__Cons_H,axiom,
% 51.10/50.79 ! [V_xs,V_x,T_a,V_n] :
% 51.10/50.79 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => 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) )
% 51.10/50.79 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_upto__rec__number__of,axiom,
% 51.10/50.79 ! [V_n,V_m] :
% 51.10/50.79 ( ( 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)))
% 51.10/50.79 => 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))) )
% 51.10/50.79 & ( ~ 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)))
% 51.10/50.79 => 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) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_select,axiom,
% 51.10/50.79 ! [V_s_2,T_b,V_xs_2] :
% 51.10/50.79 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listrel__Nil,axiom,
% 51.10/50.79 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__Cons__sing__Nil,axiom,
% 51.10/50.79 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__Cons__number__of,axiom,
% 51.10/50.79 ! [V_xs,V_x,T_a,V_v] :
% 51.10/50.79 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => 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) )
% 51.10/50.79 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__list__update,axiom,
% 51.10/50.79 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 51.10/50.79 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_upto_Opsimps,axiom,
% 51.10/50.79 ! [V_j_2,V_i_2] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 51.10/50.79 => 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)) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 51.10/50.79 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_anamorph_Osimps,axiom,
% 51.10/50.79 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 51.10/50.79 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 51.10/50.79 => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) )
% 51.10/50.79 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 51.10/50.79 => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listset_Osimps_I1_J,axiom,
% 51.10/50.79 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__Cons,axiom,
% 51.10/50.79 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list_Osimps_I5_J,axiom,
% 51.10/50.79 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list_Osimps_I4_J,axiom,
% 51.10/50.79 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listset_Osimps_I2_J,axiom,
% 51.10/50.79 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__Cons1,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_upto_Opinduct,axiom,
% 51.10/50.79 ! [V_P_2,V_a1_2,V_a0_2] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => ( ! [B_i,B_j] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 51.10/50.79 => 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)) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 51.10/50.79 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upd__upds__conv__if,axiom,
% 51.10/50.79 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 51.10/50.79 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 51.10/50.79 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upds__Nil1,axiom,
% 51.10/50.79 ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upds__Nil2,axiom,
% 51.10/50.79 ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upds__apply__nontin,axiom,
% 51.10/50.79 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__add__upds,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upds__Cons,axiom,
% 51.10/50.79 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upds__list__update2__drop,axiom,
% 51.10/50.79 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_i_2))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 51.10/50.79 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upds__twist,axiom,
% 51.10/50.79 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 51.10/50.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 51.10/50.79 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_restrict__map__upds,axiom,
% 51.10/50.79 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_D_2))
% 51.10/50.79 => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_dom__map__upds,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__upds__append1,axiom,
% 51.10/50.79 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 51.10/50.79 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sublist__Cons,axiom,
% 51.10/50.79 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append1__eq__conv,axiom,
% 51.10/50.79 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
% 51.10/50.79 <=> ( V_xs_2 = V_ys_2
% 51.10/50.79 & V_x_2 = V_y_2 ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Cons__eq__append__conv,axiom,
% 51.10/50.79 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
% 51.10/50.79 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 51.10/50.79 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 51.10/50.79 | ? [B_ys_H] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 51.10/50.79 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__eq__Cons__conv,axiom,
% 51.10/50.79 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 51.10/50.79 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 51.10/50.79 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 51.10/50.79 | ? [B_ys_H] :
% 51.10/50.79 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 51.10/50.79 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__upds__append__drop,axiom,
% 51.10/50.79 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_fun__upds__append2__drop,axiom,
% 51.10/50.79 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__length,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__append__length,axiom,
% 51.10/50.79 ! [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 ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Cons__eq__appendI,axiom,
% 51.10/50.79 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 51.10/50.79 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 51.10/50.79 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__Cons,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__append,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__append1,axiom,
% 51.10/50.79 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => 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) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_remove1__append,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.79 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) )
% 51.10/50.79 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.79 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_length__append,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_zip__append,axiom,
% 51.10/50.79 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 51.10/50.79 ( 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)
% 51.10/50.79 => ( 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)
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__append,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__append__length__plus,axiom,
% 51.10/50.79 ! [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) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_foldr__append,axiom,
% 51.10/50.79 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_map__of__append,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__of(T_b,T_c,V_ys_2),c_Map_Omap__of(T_b,T_c,V_xs_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__assoc,axiom,
% 51.10/50.79 ! [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)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__eq__append__conv2,axiom,
% 51.10/50.79 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
% 51.10/50.79 <=> ? [B_us] :
% 51.10/50.79 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 51.10/50.79 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 51.10/50.79 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 51.10/50.79 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_same__append__eq,axiom,
% 51.10/50.79 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
% 51.10/50.79 <=> V_ys_2 = V_zs_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__same__eq,axiom,
% 51.10/50.79 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
% 51.10/50.79 <=> V_ys_2 = V_zs_2 ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__eq__appendI,axiom,
% 51.10/50.79 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 51.10/50.79 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 51.10/50.79 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_set__append,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_listsum__append,axiom,
% 51.10/50.79 ! [V_ys,V_xs,T_a] :
% 51.10/50.79 ( class_Groups_Omonoid__add(T_a)
% 51.10/50.79 => 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)) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_eq__Nil__appendI,axiom,
% 51.10/50.79 ! [T_a,V_ys,V_xs] :
% 51.10/50.79 ( V_xs = V_ys
% 51.10/50.79 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__self__conv2,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__self__conv,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 51.10/50.79 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__is__Nil__conv,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 51.10/50.79 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 51.10/50.79 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_self__append__conv2,axiom,
% 51.10/50.79 ! [V_xs_2,T_b,V_ys_2] :
% 51.10/50.79 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 51.10/50.79 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_self__append__conv,axiom,
% 51.10/50.79 ! [V_ys_2,T_b,V_xs_2] :
% 51.10/50.79 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 51.10/50.79 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__Nil2,axiom,
% 51.10/50.79 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Nil__is__append__conv,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 51.10/50.79 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 51.10/50.79 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_append__Nil,axiom,
% 51.10/50.79 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexord__append__leftI,axiom,
% 51.10/50.79 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_distinct__append,axiom,
% 51.10/50.79 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 51.10/50.79 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.79 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 51.10/50.79 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_nth__append,axiom,
% 51.10/50.79 ! [V_ys,V_xs,T_a,V_n] :
% 51.10/50.79 ( ( 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)))
% 51.10/50.79 => 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) )
% 51.10/50.79 & ( ~ 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)))
% 51.10/50.79 => 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))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_list__update__append,axiom,
% 51.10/50.79 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 51.10/50.79 ( ( 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)))
% 51.10/50.79 => 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) )
% 51.10/50.79 & ( ~ 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)))
% 51.10/50.79 => 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)) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_sublist__append,axiom,
% 51.10/50.79 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexord__append__left__rightI,axiom,
% 51.10/50.79 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_take__Suc__conv__app__nth,axiom,
% 51.10/50.79 ! [V_xs,T_a,V_i] :
% 51.10/50.79 ( 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)))
% 51.10/50.79 => 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))) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 51.10/50.79 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.79 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.79 & V_x_2 = V_y_2 )
% 51.10/50.79 | ( V_xs_2 = V_ys_2
% 51.10/50.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_lexord__append__leftD,axiom,
% 51.10/50.79 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
% 51.10/50.79 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 51.10/50.79
% 51.10/50.79 fof(fact_Cons__acc__listrel1I,axiom,
% 51.10/50.79 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 51.10/50.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 51.10/50.79 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 51.10/50.79 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 51.10/50.79
% 51.10/50.80 fof(fact_listrel1__converse,axiom,
% 51.10/50.80 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 51.10/50.80 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1__mono,axiom,
% 51.10/50.80 ! [V_s_2,V_r_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 51.10/50.80 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 51.10/50.80 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 51.10/50.80 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1I2,axiom,
% 51.10/50.80 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 51.10/50.80 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 51.10/50.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1__eq__len,axiom,
% 51.10/50.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_not__Nil__listrel1,axiom,
% 51.10/50.80 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_not__listrel1__Nil,axiom,
% 51.10/50.80 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_append__listrel1I,axiom,
% 51.10/50.80 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.80 & V_us_2 = V_vs_2 )
% 51.10/50.80 | ( V_xs_2 = V_ys_2
% 51.10/50.80 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_in__listrel1__converse,axiom,
% 51.10/50.80 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 51.10/50.80 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 51.10/50.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 51.10/50.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1I1,axiom,
% 51.10/50.80 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Cons__listrel1__Cons,axiom,
% 51.10/50.80 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.80 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 51.10/50.80 & V_xs_2 = V_ys_2 )
% 51.10/50.80 | ( V_x_2 = V_y_2
% 51.10/50.80 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1__subset__listrel,axiom,
% 51.10/50.80 ! [V_r_H_2,V_r_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 51.10/50.80 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1I,axiom,
% 51.10/50.80 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 51.10/50.80 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
% 51.10/50.80 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1__iff__update,axiom,
% 51.10/50.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.80 <=> ? [B_y,B_n] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2))
% 51.10/50.80 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.80 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel1E,axiom,
% 51.10/50.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 51.10/50.80 => ~ ! [B_x,B_y] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 51.10/50.80 => ! [B_us,B_vs] :
% 51.10/50.80 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 51.10/50.80 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate1__def,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upd__conv__take__nth__drop,axiom,
% 51.10/50.80 ! [V_a,V_xs,T_a,V_i] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__append,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__Nil,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate1__is__Nil__conv,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 51.10/50.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__take,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_take__drop,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_in__set__dropD,axiom,
% 51.10/50.80 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__rotate1,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__drop__subset,axiom,
% 51.10/50.80 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct1__rotate,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 51.10/50.80 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__drop,axiom,
% 51.10/50.80 ! [V_i,V_xs,T_a] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.80 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__0,axiom,
% 51.10/50.80 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__drop,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__zip,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__rotate1,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__drop,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__Suc__Cons,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__1__Cons,axiom,
% 51.10/50.80 ! [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 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__via__drop,axiom,
% 51.10/50.80 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 51.10/50.80 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 51.10/50.80 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__all,axiom,
% 51.10/50.80 ! [V_n,V_xs,T_a] :
% 51.10/50.80 ( 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))
% 51.10/50.80 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__eq__Nil,axiom,
% 51.10/50.80 ! [V_xs_2,V_n_2,T_b] :
% 51.10/50.80 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 51.10/50.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__drop__subset__set__drop,axiom,
% 51.10/50.80 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_append__take__drop__id,axiom,
% 51.10/50.80 ! [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 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_append__eq__conv__conj,axiom,
% 51.10/50.80 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 51.10/50.80 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
% 51.10/50.80 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__Cons,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__Cons_H,axiom,
% 51.10/50.80 ! [V_xs,V_x,T_a,V_n] :
% 51.10/50.80 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.80 => 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) )
% 51.10/50.80 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.80 => 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) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__drop,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_i,V_n] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_append__eq__append__conv__if,axiom,
% 51.10/50.80 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
% 51.10/50.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
% 51.10/50.80 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 51.10/50.80 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)
% 51.10/50.80 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) )
% 51.10/50.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 51.10/50.80 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2
% 51.10/50.80 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__drop_H,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_i] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__simps,axiom,
% 51.10/50.80 ! [V_xs,V_x,T_b,T_a] :
% 51.10/50.80 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 51.10/50.80 & 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__Cons__number__of,axiom,
% 51.10/50.80 ! [V_xs,V_x,T_a,V_v] :
% 51.10/50.80 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.80 => 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) )
% 51.10/50.80 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.80 => 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) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_take__add,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_j,V_i] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate1__length01,axiom,
% 51.10/50.80 ! [V_xs,T_a] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_zip__append1,axiom,
% 51.10/50.80 ! [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))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_zip__append2,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_id__take__nth__drop,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_i] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_take__hd__drop,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_n] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__drop__conv__nth,axiom,
% 51.10/50.80 ! [V_n,T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => ( 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)))
% 51.10/50.80 => 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) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__append2,axiom,
% 51.10/50.80 ! [V_ys,T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__append,axiom,
% 51.10/50.80 ! [V_ys,T_a,V_xs] :
% 51.10/50.80 ( ( V_xs = c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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) )
% 51.10/50.80 & ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd_Osimps,axiom,
% 51.10/50.80 ! [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 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__map,axiom,
% 51.10/50.80 ! [V_f_2,T_c,T_b,V_xs_2] :
% 51.10/50.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__in__set,axiom,
% 51.10/50.80 ! [T_b,V_xs_2] :
% 51.10/50.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__conv__nth,axiom,
% 51.10/50.80 ! [T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate1__hd__tl,axiom,
% 51.10/50.80 ! [T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__rotate__conv__nth,axiom,
% 51.10/50.80 ! [V_n,T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__Suc,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__tl,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_tl__drop,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_tl_Osimps_I1_J,axiom,
% 51.10/50.80 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__is__Nil__conv,axiom,
% 51.10/50.80 ! [V_xs_2,V_n_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 51.10/50.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_take__tl,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__rotate,axiom,
% 51.10/50.80 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__rotate,axiom,
% 51.10/50.80 ! [V_xs_2,V_n_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 51.10/50.80 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__tl,axiom,
% 51.10/50.80 ! [V_xs,T_a] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.80 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__rotate,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__tl,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__rotate,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__conv__mod,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_tl_Osimps_I2_J,axiom,
% 51.10/50.80 ! [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 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_tl__append2,axiom,
% 51.10/50.80 ! [V_ys,T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate1__rotate__swap,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__Suc,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__def,axiom,
% 51.10/50.80 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_tl__append,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate0,axiom,
% 51.10/50.80 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__add,axiom,
% 51.10/50.80 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__id,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_n] :
% 51.10/50.80 ( 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)
% 51.10/50.80 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__length01,axiom,
% 51.10/50.80 ! [V_n,V_xs,T_a] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__tl,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_tl__take,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_take__Suc,axiom,
% 51.10/50.80 ! [V_n,T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__drop__take,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_fold1__set,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 51.10/50.80 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_list_Osize_I2_J,axiom,
% 51.10/50.80 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__append,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__Cons,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_list__size__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldr__conv__foldl,axiom,
% 51.10/50.80 ! [V_a_2,V_xs_2,T_b] :
% 51.10/50.80 ( class_Groups_Oab__semigroup__add(T_b)
% 51.10/50.80 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__assoc,axiom,
% 51.10/50.80 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Groups_Osemigroup__add(T_b)
% 51.10/50.80 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__absorb0,axiom,
% 51.10/50.80 ! [V_zs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Groups_Omonoid__add(T_b)
% 51.10/50.80 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_start__le__sum,axiom,
% 51.10/50.80 ! [V_ns_2,V_n_2,V_m_2] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__Nil,axiom,
% 51.10/50.80 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listsum__foldl,axiom,
% 51.10/50.80 ! [T_b] :
% 51.10/50.80 ( class_Groups_Omonoid__add(T_b)
% 51.10/50.80 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__foldr1,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( class_Groups_Omonoid__add(T_b)
% 51.10/50.80 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__foldr1__lemma,axiom,
% 51.10/50.80 ! [V_xs_2,V_a_2,T_b] :
% 51.10/50.80 ( class_Groups_Omonoid__add(T_b)
% 51.10/50.80 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sum__eq__0__conv,axiom,
% 51.10/50.80 ! [V_ns_2,V_m_2] :
% 51.10/50.80 ( 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)
% 51.10/50.80 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.80 & ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 51.10/50.80 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_list_Osize_I1_J,axiom,
% 51.10/50.80 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 51.10/50.80 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 51.10/50.80 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Sup__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.80 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Inf__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.80 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Sup__fin__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Lattices_Olattice(T_b)
% 51.10/50.80 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Inf__fin__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Lattices_Olattice(T_b)
% 51.10/50.80 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Min__fin__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Max__fin__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_SUPR__set__fold,axiom,
% 51.10/50.80 ! [V_f_2,V_xs_2,T_c,T_b] :
% 51.10/50.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.80 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_INFI__set__fold,axiom,
% 51.10/50.80 ! [V_f_2,V_xs_2,T_c,T_b] :
% 51.10/50.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 51.10/50.80 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_list__size__estimation,axiom,
% 51.10/50.80 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_list__size__estimation_H,axiom,
% 51.10/50.80 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__upds__fold__map__upd,axiom,
% 51.10/50.80 ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_elem__le__sum,axiom,
% 51.10/50.80 ! [V_ns_2,V_n_2] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_list__size__conv__listsum,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel__subset,axiom,
% 51.10/50.80 ! [V_A_2,V_r_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists__accI,axiom,
% 51.10/50.80 ! [V_r_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists_ONil,axiom,
% 51.10/50.80 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listrel__refl__on,axiom,
% 51.10/50.80 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.80 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 51.10/50.80 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists__UNIV,axiom,
% 51.10/50.80 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_equiv__listrel,axiom,
% 51.10/50.80 ! [V_r_2,V_A_2,T_b] :
% 51.10/50.80 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 51.10/50.80 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists__mono,axiom,
% 51.10/50.80 ! [V_B_2,V_A_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_append__in__lists__conv,axiom,
% 51.10/50.80 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
% 51.10/50.80 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 51.10/50.80 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Cons__in__lists__iff,axiom,
% 51.10/50.80 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
% 51.10/50.80 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 51.10/50.80 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_in__lists__conv__set,axiom,
% 51.10/50.80 ! [V_A_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 51.10/50.80 <=> ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists__eq__set,axiom,
% 51.10/50.80 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists__empty,axiom,
% 51.10/50.80 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists__accD,axiom,
% 51.10/50.80 ! [V_r_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lexord__append__rightI,axiom,
% 51.10/50.80 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 51.10/50.80 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lexord__Nil__left,axiom,
% 51.10/50.80 ! [V_r_2,V_y_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 51.10/50.80 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__list__update,axiom,
% 51.10/50.80 ! [V_x,V_k,T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => ( ( 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))
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 51.10/50.80 & ( 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))
% 51.10/50.80 => 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) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listsum__mono,axiom,
% 51.10/50.80 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 51.10/50.80 ( ( class_Groups_Omonoid__add(T_c)
% 51.10/50.80 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 51.10/50.80 => ( ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last_Osimps,axiom,
% 51.10/50.80 ! [V_x,T_a,V_xs] :
% 51.10/50.80 ( ( V_xs = c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 51.10/50.80 & ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__ConsR,axiom,
% 51.10/50.80 ! [V_x,T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__ConsL,axiom,
% 51.10/50.80 ! [V_x,T_a,V_xs] :
% 51.10/50.80 ( V_xs = c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__append,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_ys] :
% 51.10/50.80 ( ( V_ys = c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 51.10/50.80 & ( V_ys != c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__appendR,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_ys] :
% 51.10/50.80 ( V_ys != c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__appendL,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_ys] :
% 51.10/50.80 ( V_ys = c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__map,axiom,
% 51.10/50.80 ! [V_f_2,T_c,T_b,V_xs_2] :
% 51.10/50.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__in__set,axiom,
% 51.10/50.80 ! [T_b,V_as_2] :
% 51.10/50.80 ( V_as_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__snoc,axiom,
% 51.10/50.80 ! [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 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__drop,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_n] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__conv__nth,axiom,
% 51.10/50.80 ! [T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lexord__linear,axiom,
% 51.10/50.80 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 51.10/50.80 ( ! [B_a,B_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2))
% 51.10/50.80 | B_a = B_b
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) )
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 51.10/50.80 | V_x_2 = V_y_2
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lexord__irreflexive,axiom,
% 51.10/50.80 ! [V_y_2,V_r_2,T_b] :
% 51.10/50.80 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
% 51.10/50.80 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_lists_Osimps,axiom,
% 51.10/50.80 ! [V_A_2,V_a_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 51.10/50.80 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 51.10/50.80 | ? [B_a,B_l] :
% 51.10/50.80 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 51.10/50.80 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 51.10/50.80 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_list__size__pointwise,axiom,
% 51.10/50.80 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 51.10/50.80 ( ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast__take,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_n] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__take__lemma,axiom,
% 51.10/50.80 ! [V_ys,V_xs,T_a,V_k] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => ( 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)))
% 51.10/50.80 => ( ! [B_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 51.10/50.80 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 51.10/50.80 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__butlast,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast__append,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_ys] :
% 51.10/50.80 ( ( V_ys = c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 51.10/50.80 & ( V_ys != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast_Osimps_I2_J,axiom,
% 51.10/50.80 ! [V_x,T_a,V_xs] :
% 51.10/50.80 ( ( V_xs = c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 51.10/50.80 & ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_in__set__butlastD,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__butlast,axiom,
% 51.10/50.80 ! [T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.80 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast_Osimps_I1_J,axiom,
% 51.10/50.80 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast__drop,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__butlast,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_in__set__butlast__appendI,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast__snoc,axiom,
% 51.10/50.80 ! [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 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_take__butlast,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_n] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__butlast,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast__conv__take,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_butlast__list__update,axiom,
% 51.10/50.80 ! [V_x,V_xs,T_a,V_k] :
% 51.10/50.80 ( ( 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))
% 51.10/50.80 => 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) )
% 51.10/50.80 & ( 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))
% 51.10/50.80 => 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) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_append__butlast__last__id,axiom,
% 51.10/50.80 ! [T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => 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 ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_snoc__eq__iff__butlast,axiom,
% 51.10/50.80 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
% 51.10/50.80 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 51.10/50.80 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__aux__max,axiom,
% 51.10/50.80 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_partition__set,axiom,
% 51.10/50.80 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 51.10/50.80 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 51.10/50.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__filter__le,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__is__subset,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter_Osimps_I1_J,axiom,
% 51.10/50.80 ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__empty__conv,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 51.10/50.80 <=> ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__id__conv,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 51.10/50.80 <=> ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__insort__triv,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_c)
% 51.10/50.80 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__filter,axiom,
% 51.10/50.80 ! [V_P_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__remove1,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remove1__filter__not,axiom,
% 51.10/50.80 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__filter,axiom,
% 51.10/50.80 ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_partition__filter1,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sum__length__filter__compl,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter_Osimps_I2_J,axiom,
% 51.10/50.80 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 51.10/50.80 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) )
% 51.10/50.80 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__append,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_partition__filter__conv,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_partition__filter2,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__filter,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__filter__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__filter__less,axiom,
% 51.10/50.80 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__minus__filter__out,axiom,
% 51.10/50.80 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_partition__P,axiom,
% 51.10/50.80 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 51.10/50.80 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 51.10/50.80 => ( ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 51.10/50.80 => hBOOL(hAPP(V_P_2,B_x)) )
% 51.10/50.80 & ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 51.10/50.80 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_partition_Osimps_I1_J,axiom,
% 51.10/50.80 ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__in__sublist,axiom,
% 51.10/50.80 ! [V_s_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_partition_Osimps_I2_J,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__filter__conv__card,axiom,
% 51.10/50.80 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__filter__def,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,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_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__max__length,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__of__filter__in,axiom,
% 51.10/50.80 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 51.10/50.80 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2)
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 51.10/50.80 => hAPP(c_Map_Omap__of(T_c,T_b,hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__map__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose_Osimps_I2_J,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__empty,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 51.10/50.80 <=> ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.80 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__filter__simps_I2_J,axiom,
% 51.10/50.80 ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose_Osimps_I1_J,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__filter__simps_I1_J,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sublist__shift__lemma__Suc,axiom,
% 51.10/50.80 ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_select__weigth__drop__zero,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_pick__drop__zero,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__transpose,axiom,
% 51.10/50.80 ! [V_xs_2,T_b,V_i_2] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 51.10/50.80 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__transpose,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__filter__map__filter,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,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_c),c_If(tc_Option_Ooption(T_b))),V_P_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_insort__key__remove1,axiom,
% 51.10/50.80 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_c)
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 51.10/50.80 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 51.10/50.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sublist__def,axiom,
% 51.10/50.80 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted_ONil,axiom,
% 51.10/50.80 ! [T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__single,axiom,
% 51.10/50.80 ! [V_x,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__same,axiom,
% 51.10/50.80 ! [V_xs_2,V_g_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__map__same,axiom,
% 51.10/50.80 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__filter,axiom,
% 51.10/50.80 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__upt,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__eq__Cons__conv,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 51.10/50.80 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 51.10/50.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 51.10/50.80 & V_i_2 = V_x_2
% 51.10/50.80 & 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 ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__butlast,axiom,
% 51.10/50.80 ! [V_xs,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__rec__number__of,axiom,
% 51.10/50.80 ! [V_n,V_m] :
% 51.10/50.80 ( ( 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)))
% 51.10/50.80 => 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))) )
% 51.10/50.80 & ( ~ 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)))
% 51.10/50.80 => 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) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__append,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 51.10/50.80 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 51.10/50.80 & ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ! [B_xa] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__Cons,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 51.10/50.80 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 & ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__Suc,axiom,
% 51.10/50.80 ! [V_j,V_i] :
% 51.10/50.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => 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))) )
% 51.10/50.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__Suc__append,axiom,
% 51.10/50.80 ! [V_j,V_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__add__eq__append,axiom,
% 51.10/50.80 ! [V_k,V_j,V_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__many__eq,axiom,
% 51.10/50.80 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
% 51.10/50.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 51.10/50.80 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__many,axiom,
% 51.10/50.80 ! [V_zs,V_y,V_x,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 51.10/50.80 => 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))) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_take__upt,axiom,
% 51.10/50.80 ! [V_n,V_m,V_i] :
% 51.10/50.80 ( 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))
% 51.10/50.80 => 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)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__eq__Nil__conv,axiom,
% 51.10/50.80 ! [V_j_2,V_i_2] :
% 51.10/50.80 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 51.10/50.80 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__conv__Nil,axiom,
% 51.10/50.80 ! [V_i,V_j] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 51.10/50.80 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__drop,axiom,
% 51.10/50.80 ! [V_n,V_xs,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_drop__upt,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__upt,axiom,
% 51.10/50.80 ! [V_j,V_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted_Oequations_I1_J,axiom,
% 51.10/50.80 ! [T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__0,axiom,
% 51.10/50.80 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__take,axiom,
% 51.10/50.80 ! [V_n,V_xs,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__upt,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_atLeastLessThan__upt,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__distinct__set__unique,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 51.10/50.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 51.10/50.80 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 51.10/50.80 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__insort,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
% 51.10/50.80 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__upt,axiom,
% 51.10/50.80 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__remove1,axiom,
% 51.10/50.80 ! [V_a,V_xs,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__upt,axiom,
% 51.10/50.80 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__upto,axiom,
% 51.10/50.80 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__list__of__set__range,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__insort__insert,axiom,
% 51.10/50.80 ! [V_x_2,V_xs_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__conv__Cons,axiom,
% 51.10/50.80 ! [V_j,V_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => 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)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_upt__rec,axiom,
% 51.10/50.80 ! [V_j,V_i] :
% 51.10/50.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => 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)) )
% 51.10/50.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__tl,axiom,
% 51.10/50.80 ! [V_xs,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__insort__key,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
% 51.10/50.80 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__map__remove1,axiom,
% 51.10/50.80 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__Suc__upt,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__insort__insert__key,axiom,
% 51.10/50.80 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__upt,axiom,
% 51.10/50.80 ! [V_j,V_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => 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)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__insort,axiom,
% 51.10/50.80 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 51.10/50.80 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__nth,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_atLeastAtMost__upt,axiom,
% 51.10/50.80 ! [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))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_atLeast__upt,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 51.10/50.80 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 51.10/50.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 51.10/50.80 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 51.10/50.80 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 51.10/50.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 51.10/50.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__upt,axiom,
% 51.10/50.80 ! [V_j,V_k,V_i] :
% 51.10/50.80 ( 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))
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_greaterThanAtMost__upt,axiom,
% 51.10/50.80 ! [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))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted_Oequations_I2_J,axiom,
% 51.10/50.80 ! [V_a1_2,V_a2_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 51.10/50.80 <=> ( ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 51.10/50.80 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_greaterThanLessThan__upt,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__map__upt,axiom,
% 51.10/50.80 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__list__of__set,axiom,
% 51.10/50.80 ! [V_A_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 51.10/50.80 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 51.10/50.80 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 51.10/50.80 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_atMost__upto,axiom,
% 51.10/50.80 ! [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))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_insort__remove1,axiom,
% 51.10/50.80 ! [V_xs_2,V_a_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__nth__mono,axiom,
% 51.10/50.80 ! [V_j,V_i,V_xs,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => ( 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)))
% 51.10/50.80 => 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))) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__equals__nth__mono,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 <=> ! [B_j] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.80 => ! [B_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__sorted__distinct__set__unique,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_c)
% 51.10/50.80 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 51.10/50.80 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 51.10/50.80 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 51.10/50.80 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 51.10/50.80 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sublist__shift__lemma,axiom,
% 51.10/50.80 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__rectangle,axiom,
% 51.10/50.80 ! [V_n_2,T_b,V_xs_2] :
% 51.10/50.80 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 51.10/50.80 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 51.10/50.80 => ( ! [B_i] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
% 51.10/50.80 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose_Opsimps_I2_J,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
% 51.10/50.80 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose_Opsimps_I1_J,axiom,
% 51.10/50.80 ! [T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
% 51.10/50.80 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__column,axiom,
% 51.10/50.80 ! [V_i_2,V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__aux__filter__head,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_inj__on__rev,axiom,
% 51.10/50.80 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__concat,axiom,
% 51.10/50.80 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__concat,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__eq__Cons__iff,axiom,
% 51.10/50.80 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 51.10/50.80 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev_Osimps_I2_J,axiom,
% 51.10/50.80 ! [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))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev_Osimps_I1_J,axiom,
% 51.10/50.80 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat_Osimps_I1_J,axiom,
% 51.10/50.80 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Nil__is__rev__conv,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 51.10/50.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__is__Nil__conv,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 51.10/50.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_Nil__eq__concat__conv,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] :
% 51.10/50.80 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 51.10/50.80 <=> ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 51.10/50.80 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat__eq__Nil__conv,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] :
% 51.10/50.80 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 51.10/50.80 <=> ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 51.10/50.80 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__singleton__conv,axiom,
% 51.10/50.80 ! [V_x_2,V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
% 51.10/50.80 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_singleton__rev__conv,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
% 51.10/50.80 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat_Osimps_I2_J,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__concat,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__concat,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__foldl__cons,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat__conv__foldl,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__conv__concat,axiom,
% 51.10/50.80 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__append,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat__append,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__rev,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 51.10/50.80 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__concat,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__rev,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_listsum__rev,axiom,
% 51.10/50.80 ! [V_xs,T_a] :
% 51.10/50.80 ( class_Groups_Ocomm__monoid__add(T_a)
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__is__rev__conv,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 51.10/50.80 <=> V_xs_2 = V_ys_2 ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__swap,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 51.10/50.80 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__rev__ident,axiom,
% 51.10/50.80 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldr__foldl,axiom,
% 51.10/50.80 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldl__foldr,axiom,
% 51.10/50.80 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__rev,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_zip__rev,axiom,
% 51.10/50.80 ! [V_ys,T_b,V_xs,T_a] :
% 51.10/50.80 ( 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)
% 51.10/50.80 => 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)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__filter,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_last__rev,axiom,
% 51.10/50.80 ! [T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__rev,axiom,
% 51.10/50.80 ! [T_a,V_xs] :
% 51.10/50.80 ( V_xs != c_List_Olist_ONil(T_a)
% 51.10/50.80 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__transpose,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__drop,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__take,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rotate__rev,axiom,
% 51.10/50.80 ! [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)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose_Osimps_I3_J,axiom,
% 51.10/50.80 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__nth,axiom,
% 51.10/50.80 ! [V_xs,T_a,V_n] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat__injective,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 51.10/50.80 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 51.10/50.80 => ( ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 51.10/50.80 => V_xs_2 = V_ys_2 ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat__eq__concat__iff,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,T_b] :
% 51.10/50.80 ( ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 51.10/50.80 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 51.10/50.80 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 51.10/50.80 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 51.10/50.80 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_rev__update,axiom,
% 51.10/50.80 ! [V_y,V_xs,T_a,V_k] :
% 51.10/50.80 ( 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)))
% 51.10/50.80 => 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) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_concat__map__singleton,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__rev__nth__mono,axiom,
% 51.10/50.80 ! [V_j,V_i,V_xs,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 51.10/50.80 => ( 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)))
% 51.10/50.80 => 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))) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_foldr__max__sorted,axiom,
% 51.10/50.80 ! [V_y_2,V_xs_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 51.10/50.80 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 51.10/50.80 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 51.10/50.80 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose_Opsimps_I3_J,axiom,
% 51.10/50.80 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
% 51.10/50.80 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__transpose__sorted,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 51.10/50.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 51.10/50.80 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 51.10/50.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__column__length,axiom,
% 51.10/50.80 ! [V_i_2,V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__aux__filter__tail,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__nth__transpose__sorted,axiom,
% 51.10/50.80 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
% 51.10/50.80 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transpose__transpose,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 51.10/50.80 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 51.10/50.80 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_return__list__def,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_zip__takeWhile__snd,axiom,
% 51.10/50.80 ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_zip__takeWhile__fst,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__takeWhileD,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__eq__all__conv,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] :
% 51.10/50.80 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 51.10/50.80 <=> ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__takeWhile__le,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__eq__take,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__takeWhile,axiom,
% 51.10/50.80 ! [V_P_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__tail,axiom,
% 51.10/50.80 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 51.10/50.80 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 51.10/50.80 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) )
% 51.10/50.80 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__takeWhile,axiom,
% 51.10/50.80 ! [V_P_2,V_xs_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 51.10/50.80 ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__append1,axiom,
% 51.10/50.80 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_nth__length__takeWhile,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 51.10/50.80 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__nth,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 51.10/50.80 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_map__upds__def,axiom,
% 51.10/50.80 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__not__last,axiom,
% 51.10/50.80 ! [T_b,V_xs_2] :
% 51.10/50.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 51.10/50.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 51.10/50.80 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 51.10/50.80 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 51.10/50.80 ! [V_l] :
% 51.10/50.80 ( c_List_Onat__list(V_l)
% 51.10/50.80 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__remdups__concat,axiom,
% 51.10/50.80 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__remdups,axiom,
% 51.10/50.80 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__remdups__leq,axiom,
% 51.10/50.80 ! [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))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups__map__remdups,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_embed__list__def,axiom,
% 51.10/50.80 ! [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) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_set__remdups,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups_Osimps_I1_J,axiom,
% 51.10/50.80 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups__eq__nil__right__iff,axiom,
% 51.10/50.80 ! [V_x_2,T_b] :
% 51.10/50.80 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 51.10/50.80 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups__eq__nil__iff,axiom,
% 51.10/50.80 ! [V_x_2,T_b] :
% 51.10/50.80 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 51.10/50.80 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__remdups,axiom,
% 51.10/50.80 ! [V_l,T_a] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_a)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remove1__remdups,axiom,
% 51.10/50.80 ! [V_x,V_xs,T_a] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.80 => 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)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__remdups__id,axiom,
% 51.10/50.80 ! [V_xs,T_a] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 51.10/50.80 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups__id__iff__distinct,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 51.10/50.80 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__remdups__eq,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] :
% 51.10/50.80 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 51.10/50.80 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups__remdups,axiom,
% 51.10/50.80 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups__filter,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_remdups_Osimps_I2_J,axiom,
% 51.10/50.80 ! [V_xs_2,V_x_2,T_b] :
% 51.10/50.80 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) )
% 51.10/50.80 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__remdups__card__conv,axiom,
% 51.10/50.80 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 51.10/50.80 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 51.10/50.80 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 51.10/50.80 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 51.10/50.80 ! [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))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__neq__rev,axiom,
% 51.10/50.80 ! [V_x_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_dropWhile__neq__rev,axiom,
% 51.10/50.80 ! [V_x_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 51.10/50.80 => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_dropWhile__map,axiom,
% 51.10/50.80 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_takeWhile__dropWhile__id,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2 ).
% 51.10/50.80
% 51.10/50.80 fof(fact_length__dropWhile__le,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_distinct__dropWhile,axiom,
% 51.10/50.80 ! [V_P_2,V_xs_2,T_b] :
% 51.10/50.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 51.10/50.80 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 51.10/50.80 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 51.10/50.80 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) )
% 51.10/50.80 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 51.10/50.80 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_sorted__dropWhile,axiom,
% 51.10/50.80 ! [V_P_2,V_xs_2,T_b] :
% 51.10/50.80 ( class_Orderings_Olinorder(T_b)
% 51.10/50.80 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 51.10/50.80 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 51.10/50.80 ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 51.10/50.80
% 51.10/50.80 fof(fact_hd__dropWhile,axiom,
% 51.10/50.80 ! [V_xs_2,V_P_2,T_b] :
% 51.10/50.80 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 51.10/50.80 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 51.10/50.80
% 51.10/50.80 %----Arity declarations (201)
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 51.10/50.80 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Obounded__lattice(T_1)
% 51.10/50.80 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 51.10/50.80 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Obounded__lattice(T_1)
% 51.10/50.80 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Obounded__lattice(T_1)
% 51.10/50.80 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Olattice(T_1)
% 51.10/50.80 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Olattice(T_1)
% 51.10/50.80 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Odistrib__lattice(T_1)
% 51.10/50.80 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Oboolean__algebra(T_1)
% 51.10/50.80 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Orderings_Opreorder,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Orderings_Opreorder(T_1)
% 51.10/50.80 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 51.10/50.80 ! [T_1,T_2] :
% 51.10/50.80 ( ( class_Finite__Set_Ofinite(T_2)
% 51.10/50.80 & class_Finite__Set_Ofinite(T_1) )
% 51.10/50.80 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Lattices_Olattice,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Lattices_Olattice(T_1)
% 51.10/50.80 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Orderings_Oorder,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Orderings_Oorder(T_1)
% 51.10/50.80 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Orderings_Otop,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Orderings_Otop(T_1)
% 51.10/50.80 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Orderings_Oord,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Orderings_Oord(T_1)
% 51.10/50.80 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Orderings_Obot,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Orderings_Obot(T_1)
% 51.10/50.80 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Groups_Ouminus,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Groups_Ouminus(T_1)
% 51.10/50.80 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_fun__Groups_Ominus,axiom,
% 51.10/50.80 ! [T_2,T_1] :
% 51.10/50.80 ( class_Groups_Ominus(T_1)
% 51.10/50.80 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 51.10/50.80 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 51.10/50.80 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 51.10/50.80 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 51.10/50.80 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 51.10/50.80 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 51.10/50.80 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 51.10/50.80 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 51.10/50.80 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 51.10/50.80 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 51.10/50.80 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 51.10/50.80 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 51.10/50.80 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 51.10/50.80 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 51.10/50.80 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 51.10/50.80 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 51.10/50.80 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 51.10/50.80 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 51.10/50.80 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 51.10/50.80 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 51.10/50.80 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 51.10/50.80 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 51.10/50.80 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 51.10/50.80 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 51.10/50.80 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 51.10/50.80 class_Orderings_Opreorder(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 51.10/50.80 class_Orderings_Olinorder(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 51.10/50.80 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 51.10/50.80 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 51.10/50.80 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 51.10/50.80 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 51.10/50.80 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 51.10/50.80 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 51.10/50.80 class_Lattices_Olattice(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 51.10/50.80 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 51.10/50.80 class_Divides_Oring__div(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 51.10/50.80 class_Rings_Omult__zero(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 51.10/50.80 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 51.10/50.80 class_Orderings_Oorder(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 51.10/50.80 class_Int_Oring__char__0(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 51.10/50.80 class_Int_Onumber__ring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 51.10/50.80 class_Rings_Osemiring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 51.10/50.80 class_Orderings_Oord(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 51.10/50.80 class_Groups_Ouminus(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 51.10/50.80 class_Groups_Osgn__if(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 51.10/50.80 class_Groups_Oabs__if(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 51.10/50.80 class_Rings_Oring__1(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 51.10/50.80 class_Groups_Ominus(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Power_Opower,axiom,
% 51.10/50.80 class_Power_Opower(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 51.10/50.80 class_Groups_Ozero(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oring,axiom,
% 51.10/50.80 class_Rings_Oring(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 51.10/50.80 class_Rings_Oidom(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Int_Onumber,axiom,
% 51.10/50.80 class_Int_Onumber(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Groups_Oone,axiom,
% 51.10/50.80 class_Groups_Oone(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 51.10/50.80 class_Rings_Odvd(tc_Int_Oint) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 51.10/50.80 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 51.10/50.80 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 51.10/50.80 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 51.10/50.80 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 51.10/50.80 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 51.10/50.80 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 51.10/50.80 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 51.10/50.80 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 51.10/50.80 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 51.10/50.80 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 51.10/50.80 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 51.10/50.80 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 51.10/50.80 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 51.10/50.80 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 51.10/50.80 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 51.10/50.80 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 51.10/50.80 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 51.10/50.80 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 51.10/50.80 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 51.10/50.80 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 51.10/50.80 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 51.10/50.80 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 51.10/50.80 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 51.10/50.80 class_Lattices_Olattice(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 51.10/50.80 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 51.10/50.80 class_Orderings_Oorder(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 51.10/50.80 class_Rings_Osemiring(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 51.10/50.80 class_Orderings_Oord(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 51.10/50.80 class_Orderings_Obot(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 51.10/50.80 class_Groups_Ominus(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Power_Opower,axiom,
% 51.10/50.80 class_Power_Opower(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 51.10/50.80 class_Groups_Ozero(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 51.10/50.80 class_Int_Onumber(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 51.10/50.80 class_Groups_Oone(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 51.10/50.80 class_Rings_Odvd(tc_Nat_Onat) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 51.10/50.80 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 51.10/50.80 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 51.10/50.80 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 51.10/50.80 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 51.10/50.80 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 51.10/50.80 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 51.10/50.80 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 51.10/50.80 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 51.10/50.80 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 51.10/50.80 class_Lattices_Olattice(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 51.10/50.80 class_Orderings_Oorder(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 51.10/50.80 class_Orderings_Otop(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 51.10/50.80 class_Orderings_Oord(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 51.10/50.80 class_Orderings_Obot(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 51.10/50.80 class_Groups_Ouminus(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 51.10/50.80 class_Groups_Ominus(tc_HOL_Obool) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 51.10/50.80 ! [T_1,T_2] :
% 51.10/50.80 ( ( class_Finite__Set_Ofinite(T_2)
% 51.10/50.80 & class_Finite__Set_Ofinite(T_1) )
% 51.10/50.80 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 51.10/50.80 ! [T_1] :
% 51.10/50.80 ( class_Finite__Set_Ofinite(T_1)
% 51.10/50.80 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 51.10/50.80 ! [T_1,T_2] :
% 51.10/50.80 ( ( class_Finite__Set_Ofinite(T_2)
% 51.10/50.80 & class_Finite__Set_Ofinite(T_1) )
% 51.10/50.80 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_prod__Smallcheck_Osmall,axiom,
% 51.10/50.80 ! [T_1,T_2] :
% 51.10/50.80 ( ( class_Smallcheck_Osmall(T_2)
% 51.10/50.80 & class_Smallcheck_Osmall(T_1) )
% 51.10/50.80 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 51.10/50.80 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 51.10/50.80 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 51.10/50.80 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 51.10/50.80 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 51.10/50.80 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 51.10/50.80 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 51.10/50.80 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 51.10/50.80 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 51.10/50.80 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 51.10/50.80 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 51.10/50.80 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 51.10/50.80 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 51.10/50.80 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 51.10/50.80 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 51.10/50.80 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 51.10/50.80 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 51.10/50.80 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 51.10/50.80 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 51.10/50.80 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 51.10/50.80 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 51.10/50.80 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 51.10/50.80 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 51.10/50.80 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 51.10/50.80 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 51.10/50.80 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 51.10/50.80 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 51.10/50.80 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 51.10/50.80 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 51.10/50.80 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 51.10/50.80 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 51.10/50.80 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 51.10/50.80 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 51.10/50.80 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 51.10/50.80
% 51.10/50.80 %----Helper facts (20)
% 51.10/50.80 fof(help_c__COMBI__1,axiom,
% 51.10/50.80 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__COMBK__1,axiom,
% 51.10/50.80 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__COMBB__1,axiom,
% 51.10/50.80 ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__COMBC__1,axiom,
% 51.10/50.80 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__COMBS__1,axiom,
% 51.10/50.80 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fequal__1,axiom,
% 51.10/50.80 ! [V_y_2,V_x_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 51.10/50.80 | V_x_2 = V_y_2 ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fequal__2,axiom,
% 51.10/50.80 ! [V_y_2,V_x_2] :
% 51.10/50.80 ( V_x_2 != V_y_2
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fFalse__1,axiom,
% 51.10/50.80 ~ hBOOL(c_fFalse) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fTrue__1,axiom,
% 51.10/50.80 hBOOL(c_fTrue) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fNot__1,axiom,
% 51.10/50.80 ! [V_P_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 51.10/50.80 | ~ hBOOL(V_P_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fNot__2,axiom,
% 51.10/50.80 ! [V_P_2] :
% 51.10/50.80 ( ~ ~ hBOOL(V_P_2)
% 51.10/50.80 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fconj__1,axiom,
% 51.10/50.80 ! [V_Q_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(V_P_2)
% 51.10/50.80 | ~ hBOOL(V_Q_2)
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fconj__2,axiom,
% 51.10/50.80 ! [V_Q_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 51.10/50.80 | hBOOL(V_P_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fconj__3,axiom,
% 51.10/50.80 ! [V_Q_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 51.10/50.80 | hBOOL(V_Q_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fdisj__1,axiom,
% 51.10/50.80 ! [V_Q_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(V_P_2)
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fdisj__2,axiom,
% 51.10/50.80 ! [V_P_2,V_Q_2] :
% 51.10/50.80 ( ~ hBOOL(V_Q_2)
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fdisj__3,axiom,
% 51.10/50.80 ! [V_Q_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 51.10/50.80 | hBOOL(V_P_2)
% 51.10/50.80 | hBOOL(V_Q_2) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fimplies__1,axiom,
% 51.10/50.80 ! [V_Q_2,V_P_2] :
% 51.10/50.80 ( hBOOL(V_P_2)
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fimplies__2,axiom,
% 51.10/50.80 ! [V_P_2,V_Q_2] :
% 51.10/50.80 ( ~ hBOOL(V_Q_2)
% 51.10/50.80 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 51.10/50.80
% 51.10/50.80 fof(help_c__fimplies__3,axiom,
% 51.10/50.80 ! [V_Q_2,V_P_2] :
% 51.10/50.80 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 51.10/50.80 | ~ hBOOL(V_P_2)
% 51.10/50.80 | hBOOL(V_Q_2) ) ).
% 51.10/50.80
% 51.10/50.80 %----Conjectures (5)
% 51.10/50.80 fof(conj_0,hypothesis,
% 51.10/50.80 ! [B_x] :
% 51.10/50.80 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 51.10/50.80 => c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),B_x) ) ).
% 51.10/50.80
% 51.10/50.80 fof(conj_1,hypothesis,
% 51.10/50.80 ! [B_Z,B_s] :
% 51.10/50.80 ( v_P(B_Z,B_s)
% 51.10/50.80 => ! [B_s_H] :
% 51.10/50.80 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,hAPP(c_Nat_OSuc,v_na),B_s_H)
% 51.10/50.80 => v_Q(B_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,B_s_H),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,B_s_H),c_Com_ORes))) ) ) ).
% 51.10/50.80
% 51.10/50.80 fof(conj_2,hypothesis,
% 51.10/50.80 v_P(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H))) ).
% 51.10/50.80
% 51.10/50.80 fof(conj_3,hypothesis,
% 51.10/50.80 c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s_H),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),v_a(v_s_H)),v_na,v_s1) ).
% 51.10/50.80
% 51.10/50.80 fof(conj_4,conjecture,
% 51.10/50.80 v_Q(v_Z,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,v_s1),hAPP(c_Natural_Ogetlocs,v_s_H))),v_X),hAPP(hAPP(c_Natural_Ogetlocs,v_s1),c_Com_ORes))) ).
% 51.10/50.80
% 51.10/50.80 %------------------------------------------------------------------------------
% 51.10/50.80 %-------------------------------------------
% 51.10/50.80 % Proof found
% 51.10/50.80 % SZS status Theorem for theBenchmark
% 51.10/50.80 % SZS output start Proof
% 51.10/50.81 %ClaNum:10026(EqnAxiom:2787)
% 51.10/50.81 %VarNum:77835(SingletonVarNum:23385)
% 51.10/50.81 %MaxLitNum:8
% 51.10/50.81 %MaxfuncDepth:13
% 51.10/50.81 %SharedTerms:1100
% 51.10/50.81 %goalClause: 4446
% 51.10/50.81 %singleGoalClaCount:1
% 51.10/50.81 [2791]P1(a182)
% 51.10/50.81 [2792]P2(a847)
% 51.10/50.81 [2793]P2(a1)
% 51.10/50.81 [2794]P2(a106)
% 51.10/50.81 [2795]P84(a847)
% 51.10/50.81 [2796]P84(a1)
% 51.10/50.81 [2797]P84(a106)
% 51.10/50.81 [2798]P3(a847)
% 51.10/50.81 [2799]P3(a1)
% 51.10/50.81 [2800]P3(a106)
% 51.10/50.81 [2801]P62(a847)
% 51.10/50.81 [2802]P62(a1)
% 51.10/50.81 [2803]P62(a106)
% 51.10/50.81 [2804]P66(a847)
% 51.10/50.81 [2805]P66(a1)
% 51.10/50.81 [2806]P66(a106)
% 51.10/50.81 [2807]P79(a847)
% 51.10/50.81 [2808]P79(a1)
% 51.10/50.81 [2809]P79(a106)
% 51.10/50.81 [2810]P63(a847)
% 51.10/50.81 [2811]P63(a1)
% 51.10/50.81 [2812]P63(a106)
% 51.10/50.81 [2813]P80(a847)
% 51.10/50.81 [2814]P80(a1)
% 51.10/50.81 [2815]P80(a106)
% 51.10/50.81 [2816]P67(a1)
% 51.10/50.81 [2817]P71(a847)
% 51.10/50.81 [2818]P71(a1)
% 51.10/50.81 [2819]P71(a106)
% 51.10/50.81 [2820]P68(a847)
% 51.10/50.81 [2821]P68(a1)
% 51.10/50.81 [2822]P68(a106)
% 51.10/50.81 [2823]P85(a847)
% 51.10/50.81 [2824]P85(a1)
% 51.10/50.81 [2825]P85(a106)
% 51.10/50.81 [2826]P86(a1)
% 51.10/50.81 [2827]P137(a847)
% 51.10/50.81 [2828]P137(a1)
% 51.10/50.81 [2829]P87(a847)
% 51.10/50.81 [2830]P87(a1)
% 51.10/50.81 [2831]P87(a106)
% 51.10/50.81 [2832]P88(a847)
% 51.10/50.81 [2833]P88(a840)
% 51.10/50.81 [2834]P88(a1)
% 51.10/50.81 [2835]P88(a106)
% 51.10/50.81 [2836]P89(a847)
% 51.10/50.81 [2837]P89(a1)
% 51.10/50.81 [2838]P89(a106)
% 51.10/50.81 [2839]P105(a847)
% 51.10/50.81 [2840]P105(a840)
% 51.10/50.81 [2841]P105(a1)
% 51.10/50.81 [2842]P105(a106)
% 51.10/50.81 [2843]P102(a847)
% 51.10/50.81 [2844]P102(a1)
% 51.10/50.81 [2845]P102(a106)
% 51.10/50.81 [2846]P104(a847)
% 51.10/50.81 [2847]P104(a840)
% 51.10/50.81 [2848]P104(a1)
% 51.10/50.81 [2849]P104(a106)
% 51.10/50.81 [2850]P112(a1)
% 51.10/50.81 [2851]P120(a1)
% 51.10/50.81 [2852]P121(a1)
% 51.10/50.81 [2853]P90(a1)
% 51.10/50.81 [2854]P133(a1)
% 51.10/50.81 [2855]P64(a847)
% 51.10/50.81 [2856]P64(a1)
% 51.10/50.81 [2857]P64(a106)
% 51.10/50.81 [2858]P69(a1)
% 51.10/50.81 [2859]P70(a847)
% 51.10/50.81 [2860]P70(a1)
% 51.10/50.81 [2861]P70(a106)
% 51.10/50.81 [2862]P74(a847)
% 51.10/50.81 [2863]P74(a1)
% 51.10/50.81 [2864]P74(a106)
% 51.10/50.81 [2865]P75(a847)
% 51.10/50.81 [2866]P75(a1)
% 51.10/50.81 [2867]P75(a106)
% 51.10/50.81 [2868]P106(a1)
% 51.10/50.81 [2869]P76(a1)
% 51.10/50.81 [2870]P4(a1)
% 51.10/50.81 [2871]P122(a847)
% 51.10/50.81 [2872]P122(a1)
% 51.10/50.81 [2873]P122(a106)
% 51.10/50.81 [2874]P134(a1)
% 51.10/50.81 [2875]P127(a847)
% 51.10/50.81 [2876]P127(a1)
% 51.10/50.81 [2877]P127(a106)
% 51.10/50.81 [2878]P138(a847)
% 51.10/50.81 [2879]P138(a1)
% 51.10/50.81 [2880]P138(a106)
% 51.10/50.81 [2881]P111(a847)
% 51.10/50.81 [2882]P111(a1)
% 51.10/50.81 [2883]P111(a106)
% 51.10/50.81 [2884]P135(a847)
% 51.10/50.81 [2885]P135(a1)
% 51.10/50.81 [2886]P135(a106)
% 51.10/50.81 [2887]P118(a1)
% 51.10/50.81 [2888]P116(a847)
% 51.10/50.81 [2889]P116(a1)
% 51.10/50.81 [2890]P116(a106)
% 51.10/50.81 [2891]P123(a847)
% 51.10/50.81 [2892]P123(a1)
% 51.10/50.81 [2893]P123(a106)
% 51.10/50.81 [2894]P119(a1)
% 51.10/50.81 [2895]P81(a1)
% 51.10/50.81 [2896]P124(a1)
% 51.10/50.81 [2897]P77(a847)
% 51.10/50.81 [2898]P77(a1)
% 51.10/50.81 [2899]P77(a106)
% 51.10/50.81 [2900]P128(a847)
% 51.10/50.81 [2901]P128(a1)
% 51.10/50.81 [2902]P128(a106)
% 51.10/50.81 [2903]P129(a1)
% 51.10/50.81 [2904]P131(a847)
% 51.10/50.81 [2905]P131(a1)
% 51.10/50.81 [2906]P131(a106)
% 51.10/50.81 [2907]P130(a847)
% 51.10/50.81 [2908]P130(a1)
% 51.10/50.81 [2909]P130(a106)
% 51.10/50.81 [2910]P125(a847)
% 51.10/50.81 [2911]P125(a1)
% 51.10/50.81 [2912]P125(a106)
% 51.10/50.81 [2913]P126(a1)
% 51.10/50.81 [2914]P93(a840)
% 51.10/50.81 [2915]P5(a847)
% 51.10/50.81 [2916]P5(a1)
% 51.10/50.81 [2917]P5(a106)
% 51.10/50.81 [2918]P6(a1)
% 51.10/50.81 [2919]P83(a840)
% 51.10/50.81 [2920]P83(a1)
% 51.10/50.81 [2921]P72(a847)
% 51.10/50.81 [2922]P72(a840)
% 51.10/50.81 [2923]P72(a1)
% 51.10/50.81 [2924]P72(a106)
% 51.10/50.81 [2925]P91(a1)
% 51.10/50.81 [2926]P92(a847)
% 51.10/50.81 [2927]P92(a1)
% 51.10/50.81 [2928]P92(a106)
% 51.10/50.81 [2929]P78(a1)
% 51.10/50.81 [2930]P132(a1)
% 51.10/50.81 [2931]P65(a1)
% 51.10/50.81 [2932]P107(a847)
% 51.10/50.81 [2933]P107(a1)
% 51.10/50.81 [2934]P107(a106)
% 51.10/50.81 [2935]P136(a847)
% 51.10/50.81 [2936]P136(a1)
% 51.10/50.81 [2937]P136(a106)
% 51.10/50.81 [2938]P113(a847)
% 51.10/50.81 [2939]P113(a1)
% 51.10/50.81 [2940]P113(a106)
% 51.10/50.81 [2941]P110(a1)
% 51.10/50.81 [2942]P103(a847)
% 51.10/50.81 [2943]P103(a840)
% 51.10/50.81 [2944]P95(a840)
% 51.10/50.81 [2945]P97(a847)
% 51.10/50.81 [2946]P97(a840)
% 51.10/50.81 [2947]P97(a1)
% 51.10/50.81 [2948]P100(a847)
% 51.10/50.81 [2949]P100(a840)
% 51.10/50.81 [2950]P100(a1)
% 51.10/50.81 [2951]P57(a840)
% 51.10/50.81 [2952]P57(a850)
% 51.10/50.81 [2953]P101(a847)
% 51.10/50.81 [2954]P101(a840)
% 51.10/50.81 [2955]P101(a1)
% 51.10/50.81 [2956]P98(a847)
% 51.10/50.81 [2957]P98(a840)
% 51.10/50.81 [2958]P98(a1)
% 51.10/50.81 [2959]P7(a840)
% 51.10/50.81 [2960]P99(a840)
% 51.10/50.81 [2961]P108(a840)
% 51.10/50.81 [2962]P73(a847)
% 51.10/50.81 [2963]P73(a1)
% 51.10/50.81 [2964]P73(a106)
% 51.10/50.81 [2965]P109(a847)
% 51.10/50.81 [2966]P139(a1)
% 51.10/50.81 [2967]P139(a850)
% 51.10/50.81 [2968]P82(a847)
% 51.10/50.81 [2969]P82(a1)
% 51.10/50.81 [2970]P82(a106)
% 51.10/50.81 [2971]P96(a840)
% 51.10/50.81 [2983]P34(a847,a245)
% 51.10/50.81 [2984]P34(a847,a322)
% 51.10/50.81 [4325]~E(a104,a90)
% 51.10/50.81 [4326]~E(a104,a90)
% 51.10/50.81 [4327]~P1(a183)
% 51.10/50.81 [2788]E(f2(a1),a90)
% 51.10/50.81 [2789]E(f3(a106),a4)
% 51.10/50.81 [2790]E(f107(a106),a5)
% 51.10/50.81 [2972]E(f36(a25),f2(a847))
% 51.10/50.81 [2973]E(f91(a182),f2(a847))
% 51.10/50.81 [2974]E(f91(a183),f2(a847))
% 51.10/50.81 [2975]E(f184(a847),f2(a847))
% 51.10/50.81 [2976]E(f239(a847),f108(a847))
% 51.10/50.81 [2977]E(f244(a847),f109(a847))
% 51.10/50.81 [2978]E(f110(a1),f39(a1))
% 51.10/50.81 [2979]P8(f2(a1))
% 51.10/50.81 [2980]P8(f85(a1))
% 51.10/50.81 [3024]P1(f331(a26,a25))
% 51.10/50.81 [3025]P1(f331(a26,a25))
% 51.10/50.81 [3036]P34(f853(a847,a847),a45)
% 51.10/50.81 [3065]E(f171(a843,a841,a31),a32)
% 51.10/50.81 [3378]E(f324(a847,a847,a245,a245),a45)
% 51.10/50.81 [4328]~E(f85(a1),f2(a1))
% 51.10/50.81 [2981]E(f118(f2(a847)),f2(a847))
% 51.10/50.81 [2982]E(f6(f2(a106)),f2(a847))
% 51.10/50.81 [2988]E(f331(f86(a1),a90),a90)
% 51.10/50.81 [2991]E(f331(a112,f2(a1)),f2(a847))
% 51.10/50.81 [2992]E(f331(a5,f2(a847)),f2(a106))
% 51.10/50.81 [2993]E(f331(a119,f2(a847)),f85(a847))
% 51.10/50.81 [2994]E(f331(a112,f85(a1)),f85(a847))
% 51.10/50.81 [2995]E(f331(a5,f85(a847)),f85(a106))
% 51.10/50.81 [2996]E(f331(f111(a847),a90),f2(a847))
% 51.10/50.81 [2997]E(f331(f111(a1),a90),f2(a1))
% 51.10/50.81 [2998]E(f331(f111(a106),a90),f2(a106))
% 51.10/50.81 [2999]E(f331(a112,f2(a1)),f2(a847))
% 51.10/50.81 [3000]E(f331(f185(a841),a25),f2(a847))
% 51.10/50.81 [3001]E(f331(f185(a840),a182),f2(a847))
% 51.10/50.81 [3002]E(f331(f185(a840),a183),f2(a847))
% 51.10/50.81 [3003]E(f331(f111(a847),a90),f2(a847))
% 51.10/50.81 [3009]E(f331(f86(a1),f85(a1)),a104)
% 51.10/50.81 [3014]E(f331(f107(a1),f2(a847)),f2(a1))
% 51.10/50.81 [3015]E(f331(f107(a1),f85(a847)),f85(a1))
% 51.10/50.81 [3016]E(f331(f185(a847),f2(a847)),f2(a847))
% 51.10/50.81 [3017]E(f331(f185(a106),f2(a106)),f2(a847))
% 51.10/50.81 [3018]E(f331(f107(a1),f2(a847)),f2(a1))
% 51.10/50.81 [3019]E(f331(f107(a1),f85(a847)),f85(a1))
% 51.10/50.81 [3020]E(f331(f86(a1),f2(a1)),f2(a1))
% 51.10/50.81 [3032]E(f331(a112,f85(a1)),f331(a119,f2(a847)))
% 51.10/50.81 [3034]E(f323(f853(a847,a847),a45),a46)
% 51.10/50.81 [3035]E(f325(f853(a847,a847),a45),a75)
% 51.10/50.81 [3056]E(f331(f265(a847),f2(a847)),f184(f854(a847,a840)))
% 51.10/50.81 [3057]E(f331(f266(a847),f2(a847)),f247(f854(a847,a840)))
% 51.10/50.81 [3067]P36(f184(f854(a1,a840)))
% 51.10/50.81 [3103]E(f331(f331(f3(a106),f2(a106)),f85(a106)),f2(a106))
% 51.10/50.81 [3146]E(f331(f331(f147(a1,a847),a112),f120(a1)),f120(a847))
% 51.10/50.81 [3177]P1(f331(f331(f241(a1),a104),f2(a1)))
% 51.10/50.81 [3202]P1(f331(f331(f241(a1),f2(a1)),f85(a1)))
% 51.10/50.81 [3203]P1(f331(f331(f240(a1),f2(a1)),f2(a1)))
% 51.10/50.81 [3204]P1(f331(f331(f240(a1),f2(a1)),f85(a1)))
% 51.10/50.81 [3369]P1(f331(f68(a843),f174(a843,a841,a32)))
% 51.10/50.81 [3411]E(f331(f331(f289(a847,a847,a847),a322),f308(a847,a322)),a245)
% 51.10/50.81 [3452]P38(a1,a847,a112,f331(f240(a1),f2(a1)))
% 51.10/50.81 [3455]E(f331(f331(f51(a847,f854(a847,a840)),f247(f854(a847,a840))),f301(a847)),f247(f854(a847,a840)))
% 51.10/50.81 [3456]E(f331(f331(f51(a847,f854(a847,a840)),f247(f854(a847,a840))),f265(a847)),f247(f854(a847,a840)))
% 51.10/50.81 [3457]E(f331(f331(f51(a847,f854(a847,a840)),f247(f854(a847,a840))),f266(a847)),f247(f854(a847,a840)))
% 51.10/50.81 [3458]E(f331(f331(f52(a847,f854(a847,a840)),f247(f854(a847,a840))),f304(a847)),f184(f854(a847,a840)))
% 51.10/50.81 [3474]P27(a847,a1,f107(a1),f247(f854(a847,a840)))
% 51.10/50.81 [3485]P38(a847,a1,f107(a1),f331(f18(a840,a847),a182))
% 51.10/50.81 [3618]E(f331(f80(a847,a106,a1,a5),a112),f111(a106))
% 51.10/50.81 [3723]P142(a856,f331(f331(f331(a193,f331(f331(a194,a859),a195)),f40(a27)),f860(a859)))
% 51.10/50.81 [3792]P37(f331(f238(a841),f331(a32,a861)),f331(f331(f331(a193,f331(f331(a194,a859),a195)),f40(a27)),f860(a859)),a862,a863)
% 51.10/50.81 [3837]P53(a106,a847,a22,a5,f247(f854(a847,a840)))
% 51.10/50.81 [3845]P53(a1,f854(f853(a847,a847),a840),a115,a96,a105)
% 51.10/50.81 [4109]E(f260(a1,a1,a1,a1,f39(a1),f86(a1)),a63)
% 51.10/50.81 [4361]~E(f331(f111(a1),a104),f331(f111(a1),a90))
% 51.10/50.81 [4362]~P1(f331(a190,f2(a1)))
% 51.10/50.81 [4363]~P1(f331(a190,f85(a1)))
% 51.10/50.81 [4415]~P1(f331(f331(f241(a1),a90),f2(a1)))
% 51.10/50.81 [3048]E(f331(f331(f87(a1),a90),a104),a104)
% 51.10/50.81 [3049]E(f331(f331(f87(a1),a90),a90),a90)
% 51.10/50.81 [3050]E(f331(f331(f3(a1),a104),a104),a90)
% 51.10/50.81 [3064]E(f331(f107(a1),f331(a119,f2(a847))),f85(a1))
% 51.10/50.81 [3128]E(f331(f47(a850),f247(f854(a850,a840))),f85(a847))
% 51.10/50.81 [3151]P1(f331(a190,f331(f111(a1),a104)))
% 51.10/50.81 [3152]P1(f331(f331(f241(a1),a104),a90))
% 51.10/50.81 [3153]P1(f331(f331(f240(a1),a104),a104))
% 51.10/50.81 [3154]P1(f331(f331(f240(a1),a104),a90))
% 51.10/50.81 [3155]P1(f331(f331(f240(a1),a90),a90))
% 51.10/50.81 [3214]E(f331(f331(f310(a847),f2(a847)),f184(f854(a847,a840))),f331(f301(a847),f2(a847)))
% 51.10/50.81 [3267]P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),a90)))
% 51.10/50.81 [3278]E(f331(f311(a847,a847,a119),f247(f854(a847,a840))),f331(f304(a847),f2(a847)))
% 51.10/50.81 [3283]E(f331(f311(a1,a847,a112),f184(f854(a1,a840))),f184(f854(a847,a840)))
% 51.10/50.81 [3292]E(f331(f311(a847,a1,f107(a1)),f184(f854(a847,a840))),f184(f854(a1,a840)))
% 51.10/50.81 [3316]P10(f853(a847,a847),f247(f854(f853(a847,a847),a840)),a116)
% 51.10/50.81 [3625]E(f331(f80(a847,a1,a106,f107(a1)),a22),a23)
% 51.10/50.81 [3685]P34(a847,f331(f264(f853(a847,a847)),f331(f259(a847,a847,a840),f241(a847))))
% 51.10/50.81 [4406]~P1(f331(a190,f331(f111(a1),a90)))
% 51.10/50.81 [4407]~P1(f331(f331(f241(a1),a104),a104))
% 51.10/50.81 [4408]~P1(f331(f331(f241(a1),a90),a104))
% 51.10/50.81 [4409]~P1(f331(f331(f241(a1),a90),a90))
% 51.10/50.81 [4410]~P1(f331(f331(f240(a1),a90),a104))
% 51.10/50.81 [4425]~P1(f331(f68(a847),f247(f854(a847,a840))))
% 51.10/50.81 [4426]~P1(f331(f68(a1),f247(f854(a1,a840))))
% 51.10/50.81 [4446]~P143(a856,f331(f331(f331(a193,f331(f331(a194,a863),f331(a196,a859))),a857),f331(f331(a196,a863),a28)))
% 51.10/50.81 [4271]E(f331(f259(a1,a1,a840),f331(f331(f10(f854(a1,a840),f854(a1,a840),a1),f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f241(a1),f2(a1))))),f331(f331(f9(a1,a1,f854(a1,a840)),f331(f331(f10(f854(a1,f854(a1,a840)),f854(a1,f854(a1,a840)),a1),f9(a1,a1,a840)),f331(f331(f10(f854(a1,a1),f854(a1,f854(a1,a840)),a1),f331(f10(a1,f854(a1,a840),a1),a328)),a219))),f85(a1)))),a215)
% 51.10/50.81 [3319]E(f331(f331(f3(a1),f331(f331(f87(a1),a104),a104)),a104),a104)
% 51.10/50.81 [3351]E(f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104),f331(f86(a1),a104))
% 51.10/50.81 [3393]E(f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104),f331(f331(f3(a1),a90),a104))
% 51.10/50.81 [3549]E(f331(f331(f66(f853(a847,a847)),f247(f854(f853(a847,a847),a840))),a116),a105)
% 51.10/50.81 [3578]E(f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f85(a847))
% 51.10/50.81 [3579]E(f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f85(a1))
% 51.10/50.81 [3580]E(f331(f111(a106),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f85(a106))
% 51.10/50.81 [3581]E(f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f85(a847))
% 51.10/50.81 [3585]E(f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(a119,f2(a847)))
% 51.10/50.81 [3973]E(f331(f331(f108(f854(f853(f853(a847,a847),f853(a847,a847)),a840)),a45),f308(f853(a847,a847),f184(f854(f853(f853(a847,a847),f853(a847,a847)),a840)))),a77)
% 51.10/50.81 [4041]E(f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),f2(a847)),f2(a847))),f184(f854(f853(a847,a847),a840))))),f2(a1))
% 51.10/50.81 [4042]E(f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),f85(a847)),f2(a847))),f184(f854(f853(a847,a847),a840))))),f85(a1))
% 51.10/50.81 [4056]E(f331(f264(f853(a847,a847)),f331(f259(a847,a847,a840),f331(f331(f10(a847,f854(a847,a840),a847),f331(f9(a847,a847,a840),a328)),a119))),a322)
% 51.10/50.81 [4026]E(f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),f331(a119,f331(a119,f2(a847))))
% 51.10/50.81 [4027]E(f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),f331(a119,f331(a119,f2(a847))))
% 51.10/50.81 [4030]E(f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),f331(f331(f87(a847),f85(a847)),f85(a847)))
% 51.10/50.81 [4031]E(f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),f331(f47(a840),f247(f854(a840,a840))))
% 51.10/50.81 [4094]P8(f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))
% 51.10/50.81 [4165]P28(f854(f853(a847,a847),a840),f331(f331(f249(f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840),f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840)),a46),a76))
% 51.10/50.81 [4166]P28(f854(f853(a847,a847),a840),f331(f331(f249(f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840),f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840)),a75),a78))
% 51.10/50.81 [4203]E(f331(f331(f108(f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840)),f325(f853(a847,a847),a77)),f331(f331(f310(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),f184(f854(f853(a847,a847),a840))),f184(f854(f853(a847,a847),a840)))),f184(f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840)))),a78)
% 51.10/50.81 [4204]E(f331(f331(f108(f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840)),f323(f853(a847,a847),a77)),f331(f331(f310(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),f184(f854(f853(a847,a847),a840))),f184(f854(f853(a847,a847),a840)))),f184(f854(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a840)))),a76)
% 51.10/50.81 [4096]E(f331(a112,f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(a119,f331(a119,f2(a847))))
% 51.10/50.81 [4141]E(f331(a112,f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))
% 51.10/50.81 [4142]E(f331(f107(a1),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))
% 51.10/50.81 [4175]P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.81 [4176]E(f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104)),f331(a119,f331(a119,f331(a119,f2(a847)))))
% 51.10/50.81 [4216]P8(f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104)))
% 51.10/50.81 [4242]E(f331(a112,f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104)))
% 51.10/50.81 [4243]E(f331(f107(a1),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104)))
% 51.10/50.81 [4257]P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))))
% 51.10/50.81 [2985]P9(x29851,a328)
% 51.10/50.81 [3379]P27(a847,a847,a119,x33791)
% 51.10/50.81 [3004]P34(a1,f113(x30041))
% 51.10/50.81 [3005]P34(a1,f114(x30051))
% 51.10/50.81 [3008]P35(x30081,f187(x30081))
% 51.10/50.81 [3053]P34(f854(x30531,a840),f307(x30531))
% 51.10/50.81 [3094]E(f57(a1,x30941,x30941),f2(a1))
% 51.10/50.81 [3148]P17(x31481,f854(x31481,a840),f310(x31481))
% 51.10/50.81 [4331]~E(f331(a29,x43311),a25)
% 51.10/50.81 [4332]~E(f331(a29,x43321),a25)
% 51.10/50.81 [4333]~E(f331(a119,x43331),x43331)
% 51.10/50.81 [4334]~E(f331(a119,x43341),x43341)
% 51.10/50.81 [4341]~E(f331(a119,x43411),f2(a847))
% 51.10/50.81 [4342]~E(f331(a119,x43421),f2(a847))
% 51.10/50.81 [4343]~E(f331(a119,x43431),f2(a847))
% 51.10/50.81 [4344]~E(f331(a119,x43441),f2(a847))
% 51.10/50.81 [4345]~E(f331(a119,x43451),f2(a847))
% 51.10/50.81 [4346]~E(f331(a119,x43461),f2(a847))
% 51.10/50.81 [2986]E(f42(f40(x29861)),f2(a847))
% 51.10/50.81 [2987]E(f42(f41(x29871)),f2(a847))
% 51.10/50.81 [2989]E(f331(f185(a847),x29891),x29891)
% 51.10/50.81 [2990]E(f331(f111(a1),x29901),x29901)
% 51.10/50.81 [3006]E(f331(a96,f332(x30061)),x30061)
% 51.10/50.81 [3007]E(f246(x30071,f2(a106)),f2(a106))
% 51.10/50.81 [3021]E(f121(x30211,f120(x30211)),f120(x30211))
% 51.10/50.81 [3022]E(f146(x30221,f120(x30221)),f120(x30221))
% 51.10/50.81 [3026]E(f331(f185(a842),f40(x30261)),f2(a847))
% 51.10/50.81 [3027]E(f331(f185(a842),f41(x30271)),f2(a847))
% 51.10/50.81 [3028]E(f36(f331(a29,x30281)),f2(a847))
% 51.10/50.81 [3029]E(f331(f159(x30291),f120(x30291)),f120(x30291))
% 51.10/50.81 [3030]E(f331(f162(x30301),f120(x30301)),f120(x30301))
% 51.10/50.81 [3031]E(f331(f160(x30311),f120(x30311)),f120(x30311))
% 51.10/50.81 [3037]E(f331(f111(a1),x30371),f331(f110(a1),x30371))
% 51.10/50.81 [3038]E(f331(a5,f331(a22,x30381)),x30381)
% 51.10/50.81 [3039]E(f331(a5,f331(a22,x30391)),x30391)
% 51.10/50.81 [3040]E(f331(a22,f331(a5,x30401)),x30401)
% 51.10/50.81 [3041]E(f331(a96,f331(a115,x30411)),x30411)
% 51.10/50.81 [3042]P8(f331(f107(a1),x30421))
% 51.10/50.81 [3046]E(f331(f185(f851(x30461)),f187(x30461)),f2(a847))
% 51.10/50.81 [3047]E(f331(f185(f848(x30471)),f120(x30471)),f2(a847))
% 51.10/50.81 [3052]E(f331(f185(a841),f331(a29,x30521)),f2(a847))
% 51.10/50.81 [3062]E(f233(x30621,f187(x30621)),f184(f854(x30621,a840)))
% 51.10/50.81 [3070]E(f331(f331(f87(a847),x30701),f2(a847)),x30701)
% 51.10/50.81 [3071]E(f331(f331(f87(a1),x30711),f2(a1)),x30711)
% 51.10/50.81 [3072]E(f331(f331(f88(a847),x30721),f85(a847)),x30721)
% 51.10/50.81 [3073]E(f331(f331(f88(a1),x30731),f85(a1)),x30731)
% 51.10/50.81 [3074]E(f331(f331(f3(a847),x30741),f2(a847)),x30741)
% 51.10/50.81 [3075]E(f331(f331(f239(a847),x30751),f2(a847)),x30751)
% 51.10/50.81 [3076]E(f331(f331(f88(a847),x30761),f2(a847)),f2(a847))
% 51.10/50.81 [3077]E(f331(f331(f48(a1),x30771),f2(a1)),f2(a1))
% 51.10/50.81 [3078]E(f331(f331(f244(a847),x30781),f2(a847)),f2(a847))
% 51.10/50.81 [3084]E(f331(f163(x30841),f120(x30841)),f184(f854(x30841,a840)))
% 51.10/50.81 [3089]P1(f331(f132(x30891),f120(x30891)))
% 51.10/50.81 [3095]E(f331(f147(x30951,x30951),f7(x30951)),f39(f848(x30951)))
% 51.10/50.81 [3096]E(f331(f147(x30961,x30961),f39(x30961)),f39(f848(x30961)))
% 51.10/50.81 [3097]E(f331(f203(x30971,x30971),f7(x30971)),f39(f851(x30971)))
% 51.10/50.81 [3098]E(f331(f203(x30981,x30981),f39(x30981)),f39(f851(x30981)))
% 51.10/50.81 [3099]E(f57(a1,x30991,f2(a1)),x30991)
% 51.10/50.81 [3100]E(f331(f240(a847),f331(a119,x31001)),f331(f241(a847),x31001))
% 51.10/50.81 [3101]E(f331(f265(a847),f331(a119,x31011)),f331(f301(a847),x31011))
% 51.10/50.81 [3102]E(f331(f266(a847),f331(a119,x31021)),f331(f304(a847),x31021))
% 51.10/50.81 [3104]E(f57(a1,f2(a1),x31041),f2(a1))
% 51.10/50.81 [3111]E(f331(f331(f87(a847),x31111),f85(a847)),f331(a119,x31111))
% 51.10/50.81 [3121]E(f331(f302(a847,x31211),f2(a847)),f184(f854(a847,a840)))
% 51.10/50.81 [3134]E(f303(a847,f2(a847),x31341),f331(f301(a847),x31341))
% 51.10/50.81 [3180]E(f331(f331(f3(a847),f331(a119,x31801)),f85(a847)),x31801)
% 51.10/50.81 [3193]E(f59(f2(a1),x31931),f331(f331(f249(a1,a1),f2(a1)),f2(a1)))
% 51.10/50.81 [3197]E(f331(f331(f87(a847),f331(a22,x31971)),f2(a847)),f331(a22,x31971))
% 51.10/50.81 [3242]P1(f331(f331(f241(a847),x32421),f331(a119,x32421)))
% 51.10/50.81 [3254]P1(f331(f331(f241(a847),f2(a847)),f331(a119,x32541)))
% 51.10/50.81 [3265]E(f331(f331(f178(f848(x32651),f848(x32651)),f2(a847)),f159(x32651)),f39(f848(x32651)))
% 51.10/50.81 [3535]E(f331(f331(f3(a106),f331(a5,f331(a119,f331(a22,x35351)))),f85(a106)),x35351)
% 51.10/50.81 [3607]P1(f331(f331(f240(a1),f331(f86(a1),f331(f107(a1),x36071))),f2(a1)))
% 51.10/50.81 [3759]P1(f331(f331(f241(a1),f331(f86(a1),f331(f107(a1),f331(a119,x37591)))),f2(a1)))
% 51.10/50.81 [4369]~E(f247(f854(x43691,a840)),f184(f854(x43691,a840)))
% 51.10/50.81 [4416]~P1(f331(f331(f241(a847),x44161),f2(a847)))
% 51.10/50.81 [4417]~P1(f331(f331(f241(a847),x44171),f2(a847)))
% 51.10/50.81 [4418]~P1(f331(f331(f241(a847),x44181),f2(a847)))
% 51.10/50.81 [4434]~P1(f331(f331(f241(a1),f331(f107(a1),x44341)),f2(a1)))
% 51.10/50.81 [3051]E(f169(x30511,f120(f848(x30511))),f120(f848(x30511)))
% 51.10/50.81 [3054]E(f331(f331(f88(a1),a90),x30541),a90)
% 51.10/50.81 [3055]E(f331(f331(f87(a1),a90),x30551),x30551)
% 51.10/50.81 [3058]E(f331(a112,f331(f107(a1),x30581)),x30581)
% 51.10/50.81 [3059]E(f331(f331(f87(a1),x30591),a90),x30591)
% 51.10/50.81 [3060]E(f331(f331(f3(a1),x30601),a90),x30601)
% 51.10/50.81 [3063]E(f331(f331(f3(a847),x30631),x30631),f2(a847))
% 51.10/50.81 [3068]E(f331(f86(a1),f331(f86(a1),x30681)),x30681)
% 51.10/50.81 [3069]E(f331(f47(a847),f331(f265(a847),x30691)),x30691)
% 51.10/50.81 [3079]E(f331(f331(f87(a847),f2(a847)),x30791),x30791)
% 51.10/50.81 [3080]E(f331(f331(f87(a1),f2(a1)),x30801),x30801)
% 51.10/50.81 [3081]E(f331(f331(f88(a847),f85(a847)),x30811),x30811)
% 51.10/50.81 [3082]E(f331(f331(f88(a1),f85(a1)),x30821),x30821)
% 51.10/50.81 [3083]E(f331(f331(f239(a847),f2(a847)),x30831),x30831)
% 51.10/50.81 [3090]E(f331(f331(f88(a847),f2(a847)),x30901),f2(a847))
% 51.10/50.81 [3091]E(f331(f331(f48(a1),f2(a1)),x30911),f2(a1))
% 51.10/50.81 [3092]E(f331(f331(f3(a847),f2(a847)),x30921),f2(a847))
% 51.10/50.81 [3093]E(f331(f331(f244(a847),f2(a847)),x30931),f2(a847))
% 51.10/50.81 [3109]E(f331(f302(a847,f2(a847)),x31091),f331(f265(a847),x31091))
% 51.10/50.81 [3110]E(f331(f331(f88(a1),a104),x31101),f331(f86(a1),x31101))
% 51.10/50.81 [3112]E(f331(a112,f331(f111(a1),x31121)),f331(f111(a847),x31121))
% 51.10/50.81 [3113]E(f331(a112,f331(f111(a1),x31131)),f331(f111(a847),x31131))
% 51.10/50.81 [3114]E(f331(a22,f331(f111(a106),x31141)),f331(f111(a847),x31141))
% 51.10/50.81 [3115]E(f331(f47(a847),f331(f301(a847),x31151)),f331(a119,x31151))
% 51.10/50.81 [3126]E(f331(f331(f87(a847),f85(a847)),x31261),f331(a119,x31261))
% 51.10/50.81 [3130]E(f331(f110(a1),f331(f107(a1),x31301)),f331(f107(a1),x31301))
% 51.10/50.81 [3131]E(f331(f82(a1),f331(f107(a1),x31311)),f331(f107(a1),x31311))
% 51.10/50.81 [3136]E(f331(f47(x31361),f184(f854(x31361,a840))),f2(a847))
% 51.10/50.81 [3138]E(f331(f331(f48(a847),x31381),f331(a119,f2(a847))),x31381)
% 51.10/50.81 [3149]E(f57(a847,x31491,f331(a119,f2(a847))),f2(a847))
% 51.10/50.81 [3150]E(f57(a1,x31501,f331(f111(a1),a104)),f2(a1))
% 51.10/50.81 [3157]E(f331(f331(f87(a1),a104),x31571),f331(f331(f87(a1),x31571),a104))
% 51.10/50.81 [3164]E(f331(f331(f48(a1),x31641),f331(f111(a1),a104)),f331(f86(a1),x31641))
% 51.10/50.81 [3168]E(f135(a847,f331(f302(a847,x31681),f2(a847))),f120(a847))
% 51.10/50.81 [3169]E(f331(f331(f3(a1),x31691),f85(a1)),f331(f331(f87(a1),x31691),a104))
% 51.10/50.81 [3170]E(f331(f331(f87(a1),x31701),f85(a1)),f331(f331(f3(a1),x31701),a104))
% 51.10/50.81 [3172]P1(f331(f331(f191(a25),x31721),x31721))
% 51.10/50.81 [3173]P1(f331(f331(f191(a25),x31731),x31731))
% 51.10/50.81 [3174]P1(f331(f331(f240(a847),x31741),x31741))
% 51.10/50.81 [3175]P1(f331(f331(f240(a1),x31751),x31751))
% 51.10/50.81 [3176]P1(f331(f331(f287(a847),x31761),x31761))
% 51.10/50.81 [3181]E(f331(f86(a1),f331(f111(a1),x31811)),f331(f111(a1),f331(f86(a1),x31811)))
% 51.10/50.81 [3182]P1(f331(f68(a847),f331(f301(a847),x31821)))
% 51.10/50.81 [3183]P1(f331(f68(a847),f331(f265(a847),x31831)))
% 51.10/50.81 [3191]E(f153(x31911,f247(f854(x31911,a840))),f247(f854(f848(x31911),a840)))
% 51.10/50.81 [3195]P1(f331(f331(f240(a847),f2(a847)),x31951))
% 51.10/50.81 [3196]P1(f331(f331(f240(a847),f2(a847)),x31961))
% 51.10/50.81 [3207]E(f331(f331(f87(a847),f118(x32071)),f331(a119,f2(a847))),f118(f331(a119,x32071)))
% 51.10/50.81 [3208]E(f331(f264(x32081),f331(f18(a840,x32081),a183)),f184(f854(x32081,a840)))
% 51.10/50.81 [3209]E(f331(f264(x32091),f331(f18(a840,x32091),a182)),f247(f854(x32091,a840)))
% 51.10/50.81 [3213]E(f331(f331(f310(a847),x32131),f331(f265(a847),x32131)),f331(f265(a847),f331(a119,x32131)))
% 51.10/50.81 [3224]E(f331(f331(f87(a1),f85(a1)),f331(f107(a1),x32241)),f331(f107(a1),f331(a119,x32241)))
% 51.10/50.81 [3245]E(f184(f854(f853(x32451,x32451),a840)),f268(x32451,f184(f854(x32451,a840))))
% 51.10/50.81 [3246]E(f331(f309(x32461),f247(f854(x32461,a840))),f247(f854(f854(x32461,a840),a840)))
% 51.10/50.81 [3247]E(f331(f86(f854(x32471,a840)),f184(f854(x32471,a840))),f247(f854(x32471,a840)))
% 51.10/50.81 [3248]E(f331(f86(f854(x32481,a840)),f247(f854(x32481,a840))),f184(f854(x32481,a840)))
% 51.10/50.81 [3249]P1(f331(f68(x32491),f184(f854(x32491,a840))))
% 51.10/50.81 [3250]P1(f331(f68(x32501),f184(f854(x32501,a840))))
% 51.10/50.81 [3252]E(f331(f302(a847,x32521),f331(a119,x32521)),f331(f331(f310(a847),x32521),f184(f854(a847,a840))))
% 51.10/50.81 [3253]E(f92(f853(a847,a847),f60(x32531,f2(a847))),f331(f331(f249(a847,a847),f2(a847)),x32531))
% 51.10/50.81 [3266]E(f331(f331(f310(a847),f331(a119,x32661)),f331(f301(a847),x32661)),f331(f301(a847),f331(a119,x32661)))
% 51.10/50.81 [3269]P34(x32691,f184(f854(f853(x32691,x32691),a840)))
% 51.10/50.81 [3271]P1(f331(f331(f240(a1),f2(a1)),f331(f107(a1),x32711)))
% 51.10/50.81 [3272]P1(f331(f331(f240(a1),f2(a1)),f331(f107(a1),x32721)))
% 51.10/50.81 [3280]E(f331(f331(f87(a847),f331(f185(a847),x32801)),f331(a119,f2(a847))),f331(f185(a847),f331(a119,x32801)))
% 51.10/50.81 [3331]E(f331(f311(x33311,x33311,f39(x33311)),f247(f854(x33311,a840))),f247(f854(x33311,a840)))
% 51.10/50.81 [3386]P36(f331(f311(a847,a1,f107(a1)),x33861))
% 51.10/50.81 [3426]P45(x34261,f184(f854(x34261,a840)),f184(f854(f853(x34261,x34261),a840)))
% 51.10/50.81 [3449]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f3(a1),x34491),f85(a1))),f62(f331(f111(a1),a104),x34491))
% 51.10/50.81 [3450]P1(f331(f331(f333(a847),f331(a22,x34501)),f247(f854(a847,a840))))
% 51.10/50.81 [3497]P56(x34971,f331(f18(f854(x34971,a840),x34971),f331(f18(a840,x34971),a183)))
% 51.10/50.81 [3506]E(f290(a847,f287(a847),x35061,x35061),f331(f331(f310(a847),x35061),f184(f854(a847,a840))))
% 51.10/50.81 [3679]E(f331(f137(f848(x36791),f848(x36791),f130(x36791),f120(x36791)),f120(f848(x36791))),f120(x36791))
% 51.10/50.81 [3697]P1(f331(f331(f333(f854(f853(a847,a847),a840)),f332(x36971)),a105))
% 51.10/50.81 [3722]P1(f331(f331(f333(f854(f853(a847,a847),a840)),f331(a115,x37221)),a105))
% 51.10/50.81 [3855]P27(x38551,f854(x38551,a840),f331(f331(f9(x38551,f854(x38551,a840),f854(x38551,a840)),f310(x38551)),f184(f854(x38551,a840))),f247(f854(x38551,a840)))
% 51.10/50.81 [4364]~E(f331(f331(f87(a1),x43641),x43641),a104)
% 51.10/50.81 [4365]~E(f331(f331(f87(a1),x43651),x43651),a104)
% 51.10/50.81 [4404]~E(f331(a5,f331(a119,f331(a22,x44041))),f2(a106))
% 51.10/50.81 [4405]~E(f331(a5,f331(a119,f331(a22,x44051))),f2(a106))
% 51.10/50.81 [4411]~P1(f331(a190,f331(f107(a1),x44111)))
% 51.10/50.81 [4413]~P1(f331(f331(f241(a847),x44131),x44131))
% 51.10/50.81 [4414]~P1(f331(f331(f241(a847),x44141),x44141))
% 51.10/50.81 [4427]~P1(f331(f331(f240(a847),f331(a119,x44271)),x44271))
% 51.10/50.81 [3198]E(f331(a112,f331(f86(a1),f331(f107(a1),x31981))),f2(a847))
% 51.10/50.81 [3201]E(f331(f331(f87(a1),f331(f86(a1),x32011)),x32011),f2(a1))
% 51.10/50.81 [3206]E(f331(f47(a1),f331(f302(a1,f2(a1)),x32061)),f331(a112,x32061))
% 51.10/50.81 [3217]E(f331(f331(f250(a847),f331(a119,f2(a847))),x32171),f331(a119,f2(a847)))
% 51.10/50.81 [3313]E(f331(f284(x33131),f184(f854(f853(x33131,x33131),a840))),f184(f854(x33131,a840)))
% 51.10/50.81 [3315]P1(f331(f68(a1),f331(f302(a1,f2(a1)),x33151)))
% 51.10/50.81 [3321]E(f50(f854(x33211,a840),f184(f854(f854(x33211,a840),a840))),f247(f854(x33211,a840)))
% 51.10/50.81 [3322]E(f50(f854(x33221,a840),f247(f854(f854(x33221,a840),a840))),f184(f854(x33221,a840)))
% 51.10/50.81 [3323]E(f49(f854(x33231,a840),f184(f854(f854(x33231,a840),a840))),f184(f854(x33231,a840)))
% 51.10/50.81 [3324]E(f49(f854(x33241,a840),f247(f854(f854(x33241,a840),a840))),f247(f854(x33241,a840)))
% 51.10/50.81 [3329]P1(f331(f331(f287(a847),f331(a119,f2(a847))),x33291))
% 51.10/50.81 [3367]E(f331(f331(f310(f848(x33671)),f120(x33671)),f184(f854(f848(x33671),a840))),f154(x33671,f120(f854(x33671,a840))))
% 51.10/50.81 [3368]E(f331(f331(f310(f848(x33681)),f120(x33681)),f184(f854(f848(x33681),a840))),f153(x33681,f184(f854(x33681,a840))))
% 51.10/50.81 [3399]E(f331(f331(f87(a1),f331(f86(a1),x33991)),f331(f86(a1),x33991)),f331(f86(a1),f331(f331(f87(a1),x33991),x33991)))
% 51.10/50.81 [3410]E(f331(f331(f87(a847),f6(x34101)),f331(a119,f2(a847))),f6(f331(a5,f331(a119,f331(a22,x34101)))))
% 51.10/50.81 [3441]E(f331(f47(a1),f331(f311(a847,a1,f107(a1)),x34411)),f331(f47(a847),x34411))
% 51.10/50.81 [3444]P1(f331(f331(f240(a847),x34441),f331(f331(f88(a847),x34441),x34441)))
% 51.10/50.81 [3478]E(f331(f311(a1,a847,a112),f303(a1,f2(a1),f331(f107(a1),x34781))),f331(f301(a847),x34781))
% 51.10/50.81 [3492]E(f331(f331(f48(a847),f331(a119,f2(a847))),f331(f111(a847),x34921)),f331(a112,f331(f331(f48(a1),f85(a1)),f331(f111(a1),x34921))))
% 51.10/50.81 [3494]E(f331(f163(a847),f135(a847,f331(f302(a847,f2(a847)),f331(a119,x34941)))),f331(f301(a847),x34941))
% 51.10/50.81 [3495]E(f331(f331(f87(a847),f331(f185(a106),x34951)),f331(a119,f2(a847))),f331(f185(a106),f331(a5,f331(a119,f331(a22,x34951)))))
% 51.10/50.81 [3511]E(f331(f311(a1,a847,a112),f331(f311(a847,a1,f107(a1)),x35111)),x35111)
% 51.10/50.81 [3541]E(f331(f331(f310(a847),f2(a847)),f331(f311(a847,a847,a119),f331(f265(a847),x35411))),f331(f265(a847),f331(a119,x35411)))
% 51.10/50.81 [3548]P51(x35481,x35481,f308(x35481,f184(f854(f853(x35481,x35481),a840))))
% 51.10/50.81 [3554]P1(f331(a190,f331(f86(a1),f331(f107(a1),f331(a119,x35541)))))
% 51.10/50.81 [3565]E(f331(f331(f3(f854(a847,a840)),f331(f266(a847),x35651)),f331(f331(f310(a847),x35651),f184(f854(a847,a840)))),f331(f266(a847),f331(a119,x35651)))
% 51.10/50.81 [3582]E(f331(f331(f87(a1),f331(f331(f3(a1),a90),x35821)),f331(f331(f3(a1),a90),x35821)),f331(f331(f3(a1),a90),f331(f331(f87(a1),x35821),x35821)))
% 51.10/50.81 [3586]P45(x35861,f247(f854(x35861,a840)),f308(x35861,f184(f854(f853(x35861,x35861),a840))))
% 51.10/50.81 [3597]E(f331(f331(f310(f854(x35971,a840)),f184(f854(x35971,a840))),f184(f854(f854(x35971,a840),a840))),f331(f309(x35971),f184(f854(x35971,a840))))
% 51.10/50.81 [3626]E(f331(f331(f3(f854(a847,a840)),f331(f304(a847),x36261)),f331(f331(f310(a847),f331(a119,x36261)),f184(f854(a847,a840)))),f331(f304(a847),f331(a119,x36261)))
% 51.10/50.81 [3635]E(f331(f331(f310(f851(x36351)),f187(x36351)),f331(f311(x36351,f851(x36351),f234(x36351)),f247(f854(x36351,a840)))),f247(f854(f851(x36351),a840)))
% 51.10/50.81 [3735]E(f331(f111(a847),f331(f331(f87(a1),x37351),x37351)),f331(f331(f93(a847,a847),f331(f111(a847),x37351)),f331(f331(f20(a847,a847,a847),f87(a847)),f7(a847))))
% 51.10/50.81 [4118]P17(x41181,f854(x41181,a840),f331(f331(f10(f854(x41181,a840),f854(f854(x41181,a840),f854(x41181,a840)),x41181),f331(f9(f854(x41181,a840),f854(x41181,a840),f854(x41181,a840)),f3(f854(x41181,a840)))),f331(f331(f9(x41181,f854(x41181,a840),f854(x41181,a840)),f310(x41181)),f184(f854(x41181,a840)))))
% 51.10/50.81 [4202]E(f331(f264(f853(a1,a1)),f331(f259(a1,a1,a840),f331(f331(f10(f854(a1,a840),f854(a1,a840),a1),f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),x42021)))),f241(a1)))),f113(x42021))
% 51.10/50.81 [4234]E(f331(f264(f853(a1,a1)),f331(f259(a1,a1,a840),f331(f331(f20(a1,f854(a1,a840),f854(a1,a840)),f331(f331(f10(f854(a840,a840),f854(f854(a1,a840),f854(a1,a840)),a1),f10(a840,a840,a1)),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),x42341)))),f241(a1)))),f114(x42341))
% 51.10/50.81 [4286]E(f331(f264(f853(f854(x42861,a840),f854(x42861,a840))),f331(f259(f854(x42861,a840),f854(x42861,a840),a840),f331(f331(f9(f854(x42861,a840),f854(f854(x42861,a840),a840),f854(f854(x42861,a840),a840)),f331(f331(f10(f854(f854(x42861,a840),f854(a840,a840)),f854(f854(f854(x42861,a840),a840),f854(f854(x42861,a840),a840)),f854(x42861,a840)),f20(f854(x42861,a840),a840,a840)),f331(f331(f10(f854(f854(x42861,a840),a840),f854(f854(x42861,a840),f854(a840,a840)),f854(x42861,a840)),f331(f10(a840,f854(a840,a840),f854(x42861,a840)),a329)),f241(f854(x42861,a840))))),f68(x42861)))),f307(x42861))
% 51.10/50.81 [4431]~P1(f331(f68(f848(x44311)),f247(f854(f848(x44311),a840))))
% 51.10/50.81 [4444]~P1(f331(f331(f240(a1),f2(a1)),f331(f86(a1),f331(f107(a1),f331(a119,x44441)))))
% 51.10/50.81 [3345]E(f331(f331(f3(a1),f331(f331(f87(a1),x33451),a104)),a104),x33451)
% 51.10/50.81 [3361]E(f331(f163(a847),f135(a847,f331(f302(a847,f2(a847)),x33611))),f331(f265(a847),x33611))
% 51.10/50.81 [3556]E(f331(f267(x35561,x35561),f308(x35561,f184(f854(f853(x35561,x35561),a840)))),f247(f854(x35561,a840)))
% 51.10/50.81 [3557]E(f331(f269(x35571,x35571),f308(x35571,f184(f854(f853(x35571,x35571),a840)))),f247(f854(x35571,a840)))
% 51.10/50.81 [3603]E(f331(f331(f87(a1),f331(f331(f87(a1),f85(a1)),x36031)),x36031),f331(f331(f3(a1),f331(f331(f87(a1),x36031),x36031)),a104))
% 51.10/50.81 [3653]E(f331(f286(x36531,x36531),f308(x36531,f184(f854(f853(x36531,x36531),a840)))),f308(x36531,f184(f854(f853(x36531,x36531),a840))))
% 51.10/50.81 [3700]P1(f331(f331(f240(a847),x37001),f331(f331(f88(a847),x37001),f331(f331(f88(a847),x37001),x37001))))
% 51.10/50.81 [3789]E(f331(f331(f289(x37891,x37891,x37891),f184(f854(f853(x37891,x37891),a840))),f308(x37891,f184(f854(f853(x37891,x37891),a840)))),f184(f854(f853(x37891,x37891),a840)))
% 51.10/50.81 [3977]P1(f331(f68(a847),f331(f264(a847),f331(f331(f9(a847,a847,a840),f241(a847)),x39771))))
% 51.10/50.81 [3978]P1(f331(f68(a847),f331(f264(a847),f331(f331(f9(a847,a847,a840),f240(a847)),x39781))))
% 51.10/50.81 [4253]E(f331(f264(f853(x42531,x42531)),f331(f331(f10(f854(x42531,a840),a840,f853(x42531,x42531)),f94(x42531)),f331(f331(f9(f853(x42531,x42531),f854(x42531,f853(x42531,x42531)),f854(x42531,a840)),f331(f331(f10(f854(f853(x42531,x42531),a840),f854(f854(x42531,f853(x42531,x42531)),f854(x42531,a840)),f853(x42531,x42531)),f10(f853(x42531,x42531),a840,x42531)),a328)),f331(f331(f20(x42531,x42531,f853(x42531,x42531)),f249(x42531,x42531)),f7(x42531))))),f308(x42531,f184(f854(f853(x42531,x42531),a840))))
% 51.10/50.81 [4432]~E(f331(f331(f3(a1),f331(f331(f87(a1),x44321),x44321)),a104),a90)
% 51.10/50.81 [4433]~E(f331(f331(f3(a1),f331(f331(f87(a1),x44331),x44331)),a104),a90)
% 51.10/50.81 [4435]~E(f331(f331(f87(a1),f331(f331(f87(a1),f85(a1)),x44351)),x44351),f2(a1))
% 51.10/50.81 [3747]E(f331(f331(f87(a1),f331(f331(f3(a1),a104),x37471)),f331(f331(f3(a1),a104),x37471)),f331(f331(f3(a1),a104),f331(f331(f3(a1),f331(f331(f87(a1),x37471),x37471)),a104)))
% 51.10/50.81 [3864]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),a104),x38641)),f331(f331(f3(a1),a104),x38641))),a104),f331(f331(f3(a1),a104),f331(f331(f87(a1),x38641),x38641)))
% 51.10/50.81 [3898]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f87(a1),x38981),a104)),f331(f331(f87(a1),x38981),a104))),a104),f331(f331(f87(a1),f331(f331(f87(a1),x38981),x38981)),a104))
% 51.10/50.81 [3937]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),a104),x39371)),f331(f331(f3(a1),a104),x39371))),a104),f331(f331(f3(a1),a90),f331(f331(f3(a1),f331(f331(f87(a1),x39371),x39371)),a104)))
% 51.10/50.81 [4037]E(f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x40371),f2(a847))),f184(f854(f853(a847,a847),a840))))),f331(f107(a1),x40371))
% 51.10/50.81 [4047]E(f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),f336(x40471)),f357(x40471))),f184(f854(f853(a847,a847),a840))))),x40471)
% 51.10/50.81 [4077]E(f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x40771)),f331(f311(a847,a1,f107(a1)),f331(f264(a847),f331(f331(f10(a1,a840,a847),x40771),f107(a1)))))
% 51.10/50.81 [4126]P36(f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x41261)))
% 51.10/50.81 [4145]P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x41451),f184(f854(f853(a847,a847),a840)))),a78))
% 51.10/50.81 [4151]E(f331(f311(a1,a847,a112),f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),f331(f331(f10(a847,a840,a1),x41511),a112)))),f331(f264(a847),x41511))
% 51.10/50.81 [4300]E(f313(a847,f331(f331(f51(f853(a847,a847),f854(a847,a840)),f331(a115,x43001)),f331(f259(a847,a847,f854(a847,a840)),f331(f331(f9(a847,f854(a847,a840),f854(a847,f854(a847,a840))),f331(f331(f10(f854(a847,f854(f854(a847,a840),f854(a847,a840))),f854(f854(a847,a840),f854(a847,f854(a847,a840))),a847),f9(a847,f854(a847,a840),f854(a847,a840))),f331(f331(f10(f854(a847,a847),f854(a847,f854(f854(a847,a840),f854(a847,a840))),a847),f331(f10(a847,f854(f854(a847,a840),f854(a847,a840)),a847),f310(a847))),f3(a847)))),f184(f854(a847,a840)))))),f331(a112,x43001))
% 51.10/50.81 [3790]E(f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),x37901),x37901)),a104)),a104),f331(f331(f87(a1),x37901),x37901))
% 51.10/50.81 [3838]E(f331(f331(f3(a1),f331(f331(f3(a1),f331(f331(f87(a1),x38381),x38381)),a104)),a104),f331(f331(f87(a1),f331(f331(f3(a1),x38381),a104)),f331(f331(f3(a1),x38381),a104)))
% 51.10/50.81 [4054]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f87(a1),f331(f86(a1),x40541)),a104)),f331(f331(f87(a1),f331(f86(a1),x40541)),a104))),a104),f331(f86(a1),f331(f331(f3(a1),f331(f331(f87(a1),x40541),x40541)),a104)))
% 51.10/50.81 [4097]E(f331(f331(f87(a847),x40971),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(a119,f331(a119,x40971)))
% 51.10/50.81 [4098]E(f331(f331(f88(a847),x40981),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f87(a847),x40981),x40981))
% 51.10/50.81 [4099]E(f331(f331(f48(a847),f331(f331(f87(a847),x40991),x40991)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x40991)
% 51.10/50.81 [4178]E(f57(a847,f331(a119,f331(a119,x41781)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f57(a847,x41781,f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.81 [4317]E(f331(a96,f331(f331(f51(f853(a847,a847),f854(f853(a847,a847),a840)),f331(a115,x43171)),f331(f259(a847,a847,f854(f853(a847,a847),a840)),f331(f331(f10(f854(a847,f854(f853(a847,a847),a840)),f854(a847,f854(f853(a847,a847),a840)),a847),f331(f10(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840),a847),f285(f853(a847,a847),f853(a847,a847),a116))),f331(f331(f9(a847,f854(f853(a847,a847),a840),f854(a847,f854(f853(a847,a847),a840))),f331(f331(f10(f854(a847,f854(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f854(f854(f853(a847,a847),a840),f854(a847,f854(f853(a847,a847),a840))),a847),f9(a847,f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f10(f854(a847,f853(a847,a847)),f854(a847,f854(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),a847),f331(f10(f853(a847,a847),f854(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),a847),f310(f853(a847,a847)))),f331(f9(a847,a847,f853(a847,a847)),f249(a847,a847))))),f184(f854(f853(a847,a847),a840))))))),f331(f86(a1),x43171))
% 51.10/50.81 [4173]E(f331(f331(f87(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x41731),f331(a119,f331(a119,x41731)))
% 51.10/50.81 [4174]E(f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x41741),f331(f331(f87(a847),x41741),x41741))
% 51.10/50.81 [4207]E(f331(f331(f48(a847),f331(a119,f331(a119,x42071))),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(a119,f331(f331(f48(a847),x42071),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.81 [4258]E(f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42581),f331(a119,f331(a119,f331(a119,x42581))))
% 51.10/50.81 [4324]E(f331(f259(a1,a1,f853(a1,a1)),f331(f331(f20(a1,f854(a1,f853(a1,a1)),f854(a1,f853(a1,a1))),f331(f331(f10(f854(a1,f854(f853(a1,a1),f853(a1,a1))),f854(f854(a1,f853(a1,a1)),f854(a1,f853(a1,a1))),a1),f20(a1,f853(a1,a1),f853(a1,a1))),f331(f331(f10(f854(a1,f853(a1,a1)),f854(a1,f854(f853(a1,a1),f853(a1,a1))),a1),f331(f20(a1,f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),f331(f331(f10(a840,f854(f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),a1),f103(f853(a1,a1))),f331(f331(f10(a1,a840,a1),f331(f240(a1),f2(a1))),f331(f331(f9(a1,a1,a1),f3(a1)),x43241))))),f331(f331(f9(a1,f854(a1,a1),f854(a1,f853(a1,a1))),f331(f331(f10(f854(a1,f853(a1,a1)),f854(f854(a1,a1),f854(a1,f853(a1,a1))),a1),f10(a1,f853(a1,a1),a1)),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f331(f331(f9(a1,a1,a1),f331(f331(f10(a1,f854(a1,a1),a1),f87(a1)),f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f85(a1))))),f331(f331(f9(a1,a1,a1),f3(a1)),x43241))))),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))),f55(x43241))
% 51.10/50.81 [3388]P37(a25,x33881,x33882,x33881)
% 51.10/50.81 [3389]P37(a25,x33891,x33892,x33891)
% 51.10/50.81 [3045]P16(a1,f168(x30451,x30452))
% 51.10/50.81 [3144]P45(x31441,x31442,f268(x31441,x31442))
% 51.10/50.81 [3145]P51(x31451,x31451,f268(x31451,x31452))
% 51.10/50.81 [3413]P27(x34131,x34131,f7(x34131),x34132)
% 51.10/50.81 [3414]P27(x34141,x34141,f39(x34141),x34142)
% 51.10/50.81 [3420]P32(x34201,x34202,f120(x34201),f120(x34201))
% 51.10/50.81 [3421]P32(x34211,x34212,f120(x34211),f120(x34211))
% 51.10/50.81 [3422]P27(x34221,f851(x34221),f234(x34221),x34222)
% 51.10/50.81 [3431]P27(f848(x34311),f848(x34311),f160(x34311),x34312)
% 51.10/50.81 [4329]~E(f41(x43291),f40(x43292))
% 51.10/50.81 [4330]~E(f41(x43301),f40(x43302))
% 51.10/50.81 [4335]~E(f30(x43351,x43352),a25)
% 51.10/50.81 [4336]~E(f38(x43361,x43362),a25)
% 51.10/50.81 [4337]~E(f37(x43371,x43372),a25)
% 51.10/50.81 [4338]~E(f30(x43381,x43382),a25)
% 51.10/50.81 [4339]~E(f38(x43391,x43392),a25)
% 51.10/50.81 [4340]~E(f37(x43401,x43402),a25)
% 51.10/50.81 [3010]E(f331(f7(x30101),x30102),x30102)
% 51.10/50.81 [3011]E(f331(f264(x30111),x30112),x30112)
% 51.10/50.81 [3012]E(f331(f39(x30121),x30122),x30122)
% 51.10/50.81 [3013]E(f331(f39(x30131),x30132),x30132)
% 51.10/50.81 [3023]E(f331(f188(x30231),x30232),f122(x30231))
% 51.10/50.81 [3033]E(f36(f30(x30331,x30332)),f2(a847))
% 51.10/50.81 [3043]E(f92(x30431,f331(a328,x30432)),x30432)
% 51.10/50.81 [3044]E(f97(x30441,f331(a328,x30442)),x30442)
% 51.10/50.81 [3061]E(f331(f185(a841),f30(x30611,x30612)),f2(a847))
% 51.10/50.81 [3066]E(f331(f131(x30661,x30662),f120(x30661)),f120(x30661))
% 51.10/50.81 [3085]E(f308(x30851,f308(x30851,x30852)),f308(x30851,x30852))
% 51.10/50.81 [3086]E(f146(x30861,f146(x30861,x30862)),f146(x30861,x30862))
% 51.10/50.81 [3107]E(f331(f331(f130(x31071),x31072),f120(x31071)),x31072)
% 51.10/50.81 [3116]E(f331(f331(f164(x31161),x31162),f120(x31161)),f120(x31161))
% 51.10/50.81 [3117]E(f331(f331(f133(x31171),x31172),f120(x31171)),f120(x31171))
% 51.10/50.81 [3119]E(f235(x31191,x31192,f187(x31191)),f2(a847))
% 51.10/50.81 [3120]E(f148(x31201,x31202,f120(x31201)),f2(a847))
% 51.10/50.81 [3122]E(f161(x31221,x31222,f120(x31221)),f120(x31221))
% 51.10/50.81 [3123]E(f167(x31231,x31232,f120(x31231)),f120(x31231))
% 51.10/50.81 [3124]E(f134(x31241,x31242,f120(x31241)),f120(x31241))
% 51.10/50.81 [3125]E(f165(x31251,f120(x31251),x31252),f120(x31251))
% 51.10/50.81 [3129]E(f331(f163(x31291),f146(x31291,x31292)),f331(f163(x31291),x31292))
% 51.10/50.81 [3132]E(f331(f267(x31321,x31321),f268(x31321,x31322)),x31322)
% 51.10/50.81 [3133]E(f331(f269(x31331,x31331),f268(x31331,x31332)),x31332)
% 51.10/50.81 [3141]P1(f331(a26,f30(x31411,x31412)))
% 51.10/50.81 [3142]P1(f331(a26,f30(x31421,x31422)))
% 51.10/50.81 [3143]E(f331(f286(x31431,x31431),f268(x31431,x31432)),f268(x31431,x31432))
% 51.10/50.81 [3156]E(f308(f848(x31561),f150(x31561,x31562)),f151(x31561,f308(x31561,x31562)))
% 51.10/50.81 [3158]P1(f331(f132(a1),f168(x31581,x31582)))
% 51.10/50.81 [3166]E(f331(f267(x31661,x31661),f308(x31661,x31662)),f247(f854(x31661,a840)))
% 51.10/50.81 [3167]E(f331(f269(x31671,x31671),f308(x31671,x31672)),f247(f854(x31671,a840)))
% 51.10/50.81 [3171]P1(f331(f132(x31711),f146(x31711,x31712)))
% 51.10/50.81 [3178]E(f331(f163(a1),f168(x31781,x31782)),f303(a1,x31781,x31782))
% 51.10/50.81 [3179]E(f331(f163(a1),f168(x31791,x31792)),f303(a1,x31791,x31792))
% 51.10/50.81 [3194]P52(x31941,f184(f854(x31941,a840)),x31942)
% 51.10/50.81 [3199]E(f331(f258(a1,a1),f58(x31991,x31992)),f57(a1,x31991,x31992))
% 51.10/50.81 [3200]E(f331(f302(a847,x32001),f331(a119,x32002)),f303(a847,x32001,x32002))
% 51.10/50.81 [3228]E(f303(a847,f331(a119,x32281),x32282),f305(a847,x32281,x32282))
% 51.10/50.81 [3231]P45(x32311,f247(f854(x32311,a840)),f308(x32311,x32312))
% 51.10/50.81 [3291]E(f331(f331(f3(a847),x32911),f331(a119,x32912)),f331(f47(a847),f306(a847,x32912,x32911)))
% 51.10/50.81 [3346]E(f158(x33461,x33462,f120(x33461)),f331(f331(f249(f848(x33461),f848(x33461)),f120(x33461)),f120(x33461)))
% 51.10/50.81 [3365]E(f331(f259(x33651,x33652,f853(x33651,x33652)),f249(x33651,x33652)),f39(f853(x33651,x33652)))
% 51.10/50.81 [3370]P1(f331(f331(f333(f848(x33701)),f120(x33701)),f153(x33701,x33702)))
% 51.10/50.81 [3371]E(f331(f185(f848(x33711)),f121(x33711,x33712)),f331(f331(f3(a847),f331(f185(f848(x33711)),x33712)),f85(a847)))
% 51.10/50.81 [3380]P1(f331(f68(a847),f306(a847,x33801,x33802)))
% 51.10/50.81 [3381]P1(f331(f68(a847),f305(a847,x33811,x33812)))
% 51.10/50.81 [3382]P1(f331(f68(a847),f303(a847,x33821,x33822)))
% 51.10/50.81 [3383]P1(f331(f68(a1),f306(a1,x33831,x33832)))
% 51.10/50.81 [3384]P1(f331(f68(a1),f305(a1,x33841,x33842)))
% 51.10/50.81 [3385]P1(f331(f68(a1),f303(a1,x33851,x33852)))
% 51.10/50.81 [3491]E(f331(f311(a847,a847,a119),f303(a847,x34911,x34912)),f303(a847,f331(a119,x34911),f331(a119,x34912)))
% 51.10/50.81 [3508]E(f331(f331(f289(x35081,x35081,x35081),f308(x35081,x35082)),f308(x35081,x35082)),f308(x35081,x35082))
% 51.10/50.81 [3539]E(f331(f331(f249(a1,a1),f331(f331(f48(a1),x35391),x35392)),f57(a1,x35391,x35392)),f58(x35391,x35392))
% 51.10/50.81 [3540]E(f331(f331(f249(a106,a106),f331(f331(f48(a106),x35401),x35402)),f57(a106,x35401,x35402)),f24(x35401,x35402))
% 51.10/50.81 [3569]E(f331(f331(f249(a847,a847),f331(f331(f48(a847),x35691),x35692)),f57(a847,x35691,x35692)),f92(f853(a847,a847),f60(x35691,x35692)))
% 51.10/50.81 [3622]P1(f331(f331(f241(a847),f331(f331(f3(a847),x36221),x36222)),f331(a119,x36221)))
% 51.10/50.81 [3721]E(f331(f331(f87(a1),f331(f331(f88(a1),x37211),f331(f331(f48(a1),x37212),x37211))),f57(a1,x37212,x37211)),x37212)
% 51.10/50.81 [3726]E(f331(f331(f51(a847,f854(f853(f848(x37261),f848(x37261)),a840)),f247(f854(a847,a840))),f138(x37261,x37262)),f140(x37261,x37262))
% 51.10/50.81 [3952]P1(f331(f331(f333(f853(f848(x39521),f848(x39521))),f331(f331(f249(f848(x39521),f848(x39521)),f120(x39521)),f120(x39521))),f151(x39521,x39522)))
% 51.10/50.81 [4110]E(f260(x41101,x41101,x41102,x41102,f39(x41101),f39(x41102)),f39(f853(x41101,x41102)))
% 51.10/50.81 [4111]E(f260(x41111,x41111,x41112,x41112,f7(x41111),f7(x41112)),f39(f853(x41111,x41112)))
% 51.10/50.81 [4112]E(f260(x41121,x41121,x41122,x41122,f39(x41121),f39(x41122)),f39(f853(x41121,x41122)))
% 51.10/50.81 [4113]E(f260(x41131,x41131,x41132,x41132,f39(x41131),f39(x41132)),f39(f853(x41131,x41132)))
% 51.10/50.81 [4347]~E(f331(f234(x43471),x43472),f187(x43471))
% 51.10/50.81 [4348]~E(f331(f234(x43481),x43482),f187(x43481))
% 51.10/50.81 [4366]~P35(x43661,f331(f234(x43661),x43662))
% 51.10/50.81 [3105]E(f331(f238(x31051),f331(f234(x31051),x31052)),x31052)
% 51.10/50.81 [3106]E(f331(f160(x31061),f331(f160(x31061),x31062)),x31062)
% 51.10/50.81 [3108]E(f331(f331(f133(x31081),f2(a847)),x31082),x31082)
% 51.10/50.81 [3118]E(f331(f331(f164(x31181),f2(a847)),x31182),f120(x31181))
% 51.10/50.81 [3127]E(f331(f331(f130(x31271),f120(x31271)),x31272),x31272)
% 51.10/50.81 [3135]E(f331(f185(f851(x31351)),f331(f234(x31351),x31352)),f2(a847))
% 51.10/50.81 [3137]E(f49(f854(x31371,a840),f331(f309(x31371),x31372)),x31372)
% 51.10/50.81 [3139]E(f331(f163(x31391),f331(f159(x31391),x31392)),f331(f163(x31391),x31392))
% 51.10/50.81 [3140]E(f331(f163(x31401),f331(f160(x31401),x31402)),f331(f163(x31401),x31402))
% 51.10/50.81 [3147]E(f331(f331(f3(a106),x31471),x31472),f331(f331(a4,x31471),x31472))
% 51.10/50.81 [3160]E(f331(f331(f87(a847),x31601),x31602),f331(f331(f87(a847),x31602),x31601))
% 51.10/50.81 [3161]E(f331(f331(f87(a1),x31611),x31612),f331(f331(f87(a1),x31612),x31611))
% 51.10/50.81 [3162]E(f331(f331(f88(a847),x31621),x31622),f331(f331(f88(a847),x31622),x31621))
% 51.10/50.81 [3163]E(f331(f331(f88(a1),x31631),x31632),f331(f331(f88(a1),x31632),x31631))
% 51.10/50.81 [3186]E(f331(f331(f178(x31861,x31861),f2(a847)),x31862),f39(x31861))
% 51.10/50.81 [3187]E(f331(f185(f848(x31871)),f331(f159(x31871),x31872)),f331(f185(f848(x31871)),x31872))
% 51.10/50.81 [3188]E(f331(f185(f848(x31881)),f331(f160(x31881),x31882)),f331(f185(f848(x31881)),x31882))
% 51.10/50.81 [3189]E(f165(x31891,x31892,f184(f854(a847,a840))),f120(x31891))
% 51.10/50.81 [3190]E(f331(f331(f147(x31901,x31901),f7(x31901)),x31902),x31902)
% 51.10/50.81 [3192]E(f331(f248(a1,a1),f58(x31921,x31922)),f331(f331(f48(a1),x31921),x31922))
% 51.10/50.81 [3210]E(f331(f185(f848(x32101)),f146(x32101,x32102)),f331(f47(x32101),f331(f163(x32101),x32102)))
% 51.10/50.81 [3211]E(f36(f37(x32111,x32112)),f331(f331(f87(a847),f36(x32112)),f331(a119,f2(a847))))
% 51.10/50.81 [3212]E(f331(f284(x32121),f331(f286(x32121,x32121),x32122)),f331(f284(x32121),x32122))
% 51.10/50.81 [3216]P1(f331(f68(x32161),f331(f163(x32161),x32162)))
% 51.10/50.81 [3222]E(f331(f331(f87(a1),x32221),f331(f86(a1),x32222)),f331(f331(f3(a1),x32221),x32222))
% 51.10/50.81 [3223]E(f331(f331(f87(a1),x32231),f331(f86(a1),x32232)),f331(f331(f3(a1),x32231),x32232))
% 51.10/50.81 [3229]P26(x32291,x32292,f184(f854(f846(x32291),a840)))
% 51.10/50.81 [3230]P26(x32301,x32302,f184(f854(f846(x32301),a840)))
% 51.10/50.81 [3232]E(f331(f311(x32321,x32321,f7(x32321)),x32322),x32322)
% 51.10/50.81 [3233]E(f331(f311(x32331,x32331,f39(x32331)),x32332),x32332)
% 51.10/50.81 [3234]E(f331(f312(x32341,x32341,f7(x32341)),x32342),x32342)
% 51.10/50.81 [3235]E(f331(f312(x32351,x32351,f39(x32351)),x32352),x32352)
% 51.10/50.81 [3236]P1(f331(f247(f854(x32361,a840)),x32362))
% 51.10/50.81 [3238]E(f331(f47(a847),f331(f302(a847,x32381),x32382)),f331(f331(f3(a847),x32382),x32381))
% 51.10/50.81 [3239]E(f331(f302(a847,f331(a119,x32391)),x32392),f306(a847,x32391,x32392))
% 51.10/50.81 [3251]E(f331(f331(f310(x32511),x32512),f184(f854(x32511,a840))),f331(f264(x32511),f331(a328,x32512)))
% 51.10/50.81 [3255]E(f331(f331(f310(x32551),x32552),f184(f854(x32551,a840))),f233(x32551,f331(f234(x32551),x32552)))
% 51.10/50.81 [3257]E(f308(x32571,f331(f286(x32571,x32571),x32572)),f331(f286(x32571,x32571),f308(x32571,x32572)))
% 51.10/50.81 [3262]E(f331(f331(f87(a847),f331(a119,x32621)),x32622),f331(f331(f87(a847),x32621),f331(a119,x32622)))
% 51.10/50.81 [3263]E(f331(f331(f3(a847),f331(a119,x32631)),f331(a119,x32632)),f331(f331(f3(a847),x32631),x32632))
% 51.10/50.81 [3268]E(f331(f47(a847),f305(a847,x32681,x32682)),f331(f331(f3(a847),x32682),x32681))
% 51.10/50.81 [3277]P34(x32771,f331(f331(f288(a847,x32771),a245),x32772))
% 51.10/50.81 [3279]P16(a847,f135(a847,f331(f302(a847,x32791),x32792)))
% 51.10/50.81 [3281]P1(f331(f68(a847),f331(f302(a847,x32811),x32812)))
% 51.10/50.81 [3282]P1(f331(f68(a1),f331(f302(a1,x32821),x32822)))
% 51.10/50.81 [3284]E(f331(f286(f848(x32841),f848(x32841)),f150(x32841,x32842)),f150(x32841,f331(f286(x32841,x32841),x32842)))
% 51.10/50.81 [3285]E(f331(f185(a841),f37(x32851,x32852)),f331(f331(f87(a847),f331(f185(a841),x32852)),f331(a119,f2(a847))))
% 51.10/50.81 [3287]E(f331(f302(a1,x32871),f331(f331(f87(a1),x32872),f85(a1))),f303(a1,x32871,x32872))
% 51.10/50.81 [3290]E(f331(f331(f48(a1),f331(f86(a1),x32901)),f331(f86(a1),x32902)),f331(f331(f48(a1),x32901),x32902))
% 51.10/50.81 [3298]E(f176(x32981,x32982,f331(f18(f851(x32982),x32981),f187(x32982))),f184(f854(x32982,a840)))
% 51.10/50.81 [3299]E(f174(x32991,x32992,f331(f18(f851(x32992),x32991),f187(x32992))),f184(f854(x32991,a840)))
% 51.10/50.81 [3300]E(f331(f331(f178(f853(x33001,x33001),a840),f85(a847)),x33002),x33002)
% 51.10/50.81 [3302]E(f331(f331(f3(f854(x33021,a840)),x33022),f184(f854(x33021,a840))),x33022)
% 51.10/50.81 [3303]E(f331(f331(f108(f854(x33031,a840)),x33032),f184(f854(x33031,a840))),x33032)
% 51.10/50.81 [3304]E(f331(f331(f109(f854(x33041,a840)),x33042),f247(f854(x33041,a840))),x33042)
% 51.10/50.81 [3305]E(f331(f248(a847,a847),f92(f853(a847,a847),f60(x33051,x33052))),f331(f331(f48(a847),x33051),x33052))
% 51.10/50.81 [3311]E(f314(x33111,f331(a23,x33112),f331(f86(a1),f331(a23,x33112))),f331(f331(f317(a1),x33111),x33112))
% 51.10/50.81 [3312]E(f303(a1,f331(f331(f87(a1),x33121),f85(a1)),x33122),f305(a1,x33121,x33122))
% 51.10/50.81 [3317]E(f331(f258(a847,a847),f92(f853(a847,a847),f60(x33171,x33172))),f57(a847,x33171,x33172))
% 51.10/50.81 [3325]E(f315(x33251,f331(a23,x33252),f331(f86(a1),f331(a23,x33252))),f316(a1,x33251,x33252))
% 51.10/50.81 [3327]P1(f331(f331(f333(x33271),x33272),f247(f854(x33271,a840))))
% 51.10/50.81 [3328]P1(f331(f331(f333(x33281),x33282),f247(f854(x33281,a840))))
% 51.10/50.81 [3332]E(f331(f331(f3(a847),f331(a119,x33321)),x33322),f331(f47(a847),f303(a847,x33322,x33321)))
% 51.10/50.81 [3357]E(f331(f331(f3(f854(x33571,a840)),x33572),f247(f854(x33571,a840))),f184(f854(x33571,a840)))
% 51.10/50.81 [3358]E(f331(f331(f108(f854(x33581,a840)),x33582),f247(f854(x33581,a840))),f247(f854(x33581,a840)))
% 51.10/50.81 [3359]E(f331(f331(f109(f854(x33591,a840)),x33592),f184(f854(x33591,a840))),f184(f854(x33591,a840)))
% 51.10/50.81 [3372]E(f57(a1,f331(f107(a1),x33721),f331(f107(a1),x33722)),f331(f107(a1),f57(a847,x33721,x33722)))
% 51.10/50.81 [3373]E(f57(a1,f331(f107(a1),x33731),f331(f107(a1),x33732)),f331(f107(a1),f57(a847,x33731,x33732)))
% 51.10/50.81 [3374]E(f57(a1,f331(f86(a1),x33741),f331(f86(a1),x33742)),f331(f86(a1),f57(a1,x33741,x33742)))
% 51.10/50.81 [3387]E(f331(f185(f848(x33871)),f331(f162(x33871),x33872)),f331(f331(f3(a847),f331(f185(f848(x33871)),x33872)),f85(a847)))
% 51.10/50.81 [3415]E(f331(f331(f48(a1),f57(a1,x34151,x34152)),x34152),f2(a1))
% 51.10/50.81 [3424]E(f331(a5,f57(a847,f331(a22,x34241),f331(a22,x34242))),f57(a106,x34241,x34242))
% 51.10/50.81 [3460]E(f331(a5,f331(f331(f87(a847),f331(a22,x34601)),f331(a22,x34602))),f331(f331(f87(a106),x34601),x34602))
% 51.10/50.81 [3461]E(f331(a5,f331(f331(f88(a847),f331(a22,x34611)),f331(a22,x34612))),f331(f331(f88(a106),x34611),x34612))
% 51.10/50.81 [3462]E(f331(a5,f331(f331(f48(a847),f331(a22,x34621)),f331(a22,x34622))),f331(f331(f48(a106),x34621),x34622))
% 51.10/50.81 [3463]E(f331(a5,f331(f331(f3(a847),f331(a22,x34631)),f331(a22,x34632))),f331(f331(f3(a106),x34631),x34632))
% 51.10/50.81 [3472]E(f331(f311(a847,a847,a119),f331(f302(a847,x34721),x34722)),f331(f302(a847,f331(a119,x34721)),f331(a119,x34722)))
% 51.10/50.81 [3496]P1(f331(f60(x34961,x34962),f92(f853(a847,a847),f60(x34961,x34962))))
% 51.10/50.81 [3513]E(f331(f331(f87(a847),f331(f331(f87(a847),f36(x35131)),f36(x35132))),f331(a119,f2(a847))),f36(f38(x35131,x35132)))
% 51.10/50.81 [3514]E(f57(a847,f331(a119,f57(a847,x35141,x35142)),x35142),f57(a847,f331(a119,x35141),x35142))
% 51.10/50.81 [3528]E(f331(f331(f52(f854(x35281,a840),f854(x35281,a840)),x35282),f7(f854(x35281,a840))),f50(f854(x35281,a840),x35282))
% 51.10/50.81 [3529]E(f331(f331(f51(f854(x35291,a840),f854(x35291,a840)),x35292),f7(f854(x35291,a840))),f49(f854(x35291,a840),x35292))
% 51.10/50.81 [3532]P1(f331(f331(f333(f854(x35321,a840)),x35322),f331(f309(x35321),x35322)))
% 51.10/50.81 [3538]E(f57(a1,f331(f86(a1),f57(a1,x35381,x35382)),x35382),f57(a1,f331(f86(a1),x35381),x35382))
% 51.10/50.81 [3550]P1(f331(f331(f240(f854(x35501,a840)),x35502),f247(f854(x35501,a840))))
% 51.10/50.81 [3552]E(f331(f331(f289(x35521,x35521,x35521),f308(x35521,x35522)),f308(x35521,f308(x35521,x35522))),f308(x35521,x35522))
% 51.10/50.81 [3553]E(f331(f331(f108(f854(x35531,a840)),f331(f269(x35531,x35531),x35532)),f331(f267(x35531,x35531),x35532)),f331(f284(x35531),x35532))
% 51.10/50.81 [3575]E(f319(x35751,x35752,f247(f854(x35751,a840)),f247(f854(x35752,a840))),f247(f854(f855(x35751,x35752),a840)))
% 51.10/50.81 [3627]P1(f331(f331(f240(a847),f57(a847,x36271,x36272)),x36271))
% 51.10/50.81 [3651]P1(f331(f331(f240(a1),f331(f86(a1),f331(f107(a1),x36511))),f331(f107(a1),x36512)))
% 51.10/50.81 [3676]P1(f331(f331(f333(f854(x36761,a840)),f184(f854(x36761,a840))),f331(f309(x36761),x36762)))
% 51.10/50.81 [3681]E(f308(x36811,f331(f331(f289(x36811,x36811,x36811),x36812),f308(x36811,x36812))),f308(x36811,x36812))
% 51.10/50.81 [3683]E(f331(f331(f289(x36831,x36831,x36831),f308(x36831,x36832)),x36832),f331(f331(f289(x36831,x36831,x36831),x36832),f308(x36831,x36832)))
% 51.10/50.81 [3684]E(f331(f331(f289(x36841,x36841,x36841),f308(x36841,x36842)),x36842),f331(f331(f289(x36841,x36841,x36841),x36842),f308(x36841,x36842)))
% 51.10/50.81 [3686]E(f331(a112,f331(f331(f87(a1),f331(f331(f3(a1),x36861),x36862)),f85(a1))),f331(f47(a1),f303(a1,x36862,x36861)))
% 51.10/50.81 [3701]E(f331(f267(x37011,x37011),f331(f331(f289(x37011,x37011,x37011),x37012),f308(x37011,x37012))),f331(f267(x37011,x37011),x37012))
% 51.10/50.81 [3702]E(f331(f269(x37021,x37021),f331(f331(f289(x37021,x37021,x37021),x37022),f308(x37021,x37022))),f331(f269(x37021,x37021),x37022))
% 51.10/50.81 [3717]E(f331(f331(f87(a847),f331(f331(f87(a847),f331(f185(a841),x37171)),f331(f185(a841),x37172))),f331(a119,f2(a847))),f331(f185(a841),f38(x37171,x37172)))
% 51.10/50.81 [3730]P27(a847,a847,f331(f331(f9(a847,a847,a847),f87(a847)),x37301),x37302)
% 51.10/50.81 [3732]P16(a847,f331(f160(a847),f331(f331(f147(f848(x37321),a847),f185(f848(x37321))),f169(x37321,x37322))))
% 51.10/50.81 [3779]P1(f331(f331(f241(a1),f331(f86(a1),f331(f107(a1),f331(a119,x37791)))),f331(f107(a1),x37792)))
% 51.10/50.81 [3820]E(f331(f137(f848(x38201),x38201,f331(f9(x38201,f848(x38201),f848(x38201)),f145(x38201)),f120(x38201)),x38202),f331(f160(x38201),x38202))
% 51.10/50.81 [3871]P1(f331(f331(f240(f854(f853(f848(x38711),f848(x38711)),a840)),f151(x38711,x38712)),f308(f848(x38711),f150(x38711,x38712))))
% 51.10/50.81 [3902]P1(f331(f60(x39021,x39022),f331(f331(f249(a847,a847),f331(f331(f48(a847),x39021),x39022)),f57(a847,x39021,x39022))))
% 51.10/50.81 [3913]P1(f331(f331(f240(f854(f853(f848(x39131),f848(x39131)),a840)),f150(x39131,f308(x39131,x39132))),f308(f848(x39131),f150(x39131,x39132))))
% 51.10/50.81 [4137]E(f331(f331(f261(f853(a106,a106),a106,f853(a106,a106),f853(x41371,f853(a106,a106))),f272(f331(f157(a106),f331(f331(f147(f853(a106,x41371),a106),f248(a106,x41371)),x41372)))),f331(f331(f10(x41371,f854(f853(a106,a106),f853(x41371,f853(a106,a106))),a106),f249(x41371,f853(a106,a106))),f273(x41371,x41372))),f271(x41371,x41372))
% 51.10/50.81 [4282]E(f57(a847,f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42821),f331(f111(a847),x42822)),f57(a847,f331(a119,f331(a119,f331(a119,x42821))),f331(f111(a847),x42822)))
% 51.10/50.81 [4296]E(f331(f331(f48(a847),f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42961)),f331(f111(a847),x42962)),f331(f331(f48(a847),f331(a119,f331(a119,f331(a119,x42961)))),f331(f111(a847),x42962)))
% 51.10/50.81 [4316]E(f331(f259(f854(f853(x43161,x43161),a840),f854(f853(x43161,x43161),a840),f854(f854(x43162,x43161),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840)))),f331(f331(f9(f854(f853(x43161,x43161),a840),f854(f854(f853(x43161,x43161),a840),f854(f854(x43162,x43161),f854(f853(x43162,x43162),a840))),f854(f854(f853(x43161,x43161),a840),f854(f854(x43162,x43161),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840))))),f331(f331(f10(f854(f854(f854(x43162,x43161),f854(f853(x43162,x43162),a840)),f854(f854(x43162,x43161),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840)))),f854(f854(f854(f853(x43161,x43161),a840),f854(f854(x43162,x43161),f854(f853(x43162,x43162),a840))),f854(f854(f853(x43161,x43161),a840),f854(f854(x43162,x43161),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840))))),f854(f853(x43161,x43161),a840)),f10(f854(f854(x43162,x43161),f854(f853(x43162,x43162),a840)),f854(f854(x43162,x43161),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840))),f854(f853(x43161,x43161),a840))),f331(f331(f10(f854(f854(x43162,x43161),f854(f854(f853(x43162,x43162),a840),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840)))),f854(f854(f854(x43162,x43161),f854(f853(x43162,x43162),a840)),f854(f854(x43162,x43161),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840)))),f854(f853(x43161,x43161),a840)),f20(f854(x43162,x43161),f854(f853(x43162,x43162),a840),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840)))),f331(f331(f10(f854(f854(x43162,x43161),f854(f853(x43162,x43162),a840)),f854(f854(x43162,x43161),f854(f854(f853(x43162,x43162),a840),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840)))),f854(f853(x43161,x43161),a840)),f331(f10(f854(f853(x43162,x43162),a840),f854(f854(f853(x43162,x43162),a840),f853(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840))),f854(x43162,x43161)),f249(f854(f853(x43162,x43162),a840),f854(f853(x43162,x43162),a840)))),f288(x43161,x43162))))),f288(x43161,x43162))),f81(x43161,x43162))
% 51.10/50.81 [4412]~E(f331(f309(x44121),x44122),f184(f854(f854(x44121,a840),a840)))
% 51.10/50.81 [4429]~P1(f331(f331(f333(x44291),x44292),f184(f854(x44291,a840))))
% 51.10/50.81 [4430]~P1(f331(f331(f333(x44301),x44302),f184(f854(x44301,a840))))
% 51.10/50.81 [4439]~P1(f331(f331(f241(f854(x44391,a840)),x44392),f184(f854(x44391,a840))))
% 51.10/50.81 [3241]E(f331(f331(f3(a847),x32411),f331(f331(f87(a847),x32411),x32412)),f2(a847))
% 51.10/50.81 [3243]E(f331(f331(f108(f854(x32431,a840)),x32432),x32432),x32432)
% 51.10/50.81 [3244]E(f331(f331(f109(f854(x32441,a840)),x32442),x32442),x32442)
% 51.10/50.81 [3270]E(f331(f331(f3(f854(x32701,a840)),x32702),x32702),f184(f854(x32701,a840)))
% 51.10/50.81 [3273]E(f331(f138(x32731,x32732),f2(a847)),f184(f854(f853(f848(x32731),f848(x32731)),a840)))
% 51.10/50.81 [3274]E(f331(f331(f87(a847),x32741),f331(a119,x32742)),f331(a119,f331(f331(f87(a847),x32741),x32742)))
% 51.10/50.81 [3286]E(f192(f331(f107(a1),x32861),f331(f107(a1),x32862)),f331(f107(a1),f331(f331(f3(a847),x32861),x32862)))
% 51.10/50.81 [3289]E(f331(f331(f48(a1),f331(f86(a1),x32891)),x32892),f331(f331(f48(a1),x32891),f331(f86(a1),x32892)))
% 51.10/50.81 [3293]E(f331(f47(a1),f331(f302(a1,x32931),x32932)),f331(a112,f331(f331(f3(a1),x32932),x32931)))
% 51.10/50.81 [3296]E(f331(f331(f87(a847),f331(a119,x32961)),x32962),f331(a119,f331(f331(f87(a847),x32961),x32962)))
% 51.10/50.81 [3301]E(f331(f86(f854(x33011,a840)),f331(f86(f854(x33011,a840)),x33012)),x33012)
% 51.10/50.81 [3314]E(f169(x33141,f331(f331(f145(f848(x33141)),f120(x33141)),x33142)),f169(x33141,x33142))
% 51.10/50.81 [3318]E(f331(f331(f87(a847),x33181),f331(f331(f88(a847),x33181),x33182)),f331(f331(f88(a847),x33181),f331(a119,x33182)))
% 51.10/50.81 [3326]E(f331(f331(a4,f331(a5,x33261)),f331(a5,x33262)),f331(a5,f331(f331(f3(a847),x33261),x33262)))
% 51.10/50.81 [3336]E(f331(f331(f250(a1),f331(f107(a1),x33361)),x33362),f331(f107(a1),f331(f331(f250(a847),x33361),x33362)))
% 51.10/50.81 [3337]E(f331(f331(f88(a1),f331(f86(a1),x33371)),x33372),f331(f86(a1),f331(f331(f88(a1),x33371),x33372)))
% 51.10/50.81 [3338]E(f331(f331(f250(a1),f331(f107(a1),x33381)),x33382),f331(f107(a1),f331(f331(f250(a847),x33381),x33382)))
% 51.10/50.81 [3339]E(f331(f331(f250(a1),f331(f107(a1),x33391)),x33392),f331(f107(a1),f331(f331(f250(a847),x33391),x33392)))
% 51.10/50.81 [3340]E(f331(f331(f87(a106),f331(a5,x33401)),f331(a5,x33402)),f331(a5,f331(f331(f87(a847),x33401),x33402)))
% 51.10/50.81 [3341]E(f331(f331(f88(a106),f331(a5,x33411)),f331(a5,x33412)),f331(a5,f331(f331(f88(a847),x33411),x33412)))
% 51.10/50.81 [3342]E(f331(f331(f244(a847),f331(a119,x33421)),f331(a119,x33422)),f331(a119,f331(f331(f244(a847),x33421),x33422)))
% 51.10/50.81 [3343]E(f331(f331(f239(a847),f331(a119,x33431)),f331(a119,x33432)),f331(a119,f331(f331(f239(a847),x33431),x33432)))
% 51.10/50.81 [3348]E(f331(f163(a847),f135(a847,f331(f302(a847,x33481),x33482))),f331(f302(a847,x33481),x33482))
% 51.10/50.81 [3349]E(f331(f163(a847),f135(a847,f331(f302(a847,x33491),x33492))),f331(f302(a847,x33491),x33492))
% 51.10/50.81 [3350]E(f313(x33501,f331(f331(f310(x33501),x33502),f184(f854(x33501,a840)))),x33502)
% 51.10/50.81 [3355]E(f331(f267(x33551,x33552),f184(f854(f853(x33551,x33552),a840))),f184(f854(x33552,a840)))
% 51.10/50.81 [3356]E(f331(f269(x33561,x33562),f184(f854(f853(x33561,x33562),a840))),f184(f854(x33561,a840)))
% 51.10/50.81 [3360]E(f331(a112,f331(f331(f3(a1),x33601),x33602)),f331(f47(a1),f305(a1,x33602,x33601)))
% 51.10/50.81 [3364]E(f331(f331(f87(a847),x33641),f331(f331(f88(a847),x33642),x33641)),f331(f331(f88(a847),f331(a119,x33642)),x33641))
% 51.10/50.81 [3366]E(f331(f331(f66(x33661),f184(f854(x33661,a840))),x33662),f184(f854(f854(x33661,a840),a840)))
% 51.10/50.81 [3375]E(f331(f185(f848(a847)),f135(a847,f331(f302(a847,x33751),x33752))),f331(f331(f3(a847),x33752),x33751))
% 51.10/50.81 [3394]E(f331(f331(f108(f854(x33941,a840)),f184(f854(x33941,a840))),x33942),x33942)
% 51.10/50.81 [3395]E(f331(f331(f109(f854(x33951,a840)),f247(f854(x33951,a840))),x33952),x33952)
% 51.10/50.81 [3396]E(f331(f331(f88(a1),f331(f107(a1),x33961)),f331(f107(a1),x33962)),f331(f107(a1),f331(f331(f88(a847),x33961),x33962)))
% 51.10/50.81 [3397]E(f331(f331(f48(a1),f331(f107(a1),x33971)),f331(f107(a1),x33972)),f331(f107(a1),f331(f331(f48(a847),x33971),x33972)))
% 51.10/50.81 [3398]E(f331(f331(f87(a1),f331(f86(a1),x33981)),f331(f86(a1),x33982)),f331(f86(a1),f331(f331(f87(a1),x33981),x33982)))
% 51.10/50.81 [3400]E(f331(f331(f87(a1),f331(f107(a1),x34001)),f331(f107(a1),x34002)),f331(f107(a1),f331(f331(f87(a847),x34001),x34002)))
% 51.10/50.81 [3401]E(f331(f331(f87(a1),f331(f107(a1),x34011)),f331(f107(a1),x34012)),f331(f107(a1),f331(f331(f87(a847),x34011),x34012)))
% 51.10/50.81 [3402]E(f331(f331(f87(a1),f331(f111(a1),x34021)),f331(f111(a1),x34022)),f331(f111(a1),f331(f331(f87(a1),x34021),x34022)))
% 51.10/50.81 [3403]E(f331(f331(f88(a1),f331(f107(a1),x34031)),f331(f107(a1),x34032)),f331(f107(a1),f331(f331(f88(a847),x34031),x34032)))
% 51.10/50.81 [3404]E(f331(f331(f88(a1),f331(f107(a1),x34041)),f331(f107(a1),x34042)),f331(f107(a1),f331(f331(f88(a847),x34041),x34042)))
% 51.10/50.81 [3405]E(f331(f331(f88(a1),f331(f111(a1),x34051)),f331(f111(a1),x34052)),f331(f111(a1),f331(f331(f88(a1),x34051),x34052)))
% 51.10/50.81 [3406]E(f331(f331(f48(a1),f331(f107(a1),x34061)),f331(f107(a1),x34062)),f331(f107(a1),f331(f331(f48(a847),x34061),x34062)))
% 51.10/50.81 [3425]E(f331(f331(f8(x34251,a847),f331(f18(a847,x34251),f85(a847))),x34252),f331(f47(x34251),x34252))
% 51.10/50.81 [3436]E(f331(f86(a1),f57(a1,f331(f86(a1),x34361),x34362)),f57(a1,x34361,f331(f86(a1),x34362)))
% 51.10/50.81 [3438]E(f331(f163(a1),f168(x34381,f331(f331(f3(a1),x34382),f85(a1)))),f331(f302(a1,x34381),x34382))
% 51.10/50.81 [3442]P1(f331(f331(f240(a847),x34421),f331(f331(f87(a847),x34422),x34421)))
% 51.10/50.81 [3443]P1(f331(f331(f240(a847),x34431),f331(f331(f87(a847),x34431),x34432)))
% 51.10/50.81 [3446]E(f331(f331(f3(f854(x34461,a840)),f184(f854(x34461,a840))),x34462),f184(f854(x34461,a840)))
% 51.10/50.81 [3447]E(f331(f331(f108(f854(x34471,a840)),f247(f854(x34471,a840))),x34472),f247(f854(x34471,a840)))
% 51.10/50.81 [3448]E(f331(f331(f109(f854(x34481,a840)),f184(f854(x34481,a840))),x34482),f184(f854(x34481,a840)))
% 51.10/50.81 [3453]E(f331(f331(f249(a1,a1),x34531),f331(f86(a1),x34532)),f331(a63,f331(f331(f249(a1,a1),x34531),x34532)))
% 51.10/50.81 [3454]E(f331(f302(a1,f331(f331(f87(a1),x34541),f85(a1))),x34542),f306(a1,x34541,x34542))
% 51.10/50.81 [3464]E(f331(f331(f88(a847),x34641),f331(f331(f48(a847),x34642),x34641)),f331(f331(f3(a847),x34642),f57(a847,x34642,x34641)))
% 51.10/50.81 [3465]E(f331(f331(f88(a1),x34651),f331(f331(f48(a1),x34652),x34651)),f331(f331(f3(a1),x34652),f57(a1,x34652,x34651)))
% 51.10/50.81 [3469]E(f331(f163(a1),f168(f331(f331(f87(a1),x34691),f85(a1)),x34692)),f305(a1,x34691,x34692))
% 51.10/50.81 [3473]P1(f331(f331(f240(f854(x34731,a840)),x34732),x34732))
% 51.10/50.81 [3476]E(f331(f331(f108(f854(x34761,a840)),x34762),f331(f86(f854(x34761,a840)),x34762)),f247(f854(x34761,a840)))
% 51.10/50.81 [3477]E(f331(f331(f109(f854(x34771,a840)),x34772),f331(f86(f854(x34771,a840)),x34772)),f184(f854(x34771,a840)))
% 51.10/50.81 [3483]E(f331(f331(f3(a847),f331(f331(f3(a847),x34831),f85(a847))),x34832),f331(f331(f3(a847),x34831),f331(a119,x34832)))
% 51.10/50.81 [3488]E(f331(f331(f3(f854(x34881,a840)),f247(f854(x34881,a840))),x34882),f331(f86(f854(x34881,a840)),x34882))
% 51.10/50.81 [3489]E(f331(f331(f3(a1),f331(f111(a1),x34891)),f331(f111(a1),x34892)),f331(f111(a1),f331(f331(f87(a1),x34891),f331(f86(a1),x34892))))
% 51.10/50.81 [3501]E(f331(f163(a847),f135(a847,f331(f302(a847,x35011),f331(a119,x35012)))),f303(a847,x35011,x35012))
% 51.10/50.81 [3530]E(f331(f331(f178(f853(x35301,x35301),a840),f2(a847)),x35302),f308(x35301,f184(f854(f853(x35301,x35301),a840))))
% 51.10/50.81 [3534]P1(f331(f132(a847),f135(a847,f331(f302(a847,x35341),x35342))))
% 51.10/50.81 [3551]E(f331(f311(a1,a847,a112),f303(a1,f331(f107(a1),x35511),f331(f107(a1),x35512))),f303(a847,x35511,x35512))
% 51.10/50.81 [3561]E(f180(a847,f2(a847),f7(a847),f331(f331(f3(a847),x35611),x35612)),f331(f331(f3(a847),x35611),f331(a119,x35612)))
% 51.10/50.81 [3562]E(f331(a112,f331(f331(f3(a1),x35621),f331(f331(f87(a1),x35622),f85(a1)))),f331(f47(a1),f306(a1,x35622,x35621)))
% 51.10/50.81 [3598]E(f331(f331(f147(a847,a847),a119),f135(a847,f331(f302(a847,x35981),x35982))),f135(a847,f331(f302(a847,f331(a119,x35981)),f331(a119,x35982))))
% 51.10/50.81 [3605]E(f331(f163(a1),f168(f331(f331(f87(a1),x36051),f85(a1)),f331(f331(f3(a1),x36052),f85(a1)))),f306(a1,x36051,x36052))
% 51.10/50.81 [3619]P1(f331(f331(f240(f854(x36191,a840)),f184(f854(x36191,a840))),x36192))
% 51.10/50.81 [3623]E(f92(x36231,f331(f331(f9(x36231,x36231,a840),a328),x36232)),x36232)
% 51.10/50.81 [3624]E(f97(x36241,f331(f331(f9(x36241,x36241,a840),a328),x36242)),x36242)
% 51.10/50.81 [3628]E(f331(f163(a847),f135(a847,f331(f302(a847,f331(a119,x36281)),f331(a119,x36282)))),f305(a847,x36281,x36282))
% 51.10/50.81 [3654]E(f331(f331(f256(x36541,x36542),f247(f854(x36541,a840))),f331(f18(f854(x36542,a840),x36541),f247(f854(x36542,a840)))),f247(f854(f853(x36541,x36542),a840)))
% 51.10/50.81 [3688]E(f331(f264(x36881),f331(f331(f10(a840,a840,x36881),a327),x36882)),f331(f86(f854(x36881,a840)),f331(f264(x36881),x36882)))
% 51.10/50.81 [3691]E(f331(f264(x36911),f331(f331(f9(x36911,x36911,a840),a328),x36912)),f331(f331(f310(x36911),x36912),f184(f854(x36911,a840))))
% 51.10/50.81 [3698]E(f331(f331(f87(a1),f331(f331(f87(a1),x36981),x36981)),f331(f331(f87(a1),x36982),x36982)),f331(f331(f87(a1),f331(f331(f87(a1),x36981),x36982)),f331(f331(f87(a1),x36981),x36982)))
% 51.10/50.81 [3699]E(f331(f331(f3(a1),f331(f331(f87(a1),x36991),x36991)),f331(f331(f87(a1),x36992),x36992)),f331(f331(f87(a1),f331(f331(f3(a1),x36991),x36992)),f331(f331(f3(a1),x36991),x36992)))
% 51.10/50.81 [3714]P1(f331(f331(f240(a847),f331(f47(x37141),f331(f163(x37141),x37142))),f331(f185(f848(x37141)),x37142)))
% 51.10/50.81 [3715]P1(f331(f331(f240(a847),f331(f185(f848(x37151)),f146(x37151,x37152))),f331(f185(f848(x37151)),x37152)))
% 51.10/50.81 [3727]E(f331(f264(x37271),f331(f331(f9(x37271,f854(x37271,a840),a840),f333(x37271)),x37272)),x37272)
% 51.10/50.81 [3743]E(f331(f331(f164(x37431),f331(f331(f3(a847),f331(f185(f848(x37431)),x37432)),f85(a847))),x37432),f121(x37431,x37432))
% 51.10/50.81 [3766]E(f180(a847,f2(a847),f331(f331(f10(a847,a847,a847),a119),f331(f244(a847),x37661)),x37662),f331(f331(f244(a847),f331(a119,x37661)),x37662))
% 51.10/50.81 [3770]E(f49(f854(x37701,a840),f331(f311(f854(f853(x37701,x37701),a840),f854(x37701,a840),f284(x37701)),x37702)),f331(f284(x37701),f49(f854(f853(x37701,x37701),a840),x37702)))
% 51.10/50.81 [3771]E(f180(a847,f331(a119,x37711),f331(f331(f10(a847,a847,a847),a119),f331(f239(a847),x37711)),x37712),f331(f331(f239(a847),f331(a119,x37711)),x37712))
% 51.10/50.81 [3773]E(f331(f331(f249(a1,a1),f331(f331(f48(a1),f331(f82(a1),x37731)),f331(f82(a1),x37732))),f57(a1,f331(f82(a1),x37731),f331(f82(a1),x37732))),f65(x37731,x37732))
% 51.10/50.81 [3794]P1(f331(f331(f240(f854(f854(x37941,a840),a840)),x37942),f331(f309(x37941),f49(f854(x37941,a840),x37942))))
% 51.10/50.81 [3825]E(f331(f331(f51(x38251,f854(x38251,a840)),x38252),f331(f331(f9(x38251,f854(x38251,a840),f854(x38251,a840)),f310(x38251)),f184(f854(x38251,a840)))),x38252)
% 51.10/50.81 [3826]E(f331(f331(f289(x38261,x38261,x38261),f331(f286(x38261,x38261),x38262)),f308(x38261,f331(f286(x38261,x38261),x38262))),f331(f286(x38261,x38261),f331(f331(f289(x38261,x38261,x38261),x38262),f308(x38261,x38262))))
% 51.10/50.81 [3894]E(f331(f163(x38941),f331(f137(f848(x38941),f848(x38941),f130(x38941),f120(x38941)),x38942)),f331(f331(f51(f848(x38941),f854(x38941,a840)),f331(f163(f848(x38941)),x38942)),f163(x38941)))
% 51.10/50.81 [3925]E(f331(f331(f108(f854(f853(x39251,x39251),a840)),f308(x39251,f184(f854(f853(x39251,x39251),a840)))),f331(f331(f289(x39251,x39251,x39251),f308(x39251,x39252)),x39252)),f308(x39251,x39252))
% 51.10/50.81 [3962]E(f331(f331(f172(x39621,x39621),x39622),x39622),f331(f331(f147(x39621,f853(x39621,x39621)),f331(f331(f20(x39621,x39621,f853(x39621,x39621)),f249(x39621,x39621)),f7(x39621))),x39622))
% 51.10/50.81 [4073]E(f331(f137(a847,f848(x40731),f331(f9(f848(x40731),a847,a847),f331(f331(f10(a847,f854(a847,a847),f848(x40731)),f239(a847)),f185(f848(x40731)))),f2(a847)),f331(f160(f848(x40731)),x40732)),f331(f185(f848(f848(x40731))),f169(x40731,x40732)))
% 51.10/50.81 [4150]E(f331(f331(f288(f853(a847,f848(x41501)),f848(x41501)),f324(a847,f848(x41501),a245,f140(x41501,x41502))),f331(f331(f20(f848(x41501),f848(x41501),f853(a847,f848(x41501))),f331(f331(f10(a847,f854(f848(x41501),f853(a847,f848(x41501))),f848(x41501)),f249(a847,f848(x41501))),f185(f848(x41501)))),f7(f848(x41501)))),f141(x41501,x41502))
% 51.10/50.81 [4273]E(f331(f264(x42731),f331(f331(f10(f854(f854(x42731,a840),a840),a840,x42731),f95(f854(x42731,a840))),f331(f331(f10(f854(f854(x42731,a840),a840),f854(f854(x42731,a840),a840),x42731),f331(f20(f854(x42731,a840),a840,a840),f331(f331(f10(a840,f854(a840,a840),f854(x42731,a840)),a334),f331(f331(f9(f854(x42731,a840),f854(f854(x42731,a840),a840),a840),f333(f854(x42731,a840))),x42732)))),f333(x42731)))),f50(f854(x42731,a840),x42732))
% 51.10/50.81 [4440]~P1(f331(f331(f241(a1),f331(f107(a1),x44401)),f331(f86(a1),f331(f107(a1),x44402))))
% 51.10/50.81 [3362]E(f331(f331(f3(a847),f331(f331(f87(a847),x33621),x33622)),x33622),x33621)
% 51.10/50.81 [3363]E(f331(f331(f3(a847),f331(f331(f87(a847),x33631),x33632)),x33631),x33632)
% 51.10/50.81 [3437]E(f331(f331(f87(a847),f331(f331(f3(a847),x34371),x34372)),x34372),f331(f331(f239(a847),x34371),x34372))
% 51.10/50.81 [3537]E(f331(f331(f88(a847),f331(f331(f48(a847),x35371),x35372)),x35372),f331(f331(f3(a847),x35371),f57(a847,x35371,x35372)))
% 51.10/50.81 [3566]E(f331(f163(a847),f135(a847,f331(f302(a847,f331(a119,x35661)),x35662))),f306(a847,x35661,x35662))
% 51.10/50.81 [3574]E(f331(f107(a1),f218(f331(a112,f331(f82(a1),x35741)),f331(a112,f331(f82(a1),x35742)))),f331(f331(a219,x35741),x35742))
% 51.10/50.81 [3576]E(f331(f331(f108(f854(x35761,a840)),f331(f86(f854(x35761,a840)),x35762)),x35762),f247(f854(x35761,a840)))
% 51.10/50.81 [3577]E(f331(f331(f109(f854(x35771,a840)),f331(f86(f854(x35771,a840)),x35772)),x35772),f184(f854(x35771,a840)))
% 51.10/50.81 [3594]P1(f331(f331(f240(a847),f331(f331(f48(a847),x35941),x35942)),x35941))
% 51.10/50.81 [3595]P1(f331(f331(f240(a847),f331(f331(f3(a847),x35951),x35952)),x35951))
% 51.10/50.81 [3620]P1(f331(f331(f241(a847),x36201),f331(a119,f331(f331(f87(a847),x36202),x36201))))
% 51.10/50.81 [3621]P1(f331(f331(f241(a847),x36211),f331(a119,f331(f331(f87(a847),x36211),x36212))))
% 51.10/50.81 [3640]E(f331(f331(f88(a847),f331(a112,f331(f82(a1),x36401))),f331(a112,f331(f82(a1),x36402))),f331(a112,f331(f82(a1),f331(f331(f88(a1),x36401),x36402))))
% 51.10/50.81 [3647]E(f331(f331(f87(a1),f331(f331(f88(a1),x36471),x36472)),f331(f331(f88(a1),x36471),x36472)),f331(f331(f88(a1),f331(f331(f87(a1),x36471),x36471)),x36472))
% 51.10/50.81 [3650]P1(f331(f331(f240(a1),f2(a1)),f331(f331(f250(a1),f331(f82(a1),x36501)),x36502)))
% 51.10/50.81 [3720]E(f331(f285(f848(x37201),f848(x37201),f151(x37201,x37202)),f331(f331(f310(f848(x37201)),f120(x37201)),f184(f854(f848(x37201),a840)))),f331(f331(f310(f848(x37201)),f120(x37201)),f184(f854(f848(x37201),a840))))
% 51.10/50.81 [3739]E(f331(f331(f108(f854(f853(x37391,x37391),a840)),f308(x37391,x37392)),f308(x37391,f184(f854(f853(x37391,x37391),a840)))),f308(x37391,x37392))
% 51.10/50.81 [3755]E(f331(f331(f48(a1),f331(f111(a1),f331(f331(f87(a1),x37551),x37551))),f331(f111(a1),f331(f331(f87(a1),x37552),x37552))),f331(f331(f48(a1),f331(f111(a1),x37551)),f331(f111(a1),x37552)))
% 51.10/50.81 [3815]E(f331(f331(f250(a1),x38151),f331(f111(a847),f331(f331(f87(a1),x38152),x38152))),f331(f331(f93(a1,a1),f331(f331(f250(a1),x38151),f331(f111(a847),x38152))),f331(f331(f20(a1,a1,a1),f88(a1)),f7(a1))))
% 51.10/50.81 [3821]E(f331(f264(f854(x38211,a840)),f331(f331(f9(f854(x38211,a840),f854(x38211,a840),a840),f240(f854(x38211,a840))),x38212)),f331(f309(x38211),x38212))
% 51.10/50.81 [3835]E(f331(f331(f147(a1,a847),a112),f331(f331(f130(a1),f331(f331(f147(a847,a1),f107(a1)),x38351)),f331(f331(f147(a847,a1),f107(a1)),x38352))),f331(f331(f130(a847),x38351),x38352))
% 51.10/50.81 [3870]E(f331(f311(a1,a1,f331(f331(f9(a1,a1,a1),f87(a1)),x38701)),f331(f302(a1,f2(a1)),f331(f331(f3(a1),x38702),x38701))),f331(f302(a1,x38701),x38702))
% 51.10/50.81 [3873]P46(x38731,f331(f331(f3(f854(f853(x38731,x38731),a840)),x38732),f308(x38731,f184(f854(f853(x38731,x38731),a840)))))
% 51.10/50.81 [3891]E(f331(f185(f848(x38911)),f331(f137(f848(x38911),f848(x38911),f130(x38911),f120(x38911)),x38912)),f331(f157(a847),f331(f331(f147(f848(x38911),a847),f185(f848(x38911))),x38912)))
% 51.10/50.81 [3896]P45(x38961,f247(f854(x38961,a840)),f331(f331(f108(f854(f853(x38961,x38961),a840)),x38962),f308(x38961,f184(f854(f853(x38961,x38961),a840)))))
% 51.10/50.81 [3936]P1(f331(f331(f333(f853(x39361,x39361)),f331(f331(f249(x39361,x39361),x39362),x39362)),f308(x39361,f184(f854(f853(x39361,x39361),a840)))))
% 51.10/50.81 [3942]E(f180(a847,f2(a847),f331(f331(f10(a847,a847,a847),a119),f331(f331(f9(a847,a847,a847),f244(a847)),x39421)),x39422),f331(f331(f244(a847),x39422),f331(a119,x39421)))
% 51.10/50.81 [3945]E(f180(a847,f331(a119,x39451),f331(f331(f10(a847,a847,a847),a119),f331(f331(f9(a847,a847,a847),f239(a847)),x39451)),x39452),f331(f331(f239(a847),x39452),f331(a119,x39451)))
% 51.10/50.81 [3948]E(f331(f311(x39481,f848(x39481),f331(f331(f9(x39481,f848(x39481),f848(x39481)),f145(x39481)),f120(x39481))),x39482),f166(x39481,x39482,f331(f331(f310(f848(x39481)),f120(x39481)),f184(f854(f848(x39481),a840)))))
% 51.10/50.81 [3949]E(f331(f331(f108(f854(f853(x39491,x39491),a840)),f331(f331(f289(x39491,x39491,x39491),x39492),f308(x39491,x39492))),f308(x39491,f184(f854(f853(x39491,x39491),a840)))),f308(x39491,x39492))
% 51.10/50.81 [3957]P1(f331(f331(f240(f854(f853(x39571,x39571),a840)),f268(x39571,x39572)),f331(f331(f256(x39571,x39571),x39572),f331(f18(f854(x39571,a840),x39571),x39572))))
% 51.10/50.81 [3960]E(f331(f311(a1,a847,a112),f331(f331(f108(f854(a1,a840)),f331(f311(a847,a1,f107(a1)),x39601)),f331(f311(a847,a1,f107(a1)),x39602))),f331(f331(f108(f854(a847,a840)),x39601),x39602))
% 51.10/50.81 [3961]E(f331(f311(a1,a847,a112),f331(f331(f109(f854(a1,a840)),f331(f311(a847,a1,f107(a1)),x39611)),f331(f311(a847,a1,f107(a1)),x39612))),f331(f331(f109(f854(a847,a840)),x39611),x39612))
% 51.10/50.81 [3965]E(f331(f264(x39651),f331(f331(f10(a840,a840,x39651),a327),f331(f331(f9(x39651,f854(x39651,a840),a840),f333(x39651)),x39652))),f331(f86(f854(x39651,a840)),x39652))
% 51.10/50.81 [3992]E(f331(f137(f848(x39921),f848(x39921),f130(x39921),f120(x39921)),f331(f331(f147(f848(x39921),f848(x39921)),f160(x39921)),f331(f160(f848(x39921)),x39922))),f331(f160(x39921),f331(f137(f848(x39921),f848(x39921),f130(x39921),f120(x39921)),x39922)))
% 51.10/50.81 [4020]E(f331(f331(f51(a847,f854(f853(x40201,x40201),a840)),f247(f854(a847,a840))),f331(f331(f9(a847,f854(f853(x40201,x40201),a840),f854(f853(x40201,x40201),a840)),f178(f853(x40201,x40201),a840)),x40202)),f308(x40201,x40202))
% 51.10/50.81 [4038]E(f92(x40381,f331(f331(f10(f854(x40381,a840),a840,x40381),f331(a328,x40382)),f331(f331(f9(x40381,f854(x40381,a840),f854(x40381,a840)),f310(x40381)),f184(f854(x40381,a840))))),f313(x40381,x40382))
% 51.10/50.81 [4046]E(f331(f185(f848(x40461)),f146(x40461,f331(f137(f848(x40461),f848(x40461),f130(x40461),f120(x40461)),x40462))),f331(f47(x40461),f331(f331(f51(f848(x40461),f854(x40461,a840)),f331(f163(f848(x40461)),x40462)),f163(x40461))))
% 51.10/50.81 [4061]E(f331(f331(f108(f854(f853(x40611,x40611),a840)),x40612),f331(f331(f289(x40611,x40611,x40611),f331(f331(f289(x40611,x40611,x40611),x40612),f308(x40611,x40612))),x40612)),f331(f331(f289(x40611,x40611,x40611),x40612),f308(x40611,x40612)))
% 51.10/50.81 [4082]P1(f331(f331(f240(f854(f853(x40821,x40821),a840)),f331(f331(f289(x40821,x40821,x40821),x40822),f308(x40821,x40822))),f331(f331(f256(x40821,x40821),f331(f284(x40821),x40822)),f331(f18(f854(x40821,a840),x40821),f331(f284(x40821),x40822)))))
% 51.10/50.81 [4127]E(f331(f264(f848(x41271)),f331(f331(f9(f848(x41271),f854(x41271,a840),a840),f331(f331(f10(f854(x41271,a840),f854(f854(x41271,a840),a840),f848(x41271)),f240(f854(x41271,a840))),f163(x41271))),x41272)),f153(x41271,x41272))
% 51.10/50.81 [4138]E(f331(f149(f848(x41381),x41381,f120(x41381),f331(f331(f10(f848(x41381),f854(f848(x41381),f848(x41381)),x41381),f331(f9(f848(x41381),f848(x41381),f848(x41381)),f130(x41381))),f331(f331(f9(x41381,f848(x41381),f848(x41381)),f145(x41381)),f120(x41381)))),x41382),f331(f159(x41381),x41382))
% 51.10/50.81 [4177]P27(f854(x41771,x41772),f854(f853(x41771,x41772),a840),f331(f331(f10(f854(f853(x41771,x41772),a840),f854(f853(x41771,x41772),a840),f854(x41771,x41772)),f264(f853(x41771,x41772))),f331(f331(f10(f854(x41771,f854(x41772,a840)),f854(f853(x41771,x41772),a840),f854(x41771,x41772)),f259(x41771,x41772,a840)),f331(f10(x41772,f854(x41772,a840),x41771),f331(f9(x41772,x41772,a840),a328)))),f247(f854(f854(x41771,x41772),a840)))
% 51.10/50.81 [4182]E(f57(a1,f331(f111(a1),f331(f331(f87(a1),x41821),x41821)),f331(f111(a1),f331(f331(f87(a1),x41822),x41822))),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f57(a1,f331(f111(a1),x41821),f331(f111(a1),x41822))))
% 51.10/50.81 [4223]E(f331(f331(f51(x42231,f854(f853(x42231,x42231),a840)),x42232),f331(f331(f9(x42231,f854(f853(x42231,x42231),a840),f854(f853(x42231,x42231),a840)),f331(f331(f10(f853(x42231,x42231),f854(f854(f853(x42231,x42231),a840),f854(f853(x42231,x42231),a840)),x42231),f310(f853(x42231,x42231))),f331(f331(f20(x42231,x42231,f853(x42231,x42231)),f249(x42231,x42231)),f7(x42231)))),f184(f854(f853(x42231,x42231),a840)))),f268(x42231,x42232))
% 51.10/50.81 [4231]E(f205(x42311,f331(f331(f249(a1,a1),f331(f86(a1),f331(f331(f80(f853(a1,a1),a1,x42311,f248(a1,a1)),f214(x42311)),x42312))),f331(f331(f80(f853(a1,a1),a1,x42311,f258(a1,a1)),f214(x42311)),x42312))),f228(x42311,x42312))
% 51.10/50.81 [4311]E(f331(f264(f854(x43111,a840)),f331(f331(f10(f854(f854(x43111,a840),a840),a840,f854(x43111,a840)),f94(f854(x43111,a840))),f331(f331(f9(f854(x43111,a840),f854(f854(x43111,a840),a840),f854(f854(x43111,a840),a840)),f331(f331(f10(f854(f854(x43111,a840),f854(a840,a840)),f854(f854(f854(x43111,a840),a840),f854(f854(x43111,a840),a840)),f854(x43111,a840)),f20(f854(x43111,a840),a840,a840)),f331(f331(f10(f854(f854(x43111,a840),a840),f854(f854(x43111,a840),f854(a840,a840)),f854(x43111,a840)),f331(f10(a840,f854(a840,a840),f854(x43111,a840)),a329)),f331(f331(f9(f854(x43111,a840),f854(f854(x43111,a840),f854(x43111,a840)),f854(f854(x43111,a840),a840)),f331(f331(f10(f854(f854(x43111,a840),a840),f854(f854(f854(x43111,a840),f854(x43111,a840)),f854(f854(x43111,a840),a840)),f854(x43111,a840)),f10(f854(x43111,a840),a840,f854(x43111,a840))),a328)),f86(f854(x43111,a840)))))),f331(f331(f10(f854(f854(x43111,a840),a840),a840,f854(x43111,a840)),f331(f333(f854(x43111,a840)),x43112)),f309(x43111))))),f331(f309(x43111),f331(f86(f854(x43111,a840)),x43112)))
% 51.10/50.81 [4436]~E(f331(f331(f87(a1),x44361),x44361),f331(f331(f3(a1),f331(f331(f87(a1),x44362),x44362)),a104))
% 51.10/50.81 [4437]~E(f331(f331(f87(a1),x44371),x44371),f331(f331(f3(a1),f331(f331(f87(a1),x44372),x44372)),a104))
% 51.10/50.81 [4442]~P1(f331(f331(f241(a847),f331(f331(f87(a847),x44421),x44422)),x44422))
% 51.10/50.81 [4443]~P1(f331(f331(f241(a847),f331(f331(f87(a847),x44431),x44432)),x44431))
% 51.10/50.81 [3655]E(f331(f331(f3(a847),x36551),f331(f331(f88(a847),f331(f331(f48(a847),x36551),x36552)),x36552)),f57(a847,x36551,x36552))
% 51.10/50.81 [3656]E(f331(f331(f3(a1),x36561),f331(f331(f88(a1),f331(f331(f48(a1),x36561),x36562)),x36562)),f57(a1,x36561,x36562))
% 51.10/50.81 [3689]E(f331(f331(f147(a847,x36891),f331(f155(x36891),x36892)),f135(a847,f331(f302(a847,f2(a847)),f331(f185(f848(x36891)),x36892)))),x36892)
% 51.10/50.81 [3751]E(f331(f285(x37511,x37511,f308(x37511,f184(f854(f853(x37511,x37511),a840)))),x37512),x37512)
% 51.10/50.81 [3874]E(f308(x38741,f331(f331(f3(f854(f853(x38741,x38741),a840)),x38742),f308(x38741,f184(f854(f853(x38741,x38741),a840))))),f308(x38741,x38742))
% 51.10/50.81 [3875]E(f308(x38751,f331(f331(f108(f854(f853(x38751,x38751),a840)),x38752),f308(x38751,f184(f854(f853(x38751,x38751),a840))))),f308(x38751,x38752))
% 51.10/50.81 [3929]E(f331(f331(f3(a1),f331(f331(f3(a1),f331(f331(f87(a1),x39291),x39291)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x39292),x39292)),a104)),f331(f331(f87(a1),f331(f331(f3(a1),x39291),x39292)),f331(f331(f3(a1),x39291),x39292)))
% 51.10/50.81 [3970]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f87(a1),x39701),x39702)),f331(f331(f87(a1),x39701),x39702))),a104),f331(f331(f87(a1),f331(f331(f87(a1),x39701),x39701)),f331(f331(f3(a1),f331(f331(f87(a1),x39702),x39702)),a104)))
% 51.10/50.81 [3996]E(f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),x39961),x39961)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x39962),x39962)),a104)),f331(f331(f87(a1),f331(f331(f87(a1),x39961),f331(f331(f3(a1),x39962),a104))),f331(f331(f87(a1),x39961),f331(f331(f3(a1),x39962),a104))))
% 51.10/50.81 [4007]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f87(a1),x40071),x40072)),f331(f331(f87(a1),x40071),x40072))),a104),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),x40071),x40071)),a104)),f331(f331(f87(a1),x40072),x40072)))
% 51.10/50.81 [4008]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),x40081),x40082)),f331(f331(f3(a1),x40081),x40082))),a104),f331(f331(f3(a1),f331(f331(f3(a1),f331(f331(f87(a1),x40081),x40081)),a104)),f331(f331(f87(a1),x40082),x40082)))
% 51.10/50.81 [4058]E(f331(f107(a1),f331(f331(f48(a847),f331(f331(f88(a847),f331(a112,f331(f82(a1),x40581))),f331(a112,f331(f82(a1),x40582)))),f218(f331(a112,f331(f82(a1),x40581)),f331(a112,f331(f82(a1),x40582))))),f220(x40581,x40582))
% 51.10/50.81 [4103]E(f331(f331(f261(f853(a106,a106),a106,f853(a106,a106),f853(x41031,f853(a106,a106))),f272(f331(a5,f331(f185(f848(x41031)),x41032)))),f331(f331(f10(x41031,f854(f853(a106,a106),f853(x41031,f853(a106,a106))),a106),f249(x41031,f853(a106,a106))),f331(f331(f10(a847,x41031,a106),f331(f155(x41031),x41032)),a22))),f278(x41031,x41032))
% 51.10/50.81 [4183]E(f331(f137(a847,f848(x41831),f331(f9(f848(x41831),a847,a847),f331(f331(f10(a847,f854(a847,a847),f848(x41831)),f239(a847)),f185(f848(x41831)))),f2(a847)),f331(f160(f848(x41831)),f169(x41831,x41832))),f331(f185(f848(f848(x41831))),f331(f131(f848(x41831),f331(f331(f10(a840,a840,f848(x41831)),a327),f331(f331(f9(f848(x41831),f848(x41831),a840),a328),f120(x41831)))),x41832)))
% 51.10/50.81 [4189]E(f331(f331(f51(a847,f854(x41891,a840)),f247(f854(a847,a840))),f331(f331(f9(a847,f854(a847,f854(x41891,a840)),f854(x41891,a840)),f331(f331(f10(f854(a847,a840),f854(f854(a847,f854(x41891,a840)),f854(x41891,a840)),a847),f51(a847,f854(x41891,a840))),f302(a847,f2(a847)))),x41892)),f331(f331(f51(a847,f854(x41891,a840)),f247(f854(a847,a840))),x41892))
% 51.10/50.81 [4208]P1(f331(f68(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),x42081)),f331(f331(f9(a847,a847,a840),f241(a847)),x42082)))))
% 51.10/50.81 [4321]E(f331(f264(f853(f848(x43211),f848(x43211))),f331(f259(f848(x43211),f848(x43211),a840),f331(f331(f20(f848(x43211),f854(f848(x43211),a840),f854(f848(x43211),a840)),f331(f331(f10(f854(f848(x43211),f854(a840,a840)),f854(f854(f848(x43211),a840),f854(f848(x43211),a840)),f848(x43211)),f20(f848(x43211),a840,a840)),f331(f331(f10(f854(f848(x43211),a840),f854(f848(x43211),f854(a840,a840)),f848(x43211)),f331(f10(a840,f854(a840,a840),f848(x43211)),a330)),f331(f331(f9(f848(x43211),f854(f848(x43211),a847),f854(f848(x43211),a840)),f331(f331(f10(f854(a847,a840),f854(f854(f848(x43211),a847),f854(f848(x43211),a840)),f848(x43211)),f10(a847,a840,f848(x43211))),f331(f331(f10(a847,f854(a847,a840),f848(x43211)),f241(a847)),f185(f848(x43211))))),f185(f848(x43211)))))),f331(f331(f20(f848(x43211),f854(f848(x43211),a840),f854(f848(x43211),a840)),f331(f331(f10(f854(f848(x43211),f854(a840,a840)),f854(f854(f848(x43211),a840),f854(f848(x43211),a840)),f848(x43211)),f20(f848(x43211),a840,a840)),f331(f331(f10(f854(f848(x43211),a840),f854(f848(x43211),f854(a840,a840)),f848(x43211)),f331(f10(a840,f854(a840,a840),f848(x43211)),a329)),f331(f331(f9(f848(x43211),f854(f848(x43211),a847),f854(f848(x43211),a840)),f331(f331(f10(f854(a847,a840),f854(f854(f848(x43211),a847),f854(f848(x43211),a840)),f848(x43211)),f10(a847,a840,f848(x43211))),f331(f331(f10(a847,f854(a847,a840),f848(x43211)),a328),f185(f848(x43211))))),f185(f848(x43211)))))),f331(f331(f9(f848(x43211),f854(f853(f848(x43211),f848(x43211)),a840),f854(f848(x43211),a840)),f331(f331(f10(f854(f848(x43211),f854(f854(f853(f848(x43211),f848(x43211)),a840),a840)),f854(f854(f853(f848(x43211),f848(x43211)),a840),f854(f848(x43211),a840)),f848(x43211)),f9(f848(x43211),f854(f853(f848(x43211),f848(x43211)),a840),a840)),f331(f331(f10(f854(f848(x43211),f853(f848(x43211),f848(x43211))),f854(f848(x43211),f854(f854(f853(f848(x43211),f848(x43211)),a840),a840)),f848(x43211)),f331(f10(f853(f848(x43211),f848(x43211)),f854(f854(f853(f848(x43211),f848(x43211)),a840),a840),f848(x43211)),f333(f853(f848(x43211),f848(x43211))))),f249(f848(x43211),f848(x43211))))),f140(x43211,x43212)))))),f141(x43211,x43212))
% 51.10/50.81 [3999]E(f331(f331(f87(a1),f331(f331(f87(a1),f331(f331(f88(a1),x39991),x39992)),f331(f331(f88(a1),x39991),x39992))),x39992),f331(f331(f88(a1),f331(f331(f3(a1),f331(f331(f87(a1),x39991),x39991)),a104)),x39992))
% 51.10/50.81 [4101]E(f331(a112,f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x41011),x41012)),f184(f854(f853(a847,a847),a840)))))),f331(f331(f3(a847),x41011),x41012))
% 51.10/50.81 [4107]E(f331(f331(f289(x41071,x41071,x41071),f331(f331(f108(f854(f853(x41071,x41071),a840)),x41072),f308(x41071,f184(f854(f853(x41071,x41071),a840))))),f308(x41071,f331(f331(f108(f854(f853(x41071,x41071),a840)),x41072),f308(x41071,f184(f854(f853(x41071,x41071),a840)))))),f308(x41071,x41072))
% 51.10/50.81 [4143]E(f273(x41431,f331(f131(f853(a106,x41431),f331(f259(a106,x41431,a840),f331(f331(f10(a840,f854(x41431,a840),a106),f18(a840,x41431)),f331(f241(a106),f2(a106))))),x41432)),f273(x41431,x41432))
% 51.10/50.81 [4144]E(f271(x41441,f331(f131(f853(a106,x41441),f331(f259(a106,x41441,a840),f331(f331(f10(a840,f854(x41441,a840),a106),f18(a840,x41441)),f331(f241(a106),f2(a106))))),x41442)),f271(x41441,x41442))
% 51.10/50.81 [4146]E(f331(f86(a1),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x41461),x41462)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x41462),x41461)),f184(f854(f853(a847,a847),a840))))))
% 51.10/50.81 [4220]E(f331(f331(f93(a1,a847),f331(f111(a1),f331(f331(f87(a1),x42201),a104))),f331(f331(f20(a1,a847,a847),f331(f331(f9(a1,a847,f854(a847,a847)),f331(f331(f10(a840,f854(a847,f854(a847,a847)),a1),f103(a847)),a190)),f2(a847))),f331(f331(f10(a847,a847,a1),a119),f331(f331(f10(a847,a847,a1),f331(f244(a847),x42202)),a112)))),f331(f331(f244(a847),f331(a119,x42202)),f331(f111(a847),x42201)))
% 51.10/50.81 [4221]E(f331(f331(f93(a1,a847),f331(f111(a1),f331(f331(f87(a1),x42211),a104))),f331(f331(f20(a1,a847,a847),f331(f331(f9(a1,a847,f854(a847,a847)),f331(f331(f10(a840,f854(a847,f854(a847,a847)),a1),f103(a847)),a190)),f331(a119,x42212))),f331(f331(f10(a847,a847,a1),a119),f331(f331(f10(a847,a847,a1),f331(f239(a847),x42212)),a112)))),f331(f331(f239(a847),f331(a119,x42212)),f331(f111(a847),x42211)))
% 51.10/50.81 [4241]E(f331(f137(f848(x42411),f848(x42411),f130(x42411),f120(x42411)),f331(f331(f147(f848(x42411),f848(x42411)),f149(f848(x42411),x42411,f120(x42411),f331(f331(f10(f848(x42411),f854(f848(x42411),f848(x42411)),x42411),f18(f848(x42411),f848(x42411))),f331(f331(f9(x42411,f848(x42411),f848(x42411)),f145(x42411)),f120(x42411))))),x42412)),f331(f331(f147(f848(x42411),x42411),f136(x42411)),f331(f131(f848(x42411),f331(f331(f10(a840,a840,f848(x42411)),a327),f331(f331(f9(f848(x42411),f848(x42411),a840),a328),f120(x42411)))),x42412)))
% 51.10/50.81 [4301]E(f331(f259(a1,a1,a840),f331(f331(f9(a1,f854(a1,a840),f854(a1,a840)),f331(f331(f10(f854(a1,f854(a840,a840)),f854(f854(a1,a840),f854(a1,a840)),a1),f20(a1,a840,a840)),f331(f331(f10(f854(a1,a840),f854(a1,f854(a840,a840)),a1),f331(f10(a840,f854(a840,a840),a1),a329)),f331(f331(f10(f854(a1,a1),f854(a1,a840),a1),f331(f10(a1,a840,a1),f331(a328,x43011))),f331(f331(f10(a1,f854(a1,a1),a1),f87(a1)),f331(f88(a1),x43012)))))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),f331(a334,f331(f331(f241(a1),f2(a1)),x43012))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),f331(f331(f9(a1,a1,a840),f241(a1)),x43012))))),f331(f331(f10(a840,a840,a1),f331(a334,f331(a327,f331(f331(f241(a1),f2(a1)),x43012)))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f241(a1),x43012))),f331(f331(f9(a1,a1,a840),f240(a1)),f2(a1))))))),f61(x43011,x43012))
% 51.10/50.81 [4303]E(f331(f264(x43031),f331(f331(f10(f854(a847,a840),a840,x43031),f94(a847)),f331(f331(f9(x43031,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),x43031),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),x43031),f331(f10(a840,f854(a840,a840),a847),a329)),f331(f331(f9(x43031,f854(a847,x43031),f854(a847,a840)),f331(f331(f10(f854(x43031,a840),f854(f854(a847,x43031),f854(a847,a840)),x43031),f10(x43031,a840,a847)),a328)),f331(f155(x43031),x43032))))),f331(f331(f9(a847,a847,a840),f241(a847)),f331(f185(f848(x43031)),x43032))))),f331(f163(x43031),x43032))
% 51.10/50.81 [4117]E(f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),x41171),a104)),x41172)),f331(f331(f3(a1),f331(f331(f87(a1),x41171),a104)),x41172))),a104),f331(f331(f3(a1),f331(f331(f87(a1),x41171),x41171)),f331(f331(f3(a1),f331(f331(f87(a1),x41172),x41172)),a104)))
% 51.10/50.81 [4236]E(f331(f137(f848(f848(x42361)),f848(f848(x42361)),f130(f848(x42361)),f120(f848(x42361))),f331(f331(f147(f848(x42361),f848(f848(x42361))),f149(f848(f848(x42361)),x42361,f120(f848(x42361)),f331(f18(f854(f848(x42361),f848(f848(x42361))),x42361),f331(f331(f9(f848(x42361),f848(f848(x42361)),f848(f848(x42361))),f145(f848(x42361))),f120(f848(x42361)))))),x42362)),f331(f331(f147(f848(x42361),f848(x42361)),f162(x42361)),f331(f131(f848(x42361),f331(f331(f10(a840,a840,f848(x42361)),a327),f331(f331(f9(f848(x42361),f848(x42361),a840),a328),f120(x42361)))),x42362)))
% 51.10/50.81 [4246]E(f331(f331(f93(a1,a847),f331(f111(a1),f331(f331(f87(a1),x42461),a104))),f331(f331(f20(a1,a847,a847),f331(f331(f9(a1,a847,f854(a847,a847)),f331(f331(f10(a840,f854(a847,f854(a847,a847)),a1),f103(a847)),a190)),f2(a847))),f331(f331(f10(a847,a847,a1),a119),f331(f331(f9(a1,a847,a847),f331(f331(f10(a847,f854(a847,a847),a1),f244(a847)),a112)),x42462)))),f331(f331(f244(a847),f331(f111(a847),x42461)),f331(a119,x42462)))
% 51.10/50.81 [4247]E(f331(f331(f93(a1,a847),f331(f111(a1),f331(f331(f87(a1),x42471),a104))),f331(f331(f20(a1,a847,a847),f331(f331(f9(a1,a847,f854(a847,a847)),f331(f331(f10(a840,f854(a847,f854(a847,a847)),a1),f103(a847)),a190)),f331(a119,x42472))),f331(f331(f10(a847,a847,a1),a119),f331(f331(f9(a1,a847,a847),f331(f331(f10(a847,f854(a847,a847),a1),f239(a847)),a112)),x42472)))),f331(f331(f239(a847),f331(f111(a847),x42471)),f331(a119,x42472)))
% 51.10/50.81 [4235]E(f331(f259(x42351,x42351,a840),f331(f331(f20(x42351,a840,f854(x42351,a840)),f331(f331(f10(f854(x42351,f854(a840,a840)),f854(a840,f854(x42351,a840)),x42351),f9(x42351,a840,a840)),f331(f331(f10(f854(x42351,a840),f854(x42351,f854(a840,a840)),x42351),f331(f10(a840,f854(a840,a840),x42351),a329)),a328))),x42352)),f268(x42351,x42352))
% 51.10/50.81 [4279]E(f331(f331(f48(a847),x42791),f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42792)),f331(f331(f48(a847),x42791),f331(a119,f331(a119,f331(a119,x42792)))))
% 51.10/50.81 [4280]E(f57(a847,x42801,f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42802)),f57(a847,x42801,f331(a119,f331(a119,f331(a119,x42802)))))
% 51.10/50.81 [4281]E(f57(a847,f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42811),x42812),f57(a847,f331(a119,f331(a119,f331(a119,x42811))),x42812))
% 51.10/50.81 [4294]E(f127(f331(x42941,f331(f331(f88(a106),f331(f111(a106),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42942))),f331(f202(x42941),x42942))
% 51.10/50.81 [4295]E(f331(f331(f48(a847),f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),x42951)),x42952),f331(f331(f48(a847),f331(a119,f331(a119,f331(a119,x42951)))),x42952))
% 51.10/50.81 [4349]~E(f30(x43491,x43492),f331(a29,x43493))
% 51.10/50.81 [4350]~E(f38(x43501,x43502),f331(a29,x43503))
% 51.10/50.81 [4351]~E(f37(x43511,x43512),f331(a29,x43513))
% 51.10/50.81 [4352]~E(f331(a29,x43521),f30(x43522,x43523))
% 51.10/50.81 [4353]~E(f331(a29,x43531),f38(x43532,x43533))
% 51.10/50.81 [4354]~E(f331(a29,x43541),f37(x43542,x43543))
% 51.10/50.81 [4370]~E(f33(x43701,x43702,x43703),a25)
% 51.10/50.81 [4371]~E(f34(x43711,x43712,x43713),a25)
% 51.10/50.81 [4372]~E(f35(x43721,x43722,x43723),a25)
% 51.10/50.81 [4373]~E(f33(x43731,x43732,x43733),a25)
% 51.10/50.81 [4374]~E(f34(x43741,x43742,x43743),a25)
% 51.10/50.81 [4375]~E(f35(x43751,x43752,x43753),a25)
% 51.10/50.81 [3087]E(f331(f189(x30871,x30872),x30873),f125(x30871,x30872))
% 51.10/50.81 [3088]E(f331(f201(x30881,x30882),x30883),f128(x30881,x30882))
% 51.10/50.81 [3184]E(f331(f331(f147(x31841,x31842),x31843),f120(x31841)),f120(x31842))
% 51.10/50.81 [3185]E(f331(f331(f203(x31851,x31852),x31853),f187(x31851)),f187(x31852))
% 51.10/50.81 [3205]E(f36(f33(x32051,x32052,x32053)),f2(a847))
% 51.10/50.81 [3225]E(f331(f179(x32251,x32252,x32253),f2(a847)),x32252)
% 51.10/50.81 [3226]E(f331(f185(a841),f33(x32261,x32262,x32263)),f2(a847))
% 51.10/50.81 [3227]E(f331(f331(f172(x32271,x32272),x32273),f120(x32272)),f120(f853(x32271,x32272)))
% 51.10/50.81 [3261]E(f92(x32611,f69(x32611,x32612,x32613)),f331(f70(x32611,x32612),x32613))
% 51.10/50.81 [3330]E(f331(f248(f848(x33301),f848(x33301)),f158(x33301,x33302,x33303)),f331(f131(x33301,x33302),x33303))
% 51.10/50.81 [3407]E(f19(x34071,x34072,x34073,f2(a106)),x34072)
% 51.10/50.81 [3408]E(f180(x34081,x34082,x34083,f2(a847)),x34082)
% 51.10/50.81 [3409]E(f21(x34091,x34092,x34093,f2(a106)),x34092)
% 51.10/50.81 [3416]E(f156(x34161,x34162,x34163,f120(x34161)),f120(x34162))
% 51.10/50.81 [3423]E(f331(f331(f155(x34231),f331(f331(f145(x34231),x34232),x34233)),f2(a847)),x34232)
% 51.10/50.81 [3475]P27(x34751,x34752,x34753,f184(f854(x34751,a840)))
% 51.10/50.81 [3536]E(f331(f331(f130(x35361),f167(x35361,x35362,x35363)),f134(x35361,x35362,x35363)),x35363)
% 51.10/50.81 [3570]E(f270(x35701,x35702,x35703),f331(f249(f854(a106,f854(a840,f851(f849(x35701)))),f853(a106,a106)),f53(x35701)))
% 51.10/50.81 [3630]E(f331(f80(x36301,x36302,x36301,x36303),f39(x36301)),x36303)
% 51.10/50.81 [3806]P1(f331(f331(f333(f853(x38061,x38061)),f331(f331(f249(x38061,x38061),x38062),x38062)),f308(x38061,x38063)))
% 51.10/50.81 [4447]~P1(f331(f331(f333(f853(f848(x44471),f848(x44471))),f331(f331(f249(f848(x44471),f848(x44471)),x44472),f120(x44471))),f140(x44471,x44473)))
% 51.10/50.81 [4448]~P1(f331(f331(f333(f853(f848(x44481),f848(x44481))),f331(f331(f249(f848(x44481),f848(x44481)),x44482),f120(x44481))),f142(x44481,x44483)))
% 51.10/50.81 [4449]~P1(f331(f331(f333(f853(f848(x44491),f848(x44491))),f331(f331(f249(f848(x44491),f848(x44491)),x44492),f120(x44491))),f150(x44491,x44493)))
% 51.10/50.81 [4450]~P1(f331(f331(f333(f853(f848(x44501),f848(x44501))),f331(f331(f249(f848(x44501),f848(x44501)),f120(x44501)),x44502)),f140(x44501,x44503)))
% 51.10/50.81 [4451]~P1(f331(f331(f333(f853(f848(x44511),f848(x44511))),f331(f331(f249(f848(x44511),f848(x44511)),f120(x44511)),x44512)),f150(x44511,x44513)))
% 51.10/50.81 [3159]E(f331(f331(f204(x31591),x31592),x31593),f205(x31591,f217(x31592,x31593)))
% 51.10/50.81 [3215]E(f331(f286(x32151,x32152),f331(f286(x32152,x32151),x32153)),x32153)
% 51.10/50.81 [3237]E(f331(f331(f172(x32371,x32372),f120(x32371)),x32373),f120(f853(x32371,x32372)))
% 51.10/50.81 [3240]E(f165(x32401,x32402,f331(f265(a847),x32403)),f331(f331(f164(x32401),x32403),x32402))
% 51.10/50.81 [3256]E(f331(f269(x32561,x32562),f331(f286(x32562,x32561),x32563)),f331(f267(x32562,x32561),x32563))
% 51.10/50.81 [3258]E(f146(x32581,f331(f131(x32581,x32582),x32583)),f331(f131(x32581,x32582),f146(x32581,x32583)))
% 51.10/50.81 [3259]E(f331(f267(x32591,x32592),f331(f286(x32592,x32591),x32593)),f331(f269(x32592,x32591),x32593))
% 51.10/50.81 [3260]E(f331(f269(x32601,x32602),f331(f286(x32602,x32601),x32603)),f331(f267(x32602,x32601),x32603))
% 51.10/50.81 [3275]E(f331(f131(x32751,x32752),f331(f160(x32751),x32753)),f331(f160(x32751),f331(f131(x32751,x32752),x32753)))
% 51.10/50.81 [3288]E(f331(f331(f133(x32881),x32882),f331(f162(x32881),x32883)),f331(f331(f133(x32881),f331(a119,x32882)),x32883))
% 51.10/50.81 [3306]E(f36(f34(x33061,x33062,x33063)),f331(f331(f87(a847),f36(x33063)),f331(a119,f2(a847))))
% 51.10/50.81 [3307]E(f331(f311(x33071,x33072,x33073),f184(f854(x33071,a840))),f184(f854(x33072,a840)))
% 51.10/50.81 [3308]E(f331(f285(x33081,x33082,x33083),f184(f854(x33081,a840))),f184(f854(x33082,a840)))
% 51.10/50.81 [3309]E(f331(f312(x33091,x33092,x33093),f184(f854(x33092,a840))),f184(f854(x33091,a840)))
% 51.10/50.81 [3310]E(f331(f312(x33101,x33102,x33103),f247(f854(x33102,a840))),f247(f854(x33101,a840)))
% 51.10/50.81 [3347]E(f235(x33471,x33472,f331(f234(x33471),x33473)),f331(f331(f87(a847),f331(x33472,x33473)),f331(a119,f2(a847))))
% 51.10/50.81 [3427]E(f331(f185(a841),f34(x34271,x34272,x34273)),f331(f331(f87(a847),f331(f185(a841),x34273)),f331(a119,f2(a847))))
% 51.10/50.81 [3428]E(f331(f311(f853(x34281,x34282),x34282,f258(x34281,x34282)),x34283),f331(f267(x34281,x34282),x34283))
% 51.10/50.81 [3429]E(f331(f311(f853(x34291,x34292),x34291,f248(x34291,x34292)),x34293),f331(f269(x34291,x34292),x34293))
% 51.10/50.81 [3499]E(f331(f331(f249(x34991,x34992),f331(f248(x34991,x34992),x34993)),f331(f258(x34991,x34992),x34993)),x34993)
% 51.10/50.81 [3500]E(f331(f331(f249(x35001,x35002),f331(f248(x35001,x35002),x35003)),f331(f258(x35001,x35002),x35003)),x35003)
% 51.10/50.81 [3507]E(f331(f331(f259(x35071,x35072,x35071),f18(x35071,x35072)),x35073),f331(f248(x35071,x35072),x35073))
% 51.10/50.81 [3526]E(f175(x35261,x35262,x35263,f331(f18(f851(x35262),x35261),f187(x35262))),x35263)
% 51.10/50.81 [3527]E(f175(x35271,x35272,f331(f18(f851(x35272),x35271),f187(x35272)),x35273),x35273)
% 51.10/50.81 [3583]E(f36(f35(x35831,x35832,x35833)),f331(f331(f87(a847),f331(f331(f87(a847),f36(x35832)),f36(x35833))),f331(a119,f2(a847))))
% 51.10/50.81 [3634]E(f331(f80(x36341,x36341,x36342,f39(x36341)),x36343),x36343)
% 51.10/50.81 [3718]P1(f331(f68(x37181),f174(x37181,x37182,f171(x37181,x37182,x37183))))
% 51.10/50.81 [3741]P1(f331(f331(f191(f30(x37411,x37412)),x37413),f331(f331(f331(a193,x37413),x37411),f331(x37412,x37413))))
% 51.10/50.81 [3742]P1(f331(f331(f191(f30(x37421,x37422)),x37423),f331(f331(f331(a193,x37423),x37421),f331(x37422,x37423))))
% 51.10/50.81 [3744]E(f331(f185(a841),f35(x37441,x37442,x37443)),f331(f331(f87(a847),f331(f331(f87(a847),f331(f185(a841),x37442)),f331(f185(a841),x37443))),f331(a119,f2(a847))))
% 51.10/50.81 [3816]P1(f331(f331(f240(f854(x38161,a840)),f331(f163(x38161),f331(f131(x38161,x38162),x38163))),f331(f163(x38161),x38163)))
% 51.10/50.81 [3861]P1(f331(f331(f240(f854(x38611,a840)),f331(f163(x38611),f331(f331(f164(x38611),x38612),x38613))),f331(f163(x38611),x38613)))
% 51.10/50.81 [3862]P1(f331(f331(f240(f854(x38621,a840)),f331(f163(x38621),f331(f331(f133(x38621),x38622),x38623))),f331(f163(x38621),x38623)))
% 51.10/50.81 [3866]P1(f331(f331(f240(f854(x38661,a840)),f331(f163(x38661),f161(x38661,x38662,x38663))),f331(f163(x38661),x38663)))
% 51.10/50.81 [3867]P1(f331(f331(f240(f854(x38671,a840)),f331(f163(x38671),f165(x38671,x38672,x38673))),f331(f163(x38671),x38672)))
% 51.10/50.81 [3889]P27(f853(x38891,x38892),f853(x38892,x38891),f331(f259(x38891,x38892,f853(x38892,x38891)),f331(f9(x38892,x38891,f853(x38892,x38891)),f249(x38892,x38891))),x38893)
% 51.10/50.81 [3901]E(f331(f331(f331(f178(f848(x39011),f848(x39011)),f57(a847,x39012,f331(f185(f848(x39011)),x39013))),f159(x39011)),x39013),f331(f331(f331(f178(f848(x39011),f848(x39011)),x39012),f159(x39011)),x39013))
% 51.10/50.81 [3943]E(f331(f80(f848(x39431),f848(x39431),f848(x39431),f331(f331(f178(f848(x39431),f848(x39431)),x39432),f159(x39431))),f331(f331(f178(f848(x39431),f848(x39431)),x39433),f159(x39431))),f331(f331(f178(f848(x39431),f848(x39431)),f331(f331(f87(a847),x39432),x39433)),f159(x39431)))
% 51.10/50.81 [3946]P1(f331(f331(f333(f853(f848(x39461),f848(x39461))),f331(f331(f249(f848(x39461),f848(x39461)),x39462),x39462)),f151(x39461,f308(x39461,x39463))))
% 51.10/50.81 [4086]E(f92(f853(x40861,x40862),f331(f331(f20(f853(x40861,x40862),x40862,a840),f331(f331(f10(x40861,f854(x40862,a840),f853(x40861,x40862)),x40863),f248(x40861,x40862))),f258(x40861,x40862))),f92(f853(x40861,x40862),f331(f259(x40861,x40862,a840),x40863)))
% 51.10/50.81 [4087]E(f97(f853(x40871,x40872),f331(f331(f20(f853(x40871,x40872),x40872,a840),f331(f331(f10(x40871,f854(x40872,a840),f853(x40871,x40872)),x40873),f248(x40871,x40872))),f258(x40871,x40872))),f97(f853(x40871,x40872),f331(f259(x40871,x40872,a840),x40873)))
% 51.10/50.81 [4124]E(f331(f331(f288(f853(a847,x41241),x41241),f324(a847,x41241,a245,x41242)),f331(f331(f20(x41241,x41241,f853(a847,x41241)),f331(f331(f10(a847,f854(x41241,f853(a847,x41241)),x41241),f249(a847,x41241)),x41243)),f7(x41241))),f326(x41241,x41243,x41242))
% 51.10/50.81 [4185]E(f331(f260(x41851,x41851,x41852,x41852,f7(x41851),f7(x41852)),x41853),x41853)
% 51.10/50.81 [4320]E(f331(f331(f93(a1,x43201),f220(f331(f331(f80(f853(a1,a1),a1,x43201,f258(a1,a1)),f214(x43201)),x43202),f331(f331(f80(f853(a1,a1),a1,x43201,f258(a1,a1)),f214(x43201)),x43203))),f331(f331(f20(a1,a1,x43201),f331(f331(f10(a1,f854(a1,x43201),a1),f204(x43201)),f331(f331(f20(a1,a1,a1),f331(f331(f10(a1,f854(a1,a1),a1),f87(a1)),f331(f331(f10(a1,a1,a1),f331(f88(a1),f331(f331(f80(f853(a1,a1),a1,x43201,f248(a1,a1)),f214(x43201)),x43202))),f331(f331(f9(a1,a1,a1),f48(a1)),f331(f331(f80(f853(a1,a1),a1,x43201,f258(a1,a1)),f214(x43201)),x43202))))),f331(f331(f10(a1,a1,a1),f331(f88(a1),f331(f331(f80(f853(a1,a1),a1,x43201,f248(a1,a1)),f214(x43201)),x43203))),f331(f331(f9(a1,a1,a1),f48(a1)),f331(f331(f80(f853(a1,a1),a1,x43201,f258(a1,a1)),f214(x43201)),x43203)))))),f7(a1))),f231(x43201,x43202,x43203))
% 51.10/50.81 [4367]~E(f331(f331(f145(x43671),x43672),x43673),x43673)
% 51.10/50.81 [4368]~E(f331(f331(f145(x43681),x43682),x43683),x43683)
% 51.10/50.81 [4376]~E(f331(f331(f145(x43761),x43762),x43763),f120(x43761))
% 51.10/50.81 [4377]~E(f331(f331(f145(x43771),x43772),x43773),f120(x43771))
% 51.10/50.81 [4402]~E(f331(f331(f310(x44021),x44022),x44023),f184(f854(x44021,a840)))
% 51.10/50.81 [4403]~E(f331(f331(f310(x44031),x44032),x44033),f184(f854(x44031,a840)))
% 51.10/50.81 [4428]~E(f331(f311(x44281,f854(x44281,a840),x44282),x44283),f331(f309(x44281),x44283))
% 51.10/50.81 [3218]E(f331(f331(f152(x32181,f120(x32181)),x32182),x32183),f120(x32181))
% 51.10/50.81 [3219]E(f331(f331(f152(x32191,f120(x32191)),x32192),x32193),f120(x32191))
% 51.10/50.81 [3220]E(f331(f136(x32201),f331(f331(f145(x32201),x32202),x32203)),x32202)
% 51.10/50.81 [3221]E(f331(f162(x32211),f331(f331(f145(x32211),x32212),x32213)),x32213)
% 51.10/50.81 [3264]E(f331(f331(f133(x32641),f85(a847)),f331(f331(f145(x32641),x32642),x32643)),x32643)
% 51.10/50.81 [3294]E(f121(x32941,f331(f331(f133(x32941),x32942),x32943)),f331(f331(f133(x32941),x32942),f121(x32941,x32943)))
% 51.10/50.81 [3295]E(f121(x32951,f331(f331(f133(x32951),x32952),x32953)),f331(f331(f133(x32951),x32952),f121(x32951,x32953)))
% 51.10/50.81 [3297]E(f331(f331(f152(x32971,x32972),x32973),f331(f331(f155(x32971),x32972),x32973)),x32972)
% 51.10/50.81 [3320]E(f331(f331(f310(x33201),x33202),f331(f331(f310(x33201),x33202),x33203)),f331(f331(f310(x33201),x33202),x33203))
% 51.10/50.81 [3333]E(f331(f331(f310(x33331),x33332),f331(f163(x33331),x33333)),f331(f163(x33331),f331(f331(f145(x33331),x33332),x33333)))
% 51.10/50.81 [3334]E(f331(f331(f133(x33341),x33342),f331(f162(x33341),x33343)),f331(f162(x33341),f331(f331(f133(x33341),x33342),x33343)))
% 51.10/50.81 [3335]E(f331(f331(f133(x33351),x33352),f331(f162(x33351),x33353)),f331(f162(x33351),f331(f331(f133(x33351),x33352),x33353)))
% 51.10/50.81 [3344]E(f331(f331(f164(x33441),f85(a847)),f331(f331(f145(x33441),x33442),x33443)),f331(f331(f145(x33441),x33442),f120(x33441)))
% 51.10/50.81 [3376]E(f331(f171(x33761,x33762,f120(f853(x33761,x33762))),x33763),f187(x33762))
% 51.10/50.81 [3377]E(f331(f171(x33771,x33772,f120(f853(x33771,x33772))),x33773),f187(x33772))
% 51.10/50.81 [3392]E(f331(f70(x33921,x33922),f331(f331(f310(x33921),x33923),f184(f854(x33921,a840)))),x33923)
% 51.10/50.81 [3439]E(f331(f331(f87(a847),x34391),f331(f331(f87(a847),x34392),x34393)),f331(f331(f87(a847),x34392),f331(f331(f87(a847),x34391),x34393)))
% 51.10/50.81 [3440]E(f331(f331(f87(a1),x34401),f331(f331(f87(a1),x34402),x34403)),f331(f331(f87(a1),x34402),f331(f331(f87(a1),x34401),x34403)))
% 51.10/50.81 [3445]E(f331(f331(f256(x34451,x34452),f184(f854(x34451,a840))),x34453),f184(f854(f853(x34451,x34452),a840)))
% 51.10/50.81 [3467]E(f331(f331(f108(f854(x34671,a840)),x34672),x34673),f331(f331(f108(f854(x34671,a840)),x34673),x34672))
% 51.10/50.81 [3468]E(f331(f331(f109(f854(x34681,a840)),x34682),x34683),f331(f331(f109(f854(x34681,a840)),x34683),x34682))
% 51.10/50.81 [3470]E(f331(f331(f130(x34701),x34702),f331(f331(f145(x34701),x34703),f120(x34701))),f331(f159(x34701),f331(f331(f145(x34701),x34703),x34702)))
% 51.10/50.81 [3471]E(f331(f331(f130(x34711),f331(f160(x34711),x34712)),f331(f160(x34711),x34713)),f331(f160(x34711),f331(f331(f130(x34711),x34713),x34712)))
% 51.10/50.81 [3479]E(f331(f162(x34791),f331(f331(f164(x34791),f331(a119,x34792)),x34793)),f331(f331(f164(x34791),x34792),f331(f162(x34791),x34793)))
% 51.10/50.81 [3486]P1(f331(f331(f333(x34861),x34862),f331(f331(f310(x34861),x34862),x34863)))
% 51.10/50.81 [3490]E(f331(f331(f52(x34901,f854(x34902,a840)),f184(f854(x34901,a840))),x34903),f247(f854(x34902,a840)))
% 51.10/50.81 [3493]E(f331(f285(x34931,x34931,f268(x34931,x34932)),x34933),f331(f331(f109(f854(x34931,a840)),x34932),x34933))
% 51.10/50.81 [3505]E(f331(f185(f848(x35051)),f331(f331(f145(x35051),x35052),x35053)),f331(f331(f87(a847),f331(f185(f848(x35051)),x35053)),f331(a119,f2(a847))))
% 51.10/50.81 [3509]E(f139(x35091,f331(f331(f130(x35091),x35092),f331(f331(f145(x35091),x35093),f120(x35091)))),x35093)
% 51.10/50.81 [3510]E(f121(x35101,f331(f331(f130(x35101),x35102),f331(f331(f145(x35101),x35103),f120(x35101)))),x35102)
% 51.10/50.81 [3515]E(f331(f331(f130(x35151),f331(f331(f164(x35151),x35152),x35153)),f331(f331(f133(x35151),x35152),x35153)),x35153)
% 51.10/50.81 [3524]E(f331(f331(f3(a847),f331(f331(f87(a847),x35241),x35242)),f331(f331(f87(a847),x35243),x35242)),f331(f331(f3(a847),x35241),x35243))
% 51.10/50.81 [3525]E(f331(f331(f3(a847),f331(f331(f87(a847),x35251),x35252)),f331(f331(f87(a847),x35251),x35253)),f331(f331(f3(a847),x35252),x35253))
% 51.10/50.81 [3531]E(f331(f331(f130(x35311),f331(f160(x35311),x35312)),f331(f331(f145(x35311),x35313),f120(x35311))),f331(f160(x35311),f331(f331(f145(x35311),x35313),x35312)))
% 51.10/50.81 [3533]E(f331(f331(f87(a847),f331(f185(f848(x35331)),x35332)),f331(f185(f848(x35331)),x35333)),f331(f185(f848(x35331)),f331(f331(f130(x35331),x35332),x35333)))
% 51.10/50.81 [3544]E(f331(f331(f108(f854(x35441,a840)),f331(f163(x35441),x35442)),f331(f163(x35441),x35443)),f331(f163(x35441),f331(f331(f130(x35441),x35442),x35443)))
% 51.10/50.81 [3545]E(f57(a847,f331(f331(f88(a847),x35451),x35452),f331(f331(f88(a847),x35451),x35453)),f331(f331(f88(a847),x35451),f57(a847,x35452,x35453)))
% 51.10/50.81 [3558]E(f331(f331(f164(x35581),f331(f331(f3(a847),x35582),f85(a847))),f331(f162(x35581),x35583)),f331(f162(x35581),f331(f331(f164(x35581),x35582),x35583)))
% 51.10/50.81 [3563]E(f331(f331(f109(f854(x35631,a840)),x35632),f331(f86(f854(x35631,a840)),x35633)),f331(f331(f3(f854(x35631,a840)),x35632),x35633))
% 51.10/50.81 [3564]E(f331(f331(f3(f854(x35641,a840)),x35642),f331(f86(f854(x35641,a840)),x35643)),f331(f331(f109(f854(x35641,a840)),x35642),x35643))
% 51.10/50.81 [3587]E(f331(f331(f256(x35871,x35872),x35873),f331(f18(f854(x35872,a840),x35871),f184(f854(x35872,a840)))),f184(f854(f853(x35871,x35872),a840)))
% 51.10/50.81 [3589]E(f331(f331(f87(a847),f331(f331(f88(a847),x35891),x35892)),f331(f331(f88(a847),x35891),x35893)),f331(f331(f88(a847),x35891),f331(f331(f87(a847),x35892),x35893)))
% 51.10/50.81 [3590]E(f331(f331(f3(a847),f331(f331(f88(a847),x35901),x35902)),f331(f331(f88(a847),x35901),x35903)),f331(f331(f88(a847),x35901),f331(f331(f3(a847),x35902),x35903)))
% 51.10/50.81 [3591]E(f331(f331(f87(a1),f331(f331(f88(a1),x35911),x35912)),f331(f331(f88(a1),x35911),x35913)),f331(f331(f88(a1),x35911),f331(f331(f87(a1),x35912),x35913)))
% 51.10/50.81 [3592]E(f331(f331(f3(a1),f331(f331(f88(a1),x35921),x35922)),f331(f331(f88(a1),x35921),x35923)),f331(f331(f88(a1),x35921),f331(f331(f3(a1),x35922),x35923)))
% 51.10/50.81 [3593]E(f331(f331(f88(a1),f331(f331(f250(a1),x35931),x35932)),f331(f331(f250(a1),x35931),x35933)),f331(f331(f250(a1),x35931),f331(f331(f87(a847),x35932),x35933)))
% 51.10/50.81 [3606]E(f331(f331(f51(x36061,f854(x36062,a840)),x36063),f331(f18(f854(x36062,a840),x36061),f184(f854(x36062,a840)))),f184(f854(x36062,a840)))
% 51.10/50.81 [3608]E(f57(a847,f331(f331(f88(a847),x36081),x36082),f331(f331(f88(a847),x36083),x36082)),f331(f331(f88(a847),f57(a847,x36081,x36083)),x36082))
% 51.10/50.81 [3612]E(f57(a1,f331(f331(f88(a1),x36121),f57(a1,x36122,x36123)),x36123),f57(a1,f331(f331(f88(a1),x36121),x36122),x36123))
% 51.10/50.81 [3613]E(f57(a1,f331(f331(f88(a1),x36131),f57(a1,x36132,x36133)),x36133),f57(a1,f331(f331(f88(a1),x36131),x36132),x36133))
% 51.10/50.81 [3614]E(f57(a1,f331(f331(f3(a1),x36141),f57(a1,x36142,x36143)),x36143),f57(a1,f331(f331(f3(a1),x36141),x36142),x36143))
% 51.10/50.81 [3615]P1(f331(f331(f240(f854(x36151,a840)),x36152),f331(f331(f310(x36151),x36153),x36152)))
% 51.10/50.81 [3639]E(f331(f311(f853(x36391,x36392),x36391,f248(x36391,x36392)),f331(f163(f853(x36391,x36392)),x36393)),f174(x36391,x36392,f171(x36391,x36392,x36393)))
% 51.10/50.81 [3694]E(f331(f331(f52(f854(x36941,a840),f854(x36941,a840)),x36942),f331(f108(f854(x36941,a840)),x36943)),f331(f331(f108(f854(x36941,a840)),x36943),f50(f854(x36941,a840),x36942)))
% 51.10/50.81 [3695]E(f331(f331(f51(f854(x36951,a840),f854(x36951,a840)),x36952),f331(f109(f854(x36951,a840)),x36953)),f331(f331(f109(f854(x36951,a840)),x36953),f49(f854(x36951,a840),x36952)))
% 51.10/50.81 [3705]E(f331(f163(x37051),f331(f331(f331(f178(f848(x37051),f848(x37051)),x37052),f159(x37051)),x37053)),f331(f163(x37051),x37053))
% 51.10/50.81 [3709]E(f331(f331(f164(x37091),f331(f185(f848(x37091)),f167(x37091,x37092,x37093))),x37093),f167(x37091,x37092,x37093))
% 51.10/50.81 [3710]E(f174(x37101,x37102,f331(f331(f10(x37102,f851(x37102),x37101),f234(x37102)),x37103)),f247(f854(x37101,a840)))
% 51.10/50.81 [3713]E(f331(f185(f848(x37131)),f331(f331(f331(f178(f848(x37131),f848(x37131)),x37132),f159(x37131)),x37133)),f331(f185(f848(x37131)),x37133))
% 51.10/50.81 [3716]E(f331(f331(f259(x37161,x37162,x37162),f331(f18(f854(x37162,x37162),x37161),f7(x37162))),x37163),f331(f258(x37161,x37162),x37163))
% 51.10/50.81 [3724]E(f57(a1,f331(f331(f3(a1),f57(a1,x37241,x37242)),x37243),x37242),f57(a1,f331(f331(f3(a1),x37241),x37243),x37242))
% 51.10/50.81 [3725]E(f57(a1,f331(f331(f250(a1),f57(a1,x37251,x37252)),x37253),x37252),f57(a1,f331(f331(f250(a1),x37251),x37253),x37252))
% 51.10/50.81 [3728]E(f331(f331(f51(f854(f853(x37281,x37282),a840),f854(x37282,a840)),x37283),f267(x37281,x37282)),f331(f267(x37281,x37282),f49(f854(f853(x37281,x37282),a840),x37283)))
% 51.10/50.81 [3729]E(f331(f331(f51(f854(f853(x37291,x37292),a840),f854(x37291,a840)),x37293),f269(x37291,x37292)),f331(f269(x37291,x37292),f49(f854(f853(x37291,x37292),a840),x37293)))
% 51.10/50.81 [3757]E(f331(f80(x37571,x37571,x37571,x37572),f331(f331(f178(x37571,x37571),x37573),x37572)),f331(f331(f178(x37571,x37571),f331(a119,x37573)),x37572))
% 51.10/50.81 [3767]E(f236(f851(x37671),x37672,f187(x37671),f331(f331(f10(x37671,f851(x37671),x37672),f234(x37671)),x37673)),f331(f203(x37672,x37671),x37673))
% 51.10/50.81 [3774]E(f331(f331(f133(x37741),f331(f331(f3(a847),f331(f185(f848(x37741)),x37742)),x37743)),f331(f160(x37741),x37742)),f331(f160(x37741),f331(f331(f164(x37741),x37743),x37742)))
% 51.10/50.81 [3775]E(f331(f331(f164(x37751),f331(f331(f3(a847),f331(f185(f848(x37751)),x37752)),x37753)),f331(f160(x37751),x37752)),f331(f160(x37751),f331(f331(f133(x37751),x37753),x37752)))
% 51.10/50.81 [3778]E(f331(f331(f87(a847),f331(f157(a847),f331(f331(f147(x37781,a847),x37782),x37783))),f331(f185(f848(x37781)),x37783)),f148(x37781,x37782,x37783))
% 51.10/50.81 [3787]E(f331(f331(f331(f178(f848(x37871),f848(x37871)),x37872),f159(x37871)),f331(f159(x37871),x37873)),f331(f159(x37871),f331(f331(f331(f178(f848(x37871),f848(x37871)),x37872),f159(x37871)),x37873)))
% 51.10/50.81 [3795]E(f331(f159(x37951),f331(f331(f331(f178(f848(x37951),f848(x37951)),x37952),f159(x37951)),x37953)),f331(f331(f331(f178(f848(x37951),f848(x37951)),f331(a119,x37952)),f159(x37951)),x37953))
% 51.10/50.81 [3807]P1(f331(f331(f240(a847),f331(f185(f848(x38071)),f331(f131(x38071,x38072),x38073))),f331(f185(f848(x38071)),x38073)))
% 51.10/50.81 [3824]E(f331(f331(f108(f854(f854(x38241,a840),a840)),f331(f309(x38241),x38242)),f331(f311(f854(x38241,a840),f854(x38241,a840),f331(f310(x38241),x38243)),f331(f309(x38241),x38242))),f331(f309(x38241),f331(f331(f310(x38241),x38243),x38242)))
% 51.10/50.81 [3840]P26(x38401,x38402,f331(f331(f310(f846(x38401)),f331(f331(f331(f98(x38401),x38403),a25),x38403)),f184(f854(f846(x38401),a840))))
% 51.10/50.81 [3841]P26(x38411,x38412,f331(f331(f310(f846(x38411)),f331(f331(f331(f98(x38411),x38413),a25),x38413)),f184(f854(f846(x38411),a840))))
% 51.10/50.81 [3857]P1(f331(f331(f240(a847),f331(f185(f848(x38571)),f167(x38571,x38572,x38573))),f331(f185(f848(x38571)),x38573)))
% 51.10/50.81 [3858]P1(f331(f331(f240(a847),f331(f185(f848(x38581)),f134(x38581,x38582,x38583))),f331(f185(f848(x38581)),x38583)))
% 51.10/50.81 [3865]E(f331(f269(x38651,x38652),f331(f264(f853(x38651,x38652)),f331(f259(x38651,x38652,a840),x38653))),f331(f264(x38651),f331(f331(f10(f854(x38652,a840),a840,x38651),f94(x38652)),x38653)))
% 51.10/50.81 [3876]E(f331(f311(a847,a847,f331(f331(f9(a847,a847,a847),f87(a847)),x38761)),f303(a847,x38762,x38763)),f303(a847,f331(f331(f87(a847),x38762),x38761),f331(f331(f87(a847),x38763),x38761)))
% 51.10/50.81 [3892]E(f331(f311(a847,a847,f331(f331(f9(a847,a847,a847),f87(a847)),x38921)),f331(f302(a847,x38922),x38923)),f331(f302(a847,f331(f331(f87(a847),x38922),x38921)),f331(f331(f87(a847),x38923),x38921)))
% 51.10/50.81 [3910]E(f331(f331(f172(x39101,x39102),f331(f331(f147(f853(x39101,x39102),x39101),f248(x39101,x39102)),x39103)),f331(f331(f147(f853(x39101,x39102),x39102),f258(x39101,x39102)),x39103)),x39103)
% 51.10/50.81 [3915]E(f331(f331(f87(a847),f331(f331(f88(a847),x39151),f57(a847,f331(f331(f48(a847),x39152),x39151),x39153))),f57(a847,x39152,x39151)),f57(a847,x39152,f331(f331(f88(a847),x39151),x39153)))
% 51.10/50.81 [3926]P1(f331(f68(f851(x39261)),f331(f311(x39262,f851(x39261),f171(x39262,x39261,x39263)),f247(f854(x39262,a840)))))
% 51.10/50.81 [3930]E(f331(f331(f130(x39301),x39302),f331(f137(f848(x39301),f848(x39301),f130(x39301),f120(x39301)),x39303)),f331(f137(f848(x39301),f848(x39301),f130(x39301),x39302),x39303))
% 51.10/50.81 [3950]P1(f331(f331(f333(f853(x39501,x39501)),f331(f331(f249(x39501,x39501),x39502),x39502)),f331(f331(f178(f853(x39501,x39501),a840),f2(a847)),x39503)))
% 51.10/50.81 [3956]E(f331(f264(x39561),f331(f331(f10(f854(x39562,a840),a840,x39561),f94(x39562)),f331(f9(x39562,x39561,a840),x39563))),f331(f267(x39562,x39561),f331(f264(f853(x39562,x39561)),f331(f259(x39562,x39561,a840),x39563))))
% 51.10/50.81 [3974]E(f331(f331(f108(f854(x39741,a840)),f331(f331(f51(a847,f854(x39741,a840)),f303(a847,f85(a847),x39742)),x39743)),f331(x39743,f2(a847))),f331(f331(f51(a847,f854(x39741,a840)),f331(f301(a847),x39742)),x39743))
% 51.10/50.81 [3989]E(f331(f137(f848(x39891),f848(x39891),f130(x39891),f120(x39891)),f331(f331(f147(f848(x39891),f848(x39891)),f131(x39891,x39892)),x39893)),f331(f131(x39891,x39892),f331(f137(f848(x39891),f848(x39891),f130(x39891),f120(x39891)),x39893)))
% 51.10/50.81 [3994]E(f331(f258(f848(x39941),f848(x39941)),f158(x39941,x39942,x39943)),f331(f131(x39941,f331(f80(a840,a840,x39941,a327),x39942)),x39943))
% 51.10/50.81 [4040]E(f331(f331(f87(a1),f331(f331(f87(a1),f331(f331(f88(a1),x40401),f331(f331(f48(a1),x40402),x40401))),f57(a1,x40402,x40401))),x40403),f331(f331(f87(a1),x40402),x40403))
% 51.10/50.81 [4074]E(f331(f331(f87(a1),f331(f331(f87(a1),f331(f331(f88(a1),f331(f331(f48(a1),x40741),x40742)),x40742)),f57(a1,x40741,x40742))),x40743),f331(f331(f87(a1),x40741),x40743))
% 51.10/50.81 [4104]E(f92(f853(x41041,x41042),f331(f259(x41041,x41042,a840),f331(f331(f10(f854(x41042,f853(x41041,x41042)),f854(x41042,a840),x41041),f331(f10(f853(x41041,x41042),a840,x41042),x41043)),f249(x41041,x41042)))),f92(f853(x41041,x41042),x41043))
% 51.10/50.81 [4105]E(f97(f853(x41051,x41052),f331(f259(x41051,x41052,a840),f331(f331(f10(f854(x41052,f853(x41051,x41052)),f854(x41052,a840),x41051),f331(f10(f853(x41051,x41052),a840,x41052),x41053)),f249(x41051,x41052)))),f97(f853(x41051,x41052),x41053))
% 51.10/50.81 [4134]P1(f331(f331(f240(f854(x41341,a840)),f49(f854(x41341,a840),f331(f331(f109(f854(f854(x41341,a840),a840)),x41342),x41343))),f331(f331(f109(f854(x41341,a840)),f49(f854(x41341,a840),x41342)),f49(f854(x41341,a840),x41343))))
% 51.10/50.81 [4135]E(f331(f160(x41351),f331(f331(f331(f178(f848(x41351),f848(x41351)),f331(f331(f3(a847),f331(f185(f848(x41351)),x41352)),f57(a847,x41353,f331(f185(f848(x41351)),x41352)))),f159(x41351)),x41352)),f331(f331(f331(f178(f848(x41351),f848(x41351)),x41353),f159(x41351)),f331(f160(x41351),x41352)))
% 51.10/50.81 [4147]E(f331(f264(x41471),f331(f331(f10(a840,a840,x41471),a327),f331(f331(f9(x41471,f851(x41472),a840),f331(f331(f10(f851(x41472),f854(f851(x41472),a840),x41471),a328),x41473)),f187(x41472)))),f174(x41471,x41472,x41473))
% 51.10/50.81 [4210]E(f331(f264(x42101),f331(f331(f10(f854(x42102,a840),a840,x42101),f94(x42102)),f331(f331(f10(f851(x42101),f854(x42102,a840),x42101),f331(f9(x42102,f851(x42101),a840),f331(f331(f10(f851(x42101),f854(f851(x42101),a840),x42102),a328),x42103))),f234(x42101)))),f176(x42102,x42101,x42103))
% 51.10/50.81 [4441]~P1(f331(f69(x44411,x44412,f184(f854(x44411,a840))),x44413))
% 51.10/50.81 [3480]E(f331(f185(f848(x34801)),f331(f331(f164(x34801),x34802),x34803)),f331(f331(f244(a847),f331(f185(f848(x34801)),x34803)),x34802))
% 51.10/50.81 [3481]E(f331(f185(f848(x34811)),f331(f331(f133(x34811),x34812),x34813)),f331(f331(f3(a847),f331(f185(f848(x34811)),x34813)),x34812))
% 51.10/50.81 [3517]E(f331(f331(f48(a847),f331(f331(f48(a847),x35171),x35172)),x35173),f331(f331(f48(a847),x35171),f331(f331(f88(a847),x35172),x35173)))
% 51.10/50.81 [3518]E(f331(f331(f87(a847),f331(f331(f87(a847),x35181),x35182)),x35183),f331(f331(f87(a847),x35181),f331(f331(f87(a847),x35182),x35183)))
% 51.10/50.81 [3519]E(f331(f331(f87(a1),f331(f331(f87(a1),x35191),x35192)),x35193),f331(f331(f87(a1),x35191),f331(f331(f87(a1),x35192),x35193)))
% 51.10/50.81 [3520]E(f331(f331(f88(a847),f331(f331(f88(a847),x35201),x35202)),x35203),f331(f331(f88(a847),x35201),f331(f331(f88(a847),x35202),x35203)))
% 51.10/50.81 [3521]E(f331(f331(f88(a1),f331(f331(f88(a1),x35211),x35212)),x35213),f331(f331(f88(a1),x35211),f331(f331(f88(a1),x35212),x35213)))
% 51.10/50.81 [3522]E(f331(f331(f3(a847),f331(f331(f3(a847),x35221),x35222)),x35223),f331(f331(f3(a847),x35221),f331(f331(f87(a847),x35222),x35223)))
% 51.10/50.81 [3523]E(f331(f331(f250(a1),f331(f331(f250(a1),x35231),x35232)),x35233),f331(f331(f250(a1),x35231),f331(f331(f88(a847),x35232),x35233)))
% 51.10/50.81 [3542]E(f154(x35421,f331(f331(f145(f854(x35421,a840)),x35422),x35423)),f166(x35421,x35422,f154(x35421,x35423)))
% 51.10/50.81 [3588]E(f331(f331(f3(a847),f331(f331(f3(a847),x35881),x35882)),x35883),f331(f331(f3(a847),f331(f331(f3(a847),x35881),x35883)),x35882))
% 51.10/50.81 [3596]E(f331(f331(f109(f854(x35961,a840)),x35962),f331(f331(f3(f854(x35961,a840)),x35963),x35962)),f184(f854(x35961,a840)))
% 51.10/50.81 [3641]E(f50(f854(x36411,a840),f331(f331(f310(f854(x36411,a840)),x36412),x36413)),f331(f331(f109(f854(x36411,a840)),x36412),f50(f854(x36411,a840),x36413)))
% 51.10/50.81 [3642]E(f49(f854(x36421,a840),f331(f331(f310(f854(x36421,a840)),x36422),x36423)),f331(f331(f108(f854(x36421,a840)),x36422),f49(f854(x36421,a840),x36423)))
% 51.10/50.81 [3644]E(f331(f331(f87(a847),f331(f331(f88(a847),x36441),x36442)),f331(f331(f88(a847),x36443),x36442)),f331(f331(f88(a847),f331(f331(f87(a847),x36441),x36443)),x36442))
% 51.10/50.81 [3645]E(f331(f331(f3(a847),f331(f331(f88(a847),x36451),x36452)),f331(f331(f88(a847),x36453),x36452)),f331(f331(f88(a847),f331(f331(f3(a847),x36451),x36453)),x36452))
% 51.10/50.81 [3646]E(f331(f331(f87(a1),f331(f331(f88(a1),x36461),x36462)),f331(f331(f88(a1),x36463),x36462)),f331(f331(f88(a1),f331(f331(f87(a1),x36461),x36463)),x36462))
% 51.10/50.81 [3648]E(f331(f331(f3(a1),f331(f331(f88(a1),x36481),x36482)),f331(f331(f88(a1),x36483),x36482)),f331(f331(f88(a1),f331(f331(f3(a1),x36481),x36483)),x36482))
% 51.10/50.81 [3649]E(f331(f331(f244(a847),f331(f331(f3(a847),x36491),x36492)),f331(f331(f3(a847),x36493),x36492)),f331(f331(f3(a847),f331(f331(f244(a847),x36491),x36493)),x36492))
% 51.10/50.81 [3673]E(f331(f331(f108(f854(x36731,a840)),x36732),f331(f331(f3(f854(x36731,a840)),x36733),x36732)),f331(f331(f108(f854(x36731,a840)),x36732),x36733))
% 51.10/50.81 [3674]E(f331(f331(f108(f854(x36741,a840)),x36742),f331(f331(f108(f854(x36741,a840)),x36742),x36743)),f331(f331(f108(f854(x36741,a840)),x36742),x36743))
% 51.10/50.81 [3675]E(f331(f331(f109(f854(x36751,a840)),x36752),f331(f331(f109(f854(x36751,a840)),x36752),x36753)),f331(f331(f109(f854(x36751,a840)),x36752),x36753))
% 51.10/50.81 [3687]E(f331(f331(f289(x36871,x36872,x36872),x36873),f308(x36872,f184(f854(f853(x36872,x36872),a840)))),x36873)
% 51.10/50.81 [3690]E(f331(f331(f108(f854(x36901,a840)),f331(f331(f310(x36901),x36902),f184(f854(x36901,a840)))),x36903),f331(f331(f310(x36901),x36902),x36903))
% 51.10/50.81 [3708]E(f331(f331(f3(a847),f331(f331(f3(a847),f331(a119,x37081)),x37082)),f331(a119,x37083)),f331(f331(f3(a847),f331(f331(f3(a847),x37081),x37082)),x37083))
% 51.10/50.81 [3737]E(f331(f331(f109(f854(f854(x37371,a840),a840)),f331(f309(x37371),x37372)),f331(f309(x37371),x37373)),f331(f309(x37371),f331(f331(f109(f854(x37371,a840)),x37372),x37373)))
% 51.10/50.81 [3740]E(f331(f331(f108(f854(x37401,a840)),f331(f86(f854(x37401,a840)),x37402)),x37403),f331(f86(f854(x37401,a840)),f331(f331(f3(f854(x37401,a840)),x37402),x37403)))
% 51.10/50.81 [3753]E(f331(f331(f310(x37531),x37532),f331(f331(f3(f854(x37531,a840)),x37533),f331(f331(f310(x37531),x37532),f184(f854(x37531,a840))))),f331(f331(f310(x37531),x37532),x37533))
% 51.10/50.81 [3764]P1(f331(f331(f240(f854(x37641,a840)),x37642),f331(f331(f108(f854(x37641,a840)),x37643),x37642)))
% 51.10/50.81 [3765]P1(f331(f331(f240(f854(x37651,a840)),x37652),f331(f331(f108(f854(x37651,a840)),x37652),x37653)))
% 51.10/50.81 [3768]E(f331(f331(f109(f854(x37681,a840)),f331(f86(f854(x37681,a840)),x37682)),f331(f86(f854(x37681,a840)),x37683)),f331(f86(f854(x37681,a840)),f331(f331(f108(f854(x37681,a840)),x37682),x37683)))
% 51.10/50.81 [3769]E(f331(f331(f108(f854(x37691,a840)),f331(f86(f854(x37691,a840)),x37692)),f331(f86(f854(x37691,a840)),x37693)),f331(f86(f854(x37691,a840)),f331(f331(f109(f854(x37691,a840)),x37692),x37693)))
% 51.10/50.81 [3782]P1(f331(f331(f240(f854(x37821,a840)),f331(f163(x37821),x37822)),f331(f163(x37821),f331(f331(f145(x37821),x37823),x37822))))
% 51.10/50.81 [3791]E(f331(f331(f108(f854(x37911,a840)),f331(f331(f3(f854(x37911,a840)),x37912),x37913)),f331(f331(f109(f854(x37911,a840)),x37912),x37913)),x37912)
% 51.10/50.81 [3843]E(f331(f331(f11(x38431,a1),f331(f331(f10(a847,a1,x38431),f107(a1)),x38432)),x38433),f331(f107(a1),f331(f331(f11(x38431,a847),x38432),x38433)))
% 51.10/50.81 [3844]E(f331(f331(f8(x38441,a1),f331(f331(f10(a847,a1,x38441),f107(a1)),x38442)),x38443),f331(f107(a1),f331(f331(f8(x38441,a847),x38442),x38443)))
% 51.10/50.81 [3899]E(f331(f86(f854(f853(x38991,x38992),a840)),f331(f331(f256(x38991,x38992),x38993),f331(f18(f854(x38992,a840),x38991),f247(f854(x38992,a840))))),f331(f331(f256(x38991,x38992),f331(f86(f854(x38991,a840)),x38993)),f331(f18(f854(x38992,a840),x38991),f247(f854(x38992,a840)))))
% 51.10/50.81 [3900]E(f331(f86(f854(f853(x39001,x39002),a840)),f331(f331(f256(x39001,x39002),f247(f854(x39001,a840))),f331(f18(f854(x39002,a840),x39001),x39003))),f331(f331(f256(x39001,x39002),f247(f854(x39001,a840))),f331(f18(f854(x39002,a840),x39001),f331(f86(f854(x39002,a840)),x39003))))
% 51.10/50.81 [3951]E(f331(f331(f51(f854(x39511,a840),f854(x39511,a840)),x39512),f331(f331(f9(f854(x39511,a840),f854(x39511,a840),f854(x39511,a840)),f109(f854(x39511,a840))),x39513)),f331(f331(f109(f854(x39511,a840)),f49(f854(x39511,a840),x39512)),x39513))
% 51.10/50.81 [3958]E(f331(f137(f848(x39581),f848(x39581),f130(x39581),f120(x39581)),f331(f331(f145(f848(x39581)),x39582),x39583)),f331(f331(f130(x39581),x39582),f331(f137(f848(x39581),f848(x39581),f130(x39581),f120(x39581)),x39583)))
% 51.10/50.81 [3980]E(f331(f331(f310(f854(x39801,a840)),f331(f285(x39801,x39801,x39802),f331(f331(f310(x39801),x39803),f184(f854(x39801,a840))))),f184(f854(f854(x39801,a840),a840))),f331(f331(f66(x39801),f331(f331(f310(x39801),x39803),f184(f854(x39801,a840)))),x39802))
% 51.10/50.81 [3990]E(f331(f331(f87(a847),f331(f331(f88(a847),x39901),f331(f331(f48(a847),x39902),x39903))),f331(f331(f48(a847),f331(f331(f88(a847),x39901),f57(a847,x39902,x39903))),x39903)),f331(f331(f48(a847),f331(f331(f88(a847),x39901),x39902)),x39903))
% 51.10/50.81 [3991]E(f331(f331(f87(a1),f331(f331(f88(a1),x39911),f331(f331(f48(a1),x39912),x39913))),f331(f331(f48(a1),f331(f331(f88(a1),x39911),f57(a1,x39912,x39913))),x39913)),f331(f331(f48(a1),f331(f331(f88(a1),x39911),x39912)),x39913))
% 51.10/50.81 [4072]E(f331(f331(f130(x40721),f331(f137(f848(x40721),f848(x40721),f130(x40721),f120(x40721)),x40722)),f331(f137(f848(x40721),f848(x40721),f130(x40721),f120(x40721)),x40723)),f331(f137(f848(x40721),f848(x40721),f130(x40721),f120(x40721)),f331(f331(f130(f848(x40721)),x40722),x40723)))
% 51.10/50.81 [4075]E(f331(f331(f249(f848(x40751),f848(x40751)),f331(f131(x40751,x40752),x40753)),f331(f131(x40751,f331(f80(a840,a840,x40751,a327),x40752)),x40753)),f158(x40751,x40752,x40753))
% 51.10/50.81 [4078]E(f331(f331(f87(a847),f331(f331(f87(a847),f331(f331(f48(a847),x40781),x40782)),f331(f331(f48(a847),x40783),x40782))),f331(f331(f48(a847),f331(f331(f87(a847),f57(a847,x40781,x40782)),f57(a847,x40783,x40782))),x40782)),f331(f331(f48(a847),f331(f331(f87(a847),x40781),x40783)),x40782))
% 51.10/50.81 [4079]E(f331(f331(f87(a1),f331(f331(f87(a1),f331(f331(f48(a1),x40791),x40792)),f331(f331(f48(a1),x40793),x40792))),f331(f331(f48(a1),f331(f331(f87(a1),f57(a1,x40791,x40792)),f57(a1,x40793,x40792))),x40792)),f331(f331(f48(a1),f331(f331(f87(a1),x40791),x40793)),x40792))
% 51.10/50.81 [4148]E(f331(f264(x41481),f331(f331(f20(x41481,a840,a840),f331(f331(f10(a840,f854(a840,a840),x41481),a330),f331(f331(f9(x41481,x41481,a840),a328),x41482))),f331(f331(f9(x41481,f854(x41481,a840),a840),f333(x41481)),x41483))),f331(f331(f310(x41481),x41482),x41483))
% 51.10/50.81 [4149]E(f331(f264(x41491),f331(f331(f20(x41491,a840,a840),f331(f331(f10(a840,f854(a840,a840),x41491),a330),f331(f331(f9(x41491,x41491,a840),a328),x41492))),f331(f331(f9(x41491,f854(x41491,a840),a840),f333(x41491)),x41493))),f331(f331(f310(x41491),x41492),x41493))
% 51.10/50.81 [4171]E(f331(f264(x41711),f331(f331(f20(x41711,a840,a840),f331(f331(f10(a840,f854(a840,a840),x41711),a330),f331(f331(f9(x41711,f854(x41711,a840),a840),f333(x41711)),x41712))),f331(f331(f9(x41711,f854(x41711,a840),a840),f333(x41711)),x41713))),f331(f331(f108(f854(x41711,a840)),x41712),x41713))
% 51.10/50.81 [4172]E(f331(f264(x41721),f331(f331(f20(x41721,a840,a840),f331(f331(f10(a840,f854(a840,a840),x41721),a329),f331(f331(f9(x41721,f854(x41721,a840),a840),f333(x41721)),x41722))),f331(f331(f9(x41721,f854(x41721,a840),a840),f333(x41721)),x41723))),f331(f331(f109(f854(x41721,a840)),x41722),x41723))
% 51.10/50.81 [4259]E(f331(f331(f51(x42591,f854(f854(x42591,a840),a840)),x42592),f331(f331(f9(x42591,f854(f854(x42591,a840),a840),f854(f854(x42591,a840),a840)),f331(f331(f10(f854(x42591,a840),f854(f854(f854(x42591,a840),a840),f854(f854(x42591,a840),a840)),x42591),f310(f854(x42591,a840))),f331(f331(f10(f854(x42591,a840),f854(x42591,a840),x42591),f285(x42591,x42591,x42593)),f331(f331(f9(x42591,f854(x42591,a840),f854(x42591,a840)),f310(x42591)),f184(f854(x42591,a840)))))),f184(f854(f854(x42591,a840),a840)))),f331(f331(f66(x42591),x42592),x42593))
% 51.10/50.81 [4261]E(f331(f331(f204(x42611),f331(f331(f88(a1),f331(f331(f80(f853(a1,a1),a1,x42611,f248(a1,a1)),f214(x42611)),x42612)),f331(f331(f80(f853(a1,a1),a1,x42611,f248(a1,a1)),f214(x42611)),x42613))),f331(f331(f88(a1),f331(f331(f80(f853(a1,a1),a1,x42611,f258(a1,a1)),f214(x42611)),x42612)),f331(f331(f80(f853(a1,a1),a1,x42611,f258(a1,a1)),f214(x42611)),x42613))),f229(x42611,x42612,x42613))
% 51.10/50.81 [3662]E(f57(a847,f331(f331(f87(a847),f331(f331(f88(a847),x36621),x36622)),x36623),x36622),f57(a847,x36623,x36622))
% 51.10/50.81 [3707]E(f135(a847,f331(f302(a847,f331(f331(f87(a847),x37071),x37072)),x37073)),f331(f331(f133(a847),x37072),f135(a847,f331(f302(a847,x37071),x37073))))
% 51.10/50.81 [3752]E(f331(f331(f87(a1),f331(f107(a1),x37521)),f331(f331(f87(a1),f331(f107(a1),x37522)),x37523)),f331(f331(f87(a1),f331(f107(a1),f331(f331(f87(a847),x37521),x37522))),x37523))
% 51.10/50.81 [3760]E(f331(f331(f3(f854(x37601,a840)),f331(f331(f3(f854(x37601,a840)),x37602),x37603)),x37603),f331(f331(f3(f854(x37601,a840)),x37602),x37603))
% 51.10/50.81 [3761]E(f331(f331(f108(f854(x37611,a840)),f331(f331(f3(f854(x37611,a840)),x37612),x37613)),x37613),f331(f331(f108(f854(x37611,a840)),x37612),x37613))
% 51.10/50.81 [3783]E(f331(f331(f289(x37831,x37831,x37832),f308(x37831,f184(f854(f853(x37831,x37831),a840)))),x37833),x37833)
% 51.10/50.81 [3788]E(f331(f331(f108(f854(x37881,a840)),f331(f284(x37881),x37882)),f331(f284(x37881),x37883)),f331(f284(x37881),f331(f331(f108(f854(f853(x37881,x37881),a840)),x37882),x37883)))
% 51.10/50.81 [3798]E(f271(x37981,f331(f331(f145(f853(a106,x37981)),f331(f331(f249(a106,x37981),f2(a106)),x37982)),x37983)),f271(x37981,x37983))
% 51.10/50.81 [3801]E(f331(f331(f109(f854(x38011,a840)),f50(f854(x38011,a840),x38012)),f50(f854(x38011,a840),x38013)),f50(f854(x38011,a840),f331(f331(f108(f854(f854(x38011,a840),a840)),x38012),x38013)))
% 51.10/50.81 [3802]E(f331(f331(f108(f854(x38021,a840)),f49(f854(x38021,a840),x38022)),f49(f854(x38021,a840),x38023)),f49(f854(x38021,a840),f331(f331(f108(f854(f854(x38021,a840),a840)),x38022),x38023)))
% 51.10/50.81 [3836]E(f331(f331(f289(x38361,x38361,x38361),f331(f331(f178(f853(x38361,x38361),a840),x38362),x38363)),x38363),f331(f331(f178(f853(x38361,x38361),a840),f331(a119,x38362)),x38363))
% 51.10/50.81 [3885]P1(f331(f331(f240(f854(x38851,a840)),f331(f331(f3(f854(x38851,a840)),x38852),x38853)),x38852))
% 51.10/50.81 [3886]P1(f331(f331(f240(f854(x38861,a840)),f331(f331(f109(f854(x38861,a840)),x38862),x38863)),x38863))
% 51.10/50.81 [3887]P1(f331(f331(f240(f854(x38871,a840)),f331(f331(f109(f854(x38871,a840)),x38872),x38873)),x38872))
% 51.10/50.81 [3912]E(f308(x39121,f331(f331(f108(f854(f853(x39121,x39121),a840)),f308(x39121,x39122)),f308(x39121,x39123))),f308(x39121,f331(f331(f108(f854(f853(x39121,x39121),a840)),x39122),x39123)))
% 51.10/50.81 [3916]E(f49(f854(x39161,a840),f331(f331(f310(f854(x39161,a840)),x39162),f331(f331(f310(f854(x39161,a840)),x39163),f184(f854(f854(x39161,a840),a840))))),f331(f331(f108(f854(x39161,a840)),x39162),x39163))
% 51.10/50.81 [3917]E(f50(f854(x39171,a840),f331(f331(f310(f854(x39171,a840)),x39172),f331(f331(f310(f854(x39171,a840)),x39173),f184(f854(f854(x39171,a840),a840))))),f331(f331(f109(f854(x39171,a840)),x39172),x39173))
% 51.10/50.81 [3923]E(f331(f331(f289(x39231,x39231,x39231),f331(f331(f178(f853(x39231,x39231),a840),x39232),x39233)),x39233),f331(f331(f289(x39231,x39231,x39231),x39233),f331(f331(f178(f853(x39231,x39231),a840),x39232),x39233)))
% 51.10/50.81 [3995]E(f331(f331(f108(f854(x39951,a840)),f331(f264(x39951),f331(f331(f9(x39951,x39951,a840),a328),x39952))),x39953),f331(f331(f310(x39951),x39952),x39953))
% 51.10/50.81 [3997]E(f331(a112,f331(f331(f11(x39971,a1),f331(f331(f10(a847,a1,x39971),f107(a1)),x39972)),x39973)),f331(f331(f11(x39971,a847),x39972),x39973))
% 51.10/50.81 [3998]E(f331(a112,f331(f331(f8(x39981,a1),f331(f331(f10(a847,a1,x39981),f107(a1)),x39982)),x39983)),f331(f331(f8(x39981,a847),x39982),x39983))
% 51.10/50.81 [4069]E(f331(f149(f848(x40691),x40691,f331(f162(x40691),x40692),f331(f18(f854(f848(x40691),f848(x40691)),x40691),f331(f331(f9(f848(x40691),f848(x40691),f848(x40691)),f130(x40691)),x40692))),x40693),f331(f162(x40691),f331(f331(f130(x40691),x40693),x40692)))
% 51.10/50.81 [4100]P1(f331(f331(f240(f854(f854(x41001,a840),a840)),f331(f331(f108(f854(f854(x41001,a840),a840)),f331(f309(x41001),x41002)),f331(f309(x41001),x41003))),f331(f309(x41001),f331(f331(f108(f854(x41001,a840)),x41002),x41003))))
% 51.10/50.81 [4190]E(f331(f264(x41901),f331(f331(f20(x41901,a840,a840),f331(f331(f10(a840,f854(a840,a840),x41901),a329),f331(f331(f9(x41901,f854(x41901,a840),a840),f333(x41901)),x41902))),f331(f331(f10(a840,a840,x41901),a327),f331(f331(f9(x41901,f854(x41901,a840),a840),f333(x41901)),x41903)))),f331(f331(f3(f854(x41901,a840)),x41902),x41903))
% 51.10/50.81 [4211]E(f331(f47(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,a847,a840),f241(a847)),f331(f185(f848(x42111)),x42112)))),f331(f331(f10(x42111,a840,a847),x42113),f331(f155(x42111),x42112))))),f331(f185(f848(x42111)),f331(f131(x42111,x42113),x42112)))
% 51.10/50.81 [4213]E(f331(f185(f848(x42131)),f165(x42131,x42132,x42133)),f331(f47(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,a847,a840),f241(a847)),f331(f185(f848(x42131)),x42132)))),f331(f331(f9(a847,f854(a847,a840),a840),f333(a847)),x42133)))))
% 51.10/50.81 [4306]E(f331(f331(f109(f854(f853(f848(x43061),f848(x43061)),a840)),f331(f311(f853(f853(x43061,f848(x43061)),f853(x43061,f848(x43061))),f853(f848(x43061),f848(x43061)),f260(f853(x43061,f848(x43061)),f848(x43061),f853(x43061,f848(x43061)),f848(x43061),f331(f259(x43061,f848(x43061),f848(x43061)),f145(x43061)),f331(f259(x43061,f848(x43061),f848(x43061)),f145(x43061)))),f324(x43061,f848(x43061),x43062,f331(f138(x43061,x43062),x43063)))),f331(f264(f853(f848(x43061),f848(x43061))),f331(f259(f848(x43061),f848(x43061),a840),f331(f331(f9(f848(x43061),f854(f848(x43061),a840),f854(f848(x43061),a840)),f331(f331(f10(f854(a840,a840),f854(f854(f848(x43061),a840),f854(f848(x43061),a840)),f848(x43061)),f10(a840,a840,f848(x43061))),f331(f331(f10(a840,f854(a840,a840),f848(x43061)),a329),f331(f331(f9(f848(x43061),a847,a840),f331(f331(f10(a847,f854(a847,a840),f848(x43061)),a328),f185(f848(x43061)))),f331(a119,x43063))))),f331(f331(f9(f848(x43061),a847,a840),f331(f331(f10(a847,f854(a847,a840),f848(x43061)),a328),f185(f848(x43061)))),f331(a119,x43063)))))),f331(f138(x43061,x43062),f331(a119,x43063)))
% 51.10/50.81 [3803]E(f57(a847,f331(a119,f331(f331(f87(a847),f331(f331(f88(a847),x38031),x38032)),x38033)),x38032),f57(a847,f331(a119,x38033),x38032))
% 51.10/50.81 [4059]E(f331(f264(x40591),f331(f331(f20(x40591,a840,a840),f331(f331(f10(a840,f854(a840,a840),x40591),a329),x40592)),x40593)),f331(f331(f109(f854(x40591,a840)),f331(f264(x40591),x40592)),f331(f264(x40591),x40593)))
% 51.10/50.81 [4060]E(f331(f264(x40601),f331(f331(f20(x40601,a840,a840),f331(f331(f10(a840,f854(a840,a840),x40601),a330),x40602)),x40603)),f331(f331(f108(f854(x40601,a840)),f331(f264(x40601),x40602)),f331(f264(x40601),x40603)))
% 51.10/50.81 [4062]E(f331(f331(f130(x40621),f331(f331(f133(x40621),f57(a847,x40622,f331(f185(f848(x40621)),x40623))),x40623)),f331(f331(f164(x40621),f57(a847,x40622,f331(f185(f848(x40621)),x40623))),x40623)),f331(f331(f331(f178(f848(x40621),f848(x40621)),x40622),f159(x40621)),x40623))
% 51.10/50.81 [4067]E(f331(f264(x40671),f331(f331(f20(x40671,a840,a840),f331(f331(f10(a840,f854(a840,a840),x40671),a334),x40672)),x40673)),f331(f331(f108(f854(x40671,a840)),f331(f86(f854(x40671,a840)),f331(f264(x40671),x40672))),f331(f264(x40671),x40673)))
% 51.10/50.81 [4081]E(f331(f331(f87(a847),f331(f185(f848(x40811)),f331(f131(x40811,x40812),x40813))),f331(f185(f848(x40811)),f331(f131(x40811,f331(f331(f10(a840,a840,x40811),a327),x40812)),x40813))),f331(f185(f848(x40811)),x40813))
% 51.10/50.81 [4108]P1(f331(f331(f240(f854(x41081,a840)),f331(f331(f108(f854(x41081,a840)),f50(f854(x41081,a840),x41082)),f50(f854(x41081,a840),x41083))),f50(f854(x41081,a840),f331(f331(f109(f854(f854(x41081,a840),a840)),x41082),x41083))))
% 51.10/50.81 [4122]E(f331(f163(x41221),f331(f131(x41221,f331(f331(f10(a840,a840,x41221),a327),f331(f331(f9(x41221,x41221,a840),a328),x41222))),x41223)),f331(f331(f3(f854(x41221,a840)),f331(f163(x41221),x41223)),f331(f331(f310(x41221),x41222),f184(f854(x41221,a840)))))
% 51.10/50.81 [4131]P1(f331(f331(f240(f854(f853(x41311,x41311),a840)),f331(f331(f108(f854(f853(x41311,x41311),a840)),f308(x41311,x41312)),f308(x41311,x41313))),f308(x41311,f331(f331(f108(f854(f853(x41311,x41311),a840)),x41312),x41313))))
% 51.10/50.81 [4154]E(f331(f331(f88(a847),f331(a119,f331(a119,f2(a847)))),f331(f331(f8(a847,a847),f331(f331(f10(a847,a847,a847),f331(f87(a847),x41541)),f331(f331(f9(a847,a847,a847),f88(a847)),x41542))),f331(f265(a847),x41543))),f331(f331(f88(a847),x41543),f331(f331(f87(a847),x41541),f331(f331(f87(a847),x41541),f331(f331(f88(a847),f331(f331(f3(a847),x41543),f85(a847))),x41542)))))
% 51.10/50.81 [4164]E(f331(f264(x41641),f331(f331(f20(x41641,a840,a840),f331(f331(f10(a840,f854(a840,a840),x41641),a329),f331(f331(f9(x41641,f854(x41641,a840),a840),f333(x41641)),f331(f163(x41641),x41642)))),x41643)),f331(f163(x41641),f331(f131(x41641,x41643),x41642)))
% 51.10/50.81 [4305]E(f331(f264(x43051),f331(f331(f10(f854(a847,a840),a840,x43051),f94(a847)),f331(f331(f9(x43051,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),x43051),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),x43051),f331(f10(a840,f854(a840,a840),a847),a329)),f331(f331(f9(x43051,f854(a847,x43051),f854(a847,a840)),f331(f331(f10(f854(x43051,a840),f854(f854(a847,x43051),f854(a847,a840)),x43051),f10(x43051,a840,a847)),a328)),f331(f155(x43051),x43052))))),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,a847,a840),f241(a847)),f331(f185(f848(x43051)),x43052)))),f331(f331(f9(a847,f854(a847,a840),a840),f333(a847)),x43053))))),f331(f163(x43051),f165(x43051,x43052,x43053)))
% 51.10/50.81 [4201]E(f331(f264(x42011),f331(f331(f20(x42011,a840,a840),f331(f331(f10(a840,f854(a840,a840),x42011),a334),f331(f331(f10(a840,a840,x42011),a327),f331(f331(f9(x42011,x42011,a840),a328),x42012)))),x42013)),f331(f331(f310(x42011),x42012),f331(f264(x42011),x42013)))
% 51.10/50.81 [4232]E(f331(f331(f147(f853(x42321,a847),x42321),f248(x42321,a847)),f331(f131(f853(x42321,a847),f331(f331(f9(f853(x42321,a847),f854(a847,a840),a840),f331(f331(f10(a847,f854(f854(a847,a840),a840),f853(x42321,a847)),f333(a847)),f258(x42321,a847))),x42322)),f331(f331(f172(x42321,a847),x42323),f135(a847,f331(f302(a847,f2(a847)),f331(f185(f848(x42321)),x42323)))))),f165(x42321,x42323,x42322))
% 51.10/50.81 [4260]E(f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f8(a847,a1),f331(f331(f10(a1,a1,a847),f331(f87(a1),x42601)),f331(f331(f9(a847,a1,a1),f331(f331(f10(a1,f854(a1,a1),a847),f88(a1)),f107(a1))),x42602))),f331(f265(a847),x42603))),f331(f331(f88(a1),f331(f107(a1),x42603)),f331(f331(f87(a1),x42601),f331(f331(f87(a1),x42601),f331(f331(f88(a1),f331(f107(a1),f331(f331(f3(a847),x42603),f85(a847)))),x42602)))))
% 51.10/50.81 [4299]E(f331(f264(f853(x42991,x42992)),f331(f259(x42991,x42992,a840),f331(f331(f9(x42991,f854(f853(x42992,x42991),a840),f854(x42992,a840)),f331(f331(f10(f854(x42992,f854(f854(f853(x42992,x42991),a840),a840)),f854(f854(f853(x42992,x42991),a840),f854(x42992,a840)),x42991),f9(x42992,f854(f853(x42992,x42991),a840),a840)),f331(f331(f10(f854(x42992,f853(x42992,x42991)),f854(x42992,f854(f854(f853(x42992,x42991),a840),a840)),x42991),f331(f10(f853(x42992,x42991),f854(f854(f853(x42992,x42991),a840),a840),x42992),f333(f853(x42992,x42991)))),f331(f9(x42992,x42991,f853(x42992,x42991)),f249(x42992,x42991))))),x42993))),f331(f286(x42992,x42991),x42993))
% 51.10/50.81 [4322]E(f331(f264(f848(x43221)),f331(f331(f10(f854(x43221,a840),a840,f848(x43221)),f94(x43221)),f331(f331(f10(f854(x43221,f854(f848(x43221),a840)),f854(x43221,a840),f848(x43221)),f331(f10(f854(f848(x43221),a840),a840,x43221),f94(f848(x43221)))),f331(f331(f9(f848(x43221),f854(x43221,f854(f848(x43221),a840)),f854(x43221,f854(f848(x43221),a840))),f331(f331(f10(f854(x43221,f854(f854(f848(x43221),a840),f854(f848(x43221),a840))),f854(f854(x43221,f854(f848(x43221),a840)),f854(x43221,f854(f848(x43221),a840))),f848(x43221)),f20(x43221,f854(f848(x43221),a840),f854(f848(x43221),a840))),f331(f331(f10(f854(x43221,f854(f848(x43221),f854(a840,a840))),f854(x43221,f854(f854(f848(x43221),a840),f854(f848(x43221),a840))),f848(x43221)),f331(f10(f854(f848(x43221),f854(a840,a840)),f854(f854(f848(x43221),a840),f854(f848(x43221),a840)),x43221),f20(f848(x43221),a840,a840))),f331(f331(f10(f854(x43221,f854(f848(x43221),a840)),f854(x43221,f854(f848(x43221),f854(a840,a840))),f848(x43221)),f331(f10(f854(f848(x43221),a840),f854(f848(x43221),f854(a840,a840)),x43221),f331(f10(a840,f854(a840,a840),f848(x43221)),a329))),f331(f331(f9(f848(x43221),f854(x43221,f854(f848(x43221),f848(x43221))),f854(x43221,f854(f848(x43221),a840))),f331(f331(f10(f854(f854(f848(x43221),f848(x43221)),f854(f848(x43221),a840)),f854(f854(x43221,f854(f848(x43221),f848(x43221))),f854(x43221,f854(f848(x43221),a840))),f848(x43221)),f10(f854(f848(x43221),f848(x43221)),f854(f848(x43221),a840),x43221)),f331(f331(f10(f854(f848(x43221),a840),f854(f854(f848(x43221),f848(x43221)),f854(f848(x43221),a840)),f848(x43221)),f10(f848(x43221),a840,f848(x43221))),a328))),f145(x43221)))))),f331(f331(f9(x43221,f854(f848(x43221),a840),f854(f848(x43221),a840)),f331(f331(f10(f854(a840,a840),f854(f854(f848(x43221),a840),f854(f848(x43221),a840)),x43221),f10(a840,a840,f848(x43221))),f331(f331(f10(a840,f854(a840,a840),x43221),a329),f331(f331(f9(x43221,f854(x43221,a840),a840),f333(x43221)),x43222)))),f331(f331(f9(f848(x43221),f854(f848(x43221),a840),a840),f333(f848(x43221))),x43223)))))),f166(x43221,x43222,x43223))
% 51.10/50.81 [4319]E(f331(f331(f93(a1,f853(a1,a1)),f331(f331(f3(a1),x43191),x43192)),f331(f331(f9(a1,f853(a1,a1),f853(a1,a1)),f331(f331(f20(a1,f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),f331(f331(f10(a840,f854(f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),a1),f103(f853(a1,a1))),f331(f240(a1),f2(a1)))),f331(f249(a1,a1),f331(f331(f87(a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x43193)),f85(a1))))),f331(f331(f249(a1,a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x43193)),x43191))),f331(f55(x43192),f331(f331(f249(a1,a1),x43193),x43191)))
% 51.10/50.81 [4355]~E(f38(x43551,x43552),f30(x43553,x43554))
% 51.10/50.81 [4356]~E(f38(x43561,x43562),f30(x43563,x43564))
% 51.10/50.81 [4357]~E(f37(x43571,x43572),f30(x43573,x43574))
% 51.10/50.81 [4358]~E(f37(x43581,x43582),f38(x43583,x43584))
% 51.10/50.81 [4359]~E(f37(x43591,x43592),f30(x43593,x43594))
% 51.10/50.81 [4360]~E(f37(x43601,x43602),f38(x43603,x43604))
% 51.10/50.81 [4378]~E(f331(a29,x43781),f33(x43782,x43783,x43784))
% 51.10/50.81 [4379]~E(f331(a29,x43791),f34(x43792,x43793,x43794))
% 51.10/50.81 [4380]~E(f331(a29,x43801),f35(x43802,x43803,x43804))
% 51.10/50.81 [4381]~E(f33(x43811,x43812,x43813),f331(a29,x43814))
% 51.10/50.81 [4382]~E(f34(x43821,x43822,x43823),f331(a29,x43824))
% 51.10/50.81 [4383]~E(f35(x43831,x43832,x43833),f331(a29,x43834))
% 51.10/50.81 [3354]E(f331(f331(f331(f79(x33541,x33542),x33543),x33544),f331(x33543,x33544)),x33543)
% 51.10/50.81 [3417]E(f331(f331(f251(x34171,x34172,x34173),x34174),f2(a847)),x34172)
% 51.10/50.81 [3432]E(f43(x34321,x34322,x34323,f40(x34324)),f331(x34323,x34324))
% 51.10/50.81 [3433]E(f43(x34331,x34332,x34333,f41(x34334)),f331(x34332,x34334))
% 51.10/50.81 [3434]E(f44(x34341,x34342,x34343,f40(x34344)),f331(x34343,x34344))
% 51.10/50.81 [3435]E(f44(x34351,x34352,x34353,f41(x34354)),f331(x34352,x34354))
% 51.10/50.81 [3459]E(f180(x34591,x34592,x34593,f331(a119,x34594)),f331(x34593,x34594))
% 51.10/50.81 [3498]E(f161(x34981,x34982,f161(x34981,x34983,x34984)),f161(x34981,x34983,f161(x34981,x34982,x34984)))
% 51.10/50.81 [3616]P37(f30(x36161,x36162),x36163,x36164,f331(f331(f331(a193,x36163),x36161),f331(x36162,x36163)))
% 51.10/50.81 [3617]P37(f30(x36171,x36172),x36173,x36174,f331(f331(f331(a193,x36173),x36171),f331(x36172,x36173)))
% 51.10/50.81 [3629]E(f331(f236(x36291,x36292,x36293,x36294),f187(x36292)),x36293)
% 51.10/50.81 [3631]E(f331(f149(x36311,x36312,x36313,x36314),f120(x36312)),x36313)
% 51.10/50.81 [3632]E(f331(f137(x36321,x36322,x36323,x36324),f120(x36322)),x36324)
% 51.10/50.81 [3669]E(f331(f185(f852(x36691,x36692)),f222(x36691,x36692,x36693,x36694)),f2(a847))
% 51.10/50.81 [3692]E(f331(f259(x36921,x36922,x36923),f257(x36921,x36922,x36923,x36924)),x36924)
% 51.10/50.81 [3749]E(f331(f236(f851(x37491),x37492,f187(x37491),f331(f18(f851(x37491),x37492),f187(x37491))),f331(x37493,x37494)),f187(x37491))
% 51.10/50.81 [3793]E(f331(f331(f108(f854(x37931,a840)),f174(x37931,x37932,x37933)),f174(x37931,x37932,x37934)),f174(x37931,x37932,f175(x37931,x37932,x37934,x37933)))
% 51.10/50.81 [3822]E(f331(f331(f261(x38221,x38222,x38223,f853(x38222,x38223)),x38224),f249(x38222,x38223)),x38224)
% 51.10/50.81 [3831]E(f237(x38311,x38312,x38313,x38314,f187(x38312)),x38313)
% 51.10/50.81 [4114]P39(x41141,x41142,x41143,x41144,f184(f854(x41141,a840)),x41144)
% 51.10/50.81 [4115]P39(x41151,x41152,x41153,x41154,f184(f854(x41151,a840)),x41154)
% 51.10/50.81 [3165]E(f331(f331(f18(x31651,x31652),x31653),x31654),x31653)
% 51.10/50.81 [3276]E(f331(f331(f203(x32761,x32762),x32763),f331(f234(x32761),x32764)),f331(f234(x32762),f331(x32763,x32764)))
% 51.10/50.81 [3451]E(f161(x34511,x34512,f331(f131(x34511,x34513),x34514)),f331(f131(x34511,x34513),f161(x34511,x34512,x34514)))
% 51.10/50.81 [3482]E(f331(f331(f71(x34821,x34822,x34823),x34824),f184(f854(x34821,a840))),x34824)
% 51.10/50.81 [3504]E(f331(f331(f155(x35041),f331(f331(f145(x35041),x35042),x35043)),f331(a119,x35044)),f331(f331(f155(x35041),x35043),x35044))
% 51.10/50.81 [3543]P29(x35431,f2(a847),f331(f331(f331(f98(x35431),x35432),f331(a29,x35433)),x35434))
% 51.10/50.81 [3568]E(f331(f331(x35681,x35682),f331(f179(x35683,x35684,x35681),x35682)),f331(f179(x35683,x35684,x35681),f331(a119,x35682)))
% 51.10/50.81 [3609]E(f257(x36091,x36092,x36093,f331(f259(x36091,x36092,x36093),x36094)),x36094)
% 51.10/50.81 [3667]E(f331(f331(f152(x36671,f331(f331(f145(x36671),x36672),x36673)),f2(a847)),x36674),f331(f331(f145(x36671),x36674),x36673))
% 51.10/50.81 [3677]E(f331(f331(f51(f854(x36771,a840),f854(x36772,a840)),x36773),f311(x36771,x36772,x36774)),f331(f311(x36771,x36772,x36774),f49(f854(x36771,a840),x36773)))
% 51.10/50.81 [3678]E(f331(f331(f51(f854(x36781,a840),f854(x36782,a840)),x36783),f312(x36782,x36781,x36784)),f331(f312(x36782,x36781,x36784),f49(f854(x36781,a840),x36783)))
% 51.10/50.81 [3777]E(f174(x37771,x37772,f177(x37771,x37772,x37773,x37774)),f331(f331(f109(f854(x37771,a840)),f174(x37771,x37772,x37773)),x37774))
% 51.10/50.81 [3797]E(f331(f137(x37971,x37972,f331(f9(x37972,x37971,x37971),x37973),x37974),f331(f160(x37972),f120(x37972))),x37974)
% 51.10/50.81 [3842]E(f83(x38421,x38422,x38423,x38424,f184(f854(x38421,a840))),x38423)
% 51.10/50.81 [3888]E(f331(f331(f331(f331(f79(x38881,f851(x38882)),f331(f18(f851(x38882),x38881),f187(x38882))),x38883),f187(x38882)),x38884),f187(x38882))
% 51.10/50.81 [4043]E(f331(f259(x40431,x40432,x40433),f331(f331(f10(f854(x40432,f853(x40431,x40432)),f854(x40432,x40433),x40431),f331(f10(f853(x40431,x40432),x40433,x40432),x40434)),f249(x40431,x40432))),x40434)
% 51.10/50.81 [3352]E(f331(f258(x33521,x33522),f331(f331(f249(x33521,x33522),x33523),x33524)),x33524)
% 51.10/50.81 [3353]E(f331(f248(x33531,x33532),f331(f331(f249(x33531,x33532),x33533),x33534)),x33533)
% 51.10/50.81 [3390]E(f331(f185(f848(x33901)),f331(f331(f147(x33902,x33901),x33903),x33904)),f331(f185(f848(x33902)),x33904))
% 51.10/50.81 [3391]E(f331(f185(f848(x33911)),f331(f331(f152(x33911,x33912),x33913),x33914)),f331(f185(f848(x33911)),x33912))
% 51.10/50.81 [3412]E(f331(f331(f133(x34121),f331(a119,x34122)),f331(f331(f145(x34121),x34123),x34124)),f331(f331(f133(x34121),x34122),x34124))
% 51.10/50.81 [3484]E(f331(f331(f310(x34841),x34842),f331(f331(f310(x34841),x34843),x34844)),f331(f331(f310(x34841),x34843),f331(f331(f310(x34841),x34842),x34844)))
% 51.10/50.81 [3487]E(f331(f331(f147(x34871,x34872),x34873),f121(x34871,x34874)),f121(x34872,f331(f331(f147(x34871,x34872),x34873),x34874)))
% 51.10/50.81 [3502]E(f331(f160(x35021),f331(f331(f147(x35022,x35021),x35023),x35024)),f331(f331(f147(x35022,x35021),x35023),f331(f160(x35022),x35024)))
% 51.10/50.81 [3503]E(f331(f331(f147(x35031,x35032),x35033),f331(f162(x35031),x35034)),f331(f162(x35032),f331(f331(f147(x35031,x35032),x35033),x35034)))
% 51.10/50.81 [3512]E(f331(f331(f164(x35121),f331(a119,x35122)),f331(f331(f145(x35121),x35123),x35124)),f331(f331(f145(x35121),x35123),f331(f331(f164(x35121),x35122),x35124)))
% 51.10/50.81 [3516]E(f331(f163(x35161),f331(f331(f147(x35162,x35161),x35163),x35164)),f331(f311(x35162,x35161,x35163),f331(f163(x35162),x35164)))
% 51.10/50.81 [3567]E(f19(x35671,x35672,x35673,f331(a5,f331(a119,f331(a22,x35674)))),f331(x35673,x35674))
% 51.10/50.81 [3571]E(f331(f331(f130(x35711),f331(f131(x35711,x35712),x35713)),f331(f131(x35711,x35712),x35714)),f331(f131(x35711,x35712),f331(f331(f130(x35711),x35713),x35714)))
% 51.10/50.81 [3584]E(f146(x35841,f331(f331(f147(x35842,x35841),x35843),f146(x35842,x35844))),f146(x35841,f331(f331(f147(x35842,x35841),x35843),x35844)))
% 51.10/50.81 [3599]E(f331(f286(x35991,x35991),f331(f331(f288(x35992,x35991),x35993),x35994)),f331(f331(f288(x35992,x35991),f331(f286(x35992,x35992),x35993)),x35994))
% 51.10/50.81 [3610]E(f331(f331(f289(x36101,x36102,x36103),x36104),f184(f854(f853(x36102,x36103),a840))),f184(f854(f853(x36101,x36103),a840)))
% 51.10/50.81 [3611]E(f331(f331(f164(x36111),f331(f331(f3(a847),x36112),x36113)),f331(f331(f133(x36111),x36113),x36114)),f331(f331(f133(x36111),x36113),f331(f331(f164(x36111),x36112),x36114)))
% 51.10/50.81 [3633]E(f331(f331(f331(f281(x36331),x36332),x36333),x36334),f331(f249(f854(a106,f854(a840,f851(f849(x36331)))),f853(a106,a106)),f331(f54(x36331),x36332)))
% 51.10/50.81 [3657]E(f49(f854(x36571,a840),f331(f311(x36572,f854(x36571,a840),x36573),x36574)),f331(f331(f51(x36572,f854(x36571,a840)),x36574),x36573))
% 51.10/50.81 [3658]E(f50(f854(x36581,a840),f331(f311(x36582,f854(x36581,a840),x36583),x36584)),f331(f331(f52(x36582,f854(x36581,a840)),x36584),x36583))
% 51.10/50.81 [3659]E(f50(f854(x36591,a840),f331(f311(x36592,f854(x36591,a840),x36593),x36594)),f331(f331(f52(x36592,f854(x36591,a840)),x36594),x36593))
% 51.10/50.81 [3660]E(f49(f854(x36601,a840),f331(f311(x36602,f854(x36601,a840),x36603),x36604)),f331(f331(f51(x36602,f854(x36601,a840)),x36604),x36603))
% 51.10/50.81 [3661]E(f331(f185(f848(f853(x36611,x36612))),f331(f331(f172(x36611,x36612),x36613),x36614)),f331(f331(f244(a847),f331(f185(f848(x36611)),x36613)),f331(f185(f848(x36612)),x36614)))
% 51.10/50.81 [3663]E(f331(f312(x36631,x36632,x36633),f331(f86(f854(x36632,a840)),x36634)),f331(f86(f854(x36631,a840)),f331(f312(x36631,x36632,x36633),x36634)))
% 51.10/50.81 [3693]E(f331(f177(x36931,x36932,x36933,f184(f854(x36931,a840))),x36934),f187(x36932))
% 51.10/50.81 [3712]E(f331(f312(x37121,x37122,x37123),f331(f264(x37122),x37124)),f331(f264(x37121),f331(f331(f10(x37122,a840,x37121),x37124),x37123)))
% 51.10/50.81 [3731]E(f331(f331(f155(x37311),f331(f331(f130(x37311),x37312),f331(f331(f145(x37311),x37313),x37314))),f331(f185(f848(x37311)),x37312)),x37313)
% 51.10/50.81 [3736]E(f331(f177(x37361,x37362,f331(f18(f851(x37362),x37361),f187(x37362)),x37363),x37364),f187(x37362))
% 51.10/50.81 [3758]E(f331(f311(x37581,x37582,x37583),f331(f312(x37581,x37582,x37583),x37584)),f331(f331(f109(f854(x37582,a840)),x37584),f331(f311(x37581,x37582,x37583),f247(f854(x37581,a840)))))
% 51.10/50.81 [3776]P1(f331(f331(f333(x37761),f331(x37762,x37763)),f331(f311(x37764,x37761,x37762),f247(f854(x37764,a840)))))
% 51.10/50.81 [3784]E(f21(x37841,x37842,x37843,f331(a5,f331(a119,f331(a22,x37844)))),f331(f331(x37843,x37844),f21(x37841,x37842,x37843,x37844)))
% 51.10/50.81 [3800]E(f148(x38001,x38002,f331(f331(f145(x38001),x38003),x38004)),f331(f331(f87(a847),f331(f331(f87(a847),f331(x38002,x38003)),f148(x38001,x38002,x38004))),f331(a119,f2(a847))))
% 51.10/50.81 [3813]E(f180(f848(x38131),f331(f331(f145(x38131),x38132),x38133),f331(f331(f9(a847,f848(x38131),f848(x38131)),f133(x38131)),x38133),x38134),f331(f331(f133(x38131),x38134),f331(f331(f145(x38131),x38132),x38133)))
% 51.10/50.81 [3814]P27(x38141,f853(x38142,x38141),f335(x38143,x38144,x38142,x38141),f331(f331(f51(x38142,f854(x38141,a840)),x38144),x38143))
% 51.10/50.81 [3823]E(f331(f331(f3(f854(x38231,a840)),f331(f331(f3(f854(x38231,a840)),x38232),x38233)),f331(f331(f310(x38231),x38234),f184(f854(x38231,a840)))),f331(f331(f3(f854(x38231,a840)),x38232),f331(f331(f310(x38231),x38234),x38233)))
% 51.10/50.81 [3834]E(f331(f331(f178(f854(x38341,x38342),f854(x38341,x38342)),x38343),f80(x38342,x38342,x38341,x38344)),f80(x38342,x38342,x38341,f331(f331(f178(x38342,x38342),x38343),x38344)))
% 51.10/50.81 [3911]E(f331(f331(f331(f178(f848(x39111),f848(x39111)),x39112),f159(x39111)),f331(f331(f331(f178(f848(x39111),f848(x39111)),x39113),f159(x39111)),x39114)),f331(f331(f331(f178(f848(x39111),f848(x39111)),f331(f331(f87(a847),x39112),x39113)),f159(x39111)),x39114))
% 51.10/50.81 [4000]P1(f331(f331(f240(f854(x40001,a840)),f331(f163(x40001),f331(f331(f152(x40001,x40002),x40003),x40004))),f331(f331(f310(x40001),x40004),f331(f163(x40001),x40002))))
% 51.10/50.81 [4033]E(f331(f331(f51(f854(x40331,a840),f854(f853(x40331,x40332),a840)),x40333),f331(f331(f9(f854(x40331,a840),f854(x40331,f854(x40332,a840)),f854(f853(x40331,x40332),a840)),f256(x40331,x40332)),x40334)),f331(f331(f256(x40331,x40332),f49(f854(x40331,a840),x40333)),x40334))
% 51.10/50.81 [4068]E(f211(x40681,x40682,x40683,f331(f80(x40682,f854(a106,f854(a106,f854(f853(a106,a106),f854(a106,f849(x40682))))),x40681,f210(x40682)),x40684)),f212(x40681,x40682,x40684,x40683))
% 51.10/50.81 [4084]E(f207(x40841,x40842,x40843,f331(f80(x40842,f854(a106,f854(a106,f854(f853(a106,a106),f854(a106,f849(f851(x40842)))))),x40841,f206(x40842)),x40844)),f208(x40841,x40842,x40844,x40843))
% 51.10/50.81 [4088]P1(f331(f73(x40881,x40882,x40883,x40884,f184(f854(x40881,a840))),x40884))
% 51.10/50.81 [4089]P1(f331(f73(x40891,x40892,x40893,x40894,f184(f854(x40891,a840))),x40894))
% 51.10/50.81 [4133]E(f331(f331(f51(x41331,f854(x41332,a840)),x41333),f331(f331(f9(x41331,f854(x41332,a840),f854(x41332,a840)),f331(f331(f10(x41332,f854(f854(x41332,a840),f854(x41332,a840)),x41331),f310(x41332)),x41334)),f184(f854(x41332,a840)))),f331(f311(x41331,x41332,x41334),x41333))
% 51.10/50.81 [4139]P1(f331(f331(f240(f854(x41391,a840)),f331(f267(x41392,x41391),f331(f331(f109(f854(f853(x41392,x41391),a840)),x41393),x41394))),f331(f331(f109(f854(x41391,a840)),f331(f267(x41392,x41391),x41393)),f331(f267(x41392,x41391),x41394))))
% 51.10/50.81 [4140]P1(f331(f331(f240(f854(x41401,a840)),f331(f269(x41401,x41402),f331(f331(f109(f854(f853(x41401,x41402),a840)),x41403),x41404))),f331(f331(f109(f854(x41401,a840)),f331(f269(x41401,x41402),x41403)),f331(f269(x41401,x41402),x41404))))
% 51.10/50.81 [4199]P1(f331(f331(f240(f854(f853(x41991,x41992),a840)),f331(f311(x41992,f853(x41991,x41992),f335(x41993,x41994,x41991,x41992)),f331(f331(f51(x41991,f854(x41992,a840)),x41994),x41993))),f331(f331(f256(x41991,x41992),x41994),x41993)))
% 51.10/50.81 [4200]E(f279(x42001,x42002,x42003,f331(f80(x42002,f854(a106,f854(a106,f854(f853(a106,a106),f853(f854(a106,f854(a840,f851(f849(x42002)))),f853(a106,a106))))),x42001,f281(x42002)),x42004)),f282(x42001,x42002,x42004,x42003))
% 51.10/50.81 [4238]E(f92(f853(x42381,x42382),f331(f259(x42381,x42382,a840),f331(f331(f9(x42381,f854(x42382,a840),f854(x42382,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x42382,a840),f854(x42382,a840)),x42381),f10(a840,a840,x42382)),f331(f331(f10(a840,f854(a840,a840),x42381),a329),f331(a328,x42383)))),f331(a328,x42384)))),f331(f331(f249(x42381,x42382),x42383),x42384))
% 51.10/50.81 [4239]E(f97(f853(x42391,x42392),f331(f259(x42391,x42392,a840),f331(f331(f9(x42391,f854(x42392,a840),f854(x42392,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x42392,a840),f854(x42392,a840)),x42391),f10(a840,a840,x42392)),f331(f331(f10(a840,f854(a840,a840),x42391),a329),f331(a328,x42393)))),f331(a328,x42394)))),f331(f331(f249(x42391,x42392),x42393),x42394))
% 51.10/50.81 [4309]E(f331(f331(f259(f848(x43091),f848(x43091),f853(f848(x43091),f848(x43091))),f331(f331(f20(f848(x43091),f854(f848(x43091),f853(f848(x43091),f848(x43091))),f854(f848(x43091),f853(f848(x43091),f848(x43091)))),f331(f331(f10(f854(f848(x43091),f854(f853(f848(x43091),f848(x43091)),f853(f848(x43091),f848(x43091)))),f854(f854(f848(x43091),f853(f848(x43091),f848(x43091))),f854(f848(x43091),f853(f848(x43091),f848(x43091)))),f848(x43091)),f20(f848(x43091),f853(f848(x43091),f848(x43091)),f853(f848(x43091),f848(x43091)))),f331(f331(f10(f854(f848(x43091),f853(f848(x43091),f848(x43091))),f854(f848(x43091),f854(f853(f848(x43091),f848(x43091)),f853(f848(x43091),f848(x43091)))),f848(x43091)),f331(f10(f853(f848(x43091),f848(x43091)),f854(f853(f848(x43091),f848(x43091)),f853(f848(x43091),f848(x43091))),f848(x43091)),f331(f103(f853(f848(x43091),f848(x43091))),f331(x43092,x43093)))),f331(f331(f10(f848(x43091),f854(f848(x43091),f853(f848(x43091),f848(x43091))),f848(x43091)),f249(f848(x43091),f848(x43091))),f331(f145(x43091),x43093))))),f331(f331(f9(f848(x43091),f854(f848(x43091),f848(x43091)),f854(f848(x43091),f853(f848(x43091),f848(x43091)))),f331(f331(f10(f854(f848(x43091),f853(f848(x43091),f848(x43091))),f854(f854(f848(x43091),f848(x43091)),f854(f848(x43091),f853(f848(x43091),f848(x43091)))),f848(x43091)),f10(f848(x43091),f853(f848(x43091),f848(x43091)),f848(x43091))),f249(f848(x43091),f848(x43091)))),f331(f145(x43091),x43093)))),f158(x43091,x43092,x43094)),f158(x43091,x43092,f331(f331(f145(x43091),x43093),x43094)))
% 51.10/50.81 [4315]E(f331(f137(f854(x43151,f851(x43152)),f853(x43151,x43152),f331(f9(f853(x43151,x43152),f854(x43151,f851(x43152)),f854(x43151,f851(x43152))),f331(f259(x43151,x43152,f854(f854(x43151,f851(x43152)),f854(x43151,f851(x43152)))),f331(f331(f9(x43151,f854(x43152,f851(x43152)),f854(x43152,f854(f854(x43151,f851(x43152)),f854(x43151,f851(x43152))))),f331(f331(f10(f854(f851(x43152),f854(f854(x43151,f851(x43152)),f854(x43151,f851(x43152)))),f854(f854(x43152,f851(x43152)),f854(x43152,f854(f854(x43151,f851(x43152)),f854(x43151,f851(x43152))))),x43151),f10(f851(x43152),f854(f854(x43151,f851(x43152)),f854(x43151,f851(x43152))),x43152)),f331(f331(f10(f854(f854(x43151,f851(x43152)),f854(f851(x43152),f854(x43151,f851(x43152)))),f854(f851(x43152),f854(f854(x43151,f851(x43152)),f854(x43151,f851(x43152)))),x43151),f9(f854(x43151,f851(x43152)),f851(x43152),f854(x43151,f851(x43152)))),f331(f9(f854(x43151,f851(x43152)),x43151,f854(f851(x43152),f854(x43151,f851(x43152)))),f79(x43151,f851(x43152)))))),f234(x43152)))),x43153),f331(f160(f853(x43151,x43152)),x43154)),f175(x43151,x43152,x43153,f171(x43151,x43152,x43154)))
% 51.10/50.81 [3430]E(f331(f185(f846(x34301)),f331(f331(f331(f98(x34301),x34302),x34303),x34304)),f2(a847))
% 51.10/50.81 [3546]E(f331(f331(f164(x35461),x35462),f331(f331(f164(x35461),x35463),x35464)),f331(f331(f164(x35461),f331(f331(f244(a847),x35462),x35463)),x35464))
% 51.10/50.81 [3547]E(f331(f331(f133(x35471),x35472),f331(f331(f133(x35471),x35473),x35474)),f331(f331(f133(x35471),f331(f331(f87(a847),x35472),x35473)),x35474))
% 51.10/50.81 [3559]E(f331(f331(f130(x35591),f331(f331(f145(x35591),x35592),x35593)),x35594),f331(f331(f145(x35591),x35592),f331(f331(f130(x35591),x35593),x35594)))
% 51.10/50.81 [3560]E(f331(f331(f130(x35601),f331(f331(f130(x35601),x35602),x35603)),x35604),f331(f331(f130(x35601),x35602),f331(f331(f130(x35601),x35603),x35604)))
% 51.10/50.81 [3643]E(f331(f331(f155(x36431),f331(f331(f145(x36431),x36432),x36433)),x36434),f180(x36431,x36432,f331(f155(x36431),x36433),x36434))
% 51.10/50.81 [3652]E(f331(f331(f178(x36521,x36521),x36522),f331(f331(f178(x36521,x36521),x36523),x36524)),f331(f331(f178(x36521,x36521),f331(f331(f88(a847),x36523),x36522)),x36524))
% 51.10/50.81 [3680]E(f331(f331(f108(f854(x36801,a840)),x36802),f331(f331(f310(x36801),x36803),x36804)),f331(f331(f310(x36801),x36803),f331(f331(f108(f854(x36801,a840)),x36802),x36804)))
% 51.10/50.81 [3696]E(f331(f331(f331(f178(x36961,x36961),x36962),x36963),f331(x36963,x36964)),f331(x36963,f331(f331(f331(f178(x36961,x36961),x36962),x36963),x36964)))
% 51.10/50.81 [3703]E(f331(f331(f289(x37031,x37032,x37033),f184(f854(f853(x37031,x37032),a840))),x37034),f184(f854(f853(x37031,x37033),a840)))
% 51.10/50.81 [3719]E(f331(f331(f108(f854(x37191,a840)),f331(f331(f310(x37191),x37192),x37193)),x37194),f331(f331(f310(x37191),x37192),f331(f331(f108(f854(x37191,a840)),x37193),x37194)))
% 51.10/50.81 [3738]E(f331(f47(f853(x37381,x37382)),f331(f331(f256(x37381,x37382),x37383),f331(f18(f854(x37382,a840),x37381),x37384))),f331(f331(f88(a847),f331(f47(x37381),x37383)),f331(f47(x37382),x37384)))
% 51.10/50.81 [3746]E(f331(f331(f109(f854(x37461,a840)),f331(f331(f310(x37461),x37462),x37463)),f331(f331(f310(x37461),x37462),x37464)),f331(f331(f310(x37461),x37462),f331(f331(f109(f854(x37461,a840)),x37463),x37464)))
% 51.10/50.81 [3756]E(f175(x37561,x37562,f171(x37561,x37562,x37563),f171(x37561,x37562,x37564)),f171(x37561,x37562,f331(f331(f130(f853(x37561,x37562)),x37564),x37563)))
% 51.10/50.81 [3762]E(f331(f331(f108(f854(x37621,a840)),x37622),f331(f331(f108(f854(x37621,a840)),x37623),x37624)),f331(f331(f108(f854(x37621,a840)),x37623),f331(f331(f108(f854(x37621,a840)),x37622),x37624)))
% 51.10/50.81 [3763]E(f331(f331(f109(f854(x37631,a840)),x37632),f331(f331(f109(f854(x37631,a840)),x37633),x37634)),f331(f331(f109(f854(x37631,a840)),x37633),f331(f331(f109(f854(x37631,a840)),x37632),x37634)))
% 51.10/50.81 [3772]E(f71(x37721,x37722,f331(f331(f10(x37722,f854(x37722,x37722),x37721),x37723),x37724)),f331(f72(x37722,x37721,x37723),x37724))
% 51.10/50.81 [3781]E(f169(x37811,f331(f331(f147(f848(x37812),f848(x37811)),f331(f147(x37812,x37811),x37813)),x37814)),f331(f331(f147(f848(x37812),f848(x37811)),f331(f147(x37812,x37811),x37813)),f169(x37812,x37814)))
% 51.10/50.81 [3799]E(f177(x37991,x37992,x37993,f331(f86(f854(x37991,a840)),f331(f331(f310(x37991),x37994),f184(f854(x37991,a840))))),f331(f331(f331(f79(x37991,f851(x37992)),x37993),x37994),f187(x37992)))
% 51.10/50.81 [3856]E(f331(f80(x38561,x38561,x38561,f331(f331(f178(x38561,x38561),x38562),x38563)),f331(f331(f178(x38561,x38561),x38564),x38563)),f331(f331(f178(x38561,x38561),f331(f331(f87(a847),x38562),x38564)),x38563))
% 51.10/50.81 [3872]E(f331(f331(f331(f79(x38721,f851(x38722)),f171(x38721,x38722,x38723)),f331(f248(x38721,x38722),x38724)),f331(f234(x38722),f331(f258(x38721,x38722),x38724))),f171(x38721,x38722,f331(f331(f145(f853(x38721,x38722)),x38724),x38723)))
% 51.10/50.81 [3877]E(f175(x38771,x38772,x38773,f171(x38771,x38772,f331(f160(f853(x38771,x38772)),f331(f331(f172(x38771,x38772),x38774),f120(x38772))))),x38773)
% 51.10/50.81 [3880]E(f331(f331(f109(f854(x38801,a840)),f331(f331(f3(f854(x38801,a840)),x38802),x38803)),f331(f331(f3(f854(x38801,a840)),x38802),x38804)),f331(f331(f3(f854(x38801,a840)),x38802),f331(f331(f108(f854(x38801,a840)),x38803),x38804)))
% 51.10/50.81 [3881]E(f331(f331(f108(f854(x38811,a840)),f331(f331(f3(f854(x38811,a840)),x38812),x38813)),f331(f331(f3(f854(x38811,a840)),x38812),x38814)),f331(f331(f3(f854(x38811,a840)),x38812),f331(f331(f109(f854(x38811,a840)),x38813),x38814)))
% 51.10/50.81 [3882]E(f331(f331(f109(f854(x38821,a840)),f331(f331(f108(f854(x38821,a840)),x38822),x38823)),f331(f331(f108(f854(x38821,a840)),x38822),x38824)),f331(f331(f108(f854(x38821,a840)),x38822),f331(f331(f109(f854(x38821,a840)),x38823),x38824)))
% 51.10/50.81 [3883]E(f331(f331(f3(f854(x38831,a840)),f331(f331(f109(f854(x38831,a840)),x38832),x38833)),f331(f331(f109(f854(x38831,a840)),x38832),x38834)),f331(f331(f109(f854(x38831,a840)),x38832),f331(f331(f3(f854(x38831,a840)),x38833),x38834)))
% 51.10/50.81 [3884]E(f331(f331(f108(f854(x38841,a840)),f331(f331(f109(f854(x38841,a840)),x38842),x38843)),f331(f331(f109(f854(x38841,a840)),x38842),x38844)),f331(f331(f109(f854(x38841,a840)),x38842),f331(f331(f108(f854(x38841,a840)),x38843),x38844)))
% 51.10/50.81 [3890]E(f331(f47(f853(x38901,x38902)),f331(f331(f256(x38901,x38902),f331(f331(f310(x38901),x38903),f184(f854(x38901,a840)))),f331(f18(f854(x38902,a840),x38901),x38904))),f331(f47(x38902),x38904))
% 51.10/50.81 [3927]E(f331(f331(f52(x39271,f854(x39272,a840)),x39273),f331(f331(f10(f854(x39272,a840),f854(x39272,a840),x39271),f86(f854(x39272,a840))),x39274)),f331(f86(f854(x39272,a840)),f331(f331(f51(x39271,f854(x39272,a840)),x39273),x39274)))
% 51.10/50.81 [3928]E(f331(f331(f51(x39281,f854(x39282,a840)),x39283),f331(f331(f10(f854(x39282,a840),f854(x39282,a840),x39281),f86(f854(x39282,a840))),x39284)),f331(f86(f854(x39282,a840)),f331(f331(f52(x39281,f854(x39282,a840)),x39283),x39284)))
% 51.10/50.81 [3944]E(f331(f331(f289(x39441,x39441,x39441),f331(f331(f178(f853(x39441,x39441),a840),x39442),x39443)),f331(f331(f178(f853(x39441,x39441),a840),x39444),x39443)),f331(f331(f178(f853(x39441,x39441),a840),f331(f331(f87(a847),x39442),x39444)),x39443))
% 51.10/50.81 [3975]E(f331(f331(f52(x39751,f854(f854(x39752,a840),a840)),x39753),f331(f331(f10(f854(x39752,a840),f854(f854(x39752,a840),a840),x39751),f309(x39752)),x39754)),f331(f309(x39752),f331(f331(f52(x39751,f854(x39752,a840)),x39753),x39754)))
% 51.10/50.81 [4003]E(f331(f331(f51(f854(x40031,a840),f854(x40032,a840)),x40033),f331(f331(f9(f854(x40031,a840),f854(x40031,f854(x40032,a840)),f854(x40032,a840)),f51(x40031,f854(x40032,a840))),x40034)),f331(f331(f51(x40031,f854(x40032,a840)),f49(f854(x40031,a840),x40033)),x40034))
% 51.10/50.81 [4004]E(f331(f331(f52(f854(x40041,a840),f854(x40042,a840)),x40043),f331(f331(f9(f854(x40041,a840),f854(x40041,f854(x40042,a840)),f854(x40042,a840)),f52(x40041,f854(x40042,a840))),x40044)),f331(f331(f52(x40041,f854(x40042,a840)),f49(f854(x40041,a840),x40043)),x40044))
% 51.10/50.81 [4005]E(f331(f331(f51(f854(x40051,a840),f854(x40052,a840)),x40053),f331(f331(f9(f854(x40051,a840),f854(x40051,f854(x40052,a840)),f854(x40052,a840)),f51(x40051,f854(x40052,a840))),x40054)),f331(f331(f51(x40051,f854(x40052,a840)),f49(f854(x40051,a840),x40053)),x40054))
% 51.10/50.81 [4006]E(f331(f331(f52(f854(x40061,a840),f854(x40062,a840)),x40063),f331(f331(f9(f854(x40061,a840),f854(x40061,f854(x40062,a840)),f854(x40062,a840)),f52(x40061,f854(x40062,a840))),x40064)),f331(f331(f52(x40061,f854(x40062,a840)),f49(f854(x40061,a840),x40063)),x40064))
% 51.10/50.81 [4011]E(f331(f331(f147(x40111,x40112),x40113),f331(f137(f848(x40111),f848(x40111),f130(x40111),f120(x40111)),x40114)),f331(f137(f848(x40112),f848(x40112),f130(x40112),f120(x40112)),f331(f331(f147(f848(x40111),f848(x40112)),f331(f147(x40111,x40112),x40113)),x40114)))
% 51.10/50.81 [4013]E(f180(f848(x40131),f120(x40131),f331(f331(f10(f848(x40131),f848(x40131),a847),f331(f145(x40131),x40132)),f331(f331(f9(a847,f848(x40131),f848(x40131)),f164(x40131)),x40133)),x40134),f331(f331(f164(x40131),x40134),f331(f331(f145(x40131),x40132),x40133)))
% 51.10/50.81 [4053]P1(f331(f331(f240(f854(x40531,a840)),f331(f311(x40532,x40531,x40533),f331(f312(x40532,x40531,x40533),x40534))),x40534))
% 51.10/50.81 [4055]E(f331(f311(f853(x40551,x40552),f853(x40552,x40551),f331(f259(x40551,x40552,f853(x40552,x40551)),f331(f9(x40552,x40551,f853(x40552,x40551)),f249(x40552,x40551)))),f331(f331(f256(x40551,x40552),x40553),f331(f18(f854(x40552,a840),x40551),x40554))),f331(f331(f256(x40552,x40551),x40554),f331(f18(f854(x40551,a840),x40552),x40553)))
% 51.10/50.81 [4064]E(f331(f331(f51(x40641,f854(x40642,a840)),x40643),f331(f331(f10(f854(x40641,a840),f854(x40642,a840),x40641),f285(x40641,x40642,x40644)),f331(f331(f9(x40641,f854(x40641,a840),f854(x40641,a840)),f310(x40641)),f184(f854(x40641,a840))))),f331(f285(x40641,x40642,x40644),x40643))
% 51.10/50.81 [4065]E(f331(f331(f51(x40651,f854(x40652,a840)),x40653),f331(f331(f10(f854(x40651,a840),f854(x40652,a840),x40651),f312(x40652,x40651,x40654)),f331(f331(f9(x40651,f854(x40651,a840),f854(x40651,a840)),f310(x40651)),f184(f854(x40651,a840))))),f331(f312(x40652,x40651,x40654),x40653))
% 51.10/50.81 [4153]E(f331(f331(f109(f854(x41531,a840)),f331(f331(f109(f854(x41531,a840)),f331(f331(f108(f854(x41531,a840)),x41532),x41533)),f331(f331(f108(f854(x41531,a840)),x41533),x41534))),f331(f331(f108(f854(x41531,a840)),x41534),x41532)),f331(f331(f108(f854(x41531,a840)),f331(f331(f108(f854(x41531,a840)),f331(f331(f109(f854(x41531,a840)),x41532),x41533)),f331(f331(f109(f854(x41531,a840)),x41533),x41534))),f331(f331(f109(f854(x41531,a840)),x41534),x41532)))
% 51.10/50.81 [4212]E(f331(f137(f848(x42121),f848(x42121),f130(x42121),f120(x42121)),f331(f331(f147(x42122,f848(x42121)),f331(f331(f9(x42122,f848(x42121),f848(x42121)),f331(f331(f10(x42121,f854(f848(x42121),f848(x42121)),x42122),f145(x42121)),x42123)),f120(x42121))),x42124)),f331(f331(f147(x42122,x42121),x42123),x42124))
% 51.10/50.81 [4222]E(f331(f331(f93(a1,x42221),f331(f111(a1),f331(f331(f87(a1),x42222),a104))),f331(f331(f20(a1,x42221,x42221),f331(f331(f9(a1,x42221,f854(x42221,x42221)),f331(f331(f10(a840,f854(x42221,f854(x42221,x42221)),a1),f103(x42221)),a190)),x42223)),f331(f331(f10(a847,x42221,a1),x42224),a112))),f180(x42221,x42223,x42224,f331(f111(a847),x42222)))
% 51.10/50.81 [4445]~P1(f331(f331(f184(f854(x44451,f854(x44452,a840))),x44453),x44454))
% 51.10/50.81 [3706]E(f331(f331(f155(x37061),f331(f331(f130(x37061),x37062),x37063)),f331(f331(f87(a847),f331(f185(f848(x37061)),x37062)),x37064)),f331(f331(f155(x37061),x37063),x37064))
% 51.10/50.81 [3711]E(f331(f331(f133(x37111),x37112),f331(f331(f164(x37111),f331(f331(f87(a847),x37113),x37112)),x37114)),f331(f331(f164(x37111),x37113),f331(f331(f133(x37111),x37112),x37114)))
% 51.10/50.81 [3811]E(f331(f331(f108(f854(x38111,a840)),f331(f267(x38112,x38111),x38113)),f331(f267(x38112,x38111),x38114)),f331(f267(x38112,x38111),f331(f331(f108(f854(f853(x38112,x38111),a840)),x38113),x38114)))
% 51.10/50.81 [3812]E(f331(f331(f108(f854(x38121,a840)),f331(f269(x38121,x38122),x38123)),f331(f269(x38121,x38122),x38124)),f331(f269(x38121,x38122),f331(f331(f108(f854(f853(x38121,x38122),a840)),x38123),x38124)))
% 51.10/50.81 [3817]E(f331(f331(f3(f854(x38171,a840)),f331(f331(f109(f854(x38171,a840)),x38172),x38173)),x38174),f331(f331(f109(f854(x38171,a840)),x38172),f331(f331(f3(f854(x38171,a840)),x38173),x38174)))
% 51.10/50.81 [3818]E(f331(f331(f108(f854(x38181,a840)),f331(f331(f108(f854(x38181,a840)),x38182),x38183)),x38184),f331(f331(f108(f854(x38181,a840)),x38182),f331(f331(f108(f854(x38181,a840)),x38183),x38184)))
% 51.10/50.81 [3819]E(f331(f331(f109(f854(x38191,a840)),f331(f331(f109(f854(x38191,a840)),x38192),x38193)),x38194),f331(f331(f109(f854(x38191,a840)),x38192),f331(f331(f109(f854(x38191,a840)),x38193),x38194)))
% 51.10/50.81 [3859]E(f331(f331(f108(f854(f853(x38591,x38592),a840)),f331(f286(x38592,x38591),x38593)),f331(f286(x38592,x38591),x38594)),f331(f286(x38592,x38591),f331(f331(f108(f854(f853(x38592,x38591),a840)),x38593),x38594)))
% 51.10/50.81 [3860]E(f331(f331(f109(f854(f853(x38601,x38602),a840)),f331(f286(x38602,x38601),x38603)),f331(f286(x38602,x38601),x38604)),f331(f286(x38602,x38601),f331(f331(f109(f854(f853(x38602,x38601),a840)),x38603),x38604)))
% 51.10/50.81 [3893]E(f175(x38931,x38932,x38933,f171(x38931,x38932,f331(f160(f853(x38931,x38932)),f331(f331(f172(x38931,x38932),f120(x38931)),x38934)))),x38933)
% 51.10/50.81 [3931]E(f331(f331(f108(f854(x39311,a840)),f331(f331(f3(f854(x39311,a840)),x39312),x39313)),f331(f331(f3(f854(x39311,a840)),x39314),x39313)),f331(f331(f3(f854(x39311,a840)),f331(f331(f108(f854(x39311,a840)),x39312),x39314)),x39313))
% 51.10/50.81 [3932]E(f331(f331(f109(f854(x39321,a840)),f331(f331(f108(f854(x39321,a840)),x39322),x39323)),f331(f331(f108(f854(x39321,a840)),x39324),x39323)),f331(f331(f108(f854(x39321,a840)),f331(f331(f109(f854(x39321,a840)),x39322),x39324)),x39323))
% 51.10/50.81 [3933]E(f331(f331(f3(f854(x39331,a840)),f331(f331(f109(f854(x39331,a840)),x39332),x39333)),f331(f331(f109(f854(x39331,a840)),x39334),x39333)),f331(f331(f109(f854(x39331,a840)),f331(f331(f3(f854(x39331,a840)),x39332),x39334)),x39333))
% 51.10/50.81 [3934]E(f331(f331(f108(f854(x39341,a840)),f331(f331(f109(f854(x39341,a840)),x39342),x39343)),f331(f331(f109(f854(x39341,a840)),x39344),x39343)),f331(f331(f109(f854(x39341,a840)),f331(f331(f108(f854(x39341,a840)),x39342),x39344)),x39343))
% 51.10/50.81 [3935]E(f331(f331(f3(f854(x39351,a840)),f331(f331(f109(f854(x39351,a840)),x39352),x39353)),f331(f331(f109(f854(x39351,a840)),x39354),x39353)),f331(f331(f3(f854(x39351,a840)),f331(f331(f109(f854(x39351,a840)),x39352),x39353)),x39354))
% 51.10/50.81 [3947]E(f331(f331(f3(f854(x39471,a840)),f331(f331(f3(f854(x39471,a840)),x39472),f331(f331(f310(x39471),x39473),f184(f854(x39471,a840))))),x39474),f331(f331(f3(f854(x39471,a840)),x39472),f331(f331(f310(x39471),x39473),x39474)))
% 51.10/50.81 [4002]E(f331(f331(f108(f854(x40021,a840)),f331(f331(f310(x40021),x40022),f331(f331(f310(x40021),x40023),f184(f854(x40021,a840))))),f331(f284(x40021),x40024)),f331(f284(x40021),f331(f331(f310(f853(x40021,x40021)),f331(f331(f249(x40021,x40021),x40022),x40023)),x40024)))
% 51.10/50.81 [4028]E(f331(f331(f51(a847,f854(x40281,a840)),f331(f301(a847),x40282)),f331(f331(f10(a847,f854(x40281,a840),a847),x40283),f331(f331(f9(a847,a847,a847),f87(a847)),x40284))),f331(f331(f51(a847,f854(x40281,a840)),f303(a847,x40284,f331(f331(f87(a847),x40282),x40284))),x40283))
% 51.10/50.81 [4029]E(f166(x40291,f331(f285(x40291,x40291,x40292),f331(f331(f310(x40291),x40293),f184(f854(x40291,a840)))),f331(f285(f848(x40291),f848(x40291),f151(x40291,x40292)),f331(f331(f310(f848(x40291)),x40294),f184(f854(f848(x40291),a840))))),f331(f285(f848(x40291),f848(x40291),f151(x40291,x40292)),f331(f331(f310(f848(x40291)),f331(f331(f145(x40291),x40293),x40294)),f184(f854(f848(x40291),a840)))))
% 51.10/50.81 [4090]E(f171(x40901,x40902,f331(f331(f147(x40901,f853(x40901,x40902)),f331(f331(f20(x40901,x40902,f853(x40901,x40902)),f249(x40901,x40902)),x40903)),x40904)),f177(x40901,x40902,f331(f80(x40902,f851(x40902),x40901,f234(x40902)),x40903),f331(f163(x40901),x40904)))
% 51.10/50.81 [4093]E(f331(f264(x40931),f331(f331(f9(x40931,f854(x40932,a840),a840),f331(f331(f10(x40932,f854(f854(x40932,a840),a840),x40931),f333(x40932)),x40933)),x40934)),f331(f312(x40931,x40932,x40933),x40934))
% 51.10/50.81 [4184]E(f331(f264(x41841),f331(f331(f9(x41841,f854(f853(x41842,x41841),a840),a840),f331(f331(f10(f853(x41842,x41841),f854(f854(f853(x41842,x41841),a840),a840),x41841),f333(f853(x41842,x41841))),f331(f249(x41842,x41841),x41843))),x41844)),f331(f285(x41842,x41841,x41844),f331(f331(f310(x41842),x41843),f184(f854(x41842,a840)))))
% 51.10/50.81 [4198]E(f331(f331(f147(f853(x41981,a847),x41981),f248(x41981,a847)),f331(f131(f853(x41981,a847),f331(f331(f10(a847,a840,f853(x41981,a847)),x41982),f331(f331(f10(a847,a847,f853(x41981,a847)),a119),f258(x41981,a847)))),f331(f331(f172(x41981,a847),x41983),x41984))),f331(f331(f147(f853(x41981,a847),x41981),f248(x41981,a847)),f331(f131(f853(x41981,a847),f331(f331(f10(a847,a840,f853(x41981,a847)),x41982),f258(x41981,a847))),f331(f331(f172(x41981,a847),x41983),f331(f331(f147(a847,a847),a119),x41984)))))
% 51.10/50.81 [4205]P1(f331(f331(f240(f854(f854(x42051,a840),a840)),f331(f331(f51(x42052,f854(f854(x42051,a840),a840)),x42053),f331(f331(f10(f854(x42051,a840),f854(f854(x42051,a840),a840),x42052),f309(x42051)),x42054))),f331(f309(x42051),f331(f331(f51(x42052,f854(x42051,a840)),x42053),x42054))))
% 51.10/50.81 [4245]E(f331(f331(f93(a1,x42451),f331(f111(a1),f331(f331(f87(a1),x42452),a104))),f331(f331(f20(a1,x42451,x42451),f331(f331(f9(a1,x42451,f854(x42451,x42451)),f331(f331(f10(a840,f854(x42451,f854(x42451,x42451)),a1),f103(x42451)),a190)),x42453)),f331(f331(f20(a1,x42451,x42451),f331(f331(f10(a847,f854(x42451,x42451),a1),x42454),a112)),f331(f331(f10(a847,x42451,a1),f179(x42451,x42453,x42454)),a112)))),f331(f179(x42451,x42453,x42454),f331(f111(a847),x42452)))
% 51.10/50.81 [4248]E(f331(f331(f147(x42481,x42482),f331(f80(f851(x42482),x42482,x42481,f238(x42482)),x42483)),f331(f131(x42481,f331(f331(f10(a840,a840,x42481),a327),f331(f331(f9(x42481,f851(x42482),a840),f331(f331(f10(f851(x42482),f854(f851(x42482),a840),x42481),a328),x42483)),f187(x42482)))),x42484)),f156(x42481,x42482,x42483,x42484))
% 51.10/50.81 [4269]E(f331(f264(f853(x42691,x42692)),f331(f259(x42691,x42692,a840),f331(f331(f9(x42691,f854(x42692,a840),f854(x42692,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x42692,a840),f854(x42692,a840)),x42691),f10(a840,a840,x42692)),f331(f331(f10(a840,f854(a840,a840),x42691),a329),f331(f331(f9(x42691,f854(x42691,a840),a840),f333(x42691)),x42693)))),f331(f331(f9(x42692,f854(x42692,a840),a840),f333(x42692)),x42694)))),f230(x42691,x42692,x42693,x42694))
% 51.10/50.81 [4302]E(f331(f331(f51(x43021,f854(f853(x43021,x43022),a840)),x43023),f331(f331(f20(x43021,f854(x43022,f854(f853(x43021,x43022),a840)),f854(f853(x43021,x43022),a840)),f331(f331(f10(f854(x43022,a840),f854(f854(x43022,f854(f853(x43021,x43022),a840)),f854(f853(x43021,x43022),a840)),x43021),f51(x43022,f854(f853(x43021,x43022),a840))),x43024)),f331(f331(f9(x43021,f854(f853(x43021,x43022),a840),f854(x43022,f854(f853(x43021,x43022),a840))),f331(f331(f10(f854(x43022,f854(f854(f853(x43021,x43022),a840),f854(f853(x43021,x43022),a840))),f854(f854(f853(x43021,x43022),a840),f854(x43022,f854(f853(x43021,x43022),a840))),x43021),f9(x43022,f854(f853(x43021,x43022),a840),f854(f853(x43021,x43022),a840))),f331(f331(f10(f854(x43022,f853(x43021,x43022)),f854(x43022,f854(f854(f853(x43021,x43022),a840),f854(f853(x43021,x43022),a840))),x43021),f331(f10(f853(x43021,x43022),f854(f854(f853(x43021,x43022),a840),f854(f853(x43021,x43022),a840)),x43022),f310(f853(x43021,x43022)))),f249(x43021,x43022)))),f184(f854(f853(x43021,x43022),a840))))),f331(f331(f256(x43021,x43022),x43023),x43024))
% 51.10/50.81 [3868]E(f331(f331(f130(x38681),f331(f331(f164(x38681),x38682),x38683)),f331(f331(f164(x38681),f331(f331(f3(a847),x38682),f331(f185(f848(x38681)),x38683))),x38684)),f331(f331(f164(x38681),x38682),f331(f331(f130(x38681),x38683),x38684)))
% 51.10/50.81 [3869]E(f331(f331(f130(x38691),f331(f331(f133(x38691),x38692),x38693)),f331(f331(f133(x38691),f331(f331(f3(a847),x38692),f331(f185(f848(x38691)),x38693))),x38694)),f331(f331(f133(x38691),x38692),f331(f331(f130(x38691),x38693),x38694)))
% 51.10/50.81 [3920]E(f331(f331(f87(a847),f331(f331(f88(a847),x39201),x39202)),f331(f331(f87(a847),f331(f331(f88(a847),x39203),x39202)),x39204)),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f87(a847),x39201),x39203)),x39202)),x39204))
% 51.10/50.81 [4119]P1(f331(f331(f240(f854(x41191,a840)),f331(f331(f3(f854(x41191,a840)),f331(f267(x41192,x41191),x41193)),f331(f267(x41192,x41191),x41194))),f331(f267(x41192,x41191),f331(f331(f3(f854(f853(x41192,x41191),a840)),x41193),x41194))))
% 51.10/50.81 [4120]P1(f331(f331(f240(f854(x41201,a840)),f331(f331(f3(f854(x41201,a840)),f331(f269(x41201,x41202),x41203)),f331(f269(x41201,x41202),x41204))),f331(f269(x41201,x41202),f331(f331(f3(f854(f853(x41201,x41202),a840)),x41203),x41204))))
% 51.10/50.81 [4224]E(f331(f331(f87(a1),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x42241),x42242)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x42243),x42244)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),f331(f331(f87(a847),x42241),x42243)),f331(f331(f87(a847),x42242),x42244))),f184(f854(f853(a847,a847),a840))))))
% 51.10/50.81 [4264]E(f331(f331(f88(a1),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x42641),x42642)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x42643),x42644)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),f331(f331(f87(a847),f331(f331(f88(a847),x42641),x42643)),f331(f331(f88(a847),x42642),x42644))),f331(f331(f87(a847),f331(f331(f88(a847),x42641),x42644)),f331(f331(f88(a847),x42642),x42643)))),f184(f854(f853(a847,a847),a840))))))
% 51.10/50.81 [4284]E(f331(f264(x42841),f331(f331(f10(f854(x42842,a840),a840,x42841),f95(x42842)),f331(f331(f10(f854(x42842,a840),f854(x42842,a840),x42841),f331(f20(x42842,a840,a840),f331(f331(f10(a840,f854(a840,a840),x42842),a334),f331(f331(f9(x42842,f854(x42842,a840),a840),f333(x42842)),x42843)))),f331(f331(f9(x42841,f854(x42842,f854(x42841,a840)),f854(x42842,a840)),f331(f331(f10(f854(f854(x42841,a840),a840),f854(f854(x42842,f854(x42841,a840)),f854(x42842,a840)),x42841),f10(f854(x42841,a840),a840,x42842)),f333(x42841))),x42844)))),f331(f331(f52(x42842,f854(x42841,a840)),x42843),x42844))
% 51.10/50.81 [4318]E(f331(f331(f289(x43181,x43181,x43181),f331(f331(f310(f853(x43181,x43181)),f331(f331(f249(x43181,x43181),x43182),x43183)),x43184)),f308(x43181,f331(f331(f310(f853(x43181,x43181)),f331(f331(f249(x43181,x43181),x43182),x43183)),x43184))),f331(f331(f108(f854(f853(x43181,x43181),a840)),f331(f331(f289(x43181,x43181,x43181),x43184),f308(x43181,x43184))),f331(f264(f853(x43181,x43181)),f331(f259(x43181,x43181,a840),f331(f331(f9(x43181,f854(x43181,a840),f854(x43181,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x43181,a840),f854(x43181,a840)),x43181),f10(a840,a840,x43181)),f331(f331(f10(a840,f854(a840,a840),x43181),a329),f331(f331(f9(x43181,f854(f853(x43181,x43181),a840),a840),f331(f331(f10(f853(x43181,x43181),f854(f854(f853(x43181,x43181),a840),a840),x43181),f333(f853(x43181,x43181))),f331(f331(f9(x43181,x43181,f853(x43181,x43181)),f249(x43181,x43181)),x43182))),f308(x43181,x43184))))),f331(f331(f9(x43181,f854(f853(x43181,x43181),a840),a840),f331(f331(f10(f853(x43181,x43181),f854(f854(f853(x43181,x43181),a840),a840),x43181),f333(f853(x43181,x43181))),f331(f249(x43181,x43181),x43183))),f308(x43181,x43184)))))))
% 51.10/50.81 [4121]E(f331(f131(x41211,f331(f331(f20(x41211,a840,a840),f331(f331(f10(a840,f854(a840,a840),x41211),a329),x41212)),x41213)),x41214),f331(f131(x41211,x41213),f331(f131(x41211,x41212),x41214)))
% 51.10/50.81 [4218]E(f331(f331(f130(x42181),f331(f331(f331(f103(f848(x42181)),f331(f331(f333(a847),f2(a847)),x42182)),f331(f331(f145(x42181),x42183),f120(x42181))),f120(x42181))),f165(x42181,x42184,f331(f264(a847),f331(f331(f9(a847,f854(a847,a840),a840),f331(f331(f10(a847,f854(f854(a847,a840),a840),a847),f333(a847)),a119)),x42182)))),f165(x42181,f331(f331(f145(x42181),x42183),x42184),x42182))
% 51.10/50.81 [4313]E(f331(f264(f853(x43131,x43132)),f331(f331(f10(f854(a847,a840),a840,f853(x43131,x43132)),f94(a847)),f331(f331(f9(f853(x43131,x43132),f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),f853(x43131,x43132)),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),f853(x43131,x43132)),f331(f10(a840,f854(a840,a840),a847),a329)),f331(f331(f9(f853(x43131,x43132),f854(a847,f853(x43131,x43132)),f854(a847,a840)),f331(f331(f10(f854(f853(x43131,x43132),a840),f854(f854(a847,f853(x43131,x43132)),f854(a847,a840)),f853(x43131,x43132)),f10(f853(x43131,x43132),a840,a847)),a328)),f331(f331(f20(a847,x43132,f853(x43131,x43132)),f331(f331(f10(x43131,f854(x43132,f853(x43131,x43132)),a847),f249(x43131,x43132)),f331(f155(x43131),x43133))),f331(f155(x43132),x43134)))))),f331(f331(f9(a847,a847,a840),f241(a847)),f331(f331(f244(a847),f331(f185(f848(x43131)),x43133)),f331(f185(f848(x43132)),x43134)))))),f331(f163(f853(x43131,x43132)),f331(f331(f172(x43131,x43132),x43133),x43134)))
% 51.10/50.81 [4237]E(f331(f264(f853(x42371,x42372)),f331(f259(x42371,x42372,a840),f331(f331(f9(x42371,f854(x42372,a840),f854(x42372,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x42372,a840),f854(x42372,a840)),x42371),f10(a840,a840,x42372)),f331(f331(f10(a840,f854(a840,a840),x42371),a329),x42373))),x42374))),f331(f331(f256(x42371,x42372),f331(f264(x42371),x42373)),f331(f18(f854(x42372,a840),x42371),f331(f264(x42372),x42374))))
% 51.10/50.81 [4240]E(f331(f264(f853(x42401,x42402)),f331(f259(x42401,x42402,a840),f331(f331(f20(x42401,f854(x42402,a840),f854(x42402,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x42402,a840),f854(x42402,a840)),x42401),f10(a840,a840,x42402)),f331(f331(f10(a840,f854(a840,a840),x42401),a329),x42403))),x42404))),f331(f331(f256(x42401,x42402),f331(f264(x42401),x42403)),f331(f331(f10(f854(x42402,a840),f854(x42402,a840),x42401),f264(x42402)),x42404)))
% 51.10/50.81 [4255]E(f331(f264(x42551),f331(f331(f10(f854(x42552,a840),a840,x42551),f95(x42552)),f331(f331(f10(f854(x42552,a840),f854(x42552,a840),x42551),f331(f20(x42552,a840,a840),f331(f331(f10(a840,f854(a840,a840),x42552),a334),f331(f331(f9(x42552,f854(x42552,a840),a840),f333(x42552)),x42553)))),x42554))),f331(f331(f52(x42552,f854(x42551,a840)),x42553),f331(f331(f10(f854(x42551,a840),f854(x42551,a840),x42552),f264(x42551)),f331(f9(x42551,x42552,a840),x42554))))
% 51.10/50.81 [4297]E(f331(f331(f147(f853(x42971,a847),x42971),f248(x42971,a847)),f331(f131(f853(x42971,a847),f331(f331(f9(f853(x42971,a847),f854(a847,a840),a840),f331(f331(f10(a847,f854(f854(a847,a840),a840),f853(x42971,a847)),f333(a847)),f258(x42971,a847))),x42972)),f331(f331(f172(x42971,a847),x42973),f135(a847,f331(f302(a847,x42974),f331(f331(f87(a847),x42974),f331(f185(f848(x42971)),x42973))))))),f331(f331(f147(f853(x42971,a847),x42971),f248(x42971,a847)),f331(f131(f853(x42971,a847),f331(f331(f9(f853(x42971,a847),f854(a847,a840),a840),f331(f331(f10(a847,f854(f854(a847,a840),a840),f853(x42971,a847)),f333(a847)),f331(f331(f9(f853(x42971,a847),a847,a847),f331(f331(f10(a847,f854(a847,a847),f853(x42971,a847)),f87(a847)),f258(x42971,a847))),x42974))),x42972)),f331(f331(f172(x42971,a847),x42973),f135(a847,f331(f302(a847,f2(a847)),f331(f185(f848(x42971)),x42973)))))))
% 51.10/50.81 [4298]E(f331(a119,f331(f331(f239(a847),f331(f185(f848(x42981)),x42982)),f331(f137(a847,f848(x42983),f331(f9(f848(x42983),a847,a847),f331(f331(f10(a847,f854(a847,a847),f848(x42983)),f239(a847)),f331(f331(f9(f848(x42983),a847,a847),f331(f331(f10(a847,f854(a847,a847),f848(x42983)),f3(a847)),f185(f848(x42983)))),f331(a119,f2(a847))))),f2(a847)),f331(f160(f848(x42983)),f331(f131(f848(x42983),f331(f331(f10(a840,a840,f848(x42983)),a327),f331(f331(f9(f848(x42983),f848(x42983),a840),a328),f120(x42983)))),x42984))))),f331(f331(f239(a847),f331(a119,f331(f185(f848(x42981)),x42982))),f331(f137(a847,f848(x42983),f331(f9(f848(x42983),a847,a847),f331(f331(f10(a847,f854(a847,a847),f848(x42983)),f239(a847)),f185(f848(x42983)))),f2(a847)),f331(f160(f848(x42983)),x42984))))
% 51.10/50.81 [4254]E(f331(f331(f130(x42541),f165(x42541,x42542,x42543)),f165(x42541,x42544,f331(f264(a847),f331(f331(f9(a847,f854(a847,a840),a840),f331(f331(f10(a847,f854(f854(a847,a840),a840),a847),f333(a847)),f331(f331(f9(a847,a847,a847),f87(a847)),f331(f185(f848(x42541)),x42542)))),x42543)))),f165(x42541,f331(f331(f130(x42541),x42542),x42544),x42543))
% 51.10/50.81 [4304]E(f331(f331(f145(f848(x43041)),f331(f331(f145(x43041),x43042),f331(f137(f848(x43041),f848(x43041),f130(x43041),f120(x43041)),f331(f331(f147(f848(x43041),f848(x43041)),f149(f848(x43041),x43041,f120(x43041),f331(f331(f10(f848(x43041),f854(f848(x43041),f848(x43041)),x43041),f18(f848(x43041),f848(x43041))),f331(f331(f9(x43041,f848(x43041),f848(x43041)),f145(x43041)),f120(x43041))))),x43043)))),f169(x43041,f331(f331(f145(f848(x43041)),x43044),f331(f137(f848(f848(x43041)),f848(f848(x43041)),f130(f848(x43041)),f120(f848(x43041))),f331(f331(f147(f848(x43041),f848(f848(x43041))),f149(f848(f848(x43041)),x43041,f120(f848(x43041)),f331(f18(f854(f848(x43041),f848(f848(x43041))),x43041),f331(f331(f9(f848(x43041),f848(f848(x43041)),f848(f848(x43041))),f145(f848(x43041))),f120(f848(x43041)))))),x43043))))),f169(x43041,f331(f331(f145(f848(x43041)),f331(f331(f145(x43041),x43042),x43044)),x43043)))
% 51.10/50.81 [4314]E(f331(f264(f853(x43141,x43141)),f331(f259(x43141,x43141,a840),f331(f331(f9(x43141,f854(f853(x43142,x43142),a840),f854(x43141,a840)),f331(f331(f10(f854(x43141,f854(f854(f853(x43142,x43142),a840),a840)),f854(f854(f853(x43142,x43142),a840),f854(x43141,a840)),x43141),f9(x43141,f854(f853(x43142,x43142),a840),a840)),f331(f331(f10(f854(x43141,f853(x43142,x43142)),f854(x43141,f854(f854(f853(x43142,x43142),a840),a840)),x43141),f331(f10(f853(x43142,x43142),f854(f854(f853(x43142,x43142),a840),a840),x43141),f333(f853(x43142,x43142)))),f331(f331(f9(x43141,f854(x43141,x43142),f854(x43141,f853(x43142,x43142))),f331(f331(f10(f854(x43142,f853(x43142,x43142)),f854(f854(x43141,x43142),f854(x43141,f853(x43142,x43142))),x43141),f10(x43142,f853(x43142,x43142),x43141)),f331(f331(f10(x43142,f854(x43142,f853(x43142,x43142)),x43141),f249(x43142,x43142)),x43143))),x43143)))),x43144))),f331(f331(f288(x43142,x43141),x43144),x43143))
% 51.10/50.81 [4384]~E(f30(x43841,x43842),f33(x43843,x43844,x43845))
% 51.10/50.81 [4385]~E(f30(x43851,x43852),f34(x43853,x43854,x43855))
% 51.10/50.81 [4386]~E(f30(x43861,x43862),f35(x43863,x43864,x43865))
% 51.10/50.81 [4387]~E(f38(x43871,x43872),f33(x43873,x43874,x43875))
% 51.10/50.81 [4388]~E(f38(x43881,x43882),f34(x43883,x43884,x43885))
% 51.10/50.81 [4389]~E(f38(x43891,x43892),f35(x43893,x43894,x43895))
% 51.10/50.81 [4390]~E(f37(x43901,x43902),f33(x43903,x43904,x43905))
% 51.10/50.81 [4391]~E(f37(x43911,x43912),f34(x43913,x43914,x43915))
% 51.10/50.81 [4392]~E(f37(x43921,x43922),f35(x43923,x43924,x43925))
% 51.10/50.81 [4393]~E(f33(x43931,x43932,x43933),f30(x43934,x43935))
% 51.10/50.81 [4394]~E(f33(x43941,x43942,x43943),f38(x43944,x43945))
% 51.10/50.81 [4395]~E(f33(x43951,x43952,x43953),f37(x43954,x43955))
% 51.10/50.81 [4396]~E(f34(x43961,x43962,x43963),f30(x43964,x43965))
% 51.10/50.81 [4397]~E(f34(x43971,x43972,x43973),f38(x43974,x43975))
% 51.10/50.81 [4398]~E(f34(x43981,x43982,x43983),f37(x43984,x43985))
% 51.10/50.81 [4399]~E(f35(x43991,x43992,x43993),f30(x43994,x43995))
% 51.10/50.81 [4400]~E(f35(x44001,x44002,x44003),f38(x44004,x44005))
% 51.10/50.81 [4401]~E(f35(x44011,x44012,x44013),f37(x44014,x44015))
% 51.10/50.81 [3809]E(f331(f175(x38091,x38092,x38093,x38094),x38095),f331(f236(f851(x38092),x38092,f331(x38093,x38095),f234(x38092)),f331(x38094,x38095)))
% 51.10/50.81 [3895]E(f175(x38951,x38952,f175(x38951,x38952,x38953,x38954),x38955),f175(x38951,x38952,x38953,f175(x38951,x38952,x38954,x38955)))
% 51.10/50.81 [3636]E(f331(f331(f259(x36361,x36362,x36363),x36364),x36365),f331(f331(x36364,f331(f248(x36361,x36362),x36365)),f331(f258(x36361,x36362),x36365)))
% 51.10/50.81 [3637]E(f331(f331(f259(x36371,x36372,x36373),x36374),x36375),f331(f331(x36374,f331(f248(x36371,x36372),x36375)),f331(f258(x36371,x36372),x36375)))
% 51.10/50.81 [3638]E(f331(f331(f259(x36381,x36382,x36383),x36384),x36385),f331(f331(x36384,f331(f248(x36381,x36382),x36385)),f331(f258(x36381,x36382),x36385)))
% 51.10/50.81 [3664]E(f331(f236(x36641,x36642,x36643,x36644),f331(f234(x36642),x36645)),f331(x36644,x36645))
% 51.10/50.81 [3672]E(f331(f331(f331(f72(x36721,x36722,x36723),x36724),x36725),f184(f854(x36722,a840))),x36725)
% 51.10/50.81 [3839]E(f237(x38391,x38392,x38393,x38394,f331(f234(x38392),x38395)),f331(x38394,x38395))
% 51.10/50.81 [3953]E(f331(f80(f851(x39531),f851(x39532),f851(x39533),f331(f203(x39531,x39532),x39534)),f331(f203(x39533,x39531),x39535)),f331(f203(x39533,x39532),f331(f80(x39531,x39532,x39533,x39534),x39535)))
% 51.10/50.81 [3954]E(f331(f80(f848(x39541),f848(x39542),f848(x39543),f331(f147(x39541,x39542),x39544)),f331(f147(x39543,x39541),x39545)),f331(f147(x39543,x39542),f331(f80(x39541,x39542,x39543,x39544),x39545)))
% 51.10/50.81 [3955]E(f331(f80(f848(x39551),f848(x39552),f848(x39553),f331(f147(x39551,x39552),x39554)),f331(f147(x39553,x39551),x39555)),f331(f147(x39553,x39552),f331(f80(x39551,x39552,x39553,x39554),x39555)))
% 51.10/50.81 [4032]E(f92(x40321,f73(x40322,x40321,x40323,x40324,x40325)),f331(f331(f71(x40322,x40321,x40323),x40324),x40325))
% 51.10/50.81 [4066]E(f331(f331(f87(a847),f331(f331(f87(a847),f331(x40661,f331(f248(x40662,x40663),x40664))),f331(x40665,f331(f258(x40662,x40663),x40664)))),f331(a119,f2(a847))),f263(x40662,x40663,x40661,x40665,x40664))
% 51.10/50.81 [4250]E(f156(x42501,x42502,f331(f331(f9(x42501,f851(x42502),f851(x42502)),f331(f331(f20(x42501,f851(x42502),f854(f851(x42502),f851(x42502))),f331(f331(f10(a840,f854(f851(x42502),f854(f851(x42502),f851(x42502))),x42501),f103(f851(x42502))),x42503)),f331(f331(f10(x42502,f851(x42502),x42501),f234(x42502)),x42504))),f187(x42502)),x42505),f331(f331(f147(x42501,x42502),x42504),f331(f131(x42501,x42503),x42505)))
% 51.10/50.81 [4438]~E(f331(f331(f331(f79(x44381,f851(x44382)),x44383),x44384),f331(f234(x44382),x44385)),f331(f18(f851(x44382),x44381),f187(x44382)))
% 51.10/50.81 [3572]E(f331(f331(f164(x35721),x35722),f331(f331(f147(x35723,x35721),x35724),x35725)),f331(f331(f147(x35723,x35721),x35724),f331(f331(f164(x35723),x35722),x35725)))
% 51.10/50.81 [3573]E(f331(f331(f133(x35731),x35732),f331(f331(f147(x35733,x35731),x35734),x35735)),f331(f331(f147(x35733,x35731),x35734),f331(f331(f133(x35733),x35732),x35735)))
% 51.10/50.81 [3604]E(f331(f331(f147(x36041,x36042),x36043),f331(f331(f145(x36041),x36044),x36045)),f331(f331(f145(x36042),f331(x36043,x36044)),f331(f331(f147(x36041,x36042),x36043),x36045)))
% 51.10/50.81 [3668]E(f331(f311(x36681,x36682,x36683),f331(f331(f310(x36681),x36684),x36685)),f331(f331(f310(x36682),f331(x36683,x36684)),f331(f311(x36681,x36682,x36683),x36685)))
% 51.10/50.81 [3733]E(f331(f331(f172(x37331,x37332),f331(f331(f164(x37331),x37333),x37334)),f331(f331(f164(x37332),x37333),x37335)),f331(f331(f164(f853(x37331,x37332)),x37333),f331(f331(f172(x37331,x37332),x37334),x37335)))
% 51.10/50.81 [3734]E(f331(f331(f172(x37341,x37342),f331(f331(f133(x37341),x37343),x37344)),f331(f331(f133(x37342),x37343),x37345)),f331(f331(f133(f853(x37341,x37342)),x37343),f331(f331(f172(x37341,x37342),x37344),x37345)))
% 51.10/50.81 [3745]E(f331(f331(f152(x37451,f331(f331(f145(x37451),x37452),x37453)),f331(a119,x37454)),x37455),f331(f331(f145(x37451),x37452),f331(f331(f152(x37451,x37453),x37454),x37455)))
% 51.10/50.81 [3748]E(f331(f236(f851(x37481),x37482,f187(x37481),x37483),f331(f331(f18(f851(x37482),x37484),f187(x37482)),x37485)),f187(x37481))
% 51.10/50.81 [3750]E(f331(f331(f130(x37501),f331(f331(f147(x37502,x37501),x37503),x37504)),f331(f331(f147(x37502,x37501),x37503),x37505)),f331(f331(f147(x37502,x37501),x37503),f331(f331(f130(x37502),x37504),x37505)))
% 51.10/50.81 [3754]E(f331(f331(x37541,x37542),f331(f331(f251(x37543,x37544,x37541),x37542),x37545)),f331(f331(f251(x37543,x37544,x37541),x37542),f331(a119,x37545)))
% 51.10/50.81 [3796]E(f331(f331(f289(x37961,x37962,x37963),f331(f286(x37962,x37961),x37964)),f331(f286(x37963,x37962),x37965)),f331(f286(x37963,x37961),f331(f331(f289(x37963,x37962,x37961),x37965),x37964)))
% 51.10/50.81 [3827]E(f331(f331(f331(f178(f848(x38271),f848(x38271)),x38272),f159(x38271)),f331(f331(f147(x38273,x38271),x38274),x38275)),f331(f331(f147(x38273,x38271),x38274),f331(f331(f331(f178(f848(x38273),f848(x38273)),x38272),f159(x38273)),x38275)))
% 51.10/50.81 [3828]E(f331(f331(f261(x38281,x38282,x38281,x38283),f331(f249(x38282,x38281),x38284)),x38285),f331(x38285,x38284))
% 51.10/50.81 [3853]E(f148(x38531,x38532,f331(f331(f147(x38533,x38531),x38534),x38535)),f148(x38533,f331(f80(x38531,a847,x38533,x38532),x38534),x38535))
% 51.10/50.81 [3918]E(f331(f331(f80(f851(x39181),f851(x39182),x39183,f331(f203(x39181,x39182),x39184)),f331(f18(f851(x39181),x39183),f187(x39181))),x39185),f187(x39182))
% 51.10/50.81 [3919]E(f167(f853(x39191,x39192),f331(f80(x39192,a840,f853(x39191,x39192),x39193),f258(x39191,x39192)),f331(f331(f172(x39191,x39192),x39194),x39195)),f331(f331(f172(x39191,x39192),x39194),f167(x39192,x39193,x39195)))
% 51.10/50.81 [3924]E(f331(f311(x39241,x39242,f331(f331(f10(x39243,x39242,x39241),x39244),x39245)),f247(f854(x39241,a840))),f331(f311(x39243,x39242,x39244),f331(f311(x39241,x39243,x39245),f247(f854(x39241,a840)))))
% 51.10/50.81 [3938]E(f167(f853(x39381,x39382),f331(f80(x39381,a840,f853(x39381,x39382),x39383),f248(x39381,x39382)),f331(f331(f172(x39381,x39382),x39384),x39385)),f331(f331(f172(x39381,x39382),f167(x39381,x39383,x39384)),x39385))
% 51.10/50.81 [3959]E(f331(f331(f108(f854(x39591,a840)),f331(f312(x39591,x39592,x39593),f331(f331(f310(x39592),x39594),f184(f854(x39592,a840))))),f331(f312(x39591,x39592,x39593),x39595)),f331(f312(x39591,x39592,x39593),f331(f331(f310(x39592),x39594),x39595)))
% 51.10/50.81 [4018]E(f331(f331(f147(x40181,x40182),x40183),f167(x40181,f331(f80(x40182,a840,x40181,x40184),x40183),x40185)),f167(x40182,x40184,f331(f331(f147(x40181,x40182),x40183),x40185)))
% 51.10/50.81 [4019]E(f331(f331(f147(x40191,x40192),x40193),f134(x40191,f331(f80(x40192,a840,x40191,x40194),x40193),x40195)),f134(x40192,x40194,f331(f331(f147(x40191,x40192),x40193),x40195)))
% 51.10/50.81 [4024]E(f331(f137(x40241,x40242,f331(f9(x40242,x40241,x40241),f331(f9(x40241,x40242,x40241),x40243)),x40244),f331(f160(x40242),f331(f160(x40242),x40245))),f331(f137(x40241,x40242,x40243,x40244),x40245))
% 51.10/50.81 [4025]E(f331(f331(f331(f79(x40251,f851(x40252)),f177(x40251,x40252,x40253,x40254)),x40255),f331(x40253,x40255)),f177(x40251,x40252,x40253,f331(f331(f310(x40251),x40255),x40254)))
% 51.10/50.81 [4091]E(f331(f236(f848(x40911),x40911,f156(x40912,x40911,x40913,x40914),f331(f331(f9(x40911,f848(x40911),f848(x40911)),f145(x40911)),f156(x40912,x40911,x40913,x40914))),f331(x40913,x40915)),f156(x40912,x40911,x40913,f331(f331(f145(x40912),x40915),x40914)))
% 51.10/50.81 [4129]P1(f331(f331(f240(f854(x41291,a840)),f331(f311(x41292,x41291,x41293),f331(f331(f109(f854(x41292,a840)),x41294),x41295))),f331(f331(f109(f854(x41291,a840)),f331(f311(x41292,x41291,x41293),x41294)),f331(f311(x41292,x41291,x41293),x41295))))
% 51.10/50.81 [4130]P1(f331(f331(f240(f854(x41301,a840)),f331(f285(x41302,x41301,x41303),f331(f331(f109(f854(x41302,a840)),x41304),x41305))),f331(f331(f109(f854(x41301,a840)),f331(f285(x41302,x41301,x41303),x41304)),f331(f285(x41302,x41301,x41303),x41305))))
% 51.10/50.81 [4225]E(f331(f258(x42251,x42252),f331(f260(x42253,x42251,x42252,x42252,x42254,f39(x42252)),x42255)),f331(f258(x42253,x42252),x42255))
% 51.10/50.81 [4226]E(f331(f248(x42261,x42262),f331(f260(x42261,x42261,x42263,x42262,f39(x42261),x42264),x42265)),f331(f248(x42261,x42263),x42265))
% 51.10/50.81 [4229]E(f331(f248(x42291,x42292),f331(f260(x42293,x42291,x42292,x42292,x42294,f39(x42292)),x42295)),f331(x42294,f331(f248(x42293,x42292),x42295)))
% 51.10/50.81 [4230]E(f331(f258(x42301,x42302),f331(f260(x42301,x42301,x42303,x42302,f39(x42301),x42304),x42305)),f331(x42304,f331(f258(x42301,x42303),x42305)))
% 51.10/50.81 [4307]P26(x43071,x43072,f331(f331(f310(f846(x43071)),f331(f331(f331(f98(x43071),f331(f331(f9(x43071,f854(a845,a845),f854(a845,a840)),f331(f331(f10(f854(a845,a840),f854(f854(a845,a845),f854(a845,a840)),x43071),f10(a845,a840,a845)),x43073)),f331(f331(f20(a845,a847,a845),f331(f331(f9(a845,a842,f854(a847,a845)),a193),x43074)),x43075))),f30(x43074,x43075)),x43073)),f184(f854(f846(x43071),a840))))
% 51.10/50.81 [4308]P26(x43081,x43082,f331(f331(f310(f846(x43081)),f331(f331(f331(f98(x43081),f331(f331(f9(x43081,f854(a845,a845),f854(a845,a840)),f331(f331(f10(f854(a845,a840),f854(f854(a845,a845),f854(a845,a840)),x43081),f10(a845,a840,a845)),x43083)),f331(f331(f20(a845,a847,a845),f331(f331(f9(a845,a842,f854(a847,a845)),a193),x43084)),x43085))),f30(x43084,x43085)),x43083)),f184(f854(f846(x43081),a840))))
% 51.10/50.81 [4312]P26(x43121,x43122,f331(f331(f310(f846(x43121)),f331(f331(f331(f98(x43121),f331(f331(f9(x43121,f854(a845,a840),f854(a845,a840)),f331(f331(f10(f854(a845,f854(a840,a840)),f854(f854(a845,a840),f854(a845,a840)),x43121),f20(a845,a840,a840)),f331(f331(f10(f854(a845,a840),f854(a845,f854(a840,a840)),x43121),f331(f10(a840,f854(a840,a840),a845),a329)),x43123))),f331(f331(f10(a840,a840,a845),a327),x43124))),f37(x43124,x43125)),x43123)),f184(f854(f846(x43121),a840))))
% 51.10/50.81 [3418]E(f331(f331(f331(f331(f206(x34181),x34182),x34183),x34184),x34185),f189(x34181,x34182))
% 51.10/50.81 [3419]E(f331(f331(f331(f331(f210(x34191),x34192),x34193),x34194),x34195),f201(x34191,x34192))
% 51.10/50.81 [3466]E(f100(x34661,x34662,f331(f331(f331(f98(x34661),x34663),x34664),x34665)),f2(a847))
% 51.10/50.81 [3555]E(f331(f331(f331(f331(f79(x35551,x35552),x35553),x35554),x35555),x35554),x35555)
% 51.10/50.81 [3785]E(f331(f331(f51(x37851,f854(x37852,a840)),f331(f331(f310(x37851),x37853),x37854)),x37855),f331(f331(f108(f854(x37852,a840)),f331(x37855,x37853)),f331(f331(f51(x37851,f854(x37852,a840)),x37854),x37855)))
% 51.10/50.81 [3786]E(f331(f331(f52(x37861,f854(x37862,a840)),f331(f331(f310(x37861),x37863),x37864)),x37865),f331(f331(f109(f854(x37862,a840)),f331(x37865,x37863)),f331(f331(f52(x37861,f854(x37862,a840)),x37864),x37865)))
% 51.10/50.81 [3846]E(f331(f331(f108(f854(x38461,a840)),f331(f311(x38462,x38461,x38463),x38464)),f331(f311(x38462,x38461,x38463),x38465)),f331(f311(x38462,x38461,x38463),f331(f331(f108(f854(x38462,a840)),x38464),x38465)))
% 51.10/50.81 [3847]E(f331(f331(f108(f854(x38471,a840)),f331(f285(x38472,x38471,x38473),x38474)),f331(f285(x38472,x38471,x38473),x38475)),f331(f285(x38472,x38471,x38473),f331(f331(f108(f854(x38472,a840)),x38474),x38475)))
% 51.10/50.81 [3848]E(f331(f331(f3(f854(x38481,a840)),f331(f312(x38481,x38482,x38483),x38484)),f331(f312(x38481,x38482,x38483),x38485)),f331(f312(x38481,x38482,x38483),f331(f331(f3(f854(x38482,a840)),x38484),x38485)))
% 51.10/50.81 [3849]E(f331(f331(f108(f854(x38491,a840)),f331(f312(x38491,x38492,x38493),x38494)),f331(f312(x38491,x38492,x38493),x38495)),f331(f312(x38491,x38492,x38493),f331(f331(f108(f854(x38492,a840)),x38494),x38495)))
% 51.10/50.81 [3850]E(f331(f331(f109(f854(x38501,a840)),f331(f312(x38501,x38502,x38503),x38504)),f331(f312(x38501,x38502,x38503),x38505)),f331(f312(x38501,x38502,x38503),f331(f331(f109(f854(x38502,a840)),x38504),x38505)))
% 51.10/50.81 [3852]E(f177(x38521,x38522,f177(x38521,x38522,x38523,x38524),x38525),f177(x38521,x38522,x38523,f331(f331(f109(f854(x38521,a840)),x38524),x38525)))
% 51.10/50.81 [3854]E(f123(x38541,x38542,f331(x38543,x38544),f331(f331(f9(x38541,a106,f849(x38542)),x38545),x38544)),f331(f199(x38541,x38542,x38543,x38545),x38544))
% 51.10/50.81 [3914]E(f331(f331(f152(x39141,f331(f331(f130(x39141),x39142),f331(f331(f145(x39141),x39143),x39144))),f331(f185(f848(x39141)),x39142)),x39145),f331(f331(f130(x39141),x39142),f331(f331(f145(x39141),x39145),x39144)))
% 51.10/50.81 [3921]E(f331(f331(f52(x39211,f854(x39212,a840)),x39213),f331(f331(f10(f854(x39212,a840),f854(x39212,a840),x39211),f331(f310(x39212),x39214)),x39215)),f331(f331(f310(x39212),x39214),f331(f331(f52(x39211,f854(x39212,a840)),x39213),x39215)))
% 51.10/50.81 [3922]E(f331(f331(f52(x39221,f854(x39222,a840)),x39223),f331(f331(f10(f854(x39222,a840),f854(x39222,a840),x39221),f331(f310(x39222),x39224)),x39225)),f331(f331(f310(x39222),x39224),f331(f331(f52(x39221,f854(x39222,a840)),x39223),x39225)))
% 51.10/50.81 [3993]E(f177(x39931,x39932,f331(f331(f331(f79(x39931,f851(x39932)),x39933),x39934),f331(f234(x39932),x39935)),f331(f86(f854(x39931,a840)),f331(f331(f310(x39931),x39934),f184(f854(x39931,a840))))),f177(x39931,x39932,x39933,f331(f86(f854(x39931,a840)),f331(f331(f310(x39931),x39934),f184(f854(x39931,a840))))))
% 51.10/50.81 [4034]E(f331(f331(f3(f854(f853(x40341,x40342),a840)),f331(f331(f256(x40341,x40342),x40343),f331(f18(f854(x40342,a840),x40341),x40344))),f331(f331(f256(x40341,x40342),x40345),f331(f18(f854(x40342,a840),x40341),x40344))),f331(f331(f256(x40341,x40342),f331(f331(f3(f854(x40341,a840)),x40343),x40345)),f331(f18(f854(x40342,a840),x40341),x40344)))
% 51.10/50.81 [4035]E(f331(f331(f108(f854(f853(x40351,x40352),a840)),f331(f331(f256(x40351,x40352),x40353),f331(f18(f854(x40352,a840),x40351),x40354))),f331(f331(f256(x40351,x40352),x40355),f331(f18(f854(x40352,a840),x40351),x40354))),f331(f331(f256(x40351,x40352),f331(f331(f108(f854(x40351,a840)),x40353),x40355)),f331(f18(f854(x40352,a840),x40351),x40354)))
% 51.10/50.81 [4036]E(f331(f331(f109(f854(f853(x40361,x40362),a840)),f331(f331(f256(x40361,x40362),x40363),f331(f18(f854(x40362,a840),x40361),x40364))),f331(f331(f256(x40361,x40362),x40365),f331(f18(f854(x40362,a840),x40361),x40364))),f331(f331(f256(x40361,x40362),f331(f331(f109(f854(x40361,a840)),x40363),x40365)),f331(f18(f854(x40362,a840),x40361),x40364)))
% 51.10/50.81 [4076]E(f331(f331(f147(x40761,x40762),x40763),f331(f131(x40761,f331(f80(x40762,a840,x40761,x40764),x40763)),x40765)),f331(f131(x40762,x40764),f331(f331(f147(x40761,x40762),x40763),x40765)))
% 51.10/50.81 [4083]E(f331(f185(f848(x40831)),f331(f131(x40831,x40832),f331(f331(f147(x40833,x40831),x40834),x40835))),f331(f185(f848(x40833)),f331(f131(x40833,f331(f80(x40831,a840,x40833,x40832),x40834)),x40835)))
% 51.10/50.81 [4217]E(f331(f331(f108(f854(x42171,a840)),f331(f331(f3(f854(x42171,a840)),f174(x42171,x42172,x42173)),f331(f264(x42171),f331(f331(f9(x42171,f854(x42171,a840),a840),f333(x42171)),f331(f331(f3(f854(x42171,a840)),x42174),f174(x42171,x42172,x42175)))))),f331(f264(x42171),f331(f331(f9(x42171,f854(x42171,a840),a840),f333(x42171)),f331(f331(f109(f854(x42171,a840)),x42174),f174(x42171,x42172,x42175))))),f174(x42171,x42172,f83(x42171,f851(x42172),x42173,x42175,x42174)))
% 51.10/50.81 [4289]E(f331(f149(f848(f853(x42891,x42892)),x42892,f120(f853(x42891,x42892)),f331(f331(f9(x42892,f854(f848(x42892),f848(f853(x42891,x42892))),f854(f848(x42892),f848(f853(x42891,x42892)))),f331(f331(f10(f854(f848(f853(x42891,x42892)),f848(f853(x42891,x42892))),f854(f854(f848(x42892),f848(f853(x42891,x42892))),f854(f848(x42892),f848(f853(x42891,x42892)))),x42892),f10(f848(f853(x42891,x42892)),f848(f853(x42891,x42892)),f848(x42892))),f331(f331(f10(f853(x42891,x42892),f854(f848(f853(x42891,x42892)),f848(f853(x42891,x42892))),x42892),f145(f853(x42891,x42892))),f331(f249(x42891,x42892),x42893)))),f331(f172(x42891,x42892),x42894))),x42895),f331(f331(f172(x42891,x42892),f331(f331(f145(x42891),x42893),x42894)),x42895))
% 51.10/50.81 [3780]E(f331(f331(f152(x37801,f331(f331(f152(x37801,x37802),x37803),x37804)),x37803),x37805),f331(f331(f152(x37801,x37802),x37803),x37805))
% 51.10/50.81 [3829]E(f331(f267(x38291,x38292),f331(f331(f310(f853(x38291,x38292)),f331(f331(f249(x38291,x38292),x38293),x38294)),x38295)),f331(f331(f310(x38292),x38294),f331(f267(x38291,x38292),x38295)))
% 51.10/50.81 [3830]E(f331(f269(x38301,x38302),f331(f331(f310(f853(x38301,x38302)),f331(f331(f249(x38301,x38302),x38303),x38304)),x38305)),f331(f331(f310(x38301),x38303),f331(f269(x38301,x38302),x38305)))
% 51.10/50.81 [3878]E(f126(x38781,x38782,f331(x38783,x38784),f331(f331(f9(x38781,a106,f849(f851(x38782))),x38785),x38784)),f331(f197(x38781,x38782,x38783,x38785),x38784))
% 51.10/50.81 [3907]E(f331(f331(f3(f854(f853(x39071,x39072),a840)),f331(f331(f256(x39071,x39072),x39073),x39074)),f331(f331(f256(x39071,x39072),x39075),x39074)),f331(f331(f256(x39071,x39072),f331(f331(f3(f854(x39071,a840)),x39073),x39075)),x39074))
% 51.10/50.81 [3908]E(f331(f331(f108(f854(f853(x39081,x39082),a840)),f331(f331(f256(x39081,x39082),x39083),x39084)),f331(f331(f256(x39081,x39082),x39085),x39084)),f331(f331(f256(x39081,x39082),f331(f331(f108(f854(x39081,a840)),x39083),x39085)),x39084))
% 51.10/50.81 [3909]E(f331(f331(f109(f854(f853(x39091,x39092),a840)),f331(f331(f256(x39091,x39092),x39093),x39094)),f331(f331(f256(x39091,x39092),x39095),x39094)),f331(f331(f256(x39091,x39092),f331(f331(f109(f854(x39091,a840)),x39093),x39095)),x39094))
% 51.10/50.81 [3971]E(f331(f331(f108(f854(x39711,a840)),f331(f331(f51(x39712,f854(x39711,a840)),x39713),x39714)),f331(f331(f51(x39712,f854(x39711,a840)),x39715),x39714)),f331(f331(f51(x39712,f854(x39711,a840)),f331(f331(f108(f854(x39712,a840)),x39713),x39715)),x39714))
% 51.10/50.81 [3972]E(f331(f331(f109(f854(x39721,a840)),f331(f331(f52(x39722,f854(x39721,a840)),x39723),x39724)),f331(f331(f52(x39722,f854(x39721,a840)),x39725),x39724)),f331(f331(f52(x39722,f854(x39721,a840)),f331(f331(f108(f854(x39722,a840)),x39723),x39725)),x39724))
% 51.10/50.81 [3981]E(f331(f331(f51(x39811,f854(x39812,a840)),x39813),f331(f331(f10(f854(x39812,a840),f854(x39812,a840),x39811),f331(f3(f854(x39812,a840)),x39814)),x39815)),f331(f331(f3(f854(x39812,a840)),x39814),f331(f331(f52(x39811,f854(x39812,a840)),x39813),x39815)))
% 51.10/50.81 [3982]E(f331(f331(f52(x39821,f854(x39822,a840)),x39823),f331(f331(f10(f854(x39822,a840),f854(x39822,a840),x39821),f331(f108(f854(x39822,a840)),x39824)),x39825)),f331(f331(f108(f854(x39822,a840)),x39824),f331(f331(f52(x39821,f854(x39822,a840)),x39823),x39825)))
% 51.10/50.81 [3983]E(f331(f331(f52(x39831,f854(x39832,a840)),x39833),f331(f331(f10(f854(x39832,a840),f854(x39832,a840),x39831),f331(f108(f854(x39832,a840)),x39834)),x39835)),f331(f331(f108(f854(x39832,a840)),x39834),f331(f331(f52(x39831,f854(x39832,a840)),x39833),x39835)))
% 51.10/50.81 [3984]E(f331(f331(f51(x39841,f854(x39842,a840)),x39843),f331(f331(f10(f854(x39842,a840),f854(x39842,a840),x39841),f331(f109(f854(x39842,a840)),x39844)),x39845)),f331(f331(f109(f854(x39842,a840)),x39844),f331(f331(f51(x39841,f854(x39842,a840)),x39843),x39845)))
% 51.10/50.81 [3985]E(f331(f331(f51(x39851,f854(x39852,a840)),x39853),f331(f331(f10(f854(x39852,a840),f854(x39852,a840),x39851),f331(f109(f854(x39852,a840)),x39854)),x39855)),f331(f331(f109(f854(x39852,a840)),x39854),f331(f331(f51(x39851,f854(x39852,a840)),x39853),x39855)))
% 51.10/50.81 [3986]E(f331(f331(f51(x39861,f854(x39862,a840)),x39863),f331(f331(f10(f854(x39862,a840),f854(x39862,a840),x39861),f331(f3(f854(x39862,a840)),x39864)),x39865)),f331(f331(f3(f854(x39862,a840)),x39864),f331(f331(f52(x39861,f854(x39862,a840)),x39863),x39865)))
% 51.10/50.81 [3987]E(f331(f331(f51(x39871,f854(x39872,a840)),x39873),f331(f331(f10(f854(x39872,a840),f854(x39872,a840),x39871),f331(f109(f854(x39872,a840)),x39874)),x39875)),f331(f331(f109(f854(x39872,a840)),x39874),f331(f331(f51(x39871,f854(x39872,a840)),x39873),x39875)))
% 51.10/50.81 [3988]E(f331(f331(f52(x39881,f854(x39882,a840)),x39883),f331(f331(f10(f854(x39882,a840),f854(x39882,a840),x39881),f331(f108(f854(x39882,a840)),x39884)),x39885)),f331(f331(f108(f854(x39882,a840)),x39884),f331(f331(f52(x39881,f854(x39882,a840)),x39883),x39885)))
% 51.10/50.81 [4044]E(f180(f848(x40441),f331(f331(f145(x40441),x40442),x40443),f331(f331(f10(f848(x40441),f848(x40441),a847),f331(f145(x40441),x40444)),f331(f331(f9(a847,x40441,f848(x40441)),f152(x40441,x40443)),x40442)),x40445),f331(f331(f152(x40441,f331(f331(f145(x40441),x40444),x40443)),x40445),x40442))
% 51.10/50.81 [4048]E(f331(f331(f51(x40481,f854(f853(x40482,x40483),a840)),x40484),f331(f331(f10(f854(f853(x40483,x40482),a840),f854(f853(x40482,x40483),a840),x40481),f286(x40483,x40482)),x40485)),f331(f286(x40483,x40482),f331(f331(f51(x40481,f854(f853(x40483,x40482),a840)),x40484),x40485)))
% 51.10/50.81 [4049]E(f331(f331(f52(x40491,f854(f853(x40492,x40493),a840)),x40494),f331(f331(f10(f854(f853(x40493,x40492),a840),f854(f853(x40492,x40493),a840),x40491),f286(x40493,x40492)),x40495)),f331(f286(x40493,x40492),f331(f331(f52(x40491,f854(f853(x40493,x40492),a840)),x40494),x40495)))
% 51.10/50.81 [4102]E(f174(x41021,x41022,f331(f331(f20(x41021,f851(x41023),f851(x41022)),f331(f331(f10(f854(x41023,x41022),f854(f851(x41023),f851(x41022)),x41021),f203(x41023,x41022)),x41024)),x41025)),f174(x41021,x41023,x41025))
% 51.10/50.81 [4152]P1(f331(f331(f240(f854(x41521,a840)),f331(f331(f3(f854(x41521,a840)),f331(f311(x41522,x41521,x41523),x41524)),f331(f311(x41522,x41521,x41523),x41525))),f331(f311(x41522,x41521,x41523),f331(f331(f3(f854(x41522,a840)),x41524),x41525))))
% 51.10/50.81 [4293]E(f331(f149(f848(f853(x42931,x42932)),x42931,f120(f853(x42931,x42932)),f331(f331(f9(x42931,f854(f848(x42931),f848(f853(x42931,x42932))),f854(f848(x42931),f848(f853(x42931,x42932)))),f331(f331(f10(f854(f848(f853(x42931,x42932)),f848(f853(x42931,x42932))),f854(f854(f848(x42931),f848(f853(x42931,x42932))),f854(f848(x42931),f848(f853(x42931,x42932)))),x42931),f10(f848(f853(x42931,x42932)),f848(f853(x42931,x42932)),f848(x42931))),f331(f331(f10(f853(x42931,x42932),f854(f848(f853(x42931,x42932)),f848(f853(x42931,x42932))),x42931),f145(f853(x42931,x42932))),f331(f331(f9(x42931,x42932,f853(x42931,x42932)),f249(x42931,x42932)),x42933)))),f331(f331(f9(f848(x42931),f848(x42932),f848(f853(x42931,x42932))),f172(x42931,x42932)),x42934))),x42935),f331(f331(f172(x42931,x42932),x42935),f331(f331(f145(x42932),x42933),x42934)))
% 51.10/50.81 [4310]E(f331(f137(f854(x43101,f851(x43102)),f853(x43101,x43102),f331(f331(f10(f854(x43101,f854(x43102,f854(x43101,f851(x43102)))),f854(f853(x43101,x43102),f854(x43101,f851(x43102))),f854(x43101,f851(x43102))),f259(x43101,x43102,f854(x43101,f851(x43102)))),f331(f331(f9(f854(x43101,f851(x43102)),f854(x43102,f851(x43102)),f854(x43101,f854(x43102,f854(x43101,f851(x43102))))),f331(f331(f10(f854(x43101,f854(f854(x43102,f851(x43102)),f854(x43102,f854(x43101,f851(x43102))))),f854(f854(x43102,f851(x43102)),f854(x43101,f854(x43102,f854(x43101,f851(x43102))))),f854(x43101,f851(x43102))),f9(x43101,f854(x43102,f851(x43102)),f854(x43102,f854(x43101,f851(x43102))))),f331(f331(f10(f854(x43101,f854(f851(x43102),f854(x43101,f851(x43102)))),f854(x43101,f854(f854(x43102,f851(x43102)),f854(x43102,f854(x43101,f851(x43102))))),f854(x43101,f851(x43102))),f331(f10(f854(f851(x43102),f854(x43101,f851(x43102))),f854(f854(x43102,f851(x43102)),f854(x43102,f854(x43101,f851(x43102)))),x43101),f10(f851(x43102),f854(x43101,f851(x43102)),x43102))),f79(x43101,f851(x43102))))),f234(x43102))),x43103),f331(f331(f172(x43101,x43102),x43104),x43105)),f175(x43101,x43102,x43103,f171(x43101,x43102,f331(f160(f853(x43101,x43102)),f331(f331(f172(x43101,x43102),x43104),x43105)))))
% 51.10/50.81 [4012]E(f331(f331(f108(f854(x40121,a840)),f331(f285(x40122,x40121,x40123),x40124)),f331(f285(x40122,x40121,x40125),x40124)),f331(f285(x40122,x40121,f331(f331(f108(f854(f853(x40122,x40121),a840)),x40123),x40125)),x40124))
% 51.10/50.81 [4051]E(f331(f331(f130(f853(x40511,x40512)),f331(f331(f172(x40511,x40512),x40513),f331(f331(f164(x40512),f331(f185(f848(x40511)),x40513)),x40514))),f331(f331(f172(x40511,x40512),x40515),f331(f331(f133(x40512),f331(f185(f848(x40511)),x40513)),x40514))),f331(f331(f172(x40511,x40512),f331(f331(f130(x40511),x40513),x40515)),x40514))
% 51.10/50.81 [4080]E(f174(x40801,x40802,f175(x40801,x40802,x40803,f171(x40801,x40802,f331(f160(f853(x40801,x40802)),f331(f331(f172(x40801,x40802),x40804),x40805))))),f331(f331(f108(f854(x40801,a840)),f331(f163(x40801),f331(f331(f164(x40801),f331(f185(f848(x40802)),x40805)),x40804))),f174(x40801,x40802,x40803)))
% 51.10/50.81 [4155]E(f331(f331(f256(x41551,x41552),x41553),f331(f331(f20(x41551,f854(x41552,a840),f854(x41552,a840)),f331(f331(f10(f854(x41552,a840),f854(f854(x41552,a840),f854(x41552,a840)),x41551),f3(f854(x41552,a840))),x41554)),x41555)),f331(f331(f3(f854(f853(x41551,x41552),a840)),f331(f331(f256(x41551,x41552),x41553),x41554)),f331(f331(f256(x41551,x41552),x41553),x41555)))
% 51.10/50.81 [4156]E(f331(f331(f256(x41561,x41562),x41563),f331(f331(f20(x41561,f854(x41562,a840),f854(x41562,a840)),f331(f331(f10(f854(x41562,a840),f854(f854(x41562,a840),f854(x41562,a840)),x41561),f108(f854(x41562,a840))),x41564)),x41565)),f331(f331(f108(f854(f853(x41561,x41562),a840)),f331(f331(f256(x41561,x41562),x41563),x41564)),f331(f331(f256(x41561,x41562),x41563),x41565)))
% 51.10/50.81 [4157]E(f331(f331(f256(x41571,x41572),x41573),f331(f331(f20(x41571,f854(x41572,a840),f854(x41572,a840)),f331(f331(f10(f854(x41572,a840),f854(f854(x41572,a840),f854(x41572,a840)),x41571),f109(f854(x41572,a840))),x41574)),x41575)),f331(f331(f109(f854(f853(x41571,x41572),a840)),f331(f331(f256(x41571,x41572),x41573),x41574)),f331(f331(f256(x41571,x41572),x41573),x41575)))
% 51.10/50.81 [4158]E(f331(f331(f51(x41581,f854(x41582,a840)),x41583),f331(f331(f9(x41581,f854(x41582,a840),f854(x41582,a840)),f331(f331(f10(f854(x41582,a840),f854(f854(x41582,a840),f854(x41582,a840)),x41581),f3(f854(x41582,a840))),x41584)),x41585)),f331(f331(f3(f854(x41582,a840)),f331(f331(f51(x41581,f854(x41582,a840)),x41583),x41584)),x41585))
% 51.10/50.81 [4159]E(f331(f331(f52(x41591,f854(x41592,a840)),x41593),f331(f331(f9(x41591,f854(x41592,a840),f854(x41592,a840)),f331(f331(f10(f854(x41592,a840),f854(f854(x41592,a840),f854(x41592,a840)),x41591),f108(f854(x41592,a840))),x41594)),x41595)),f331(f331(f108(f854(x41592,a840)),f331(f331(f52(x41591,f854(x41592,a840)),x41593),x41594)),x41595))
% 51.10/50.81 [4160]E(f331(f331(f51(x41601,f854(x41602,a840)),x41603),f331(f331(f9(x41601,f854(x41602,a840),f854(x41602,a840)),f331(f331(f10(f854(x41602,a840),f854(f854(x41602,a840),f854(x41602,a840)),x41601),f109(f854(x41602,a840))),x41604)),x41605)),f331(f331(f109(f854(x41602,a840)),f331(f331(f51(x41601,f854(x41602,a840)),x41603),x41604)),x41605))
% 51.10/50.81 [4161]E(f331(f331(f51(x41611,f854(x41612,a840)),x41613),f331(f331(f9(x41611,f854(x41612,a840),f854(x41612,a840)),f331(f331(f10(f854(x41612,a840),f854(f854(x41612,a840),f854(x41612,a840)),x41611),f3(f854(x41612,a840))),x41614)),x41615)),f331(f331(f3(f854(x41612,a840)),f331(f331(f51(x41611,f854(x41612,a840)),x41613),x41614)),x41615))
% 51.10/50.81 [4162]E(f331(f331(f51(x41621,f854(x41622,a840)),x41623),f331(f331(f9(x41621,f854(x41622,a840),f854(x41622,a840)),f331(f331(f10(f854(x41622,a840),f854(f854(x41622,a840),f854(x41622,a840)),x41621),f109(f854(x41622,a840))),x41624)),x41625)),f331(f331(f109(f854(x41622,a840)),f331(f331(f51(x41621,f854(x41622,a840)),x41623),x41624)),x41625))
% 51.10/50.81 [4163]E(f331(f331(f52(x41631,f854(x41632,a840)),x41633),f331(f331(f9(x41631,f854(x41632,a840),f854(x41632,a840)),f331(f331(f10(f854(x41632,a840),f854(f854(x41632,a840),f854(x41632,a840)),x41631),f108(f854(x41632,a840))),x41634)),x41635)),f331(f331(f108(f854(x41632,a840)),f331(f331(f52(x41631,f854(x41632,a840)),x41633),x41634)),x41635))
% 51.10/50.81 [4167]E(f331(f331(f51(x41671,f854(x41672,a840)),x41673),f331(f331(f20(x41671,f854(x41672,a840),f854(x41672,a840)),f331(f331(f10(f854(x41672,a840),f854(f854(x41672,a840),f854(x41672,a840)),x41671),f108(f854(x41672,a840))),x41674)),x41675)),f331(f331(f108(f854(x41672,a840)),f331(f331(f51(x41671,f854(x41672,a840)),x41673),x41674)),f331(f331(f51(x41671,f854(x41672,a840)),x41673),x41675)))
% 51.10/50.81 [4168]E(f331(f331(f52(x41681,f854(x41682,a840)),x41683),f331(f331(f20(x41681,f854(x41682,a840),f854(x41682,a840)),f331(f331(f10(f854(x41682,a840),f854(f854(x41682,a840),f854(x41682,a840)),x41681),f109(f854(x41682,a840))),x41684)),x41685)),f331(f331(f109(f854(x41682,a840)),f331(f331(f52(x41681,f854(x41682,a840)),x41683),x41684)),f331(f331(f52(x41681,f854(x41682,a840)),x41683),x41685)))
% 51.10/50.81 [4180]E(f331(f331(f51(x41801,f854(x41802,a840)),x41803),f331(f331(f20(x41801,f854(x41802,a840),f854(x41802,a840)),f331(f331(f10(f854(x41802,a840),f854(f854(x41802,a840),f854(x41802,a840)),x41801),f108(f854(x41802,a840))),x41804)),x41805)),f331(f331(f108(f854(x41802,a840)),f49(f854(x41802,a840),f331(f311(x41801,f854(x41802,a840),x41804),x41803))),f49(f854(x41802,a840),f331(f311(x41801,f854(x41802,a840),x41805),x41803))))
% 51.10/50.81 [4181]E(f331(f331(f52(x41811,f854(x41812,a840)),x41813),f331(f331(f20(x41811,f854(x41812,a840),f854(x41812,a840)),f331(f331(f10(f854(x41812,a840),f854(f854(x41812,a840),f854(x41812,a840)),x41811),f109(f854(x41812,a840))),x41814)),x41815)),f331(f331(f109(f854(x41812,a840)),f50(f854(x41812,a840),f331(f311(x41811,f854(x41812,a840),x41814),x41813))),f50(f854(x41812,a840),f331(f311(x41811,f854(x41812,a840),x41815),x41813))))
% 51.10/50.81 [4092]E(f331(f331(f130(f853(x40921,x40922)),f331(f331(f172(x40921,x40922),f331(f331(f164(x40921),f331(f185(f848(x40922)),x40923)),x40924)),x40923)),f331(f331(f172(x40921,x40922),f331(f331(f133(x40921),f331(f185(f848(x40922)),x40923)),x40924)),x40925)),f331(f331(f172(x40921,x40922),x40924),f331(f331(f130(x40922),x40923),x40925)))
% 51.10/50.81 [4206]E(f92(x42061,f331(f331(f20(x42061,a840,a840),f331(f331(f10(a840,f854(a840,a840),x42061),a329),f331(f331(f9(x42061,f854(x42061,a840),a840),f333(x42061)),x42062))),f331(f331(f9(x42061,x42063,a840),f331(f331(f10(x42063,f854(x42063,a840),x42061),a328),x42064)),x42065))),f331(f84(x42061,x42063,x42062,x42064),x42065))
% 51.10/50.81 [4256]E(f331(f331(f93(a1,x42561),f331(f111(a1),f331(f331(f87(a1),x42562),a104))),f331(f331(f20(a1,x42561,x42561),f331(f331(f9(a1,x42561,f854(x42561,x42561)),f331(f331(f10(a840,f854(x42561,f854(x42561,x42561)),a1),f103(x42561)),a190)),f180(x42561,x42563,x42564,x42565))),f331(f331(f10(a847,x42561,a1),x42564),f331(f331(f9(a1,a847,a847),f331(f331(f10(a847,f854(a847,a847),a1),f87(a847)),a112)),x42565)))),f180(x42561,x42563,x42564,f331(f331(f87(a847),f331(f111(a847),x42562)),x42565)))
% 51.10/50.81 [4290]E(f171(x42901,x42902,f331(f331(f147(f853(x42901,x42903),f853(x42901,x42902)),f331(f259(x42901,x42903,f853(x42901,x42902)),f331(f331(f9(x42901,f854(x42903,x42902),f854(x42903,f853(x42901,x42902))),f331(f331(f10(f854(x42902,f853(x42901,x42902)),f854(f854(x42903,x42902),f854(x42903,f853(x42901,x42902))),x42901),f10(x42902,f853(x42901,x42902),x42903)),f249(x42901,x42902))),x42904))),x42905)),f331(f80(f851(x42903),f851(x42902),x42901,f331(f203(x42903,x42902),x42904)),f171(x42901,x42903,x42905)))
% 51.10/50.81 [4249]E(f174(x42491,x42492,f331(f331(f20(x42491,f851(x42492),f851(x42492)),f331(f331(f20(x42491,f851(x42492),f854(f851(x42492),f851(x42492))),f331(f331(f10(a840,f854(f851(x42492),f854(f851(x42492),f851(x42492))),x42491),f103(f851(x42492))),x42493)),x42494)),x42495)),f331(f331(f108(f854(x42491,a840)),f331(f331(f109(f854(x42491,a840)),f174(x42491,x42492,x42494)),f331(f264(x42491),x42493))),f331(f331(f109(f854(x42491,a840)),f174(x42491,x42492,x42495)),f331(f264(x42491),f331(f331(f10(a840,a840,x42491),a327),x42493)))))
% 51.10/50.81 [4288]E(f331(f331(f93(a1,x42881),f331(f111(a1),f331(f331(f87(a1),x42882),a104))),f331(f331(f20(a1,x42881,x42881),f331(f331(f9(a1,x42881,f854(x42881,x42881)),f331(f331(f10(a840,f854(x42881,f854(x42881,x42881)),a1),f103(x42881)),a190)),f331(f179(x42881,x42883,x42884),x42885))),f331(f331(f20(a1,x42881,x42881),f331(f331(f10(a847,f854(x42881,x42881),a1),x42884),f331(f331(f9(a1,a847,a847),f331(f331(f10(a847,f854(a847,a847),a1),f87(a847)),a112)),x42885))),f331(f331(f10(a847,x42881,a1),f179(x42881,x42883,x42884)),f331(f331(f9(a1,a847,a847),f331(f331(f10(a847,f854(a847,a847),a1),f87(a847)),a112)),x42885))))),f331(f179(x42881,x42883,x42884),f331(f331(f87(a847),f331(f111(a847),x42882)),x42885)))
% 51.10/50.81 [4323]E(f331(f264(f853(x43231,x43232)),f331(f259(x43231,x43232,a840),f331(f331(f10(f854(x43232,f854(x43233,a840)),f854(x43232,a840),x43231),f331(f10(f854(x43233,a840),a840,x43232),f94(x43233))),f331(f331(f9(x43231,f854(x43232,f854(x43233,a840)),f854(x43232,f854(x43233,a840))),f331(f331(f10(f854(f854(x43233,a840),f854(x43233,a840)),f854(f854(x43232,f854(x43233,a840)),f854(x43232,f854(x43233,a840))),x43231),f10(f854(x43233,a840),f854(x43233,a840),x43232)),f331(f331(f10(f854(x43233,f854(a840,a840)),f854(f854(x43233,a840),f854(x43233,a840)),x43231),f20(x43233,a840,a840)),f331(f331(f10(f854(x43233,a840),f854(x43233,f854(a840,a840)),x43231),f331(f10(a840,f854(a840,a840),x43233),a329)),f331(f331(f9(x43231,f854(f853(x43231,x43233),a840),f854(x43233,a840)),f331(f331(f10(f854(x43233,f854(f854(f853(x43231,x43233),a840),a840)),f854(f854(f853(x43231,x43233),a840),f854(x43233,a840)),x43231),f9(x43233,f854(f853(x43231,x43233),a840),a840)),f331(f331(f10(f854(x43233,f853(x43231,x43233)),f854(x43233,f854(f854(f853(x43231,x43233),a840),a840)),x43231),f331(f10(f853(x43231,x43233),f854(f854(f853(x43231,x43233),a840),a840),x43233),f333(f853(x43231,x43233)))),f249(x43231,x43233)))),x43234))))),f331(f331(f9(x43232,f854(f853(x43233,x43232),a840),f854(x43233,a840)),f331(f331(f10(f854(x43233,f854(f854(f853(x43233,x43232),a840),a840)),f854(f854(f853(x43233,x43232),a840),f854(x43233,a840)),x43232),f9(x43233,f854(f853(x43233,x43232),a840),a840)),f331(f331(f10(f854(x43233,f853(x43233,x43232)),f854(x43233,f854(f854(f853(x43233,x43232),a840),a840)),x43232),f331(f10(f853(x43233,x43232),f854(f854(f853(x43233,x43232),a840),a840),x43233),f333(f853(x43233,x43232)))),f331(f9(x43233,x43232,f853(x43233,x43232)),f249(x43233,x43232))))),x43235))))),f331(f331(f289(x43231,x43233,x43232),x43234),x43235))
% 51.10/50.81 [4419]~E(f34(x44191,x44192,x44193),f33(x44194,x44195,x44196))
% 51.10/50.81 [4420]~E(f34(x44201,x44202,x44203),f33(x44204,x44205,x44206))
% 51.10/50.81 [4421]~E(f35(x44211,x44212,x44213),f33(x44214,x44215,x44216))
% 51.10/50.81 [4422]~E(f35(x44221,x44222,x44223),f34(x44224,x44225,x44226))
% 51.10/50.81 [4423]~E(f35(x44231,x44232,x44233),f33(x44234,x44235,x44236))
% 51.10/50.81 [4424]~E(f35(x44241,x44242,x44243),f34(x44244,x44245,x44246))
% 51.10/50.81 [3939]E(f225(x39391,x39392,x39393,x39394,f222(x39391,x39392,x39395,x39396)),f331(f331(x39394,x39395),x39396))
% 51.10/50.81 [3940]E(f226(x39401,x39402,x39403,x39404,f222(x39401,x39402,x39405,x39406)),f331(f331(x39404,x39405),x39406))
% 51.10/50.81 [4196]E(f331(f80(f853(x41961,x41962),x41962,f853(x41963,x41964),f258(x41961,x41962)),f260(x41963,x41961,x41964,x41962,x41965,x41966)),f331(f80(x41964,x41962,f853(x41963,x41964),x41966),f258(x41963,x41964)))
% 51.10/50.81 [4197]E(f331(f80(f853(x41971,x41972),x41971,f853(x41973,x41974),f248(x41971,x41972)),f260(x41973,x41971,x41974,x41972,x41975,x41976)),f331(f80(x41973,x41971,f853(x41973,x41974),x41975),f248(x41973,x41974)))
% 51.10/50.81 [3804]E(f331(f331(f80(x38041,x38042,x38043,x38044),x38045),x38046),f331(x38044,f331(x38045,x38046)))
% 51.10/50.81 [3805]E(f331(f331(f80(x38051,x38052,x38053,x38054),x38055),x38056),f331(x38054,f331(x38055,x38056)))
% 51.10/50.81 [4001]E(f227(x40011,x40012,x40013,x40014,f222(x40011,x40012,x40015,x40016)),f331(f331(f87(a847),f331(f331(f87(a847),f331(x40013,x40015)),f331(x40014,x40016))),f331(a119,f2(a847))))
% 51.10/50.81 [3600]E(f331(f331(f259(x36001,x36002,x36003),x36004),f331(f331(f249(x36001,x36002),x36005),x36006)),f331(f331(x36004,x36005),x36006))
% 51.10/50.81 [3601]E(f331(f331(f259(x36011,x36012,x36013),x36014),f331(f331(f249(x36011,x36012),x36015),x36016)),f331(f331(x36014,x36015),x36016))
% 51.10/50.81 [3602]E(f331(f331(f259(x36021,x36022,x36023),x36024),f331(f331(f249(x36021,x36022),x36025),x36026)),f331(f331(x36024,x36025),x36026))
% 51.10/50.81 [3665]E(f331(f331(f331(f10(x36651,x36652,x36653),x36654),x36655),x36656),f331(x36654,f331(x36655,x36656)))
% 51.10/50.81 [3666]E(f331(f331(f331(f9(x36661,x36662,x36663),x36664),x36665),x36666),f331(f331(x36664,x36666),x36665))
% 51.10/50.81 [3682]E(f331(f331(f331(f20(x36821,x36822,x36823),x36824),x36825),x36826),f331(f331(x36824,x36826),f331(x36825,x36826)))
% 51.10/50.81 [3704]E(f331(f149(x37041,x37042,x37043,x37044),f331(f331(f145(x37042),x37045),x37046)),f331(f331(x37044,x37045),x37046))
% 51.10/50.81 [3808]E(f331(f331(f145(f853(x38081,x38082)),f331(f331(f249(x38081,x38082),x38083),x38084)),f331(f331(f172(x38081,x38082),x38085),x38086)),f331(f331(f172(x38081,x38082),f331(f331(f145(x38081),x38083),x38085)),f331(f331(f145(x38082),x38084),x38086)))
% 51.10/50.81 [3810]E(f331(f331(f147(x38101,x38102),x38103),f331(f331(f152(x38101,x38104),x38105),x38106)),f331(f331(f152(x38102,f331(f331(f147(x38101,x38102),x38103),x38104)),x38105),f331(x38103,x38106)))
% 51.10/50.81 [3832]E(f331(f331(f257(x38321,x38322,x38323,x38324),x38325),x38326),f331(x38324,f331(f331(f249(x38321,x38322),x38325),x38326)))
% 51.10/50.81 [3833]E(f331(f331(f257(x38331,x38332,x38333,x38334),x38335),x38336),f331(x38334,f331(f331(f249(x38331,x38332),x38335),x38336)))
% 51.10/50.81 [3851]E(f331(f137(x38511,x38512,x38513,x38514),f331(f331(f145(x38512),x38515),x38516)),f331(f137(x38511,x38512,x38513,f331(f331(x38513,x38514),x38515)),x38516))
% 51.10/50.81 [3879]E(f262(x38791,x38792,x38793,x38794,f331(f331(f249(x38791,x38792),x38795),x38796)),f331(f331(x38794,x38795),x38796))
% 51.10/50.81 [3964]E(f331(f331(f51(x39641,f854(x39642,a840)),x39643),f331(f80(x39644,f854(x39642,a840),x39641,x39645),x39646)),f331(f331(f51(x39644,f854(x39642,a840)),f331(f311(x39641,x39644,x39646),x39643)),x39645))
% 51.10/50.81 [4014]E(f331(f331(f147(x40141,x40142),x40143),f331(f331(f147(x40144,x40141),x40145),x40146)),f331(f331(f147(x40144,x40142),f331(f80(x40141,x40142,x40144,x40143),x40145)),x40146))
% 51.10/50.81 [4015]E(f331(f331(f147(x40151,x40152),x40153),f331(f331(f147(x40154,x40151),x40155),x40156)),f331(f331(f147(x40154,x40152),f331(f80(x40151,x40152,x40154,x40153),x40155)),x40156))
% 51.10/50.81 [4016]E(f331(f331(f203(x40161,x40162),x40163),f331(f331(f203(x40164,x40161),x40165),x40166)),f331(f331(f203(x40164,x40162),f331(f80(x40161,x40162,x40164,x40163),x40165)),x40166))
% 51.10/50.81 [4017]E(f331(f331(f203(x40171,x40172),x40173),f331(f331(f203(x40174,x40171),x40175),x40176)),f331(f331(f203(x40174,x40172),f331(f80(x40171,x40172,x40174,x40173),x40175)),x40176))
% 51.10/50.81 [4022]E(f331(f311(x40221,x40222,f331(f80(x40223,x40222,x40221,x40224),x40225)),x40226),f331(f311(x40223,x40222,x40224),f331(f311(x40221,x40223,x40225),x40226)))
% 51.10/50.81 [4023]E(f331(f312(x40231,x40232,f331(f80(x40233,x40232,x40231,x40234),x40235)),x40236),f331(f312(x40231,x40233,x40235),f331(f312(x40233,x40232,x40234),x40236)))
% 51.10/50.81 [4050]E(f175(x40501,x40502,x40503,f331(f331(f331(f79(x40501,f851(x40502)),x40504),x40505),f331(f234(x40502),x40506))),f331(f331(f331(f79(x40501,f851(x40502)),f175(x40501,x40502,x40503,x40504)),x40505),f331(f234(x40502),x40506)))
% 51.10/50.81 [4052]E(f331(f137(x40521,x40522,x40523,f331(f137(x40521,x40522,x40523,x40524),x40525)),x40526),f331(f137(x40521,x40522,x40523,x40524),f331(f331(f130(x40522),x40525),x40526)))
% 51.10/50.81 [4186]E(f331(f260(x41861,x41861,x41862,x41863,f39(x41861),x41864),f331(f331(f249(x41861,x41862),x41865),x41866)),f331(f331(f249(x41861,x41863),x41865),f331(x41864,x41866)))
% 51.10/50.81 [4187]E(f331(f260(x41871,x41872,x41873,x41873,x41874,f39(x41873)),f331(f331(f249(x41871,x41873),x41875),x41876)),f331(f331(f249(x41872,x41873),f331(x41874,x41875)),x41876))
% 51.10/50.81 [4272]E(f331(f331(f147(f853(x42721,x42722),f853(x42721,x42723)),f331(f259(x42721,x42722,f853(x42721,x42723)),f331(f331(f9(x42721,f854(x42722,x42723),f854(x42722,f853(x42721,x42723))),f331(f331(f10(f854(x42723,f853(x42721,x42723)),f854(f854(x42722,x42723),f854(x42722,f853(x42721,x42723))),x42721),f10(x42723,f853(x42721,x42723),x42722)),f249(x42721,x42723))),x42724))),f331(f331(f172(x42721,x42722),x42725),x42726)),f331(f331(f172(x42721,x42723),x42725),f331(f331(f147(x42722,x42723),x42724),x42726)))
% 51.10/50.81 [3670]E(f101(x36701,x36702,x36703,f331(f331(f331(f98(x36701),x36704),x36705),x36706)),f331(f331(f331(x36703,x36704),x36705),x36706))
% 51.10/50.81 [3671]E(f102(x36711,x36712,x36713,f331(f331(f331(f98(x36711),x36714),x36715),x36716)),f331(f331(f331(x36713,x36714),x36715),x36716))
% 51.10/50.81 [3863]E(f331(f331(f80(x38631,x38632,x38633,f331(f18(x38632,x38631),x38634)),x38635),x38636),x38634)
% 51.10/50.81 [3897]E(f331(f311(x38971,x38972,x38973),f331(f311(x38974,x38971,x38975),x38976)),f331(f311(x38974,x38972,f331(f331(f10(x38971,x38972,x38974),x38973),x38975)),x38976))
% 51.10/50.81 [3903]E(f331(f331(f51(x39031,f854(x39032,a840)),f331(f311(x39033,x39031,x39034),x39035)),x39036),f331(f331(f51(x39033,f854(x39032,a840)),x39035),f331(f331(f10(x39031,f854(x39032,a840),x39033),x39036),x39034)))
% 51.10/50.81 [3904]E(f331(f331(f52(x39041,f854(x39042,a840)),f331(f311(x39043,x39041,x39044),x39045)),x39046),f331(f331(f52(x39043,f854(x39042,a840)),x39045),f331(f331(f10(x39041,f854(x39042,a840),x39043),x39046),x39044)))
% 51.10/50.81 [3905]E(f331(f331(f51(x39051,f854(x39052,a840)),x39053),f331(f331(f10(x39054,f854(x39052,a840),x39051),x39055),x39056)),f331(f331(f51(x39054,f854(x39052,a840)),f331(f311(x39051,x39054,x39056),x39053)),x39055))
% 51.10/50.81 [3906]E(f331(f331(f52(x39061,f854(x39062,a840)),x39063),f331(f331(f10(x39064,f854(x39062,a840),x39061),x39065),x39066)),f331(f331(f52(x39064,f854(x39062,a840)),f331(f311(x39061,x39064,x39066),x39063)),x39065))
% 51.10/50.81 [3966]E(f331(f331(f51(x39661,f854(x39662,a840)),x39663),f331(f331(f10(f854(x39664,a840),f854(x39662,a840),x39661),f311(x39664,x39662,x39665)),x39666)),f331(f311(x39664,x39662,x39665),f331(f331(f51(x39661,f854(x39664,a840)),x39663),x39666)))
% 51.10/50.81 [3967]E(f331(f331(f51(x39671,f854(x39672,a840)),x39673),f331(f331(f10(f854(x39674,a840),f854(x39672,a840),x39671),f285(x39674,x39672,x39675)),x39676)),f331(f285(x39674,x39672,x39675),f331(f331(f51(x39671,f854(x39674,a840)),x39673),x39676)))
% 51.10/50.81 [3968]E(f331(f331(f51(x39681,f854(x39682,a840)),x39683),f331(f331(f10(f854(x39684,a840),f854(x39682,a840),x39681),f312(x39682,x39684,x39685)),x39686)),f331(f312(x39682,x39684,x39685),f331(f331(f51(x39681,f854(x39684,a840)),x39683),x39686)))
% 51.10/50.81 [3969]E(f331(f331(f52(x39691,f854(x39692,a840)),x39693),f331(f331(f10(f854(x39694,a840),f854(x39692,a840),x39691),f312(x39692,x39694,x39695)),x39696)),f331(f312(x39692,x39694,x39695),f331(f331(f52(x39691,f854(x39694,a840)),x39693),x39696)))
% 51.10/50.81 [4057]E(f331(f137(x40571,x40572,f331(f9(x40572,x40571,x40571),x40573),x40574),f331(f160(x40572),f331(f331(f145(x40572),x40575),x40576))),f331(f331(x40573,x40575),f331(f137(x40571,x40572,f331(f9(x40572,x40571,x40571),x40573),x40574),f331(f160(x40572),x40576))))
% 51.10/50.81 [4116]E(f331(f331(f20(f853(x41161,x41162),x41162,x41163),f331(f331(f10(x41164,f854(x41162,x41163),f853(x41161,x41162)),x41165),f331(f331(f10(x41161,x41164,f853(x41161,x41162)),x41166),f248(x41161,x41162)))),f258(x41161,x41162)),f331(f259(x41161,x41162,x41163),f331(f331(f10(x41164,f854(x41162,x41163),x41161),x41165),x41166)))
% 51.10/50.81 [4123]E(f331(f137(x41231,x41232,f331(f9(x41232,x41231,x41231),x41233),f331(f137(x41231,x41232,f331(f9(x41232,x41231,x41231),x41233),x41234),f331(f160(x41232),x41235))),f331(f160(x41232),x41236)),f331(f137(x41231,x41232,f331(f9(x41232,x41231,x41231),x41233),x41234),f331(f160(x41232),f331(f331(f130(x41232),x41236),x41235))))
% 51.10/50.81 [4125]E(f331(f331(f147(f853(x41251,x41252),f853(x41253,x41252)),f331(f259(x41251,x41252,f853(x41253,x41252)),f331(f331(f10(x41253,f854(x41252,f853(x41253,x41252)),x41251),f249(x41253,x41252)),x41254))),f331(f331(f172(x41251,x41252),x41255),x41256)),f331(f331(f172(x41253,x41252),f331(f331(f147(x41251,x41253),x41254),x41255)),x41256))
% 51.10/50.81 [4170]P1(f331(f331(f240(f854(x41701,a840)),f331(f285(x41702,x41701,x41703),f331(f331(f52(x41704,f854(x41702,a840)),x41705),x41706))),f331(f331(f52(x41704,f854(x41701,a840)),x41705),f331(f331(f10(f854(x41702,a840),f854(x41701,a840),x41704),f285(x41702,x41701,x41703)),x41706))))
% 51.10/50.81 [3979]E(f331(f331(f172(x39791,x39792),f331(f331(f152(x39791,x39793),x39794),f331(f248(x39791,x39792),x39795))),f331(f331(f152(x39792,x39796),x39794),f331(f258(x39791,x39792),x39795))),f331(f331(f152(f853(x39791,x39792),f331(f331(f172(x39791,x39792),x39793),x39796)),x39794),x39795))
% 51.10/50.81 [4039]E(f331(f331(f108(f854(f853(x40391,x40392),a840)),f331(f331(f289(x40391,x40393,x40392),x40394),x40395)),f331(f331(f289(x40391,x40393,x40392),x40394),x40396)),f331(f331(f289(x40391,x40393,x40392),x40394),f331(f331(f108(f854(f853(x40393,x40392),a840)),x40395),x40396)))
% 51.10/50.81 [4136]E(f331(f331(f310(f853(x41361,x41362)),f331(f331(f249(x41361,x41362),x41363),x41364)),f331(f331(f108(f854(f853(x41361,x41362),a840)),f331(f331(f256(x41361,x41362),x41365),f331(f18(f854(x41362,a840),x41361),f331(f331(f310(x41362),x41364),x41366)))),f331(f331(f256(x41361,x41362),f331(f331(f310(x41361),x41363),x41365)),f331(f18(f854(x41362,a840),x41361),x41366)))),f331(f331(f256(x41361,x41362),f331(f331(f310(x41361),x41363),x41365)),f331(f18(f854(x41362,a840),x41361),f331(f331(f310(x41362),x41364),x41366))))
% 51.10/50.81 [4209]E(f331(f331(f109(f854(x42091,a840)),f331(f312(x42091,x42092,f331(f80(f853(x42092,x42093),x42092,x42091,f248(x42092,x42093)),x42094)),x42095)),f331(f312(x42091,x42093,f331(f80(f853(x42092,x42093),x42093,x42091,f258(x42092,x42093)),x42094)),x42096)),f331(f312(x42091,f853(x42092,x42093),x42094),f331(f331(f256(x42092,x42093),x42095),f331(f18(f854(x42093,a840),x42092),x42096))))
% 51.10/50.81 [3963]E(f331(f331(f331(f79(x39631,x39632),f331(f331(f331(f79(x39631,x39632),x39633),x39634),x39635)),x39634),x39636),f331(f331(f331(f79(x39631,x39632),x39633),x39634),x39636))
% 51.10/50.81 [4063]E(f331(f331(f108(f854(f853(x40631,x40632),a840)),f331(f331(f289(x40631,x40633,x40632),x40634),x40635)),f331(f331(f289(x40631,x40633,x40632),x40636),x40635)),f331(f331(f289(x40631,x40633,x40632),f331(f331(f108(f854(f853(x40631,x40633),a840)),x40634),x40636)),x40635))
% 51.10/50.81 [4085]E(f175(x40851,x40852,f175(x40851,x40852,x40853,x40854),f171(x40851,x40852,f331(f160(f853(x40851,x40852)),f331(f331(f172(x40851,x40852),x40855),x40856)))),f175(x40851,x40852,x40853,f175(x40851,x40852,x40854,f171(x40851,x40852,f331(f160(f853(x40851,x40852)),f331(f331(f172(x40851,x40852),x40855),x40856))))))
% 51.10/50.81 [4191]E(f331(f331(f51(x41911,f854(x41912,a840)),x41913),f331(f331(f9(x41911,f854(x41914,f854(x41912,a840)),f854(x41912,a840)),f331(f331(f10(f854(x41914,a840),f854(f854(x41914,f854(x41912,a840)),f854(x41912,a840)),x41911),f51(x41914,f854(x41912,a840))),x41915)),x41916)),f331(f331(f51(x41914,f854(x41912,a840)),f331(f331(f51(x41911,f854(x41914,a840)),x41913),x41915)),x41916))
% 51.10/50.81 [4192]E(f331(f331(f51(x41921,f854(x41922,a840)),x41923),f331(f331(f9(x41921,f854(x41924,f854(x41922,a840)),f854(x41922,a840)),f331(f331(f10(f854(x41924,a840),f854(f854(x41924,f854(x41922,a840)),f854(x41922,a840)),x41921),f51(x41924,f854(x41922,a840))),x41925)),x41926)),f331(f331(f51(x41924,f854(x41922,a840)),f331(f331(f51(x41921,f854(x41924,a840)),x41923),x41925)),x41926))
% 51.10/50.81 [4193]E(f331(f331(f52(x41931,f854(x41932,a840)),x41933),f331(f331(f9(x41931,f854(x41934,f854(x41932,a840)),f854(x41932,a840)),f331(f331(f10(f854(x41934,a840),f854(f854(x41934,f854(x41932,a840)),f854(x41932,a840)),x41931),f52(x41934,f854(x41932,a840))),x41935)),x41936)),f331(f331(f52(x41934,f854(x41932,a840)),f331(f331(f51(x41931,f854(x41934,a840)),x41933),x41935)),x41936))
% 51.10/50.81 [4194]E(f331(f331(f51(x41941,f854(x41942,a840)),x41943),f331(f331(f9(x41941,f854(x41944,f854(x41942,a840)),f854(x41942,a840)),f331(f331(f10(f854(x41944,a840),f854(f854(x41944,f854(x41942,a840)),f854(x41942,a840)),x41941),f51(x41944,f854(x41942,a840))),x41945)),x41946)),f331(f331(f51(x41944,f854(x41942,a840)),f331(f331(f51(x41941,f854(x41944,a840)),x41943),x41945)),x41946))
% 51.10/50.81 [4195]E(f331(f331(f52(x41951,f854(x41952,a840)),x41953),f331(f331(f9(x41951,f854(x41954,f854(x41952,a840)),f854(x41952,a840)),f331(f331(f10(f854(x41954,a840),f854(f854(x41954,f854(x41952,a840)),f854(x41952,a840)),x41951),f52(x41954,f854(x41952,a840))),x41955)),x41956)),f331(f331(f52(x41954,f854(x41952,a840)),f331(f331(f51(x41951,f854(x41954,a840)),x41953),x41955)),x41956))
% 51.10/50.81 [4244]E(f331(f259(x42441,x42442,f853(x42443,x42444)),f331(f331(f9(x42441,f854(x42442,x42444),f854(x42442,f853(x42443,x42444))),f331(f331(f10(f854(x42444,f853(x42443,x42444)),f854(f854(x42442,x42444),f854(x42442,f853(x42443,x42444))),x42441),f10(x42444,f853(x42443,x42444),x42442)),f331(f331(f10(x42443,f854(x42444,f853(x42443,x42444)),x42441),f249(x42443,x42444)),x42445))),x42446)),f260(x42441,x42443,x42442,x42444,x42445,x42446))
% 51.10/50.81 [4169]E(f331(f331(f331(f79(x41691,f851(x41692)),f177(x41691,x41692,x41693,f331(f331(f3(f854(x41691,a840)),x41694),f331(f331(f310(x41691),x41695),f184(f854(x41691,a840)))))),x41695),x41696),f331(f331(f331(f79(x41691,f851(x41692)),f177(x41691,x41692,x41693,x41694)),x41695),x41696))
% 51.10/50.81 [4267]E(f331(f311(x42671,x42672,f331(f331(f20(x42671,x42672,x42672),f331(f331(f20(x42671,x42672,f854(x42672,x42672)),f331(f331(f10(a840,f854(x42672,f854(x42672,x42672)),x42671),f103(x42672)),x42673)),x42674)),x42675)),x42676),f331(f331(f108(f854(x42672,a840)),f331(f311(x42671,x42672,x42674),f331(f331(f109(f854(x42671,a840)),x42676),f331(f264(x42671),x42673)))),f331(f311(x42671,x42672,x42675),f331(f331(f109(f854(x42671,a840)),x42676),f331(f264(x42671),f331(f331(f10(a840,a840,x42671),a327),x42673))))))
% 51.10/50.81 [4278]E(f331(f311(x42781,f853(x42782,x42783),f331(f331(f20(x42781,x42783,f853(x42782,x42783)),f331(f331(f10(x42782,f854(x42783,f853(x42782,x42783)),x42781),f249(x42782,x42783)),x42784)),x42785)),x42786),f331(f331(f256(x42782,x42783),f331(f311(x42781,x42782,x42784),x42786)),f331(f331(f10(f854(x42781,a840),f854(x42783,a840),x42782),f311(x42781,x42783,x42785)),f331(f331(f9(x42782,f854(x42781,a840),f854(x42781,a840)),f331(f331(f10(f854(x42781,a840),f854(f854(x42781,a840),f854(x42781,a840)),x42782),f109(f854(x42781,a840))),f331(f331(f10(f854(x42782,a840),f854(x42781,a840),x42782),f312(x42781,x42782,x42784)),f331(f331(f9(x42782,f854(x42782,a840),f854(x42782,a840)),f310(x42782)),f184(f854(x42782,a840)))))),x42786))))
% 51.10/50.81 [4227]E(f331(f258(x42271,x42272),f331(f260(x42273,x42271,x42274,x42272,x42275,x42276),x42277)),f331(x42276,f331(f258(x42273,x42274),x42277)))
% 51.10/50.81 [4228]E(f331(f248(x42281,x42282),f331(f260(x42283,x42281,x42284,x42282,x42285,x42286),x42287)),f331(x42285,f331(f248(x42283,x42284),x42287)))
% 51.10/50.81 [3941]E(f331(f331(f172(x39411,x39412),f331(f331(f152(x39411,x39413),x39414),x39415)),f331(f331(f152(x39412,x39416),x39414),x39417)),f331(f331(f152(f853(x39411,x39412),f331(f331(f172(x39411,x39412),x39413),x39416)),x39414),f331(f331(f249(x39411,x39412),x39415),x39417)))
% 51.10/50.81 [4009]E(f331(f331(f331(f261(x40091,x40092,x40093,x40094),x40095),x40096),x40097),f331(f331(f259(x40092,x40093,x40094),x40096),f331(x40095,x40097)))
% 51.10/50.81 [4010]E(f331(f331(f331(f261(x40101,x40102,x40103,x40104),x40105),x40106),x40107),f331(f331(f259(x40102,x40103,x40104),x40106),f331(x40105,x40107)))
% 51.10/50.81 [4021]E(f331(f331(f331(f261(x40211,x40212,x40213,x40214),x40215),x40216),x40217),f331(f331(x40216,f331(f248(x40212,x40213),f331(x40215,x40217))),f331(f258(x40212,x40213),f331(x40215,x40217))))
% 51.10/50.81 [4070]E(f331(f80(x40701,x40702,x40703,x40704),f331(f80(x40705,x40701,x40703,x40706),x40707)),f331(f80(x40705,x40702,x40703,f331(f80(x40701,x40702,x40705,x40704),x40706)),x40707))
% 51.10/50.81 [4132]E(f331(f80(f851(x41321),f851(x41322),x41323,f331(f203(x41321,x41322),x41324)),f331(f331(f331(f79(x41323,f851(x41321)),x41325),x41326),f331(f234(x41321),x41327))),f331(f331(f331(f79(x41323,f851(x41322)),f331(f80(f851(x41321),f851(x41322),x41323,f331(f203(x41321,x41322),x41324)),x41325)),x41326),f331(f234(x41322),f331(x41324,x41327))))
% 51.10/50.81 [4251]E(f331(f260(x42511,x42512,x42513,x42513,x42514,f39(x42513)),f331(f260(x42511,x42511,x42515,x42513,f39(x42511),x42516),x42517)),f331(f331(f249(x42512,x42513),f331(x42514,f331(f248(x42511,x42515),x42517))),f331(x42516,f331(f258(x42511,x42515),x42517))))
% 51.10/50.81 [4252]E(f331(f260(x42521,x42521,x42522,x42523,f39(x42521),x42524),f331(f260(x42525,x42521,x42522,x42522,x42526,f39(x42522)),x42527)),f331(f331(f249(x42521,x42523),f331(x42526,f331(f248(x42525,x42522),x42527))),f331(x42524,f331(f258(x42525,x42522),x42527))))
% 51.10/50.81 [4265]E(f331(f260(x42651,x42652,x42653,x42653,x42654,f39(x42653)),f331(f260(x42655,x42651,x42653,x42653,x42656,f39(x42653)),x42657)),f331(f260(x42655,x42652,x42653,x42653,f331(f80(x42651,x42652,x42655,x42654),x42656),f39(x42653)),x42657))
% 51.10/50.81 [4266]E(f331(f260(x42661,x42661,x42662,x42663,f39(x42661),x42664),f331(f260(x42661,x42661,x42665,x42662,f39(x42661),x42666),x42667)),f331(f260(x42661,x42661,x42665,x42663,f39(x42661),f331(f80(x42662,x42663,x42665,x42664),x42666)),x42667))
% 51.10/50.81 [4275]E(f331(f260(x42751,x42752,x42753,x42753,x42754,f39(x42753)),f331(f260(x42751,x42751,x42755,x42753,f39(x42751),x42756),x42757)),f331(f260(x42752,x42752,x42755,x42753,f39(x42752),x42756),f331(f260(x42751,x42752,x42755,x42755,x42754,f39(x42755)),x42757)))
% 51.10/50.81 [3976]E(f331(f331(f289(x39761,x39762,x39763),f331(f331(f289(x39761,x39764,x39762),x39765),x39766)),x39767),f331(f331(f289(x39761,x39764,x39763),x39765),f331(f331(f289(x39764,x39762,x39763),x39766),x39767)))
% 51.10/50.81 [4045]E(f331(f331(f259(x40451,x40452,x40453),f331(f80(x40454,f854(x40452,x40453),x40451,x40455),x40456)),x40457),f331(f331(x40455,f331(x40456,f331(f248(x40451,x40452),x40457))),f331(f258(x40451,x40452),x40457)))
% 51.10/50.81 [4095]E(f331(f80(x40951,x40952,x40953,x40954),f331(f331(f331(f79(x40953,x40951),x40955),x40956),x40957)),f331(f331(f331(f79(x40953,x40952),f331(f80(x40951,x40952,x40953,x40954),x40955)),x40956),f331(x40954,x40957)))
% 51.10/50.81 [4128]E(f331(f137(x41281,x41282,f331(f9(x41282,x41281,x41281),x41283),x41284),f331(f160(x41282),f331(f331(f147(x41285,x41282),x41286),x41287))),f331(f137(x41281,x41285,f331(f9(x41285,x41281,x41281),f331(f80(x41282,f854(x41281,x41281),x41285,x41283),x41286)),x41284),f331(f160(x41285),x41287)))
% 51.10/50.81 [4071]E(f331(f331(f51(x40711,f854(f853(x40712,x40713),a840)),x40714),f331(f331(f10(f854(f853(x40715,x40713),a840),f854(f853(x40712,x40713),a840),x40711),f331(f289(x40712,x40715,x40713),x40716)),x40717)),f331(f331(f289(x40712,x40715,x40713),x40716),f331(f331(f51(x40711,f854(f853(x40715,x40713),a840)),x40714),x40717)))
% 51.10/50.81 [4106]E(f175(x41061,x41062,f331(f331(f331(f79(x41061,f851(x41062)),x41063),x41064),f331(f234(x41062),x41065)),f171(x41061,x41062,f331(f160(f853(x41061,x41062)),f331(f331(f172(x41061,x41062),x41066),x41067)))),f175(x41061,x41062,x41063,f171(x41061,x41062,f331(f160(f853(x41061,x41062)),f331(f331(f172(x41061,x41062),f331(f331(f145(x41061),x41064),x41066)),f331(f331(f145(x41062),x41065),x41067))))))
% 51.10/50.81 [4214]E(f331(f331(f51(x42141,f854(f853(x42142,x42143),a840)),x42144),f331(f331(f9(x42141,f854(f853(x42145,x42143),a840),f854(f853(x42142,x42143),a840)),f331(f331(f10(f854(f853(x42142,x42145),a840),f854(f854(f853(x42145,x42143),a840),f854(f853(x42142,x42143),a840)),x42141),f289(x42142,x42145,x42143)),x42146)),x42147)),f331(f331(f289(x42142,x42145,x42143),f331(f331(f51(x42141,f854(f853(x42142,x42145),a840)),x42144),x42146)),x42147))
% 51.10/50.81 [4215]E(f331(f137(x42151,x42152,f331(f331(f9(x42151,f854(x42152,x42153),f854(x42152,x42151)),f331(f331(f10(f854(x42153,x42151),f854(f854(x42152,x42153),f854(x42152,x42151)),x42151),f10(x42153,x42151,x42152)),x42154)),x42155),x42156),x42157),f331(f137(x42151,x42153,x42154,x42156),f331(f331(f147(x42152,x42153),x42155),x42157)))
% 51.10/50.81 [4276]E(f331(f331(f52(x42761,f854(x42762,a840)),x42763),f331(f331(f10(f854(x42764,f854(x42762,a840)),f854(x42762,a840),x42761),f331(f52(x42764,f854(x42762,a840)),x42765)),f331(f331(f9(x42761,f854(x42764,f854(x42762,a840)),f854(x42764,f854(x42762,a840))),f331(f331(f10(f854(f854(x42762,a840),f854(x42762,a840)),f854(f854(x42764,f854(x42762,a840)),f854(x42764,f854(x42762,a840))),x42761),f10(f854(x42762,a840),f854(x42762,a840),x42764)),f331(f331(f10(f854(x42762,a840),f854(f854(x42762,a840),f854(x42762,a840)),x42761),f108(f854(x42762,a840))),x42766))),x42767))),f331(f331(f108(f854(x42762,a840)),f331(f331(f52(x42761,f854(x42762,a840)),x42763),x42766)),f331(f331(f52(x42764,f854(x42762,a840)),x42765),x42767)))
% 51.10/50.81 [4277]E(f331(f331(f51(x42771,f854(x42772,a840)),x42773),f331(f331(f10(f854(x42774,f854(x42772,a840)),f854(x42772,a840),x42771),f331(f51(x42774,f854(x42772,a840)),x42775)),f331(f331(f9(x42771,f854(x42774,f854(x42772,a840)),f854(x42774,f854(x42772,a840))),f331(f331(f10(f854(f854(x42772,a840),f854(x42772,a840)),f854(f854(x42774,f854(x42772,a840)),f854(x42774,f854(x42772,a840))),x42771),f10(f854(x42772,a840),f854(x42772,a840),x42774)),f331(f331(f10(f854(x42772,a840),f854(f854(x42772,a840),f854(x42772,a840)),x42771),f109(f854(x42772,a840))),x42776))),x42777))),f331(f331(f109(f854(x42772,a840)),f331(f331(f51(x42771,f854(x42772,a840)),x42773),x42776)),f331(f331(f51(x42774,f854(x42772,a840)),x42775),x42777)))
% 51.10/50.81 [4270]E(f199(x42701,x42702,f331(f331(f331(x42703,x42704),x42705),x42706),f331(f331(f9(x42701,f853(a106,a106),f854(a106,f849(x42702))),f331(f331(f9(x42701,a106,f854(f853(a106,a106),f854(a106,f849(x42702)))),f331(f331(f9(x42701,a106,f854(a106,f854(f853(a106,a106),f854(a106,f849(x42702))))),x42707),x42704)),x42705)),x42706)),f331(f331(f331(f211(x42701,x42702,x42703,x42707),x42704),x42705),x42706))
% 51.10/50.81 [4283]E(f200(x42831,x42832,f331(f331(f331(x42833,x42834),x42835),x42836),f331(f331(f9(x42831,f853(a106,a106),f854(a106,f849(x42832))),f331(f331(f9(x42831,a106,f854(f853(a106,a106),f854(a106,f849(x42832)))),f331(f331(f9(x42831,a106,f854(a106,f854(f853(a106,a106),f854(a106,f849(x42832))))),x42837),x42834)),x42835)),x42836)),f213(x42831,x42832,x42833,x42837,x42834,x42835,x42836))
% 51.10/50.81 [4274]E(f197(x42741,x42742,f331(f331(f331(x42743,x42744),x42745),x42746),f331(f331(f9(x42741,f853(a106,a106),f854(a106,f849(f851(x42742)))),f331(f331(f9(x42741,a106,f854(f853(a106,a106),f854(a106,f849(f851(x42742))))),f331(f331(f9(x42741,a106,f854(a106,f854(f853(a106,a106),f854(a106,f849(f851(x42742)))))),x42747),x42744)),x42745)),x42746)),f331(f331(f331(f207(x42741,x42742,x42743,x42747),x42744),x42745),x42746))
% 51.10/50.81 [4285]E(f198(x42851,x42852,f331(f331(f331(x42853,x42854),x42855),x42856),f331(f331(f9(x42851,f853(a106,a106),f854(a106,f849(f851(x42852)))),f331(f331(f9(x42851,a106,f854(f853(a106,a106),f854(a106,f849(f851(x42852))))),f331(f331(f9(x42851,a106,f854(a106,f854(f853(a106,a106),f854(a106,f849(f851(x42852)))))),x42857),x42854)),x42855)),x42856)),f209(x42851,x42852,x42853,x42857,x42854,x42855,x42856))
% 51.10/50.81 [4188]E(f331(f260(x41881,x41882,x41883,x41884,x41885,x41886),f331(f331(f249(x41881,x41883),x41887),x41888)),f331(f331(f249(x41882,x41884),f331(x41885,x41887)),f331(x41886,x41888)))
% 51.10/50.81 [4287]E(f331(f331(f147(f853(x42871,x42872),f853(x42873,x42874)),f331(f259(x42871,x42872,f853(x42873,x42874)),f331(f331(f9(x42871,f854(x42872,x42874),f854(x42872,f853(x42873,x42874))),f331(f331(f10(f854(x42874,f853(x42873,x42874)),f854(f854(x42872,x42874),f854(x42872,f853(x42873,x42874))),x42871),f10(x42874,f853(x42873,x42874),x42872)),f331(f331(f10(x42873,f854(x42874,f853(x42873,x42874)),x42871),f249(x42873,x42874)),x42875))),x42876))),f331(f331(f172(x42871,x42872),x42877),x42878)),f331(f331(f172(x42873,x42874),f331(f331(f147(x42871,x42873),x42875),x42877)),f331(f331(f147(x42872,x42874),x42876),x42878)))
% 51.10/50.81 [4291]E(f331(f331(f147(f853(x42911,x42912),x42913),f331(f259(x42911,x42912,x42913),f331(f331(f10(f854(x42912,f853(x42911,x42914)),f854(x42912,x42913),x42911),f331(f10(f853(x42911,x42914),x42913,x42912),x42915)),f331(f331(f9(x42911,f854(x42912,x42914),f854(x42912,f853(x42911,x42914))),f331(f331(f10(f854(x42914,f853(x42911,x42914)),f854(f854(x42912,x42914),f854(x42912,f853(x42911,x42914))),x42911),f10(x42914,f853(x42911,x42914),x42912)),f249(x42911,x42914))),x42916)))),f331(f331(f172(x42911,x42912),x42917),x42918)),f331(f331(f147(f853(x42911,x42914),x42913),x42915),f331(f331(f172(x42911,x42914),x42917),f331(f331(f147(x42912,x42914),x42916),x42918))))
% 51.10/50.81 [4219]E(f331(f331(f147(f853(x42191,x42192),x42193),f331(f259(x42191,x42192,x42193),f331(f331(f10(f854(x42192,f853(x42194,x42192)),f854(x42192,x42193),x42191),f331(f10(f853(x42194,x42192),x42193,x42192),x42195)),f331(f331(f10(x42194,f854(x42192,f853(x42194,x42192)),x42191),f249(x42194,x42192)),x42196)))),f331(f331(f172(x42191,x42192),x42197),x42198)),f331(f331(f147(f853(x42194,x42192),x42193),x42195),f331(f331(f172(x42194,x42192),f331(f331(f147(x42191,x42194),x42196),x42197)),x42198)))
% 51.10/50.81 [4179]E(f331(f331(f259(x41791,x41792,x41793),f331(f331(f10(f854(x41792,f853(x41794,x41795)),f854(x41792,x41793),x41791),f331(f10(f853(x41794,x41795),x41793,x41792),f331(f259(x41794,x41795,x41793),x41796))),x41797)),x41798),f331(f331(f259(x41794,x41795,x41793),x41796),f331(f331(f259(x41791,x41792,f853(x41794,x41795)),x41797),x41798)))
% 51.10/50.81 [4292]E(f331(f331(f51(f853(x42921,x42922),f854(f853(x42923,x42924),a840)),f331(f331(f256(x42921,x42922),x42925),f331(f18(f854(x42922,a840),x42921),x42926))),f331(f259(x42921,x42922,f854(f853(x42923,x42924),a840)),f331(f331(f9(x42921,f854(x42922,f854(x42923,f854(x42924,a840))),f854(x42922,f854(f853(x42923,x42924),a840))),f331(f331(f10(f854(f854(x42923,f854(x42924,a840)),f854(f853(x42923,x42924),a840)),f854(f854(x42922,f854(x42923,f854(x42924,a840))),f854(x42922,f854(f853(x42923,x42924),a840))),x42921),f10(f854(x42923,f854(x42924,a840)),f854(f853(x42923,x42924),a840),x42922)),f331(f331(f10(f854(x42923,a840),f854(f854(x42923,f854(x42924,a840)),f854(f853(x42923,x42924),a840)),x42921),f256(x42923,x42924)),x42927))),f331(f331(f10(f854(x42924,a840),f854(x42923,f854(x42924,a840)),x42922),f18(f854(x42924,a840),x42923)),x42928)))),f331(f331(f256(x42923,x42924),f331(f331(f51(x42921,f854(x42923,a840)),x42925),x42927)),f331(f18(f854(x42924,a840),x42923),f331(f331(f51(x42922,f854(x42924,a840)),x42926),x42928))))
% 51.10/50.81 [4233]E(f331(f331(f261(x42331,x42332,x42333,x42334),f331(f331(f261(x42331,x42335,x42336,f853(x42332,x42333)),x42337),x42338)),x42339),f331(f331(f261(x42331,x42335,x42336,x42334),x42337),f331(f331(f9(x42335,f854(x42332,f854(x42333,x42334)),f854(x42336,x42334)),f331(f331(f10(f854(x42336,f853(x42332,x42333)),f854(f854(x42332,f854(x42333,x42334)),f854(x42336,x42334)),x42335),f261(x42336,x42332,x42333,x42334)),x42338)),x42339)))
% 51.10/50.81 [4262]E(f331(f80(f853(x42621,x42622),f853(x42623,x42624),f853(x42625,x42626),f260(x42621,x42623,x42622,x42624,x42627,x42628)),f260(x42625,x42621,x42626,x42622,x42629,x426210)),f260(x42625,x42623,x42626,x42624,f331(f80(x42621,x42623,x42625,x42627),x42629),f331(f80(x42622,x42624,x42626,x42628),x426210)))
% 51.10/50.81 [4263]E(f331(f80(f853(x42631,x42632),f853(x42633,x42634),f853(x42635,x42636),f260(x42631,x42633,x42632,x42634,x42637,x42638)),f260(x42635,x42631,x42636,x42632,x42639,x426310)),f260(x42635,x42633,x42636,x42634,f331(f80(x42631,x42633,x42635,x42637),x42639),f331(f80(x42632,x42634,x42636,x42638),x426310)))
% 51.10/50.81 [4268]E(f331(f260(x42681,x42682,x42683,x42684,x42685,x42686),f331(f260(x42687,x42681,x42688,x42683,x42689,x426810),x426811)),f331(f260(x42687,x42682,x42688,x42684,f331(f80(x42681,x42682,x42687,x42685),x42689),f331(f80(x42683,x42684,x42688,x42686),x426810)),x426811))
% 51.10/50.81 [6334]P11(a500)+P1(f331(f331(f333(f853(a843,a841)),a702),f331(f163(f853(a843,a841)),a31)))
% 51.10/50.81 [8373]P11(a500)+~P1(f331(f331(f259(a843,a841,a840),f331(f18(f854(a841,a840),a843),a26)),a702))
% 51.10/50.81 [4454]~P57(x44541)+P57(f851(x44541))
% 51.10/50.81 [4456]~P138(x44561)+~E(f85(x44561),f2(x44561))
% 51.10/50.81 [4457]~P138(x44571)+~E(f85(x44571),f2(x44571))
% 51.10/50.81 [4459]~E(x44591,f2(a106))+E(f331(a23,x44591),f2(a1))
% 51.10/50.81 [4460]~E(x44601,f2(a1))+E(f89(a1,x44601),f2(a1))
% 51.10/50.81 [4467]~P84(x44671)+P31(x44671,f2(x44671))
% 51.10/50.81 [4468]~P102(x44681)+P16(x44681,f120(x44681))
% 51.10/50.81 [4469]~P102(x44691)+P16(x44691,f120(x44691))
% 51.10/50.81 [4478]P1(x44781)+P1(f331(a327,x44781))
% 51.10/50.81 [4521]~P84(x45211)+~P31(x45211,f85(x45211))
% 51.10/50.81 [4565]~P1(x45651)+~P1(f331(a327,x45651))
% 51.10/50.81 [4588]E(f331(a112,x45881),f2(a847))+~P1(f331(a190,x45881))
% 51.10/50.81 [4649]~P94(x46491)+P17(x46491,x46491,f88(x46491))
% 51.10/50.81 [4650]~P102(x46501)+P17(x46501,x46501,f244(x46501))
% 51.10/50.81 [4651]~P102(x46511)+P17(x46511,x46511,f239(x46511))
% 51.10/50.81 [4652]~P100(x46521)+P17(x46521,x46521,f108(x46521))
% 51.10/50.81 [4653]~P101(x46531)+P17(x46531,x46531,f109(x46531))
% 51.10/50.81 [4654]~P64(x46541)+P18(x46541,x46541,f88(x46541))
% 51.10/50.81 [4464]~E(x44641,f2(a847))+E(f331(f107(a1),x44641),f2(a1))
% 51.10/50.81 [4471]~P91(x44711)+E(f331(f111(x44711),a90),f2(x44711))
% 51.10/50.81 [4472]~P91(x44721)+E(f331(f111(x44721),a90),f2(x44721))
% 51.10/50.81 [4474]~E(f590(x44741),f2(a847))+E(f331(f157(a847),x44741),f2(a847))
% 51.10/50.81 [4475]~P104(x44751)+E(f242(x44751,f240(x44751)),f244(x44751))
% 51.10/50.81 [4476]~P104(x44761)+E(f243(x44761,f240(x44761)),f239(x44761))
% 51.10/50.81 [4477]~P81(x44771)+E(f89(x44771,f2(x44771)),f2(x44771))
% 51.10/50.81 [4486]~P84(x44861)+E(f331(f107(x44861),f2(a847)),f2(x44861))
% 51.10/50.81 [4487]~P84(x44871)+E(f331(f107(x44871),f85(a847)),f85(x44871))
% 51.10/50.81 [4488]~P133(x44881)+E(f331(f110(x44881),f2(a1)),f2(x44881))
% 51.10/50.81 [4489]~P133(x44891)+E(f331(f110(x44891),f85(a1)),f85(x44891))
% 51.10/50.81 [4490]E(x44901,f2(a847))+~E(f331(f107(a1),x44901),f2(a1))
% 51.10/50.81 [4515]~P69(x45151)+E(f331(f86(x45151),f2(x45151)),f2(x45151))
% 51.10/50.81 [4516]~P93(x45161)+E(f331(f86(x45161),f184(x45161)),f247(x45161))
% 51.10/50.81 [4517]~P93(x45171)+E(f331(f86(x45171),f247(x45171)),f184(x45171))
% 51.10/50.81 [4518]~P78(x45181)+E(f331(f82(x45181),f2(x45181)),f2(x45181))
% 51.10/50.81 [4519]~P86(x45191)+E(f331(f82(x45191),f85(x45191)),f85(x45191))
% 51.10/50.81 [4520]~P71(x45201)+E(f331(f157(x45201),f120(x45201)),f2(x45201))
% 51.10/50.81 [4541]~P33(x45411)+P36(f331(f163(a1),x45411))
% 51.10/50.81 [4569]~P91(x45691)+E(f331(f86(x45691),f85(x45691)),f331(f111(x45691),a104))
% 51.10/50.81 [4570]~P91(x45701)+E(f331(f86(x45701),f85(x45701)),f331(f111(x45701),a104))
% 51.10/50.81 [4587]~P91(x45871)+P31(x45871,f331(f111(x45871),a90))
% 51.10/50.81 [4612]P33(x46121)+~P36(f331(f163(a1),x46121))
% 51.10/50.81 [4655]E(f331(f107(a1),f331(a112,x46551)),x46551)+P1(f331(a190,x46551))
% 51.10/50.81 [4722]~P107(x47221)+E(f251(x47221,f85(x47221),f88(x47221)),f250(x47221))
% 51.10/50.81 [4752]~P91(x47521)+~P31(x47521,f331(f111(x47521),a104))
% 51.10/50.81 [4762]E(f331(a32,x47621),f187(a841))+P1(f331(a26,f331(a29,x47621)))
% 51.10/50.81 [4839]~E(x48391,f2(a847))+P1(f331(f331(f240(a847),x48391),f2(a847)))
% 51.10/50.81 [4840]~E(x48401,f85(a847))+P1(f331(f331(f287(a847),x48401),f85(a847)))
% 51.10/50.81 [4892]E(f331(f82(a1),x48921),x48921)+P1(f331(f331(f241(a1),x48921),f2(a1)))
% 51.10/50.81 [4912]~E(f331(a112,x49121),f2(a847))+P1(f331(f331(f240(a1),x49121),f2(a1)))
% 51.10/50.81 [4943]~E(f331(f82(a1),x49431),f85(a1))+P1(f331(f331(f287(a1),x49431),f85(a1)))
% 51.10/50.81 [4973]~P1(f331(a190,x49731))+P1(f331(f331(f241(a1),x49731),f2(a1)))
% 51.10/50.81 [5013]~P85(x50131)+P1(f331(f331(f241(x50131),f2(x50131)),f85(x50131)))
% 51.10/50.81 [5014]~P85(x50141)+P1(f331(f331(f240(x50141),f2(x50141)),f85(x50141)))
% 51.10/50.81 [5015]~P84(x50151)+P1(f331(f331(f333(x50151),f2(x50151)),f181(x50151)))
% 51.10/50.81 [5016]~P133(x50161)+P1(f331(f331(f333(x50161),f2(x50161)),f117(x50161)))
% 51.10/50.81 [5017]~P84(x50171)+P1(f331(f331(f333(x50171),f85(x50171)),f181(x50171)))
% 51.10/50.81 [5018]~P133(x50181)+P1(f331(f331(f333(x50181),f85(x50181)),f117(x50181)))
% 51.10/50.81 [5021]E(f331(f234(a841),f391(x50211)),f331(a32,x50211))+~P1(f331(a26,f331(a29,x50211)))
% 51.10/50.81 [5022]E(f331(f234(a841),f448(x50221)),f331(a32,x50221))+~P1(f331(a26,f331(a29,x50221)))
% 51.10/50.81 [5074]E(x50741,f2(a847))+~P1(f331(f331(f240(a847),x50741),f2(a847)))
% 51.10/50.81 [5075]E(x50751,f85(a847))+~P1(f331(f331(f287(a847),x50751),f85(a847)))
% 51.10/50.81 [5115]E(f331(a112,x51151),f2(a847))+~P1(f331(f331(f240(a1),x51151),f2(a1)))
% 51.10/50.81 [5116]E(f331(a112,x51161),f2(a847))+~P1(f331(f331(f240(a1),x51161),f2(a1)))
% 51.10/50.81 [5144]E(f331(f82(a1),x51441),f85(a1))+~P1(f331(f331(f287(a1),x51441),f85(a1)))
% 51.10/50.81 [5171]P1(f331(a190,x51711))+~P1(f331(f331(f241(a1),x51711),f2(a1)))
% 51.10/50.81 [5176]~P102(x51761)+P18(x51761,f848(x51761),f143(x51761,x51761,f7(x51761)))
% 51.10/50.81 [5194]P36(x51941)+~P1(f331(f331(f240(a1),f2(a1)),f360(x51941)))
% 51.10/50.81 [5200]E(f331(f82(a1),x52001),f331(f86(a1),x52001))+~P1(f331(f331(f241(a1),x52001),f2(a1)))
% 51.10/50.81 [5369]~P85(x53691)+~P1(f331(f331(f241(x53691),f85(x53691)),f2(x53691)))
% 51.10/50.81 [5370]~P85(x53701)+~P1(f331(f331(f240(x53701),f85(x53701)),f2(x53701)))
% 51.10/50.81 [5382]~E(x53821,f2(a1))+P1(f331(f331(f241(a1),f331(f82(a1),x53821)),f85(a1)))
% 51.10/50.81 [5383]~E(x53831,f2(a847))+P1(f331(f331(f240(a1),f331(f107(a1),x53831)),f2(a1)))
% 51.10/50.81 [5500]~P71(x55001)+E(f137(x55001,x55001,f87(x55001),f2(x55001)),f157(x55001))
% 51.10/50.81 [5676]~P89(x56761)+P27(a847,x56761,f107(x56761),f247(f854(a847,a840)))
% 51.10/50.81 [5874]E(x58741,f2(a847))+~P1(f331(f331(f240(a1),f331(f107(a1),x58741)),f2(a1)))
% 51.10/50.81 [5875]E(x58751,f2(a1))+~P1(f331(f331(f241(a1),f331(f82(a1),x58751)),f85(a1)))
% 51.10/50.81 [6705]~P1(f331(f331(f241(a1),x67051),f2(a1)))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x67051),x67051)),f2(a1)))
% 51.10/50.81 [7277]P1(f331(f331(f241(a1),x72771),f2(a1)))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x72771),x72771)),f2(a1)))
% 51.10/50.81 [7843]E(x78431,f331(a5,f2(a847)))+P1(f331(f331(f241(a847),f331(f331(f3(a847),f331(a22,x78431)),f331(a119,f2(a847)))),f331(a22,x78431)))
% 51.10/50.81 [8584]~P1(f331(f331(f241(a1),x85841),f2(a1)))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x85841),x85841)),a104)),f2(a1)))
% 51.10/50.81 [8668]~P1(f331(f331(f241(a1),x86681),f2(a1)))+P1(f331(f331(f241(a1),f331(f331(f87(a1),f331(f331(f87(a1),f85(a1)),x86681)),x86681)),f2(a1)))
% 51.10/50.81 [8950]P1(f331(f331(f241(a1),x89501),f2(a1)))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89501),x89501)),a104)),f2(a1)))
% 51.10/50.81 [9012]P1(f331(f331(f241(a1),x90121),f2(a1)))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),f331(f331(f87(a1),f85(a1)),x90121)),x90121)),f2(a1)))
% 51.10/50.81 [4558]~E(a90,x45581)+E(f331(f331(f87(a1),x45581),x45581),a90)
% 51.10/50.81 [4559]~E(x45591,a90)+E(f331(f331(f87(a1),x45591),x45591),a90)
% 51.10/50.81 [4573]E(x45731,f2(a1))+E(f331(f331(f48(a1),x45731),x45731),f85(a1))
% 51.10/50.81 [4700]E(x47001,a90)+~E(f331(f331(f87(a1),x47001),x47001),a90)
% 51.10/50.81 [4701]E(a90,x47011)+~E(f331(f331(f87(a1),x47011),x47011),a90)
% 51.10/50.81 [4702]~P91(x47021)+E(f331(f110(x47021),f331(f111(a1),a104)),f331(f111(x47021),a104))
% 51.10/50.81 [4712]~P7(x47121)+E(f50(x47121,f184(f854(x47121,a840))),f247(x47121))
% 51.10/50.81 [4713]~P7(x47131)+E(f50(x47131,f247(f854(x47131,a840))),f184(x47131))
% 51.10/50.81 [4714]~P7(x47141)+E(f49(x47141,f184(f854(x47141,a840))),f184(x47141))
% 51.10/50.81 [4715]~P7(x47151)+E(f49(x47151,f247(f854(x47151,a840))),f247(x47151))
% 51.10/50.81 [4716]~P102(x47161)+E(f135(x47161,f184(f854(x47161,a840))),f120(x47161))
% 51.10/50.81 [4851]E(x48511,f2(a847))+P1(f331(f331(f241(a847),f2(a847)),x48511))
% 51.10/50.81 [4852]E(x48521,f2(a847))+P1(f331(f331(f241(a847),f2(a847)),x48521))
% 51.10/50.81 [4872]~P8(x48721)+P1(f331(f331(f240(a1),f2(a1)),x48721))
% 51.10/50.81 [4902]~E(f331(f111(a847),x49021),f2(a847))+P1(f331(f331(f240(a1),x49021),a90))
% 51.10/50.81 [4903]~E(f331(f111(a847),x49031),f2(a847))+P1(f331(f331(f240(a1),x49031),a90))
% 51.10/50.81 [4908]P36(x49081)+P1(f331(f331(f333(a1),f360(x49081)),x49081))
% 51.10/50.81 [4909]E(x49091,f331(a5,f2(a847)))+P1(f331(f331(f240(a106),f85(a106)),x49091))
% 51.10/50.81 [4948]P1(f331(a190,x49481))+P1(f331(f331(f240(a1),f2(a1)),x49481))
% 51.10/50.81 [4995]E(f331(f107(a1),f331(a112,x49951)),f2(a1))+P1(f331(f331(f240(a1),f2(a1)),x49951))
% 51.10/50.81 [5048]~P57(x50481)+P1(f331(f68(x50481),f247(f854(x50481,a840))))
% 51.10/50.81 [5061]E(f331(f107(a1),f331(f111(a847),x50611)),f331(f111(a1),x50611))+P1(f331(a190,f331(f111(a1),x50611)))
% 51.10/50.81 [5064]~E(x50641,f2(a847))+P1(f331(f331(f241(a847),x50641),f331(a119,f2(a847))))
% 51.10/50.81 [5080]E(f331(f111(a847),x50801),f2(a847))+~P1(f331(f331(f240(a1),x50801),a90))
% 51.10/50.81 [5081]E(f331(f111(a847),x50811),f2(a847))+~P1(f331(a190,f331(f111(a1),x50811)))
% 51.10/50.81 [5082]E(f331(f111(a847),x50821),f2(a847))+~P1(f331(f331(f240(a1),x50821),a90))
% 51.10/50.81 [5113]P8(x51131)+~P1(f331(f331(f240(a1),f2(a1)),x51131))
% 51.10/50.81 [5131]~E(x51311,f2(a847))+~P1(f331(f331(f241(a847),f2(a847)),x51311))
% 51.10/50.81 [5154]~E(x51541,f331(a119,f2(a847)))+P1(f331(f331(f287(a847),x51541),f331(a119,f2(a847))))
% 51.10/50.81 [5179]E(f331(a119,f404(x51791)),x51791)+~P1(f331(f331(f241(a847),f2(a847)),x51791))
% 51.10/50.81 [5180]E(f331(a119,f564(x51801)),x51801)+~P1(f331(f331(f241(a847),f2(a847)),x51801))
% 51.10/50.81 [5188]E(f331(a119,f331(f111(a847),x51881)),f85(a847))+~P1(f331(a190,f331(f111(a1),x51881)))
% 51.10/50.81 [5196]E(f331(f107(a1),f615(x51961)),x51961)+~P1(f331(f331(f241(a1),f2(a1)),x51961))
% 51.10/50.81 [5203]~E(x52031,f331(a5,f2(a847)))+~P1(f331(f331(f240(a106),f85(a106)),x52031))
% 51.10/50.81 [5210]E(f331(f107(a1),f331(f111(a847),x52101)),f2(a1))+~P1(f331(a190,f331(f111(a1),x52101)))
% 51.10/50.81 [5234]E(f331(f157(a847),x52341),f2(a847))+P1(f331(f331(f333(a847),f590(x52341)),f331(f163(a847),x52341)))
% 51.10/50.81 [5253]E(f331(f107(a1),f331(a112,x52531)),x52531)+~P1(f331(f331(f240(a1),f2(a1)),x52531))
% 51.10/50.81 [5254]E(f331(f107(a1),f331(a112,x52541)),x52541)+~P1(f331(f331(f240(a1),f2(a1)),x52541))
% 51.10/50.81 [5263]~P1(f331(a190,x52631))+~P1(f331(f331(f240(a1),f2(a1)),x52631))
% 51.10/50.81 [5362]E(f331(f331(f87(a847),f85(a847)),f331(f111(a847),x53621)),f85(a847))+~P1(f331(f331(f241(a1),x53621),a90))
% 51.10/50.81 [5420]E(x54201,f2(a847))+~P1(f331(f331(f241(a847),x54201),f331(a119,f2(a847))))
% 51.10/50.81 [5441]E(x54411,f331(a119,f2(a847)))+~P1(f331(f331(f287(a847),x54411),f331(a119,f2(a847))))
% 51.10/50.81 [5460]E(f331(f331(f87(a847),f331(f111(a847),x54601)),f85(a847)),f85(a847))+~P1(f331(f331(f241(a1),x54601),a90))
% 51.10/50.81 [5461]E(f331(f331(f3(a847),f331(f111(a847),x54611)),f85(a847)),f2(a847))+~P1(f331(f331(f240(a1),x54611),a90))
% 51.10/50.81 [5471]~P36(x54711)+E(f331(f47(a847),f331(f311(a1,a847,a112),x54711)),f331(f47(a1),x54711))
% 51.10/50.81 [5501]~P102(x55011)+E(f242(x55011,f331(f9(x55011,x55011,a840),f240(x55011))),f239(x55011))
% 51.10/50.81 [5502]~P102(x55021)+E(f243(x55021,f331(f9(x55021,x55021,a840),f240(x55021))),f244(x55021))
% 51.10/50.82 [5511]E(f57(a847,f331(a119,f2(a847)),f331(f111(a847),x55111)),f331(a119,f2(a847)))+~P1(f331(a190,f331(f111(a1),x55111)))
% 51.10/50.82 [5520]P1(f331(f331(f241(a1),f2(a1)),x55201))+~P1(f331(f331(f240(a1),f85(a1)),x55201))
% 51.10/50.82 [5521]~P1(f331(f331(f241(a1),f2(a1)),x55211))+P1(f331(f331(f240(a1),f85(a1)),x55211))
% 51.10/50.82 [5530]E(f331(a119,f331(f331(f3(a847),x55301),f85(a847))),x55301)+~P1(f331(f331(f241(a847),f2(a847)),x55301))
% 51.10/50.82 [5531]E(f331(a119,f331(f331(f3(a847),x55311),f85(a847))),x55311)+~P1(f331(f331(f241(a847),f2(a847)),x55311))
% 51.10/50.82 [5589]P1(f331(f331(f241(a847),f2(a847)),f615(x55891)))+~P1(f331(f331(f241(a1),f2(a1)),x55891))
% 51.10/50.82 [5646]E(f57(a1,f331(f111(a1),a104),x56461),f331(f331(f3(a1),x56461),f85(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x56461))
% 51.10/50.82 [5691]~P1(f331(f331(f241(a1),a90),x56911))+P1(f331(f331(f241(a847),f2(a847)),f331(f111(a847),x56911)))
% 51.10/50.82 [5745]P1(f331(f331(f241(a847),f2(a847)),f331(a112,x57451)))+~P1(f331(f331(f241(a1),f2(a1)),x57451))
% 51.10/50.82 [5768]E(f331(a22,f331(a5,x57681)),x57681)+~P1(f331(f331(f333(a847),x57681),f247(f854(a847,a840))))
% 51.10/50.82 [5793]~P1(f331(f331(f241(a847),f2(a847)),x57931))+P1(f331(f331(f241(a1),f2(a1)),f331(f107(a1),x57931)))
% 51.10/50.82 [5828]~P1(f331(f331(f241(a847),f2(a847)),f331(a112,x58281)))+P1(f331(f331(f241(a1),f2(a1)),x58281))
% 51.10/50.82 [5843]~P36(x58431)+E(f331(f311(a847,a1,f107(a1)),f331(f311(a1,a847,a112),x58431)),x58431)
% 51.10/50.82 [5854]P1(f331(f331(f241(a1),a90),x58541))+~P1(f331(f331(f241(a847),f2(a847)),f331(f111(a847),x58541)))
% 51.10/50.82 [5916]P1(f331(f331(f241(a847),f2(a847)),x59161))+~P1(f331(f331(f241(a1),f2(a1)),f331(f107(a1),x59161)))
% 51.10/50.82 [5949]E(f169(x59491,f120(f848(x59491))),f120(f848(x59491)))+~P1(f331(f320(f848(f848(x59491)),f170(x59491)),f120(f848(x59491))))
% 51.10/50.82 [6033]E(f331(f311(a847,a1,f107(a1)),f331(f265(a847),f331(a112,x60331))),f331(f302(a1,f2(a1)),x60331))+~P1(f331(f331(f240(a1),f2(a1)),x60331))
% 51.10/50.82 [6049]~P85(x60491)+P1(f331(f331(f241(x60491),f2(x60491)),f331(f331(f87(x60491),f85(x60491)),f85(x60491))))
% 51.10/50.82 [6101]P1(f331(f331(f241(a847),f331(a119,f2(a847))),f331(a112,x61011)))+~P1(f331(f331(f241(a1),f85(a1)),x61011))
% 51.10/50.82 [6198]E(x61981,f2(a1))+P1(f331(f61(f2(a1),x61981),f331(f331(f249(a1,a1),f2(a1)),f2(a1))))
% 51.10/50.82 [6377]~P1(f331(f331(f241(a847),f331(a119,f2(a847))),f331(a112,x63771)))+P1(f331(f331(f241(a1),f85(a1)),x63771))
% 51.10/50.82 [6428]E(f331(a119,f331(f331(f3(a847),f331(f111(a847),x64281)),f85(a847))),f331(f111(a847),x64281))+~P1(f331(f331(f241(a847),f2(a847)),f331(f111(a847),x64281)))
% 51.10/50.82 [6826]~P109(x68261)+P34(x68261,f331(f264(f853(x68261,x68261)),f331(f259(x68261,x68261,a840),f241(x68261))))
% 51.10/50.82 [5410]E(f331(f111(a847),f331(f331(f3(a1),x54101),a104)),f331(a119,f331(f111(a847),x54101)))+P1(f331(a190,f331(f111(a1),x54101)))
% 51.10/50.82 [5423]~P33(x54231)+E(f331(f331(f147(a847,a1),f107(a1)),f331(f331(f147(a1,a847),a112),x54231)),x54231)
% 51.10/50.82 [5519]P29(a839,f331(a119,a862),x55191)+~P1(f331(f331(f333(f846(a839)),x55191),a858))
% 51.10/50.82 [5537]E(f331(f86(a1),f331(f107(a1),f331(a119,f658(x55371)))),x55371)+~P1(f331(f331(f241(a1),x55371),f2(a1)))
% 51.10/50.82 [5547]E(f331(f331(f87(a847),f85(a847)),f331(f111(a847),x55471)),f331(f111(a847),f331(f331(f3(a1),x55471),a104)))+P1(f331(f331(f241(a1),x55471),a90))
% 51.10/50.82 [5591]E(f331(f331(f48(a1),f331(f111(a1),a104)),x55911),f331(f111(a1),a104))+~P1(f331(f331(f241(a1),f2(a1)),x55911))
% 51.10/50.82 [5687]E(f331(f331(f87(a847),f331(f111(a847),x56871)),f85(a847)),f331(f111(a847),f331(f331(f3(a1),x56871),a104)))+P1(f331(f331(f241(a1),x56871),a90))
% 51.10/50.82 [5688]E(f331(f331(f3(a847),f331(f111(a847),x56881)),f85(a847)),f331(f111(a847),f331(f331(f87(a1),x56881),a104)))+P1(f331(f331(f240(a1),x56881),a90))
% 51.10/50.82 [5731]E(f331(a112,f331(f331(f87(a1),f85(a1)),x57311)),f331(a119,f331(a112,x57311)))+~P1(f331(f331(f240(a1),f2(a1)),x57311))
% 51.10/50.82 [5770]E(f331(a119,f331(f331(f3(a847),x57701),f331(a119,f2(a847)))),x57701)+~P1(f331(f331(f241(a847),f2(a847)),x57701))
% 51.10/50.82 [5978]E(f57(a847,f331(a119,f2(a847)),f331(f111(a847),x59781)),f331(a112,f57(a1,f85(a1),f331(f111(a1),x59781))))+P1(f331(a190,f331(f111(a1),x59781)))
% 51.10/50.82 [6024]~P1(f331(f331(f241(a1),a104),x60241))+P1(f331(f331(f241(a1),a104),f331(f331(f87(a1),x60241),x60241)))
% 51.10/50.82 [6025]~P1(f331(f331(f241(a1),a90),x60251))+P1(f331(f331(f241(a1),a90),f331(f331(f87(a1),x60251),x60251)))
% 51.10/50.82 [6026]~P1(f331(f331(f241(a1),a104),x60261))+P1(f331(f331(f240(a1),a104),f331(f331(f87(a1),x60261),x60261)))
% 51.10/50.82 [6027]~P1(f331(f331(f240(a1),a90),x60271))+P1(f331(f331(f240(a1),a90),f331(f331(f87(a1),x60271),x60271)))
% 51.10/50.82 [6212]~P1(f331(f68(x62121),f247(f854(x62121,a840))))+P1(f331(f68(f851(x62121)),f247(f854(f851(x62121),a840))))
% 51.10/50.82 [6302]~P1(f331(f331(f240(a1),f2(a1)),x63021))+P1(f331(f331(f241(a1),f2(a1)),f331(f331(f87(a1),f85(a1)),x63021)))
% 51.10/50.82 [6308]E(f331(f248(a1,a1),f59(f85(a1),f331(f111(a1),x63081))),f331(f331(f48(a1),f85(a1)),f331(f111(a1),x63081)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x63081)))
% 51.10/50.82 [6333]E(f331(f258(a1,a1),f59(f85(a1),f331(f111(a1),x63331))),f57(a1,f85(a1),f331(f111(a1),x63331)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x63331)))
% 51.10/50.82 [6346]P1(f331(f68(x63461),f247(f854(x63461,a840))))+~P1(f331(f68(f851(x63461)),f247(f854(f851(x63461),a840))))
% 51.10/50.82 [6378]P1(f331(f331(f241(a1),a104),x63781))+~P1(f331(f331(f241(a1),a104),f331(f331(f87(a1),x63781),x63781)))
% 51.10/50.82 [6379]P1(f331(f331(f241(a1),a104),x63791))+~P1(f331(f331(f240(a1),a104),f331(f331(f87(a1),x63791),x63791)))
% 51.10/50.82 [6380]P1(f331(f331(f241(a1),a90),x63801))+~P1(f331(f331(f241(a1),a90),f331(f331(f87(a1),x63801),x63801)))
% 51.10/50.82 [6381]P1(f331(f331(f240(a1),a90),x63811))+~P1(f331(f331(f240(a1),a90),f331(f331(f87(a1),x63811),x63811)))
% 51.10/50.82 [6575]~P1(f331(f68(a847),x65751))+P1(f331(f68(a1),f331(f311(a847,a1,f107(a1)),x65751)))
% 51.10/50.82 [6710]~P1(f331(f68(x67101),f247(f854(x67101,a840))))+P1(f331(f331(f241(a847),f2(a847)),f331(f47(x67101),f247(f854(x67101,a840)))))
% 51.10/50.82 [7322]P1(f331(f68(a847),x73221))+~P1(f331(f68(a1),f331(f311(a847,a1,f107(a1)),x73221)))
% 51.10/50.82 [5337]~E(a104,x53371)+E(f331(f331(f3(a1),f331(f331(f87(a1),x53371),x53371)),a104),a104)
% 51.10/50.82 [5338]~E(x53381,a104)+E(f331(f331(f3(a1),f331(f331(f87(a1),x53381),x53381)),a104),a104)
% 51.10/50.82 [5848]E(x58481,a104)+~E(f331(f331(f3(a1),f331(f331(f87(a1),x58481),x58481)),a104),a104)
% 51.10/50.82 [5849]E(a104,x58491)+~E(f331(f331(f3(a1),f331(f331(f87(a1),x58491),x58491)),a104),a104)
% 51.10/50.82 [6271]~E(f331(f111(a847),x62711),f2(a847))+P1(f331(a190,f331(f111(a1),f331(f331(f87(a1),x62711),a104))))
% 51.10/50.82 [6635]~P1(f331(a190,f331(f111(a1),x66351)))+P1(f331(a190,f331(f111(a1),f331(f331(f87(a1),x66351),x66351))))
% 51.10/50.82 [6636]~P1(f331(f331(f240(a1),x66361),a104))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x66361),x66361)),a104))
% 51.10/50.82 [6637]~P1(f331(f331(f241(a1),x66371),a90))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x66371),x66371)),a90))
% 51.10/50.82 [6638]~P1(f331(f331(f240(a1),x66381),a104))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x66381),x66381)),a104))
% 51.10/50.82 [6639]~P1(f331(f331(f240(a1),x66391),a90))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x66391),x66391)),a90))
% 51.10/50.82 [6968]E(f331(f111(a847),x69681),f2(a847))+~P1(f331(a190,f331(f111(a1),f331(f331(f87(a1),x69681),a104))))
% 51.10/50.82 [7225]~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x72251)))+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),f331(f331(f87(a1),x72251),x72251))))
% 51.10/50.82 [7226]P1(f331(a190,f331(f111(a1),x72261)))+~P1(f331(a190,f331(f111(a1),f331(f331(f87(a1),x72261),x72261))))
% 51.10/50.82 [7227]P1(f331(f331(f241(a1),x72271),a90))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x72271),x72271)),a90))
% 51.10/50.82 [7228]P1(f331(f331(f240(a1),x72281),a104))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x72281),x72281)),a104))
% 51.10/50.82 [7229]P1(f331(f331(f240(a1),x72291),a104))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x72291),x72291)),a104))
% 51.10/50.82 [7230]P1(f331(f331(f240(a1),x72301),a90))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x72301),x72301)),a90))
% 51.10/50.82 [7610]E(f331(a115,f558(x76101)),x76101)+~P1(f331(f331(f333(f854(f853(a847,a847),a840)),x76101),a105))
% 51.10/50.82 [6184]~P91(x61841)+E(f331(f111(x61841),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f85(x61841))
% 51.10/50.82 [6185]~P91(x61851)+E(f331(f111(x61851),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f85(x61851))
% 51.10/50.82 [6689]~P1(f331(a190,f331(f111(a1),x66891)))+E(f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x66891),x66891)),a104)),f2(a847))
% 51.10/50.82 [7789]~P1(f331(f331(f241(a1),f331(f111(a1),x77891)),f2(a1)))+E(f331(f248(a1,a1),f331(a63,f62(f331(f86(a1),f85(a1)),f331(f86(a1),f331(f111(a1),x77891))))),f331(f331(f48(a1),f85(a1)),f331(f111(a1),x77891)))
% 51.10/50.82 [7802]~P1(f331(f331(f241(a1),f331(f111(a1),x78021)),f2(a1)))+E(f331(f258(a1,a1),f331(a63,f62(f331(f86(a1),f85(a1)),f331(f86(a1),f331(f111(a1),x78021))))),f57(a1,f85(a1),f331(f111(a1),x78021)))
% 51.10/50.82 [7849]~P1(f331(f331(f241(a1),a104),x78491))+P1(f331(f331(f241(a1),a104),f331(f331(f3(a1),f331(f331(f87(a1),x78491),x78491)),a104)))
% 51.10/50.82 [7850]~P1(f331(f331(f240(a1),a90),x78501))+P1(f331(f331(f241(a1),a90),f331(f331(f3(a1),f331(f331(f87(a1),x78501),x78501)),a104)))
% 51.10/50.82 [7851]~P1(f331(f331(f240(a1),a104),x78511))+P1(f331(f331(f240(a1),a104),f331(f331(f3(a1),f331(f331(f87(a1),x78511),x78511)),a104)))
% 51.10/50.82 [7852]~P1(f331(f331(f240(a1),a90),x78521))+P1(f331(f331(f240(a1),a90),f331(f331(f3(a1),f331(f331(f87(a1),x78521),x78521)),a104)))
% 51.10/50.82 [8149]~P91(x81491)+~P31(x81491,f331(f111(x81491),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))
% 51.10/50.82 [8330]P1(f331(f331(f241(a1),a104),x83301))+~P1(f331(f331(f241(a1),a104),f331(f331(f3(a1),f331(f331(f87(a1),x83301),x83301)),a104)))
% 51.10/50.82 [8331]P1(f331(f331(f240(a1),a104),x83311))+~P1(f331(f331(f240(a1),a104),f331(f331(f3(a1),f331(f331(f87(a1),x83311),x83311)),a104)))
% 51.10/50.82 [8332]P1(f331(f331(f240(a1),a90),x83321))+~P1(f331(f331(f241(a1),a90),f331(f331(f3(a1),f331(f331(f87(a1),x83321),x83321)),a104)))
% 51.10/50.82 [8333]P1(f331(f331(f240(a1),a90),x83331))+~P1(f331(f331(f240(a1),a90),f331(f331(f3(a1),f331(f331(f87(a1),x83331),x83331)),a104)))
% 51.10/50.82 [8627]E(f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x86271),x86271)),a104)),f331(f331(f93(a847,a847),f331(f111(a847),x86271)),f331(f331(f10(a847,a847,a847),a119),f331(f331(f20(a847,a847,a847),f87(a847)),f7(a847)))))+P1(f331(a190,f331(f111(a1),x86271)))
% 51.10/50.82 [9398]E(x93981,f184(f854(f853(a847,a847),a840)))+P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x93981),f184(f854(f853(a847,a847),a840)))),a75))
% 51.10/50.82 [8561]~P1(f331(a190,f331(f111(a1),x85611)))+P1(f331(a190,f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),x85611),x85611)),a104))))
% 51.10/50.82 [8562]~P1(f331(f331(f241(a1),x85621),a104))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x85621),x85621)),a104)),a104))
% 51.10/50.82 [8563]~P1(f331(f331(f241(a1),x85631),a90))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x85631),x85631)),a104)),a90))
% 51.10/50.82 [8564]~P1(f331(f331(f240(a1),x85641),a104))+P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x85641),x85641)),a104)),a104))
% 51.10/50.82 [8565]~P1(f331(f331(f241(a1),x85651),a90))+P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x85651),x85651)),a104)),a90))
% 51.10/50.82 [8661]~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x86611)))+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),x86611),x86611)),a104))))
% 51.10/50.82 [8791]~P91(x87911)+E(f331(f331(f87(x87911),f85(x87911)),f85(x87911)),f331(f111(x87911),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))
% 51.10/50.82 [8936]P1(f331(a190,f331(f111(a1),x89361)))+~P1(f331(a190,f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89361),x89361)),a104))))
% 51.10/50.82 [8937]P1(f331(f331(f241(a1),x89371),a104))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89371),x89371)),a104)),a104))
% 51.10/50.82 [8938]P1(f331(f331(f241(a1),x89381),a90))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89381),x89381)),a104)),a90))
% 51.10/50.82 [8939]P1(f331(f331(f241(a1),x89391),a90))+~P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89391),x89391)),a104)),a90))
% 51.10/50.82 [8940]P1(f331(f331(f240(a1),x89401),a104))+~P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89401),x89401)),a104)),a104))
% 51.10/50.82 [9448]~P1(f331(f68(f853(a847,a847)),x94481))+P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),f184(f854(f853(a847,a847),a840))),x94481)),a76))
% 51.10/50.82 [9229]~P84(x92291)+E(f331(f331(f250(x92291),f2(x92291)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f2(x92291))
% 51.10/50.82 [9230]~P84(x92301)+E(f331(f331(f250(x92301),f85(x92301)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f85(x92301))
% 51.10/50.82 [9653]~P1(f331(f331(f241(a847),f85(a847)),x96531))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f48(a847),x96531),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.82 [9659]~P1(f331(f331(f241(a847),f2(a847)),x96591))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f48(a847),f331(f331(f87(a847),x96591),f85(a847))),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.82 [9699]~E(f57(a847,x96991,f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f85(a847))+P1(f331(f331(f241(a847),f2(a847)),f57(a847,x96991,f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.82 [9734]E(f57(a847,x97341,f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f85(a847))+~P1(f331(f331(f241(a847),f2(a847)),f57(a847,x97341,f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.82 [4494]~P34(x44941,x44942)+P54(x44941,x44942)
% 51.10/50.82 [4495]~P40(x44951,x44952)+P54(x44951,x44952)
% 51.10/50.82 [4452]E(x44521,x44522)+~E(f40(x44521),f40(x44522))
% 51.10/50.82 [4453]E(x44531,x44532)+~E(f41(x44531),f41(x44532))
% 51.10/50.82 [4455]~E(x44551,x44552)+E(f274(x44551,x44552),f85(a106))
% 51.10/50.82 [4458]E(f218(x44581,x44582),x44581)+~E(x44582,f2(a847))
% 51.10/50.82 [4463]P35(x44631,x44632)+~E(x44632,f187(x44631))
% 51.10/50.82 [4465]~E(x44652,f120(x44651))+E(f146(x44651,x44652),f120(x44651))
% 51.10/50.82 [4466]~E(x44662,f120(x44661))+E(f146(x44661,x44662),f120(x44661))
% 51.10/50.82 [4470]~P35(x44702,x44701)+E(x44701,f187(x44702))
% 51.10/50.82 [4484]~E(f146(x44842,x44841),f120(x44842))+E(x44841,f120(x44842))
% 51.10/50.82 [4485]~E(f146(x44852,x44851),f120(x44852))+E(x44851,f120(x44852))
% 51.10/50.82 [4499]~P88(x44992)+P88(f854(x44991,x44992))
% 51.10/50.82 [4500]~P105(x45002)+P105(f854(x45001,x45002))
% 51.10/50.82 [4501]~P104(x45012)+P104(f854(x45011,x45012))
% 51.10/50.82 [4502]~P93(x45022)+P93(f854(x45021,x45022))
% 51.10/50.82 [4503]~P83(x45032)+P83(f854(x45031,x45032))
% 51.10/50.82 [4504]~P72(x45042)+P72(f854(x45041,x45042))
% 51.10/50.82 [4505]~P103(x45052)+P103(f854(x45051,x45052))
% 51.10/50.82 [4506]~P96(x45062)+P95(f854(x45061,x45062))
% 51.10/50.82 [4507]~P97(x45072)+P97(f854(x45071,x45072))
% 51.10/50.82 [4508]~P97(x45082)+P100(f854(x45081,x45082))
% 51.10/50.82 [4509]~P97(x45092)+P101(f854(x45091,x45092))
% 51.10/50.82 [4510]~P98(x45102)+P98(f854(x45101,x45102))
% 51.10/50.82 [4511]~P7(x45112)+P7(f854(x45111,x45112))
% 51.10/50.82 [4512]~P96(x45122)+P99(f854(x45121,x45122))
% 51.10/50.82 [4513]~P108(x45132)+P108(f854(x45131,x45132))
% 51.10/50.82 [4514]~P96(x45142)+P96(f854(x45141,x45142))
% 51.10/50.82 [4526]E(x45261,x45262)+~E(f331(a119,x45261),f331(a119,x45262))
% 51.10/50.82 [4527]E(x45271,x45272)+~E(f331(a119,x45271),f331(a119,x45272))
% 51.10/50.82 [4528]E(x45281,x45282)+~E(f331(a29,x45281),f331(a29,x45282))
% 51.10/50.82 [4529]E(x45291,x45292)+~E(f331(a5,x45291),f331(a5,x45292))
% 51.10/50.82 [4530]E(x45301,x45302)+~E(f331(a22,x45301),f331(a22,x45302))
% 51.10/50.82 [4531]E(x45311,x45312)+~E(f331(a22,x45311),f331(a22,x45312))
% 51.10/50.82 [4532]E(x45321,x45322)+~E(f331(a115,x45321),f331(a115,x45322))
% 51.10/50.82 [4628]~P5(x46281)+E(f57(x46281,x46282,x46282),f2(x46281))
% 51.10/50.82 [4662]~P34(x46621,x46622)+P34(f848(x46621),f141(x46621,x46622))
% 51.10/50.82 [4663]~P34(x46631,x46632)+P34(f848(x46631),f140(x46631,x46632))
% 51.10/50.82 [4757]~P34(x47571,x47572)+P34(f854(x47571,a840),f325(x47571,x47572))
% 51.10/50.82 [4758]~P34(x47581,x47582)+P34(f854(x47581,a840),f323(x47581,x47582))
% 51.10/50.82 [4877]~P8(x48771)+P36(f303(a1,x48771,x48772))
% 51.10/50.82 [4976]~P34(x49761,x49762)+P56(x49761,f74(x49761,x49761,x49762))
% 51.10/50.82 [5465]~P76(x54651)+P27(x54651,x54651,f86(x54651),x54652)
% 51.10/50.82 [4479]~E(x44792,f120(x44791))+E(f331(f160(x44791),x44792),f120(x44791))
% 51.10/50.82 [4480]~E(x44802,f120(x44801))+E(f331(f159(x44801),x44802),f120(x44801))
% 51.10/50.82 [4481]~E(x44812,f120(x44811))+E(f331(f160(x44811),x44812),f120(x44811))
% 51.10/50.82 [4536]E(x45361,f331(a112,x45362))+~E(f331(f107(a1),x45361),x45362)
% 51.10/50.82 [4538]E(x45381,f120(x45382))+~E(f331(f160(x45382),x45381),f120(x45382))
% 51.10/50.82 [4539]E(x45391,f120(x45392))+~E(f331(f159(x45392),x45391),f120(x45392))
% 51.10/50.82 [4540]E(x45401,f120(x45402))+~E(f331(f160(x45402),x45401),f120(x45402))
% 51.10/50.82 [4555]~P91(x45551)+E(f331(f111(x45551),x45552),f331(f110(x45551),x45552))
% 51.10/50.82 [4562]~E(x45622,f187(x45621))+E(f233(x45621,x45622),f184(f854(x45621,a840)))
% 51.10/50.82 [4563]~P57(x45631)+P1(f331(f68(x45631),x45632))
% 51.10/50.82 [4564]~P57(x45641)+P1(f331(f68(x45641),x45642))
% 51.10/50.82 [4571]E(x45711,f187(x45712))+E(f331(f234(x45712),f359(x45712,x45711)),x45711)
% 51.10/50.82 [4572]E(x45721,f187(x45722))+E(f331(f234(x45722),f469(x45722,x45721)),x45721)
% 51.10/50.82 [4574]~E(f720(x45742,x45741),f120(x45741))+E(f169(x45741,x45742),f120(f848(x45741)))
% 51.10/50.82 [4583]~E(x45832,f120(x45831))+E(f331(f163(x45831),x45832),f184(f854(x45831,a840)))
% 51.10/50.82 [4584]~E(x45842,f120(x45841))+E(f184(f854(x45841,a840)),f331(f163(x45841),x45842))
% 51.10/50.82 [4585]E(x45851,x45852)+~E(f331(f107(a1),x45851),f331(f107(a1),x45852))
% 51.10/50.82 [4586]E(x45861,x45862)+~E(f331(f107(a1),x45861),f331(f107(a1),x45862))
% 51.10/50.82 [4589]E(f216(x45891,x45892),f2(a847))+P1(f331(f68(x45891),x45892))
% 51.10/50.82 [4607]~P86(x46071)+E(f89(x46071,f89(x46071,x46072)),f89(x46071,x46072))
% 51.10/50.82 [4619]~P87(x46191)+E(f331(f331(f250(x46191),x46192),f85(a847)),x46192)
% 51.10/50.82 [4620]~P74(x46201)+E(f331(f331(f250(x46201),x46202),f85(a847)),x46202)
% 51.10/50.82 [4622]E(x46221,x46222)+E(f274(x46221,x46222),f331(f331(f87(a106),x46222),f85(a106)))
% 51.10/50.82 [4623]E(f331(f47(x46231),x46232),f2(a847))+P1(f331(f68(x46231),x46232))
% 51.10/50.82 [4624]E(f331(f47(x46241),x46242),f2(a847))+P1(f331(f68(x46241),x46242))
% 51.10/50.82 [4625]E(f331(f47(x46251),x46252),f2(a847))+P1(f331(f68(x46251),x46252))
% 51.10/50.82 [4629]~E(f146(x46291,x46292),x46292)+P1(f331(f132(x46291),x46292))
% 51.10/50.82 [4632]~P71(x46321)+E(f331(f331(f87(x46321),x46322),f2(x46321)),x46322)
% 51.10/50.82 [4633]~P68(x46331)+E(f331(f331(f87(x46331),x46332),f2(x46331)),x46332)
% 51.10/50.82 [4634]~P87(x46341)+E(f331(f331(f87(x46341),x46342),f2(x46341)),x46342)
% 51.10/50.82 [4635]~P87(x46351)+E(f331(f331(f88(x46351),x46352),f85(x46351)),x46352)
% 51.10/50.82 [4636]~P70(x46361)+E(f331(f331(f88(x46361),x46362),f85(x46361)),x46362)
% 51.10/50.82 [4637]~P74(x46371)+E(f331(f331(f88(x46371),x46372),f85(x46371)),x46372)
% 51.10/50.82 [4638]~P5(x46381)+E(f331(f331(f48(x46381),x46382),f85(x46381)),x46382)
% 51.10/50.82 [4639]~P69(x46391)+E(f331(f331(f3(x46391),x46392),f2(x46391)),x46392)
% 51.10/50.82 [4640]~P114(x46401)+E(f331(f331(f291(x46401),x46402),f85(x46401)),x46402)
% 51.10/50.82 [4641]~P95(x46411)+E(f331(f331(f108(x46411),x46412),f184(x46411)),x46412)
% 51.10/50.82 [4642]~P99(x46421)+E(f331(f331(f109(x46421),x46422),f247(x46421)),x46422)
% 51.10/50.82 [4643]~P87(x46431)+E(f331(f331(f250(x46431),x46432),f2(a847)),f85(x46431))
% 51.10/50.82 [4644]~P107(x46441)+E(f331(f331(f250(x46441),x46442),f2(a847)),f85(x46441))
% 51.10/50.82 [4645]~E(x46452,f184(f854(x46451,a840)))+E(f331(f47(x46451),x46452),f2(a847))
% 51.10/50.82 [4656]~P5(x46561)+E(f57(x46561,x46562,f2(x46561)),x46562)
% 51.10/50.82 [4664]~P87(x46641)+E(f331(f331(f88(x46641),x46642),f2(x46641)),f2(x46641))
% 51.10/50.82 [4665]~P122(x46651)+E(f331(f331(f88(x46651),x46652),f2(x46651)),f2(x46651))
% 51.10/50.82 [4666]~P5(x46661)+E(f331(f331(f48(x46661),x46662),f2(x46661)),f2(x46661))
% 51.10/50.82 [4667]~P115(x46671)+E(f331(f331(f291(x46671),x46672),f2(x46671)),f2(x46671))
% 51.10/50.82 [4668]~P99(x46681)+E(f331(f331(f108(x46681),x46682),f247(x46681)),f247(x46681))
% 51.10/50.82 [4669]~P95(x46691)+E(f331(f331(f109(x46691),x46692),f184(x46691)),f184(x46691))
% 51.10/50.82 [4670]E(x46701,f187(x46702))+~E(f233(x46702,x46701),f184(f854(x46702,a840)))
% 51.10/50.82 [4672]~P5(x46721)+E(f57(x46721,x46722,f85(x46721)),f2(x46721))
% 51.10/50.82 [4673]~P5(x46731)+E(f57(x46731,f2(x46731),x46732),f2(x46731))
% 51.10/50.82 [4724]P34(x47241,x47242)+~E(f591(x47242,x47241),f184(f854(x47241,a840)))
% 51.10/50.82 [4725]E(x47251,f120(x47252))+~E(f331(f163(x47252),x47251),f184(f854(x47252,a840)))
% 51.10/50.82 [4726]E(x47261,f120(x47262))+~E(f184(f854(x47262,a840)),f331(f163(x47262),x47261))
% 51.10/50.82 [4729]~E(x47291,x47292)+P1(f331(f331(a328,x47291),x47292))
% 51.10/50.82 [4739]P1(x47391)+P1(f331(f331(a334,x47391),x47392))
% 51.10/50.82 [4740]E(x47401,f120(x47402))+E(f331(f331(f155(x47402),x47401),f2(a847)),f331(f136(x47402),x47401))
% 51.10/50.82 [4742]E(f146(x47421,x47422),x47422)+~P1(f331(f132(x47421),x47422))
% 51.10/50.82 [4743]E(f146(x47431,x47432),x47432)+~P1(f331(f132(x47431),x47432))
% 51.10/50.82 [4748]~P1(x47482)+P1(f331(f331(a334,x47481),x47482))
% 51.10/50.82 [4749]~P1(x47492)+P1(f331(f331(a330,x47491),x47492))
% 51.10/50.82 [4750]~P1(x47501)+P1(f331(f331(a330,x47501),x47502))
% 51.10/50.82 [4760]~E(f721(x47602,x47601),f726(x47602,x47601))+P1(f331(f132(x47601),x47602))
% 51.10/50.82 [4768]E(f331(f264(x47681),x47682),f184(f854(x47681,a840)))+P1(f331(x47682,f538(x47682)))
% 51.10/50.82 [4769]E(f184(f854(x47691,a840)),f331(f264(x47691),x47692))+P1(f331(x47692,f539(x47692)))
% 51.10/50.82 [4833]~P86(x48331)+E(f331(f331(f88(x48331),x48332),f89(x48331,x48332)),f331(f82(x48331),x48332))
% 51.10/50.82 [4844]~E(x48441,f2(a1))+E(f58(x48441,x48442),f331(f331(f249(a1,a1),f2(a1)),f2(a1)))
% 51.10/50.82 [4845]~E(x48451,f2(a1))+E(f58(x48451,x48452),f331(f331(f249(a1,a1),f2(a1)),f2(a1)))
% 51.10/50.82 [4876]~P54(x48761,x48762)+P54(x48761,f331(f286(x48761,x48761),x48762))
% 51.10/50.82 [4893]~E(f331(a32,x48931),f331(f234(a841),x48932))+P1(f331(a26,f331(a29,x48931)))
% 51.10/50.82 [4897]E(x48971,x48972)+~P1(f331(f331(a328,x48971),x48972))
% 51.10/50.82 [4900]~P1(f331(a26,x49002))+P1(f331(a26,f37(x49001,x49002)))
% 51.10/50.82 [4901]~P1(f331(a26,x49012))+P1(f331(a26,f37(x49011,x49012)))
% 51.10/50.82 [4910]P1(x49101)+~P1(f331(f331(a329,x49102),x49101))
% 51.10/50.82 [4911]P1(x49111)+~P1(f331(f331(a329,x49111),x49112))
% 51.10/50.82 [4915]~P108(x49151)+P1(f331(f331(f240(x49151),x49152),f247(x49151)))
% 51.10/50.82 [4916]~P87(x49161)+P1(f331(f331(f287(x49161),x49162),f2(x49161)))
% 51.10/50.82 [4920]E(x49201,x49202)+~E(f331(x49201,f362(x49202,x49201)),f331(x49202,f362(x49202,x49201)))
% 51.10/50.82 [4950]E(x49501,f2(a847))+E(f218(x49501,f57(a847,x49502,x49501)),f218(x49502,x49501))
% 51.10/50.82 [4955]~P102(x49551)+P16(x49551,f331(f331(f145(x49551),x49552),f120(x49551)))
% 51.10/50.82 [4957]E(x49571,f2(a1))+P1(f331(f61(x49572,x49571),f58(x49572,x49571)))
% 51.10/50.82 [4974]~E(x49741,x49742)+P1(f331(f331(f241(a847),x49741),f331(a119,x49742)))
% 51.10/50.82 [4984]~E(x49841,f2(a847))+P1(f331(f331(f241(a847),x49841),f331(a119,x49842)))
% 51.10/50.82 [4994]P1(f331(x49941,x49942))+P1(f331(f331(f240(a1),f2(a1)),f760(x49941)))
% 51.10/50.82 [5031]P1(f331(a26,x50311))+~P1(f331(a26,f37(x50312,x50311)))
% 51.10/50.82 [5032]P1(f331(a26,x50321))+~P1(f331(a26,f37(x50322,x50321)))
% 51.10/50.82 [5033]P1(f331(a26,x50331))+~P1(f331(a26,f38(x50332,x50331)))
% 51.10/50.82 [5034]P1(f331(a26,x50341))+~P1(f331(a26,f38(x50342,x50341)))
% 51.10/50.82 [5035]P1(f331(a26,x50351))+~P1(f331(a26,f38(x50351,x50352)))
% 51.10/50.82 [5036]P1(f331(a26,x50361))+~P1(f331(a26,f38(x50361,x50362)))
% 51.10/50.82 [5065]P54(x50651,x50652)+~P54(x50651,f331(f286(x50651,x50651),x50652))
% 51.10/50.82 [5067]~E(f57(a847,x50672,x50671),f2(a847))+E(f331(f331(f88(a847),x50671),f777(x50671,x50672)),x50672)
% 51.10/50.82 [5068]~E(f57(a1,x50682,x50681),f2(a1))+E(f331(f331(f88(a1),x50681),f778(x50681,x50682)),x50682)
% 51.10/50.82 [5073]~E(x50731,f331(a119,x50732))+P1(f331(f331(f240(a847),x50731),f331(a119,x50732)))
% 51.10/50.82 [5094]~P1(f331(x50941,x50942))+P1(f331(f331(f240(a1),f2(a1)),f727(x50941)))
% 51.10/50.82 [5105]E(f331(f331(f3(a847),f331(a112,x51051)),f331(a112,x51052)),f331(a112,x51051))+~P1(f331(a190,x51052))
% 51.10/50.82 [5133]E(f275(x51331,x51332),f85(a106))+~P1(f331(f331(f240(a106),x51331),f85(a106)))
% 51.10/50.82 [5222]E(f331(f331(f155(x52221),x52222),f721(x52222,x52221)),f331(f331(f155(x52221),x52222),f726(x52222,x52221)))+P1(f331(f132(x52221),x52222))
% 51.10/50.82 [5264]~P1(f331(x52641,f97(x52642,x52641)))+P1(f331(x52641,f592(x52642,x52641)))
% 51.10/50.82 [5327]P56(x53271,x53272)+~P1(f331(f320(x53271,x53272),f579(x53272,x53271)))
% 51.10/50.82 [5472]~E(f331(a119,f57(a847,x54721,x54722)),x54722)+E(f57(a847,f331(a119,x54721),x54722),f2(a847))
% 51.10/50.82 [5527]P34(x55271,x55272)+P1(f331(f331(f333(x55271),f691(x55272,x55271)),f692(x55272,x55271)))
% 51.10/50.82 [5533]~P84(x55331)+P1(f331(f331(f333(x55331),f331(f107(x55331),x55332)),f181(x55331)))
% 51.10/50.82 [5534]~P133(x55341)+P1(f331(f331(f333(x55341),f331(f107(x55341),x55342)),f117(x55341)))
% 51.10/50.82 [5535]~P133(x55351)+P1(f331(f331(f333(x55351),f331(f110(x55351),x55352)),f117(x55351)))
% 51.10/50.82 [5536]~P91(x55361)+P1(f331(f331(f333(x55361),f331(f111(x55361),x55362)),f117(x55361)))
% 51.10/50.82 [5690]E(f331(a119,f57(a847,x56901,x56902)),x56902)+E(f57(a847,f331(a119,x56901),x56902),f331(a119,f57(a847,x56901,x56902)))
% 51.10/50.82 [6114]P34(x61141,x61142)+~P1(f331(f331(f333(x61141),f569(x61142,x61141)),f321(x61141,x61142)))
% 51.10/50.82 [6148]~P85(x61481)+~P1(f331(f331(f241(x61481),f331(f107(x61481),x61482)),f2(x61481)))
% 51.10/50.82 [6149]~P78(x61491)+~P1(f331(f331(f241(x61491),f331(f82(x61491),x61492)),f2(x61491)))
% 51.10/50.82 [6240]P1(f331(f331(f241(a1),x62401),f57(a1,x62402,x62401)))+~P1(f331(f331(f241(a1),x62401),f2(a1)))
% 51.10/50.82 [6241]P1(f331(f331(f241(a1),x62411),f57(a1,x62412,x62411)))+~P1(f331(f331(f241(a1),x62411),f2(a1)))
% 51.10/50.82 [6348]E(f331(f331(f310(a847),f331(a119,x63481)),f303(a847,x63482,x63481)),f303(a847,x63482,f331(a119,x63481)))+~P1(f331(f331(f240(a847),x63482),f331(a119,x63481)))
% 51.10/50.82 [6573]E(f331(f159(x65731),x65732),x65732)+~P1(f331(f331(f240(a847),f331(f185(f848(x65731)),x65732)),f85(a847)))
% 51.10/50.82 [6596]~P78(x65961)+P1(f331(f331(f240(x65961),f331(f86(x65961),f331(f82(x65961),x65962))),f2(x65961)))
% 51.10/50.82 [6632]~P34(x66321,x66322)+P34(x66321,f331(f331(f289(x66321,x66321,x66321),x66322),f308(x66321,x66322)))
% 51.10/50.82 [6862]~P1(f331(f331(f241(a1),x68622),f2(a1)))+P1(f331(f331(f240(a1),f57(a1,x68621,x68622)),f2(a1)))
% 51.10/50.82 [6863]~P1(f331(f331(f241(a1),x68632),f2(a1)))+P1(f331(f331(f240(a1),f57(a1,x68631,x68632)),f2(a1)))
% 51.10/50.82 [7272]~P84(x72721)+E(f186(x72721,f331(f331(f9(x72721,x72721,x72721),f87(x72721)),f85(x72721)),x72722,f2(x72721)),f331(f107(x72721),x72722))
% 51.10/50.82 [7305]~P119(x73051)+~P1(f331(f331(f241(x73051),f331(f331(f88(x73051),x73052),x73052)),f2(x73051)))
% 51.10/50.82 [9833]~P86(x98331)+~P1(f331(f331(f241(x98331),f331(f331(f250(x98331),x98332),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f2(x98331)))
% 51.10/50.82 [4537]~E(x45372,f120(x45371))+E(f331(f185(f848(x45371)),x45372),f2(a847))
% 51.10/50.82 [4575]~E(x45751,f2(a847))+E(f331(f331(f87(a847),x45751),x45752),x45752)
% 51.10/50.82 [4576]~E(x45762,f2(a847))+E(f331(f331(f88(a847),x45761),x45762),f2(a847))
% 51.10/50.82 [4577]~E(x45771,f2(a847))+E(f331(f331(f88(a847),x45771),x45772),f2(a847))
% 51.10/50.82 [4578]~E(x45781,f2(a847))+E(f331(f331(f88(a847),x45781),x45782),f2(a847))
% 51.10/50.82 [4579]~E(x45792,f2(a1))+E(f331(f331(f48(a1),x45791),x45792),f2(a1))
% 51.10/50.82 [4580]~E(x45802,f2(a847))+E(f331(f331(f250(a847),x45801),x45802),f85(a847))
% 51.10/50.82 [4590]E(x45901,f120(x45902))+~E(f331(f185(f848(x45902)),x45901),f2(a847))
% 51.10/50.82 [4591]~P94(x45911)+E(f331(f331(f88(x45911),x45912),x45912),x45912)
% 51.10/50.82 [4592]~P94(x45921)+E(f331(f331(f88(x45921),x45922),x45922),x45922)
% 51.10/50.82 [4593]~P102(x45931)+E(f331(f331(f244(x45931),x45932),x45932),x45932)
% 51.10/50.82 [4594]~P102(x45941)+E(f331(f331(f244(x45941),x45942),x45942),x45942)
% 51.10/50.82 [4595]~P102(x45951)+E(f331(f331(f239(x45951),x45952),x45952),x45952)
% 51.10/50.82 [4596]~P102(x45961)+E(f331(f331(f239(x45961),x45962),x45962),x45962)
% 51.10/50.82 [4597]~P97(x45971)+E(f331(f331(f108(x45971),x45972),x45972),x45972)
% 51.10/50.82 [4598]~P100(x45981)+E(f331(f331(f108(x45981),x45982),x45982),x45982)
% 51.10/50.82 [4599]~P100(x45991)+E(f331(f331(f108(x45991),x45992),x45992),x45992)
% 51.10/50.82 [4600]~P97(x46001)+E(f331(f331(f109(x46001),x46002),x46002),x46002)
% 51.10/50.82 [4601]~P101(x46011)+E(f331(f331(f109(x46011),x46012),x46012),x46012)
% 51.10/50.82 [4602]~P101(x46021)+E(f331(f331(f109(x46021),x46022),x46022),x46022)
% 51.10/50.82 [4618]~P69(x46181)+E(f331(f331(f3(x46181),x46182),x46182),f2(x46181))
% 51.10/50.82 [4630]~P69(x46301)+E(f331(f86(x46301),f331(f86(x46301),x46302)),x46302)
% 51.10/50.82 [4631]~P93(x46311)+E(f331(f86(x46311),f331(f86(x46311),x46312)),x46312)
% 51.10/50.82 [4648]~E(x46482,f2(a847))+E(f331(f331(f250(a847),x46481),x46482),f331(a119,f2(a847)))
% 51.10/50.82 [4681]~P71(x46811)+E(f331(f331(f87(x46811),f2(x46811)),x46812),x46812)
% 51.10/50.82 [4682]~P68(x46821)+E(f331(f331(f87(x46821),f2(x46821)),x46822),x46822)
% 51.10/50.82 [4683]~P87(x46831)+E(f331(f331(f87(x46831),f2(x46831)),x46832),x46832)
% 51.10/50.82 [4684]~P87(x46841)+E(f331(f331(f88(x46841),f85(x46841)),x46842),x46842)
% 51.10/50.82 [4685]~P70(x46851)+E(f331(f331(f88(x46851),f85(x46851)),x46852),x46852)
% 51.10/50.82 [4686]~P74(x46861)+E(f331(f331(f88(x46861),f85(x46861)),x46862),x46862)
% 51.10/50.82 [4687]~P95(x46871)+E(f331(f331(f108(x46871),f184(x46871)),x46872),x46872)
% 51.10/50.82 [4688]~P99(x46881)+E(f331(f331(f109(x46881),f247(x46881)),x46882),x46882)
% 51.10/50.82 [4705]~P87(x47051)+E(f331(f331(f88(x47051),f2(x47051)),x47052),f2(x47051))
% 51.10/50.82 [4706]~P122(x47061)+E(f331(f331(f88(x47061),f2(x47061)),x47062),f2(x47061))
% 51.10/50.82 [4707]~P5(x47071)+E(f331(f331(f48(x47071),f2(x47071)),x47072),f2(x47071))
% 51.10/50.82 [4708]~P74(x47081)+E(f331(f331(f250(x47081),f85(x47081)),x47082),f85(x47081))
% 51.10/50.82 [4709]~P114(x47091)+E(f331(f331(f291(x47091),f2(x47091)),x47092),f2(x47091))
% 51.10/50.82 [4710]~P99(x47101)+E(f331(f331(f108(x47101),f247(x47101)),x47102),f247(x47101))
% 51.10/50.82 [4711]~P95(x47111)+E(f331(f331(f109(x47111),f184(x47111)),x47112),f184(x47111))
% 51.10/50.82 [4719]E(x47191,f120(x47192))+E(f139(x47192,f331(f160(x47192),x47191)),f331(f136(x47192),x47191))
% 51.10/50.82 [4720]E(x47201,f120(x47202))+E(f331(f136(x47202),f331(f160(x47202),x47201)),f139(x47202,x47201))
% 51.10/50.82 [4721]E(x47211,f2(a847))+~E(f331(f331(f87(a847),x47212),x47211),x47212)
% 51.10/50.82 [4727]~P133(x47271)+E(f331(f110(x47271),f331(f107(a1),x47272)),f331(f107(x47271),x47272))
% 51.10/50.82 [4728]~P91(x47281)+E(f331(f110(x47281),f331(f111(a1),x47282)),f331(f111(x47281),x47282))
% 51.10/50.82 [4733]E(x47331,f85(a847))+~E(f331(f331(f88(a847),x47332),x47331),f85(a847))
% 51.10/50.82 [4734]E(x47341,f85(a847))+~E(f331(f331(f88(a847),x47341),x47342),f85(a847))
% 51.10/50.82 [4735]E(x47351,f2(a847))+~E(f331(f331(f87(a847),x47352),x47351),f2(a847))
% 51.10/50.82 [4736]E(x47361,f2(a847))+~E(f331(f331(f87(a847),x47361),x47362),f2(a847))
% 51.10/50.82 [4737]E(x47371,f85(a847))+~E(f331(f331(f88(a847),x47372),x47371),f85(a847))
% 51.10/50.82 [4738]E(x47381,f85(a847))+~E(f331(f331(f88(a847),x47381),x47382),f85(a847))
% 51.10/50.82 [4753]~P86(x47531)+E(f331(f82(x47531),f331(f107(x47531),x47532)),f331(f107(x47531),x47532))
% 51.10/50.82 [4754]~P78(x47541)+E(f331(f82(x47541),f331(f86(x47541),x47542)),f331(f82(x47541),x47542))
% 51.10/50.82 [4755]~P78(x47551)+E(f331(f82(x47551),f331(f82(x47551),x47552)),f331(f82(x47551),x47552))
% 51.10/50.82 [4756]~P68(x47561)+E(f331(f157(x47561),f331(f160(x47561),x47562)),f331(f157(x47561),x47562))
% 51.10/50.82 [4761]~E(x47611,f331(a119,f2(a847)))+E(f331(f331(f250(a847),x47611),x47612),f331(a119,f2(a847)))
% 51.10/50.82 [4771]~P69(x47711)+E(f331(f331(f3(x47711),f2(x47711)),x47712),f331(f86(x47711),x47712))
% 51.10/50.82 [4772]~E(x47722,f2(a847))+E(f135(a847,f331(f302(a847,x47721),x47722)),f120(a847))
% 51.10/50.82 [4781]~P91(x47811)+E(f331(f331(f87(x47811),x47812),f331(f111(x47811),a90)),x47812)
% 51.10/50.82 [4782]E(x47821,f2(a1))+E(f59(f331(f82(a1),x47822),f331(f82(a1),x47821)),f65(x47822,x47821))
% 51.10/50.82 [4792]~E(x47921,x47922)+P1(f331(f331(f240(a847),x47921),x47922))
% 51.10/50.82 [4793]~E(x47931,x47932)+P1(f331(f331(f240(a847),x47931),x47932))
% 51.10/50.82 [4794]~E(x47941,x47942)+P1(f331(f331(f240(a847),x47941),x47942))
% 51.10/50.82 [4795]~E(x47951,x47952)+P1(f331(f331(f287(a847),x47951),x47952))
% 51.10/50.82 [4796]~E(x47961,x47962)+P1(f331(f331(f287(a847),x47961),x47962))
% 51.10/50.82 [4797]~E(x47971,x47972)+P1(f331(f331(f287(a847),x47971),x47972))
% 51.10/50.82 [4798]~E(x47981,x47982)+P1(f331(f331(f287(a847),x47981),x47982))
% 51.10/50.82 [4805]~E(x48051,f2(a106))+E(f331(f331(f87(a847),f331(a22,x48051)),x48052),x48052)
% 51.10/50.82 [4806]~E(f331(f111(a1),x48062),f331(f107(a1),x48061))+E(x48061,f331(a112,f331(f111(a1),x48062)))
% 51.10/50.82 [4815]~P8(x48151)+P8(f331(f331(f250(a1),x48151),x48152))
% 51.10/50.82 [4816]~P69(x48161)+E(f331(f331(f87(x48161),x48162),f331(f86(x48161),x48162)),f2(x48161))
% 51.10/50.82 [4817]~P93(x48171)+E(f331(f331(f108(x48171),x48172),f331(f86(x48171),x48172)),f247(x48171))
% 51.10/50.82 [4818]~P93(x48181)+E(f331(f331(f109(x48181),x48182),f331(f86(x48181),x48182)),f184(x48181))
% 51.10/50.82 [4842]E(x48421,f2(a847))+~E(f331(f86(a1),f331(f107(a1),x48422)),f331(f107(a1),x48421))
% 51.10/50.82 [4843]E(x48431,f2(a847))+~E(f331(f86(a1),f331(f107(a1),x48431)),f331(f107(a1),x48432))
% 51.10/50.82 [4853]E(f192(x48531,x48532),f2(a1))+P1(f331(f331(f240(a1),x48532),x48531))
% 51.10/50.82 [4854]E(f246(x48541,x48542),f2(a106))+P1(f331(f331(f241(a106),x48541),x48542))
% 51.10/50.82 [4855]E(f168(x48551,x48552),f120(a1))+P1(f331(f331(f240(a1),x48551),x48552))
% 51.10/50.82 [4868]E(x48681,f331(a119,f2(a847)))+~E(f331(f331(f88(a847),x48682),x48681),f331(a119,f2(a847)))
% 51.10/50.82 [4869]E(x48691,f331(a119,f2(a847)))+~E(f331(f331(f88(a847),x48691),x48692),f331(a119,f2(a847)))
% 51.10/50.82 [4870]~P105(x48701)+P1(f331(f331(f240(x48701),x48702),x48702))
% 51.10/50.82 [4871]~P87(x48711)+P1(f331(f331(f287(x48711),x48712),x48712))
% 51.10/50.82 [4874]~P91(x48741)+E(f331(f331(f88(x48741),x48742),f331(f111(x48741),a104)),f331(f86(x48741),x48742))
% 51.10/50.82 [4889]~P91(x48891)+E(f331(f86(x48891),f331(f111(x48891),x48892)),f331(f111(x48891),f331(f86(a1),x48892)))
% 51.10/50.82 [4890]~P133(x48901)+E(f331(f86(x48901),f331(f110(x48901),x48902)),f331(f110(x48901),f331(f86(a1),x48902)))
% 51.10/50.82 [4891]~P91(x48911)+E(f331(f86(x48911),f331(f111(x48911),x48912)),f331(f111(x48911),f331(f86(a1),x48912)))
% 51.10/50.82 [4921]~E(x49211,f331(a119,x49212))+P1(f331(f331(f241(a847),f2(a847)),x49211))
% 51.10/50.82 [4938]~P102(x49381)+E(f331(f86(f854(x49381,a840)),f331(f301(x49381),x49382)),f331(f304(x49381),x49382))
% 51.10/50.82 [4939]~P102(x49391)+E(f331(f86(f854(x49391,a840)),f331(f265(x49391),x49392)),f331(f266(x49391),x49392))
% 51.10/50.82 [4940]~P102(x49401)+E(f331(f86(f854(x49401,a840)),f331(f266(x49401),x49402)),f331(f265(x49401),x49402))
% 51.10/50.82 [4941]~P102(x49411)+E(f331(f86(f854(x49411,a840)),f331(f304(x49411),x49412)),f331(f301(x49411),x49412))
% 51.10/50.82 [4949]~E(f331(f107(a1),x49492),x49491)+P1(f331(f331(f240(a1),f2(a1)),x49491))
% 51.10/50.82 [4956]~E(x49562,f2(a1))+E(f65(x49561,x49562),f331(f331(f249(a1,a1),f2(a1)),f331(f82(a1),x49561)))
% 51.10/50.82 [4958]~P103(x49581)+P1(f331(f331(f240(x49581),f184(x49581)),x49582))
% 51.10/50.82 [4959]~P87(x49591)+P1(f331(f331(f287(x49591),f85(x49591)),x49592))
% 51.10/50.82 [4989]E(x49891,x49892)+~E(f331(f331(f87(a1),x49891),x49891),f331(f331(f87(a1),x49892),x49892))
% 51.10/50.82 [4993]~P1(f331(x49931,x49932))+P1(f331(x49931,f331(a112,f727(x49931))))
% 51.10/50.82 [5019]~P86(x50191)+E(f331(f331(f88(x50191),f89(x50191,x50192)),f331(f82(x50191),x50192)),x50192)
% 51.10/50.82 [5020]E(x50201,x50202)+~P1(f331(f331(f191(a25),x50201),x50202))
% 51.10/50.82 [5030]~E(x50302,f2(a847))+E(f92(f853(a847,a847),f60(x50301,x50302)),f331(f331(f249(a847,a847),f2(a847)),x50301))
% 51.10/50.82 [5037]~E(x50371,x50372)+~P1(f331(f331(f241(a847),x50371),x50372))
% 51.10/50.82 [5038]~E(x50381,x50382)+~P1(f331(f331(f241(a847),x50381),x50382))
% 51.10/50.82 [5039]~E(x50391,x50392)+~P1(f331(f331(f241(a847),x50391),x50392))
% 51.10/50.82 [5040]~E(x50401,x50402)+~P1(f331(f331(f241(a847),x50401),x50402))
% 51.10/50.82 [5041]~E(x50411,x50412)+~P1(f331(f331(f241(a847),x50411),x50412))
% 51.10/50.82 [5042]~E(x50421,x50422)+~P1(f331(f331(f241(a1),x50421),x50422))
% 51.10/50.82 [5045]~P84(x50451)+E(f331(f331(f87(x50451),f85(x50451)),f331(f107(x50451),x50452)),f331(f107(x50451),f331(a119,x50452)))
% 51.10/50.82 [5049]~E(x50491,f2(a847))+~P1(f331(f331(f241(a847),x50492),x50491))
% 51.10/50.82 [5062]E(f146(x50621,x50622),x50622)+~E(f331(f185(f848(x50621)),f146(x50621,x50622)),f331(f185(f848(x50621)),x50622))
% 51.10/50.82 [5063]E(f331(f47(x50631),f331(f163(x50631),x50632)),f331(f185(f848(x50631)),x50632))+~P1(f331(f132(x50631),x50632))
% 51.10/50.82 [5072]~P1(f331(x50721,f722(x50721)))+P1(f331(x50721,f331(f107(a1),x50722)))
% 51.10/50.82 [5083]E(f246(x50831,x50832),x50832)+~P1(f331(f331(f241(a106),x50831),x50832))
% 51.10/50.82 [5085]E(f275(x50851,x50852),f85(a106))+~P1(f331(f331(f241(a106),x50852),x50851))
% 51.10/50.82 [5086]E(f168(x50861,x50862),f120(a1))+~P1(f331(f331(f241(a1),x50862),x50861))
% 51.10/50.82 [5089]~P88(x50891)+E(f303(x50891,x50892,x50892),f331(f331(f310(x50891),x50892),f184(f854(x50891,a840))))
% 51.10/50.82 [5108]~E(f331(f331(f3(a847),x51081),x51082),f2(a847))+P1(f331(f331(f240(a847),x51081),x51082))
% 51.10/50.82 [5134]~P105(x51341)+~P1(f331(f331(f241(x51341),x51342),x51342))
% 51.10/50.82 [5136]~E(f57(a1,x51361,x51362),f2(a1))+E(f57(a1,x51361,f331(f86(a1),x51362)),f2(a1))
% 51.10/50.82 [5137]~E(f57(a1,x51371,x51372),f2(a1))+E(f57(a1,x51371,f331(f86(a1),x51372)),f2(a1))
% 51.10/50.82 [5138]~E(f57(a1,x51381,x51382),f2(a1))+E(f57(a1,f331(f86(a1),x51381),x51382),f2(a1))
% 51.10/50.82 [5139]~E(f57(a1,x51391,x51392),f2(a1))+E(f57(a1,f331(f86(a1),x51391),x51392),f2(a1))
% 51.10/50.82 [5146]E(f331(f302(a847,x51461),f331(a119,x51462)),f184(f854(a847,a840)))+P1(f331(f331(f240(a847),x51461),x51462))
% 51.10/50.82 [5163]E(f135(a847,f331(f302(a847,x51631),x51632)),f120(a847))+P1(f331(f331(f241(a847),x51631),x51632))
% 51.10/50.82 [5168]~E(f331(f47(x51681),f331(f163(x51681),x51682)),f331(f185(f848(x51681)),x51682))+P1(f331(f132(x51681),x51682))
% 51.10/50.82 [5172]~P1(f331(f132(x51721),x51722))+P1(f331(f132(x51721),f331(f159(x51721),x51722)))
% 51.10/50.82 [5173]~P1(f331(f132(x51731),x51732))+P1(f331(f132(x51731),f331(f162(x51731),x51732)))
% 51.10/50.82 [5174]~P1(f331(f132(x51741),x51742))+P1(f331(f132(x51741),f331(f160(x51741),x51742)))
% 51.10/50.82 [5182]P1(f331(x51821,x51822))+~P1(f331(x51821,f331(a112,f760(x51821))))
% 51.10/50.82 [5183]P1(f331(f331(f240(a847),x51832),x51831))+P1(f331(f331(f240(a847),x51831),x51832))
% 51.10/50.82 [5184]P1(f331(f331(f240(a1),x51842),x51841))+P1(f331(f331(f240(a1),x51841),x51842))
% 51.10/50.82 [5186]~P78(x51861)+P1(f331(f331(f240(x51861),x51862),f331(f82(x51861),x51862)))
% 51.10/50.82 [5189]P1(f331(x51891,f656(x51891)))+~P1(f331(x51891,f331(f107(a1),x51892)))
% 51.10/50.82 [5213]E(f331(f331(f48(a847),x52131),x52132),f2(a847))+~P1(f331(f331(f241(a847),x52131),x52132))
% 51.10/50.82 [5214]E(f331(f331(f3(a847),x52141),x52142),f2(a847))+~P1(f331(f331(f240(a847),x52141),x52142))
% 51.10/50.82 [5215]E(f331(f331(f3(a847),x52151),x52152),f2(a847))+~P1(f331(f331(f240(a847),x52151),x52152))
% 51.10/50.82 [5231]E(f57(a847,x52311,x52312),x52311)+~P1(f331(f331(f241(a847),x52311),x52312))
% 51.10/50.82 [5232]E(f57(a847,x52321,x52322),x52321)+~P1(f331(f331(f241(a847),x52321),x52322))
% 51.10/50.82 [5239]E(f57(a1,x52391,f331(f86(a1),x52392)),f292(x52391,x52392))+P1(f331(f331(f240(a1),f2(a1)),x52392))
% 51.10/50.82 [5251]E(f331(f331(f3(a1),x52511),x52512),f192(x52511,x52512))+~P1(f331(f331(f240(a1),x52512),x52511))
% 51.10/50.82 [5252]E(f331(f331(f3(a1),x52521),x52522),f192(x52521,x52522))+~P1(f331(f331(f240(a1),x52522),x52521))
% 51.10/50.82 [5270]P1(f331(f331(f240(a1),f2(a1)),f722(x52701)))+P1(f331(x52701,f331(f107(a1),x52702)))
% 51.10/50.82 [5282]~P85(x52821)+P1(f331(f331(f240(x52821),f2(x52821)),f331(f107(x52821),x52822)))
% 51.10/50.82 [5283]~P85(x52831)+P1(f331(f331(f240(x52831),f2(x52831)),f331(f107(x52831),x52832)))
% 51.10/50.82 [5284]~P78(x52841)+P1(f331(f331(f240(x52841),f2(x52841)),f331(f82(x52841),x52842)))
% 51.10/50.82 [5312]E(f331(f331(f87(a847),x53121),f657(x53122,x53121)),x53122)+~P1(f331(f331(f240(a847),x53121),x53122))
% 51.10/50.82 [5313]E(f331(f331(f87(a847),x53131),f565(x53132,x53131)),x53132)+~P1(f331(f331(f241(a847),x53131),x53132))
% 51.10/50.82 [5325]~E(f331(f111(a1),x53251),f331(f107(a1),x53252))+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x53251)))
% 51.10/50.82 [5328]E(f303(a1,x53281,x53282),f184(f854(a1,a840)))+~P1(f331(f331(f241(a1),x53282),x53281))
% 51.10/50.82 [5331]~P86(x53311)+E(f331(f331(f88(x53311),f331(f82(x53311),x53312)),f331(f82(x53311),x53312)),f331(f331(f88(x53311),x53312),x53312))
% 51.10/50.82 [5336]E(f135(a847,f331(f302(a847,x53361),f331(a119,x53362))),f120(a847))+P1(f331(f331(f240(a847),x53361),x53362))
% 51.10/50.82 [5340]E(f331(f331(f48(a1),x53401),x53402),f293(x53401,x53402))+~P1(f331(f331(f240(a1),f2(a1)),x53402))
% 51.10/50.82 [5360]P1(f331(f132(x53601),x53602))+~P1(f331(f132(x53601),f331(f159(x53601),x53602)))
% 51.10/50.82 [5361]P1(f331(f132(x53611),x53612))+~P1(f331(f132(x53611),f331(f160(x53611),x53612)))
% 51.10/50.82 [5384]P1(f331(f68(a847),x53841))+P1(f331(f331(f333(a847),f364(x53841,x53842)),x53841))
% 51.10/50.82 [5385]P1(f331(f68(a847),x53851))+P1(f331(f331(f333(a847),f368(x53851,x53852)),x53851))
% 51.10/50.82 [5386]P1(f331(f331(f241(a847),x53862),f331(a119,x53861)))+P1(f331(f331(f241(a847),x53861),x53862))
% 51.10/50.82 [5387]E(f57(a1,x53871,x53872),f292(x53871,x53872))+~P1(f331(f331(f240(a1),f2(a1)),x53872))
% 51.10/50.82 [5389]E(f135(a847,f331(f302(a847,x53891),x53892)),f120(a847))+~P1(f331(f331(f240(a847),x53892),x53891))
% 51.10/50.82 [5390]E(f135(a847,f331(f302(a847,x53901),x53902)),f120(a847))+~P1(f331(f331(f240(a847),x53902),x53901))
% 51.10/50.82 [5391]~P76(x53911)+E(f331(f311(x53911,x53911,f86(x53911)),f331(f301(x53911),x53912)),f331(f266(x53911),f331(f86(x53911),x53912)))
% 51.10/50.82 [5392]~P76(x53921)+E(f331(f311(x53921,x53921,f86(x53921)),f331(f265(x53921),x53922)),f331(f304(x53921),f331(f86(x53921),x53922)))
% 51.10/50.82 [5393]~P76(x53931)+E(f331(f311(x53931,x53931,f86(x53931)),f331(f266(x53931),x53932)),f331(f301(x53931),f331(f86(x53931),x53932)))
% 51.10/50.82 [5394]~P76(x53941)+E(f331(f311(x53941,x53941,f86(x53941)),f331(f304(x53941),x53942)),f331(f265(x53941),f331(f86(x53941),x53942)))
% 51.10/50.82 [5405]E(x54051,f184(f854(x54052,a840)))+P1(f331(f331(f333(x54052),f337(x54051,x54052)),x54051))
% 51.10/50.82 [5406]E(x54061,f184(f854(x54062,a840)))+P1(f331(f331(f333(x54062),f342(x54061,x54062)),x54061))
% 51.10/50.82 [5414]~P1(f331(f331(f241(a847),x54141),x54142))+P1(f331(f331(f240(a847),x54141),x54142))
% 51.10/50.82 [5415]~P1(f331(f331(f241(a847),x54151),x54152))+P1(f331(f331(f240(a847),x54151),x54152))
% 51.10/50.82 [5416]~P1(f331(f331(f241(a847),x54161),x54162))+P1(f331(f331(f240(a847),x54161),x54162))
% 51.10/50.82 [5417]~P1(f331(f331(f241(a847),x54171),x54172))+P1(f331(f331(f240(a847),x54171),x54172))
% 51.10/50.82 [5418]~P1(f331(f331(f241(a847),x54181),x54182))+P1(f331(f331(f240(a847),x54181),x54182))
% 51.10/50.82 [5419]~P1(f331(f331(f241(a1),x54191),x54192))+P1(f331(f331(f240(a1),x54191),x54192))
% 51.10/50.82 [5432]E(f59(x54321,x54322),f331(f331(f249(a1,a1),f2(a1)),x54321))+~P1(f331(f331(f241(a1),x54321),x54322))
% 51.10/50.82 [5433]E(f217(f331(f86(a1),x54331),f331(f86(a1),x54332)),f217(x54331,x54332))+~P1(f331(f331(f241(a1),x54332),f2(a1)))
% 51.10/50.82 [5445]E(x54451,x54452)+~E(f331(a5,f331(a119,f331(a22,x54451))),f331(a5,f331(a119,f331(a22,x54452))))
% 51.10/50.82 [5450]E(f59(x54501,x54502),f331(f331(f249(a1,a1),f2(a1)),x54501))+~P1(f331(f331(f240(a1),x54502),f2(a1)))
% 51.10/50.82 [5478]E(f57(a847,f331(f111(a847),x54781),f331(f111(a847),x54782)),f2(a847))+~P1(f331(a190,f331(f111(a1),x54781)))
% 51.10/50.82 [5492]P1(f331(f331(f240(a1),f2(a1)),f656(x54921)))+~P1(f331(x54921,f331(f107(a1),x54922)))
% 51.10/50.82 [5525]P36(f303(a1,x55251,x55252))+~P1(f331(f331(f240(a1),f2(a1)),x55251))
% 51.10/50.82 [5529]~P1(f331(f68(x55291),x55292))+P1(f331(f68(f854(x55291,a840)),f331(f309(x55291),x55292)))
% 51.10/50.82 [5542]E(f331(f331(f87(a1),x55421),f331(f107(a1),f779(x55422,x55421))),x55422)+~P1(f331(f331(f240(a1),x55421),x55422))
% 51.10/50.82 [5550]P1(f331(f331(f240(a847),x55501),x55502))+P1(f331(f331(f240(a847),f331(a119,x55502)),x55501))
% 51.10/50.82 [5595]E(f331(f331(f48(a847),f331(f111(a847),x55951)),f331(f111(a847),x55952)),f2(a847))+~P1(f331(a190,f331(f111(a1),x55951)))
% 51.10/50.82 [5596]E(f331(f331(f88(a847),f331(f111(a847),x55961)),f331(f111(a847),x55962)),f2(a847))+~P1(f331(f331(f241(a1),x55961),a90))
% 51.10/50.82 [5597]P1(f331(f331(f241(a847),x55971),f331(a119,x55972)))+~P1(f331(f331(f241(a847),x55971),x55972))
% 51.10/50.82 [5598]P1(f331(f331(f241(a847),x55981),f331(a119,x55982)))+~P1(f331(f331(f241(a847),x55981),x55982))
% 51.10/50.82 [5599]P1(f331(f331(f241(a847),x55991),f331(a119,x55992)))+~P1(f331(f331(f240(a847),x55991),x55992))
% 51.10/50.82 [5600]P1(f331(f331(f241(a847),x56001),f331(a119,x56002)))+~P1(f331(f331(f240(a847),x56001),x56002))
% 51.10/50.82 [5601]P1(f331(f331(f240(a847),x56011),f331(a119,x56012)))+~P1(f331(f331(f240(a847),x56011),x56012))
% 51.10/50.82 [5602]P1(f331(f331(f240(a847),x56021),f331(a119,x56022)))+~P1(f331(f331(f240(a847),x56021),x56022))
% 51.10/50.82 [5603]~E(x56031,x56032)+P1(f331(f331(f241(a1),x56031),f331(f331(f87(a1),x56032),f85(a1))))
% 51.10/50.82 [5606]E(f57(a1,x56061,x56062),f2(a1))+E(f331(f331(f3(a1),x56062),f57(a1,x56061,x56062)),f57(a1,f331(f86(a1),x56061),x56062))
% 51.10/50.82 [5614]E(x56141,f120(x56142))+P1(f331(f331(f333(x56142),f139(x56142,x56141)),f331(f163(x56142),x56141)))
% 51.10/50.82 [5625]E(f92(f853(a847,a847),f60(x56251,x56252)),f331(f331(f249(a847,a847),f2(a847)),x56251))+~P1(f331(f331(f241(a847),x56251),x56252))
% 51.10/50.82 [5626]E(f92(f853(a847,a847),f60(x56261,x56262)),f331(f331(f249(a847,a847),f2(a847)),x56261))+~P1(f331(f331(f241(a847),x56261),x56262))
% 51.10/50.82 [5666]E(f331(f331(f87(a847),f331(f111(a847),x56661)),f331(f111(a847),x56662)),f331(f111(a847),x56662))+~P1(f331(f331(f241(a1),x56661),a90))
% 51.10/50.82 [5667]E(f331(f331(f3(a847),f331(f111(a847),x56671)),f331(f111(a847),x56672)),f331(f111(a847),x56671))+~P1(f331(f331(f241(a1),x56672),a90))
% 51.10/50.82 [5672]E(f331(a119,f331(f331(f87(a847),x56721),f405(x56722,x56721))),x56722)+~P1(f331(f331(f241(a847),x56721),x56722))
% 51.10/50.82 [5673]E(f331(a119,f331(f331(f87(a847),x56731),f540(x56732,x56731))),x56732)+~P1(f331(f331(f241(a847),x56731),x56732))
% 51.10/50.82 [5680]~P1(f331(f331(f287(a1),x56801),x56802))+P1(f331(f331(f287(a1),x56801),f331(f86(a1),x56802)))
% 51.10/50.82 [5681]P1(f331(f331(f241(a847),f2(a847)),f565(x56811,x56812)))+~P1(f331(f331(f241(a847),x56812),x56811))
% 51.10/50.82 [5700]P1(f331(x57001,x57002))+~P1(f331(x57001,f331(a96,f593(x57002,x57001))))
% 51.10/50.82 [5708]~P1(f331(f331(f241(a847),x57081),f331(a119,x57082)))+P1(f331(f331(f240(a847),x57081),x57082))
% 51.10/50.82 [5758]E(f331(f331(f310(a847),x57581),f331(f302(a847,x57582),x57581)),f331(f302(a847,x57582),f331(a119,x57581)))+~P1(f331(f331(f240(a847),x57582),x57581))
% 51.10/50.82 [5763]E(x57631,f120(x57632))+E(f331(f331(f130(x57632),f121(x57632,x57631)),f331(f331(f145(x57632),f139(x57632,x57631)),f120(x57632))),x57631)
% 51.10/50.82 [5773]P1(f331(f68(x57731),x57732))+~P1(f331(f331(f241(a847),f2(a847)),f331(f47(x57731),x57732)))
% 51.10/50.82 [5774]P1(f331(f68(x57741),x57742))+~P1(f331(f331(f241(a847),f2(a847)),f331(f47(x57741),x57742)))
% 51.10/50.82 [5778]~E(x57781,f184(f854(x57782,a840)))+~P1(f331(f331(f241(a847),f2(a847)),f331(f47(x57782),x57781)))
% 51.10/50.82 [5786]~P1(f331(f331(f241(a847),x57861),x57862))+P1(f331(f331(f240(a847),f331(a119,x57861)),x57862))
% 51.10/50.82 [5787]~P1(f331(f331(f241(a847),x57871),x57872))+P1(f331(f331(f240(a847),f331(a119,x57871)),x57872))
% 51.10/50.82 [5788]~P1(f331(f331(f241(a847),x57881),x57882))+P1(f331(f331(f240(a847),f331(a119,x57881)),x57882))
% 51.10/50.82 [5796]E(x57961,f120(x57962))+P1(f331(f331(f333(x57962),f331(f136(x57962),x57961)),f331(f163(x57962),x57961)))
% 51.10/50.82 [5802]~P85(x58021)+P1(f331(f331(f241(x58021),x58022),f331(f331(f87(x58021),x58022),f85(x58021))))
% 51.10/50.82 [5804]~P78(x58041)+P1(f331(f331(f240(x58041),f331(f86(x58041),x58042)),f331(f82(x58041),x58042)))
% 51.10/50.82 [5816]P1(f331(f331(f287(a1),x58161),x58162))+~P1(f331(f331(f287(a1),x58161),f331(f86(a1),x58162)))
% 51.10/50.82 [5817]~E(x58171,x58172)+E(f290(a847,f287(a847),x58171,x58172),f331(f331(f310(a847),x58171),f184(f854(a847,a840))))
% 51.10/50.82 [5835]P1(f331(f68(a847),x58351))+~P1(f331(f331(f241(a847),f368(x58351,x58352)),x58352))
% 51.10/50.82 [5836]P1(f331(f68(a847),x58361))+~P1(f331(f331(f240(a847),f364(x58361,x58362)),x58362))
% 51.10/50.82 [5840]~P1(f331(f68(f853(x58401,x58401)),x58402))+P1(f331(f68(x58401),f331(f284(x58401),x58402)))
% 51.10/50.82 [5890]E(f290(a847,f287(a847),x58901,x58902),f184(f854(a847,a840)))+P1(f331(f331(f287(a847),x58901),x58902))
% 51.10/50.82 [5891]E(f290(a847,f287(a847),x58911,x58912),f184(f854(a847,a840)))+P1(f331(f331(f287(a847),x58911),x58912))
% 51.10/50.82 [5892]E(f168(f331(f111(a1),x58921),f331(f111(a1),x58922)),f120(a1))+P1(f331(f331(f240(a1),f331(f111(a1),x58921)),f331(f111(a1),x58922)))
% 51.10/50.82 [5897]~P1(f331(f331(f241(a847),x58972),f331(a119,x58971)))+~P1(f331(f331(f241(a847),x58971),x58972))
% 51.10/50.82 [5898]~P88(x58981)+E(f331(f331(f109(f854(x58981,a840)),f331(f301(x58981),x58982)),f331(f266(x58981),x58982)),f331(f331(f310(x58981),x58982),f184(f854(x58981,a840))))
% 51.10/50.82 [5900]E(f331(f331(f250(a847),f331(f111(a847),x59001)),f331(f111(a847),x59002)),f331(f331(f250(a847),f2(a847)),f331(f111(a847),x59002)))+~P1(f331(a190,f331(f111(a1),x59001)))
% 51.10/50.82 [5911]P1(f331(f68(x59111),x59112))+~P1(f331(f68(f854(x59111,a840)),f331(f309(x59111),x59112)))
% 51.10/50.82 [5935]P1(f331(f331(f241(a847),f331(a119,x59351)),f331(a119,x59352)))+~P1(f331(f331(f241(a847),x59351),x59352))
% 51.10/50.82 [5936]P1(f331(f331(f241(a847),f331(a119,x59361)),f331(a119,x59362)))+~P1(f331(f331(f241(a847),x59361),x59362))
% 51.10/50.82 [5937]P1(f331(f331(f241(a847),f331(a22,x59371)),f331(a22,x59372)))+~P1(f331(f331(f241(a106),x59371),x59372))
% 51.10/50.82 [5938]P1(f331(f331(f241(a106),f331(a5,x59381)),f331(a5,x59382)))+~P1(f331(f331(f241(a847),x59381),x59382))
% 51.10/50.82 [5939]P1(f331(f331(f240(a847),f331(a119,x59391)),f331(a119,x59392)))+~P1(f331(f331(f240(a847),x59391),x59392))
% 51.10/50.82 [5940]P1(f331(f331(f240(a847),f331(a22,x59401)),f331(a22,x59402)))+~P1(f331(f331(f240(a106),x59401),x59402))
% 51.10/50.82 [5941]P1(f331(f331(f240(a106),f331(a5,x59411)),f331(a5,x59412)))+~P1(f331(f331(f240(a847),x59411),x59412))
% 51.10/50.82 [5944]E(x59441,x59442)+~E(f331(f311(a847,a1,f107(a1)),x59441),f331(f311(a847,a1,f107(a1)),x59442))
% 51.10/50.82 [5960]P1(f331(f331(f241(a847),x59601),x59602))+~P1(f331(f331(f241(a847),f331(a119,x59601)),x59602))
% 51.10/50.82 [5961]P1(f331(f331(f241(a847),x59611),x59612))+~P1(f331(f331(f240(a847),f331(a119,x59611)),x59612))
% 51.10/50.82 [5962]P1(f331(f331(f241(a847),x59621),x59622))+~P1(f331(f331(f240(a847),f331(a119,x59621)),x59622))
% 51.10/50.82 [5963]P1(f331(f331(f241(a847),x59631),x59632))+~P1(f331(f331(f240(a847),f331(a119,x59631)),x59632))
% 51.10/50.82 [5964]P1(f331(f331(f240(a847),x59641),x59642))+~P1(f331(f331(f240(a847),f331(a119,x59641)),x59642))
% 51.10/50.82 [5981]E(f57(a1,x59811,x59812),f2(a1))+E(f331(f331(f3(a1),f57(a1,x59811,x59812)),x59812),f57(a1,x59811,f331(f86(a1),x59812)))
% 51.10/50.82 [6052]E(f331(f47(f854(x60521,a840)),f331(f309(x60521),x60522)),f331(f331(f250(a847),f331(a119,f331(a119,f2(a847)))),f331(f47(x60521),x60522)))+~P1(f331(f68(x60521),x60522))
% 51.10/50.82 [6055]E(x60551,f120(x60552))+E(f331(f331(f155(x60552),x60551),f331(f331(f3(a847),f331(f185(f848(x60552)),x60551)),f85(a847))),f139(x60552,x60551))
% 51.10/50.82 [6080]E(x60801,f120(x60802))+E(f331(f331(f130(x60802),f331(f162(x60802),x60801)),f331(f331(f145(x60802),f331(f136(x60802),x60801)),f120(x60802))),f331(f159(x60802),x60801))
% 51.10/50.82 [6081]~P1(f331(f184(f854(x60811,a840)),x60812))+P1(f331(f331(f333(x60811),x60812),f184(f854(x60811,a840))))
% 51.10/50.82 [6111]~P1(f331(f68(x61111),f49(f854(x61111,a840),x61112)))+P1(f331(f68(f854(x61111,a840)),x61112))
% 51.10/50.82 [6132]P1(f331(f331(f240(a847),f331(f111(a847),x61321)),f331(f111(a847),x61322)))+~P1(f331(f331(f240(a1),x61321),a90))
% 51.10/50.82 [6152]~P1(f331(f331(f241(a1),x61521),x61522))+P1(f331(f331(f241(a1),x61521),f331(f331(f87(a1),x61522),f85(a1))))
% 51.10/50.82 [6153]~P1(f331(f331(f240(a1),x61531),x61532))+P1(f331(f331(f241(a1),x61531),f331(f331(f87(a1),x61532),f85(a1))))
% 51.10/50.82 [6154]~P1(f331(f331(f241(a1),x61541),x61542))+P1(f331(f331(f240(a1),x61541),f331(f331(f3(a1),x61542),f85(a1))))
% 51.10/50.82 [6156]~P1(f331(f331(f241(a847),x61561),x61562))+P1(f331(f331(f241(a1),f331(f107(a1),x61561)),f331(f107(a1),x61562)))
% 51.10/50.82 [6157]~P1(f331(f331(f241(a847),x61571),x61572))+P1(f331(f331(f241(a1),f331(f107(a1),x61571)),f331(f107(a1),x61572)))
% 51.10/50.82 [6158]~P1(f331(f331(f241(a1),x61581),x61582))+P1(f331(f331(f241(a1),f331(f111(a1),x61581)),f331(f111(a1),x61582)))
% 51.10/50.82 [6159]~P1(f331(f331(f240(a1),x61591),x61592))+P1(f331(f331(f240(a847),f331(f111(a847),x61591)),f331(f111(a847),x61592)))
% 51.10/50.82 [6160]~P1(f331(f331(f240(a847),x61601),x61602))+P1(f331(f331(f240(a1),f331(f107(a1),x61601)),f331(f107(a1),x61602)))
% 51.10/50.82 [6161]~P1(f331(f331(f240(a847),x61611),x61612))+P1(f331(f331(f240(a1),f331(f107(a1),x61611)),f331(f107(a1),x61612)))
% 51.10/50.82 [6162]~P1(f331(f331(f240(a1),x61621),x61622))+P1(f331(f331(f240(a1),f331(f111(a1),x61621)),f331(f111(a1),x61622)))
% 51.10/50.82 [6163]~P1(f331(f331(f287(a847),x61631),x61632))+P1(f331(f331(f287(a1),f331(f107(a1),x61631)),f331(f107(a1),x61632)))
% 51.10/50.82 [6164]~P1(f331(f331(f287(a847),x61641),x61642))+P1(f331(f331(f287(a1),f331(f107(a1),x61641)),f331(f107(a1),x61642)))
% 51.10/50.82 [6171]~E(x61712,f184(f854(x61711,a840)))+P1(f331(f331(f240(f854(x61711,a840)),x61712),f184(f854(x61711,a840))))
% 51.10/50.82 [6180]~P1(f331(f331(f240(a847),x61801),x61802))+~P1(f331(f331(f240(a847),f331(a119,x61802)),x61801))
% 51.10/50.82 [6227]~P1(f331(f331(f241(a847),f331(a119,x62271)),f331(a119,x62272)))+P1(f331(f331(f241(a847),x62271),x62272))
% 51.10/50.82 [6228]~P1(f331(f331(f241(a847),f331(a119,x62281)),f331(a119,x62282)))+P1(f331(f331(f241(a847),x62281),x62282))
% 51.10/50.82 [6229]~P1(f331(f331(f241(a106),f331(a5,x62291)),f331(a5,x62292)))+P1(f331(f331(f241(a847),x62291),x62292))
% 51.10/50.82 [6230]~P1(f331(f331(f241(a847),f331(a112,x62301)),f331(a112,x62302)))+P1(f331(f331(f241(a1),x62301),x62302))
% 51.10/50.82 [6231]~P1(f331(f331(f241(a847),f331(a22,x62311)),f331(a22,x62312)))+P1(f331(f331(f241(a106),x62311),x62312))
% 51.10/50.82 [6232]~P1(f331(f331(f240(a847),f331(a119,x62321)),f331(a119,x62322)))+P1(f331(f331(f240(a847),x62321),x62322))
% 51.10/50.82 [6233]~P1(f331(f331(f240(a106),f331(a5,x62331)),f331(a5,x62332)))+P1(f331(f331(f240(a847),x62331),x62332))
% 51.10/50.82 [6234]~P1(f331(f331(f240(a847),f331(a22,x62341)),f331(a22,x62342)))+P1(f331(f331(f240(a106),x62341),x62342))
% 51.10/50.82 [6251]~P1(f331(f331(f287(a847),x62512),x62511))+P1(f331(f331(f333(a847),x62511),f294(a847,f287(a847),x62512)))
% 51.10/50.82 [6252]~P1(f331(f331(f287(a847),x62521),x62522))+P1(f331(f331(f333(a847),x62521),f296(a847,f287(a847),x62522)))
% 51.10/50.82 [6256]~P1(f331(f331(f333(x62561),x62562),f184(f854(x62561,a840))))+P1(f331(f184(f854(x62561,a840)),x62562))
% 51.10/50.82 [6277]~P1(f331(f331(f241(a847),f331(a112,x62772)),f331(a112,x62771)))+P1(f331(f331(f241(a1),f2(a1)),x62771))
% 51.10/50.82 [6288]~E(f57(a1,f331(f111(a1),x62882),f331(f111(a1),x62881)),f2(a1))+P1(f331(f331(f287(a1),f331(f111(a1),x62881)),f331(f111(a1),x62882)))
% 51.10/50.82 [6306]P1(f331(f331(f240(a1),f2(a1)),f57(a1,x63061,x63062)))+~P1(f331(f331(f241(a1),f2(a1)),x63062))
% 51.10/50.82 [6307]P1(f331(f331(f240(a1),f2(a1)),f57(a1,x63071,x63072)))+~P1(f331(f331(f241(a1),f2(a1)),x63072))
% 51.10/50.82 [6475]P34(x64751,x64752)+~E(f331(f331(f289(x64751,x64751,x64751),x64752),x64752),f184(f854(f853(x64751,x64751),a840)))
% 51.10/50.82 [6491]~P34(x64911,x64912)+P34(x64911,f331(f331(f289(x64911,x64911,x64911),x64912),x64912))
% 51.10/50.82 [6503]P1(f331(f331(f241(a1),x65031),x65032))+~P1(f331(f331(f240(a1),x65031),f331(f331(f3(a1),x65032),f85(a1))))
% 51.10/50.82 [6504]P1(f331(f331(f240(a1),x65041),x65042))+~P1(f331(f331(f241(a1),x65041),f331(f331(f87(a1),x65042),f85(a1))))
% 51.10/50.82 [6506]P1(f331(f331(f241(a847),x65061),x65062))+~P1(f331(f331(f241(a1),f331(f107(a1),x65061)),f331(f107(a1),x65062)))
% 51.10/50.82 [6507]P1(f331(f331(f241(a847),x65071),x65072))+~P1(f331(f331(f241(a1),f331(f107(a1),x65071)),f331(f107(a1),x65072)))
% 51.10/50.82 [6508]P1(f331(f331(f241(a1),x65081),x65082))+~P1(f331(f331(f241(a847),f331(f111(a847),x65081)),f331(f111(a847),x65082)))
% 51.10/50.82 [6509]P1(f331(f331(f241(a1),x65091),x65092))+~P1(f331(f331(f241(a1),f331(f111(a1),x65091)),f331(f111(a1),x65092)))
% 51.10/50.82 [6510]P1(f331(f331(f240(a847),x65101),x65102))+~P1(f331(f331(f240(a1),f331(f107(a1),x65101)),f331(f107(a1),x65102)))
% 51.10/50.82 [6511]P1(f331(f331(f240(a847),x65111),x65112))+~P1(f331(f331(f240(a1),f331(f107(a1),x65111)),f331(f107(a1),x65112)))
% 51.10/50.82 [6512]P1(f331(f331(f240(a1),x65121),x65122))+~P1(f331(f331(f240(a1),f331(f111(a1),x65121)),f331(f111(a1),x65122)))
% 51.10/50.82 [6513]P1(f331(f331(f287(a847),x65131),x65132))+~P1(f331(f331(f287(a1),f331(f107(a1),x65131)),f331(f107(a1),x65132)))
% 51.10/50.82 [6514]P1(f331(f331(f287(a847),x65141),x65142))+~P1(f331(f331(f287(a1),f331(f107(a1),x65141)),f331(f107(a1),x65142)))
% 51.10/50.82 [6569]E(f57(a1,f331(f111(a1),x65691),f331(f111(a1),x65692)),f2(a1))+~P1(f331(f331(f287(a1),f331(f111(a1),x65692)),f331(f111(a1),x65691)))
% 51.10/50.82 [6583]~E(f290(a847,f287(a847),x65831,x65832),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x65831),x65832))
% 51.10/50.82 [6584]~E(f290(a847,f287(a847),x65841,x65842),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x65841),x65842))
% 51.10/50.82 [6610]P1(f331(f331(f287(a847),x66101),x66102))+~P1(f331(f331(f333(a847),x66102),f294(a847,f287(a847),x66101)))
% 51.10/50.82 [6611]P1(f331(f331(f287(a847),x66111),x66112))+~P1(f331(f331(f333(a847),x66111),f296(a847,f287(a847),x66112)))
% 51.10/50.82 [6612]~E(f769(x66122,x66121),f120(x66121))+E(f331(f137(f848(x66121),f848(x66121),f130(x66121),f120(x66121)),x66122),f120(x66121))
% 51.10/50.82 [6613]~E(f771(x66132,x66131),f120(x66131))+E(f331(f137(f848(x66131),f848(x66131),f130(x66131),f120(x66131)),x66132),f120(x66131))
% 51.10/50.82 [6620]~P7(x66201)+E(f331(f137(x66201,x66201,f109(x66201),f247(x66201)),x66202),f50(x66201,f331(f163(x66201),x66202)))
% 51.10/50.82 [6621]~P7(x66211)+E(f331(f137(x66211,x66211,f108(x66211),f184(x66211)),x66212),f49(x66211,f331(f163(x66211),x66212)))
% 51.10/50.82 [6633]E(x66331,f2(a106))+E(f331(f331(f87(a847),f331(a22,f331(f331(f3(a106),x66331),f85(a106)))),f331(a119,x66332)),f331(f331(f87(a847),f331(a22,x66331)),x66332))
% 51.10/50.82 [6685]P1(f331(f331(f241(a1),f331(f331(f3(a1),x66851),x66852)),f2(a1)))+~P1(f331(f331(f241(a1),x66851),x66852))
% 51.10/50.82 [6712]~P102(x67121)+E(f331(f331(f108(f854(x67121,a840)),f331(f331(f310(x67121),x67122),f184(f854(x67121,a840)))),f331(f304(x67121),x67122)),f331(f266(x67121),x67122))
% 51.10/50.82 [6794]~P56(x67941,x67942)+P34(x67941,f331(f264(f853(x67941,x67941)),f331(f259(x67941,x67941,a840),x67942)))
% 51.10/50.82 [6795]~P56(x67951,x67952)+P54(x67951,f331(f264(f853(x67951,x67951)),f331(f259(x67951,x67951,a840),x67952)))
% 51.10/50.82 [6796]E(x67961,f184(f854(x67962,a840)))+~P1(f331(f331(f240(f854(x67962,a840)),x67961),f184(f854(x67962,a840))))
% 51.10/50.82 [6881]~P1(f331(f331(f241(a847),f2(a847)),x68812))+P1(f331(f331(f241(a847),f57(a847,x68811,x68812)),x68812))
% 51.10/50.82 [6882]~P1(f331(f331(f241(a1),f2(a1)),x68822))+P1(f331(f331(f241(a1),f57(a1,x68821,x68822)),x68822))
% 51.10/50.82 [6883]~P1(f331(f331(f241(a1),f2(a1)),x68832))+P1(f331(f331(f241(a1),f57(a1,x68831,x68832)),x68832))
% 51.10/50.82 [6884]~P1(f331(f331(f241(a847),f2(a847)),x68842))+P1(f331(f331(f240(a847),f57(a847,x68841,x68842)),x68842))
% 51.10/50.82 [6885]~P1(f331(f331(f240(a1),f2(a1)),x68851))+P1(f331(f331(f240(a1),f57(a1,x68851,x68852)),x68851))
% 51.10/50.82 [6957]~P88(x69571)+E(f331(f331(f3(f854(x69571,a840)),f331(f331(f310(x69571),x69572),f184(f854(x69571,a840)))),f331(f265(x69571),x69572)),f331(f331(f310(x69571),x69572),f184(f854(x69571,a840))))
% 51.10/50.82 [7035]~P47(x70351,x70352)+P45(x70351,f247(f854(x70351,a840)),f331(f264(f853(x70351,x70351)),f331(f259(x70351,x70351,a840),x70352)))
% 51.10/50.82 [7036]P1(f331(x70361,x70362))+P1(f331(f331(f333(f854(f853(a847,a847),a840)),f593(x70362,x70361)),a105))
% 51.10/50.82 [7078]E(f331(f331(f130(a847),f135(a847,f331(f302(a847,x70781),x70782))),f331(f331(f145(a847),x70782),f120(a847))),f135(a847,f331(f302(a847,x70781),f331(a119,x70782))))+~P1(f331(f331(f240(a847),x70781),x70782))
% 51.10/50.82 [7079]E(f331(f331(f130(a847),f135(a847,f331(f302(a847,x70791),x70792))),f331(f331(f145(a847),x70792),f120(a847))),f135(a847,f331(f302(a847,x70791),f331(a119,x70792))))+~P1(f331(f331(f240(a847),x70791),x70792))
% 51.10/50.82 [7234]E(x72341,f2(a847))+~E(f331(f137(a847,a847,f87(a847),x72341),x72342),f2(a847))
% 51.10/50.82 [7263]~P1(f331(f331(f241(a1),f331(f331(f3(a1),x72631),x72632)),f2(a1)))+P1(f331(f331(f241(a1),x72631),x72632))
% 51.10/50.82 [7293]P34(x72931,x72932)+~P34(x72931,f331(f331(f289(x72931,x72931,x72931),x72932),x72932))
% 51.10/50.82 [7325]~P1(f331(f331(f240(a847),f331(a119,x73251)),x73252))+P1(f180(a840,a183,f331(f240(a847),x73251),x73252))
% 51.10/50.82 [7486]P27(a847,a847,f331(f331(f9(a847,a847,a847),f3(a847)),x74861),x74862)+P1(f331(f331(f333(a847),f599(x74861,x74862)),x74862))
% 51.10/50.82 [7544]E(f331(f331(f331(f72(a847,x75441,f87(a847)),f331(f18(a847,x75441),f85(a847))),f2(a847)),x75442),f331(f47(x75441),x75442))+~P1(f331(f68(x75441),x75442))
% 51.10/50.82 [7545]E(f331(f331(f331(f72(a847,x75451,f87(a847)),f331(f18(a847,x75451),f85(a847))),f2(a847)),x75452),f331(f47(x75451),x75452))+~P1(f331(f68(x75451),x75452))
% 51.10/50.82 [7588]P27(a847,a847,f331(f331(f9(a847,a847,a847),f3(a847)),x75881),x75882)+~P1(f331(f331(f240(a847),x75881),f599(x75881,x75882)))
% 51.10/50.82 [7645]P34(x76451,x76452)+P1(f331(f331(f240(f854(x76451,a840)),f591(x76452,x76451)),f331(f285(x76451,x76451,x76452),f591(x76452,x76451))))
% 51.10/50.82 [7649]P56(x76491,x76492)+~P34(x76491,f331(f264(f853(x76491,x76491)),f331(f259(x76491,x76491,a840),x76492)))
% 51.10/50.82 [7721]P1(f331(f331(f240(a847),f331(a119,x77211)),x77212))+~P1(f180(a840,a183,f331(f240(a847),x77211),x77212))
% 51.10/50.82 [7777]P1(f331(f331(f333(f853(a847,a847)),f331(f331(f249(a847,a847),x77771),x77772)),f308(a847,a322)))+~P1(f331(f331(f240(a847),x77771),x77772))
% 51.10/50.82 [7871]P47(x78711,x78712)+~P45(x78711,f247(f854(x78711,a840)),f331(f264(f853(x78711,x78711)),f331(f259(x78711,x78711,a840),x78712)))
% 51.10/50.82 [8127]~P34(x81271,f331(f286(x81271,x81271),x81272))+P34(x81271,f331(f286(x81271,x81271),f331(f331(f289(x81271,x81271,x81271),x81272),f308(x81271,x81272))))
% 51.10/50.82 [8246]P1(f331(f68(f853(x82461,x82461)),f331(f331(f289(x82461,x82461,x82461),x82462),f308(x82461,x82462))))+~P1(f331(f68(f853(x82461,x82461)),x82462))
% 51.10/50.82 [8276]E(x82761,f2(a1))+P1(f331(f61(x82762,x82761),f331(f331(f249(a1,a1),f331(f331(f48(a1),x82762),x82761)),f57(a1,x82762,x82761))))
% 51.10/50.82 [8290]~P1(f331(f331(f333(f853(a847,a847)),f331(f331(f249(a847,a847),x82901),x82902)),f308(a847,a322)))+P1(f331(f331(f240(a847),x82901),x82902))
% 51.10/50.82 [8310]~P71(x83101)+E(f331(f137(x83101,x83101,f331(f9(x83101,x83101,x83101),f87(x83101)),f2(x83101)),f331(f160(x83101),x83102)),f331(f137(x83101,x83101,f87(x83101),f2(x83101)),x83102))
% 51.10/50.82 [8583]P1(f331(f331(f333(f853(a847,a847)),f331(f331(f249(a847,a847),x85831),x85832)),f331(f331(f289(a847,a847,a847),a322),f308(a847,a322))))+~P1(f331(f331(f241(a847),x85831),x85832))
% 51.10/50.82 [8625]~P1(f331(f68(f853(x86251,x86251)),f331(f331(f289(x86251,x86251,x86251),x86252),f308(x86251,x86252))))+P1(f331(f68(f853(x86251,x86251)),x86252))
% 51.10/50.82 [8844]P54(x88441,x88442)+P1(f331(f331(f333(f853(x88441,x88441)),f331(f331(f249(x88441,x88441),f630(x88442,x88441)),f630(x88442,x88441))),f331(f331(f289(x88441,x88441,x88441),x88442),f308(x88441,x88442))))
% 51.10/50.82 [8845]P54(x88451,x88452)+P1(f331(f331(f333(f853(x88451,x88451)),f331(f331(f249(x88451,x88451),f673(x88452,x88451)),f673(x88452,x88451))),f331(f331(f289(x88451,x88451,x88451),x88452),f308(x88451,x88452))))
% 51.10/50.82 [8953]~P1(f331(f331(f333(f853(a847,a847)),f331(f331(f249(a847,a847),x89531),x89532)),f331(f331(f289(a847,a847,a847),a322),f308(a847,a322))))+P1(f331(f331(f241(a847),x89531),x89532))
% 51.10/50.82 [4934]~P91(x49341)+E(f331(f331(f87(x49341),f331(f111(x49341),a90)),x49342),x49342)
% 51.10/50.82 [4964]~P69(x49641)+E(f331(f331(f87(x49641),f331(f86(x49641),x49642)),x49642),f2(x49641))
% 51.10/50.82 [4965]~P4(x49651)+E(f331(f331(f87(x49651),f331(f86(x49651),x49652)),x49652),f2(x49651))
% 51.10/50.82 [4966]~P93(x49661)+E(f331(f331(f108(x49661),f331(f86(x49661),x49662)),x49662),f247(x49661))
% 51.10/50.82 [4967]~P93(x49671)+E(f331(f331(f109(x49671),f331(f86(x49671),x49672)),x49672),f184(x49671))
% 51.10/50.82 [4997]~P91(x49971)+E(f331(f331(f88(x49971),f331(f111(x49971),a104)),x49972),f331(f86(x49971),x49972))
% 51.10/50.82 [5157]~P106(x51571)+E(f331(f331(f88(x51571),f331(f86(x51571),f85(x51571))),x51572),f331(f86(x51571),x51572))
% 51.10/50.82 [5199]E(f331(f82(a1),x51991),f85(a1))+~E(f331(f82(a1),f331(f331(f88(a1),x51991),x51992)),f85(a1))
% 51.10/50.82 [5286]~P91(x52861)+E(f331(f331(f87(x52861),f85(x52861)),f331(f111(x52861),x52862)),f331(f111(x52861),f331(f331(f3(a1),x52862),a104)))
% 51.10/50.82 [5341]~P97(x53411)+E(f12(x53411,f331(f331(f310(x53411),x53412),f184(f854(x53411,a840)))),x53412)
% 51.10/50.82 [5342]~P97(x53421)+E(f15(x53421,f331(f331(f310(x53421),x53422),f184(f854(x53421,a840)))),x53422)
% 51.10/50.82 [5343]~P102(x53431)+E(f16(x53431,f331(f331(f310(x53431),x53432),f184(f854(x53431,a840)))),x53432)
% 51.10/50.82 [5344]~P102(x53441)+E(f17(x53441,f331(f331(f310(x53441),x53442),f184(f854(x53441,a840)))),x53442)
% 51.10/50.82 [5345]~P7(x53451)+E(f50(x53451,f331(f331(f310(x53451),x53452),f184(f854(x53451,a840)))),x53452)
% 51.10/50.82 [5346]~P7(x53461)+E(f49(x53461,f331(f331(f310(x53461),x53462),f184(f854(x53461,a840)))),x53462)
% 51.10/50.82 [5368]E(f331(f331(f87(a847),x53681),f331(f331(f3(a847),x53682),x53681)),x53682)+P1(f331(f331(f241(a847),x53682),x53681))
% 51.10/50.82 [5400]E(x54001,f120(x54002))+P1(f331(f331(f241(a847),f2(a847)),f331(f185(f848(x54002)),x54001)))
% 51.10/50.82 [5522]~P102(x55221)+E(f13(x55221,f239(x55221),f331(f331(f310(x55221),x55222),f184(f854(x55221,a840)))),x55222)
% 51.10/50.82 [5523]~P102(x55231)+E(f14(x55231,f244(x55231),f331(f331(f310(x55231),x55232),f184(f854(x55231,a840)))),x55232)
% 51.10/50.82 [5584]E(f331(f331(f87(a847),x55841),f331(f331(f3(a847),x55842),x55841)),x55842)+~P1(f331(f331(f240(a847),x55841),x55842))
% 51.10/50.82 [5585]E(f331(f331(f88(a1),x55851),f331(f331(f48(a1),x55852),x55851)),x55852)+~P1(f331(f331(f287(a1),x55851),x55852))
% 51.10/50.82 [5586]E(f331(f331(f3(a847),x55861),f331(f331(f3(a847),x55861),x55862)),x55862)+~P1(f331(f331(f240(a847),x55862),x55861))
% 51.10/50.82 [5604]E(f57(a847,f331(f331(f3(a847),x56041),x56042),x56042),f57(a847,x56041,x56042))+P1(f331(f331(f241(a847),x56041),x56042))
% 51.10/50.82 [5605]E(f57(a847,f331(f331(f3(a847),x56051),x56052),x56052),f57(a847,x56051,x56052))+P1(f331(f331(f241(a847),x56051),x56052))
% 51.10/50.82 [5615]E(f331(f86(a1),f331(f331(f48(a1),x56151),f331(f86(a1),x56152))),f293(x56151,x56152))+P1(f331(f331(f240(a1),f2(a1)),x56152))
% 51.10/50.82 [5617]~E(x56172,f2(a847))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f250(a847),x56171),x56172)))
% 51.10/50.82 [5677]~P91(x56771)+E(f331(f331(f87(x56771),f331(f86(x56771),f85(x56771))),f331(f111(x56771),x56772)),f331(f111(x56771),f331(f331(f87(a1),x56772),a104)))
% 51.10/50.82 [5678]E(f331(f331(f250(a847),f331(f111(a847),x56781)),x56782),f331(f331(f250(a847),f2(a847)),x56782))+~P1(f331(a190,f331(f111(a1),x56781)))
% 51.10/50.82 [5780]E(f331(f136(a847),f135(a847,f331(f302(a847,x57801),x57802))),x57801)+~P1(f331(f331(f241(a847),x57801),x57802))
% 51.10/50.82 [5797]E(f331(f331(f88(a847),f331(f111(a847),x57971)),f331(f111(a847),x57972)),f331(f111(a847),f331(f331(f88(a1),x57971),x57972)))+P1(f331(f331(f241(a1),x57971),a90))
% 51.10/50.82 [5803]~P119(x58031)+P1(f331(f331(f240(x58031),f2(x58031)),f331(f331(f88(x58031),x58032),x58032)))
% 51.10/50.82 [5815]E(f331(f331(f3(a847),f331(a119,x58151)),x58152),f331(a119,f331(f331(f3(a847),x58151),x58152)))+~P1(f331(f331(f240(a847),x58152),x58151))
% 51.10/50.82 [5818]E(f57(a847,f331(f331(f3(a847),x58181),x58182),x58182),f57(a847,x58181,x58182))+~P1(f331(f331(f240(a847),x58182),x58181))
% 51.10/50.82 [5869]E(f331(f331(f250(a847),f331(a112,x58691)),x58692),f331(a112,f331(f331(f250(a1),x58691),x58692)))+~P1(f331(f331(f240(a1),f2(a1)),x58691))
% 51.10/50.82 [5870]E(f331(f331(f250(a847),f331(a112,x58701)),x58702),f331(a112,f331(f331(f250(a1),x58701),x58702)))+~P1(f331(f331(f240(a1),f2(a1)),x58701))
% 51.10/50.82 [5886]P1(f331(f132(x58861),x58862))+P1(f331(f331(f241(a847),f721(x58862,x58861)),f331(f185(f848(x58861)),x58862)))
% 51.10/50.82 [5887]P1(f331(f132(x58871),x58872))+P1(f331(f331(f241(a847),f726(x58872,x58871)),f331(f185(f848(x58871)),x58872)))
% 51.10/50.82 [5902]~P1(f331(f331(f287(a1),x59021),x59022))+P1(f331(f331(f287(a1),f331(f86(a1),x59021)),x59022))
% 51.10/50.82 [5905]~E(x59051,f120(x59052))+~P1(f331(f331(f241(a847),f2(a847)),f331(f185(f848(x59052)),x59051)))
% 51.10/50.82 [5918]E(f139(a847,f135(a847,f331(f302(a847,x59181),x59182))),f331(f331(f3(a847),x59182),f85(a847)))+~P1(f331(f331(f241(a847),x59181),x59182))
% 51.10/50.82 [5921]E(f331(f331(f87(a1),x59211),f331(f107(a1),f331(a119,f622(x59212,x59211)))),x59212)+~P1(f331(f331(f241(a1),x59211),x59212))
% 51.10/50.82 [5928]E(x59281,f2(a847))+E(f331(f331(f88(a847),x59282),f331(f331(f250(a847),x59282),f331(f331(f3(a847),x59281),f85(a847)))),f331(f331(f250(a847),x59282),x59281))
% 51.10/50.82 [5954]E(f331(f331(f88(a847),f331(a112,x59541)),f331(a112,x59542)),f331(a112,f331(f331(f88(a1),x59541),x59542)))+~P1(f331(f331(f240(a1),f2(a1)),x59541))
% 51.10/50.82 [5955]E(f331(f331(f48(a847),f331(a112,x59551)),f331(a112,x59552)),f331(a112,f331(f331(f48(a1),x59551),x59552)))+~P1(f331(f331(f240(a1),f2(a1)),x59551))
% 51.10/50.82 [5969]~P87(x59691)+E(f331(f331(f87(x59691),x59692),x59692),f331(f331(f88(x59691),f331(f331(f87(x59691),f85(x59691)),f85(x59691))),x59692))
% 51.10/50.82 [5988]E(f331(f331(f48(a1),f331(f82(a1),x59881)),f331(f82(a1),x59882)),f331(f82(a1),f331(f331(f48(a1),x59881),x59882)))+~P1(f331(f331(f287(a1),x59882),x59881))
% 51.10/50.82 [5989]E(f331(f331(f3(a1),f331(f107(a1),x59891)),f331(f107(a1),x59892)),f331(f107(a1),f331(f331(f3(a847),x59891),x59892)))+~P1(f331(f331(f240(a847),x59892),x59891))
% 51.10/50.82 [5991]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f87(a1),x59911),x59912)),f62(x59911,x59912))+~P1(f331(f331(f240(a1),x59912),f2(a1)))
% 51.10/50.82 [6030]E(f169(x60301,x60302),f120(f848(x60301)))+P1(f331(f331(f333(f848(x60301)),f720(x60302,x60301)),f331(f163(f848(x60301)),x60302)))
% 51.10/50.82 [6095]~P1(f331(f331(f287(a847),x60951),x60952))+P1(f331(f331(f287(a847),x60951),f331(f331(f87(a847),x60952),x60951)))
% 51.10/50.82 [6117]E(f331(f331(f145(a1),x61171),f168(f331(f331(f87(a1),x61171),f85(a1)),x61172)),f168(x61171,x61172))+~P1(f331(f331(f240(a1),x61171),x61172))
% 51.10/50.82 [6155]~P1(f331(f331(f241(a847),x61552),x61551))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f3(a847),x61551),x61552)))
% 51.10/50.82 [6187]~P1(f331(f331(f241(a847),x61871),f331(a112,x61872)))+P1(f331(f331(f241(a1),f331(f107(a1),x61871)),x61872))
% 51.10/50.82 [6188]P1(f331(f331(f287(a1),x61881),x61882))+~P1(f331(f331(f287(a1),f331(f86(a1),x61881)),x61882))
% 51.10/50.82 [6218]~P102(x62181)+E(f331(f331(f108(f854(x62181,a840)),f331(f265(x62181),x62182)),f331(f331(f310(x62181),x62182),f184(f854(x62181,a840)))),f331(f301(x62181),x62182))
% 51.10/50.82 [6219]~P1(f331(f331(f241(a847),f2(a847)),x62192))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f87(a847),x62191),x62192)))
% 51.10/50.82 [6220]~P1(f331(f331(f241(a847),f2(a847)),x62201))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f87(a847),x62201),x62202)))
% 51.10/50.82 [6221]~P1(f331(f331(f241(a847),f2(a847)),x62211))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f250(a847),x62211),x62212)))
% 51.10/50.82 [6222]~P1(f331(f331(f240(a1),f2(a1)),x62221))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f250(a1),x62221),x62222)))
% 51.10/50.82 [6250]~E(f331(x62501,f2(a847)),f2(a847))+E(f331(f331(f8(a847,a847),x62501),f303(a847,f331(a119,f2(a847)),x62502)),f331(f331(f8(a847,a847),x62501),f303(a847,f2(a847),x62502)))
% 51.10/50.82 [6315]~P91(x63151)+E(f331(f331(f88(x63151),f331(f331(f87(x63151),f85(x63151)),f85(x63151))),f331(f111(x63151),x63152)),f331(f111(x63151),f331(f331(f87(a1),x63152),x63152)))
% 51.10/50.82 [6337]E(f331(f331(f310(a1),x63371),f303(a1,f331(f331(f87(a1),x63371),f85(a1)),x63372)),f303(a1,x63371,x63372))+P1(f331(f331(f241(a1),x63372),x63371))
% 51.10/50.82 [6338]P1(f331(f331(f241(a847),x63381),f331(a112,x63382)))+~P1(f331(f331(f241(a1),f331(f107(a1),x63381)),x63382))
% 51.10/50.82 [6440]P1(f331(f331(f287(a847),x64401),x64402))+~P1(f331(f331(f287(a847),x64401),f331(f331(f87(a847),x64402),x64401)))
% 51.10/50.82 [6445]E(f331(a112,f331(f331(f48(a1),f331(f111(a1),x64451)),f331(f111(a1),x64452))),f331(f331(f48(a847),f331(f111(a847),x64451)),f331(f111(a847),x64452)))+P1(f331(a190,f331(f111(a1),x64451)))
% 51.10/50.82 [6446]E(f331(a112,f331(f331(f250(a1),f331(f111(a1),x64461)),f331(f111(a847),x64462))),f331(f331(f250(a847),f331(f111(a847),x64461)),f331(f111(a847),x64462)))+P1(f331(a190,f331(f111(a1),x64461)))
% 51.10/50.82 [6505]P1(f331(f331(f241(a847),x65051),x65052))+~P1(f331(f331(f241(a847),f2(a847)),f331(f331(f3(a847),x65052),x65051)))
% 51.10/50.82 [6548]P1(f331(f331(f241(a847),f2(a847)),x65481))+~P1(f331(f331(f241(a847),f2(a847)),f331(f331(f88(a847),x65482),x65481)))
% 51.10/50.82 [6549]P1(f331(f331(f241(a847),f2(a847)),x65491))+~P1(f331(f331(f241(a847),f2(a847)),f331(f331(f88(a847),x65491),x65492)))
% 51.10/50.82 [6563]E(f135(a847,f331(f302(a847,f331(f111(a847),x65631)),f331(f111(a847),x65632))),f120(a847))+P1(f331(f331(f241(a847),f331(f111(a847),x65631)),f331(f111(a847),x65632)))
% 51.10/50.82 [6565]~P1(f331(f331(f240(a1),x65651),f2(a1)))+E(f331(f331(f88(a847),f331(a112,f331(f86(a1),x65651))),f331(a112,f331(f86(a1),x65652))),f331(a112,f331(f331(f88(a1),x65651),x65652)))
% 51.10/50.82 [6631]~E(x66312,f184(f854(x66311,a840)))+P1(f331(f331(f240(f854(x66311,a840)),x66312),f331(f86(f854(x66311,a840)),x66312)))
% 51.10/50.82 [6694]~P91(x66941)+E(f331(f331(f87(x66941),f331(f331(f87(x66941),f2(x66941)),f331(f111(x66941),x66942))),f331(f111(x66941),x66942)),f331(f111(x66941),f331(f331(f87(a1),x66942),x66942)))
% 51.10/50.82 [6703]~P1(f331(f331(f287(a1),f331(f107(a1),x67031)),x67032))+P1(f331(f331(f287(a847),x67031),f331(a112,f331(f82(a1),x67032))))
% 51.10/50.82 [6753]~P1(f331(f331(f241(a1),x67531),x67532))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x67531),f85(a1))),x67532))
% 51.10/50.82 [6754]~P1(f331(f331(f241(a1),x67541),x67542))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x67541),f85(a1))),x67542))
% 51.10/50.82 [6793]P1(f331(f331(f287(a1),f331(f107(a1),x67931)),x67932))+~P1(f331(f331(f287(a847),x67931),f331(a112,f331(f82(a1),x67932))))
% 51.10/50.82 [6827]E(x68271,f2(a847))+~P1(f331(f331(f240(a1),f331(f107(a1),x68272)),f331(f86(a1),f331(f107(a1),x68271))))
% 51.10/50.82 [6828]E(x68281,f2(a847))+~P1(f331(f331(f240(a1),f331(f107(a1),x68281)),f331(f86(a1),f331(f107(a1),x68282))))
% 51.10/50.82 [6933]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f87(a1),x69331),x69332)),f62(x69331,x69332))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),x69331),x69332)))
% 51.10/50.82 [6970]~P28(x69701,x69702)+P34(x69701,f331(f248(f854(f853(x69701,x69701),a840),f854(f853(x69701,x69701),a840)),x69702))
% 51.10/50.82 [6991]~P1(f331(f331(f240(a847),f331(a119,f2(a847))),x69911))+P1(f331(f331(f240(a847),f331(a119,f2(a847))),f331(f331(f250(a847),x69911),x69912)))
% 51.10/50.82 [7158]~P1(f331(f331(f241(a1),x71581),x71582))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x71581),x71581)),f331(f331(f87(a1),x71582),x71582)))
% 51.10/50.82 [7159]~P1(f331(f331(f241(a1),x71591),x71592))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x71591),x71591)),f331(f331(f87(a1),x71592),x71592)))
% 51.10/50.82 [7170]~P1(f331(f331(f240(a1),x71701),x71702))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x71701),x71701)),f331(f331(f87(a1),x71702),x71702)))
% 51.10/50.82 [7171]~P1(f331(f331(f240(a1),x71711),x71712))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x71711),x71711)),f331(f331(f87(a1),x71712),x71712)))
% 51.10/50.82 [7238]~P1(f331(f331(f241(a847),f2(a847)),x72381))+P1(f331(f331(f241(a847),f331(f331(f3(a847),x72381),f331(a119,x72382))),x72381))
% 51.10/50.82 [7275]P1(f331(f331(f240(a847),f331(a119,f2(a847))),x72751))+~P1(f331(f331(f240(a847),f331(a119,f2(a847))),f331(f331(f88(a847),x72752),x72751)))
% 51.10/50.82 [7276]P1(f331(f331(f240(a847),f331(a119,f2(a847))),x72761))+~P1(f331(f331(f240(a847),f331(a119,f2(a847))),f331(f331(f88(a847),x72761),x72762)))
% 51.10/50.82 [7280]P1(f331(f331(f240(a847),f331(f331(f155(a847),x72801),x72802)),f331(f157(a847),x72801)))+~P1(f331(f331(f241(a847),x72802),f331(f185(f848(a847)),x72801)))
% 51.10/50.82 [7324]P1(f331(f331(f241(a1),x73241),x73242))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x73241),f85(a1))),x73242))
% 51.10/50.82 [7333]~P1(f331(f331(f333(a847),x73331),x73332))+P1(f331(f331(f333(a1),f331(f107(a1),x73331)),f331(f311(a847,a1,f107(a1)),x73332)))
% 51.10/50.82 [7370]P1(f331(f68(x73701),f247(f854(x73701,a840))))+~P1(f331(f68(f854(x73702,x73701)),f247(f854(f854(x73702,x73701),a840))))
% 51.10/50.82 [7371]P1(f331(f68(x73711),f247(f854(x73711,a840))))+~P1(f331(f68(f855(x73712,x73711)),f247(f854(f855(x73712,x73711),a840))))
% 51.10/50.82 [7372]P1(f331(f68(x73721),f247(f854(x73721,a840))))+~P1(f331(f68(f855(x73721,x73722)),f247(f854(f855(x73721,x73722),a840))))
% 51.10/50.82 [7411]E(x74111,f184(f854(x74112,a840)))+~P1(f331(f331(f240(f854(x74112,a840)),x74111),f331(f86(f854(x74112,a840)),x74111)))
% 51.10/50.82 [7555]E(f331(f137(f848(x75551),f848(x75551),f130(x75551),f120(x75551)),x75552),f120(x75551))+P1(f331(f331(f333(f848(x75551)),f769(x75552,x75551)),f331(f163(f848(x75551)),x75552)))
% 51.10/50.82 [7556]E(f331(f137(f848(x75561),f848(x75561),f130(x75561),f120(x75561)),x75562),f120(x75561))+P1(f331(f331(f333(f848(x75561)),f771(x75562,x75561)),f331(f163(f848(x75561)),x75562)))
% 51.10/50.82 [7692]E(f169(x76921,f331(f331(f145(f848(x76921)),f120(x76921)),x76922)),f169(x76921,x76922))+~P1(f331(f320(f848(f848(x76921)),f170(x76921)),f331(f331(f145(f848(x76921)),f120(x76921)),x76922)))
% 51.10/50.82 [7796]P1(f331(f331(f241(a1),x77961),x77962))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x77961),x77961)),f331(f331(f87(a1),x77962),x77962)))
% 51.10/50.82 [7797]P1(f331(f331(f241(a1),x77971),x77972))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x77971),x77971)),f331(f331(f87(a1),x77972),x77972)))
% 51.10/50.82 [7799]P1(f331(f331(f240(a1),x77991),x77992))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x77991),x77991)),f331(f331(f87(a1),x77992),x77992)))
% 51.10/50.82 [7800]P1(f331(f331(f240(a1),x78001),x78002))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x78001),x78001)),f331(f331(f87(a1),x78002),x78002)))
% 51.10/50.82 [7892]~P87(x78921)+E(f331(f331(f88(x78921),f331(f331(f87(x78921),f85(x78921)),f85(x78921))),f331(f331(f8(a847,x78921),f107(x78921)),f303(a847,f85(a847),x78922))),f331(f331(f88(x78921),f331(f107(x78921),x78922)),f331(f331(f87(x78921),f331(f107(x78921),x78922)),f85(x78921))))
% 51.10/50.82 [7933]E(f331(f331(f145(a1),f331(f111(a1),x79331)),f168(f331(f331(f87(a1),f331(f111(a1),x79331)),f85(a1)),f331(f111(a1),x79332))),f168(f331(f111(a1),x79331),f331(f111(a1),x79332)))+~P1(f331(f331(f240(a1),f331(f111(a1),x79331)),f331(f111(a1),x79332)))
% 51.10/50.82 [7948]P1(f331(f331(f333(a847),x79481),x79482))+~P1(f331(f331(f333(a1),f331(f107(a1),x79481)),f331(f311(a847,a1,f107(a1)),x79482)))
% 51.10/50.82 [8098]~P1(f331(f68(x80981),x80982))+E(f331(f311(a847,x80981,f570(x80982,x80981)),f331(f264(a847),f331(f331(f9(a847,a847,a840),f241(a847)),f571(x80982,x80981)))),x80982)
% 51.10/50.82 [8382]P46(x83821,x83822)+P1(f331(f331(f333(f853(x83821,x83821)),f331(f331(f249(x83821,x83821),f355(x83822,x83821)),f355(x83822,x83821))),x83822))
% 51.10/50.82 [8516]~P91(x85161)+E(f331(f331(f3(x85161),f85(x85161)),f331(f111(x85161),x85162)),f331(f111(x85161),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f86(a1),x85162))))
% 51.10/50.82 [8621]~P1(f331(f331(f241(f854(a847,a840)),x86211),x86212))+P1(f331(f331(f241(f854(a1,a840)),f331(f311(a847,a1,f107(a1)),x86211)),f331(f311(a847,a1,f107(a1)),x86212)))
% 51.10/50.82 [8622]~P1(f331(f331(f240(f854(a847,a840)),x86221),x86222))+P1(f331(f331(f240(f854(a1,a840)),f331(f311(a847,a1,f107(a1)),x86221)),f331(f311(a847,a1,f107(a1)),x86222)))
% 51.10/50.82 [8647]~P1(f331(f331(f241(a1),x86471),x86472))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x86471),x86471)),a104)),f331(f331(f87(a1),x86472),x86472)))
% 51.10/50.82 [8648]~P1(f331(f331(f241(a1),x86481),x86482))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x86481),x86481)),a104)),f331(f331(f87(a1),x86482),x86482)))
% 51.10/50.82 [8649]~P1(f331(f331(f241(a1),x86491),x86492))+P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x86491),x86491)),a104)),f331(f331(f87(a1),x86492),x86492)))
% 51.10/50.82 [8650]~P1(f331(f331(f241(a1),x86501),x86502))+P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x86501),x86501)),a104)),f331(f331(f87(a1),x86502),x86502)))
% 51.10/50.82 [8717]~P1(f331(f331(f333(a847),x87171),f331(f163(a847),x87172)))+P1(f331(f331(f240(a847),x87171),f331(f137(a847,a847,f87(a847),f2(a847)),x87172)))
% 51.10/50.82 [8789]P42(x87891,x87892)+~P1(f331(f331(f333(f853(x87891,x87891)),f331(f331(f249(x87891,x87891),f345(x87892,x87891)),f345(x87892,x87891))),x87892))
% 51.10/50.82 [8920]~P1(f331(f331(f241(f854(a1,a840)),f331(f311(a847,a1,f107(a1)),x89201)),f331(f311(a847,a1,f107(a1)),x89202)))+P1(f331(f331(f241(f854(a847,a840)),x89201),x89202))
% 51.10/50.82 [8921]~P1(f331(f331(f240(f854(a1,a840)),f331(f311(a847,a1,f107(a1)),x89211)),f331(f311(a847,a1,f107(a1)),x89212)))+P1(f331(f331(f240(f854(a847,a840)),x89211),x89212))
% 51.10/50.82 [8999]P1(f331(f331(f241(a1),x89991),x89992))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89991),x89991)),a104)),f331(f331(f87(a1),x89992),x89992)))
% 51.10/50.82 [9000]P1(f331(f331(f241(a1),x90001),x90002))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x90001),x90001)),a104)),f331(f331(f87(a1),x90002),x90002)))
% 51.10/50.82 [9001]P1(f331(f331(f241(a1),x90011),x90012))+~P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x90011),x90011)),a104)),f331(f331(f87(a1),x90012),x90012)))
% 51.10/50.82 [9002]P1(f331(f331(f241(a1),x90021),x90022))+~P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x90021),x90021)),a104)),f331(f331(f87(a1),x90022),x90022)))
% 51.10/50.82 [9873]~P1(f331(f68(x98731),x98732))+E(f331(f185(f848(x98731)),f97(f848(x98731),f331(f331(f20(f848(x98731),a840,a840),f331(f331(f10(a840,f854(a840,a840),f848(x98731)),a329),f331(f331(f9(f848(x98731),f854(x98731,a840),a840),f331(f331(f10(f854(x98731,a840),f854(f854(x98731,a840),a840),f848(x98731)),a328),f163(x98731))),x98732))),f132(x98731)))),f216(x98731,x98732))
% 51.10/50.82 [5917]E(f331(f331(f87(a847),f331(f331(f3(a847),x59171),x59172)),x59172),x59171)+~P1(f331(f331(f240(a847),x59172),x59171))
% 51.10/50.82 [5984]E(f331(f331(f48(a847),f331(f331(f88(a847),x59841),x59842)),x59842),x59841)+~P1(f331(f331(f241(a847),f2(a847)),x59842))
% 51.10/50.82 [5985]E(f331(f331(f48(a847),f331(f331(f88(a847),x59851),x59852)),x59851),x59852)+~P1(f331(f331(f241(a847),f2(a847)),x59851))
% 51.10/50.82 [5990]~P68(x59901)+E(f331(f331(f8(a847,x59901),f331(f155(x59901),x59902)),f331(f302(a847,f2(a847)),f331(f185(f848(x59901)),x59902))),f331(f157(x59901),x59902))
% 51.10/50.82 [6109]E(f57(a847,f331(a119,f331(f331(f88(a847),x61091),x61092)),x61091),f85(a847))+~P1(f331(f331(f241(a847),f85(a847)),x61091))
% 51.10/50.82 [6115]E(f331(a119,f331(f331(f87(a847),f331(f111(a847),x61151)),x61152)),f331(f331(f87(a847),f85(a847)),x61152))+~P1(f331(a190,f331(f111(a1),x61151)))
% 51.10/50.82 [6141]E(f331(a112,f331(f331(f250(a1),f331(f111(a1),x61411)),x61412)),f331(f331(f250(a847),f331(f111(a847),x61411)),x61412))+P1(f331(a190,f331(f111(a1),x61411)))
% 51.10/50.82 [6393]E(f331(f331(f3(a847),x63931),f331(f111(a847),f331(f331(f87(a1),x63932),a104))),f331(f331(f3(a847),f331(a119,x63931)),f331(f111(a847),x63932)))+~P1(f331(f331(f241(a1),a90),x63932))
% 51.10/50.82 [6474]E(x64741,f2(a847))+E(f331(a119,f331(f331(f87(a847),f331(f331(f3(a847),x64741),f85(a847))),x64742)),f331(f331(f87(a847),x64741),x64742))
% 51.10/50.82 [6519]E(x65191,f2(a1))+P1(f331(f331(f241(a1),f2(a1)),f331(f331(f250(a1),f331(f82(a1),x65191)),x65192)))
% 51.10/50.82 [6534]~E(x65342,f2(a847))+P1(f331(f331(f241(a1),f2(a1)),f331(f331(f250(a1),f331(f82(a1),x65341)),x65342)))
% 51.10/50.82 [6570]E(x65701,f2(a847))+E(f331(f331(f87(a847),x65702),f331(f331(f88(a847),f331(f331(f3(a847),x65701),f85(a847))),x65702)),f331(f331(f88(a847),x65701),x65702))
% 51.10/50.82 [6625]~P1(f331(f331(f240(a1),x66251),x66252))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x66251),a104)),x66252))
% 51.10/50.82 [6757]E(f331(f331(f145(a847),x67571),f135(a847,f331(f302(a847,f331(a119,x67571)),x67572))),f135(a847,f331(f302(a847,x67571),x67572)))+~P1(f331(f331(f241(a847),x67571),x67572))
% 51.10/50.82 [6758]E(f331(f331(f145(a847),x67581),f135(a847,f331(f302(a847,f331(a119,x67581)),x67582))),f135(a847,f331(f302(a847,x67581),x67582)))+~P1(f331(f331(f241(a847),x67581),x67582))
% 51.10/50.82 [6927]~P1(f331(f331(f287(a1),x69271),f331(f107(a1),x69272)))+P1(f331(f331(f287(a847),f331(a112,f331(f82(a1),x69271))),x69272))
% 51.10/50.82 [6961]E(x69611,x69612)+~E(f331(f331(f3(a1),f331(f331(f87(a1),x69611),x69611)),a104),f331(f331(f3(a1),f331(f331(f87(a1),x69612),x69612)),a104))
% 51.10/50.82 [6964]E(x69641,f120(x69642))+E(f271(x69642,f331(f331(f147(x69642,f853(a106,x69642)),f331(f249(a106,x69642),f85(a106))),x69641)),f278(x69642,x69641))
% 51.10/50.82 [7201]P1(f331(f331(f240(a1),x72011),x72012))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x72011),a104)),x72012))
% 51.10/50.82 [7343]P1(f331(f331(f287(a1),x73431),f331(f107(a1),x73432)))+~P1(f331(f331(f287(a847),f331(a112,f331(f82(a1),x73431))),x73432))
% 51.10/50.82 [7694]~P1(f331(f331(f241(a847),x76941),x76942))+P1(f331(f331(f333(f853(a847,a847)),f331(f331(f249(a847,a847),x76941),x76942)),a245))
% 51.10/50.82 [7922]~P1(f331(f331(f241(a106),f2(a106)),x79221))+P1(f331(f331(f241(a106),f331(f248(a106,f853(a106,a106)),f331(f272(x79221),x79222))),x79221))
% 51.10/50.82 [8225]~P78(x82251)+P1(f331(f331(f240(x82251),f331(f82(x82251),f331(f157(x82251),x82252))),f331(f157(x82251),f331(f331(f147(x82251,x82251),f82(x82251)),x82252))))
% 51.10/50.82 [8248]P1(f331(f331(f241(a847),x82481),x82482))+~P1(f331(f331(f333(f853(a847,a847)),f331(f331(f249(a847,a847),x82481),x82482)),a245))
% 51.10/50.82 [8407]E(f331(f331(f249(x84071,x84071),f688(x84072,x84071)),f688(x84072,x84071)),x84072)+~P1(f331(f331(f333(f853(x84071,x84071)),x84072),f308(x84071,f184(f854(f853(x84071,x84071),a840)))))
% 51.10/50.82 [8449]E(f331(f302(a847,x84491),f331(f331(f87(a847),x84491),f331(f47(a847),x84492))),x84492)+~P1(f331(f331(f240(f854(a847,a840)),x84492),f331(f302(a847,x84491),f331(f331(f87(a847),x84491),f331(f47(a847),x84492)))))
% 51.10/50.82 [8470]E(f331(f331(f145(a847),f331(f111(a847),x84701)),f135(a847,f331(f302(a847,f331(a119,f331(f111(a847),x84701))),f331(f111(a847),x84702)))),f135(a847,f331(f302(a847,f331(f111(a847),x84701)),f331(f111(a847),x84702))))+~P1(f331(f331(f241(a847),f331(f111(a847),x84701)),f331(f111(a847),x84702)))
% 51.10/50.82 [8750]E(f331(f331(f48(a1),f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),x87501),x87501)),a104))),f331(f111(a1),f331(f331(f87(a1),x87502),x87502))),f331(f331(f48(a1),f331(f111(a1),x87501)),f331(f111(a1),x87502)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x87502)))
% 51.10/50.82 [8854]E(f167(f848(x88541),f331(f331(f10(a840,a840,f848(x88541)),a327),f331(f331(f9(f848(x88541),f848(x88541),a840),a328),f120(x88541))),x88542),f169(x88541,f169(x88541,x88542)))+~P16(a847,f331(f160(a847),f331(f331(f147(f848(x88541),a847),f185(f848(x88541))),x88542)))
% 51.10/50.82 [8857]E(f331(f331(f48(a1),f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),x88571),x88571)),a104))),f331(f111(a1),f331(f331(f87(a1),x88572),x88572))),f331(f331(f48(a1),f331(f331(f87(a1),f331(f111(a1),x88571)),f85(a1))),f331(f111(a1),x88572)))+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x88572)))
% 51.10/50.82 [9638]P1(f331(a190,x96382))+E(f331(f331(f93(a1,a847),f331(f331(f3(a1),x96381),x96382)),f331(f331(f20(a1,a847,a847),f331(f331(f9(a1,a847,f854(a847,a847)),f331(f331(f10(a840,f854(a847,f854(a847,a847)),a1),f103(a847)),a190)),f2(a847))),a112)),f331(f331(f3(a847),f331(a112,x96381)),f331(a112,x96382)))
% 51.10/50.82 [9642]E(f331(f331(f93(a1,a847),f331(f111(a1),f331(f331(f87(a1),x96421),f331(f86(a1),x96422)))),f331(f331(f20(a1,a847,a847),f331(f331(f9(a1,a847,f854(a847,a847)),f331(f331(f10(a840,f854(a847,f854(a847,a847)),a1),f103(a847)),a190)),f2(a847))),a112)),f331(f331(f3(a847),f331(f111(a847),x96421)),f331(f111(a847),x96422)))+P1(f331(f331(f241(a1),x96422),a90))
% 51.10/50.82 [9643]~P28(x96431,x96432)+P1(f331(f331(f240(f854(f853(x96431,x96431),a840)),f331(f331(f289(x96431,x96431,x96431),f331(f248(f854(f853(x96431,x96431),a840),f854(f853(x96431,x96431),a840)),x96432)),f331(f258(f854(f853(x96431,x96431),a840),f854(f853(x96431,x96431),a840)),x96432))),f331(f248(f854(f853(x96431,x96431),a840),f854(f853(x96431,x96431),a840)),x96432)))
% 51.10/50.82 [9700]~E(f331(f47(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,f854(a847,a840),a840),f333(a847)),x97001))),f331(f331(f9(a847,a847,a840),f241(a847)),f331(a119,x97002))))),f2(a847))+~P1(f331(f331(f333(a847),f2(a847)),x97001))
% 51.10/50.82 [9713]E(f299(a847,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97131,x97132),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x97132),x97131))
% 51.10/50.82 [9719]E(f300(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97191,x97192),f184(f854(a847,a840)))+P1(f331(f331(f287(a847),x97191),x97192))
% 51.10/50.82 [9720]E(f297(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97201,x97202),f184(f854(a847,a840)))+P1(f331(f331(f287(a847),x97201),x97202))
% 51.10/50.82 [9721]E(f300(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97211,x97212),f184(f854(a847,a840)))+P1(f331(f331(f287(a847),x97211),x97212))
% 51.10/50.82 [9722]E(f297(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97221,x97222),f184(f854(a847,a840)))+P1(f331(f331(f287(a847),x97221),x97222))
% 51.10/50.82 [9723]E(f300(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97231,x97232),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x97232),x97231))
% 51.10/50.82 [9724]E(f297(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97241,x97242),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x97242),x97241))
% 51.10/50.82 [9725]E(f300(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97251,x97252),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x97252),x97251))
% 51.10/50.82 [9726]E(f300(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97261,x97262),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x97262),x97261))
% 51.10/50.82 [9727]E(f297(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97271,x97272),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x97272),x97271))
% 51.10/50.82 [9728]E(f297(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97281,x97282),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x97282),x97281))
% 51.10/50.82 [9771]E(f57(a1,f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),x97711),x97711)),a104)),f331(f111(a1),f331(f331(f87(a1),x97712),x97712))),f331(f331(f87(a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f57(a1,f331(f111(a1),x97711),f331(f111(a1),x97712)))),f85(a1)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x97712)))
% 51.10/50.82 [9780]E(f57(a1,f331(f111(a1),f331(f331(f3(a1),f331(f331(f87(a1),x97801),x97801)),a104)),f331(f111(a1),f331(f331(f87(a1),x97802),x97802))),f331(f331(f3(a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f57(a1,f331(f331(f87(a1),f331(f111(a1),x97801)),f85(a1)),f331(f111(a1),x97802)))),f85(a1)))+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x97802)))
% 51.10/50.82 [9842]~P7(x98421)+E(f49(x98421,f331(f264(x98421),f331(f331(f10(f854(x98421,a840),a840,x98421),f95(x98421)),f331(f331(f10(f854(x98421,a840),f854(x98421,a840),x98421),f331(f20(x98421,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98421),a334),f331(f331(f9(x98421,f854(x98421,a840),a840),f333(x98421)),x98422)))),f240(x98421))))),f50(x98421,x98422))
% 51.10/50.82 [9866]~P34(x98661,x98662)+P56(x98661,f331(f331(f9(x98661,f854(f853(x98661,x98661),a840),f854(x98661,a840)),f331(f331(f10(f854(x98661,f854(f854(f853(x98661,x98661),a840),a840)),f854(f854(f853(x98661,x98661),a840),f854(x98661,a840)),x98661),f9(x98661,f854(f853(x98661,x98661),a840),a840)),f331(f331(f10(f854(x98661,f853(x98661,x98661)),f854(x98661,f854(f854(f853(x98661,x98661),a840),a840)),x98661),f331(f10(f853(x98661,x98661),f854(f854(f853(x98661,x98661),a840),a840),x98661),f333(f853(x98661,x98661)))),f249(x98661,x98661)))),x98662))
% 51.10/50.82 [9867]~P10(x98671,f247(f854(x98671,a840)),x98672)+P9(x98671,f331(f331(f9(x98671,f854(f853(x98671,x98671),a840),f854(x98671,a840)),f331(f331(f10(f854(x98671,f854(f854(f853(x98671,x98671),a840),a840)),f854(f854(f853(x98671,x98671),a840),f854(x98671,a840)),x98671),f9(x98671,f854(f853(x98671,x98671),a840),a840)),f331(f331(f10(f854(x98671,f853(x98671,x98671)),f854(x98671,f854(f854(f853(x98671,x98671),a840),a840)),x98671),f331(f10(f853(x98671,x98671),f854(f854(f853(x98671,x98671),a840),a840),x98671),f333(f853(x98671,x98671)))),f249(x98671,x98671)))),x98672))
% 51.10/50.82 [9904]P34(x99041,x99042)+~P56(x99041,f331(f331(f9(x99041,f854(f853(x99041,x99041),a840),f854(x99041,a840)),f331(f331(f10(f854(x99041,f854(f854(f853(x99041,x99041),a840),a840)),f854(f854(f853(x99041,x99041),a840),f854(x99041,a840)),x99041),f9(x99041,f854(f853(x99041,x99041),a840),a840)),f331(f331(f10(f854(x99041,f853(x99041,x99041)),f854(x99041,f854(f854(f853(x99041,x99041),a840),a840)),x99041),f331(f10(f853(x99041,x99041),f854(f854(f853(x99041,x99041),a840),a840),x99041),f333(f853(x99041,x99041)))),f249(x99041,x99041)))),x99042))
% 51.10/50.82 [9905]P10(x99051,f247(f854(x99051,a840)),x99052)+~P9(x99051,f331(f331(f9(x99051,f854(f853(x99051,x99051),a840),f854(x99051,a840)),f331(f331(f10(f854(x99051,f854(f854(f853(x99051,x99051),a840),a840)),f854(f854(f853(x99051,x99051),a840),f854(x99051,a840)),x99051),f9(x99051,f854(f853(x99051,x99051),a840),a840)),f331(f331(f10(f854(x99051,f853(x99051,x99051)),f854(x99051,f854(f854(f853(x99051,x99051),a840),a840)),x99051),f331(f10(f853(x99051,x99051),f854(f854(f853(x99051,x99051),a840),a840),x99051),f333(f853(x99051,x99051)))),f249(x99051,x99051)))),x99052))
% 51.10/50.82 [7147]E(f331(f331(f87(a847),f331(f111(a847),f331(f331(f3(a1),x71471),a104))),x71472),f331(a119,f331(f331(f87(a847),f331(f111(a847),x71471)),x71472)))+P1(f331(a190,f331(f111(a1),x71471)))
% 51.10/50.82 [7613]~P91(x76131)+E(f331(f331(f87(x76131),f331(f331(f87(x76131),f85(x76131)),f331(f111(x76131),x76132))),f331(f111(x76131),x76132)),f331(f111(x76131),f331(f331(f3(a1),f331(f331(f87(a1),x76132),x76132)),a104)))
% 51.10/50.82 [8249]~P1(f331(f331(f240(a1),x82491),x82492))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x82491),x82491)),f331(f331(f3(a1),f331(f331(f87(a1),x82492),x82492)),a104)))
% 51.10/50.82 [8250]~P1(f331(f331(f240(a1),x82501),x82502))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x82501),x82501)),f331(f331(f3(a1),f331(f331(f87(a1),x82502),x82502)),a104)))
% 51.10/50.82 [8251]~P1(f331(f331(f240(a1),x82511),x82512))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x82511),x82511)),f331(f331(f3(a1),f331(f331(f87(a1),x82512),x82512)),a104)))
% 51.10/50.82 [8252]~P1(f331(f331(f240(a1),x82521),x82522))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x82521),x82521)),f331(f331(f3(a1),f331(f331(f87(a1),x82522),x82522)),a104)))
% 51.10/50.82 [8651]P1(f331(f331(f240(a1),x86511),x86512))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x86511),x86511)),f331(f331(f3(a1),f331(f331(f87(a1),x86512),x86512)),a104)))
% 51.10/50.82 [8652]P1(f331(f331(f240(a1),x86521),x86522))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),x86521),x86521)),f331(f331(f3(a1),f331(f331(f87(a1),x86522),x86522)),a104)))
% 51.10/50.82 [8653]P1(f331(f331(f240(a1),x86531),x86532))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x86531),x86531)),f331(f331(f3(a1),f331(f331(f87(a1),x86532),x86532)),a104)))
% 51.10/50.82 [8654]P1(f331(f331(f240(a1),x86541),x86542))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x86541),x86541)),f331(f331(f3(a1),f331(f331(f87(a1),x86542),x86542)),a104)))
% 51.10/50.82 [8910]~P1(f331(f331(f241(a1),x89101),x89102))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89101),x89101)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x89102),x89102)),a104)))
% 51.10/50.82 [8911]~P1(f331(f331(f241(a1),x89111),x89112))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89111),x89111)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x89112),x89112)),a104)))
% 51.10/50.82 [8912]~P1(f331(f331(f240(a1),x89121),x89122))+P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89121),x89121)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x89122),x89122)),a104)))
% 51.10/50.82 [8913]~P1(f331(f331(f240(a1),x89131),x89132))+P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x89131),x89131)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x89132),x89132)),a104)))
% 51.10/50.82 [9143]P1(f331(f331(f241(a1),x91431),x91432))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x91431),x91431)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x91432),x91432)),a104)))
% 51.10/50.82 [9144]P1(f331(f331(f241(a1),x91441),x91442))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),x91441),x91441)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x91442),x91442)),a104)))
% 51.10/50.82 [9145]P1(f331(f331(f240(a1),x91451),x91452))+~P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x91451),x91451)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x91452),x91452)),a104)))
% 51.10/50.82 [9146]P1(f331(f331(f240(a1),x91461),x91462))+~P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),x91461),x91461)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),x91462),x91462)),a104)))
% 51.10/50.82 [9177]~P1(f331(f68(x91771),x91772))+P1(f331(f68(f854(x91771,a840)),f331(f264(f854(x91771,a840)),f331(f331(f9(f854(x91771,a840),f854(x91771,a840),a840),f240(f854(x91771,a840))),x91772))))
% 51.10/50.82 [9224]~E(f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),x92241),f184(f854(f853(a847,a847),a840)))),f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),x92242),f184(f854(f853(a847,a847),a840)))))+P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),x92241),x92242)),a116))
% 51.10/50.82 [9311]E(f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),x93111),f184(f854(f853(a847,a847),a840)))),f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),x93112),f184(f854(f853(a847,a847),a840)))))+~P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),x93111),x93112)),a116))
% 51.10/50.82 [9345]P1(f331(f331(f240(a1),f2(a1)),f697(x93451,x93452)))+E(f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x93451)),f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x93452)))
% 51.10/50.82 [9852]~P7(x98521)+E(f50(x98521,f331(f264(x98521),f331(f331(f10(f854(x98521,a840),a840,x98521),f95(x98521)),f331(f331(f10(f854(x98521,a840),f854(x98521,a840),x98521),f331(f20(x98521,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98521),a334),f331(f331(f9(x98521,f854(x98521,a840),a840),f333(x98521)),x98522)))),f331(f9(x98521,x98521,a840),f240(x98521)))))),f49(x98521,x98522))
% 51.10/50.82 [9872]P1(f331(f331(f333(a847),f2(a847)),x98721))+E(f331(f47(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,f854(a847,a840),a840),f331(f331(f10(a847,f854(f854(a847,a840),a840),a847),f333(a847)),a119)),x98721))),f331(f331(f9(a847,a847,a840),f241(a847)),x98722)))),f331(f47(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,f854(a847,a840),a840),f333(a847)),x98721))),f331(f331(f9(a847,a847,a840),f241(a847)),f331(a119,x98722))))))
% 51.10/50.82 [9919]P1(f331(f331(f287(a847),x99191),x99192))+~P1(f331(f331(f333(a847),x99192),f295(a847,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x99191)))
% 51.10/50.82 [9920]P1(f331(f331(f287(a847),x99201),x99202))+~P1(f331(f331(f333(a847),x99201),f298(a847,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x99202)))
% 51.10/50.82 [9921]~P1(f331(f331(f287(a847),x99211),x99212))+~P1(f331(f331(f333(a847),x99212),f298(a847,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x99211)))
% 51.10/50.82 [9922]~P1(f331(f331(f287(a847),x99221),x99222))+~P1(f331(f331(f333(a847),x99221),f295(a847,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x99222)))
% 51.10/50.82 [7480]~P91(x74801)+E(f331(f331(f88(x74801),x74802),f331(f111(x74801),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),x74802)
% 51.10/50.82 [7747]~P91(x77471)+E(f331(f331(f87(x77471),f331(f111(x77471),x77472)),f85(x77471)),f331(f111(x77471),f331(f331(f87(a1),x77472),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))
% 51.10/50.82 [7891]P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x78912)))+E(f331(f331(f250(a1),x78911),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x78912),x78912)),a104))),f85(a1))
% 51.10/50.82 [9201]~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x92012)))+E(f331(f331(f250(a1),x92011),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x92012),x92012)),a104))),f331(f331(f93(a1,a1),f331(f331(f250(a1),x92011),f331(f111(a847),x92012))),f331(f331(f20(a1,a1,a1),f331(f331(f10(a1,f854(a1,a1),a1),f88(a1)),f331(f88(a1),x92011))),f7(a1))))
% 51.10/50.82 [9690]~P1(f331(f331(f241(a847),f331(f111(a847),x96901)),f331(a119,x96902)))+P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x96901),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),f241(a847)),a112)),x96902))))
% 51.10/50.82 [9691]~P1(f331(f331(f240(a847),f331(f111(a847),x96911)),f331(a119,x96912)))+P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x96911),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),f240(a847)),a112)),x96912))))
% 51.10/50.82 [9755]P1(f331(f331(f241(a847),f331(f111(a847),x97551)),f331(a119,x97552)))+~P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x97551),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),f241(a847)),a112)),x97552))))
% 51.10/50.82 [9756]P1(f331(f331(f240(a847),f331(f111(a847),x97561)),f331(a119,x97562)))+~P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x97561),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),f240(a847)),a112)),x97562))))
% 51.10/50.82 [9786]~P1(f331(f331(f241(a847),f331(a119,x97862)),f331(f111(a847),x97861)))+P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x97861),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f10(a847,a840,a1),f331(f241(a847),x97862)),a112)))))
% 51.10/50.82 [9787]~P1(f331(f331(f240(a847),f331(a119,x97872)),f331(f111(a847),x97871)))+P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x97871),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f10(a847,a840,a1),f331(f240(a847),x97872)),a112)))))
% 51.10/50.82 [9840]P1(f331(f331(f241(a847),f331(a119,x98401)),f331(f111(a847),x98402)))+~P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x98402),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f10(a847,a840,a1),f331(f241(a847),x98401)),a112)))))
% 51.10/50.82 [9841]P1(f331(f331(f240(a847),f331(a119,x98411)),f331(f111(a847),x98412)))+~P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x98412),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f10(a847,a840,a1),f331(f240(a847),x98411)),a112)))))
% 51.10/50.82 [9912]~P1(f331(f331(f333(a847),f2(a847)),x99121))+E(f331(a119,f331(f47(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,f854(a847,a840),a840),f331(f331(f10(a847,f854(f854(a847,a840),a840),a847),f333(a847)),a119)),x99121))),f331(f331(f9(a847,a847,a840),f241(a847)),x99122))))),f331(f47(a847),f331(f264(a847),f331(f331(f20(a847,a840,a840),f331(f331(f10(a840,f854(a840,a840),a847),a329),f331(f331(f9(a847,f854(a847,a840),a840),f333(a847)),x99121))),f331(f331(f9(a847,a847,a840),f241(a847)),f331(a119,x99122))))))
% 51.10/50.82 [8433]~P91(x84331)+E(f331(f331(f88(x84331),f331(f111(x84331),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),x84332),x84332)
% 51.10/50.82 [8490]~P91(x84901)+E(f331(f331(f87(x84901),f85(x84901)),f331(f111(x84901),x84902)),f331(f111(x84901),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),x84902)))
% 51.10/50.82 [8536]~P91(x85361)+E(f331(f331(f3(x85361),f331(f111(x85361),x85362)),f85(x85361)),f331(f111(x85361),f331(f331(f87(a1),x85362),f331(f86(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [8670]~P1(f331(f331(f241(a847),f331(f111(a847),a90)),x86702))+E(f331(f331(f3(a847),x86701),f331(f331(f3(a847),x86702),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f3(a847),f331(a119,x86701)),x86702))
% 51.10/50.82 [9241]~P87(x92411)+E(f331(f331(f88(x92411),x92412),x92412),f331(f331(f250(x92411),x92412),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9242]~P74(x92421)+E(f331(f331(f250(x92421),x92422),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f88(x92421),x92422),x92422))
% 51.10/50.82 [9244]~P91(x92441)+E(f331(f331(f88(x92441),x92442),f331(f111(x92441),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f87(x92441),x92442),x92442))
% 51.10/50.82 [9482]~P133(x94821)+E(f331(f331(f250(x94821),f331(f86(x94821),x94822)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f250(x94821),x94822),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9483]~P86(x94831)+E(f331(f331(f250(x94831),f331(f82(x94831),x94832)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f250(x94831),x94832),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9479]~P91(x94791)+E(f331(f331(f88(x94791),f331(f111(x94791),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x94792),f331(f331(f87(x94791),x94792),x94792))
% 51.10/50.82 [9600]~P86(x96001)+E(f331(f82(x96001),f331(f331(f250(x96001),x96002),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x96001),x96002),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9650]~P86(x96501)+P1(f331(f331(f240(x96501),f2(x96501)),f331(f331(f250(x96501),x96502),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.82 [9831]~E(f331(a119,x98312),f331(f111(a847),x98311))+P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x98311),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),a328),a112)),x98312)))))
% 51.10/50.82 [9832]~E(f331(f111(a847),x98321),f331(a119,x98322))+P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x98321),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),a328),a112)),x98322)))))
% 51.10/50.82 [9875]E(f331(a119,x98751),f331(f111(a847),x98752))+~P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x98752),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),a328),a112)),x98751)))))
% 51.10/50.82 [9876]E(f331(f111(a847),x98761),f331(a119,x98762))+~P1(f331(f331(f93(a1,a840),f331(f111(a1),f331(f331(f87(a1),x98761),a104))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a334),f331(f331(f10(a840,a840,a1),a327),a190))),f331(f331(f9(a1,a847,a840),f331(f331(f10(a847,f854(a847,a840),a1),a328),a112)),x98762)))))
% 51.10/50.82 [9648]~P91(x96481)+E(f331(f331(f250(x96481),f331(f111(x96481),a104)),f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x96482)),f85(x96481))
% 51.10/50.82 [9649]~P133(x96491)+E(f331(f331(f250(x96491),f331(f86(x96491),f85(x96491))),f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x96492)),f85(x96491))
% 51.10/50.82 [9652]~P74(x96521)+E(f331(f331(f250(x96521),x96522),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),a104))),f331(f331(f88(x96521),f331(f331(f88(x96521),x96522),x96522)),x96522))
% 51.10/50.82 [9855]~P1(f331(f331(f240(a1),f2(a1)),x98552))+E(f57(a1,f331(f331(f87(a1),f85(a1)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98551)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98552)),f331(f331(f87(a1),f85(a1)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f57(a1,x98551,x98552))))
% 51.10/50.82 [9878]~P1(f331(f331(f240(a1),f2(a1)),x98782))+E(f331(f331(f48(a1),f331(f331(f87(a1),f85(a1)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98781))),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98782)),f331(f331(f48(a1),x98781),x98782))
% 51.10/50.82 [9880]~P1(f331(f331(f240(a1),x98802),f2(a1)))+E(f331(f331(f48(a1),f331(f331(f87(a1),f85(a1)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98801))),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98802)),f331(f331(f48(a1),f331(f331(f87(a1),x98801),f85(a1))),x98802))
% 51.10/50.82 [9881]~P1(f331(f331(f240(a1),x98812),f2(a1)))+E(f57(a1,f331(f331(f87(a1),f85(a1)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98811)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98812)),f331(f331(f3(a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f57(a1,f331(f331(f87(a1),x98811),f85(a1)),x98812))),f85(a1)))
% 51.10/50.82 [9746]~P91(x97461)+E(f331(f331(f250(x97461),f331(f111(x97461),a104)),f331(a119,f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97462))),f331(f111(x97461),a104))
% 51.10/50.82 [9748]~P133(x97481)+E(f331(f331(f250(x97481),f331(f86(x97481),f85(x97481))),f331(a119,f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97482))),f331(f86(x97481),f85(x97481)))
% 51.10/50.82 [5970]E(x59701,x59702)+~P37(a25,x59701,x59703,x59702)
% 51.10/50.82 [4975]~P34(x49751,x49753)+P34(x49751,f326(x49751,x49752,x49753))
% 51.10/50.82 [5140]P29(x51401,x51402,x51403)+~P29(x51401,f331(a119,x51402),x51403)
% 51.10/50.82 [5223]~P10(x52231,x52232,x52233)+P10(f848(x52231),f153(x52231,x52232),f151(x52231,x52233))
% 51.10/50.82 [5224]~P45(x52241,x52242,x52243)+P45(f848(x52241),f153(x52241,x52242),f151(x52241,x52243))
% 51.10/50.82 [5333]P51(x53331,x53332,x53333)+~E(f646(x53333,x53332,x53331),f616(x53333,x53332,x53331))
% 51.10/50.82 [5334]P52(x53341,x53342,x53343)+~E(f647(x53343,x53342,x53341),f648(x53343,x53342,x53341))
% 51.10/50.82 [6292]P30(x62921,x62922,x62923)+~P29(x62921,f594(x62923,x62922,x62921),f597(x62923,x62922,x62921))
% 51.10/50.82 [4533]~E(x45331,f187(x45332))+~E(x45331,f331(f234(x45332),x45333))
% 51.10/50.82 [4534]~E(x45341,f187(x45342))+~E(x45341,f331(f234(x45342),x45343))
% 51.10/50.82 [4581]~E(f331(f160(x45812),x45811),x45813)+E(x45811,f331(f160(x45812),x45813))
% 51.10/50.82 [4582]~E(x45822,f331(f160(x45821),x45823))+E(f331(f160(x45821),x45822),x45823)
% 51.10/50.82 [4626]E(x46261,x46262)+~E(f331(f234(x46263),x46261),f331(f234(x46263),x46262))
% 51.10/50.82 [4627]E(x46271,x46272)+~E(f331(f160(x46273),x46271),f331(f160(x46273),x46272))
% 51.10/50.82 [4829]~P9(x48293,x48291)+P1(f331(f331(x48291,x48292),x48292))
% 51.10/50.82 [4830]~P47(x48303,x48301)+P1(f331(f331(x48301,x48302),x48302))
% 51.10/50.82 [4831]~P56(x48311,x48312)+P1(f331(f320(x48311,x48312),x48313))
% 51.10/50.82 [4832]~P56(x48321,x48322)+P1(f331(f320(x48321,x48322),x48323))
% 51.10/50.82 [4894]~P34(x48941,x48942)+P34(f848(x48941),f331(f138(x48941,x48942),x48943))
% 51.10/50.82 [4898]~P1(f331(x48982,x48983))+~E(f331(f264(x48981),x48982),f184(f854(x48981,a840)))
% 51.10/50.82 [4899]~P1(f331(x48992,x48993))+~E(f184(f854(x48991,a840)),f331(f264(x48991),x48992))
% 51.10/50.82 [4928]~P1(f331(x49281,x49283))+P1(f331(x49281,f97(x49282,x49281)))
% 51.10/50.82 [4929]~P1(f331(x49291,x49293))+P1(f331(x49291,f97(x49292,x49291)))
% 51.10/50.82 [4930]~P1(f331(x49301,x49303))+P1(f331(x49301,f97(x49302,x49301)))
% 51.10/50.82 [4931]~P1(f331(x49311,x49313))+P1(f331(x49311,f97(x49312,x49311)))
% 51.10/50.82 [5056]~E(x50562,x50563)+P1(f331(f331(f333(x50561),x50562),f331(a328,x50563)))
% 51.10/50.82 [5109]E(f331(f160(x51091),x51092),f331(f331(f145(x51091),x51093),f120(x51091)))+~E(x51092,f331(f331(f145(x51091),x51093),f120(x51091)))
% 51.10/50.82 [5110]~E(x51103,f331(f331(f145(x51101),x51102),f120(x51101)))+E(f331(f331(f145(x51101),x51102),f120(x51101)),f331(f160(x51101),x51103))
% 51.10/50.82 [5135]~E(x51353,f331(f18(f851(x51352),x51351),f187(x51352)))+E(f174(x51351,x51352,x51353),f184(f854(x51351,a840)))
% 51.10/50.82 [5156]E(f331(f47(x51561),f363(x51562,x51563,x51561)),x51562)+~E(f331(f47(x51561),x51563),f331(a119,x51562))
% 51.10/50.82 [5161]~P34(x51611,x51613)+P1(f331(f331(f333(x51611),x51612),f321(x51611,x51613)))
% 51.10/50.82 [5162]~P34(x51621,x51623)+P1(f331(f331(f333(x51621),x51622),f321(x51621,x51623)))
% 51.10/50.82 [5165]~E(f331(f160(x51652),x51651),f331(f331(f145(x51652),x51653),f120(x51652)))+E(x51651,f331(f331(f145(x51652),x51653),f120(x51652)))
% 51.10/50.82 [5166]~E(f331(f331(f145(x51662),x51663),f120(x51662)),f331(f160(x51662),x51661))+E(x51661,f331(f331(f145(x51662),x51663),f120(x51662)))
% 51.10/50.82 [5181]E(x51811,f331(f18(f851(x51812),x51813),f187(x51812)))+~E(f174(x51813,x51812,x51811),f184(f854(x51813,a840)))
% 51.10/50.82 [5187]E(f92(f853(a847,a847),f60(x51871,x51872)),x51873)+~P1(f331(f60(x51871,x51872),x51873))
% 51.10/50.82 [5195]~E(x51953,f331(f234(x51951),x51952))+P1(f331(f331(f333(x51951),x51952),f233(x51951,x51953)))
% 51.10/50.82 [5285]~E(x52852,f120(x52851))+P1(f331(f331(f333(f848(x52851)),x52852),f153(x52851,x52853)))
% 51.10/50.82 [5293]~P45(x52931,x52932,x52933)+P45(x52931,x52932,f331(f286(x52931,x52931),x52933))
% 51.10/50.82 [5294]~P52(x52941,x52942,x52943)+P52(x52941,x52942,f331(f286(x52941,x52941),x52943))
% 51.10/50.82 [5314]~P5(x53141)+E(f57(x53141,f57(x53141,x53142,x53143),x53143),f57(x53141,x53142,x53143))
% 51.10/50.82 [5412]E(x54121,x54122)+~P1(f331(f331(f333(x54123),x54121),f331(a328,x54122)))
% 51.10/50.82 [5455]~P84(x54551)+E(f186(x54551,x54552,f2(a847),x54553),x54553)
% 51.10/50.82 [5476]P45(x54761,x54762,x54763)+~P45(x54761,x54762,f331(f286(x54761,x54761),x54763))
% 51.10/50.82 [5477]P52(x54771,x54772,x54773)+~P52(x54771,x54772,f331(f286(x54771,x54771),x54773))
% 51.10/50.82 [5493]E(f161(x54931,x54932,f146(x54931,x54933)),f146(x54931,f161(x54931,x54932,x54933)))+~P1(f331(f132(x54931),x54933))
% 51.10/50.82 [5499]E(x54991,f331(f234(x54992),x54993))+~P1(f331(f331(f333(x54992),x54993),f233(x54992,x54991)))
% 51.10/50.82 [5581]~P1(f331(a26,x55813))+P1(f331(a26,f34(x55811,x55812,x55813)))
% 51.10/50.82 [5582]~P1(f331(a26,x55823))+P1(f331(a26,f34(x55821,x55822,x55823)))
% 51.10/50.82 [5594]E(f331(f131(x55941,x55942),x55943),f120(x55941))+P1(f331(x55942,f745(x55943,x55942,x55941)))
% 51.10/50.82 [5750]~P1(f331(f132(x57501),x57503))+P1(f331(f132(x57501),f161(x57501,x57502,x57503)))
% 51.10/50.82 [5751]~P1(f331(f132(x57511),x57512))+P1(f331(f132(x57511),f165(x57511,x57512,x57513)))
% 51.10/50.82 [5752]~P1(f331(f132(x57521),x57523))+P1(f331(f132(x57521),f167(x57521,x57522,x57523)))
% 51.10/50.82 [5753]~P1(f331(f132(x57531),x57533))+P1(f331(f132(x57531),f134(x57531,x57532,x57533)))
% 51.10/50.82 [5754]~P140(x57541,x57543,x57542)+P1(f331(x57541,f57(a1,x57542,x57543)))
% 51.10/50.82 [5852]P1(f331(a26,f33(x58521,x58522,x58523)))+~P1(f331(a26,f331(a29,x58522)))
% 51.10/50.82 [5853]P1(f331(a26,f33(x58531,x58532,x58533)))+~P1(f331(a26,f331(a29,x58532)))
% 51.10/50.82 [5865]~P88(x58651)+E(f331(f331(f109(f854(x58651,a840)),f331(f301(x58651),x58652)),f306(x58651,x58652,x58653)),f184(f854(x58651,a840)))
% 51.10/50.82 [5866]~P88(x58661)+E(f331(f331(f109(f854(x58661,a840)),f331(f301(x58661),x58662)),f305(x58661,x58662,x58663)),f184(f854(x58661,a840)))
% 51.10/50.82 [5867]~P88(x58671)+E(f331(f331(f109(f854(x58671,a840)),f331(f265(x58671),x58672)),f303(x58671,x58672,x58673)),f184(f854(x58671,a840)))
% 51.10/50.82 [6018]P1(f331(a26,x60181))+~P1(f331(a26,f34(x60182,x60183,x60181)))
% 51.10/50.82 [6019]P1(f331(a26,x60191))+~P1(f331(a26,f34(x60192,x60193,x60191)))
% 51.10/50.82 [6020]P1(f331(a26,x60201))+~P1(f331(a26,f35(x60202,x60203,x60201)))
% 51.10/50.82 [6021]P1(f331(a26,x60211))+~P1(f331(a26,f35(x60212,x60213,x60211)))
% 51.10/50.82 [6022]P1(f331(a26,x60221))+~P1(f331(a26,f35(x60222,x60221,x60223)))
% 51.10/50.82 [6023]P1(f331(a26,x60231))+~P1(f331(a26,f35(x60232,x60231,x60233)))
% 51.10/50.82 [6104]E(f331(f131(x61041,x61042),x61043),x61043)+~P1(f331(x61042,f759(x61043,x61042,x61041)))
% 51.10/50.82 [6106]E(f331(f331(f310(x61061),f373(x61062,x61063,x61061)),f363(x61062,x61063,x61061)),x61063)+~E(f331(f47(x61061),x61063),f331(a119,x61062))
% 51.10/50.82 [6121]P140(x61211,x61212,x61213)+~P1(f331(x61211,f57(a1,x61213,x61212)))
% 51.10/50.82 [6173]E(f167(x61731,x61732,x61733),x61733)+~P1(f331(x61732,f768(x61733,x61732,x61731)))
% 51.10/50.82 [6213]~P1(f331(a26,f33(x62132,x62131,x62133)))+P1(f331(a26,f331(a29,x62131)))
% 51.10/50.82 [6214]~P1(f331(a26,f33(x62142,x62141,x62143)))+P1(f331(a26,f331(a29,x62141)))
% 51.10/50.82 [6261]~P1(f331(x62612,f581(x62613,x62612,x62611)))+P1(f331(f253(x62611,x62612),x62613))
% 51.10/50.82 [6520]~P1(f331(f320(x65201,x65202),f806(x65203,x65202,x65201)))+P1(f331(f320(x65201,x65202),x65203))
% 51.10/50.82 [6521]~P1(f331(f320(x65211,x65212),f813(x65213,x65212,x65211)))+P1(f331(f320(x65211,x65212),x65213))
% 51.10/50.82 [7148]~P5(x71481)+E(f331(f331(f87(x71481),f331(f331(f88(x71481),x71482),f331(f331(f48(x71481),x71483),x71482))),f57(x71481,x71483,x71482)),x71483)
% 51.10/50.82 [7637]E(f331(f331(f249(x76371,x76371),f417(x76372,x76373,x76371)),f417(x76372,x76373,x76371)),x76373)+~P1(f331(f331(f333(f853(x76371,x76371)),x76373),f268(x76371,x76372)))
% 51.10/50.82 [7756]~P1(f331(f331(f333(x77561),f366(x77563,x77562,x77561)),f321(x77561,x77563)))+P1(f331(f331(f333(x77561),x77562),f321(x77561,x77563)))
% 51.10/50.82 [7757]~P1(f331(f331(f333(x77571),f618(x77573,x77572,x77571)),f321(x77571,x77573)))+P1(f331(f331(f333(x77571),x77572),f321(x77571,x77573)))
% 51.10/50.82 [7758]~P1(f331(f331(f333(x77581),f620(x77583,x77582,x77581)),f321(x77581,x77583)))+P1(f331(f331(f333(x77581),x77582),f321(x77581,x77583)))
% 51.10/50.82 [7943]~P5(x79431)+E(f331(f331(f87(x79431),f331(f331(f88(x79431),f331(f331(f48(x79431),x79432),x79433)),x79433)),f57(x79431,x79432,x79433)),x79432)
% 51.10/50.82 [7944]~P5(x79441)+E(f331(f331(f87(x79441),f331(f331(f88(x79441),f331(f331(f48(x79441),x79442),x79443)),x79443)),f57(x79441,x79442,x79443)),x79442)
% 51.10/50.82 [7985]~E(f331(f47(x79851),x79852),f331(a119,x79853))+~P1(f331(f331(f333(x79851),f373(x79853,x79852,x79851)),f363(x79853,x79852,x79851)))
% 51.10/50.82 [8585]P1(f331(f331(f240(f854(f853(x85851,x85851),a840)),f308(x85851,x85852)),f308(x85851,x85853)))+~P1(f331(f331(f240(f854(f853(x85851,x85851),a840)),x85852),f308(x85851,x85853)))
% 51.10/50.82 [8823]E(x88231,f120(x88232))+~P1(f331(f331(f333(f853(f848(x88232),f848(x88232))),f331(f331(f249(f848(x88232),f848(x88232)),x88231),f120(x88232))),f151(x88232,x88233)))
% 51.10/50.82 [8848]E(x88481,f120(x88482))+~P1(f331(f331(f333(f853(f848(x88482),f848(x88482))),f331(f331(f249(f848(x88482),f848(x88482)),f120(x88482)),x88481)),f151(x88482,x88483)))
% 51.10/50.82 [8970]E(f331(f331(f145(x89701),f750(x89702,x89703,x89701)),f751(x89702,x89703,x89701)),x89703)+~P1(f331(f331(f333(f853(f848(x89701),f848(x89701))),f331(f331(f249(f848(x89701),f848(x89701)),f120(x89701)),x89703)),f142(x89701,x89702)))
% 51.10/50.82 [9170]~P119(x91701)+~P1(f331(f331(f241(x91701),f331(f331(f87(x91701),f331(f331(f88(x91701),x91702),x91702)),f331(f331(f88(x91701),x91703),x91703))),f2(x91701)))
% 51.10/50.82 [9219]P1(f331(f68(x92191),x92192))+~P1(f331(f331(f333(f853(f854(x92191,a840),f854(x92191,a840))),f331(f331(f249(f854(x92191,a840),f854(x92191,a840)),x92193),x92192)),f307(x92191)))
% 51.10/50.82 [9504]~P43(x95041,x95042,x95043)+P1(f331(f331(f241(a1),f331(f331(f80(f853(a1,a1),a1,x95041,f248(a1,a1)),f214(x95041)),f231(x95041,x95042,f228(x95041,x95043)))),f2(a1)))
% 51.10/50.82 [9505]~P44(x95051,x95052,x95053)+P1(f331(f331(f240(a1),f331(f331(f80(f853(a1,a1),a1,x95051,f248(a1,a1)),f214(x95051)),f231(x95051,x95052,f228(x95051,x95053)))),f2(a1)))
% 51.10/50.82 [9625]P43(x96251,x96252,x96253)+~P1(f331(f331(f241(a1),f331(f331(f80(f853(a1,a1),a1,x96251,f248(a1,a1)),f214(x96251)),f231(x96251,x96252,f228(x96251,x96253)))),f2(a1)))
% 51.10/50.82 [9626]P44(x96261,x96262,x96263)+~P1(f331(f331(f240(a1),f331(f331(f80(f853(a1,a1),a1,x96261,f248(a1,a1)),f214(x96261)),f231(x96261,x96262,f228(x96261,x96263)))),f2(a1)))
% 51.10/50.82 [9963]~P86(x99631)+~P1(f331(f331(f241(x99631),f331(f331(f87(x99631),f331(f331(f250(x99631),x99632),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x99631),x99633),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f2(x99631)))
% 51.10/50.82 [4608]~E(x46083,f120(x46081))+E(f331(f331(f130(x46081),x46082),x46083),x46082)
% 51.10/50.82 [4609]~E(x46092,f120(x46091))+E(f331(f331(f130(x46091),x46092),x46093),x46093)
% 51.10/50.82 [4610]~E(x46103,f120(x46101))+E(f331(f331(f130(x46101),x46102),x46103),x46102)
% 51.10/50.82 [4611]~E(x46112,f120(x46111))+E(f331(f331(f130(x46111),x46112),x46113),x46113)
% 51.10/50.82 [4617]~E(x46172,f2(a847))+E(f331(f331(f164(x46171),x46172),x46173),f120(x46171))
% 51.10/50.82 [4621]~E(x46213,f120(x46211))+E(f331(f331(f164(x46211),x46212),x46213),f120(x46211))
% 51.10/50.82 [4661]~E(x46611,x46613)+E(x46611,f331(f331(f130(x46612),f120(x46612)),x46613))
% 51.10/50.82 [4745]~P103(x47452)+E(f331(f184(f854(x47451,x47452)),x47453),f184(x47452))
% 51.10/50.82 [4746]~P103(x47462)+E(f331(f184(f854(x47461,x47462)),x47463),f184(x47462))
% 51.10/50.82 [4747]~P108(x47472)+E(f331(f247(f854(x47471,x47472)),x47473),f247(x47472))
% 51.10/50.82 [4764]E(x47641,f120(x47642))+~E(f331(f331(f130(x47642),x47641),x47643),x47643)
% 51.10/50.82 [4765]E(x47651,f120(x47652))+~E(f331(f331(f130(x47652),x47653),x47651),x47653)
% 51.10/50.82 [4766]E(x47661,f120(x47662))+~E(f331(f331(f130(x47662),x47663),x47661),x47663)
% 51.10/50.82 [4767]E(x47671,f120(x47672))+~E(f331(f331(f130(x47672),x47671),x47673),x47673)
% 51.10/50.82 [4773]E(x47731,f120(x47732))+~E(f331(f331(f130(x47732),x47733),x47731),f120(x47732))
% 51.10/50.82 [4774]E(x47741,f120(x47742))+~E(f331(f331(f130(x47742),x47741),x47743),f120(x47742))
% 51.10/50.82 [4775]E(x47751,f120(x47752))+~E(f331(f331(f130(x47752),x47753),x47751),f120(x47752))
% 51.10/50.82 [4776]E(x47761,f120(x47762))+~E(f331(f331(f130(x47762),x47761),x47763),f120(x47762))
% 51.10/50.82 [4801]~E(x48012,f2(a847))+E(f331(f331(f88(a847),x48011),x48012),f331(f331(f88(a847),x48013),x48012))
% 51.10/50.82 [4802]~E(x48021,f2(a847))+E(f331(f331(f88(a847),x48021),x48022),f331(f331(f88(a847),x48021),x48023))
% 51.10/50.82 [4803]~E(x48031,f2(a847))+E(f331(f331(f88(a847),x48031),x48032),f331(f331(f88(a847),x48031),x48033))
% 51.10/50.82 [4856]~P87(x48561)+E(f331(f331(f87(x48561),x48562),x48563),f331(f331(f87(x48561),x48563),x48562))
% 51.10/50.82 [4857]~P87(x48571)+E(f331(f331(f88(x48571),x48572),x48573),f331(f331(f88(x48571),x48573),x48572))
% 51.10/50.82 [4858]~P102(x48581)+E(f331(f331(f244(x48581),x48582),x48583),f331(f331(f244(x48581),x48583),x48582))
% 51.10/50.82 [4859]~P102(x48591)+E(f331(f331(f244(x48591),x48592),x48593),f331(f331(f244(x48591),x48593),x48592))
% 51.10/50.82 [4860]~P102(x48601)+E(f331(f331(f239(x48601),x48602),x48603),f331(f331(f239(x48601),x48603),x48602))
% 51.10/50.82 [4861]~P102(x48611)+E(f331(f331(f239(x48611),x48612),x48613),f331(f331(f239(x48611),x48613),x48612))
% 51.10/50.82 [4862]~P97(x48621)+E(f331(f331(f108(x48621),x48622),x48623),f331(f331(f108(x48621),x48623),x48622))
% 51.10/50.82 [4863]~P100(x48631)+E(f331(f331(f108(x48631),x48632),x48633),f331(f331(f108(x48631),x48633),x48632))
% 51.10/50.82 [4864]~P100(x48641)+E(f331(f331(f108(x48641),x48642),x48643),f331(f331(f108(x48641),x48643),x48642))
% 51.10/50.82 [4865]~P97(x48651)+E(f331(f331(f109(x48651),x48652),x48653),f331(f331(f109(x48651),x48653),x48652))
% 51.10/50.82 [4866]~P101(x48661)+E(f331(f331(f109(x48661),x48662),x48663),f331(f331(f109(x48661),x48663),x48662))
% 51.10/50.82 [4867]~P101(x48671)+E(f331(f331(f109(x48671),x48672),x48673),f331(f331(f109(x48671),x48673),x48672))
% 51.10/50.82 [4926]E(f57(a847,x49261,x49262),f2(a847))+~E(x49261,f331(f331(f88(a847),x49262),x49263))
% 51.10/50.82 [4927]E(f57(a1,x49271,x49272),f2(a1))+~E(x49271,f331(f331(f88(a1),x49272),x49273))
% 51.10/50.82 [4987]E(x49871,x49872)+~E(f331(f331(f87(a847),x49873),x49871),f331(f331(f87(a847),x49873),x49872))
% 51.10/50.82 [4988]E(x49881,x49882)+~E(f331(f331(f87(a847),x49881),x49883),f331(f331(f87(a847),x49882),x49883))
% 51.10/50.82 [4998]~P69(x49981)+E(f331(f331(f87(x49981),x49982),f331(f86(x49981),x49983)),f331(f331(f3(x49981),x49982),x49983))
% 51.10/50.82 [4999]~P106(x49991)+E(f331(f331(f87(x49991),x49992),f331(f86(x49991),x49993)),f331(f331(f3(x49991),x49992),x49993))
% 51.10/50.82 [5000]~P4(x50001)+E(f331(f331(f87(x50001),x50002),f331(f86(x50001),x50003)),f331(f331(f3(x50001),x50002),x50003))
% 51.10/50.82 [5001]~P93(x50011)+E(f331(f331(f109(x50011),x50012),f331(f86(x50011),x50013)),f331(f331(f3(x50011),x50012),x50013))
% 51.10/50.82 [5002]~P69(x50021)+E(f331(f331(f3(x50021),x50022),f331(f86(x50021),x50023)),f331(f331(f87(x50021),x50022),x50023))
% 51.10/50.82 [5050]~P1(f331(x50503,x50502))+P1(f331(f331(f333(x50501),x50502),x50503))
% 51.10/50.82 [5051]~P70(x50512)+E(f331(f331(f11(x50511,x50512),x50513),f184(f854(x50511,a840))),f85(x50512))
% 51.10/50.82 [5052]~P70(x50522)+E(f331(f331(f11(x50521,x50522),x50523),f184(f854(x50521,a840))),f85(x50522))
% 51.10/50.82 [5053]~P68(x50532)+E(f331(f331(f8(x50531,x50532),x50533),f184(f854(x50531,a840))),f2(x50532))
% 51.10/50.82 [5054]~P68(x50542)+E(f331(f331(f8(x50541,x50542),x50543),f184(f854(x50541,a840))),f2(x50542))
% 51.10/50.82 [5099]~E(x50992,f331(f331(f87(a847),x50991),x50993))+P1(f331(f331(f240(a847),x50991),x50992))
% 51.10/50.82 [5101]~E(x51012,f184(f854(x51011,a840)))+E(f331(f331(f66(x51011),x51012),x51013),f184(f854(f854(x51011,a840),a840)))
% 51.10/50.82 [5102]~E(x51022,f184(f854(x51021,a840)))+E(f184(f854(f854(x51021,a840),a840)),f331(f331(f66(x51021),x51022),x51023))
% 51.10/50.82 [5169]~E(f331(f267(x51692,x51693),x51691),f184(f854(x51693,a840)))+E(x51691,f184(f854(f853(x51692,x51693),a840)))
% 51.10/50.82 [5170]~E(f331(f269(x51702,x51703),x51701),f184(f854(x51702,a840)))+E(x51701,f184(f854(f853(x51702,x51703),a840)))
% 51.10/50.82 [5201]E(f331(f267(x52011,x52012),x52013),f184(f854(x52012,a840)))+~E(x52013,f184(f854(f853(x52011,x52012),a840)))
% 51.10/50.82 [5202]E(f331(f269(x52021,x52022),x52023),f184(f854(x52021,a840)))+~E(x52023,f184(f854(f853(x52021,x52022),a840)))
% 51.10/50.82 [5205]E(f277(x52051,x52052,x52053),f331(f331(f3(a106),x52052),x52053))+P1(f331(f331(f241(a106),x52052),x52053))
% 51.10/50.82 [5221]P1(f331(x52211,x52212))+~P1(f331(f331(f333(x52213),x52212),x52211))
% 51.10/50.82 [5257]E(x52571,x52572)+~E(f331(f86(f854(x52573,a840)),x52571),f331(f86(f854(x52573,a840)),x52572))
% 51.10/50.82 [5262]E(f314(x52621,x52622,x52623),f187(f848(a838)))+~P1(f331(f331(f241(a1),x52622),x52623))
% 51.10/50.82 [5265]~E(x52651,f184(f854(x52652,a840)))+~P1(f331(f331(f333(x52652),x52653),x52651))
% 51.10/50.82 [5266]~E(x52661,f184(f854(x52662,a840)))+~P1(f331(f331(f333(x52662),x52663),x52661))
% 51.10/50.82 [5267]~E(x52671,f184(f854(x52672,a840)))+~P1(f331(f331(f333(x52672),x52673),x52671))
% 51.10/50.82 [5295]~E(x52952,f331(f331(f87(a1),x52951),f331(f107(a1),x52953)))+P1(f331(f331(f240(a1),x52951),x52952))
% 51.10/50.82 [5311]E(f331(f331(f310(x53111),x53112),x53113),x53113)+~P1(f331(f331(f333(x53111),x53112),x53113))
% 51.10/50.82 [5323]E(x53231,f184(f854(x53232,a840)))+~E(f331(f331(f66(x53232),x53231),x53233),f184(f854(f854(x53232,a840),a840)))
% 51.10/50.82 [5324]E(x53241,f184(f854(x53242,a840)))+~E(f184(f854(f854(x53242,a840),a840)),f331(f331(f66(x53242),x53241),x53243))
% 51.10/50.82 [5330]~P121(x53301)+E(f331(f331(f88(x53301),f331(f86(x53301),x53302)),f331(f86(x53301),x53303)),f331(f331(f88(x53301),x53302),x53303))
% 51.10/50.82 [5332]~P58(x53321)+E(f331(f331(f291(x53321),f331(f86(x53321),x53322)),f331(f86(x53321),x53323)),f331(f331(f291(x53321),x53322),x53323))
% 51.10/50.82 [5363]~P1(f331(x53633,x53632))+P1(f331(f331(f333(x53631),x53632),f331(f264(x53631),x53633)))
% 51.10/50.82 [5364]~P1(f331(x53643,x53642))+P1(f331(f331(f333(x53641),x53642),f331(f264(x53641),x53643)))
% 51.10/50.82 [5404]E(f161(x54041,x54042,x54043),x54043)+P1(f331(f331(f333(x54041),x54042),f331(f163(x54041),x54043)))
% 51.10/50.82 [5484]~P1(f331(f132(x54841),x54843))+P1(f331(f132(x54841),f331(f131(x54841,x54842),x54843)))
% 51.10/50.82 [5528]~P5(x55281)+E(f331(f331(f48(x55281),f57(x55281,x55282,x55283)),x55283),f2(x55281))
% 51.10/50.82 [5546]E(f165(x55461,f331(f331(f145(x55461),x55462),f120(x55461)),x55463),f120(x55461))+P1(f331(f331(f333(a847),f2(a847)),x55463))
% 51.10/50.82 [5611]E(x56111,x56112)+~E(f331(f331(f88(a847),f331(a119,x56113)),x56111),f331(f331(f88(a847),f331(a119,x56113)),x56112))
% 51.10/50.82 [5612]~E(x56122,f331(f331(f87(a1),x56121),f331(f107(a1),f331(a119,x56123))))+P1(f331(f331(f241(a1),x56121),x56122))
% 51.10/50.82 [5730]~E(x57303,f120(x57301))+E(f331(f331(f331(f178(f848(x57301),f848(x57301)),x57302),f159(x57301)),x57303),f120(x57301))
% 51.10/50.82 [5732]P1(f331(x57321,x57322))+~P1(f331(f331(f333(x57323),x57322),f331(f264(x57323),x57321)))
% 51.10/50.82 [5733]P1(f331(x57331,x57332))+~P1(f331(f331(f333(x57333),x57332),f331(f264(x57333),x57331)))
% 51.10/50.82 [5734]P1(f331(x57341,x57342))+~P1(f331(f331(f333(x57343),x57342),f331(f264(x57343),x57341)))
% 51.10/50.82 [5769]E(x57691,x57692)+~E(f331(f331(f310(x57693),x57691),f184(f854(x57693,a840))),f331(f331(f310(x57693),x57692),f184(f854(x57693,a840))))
% 51.10/50.82 [5779]~P88(x57791)+E(f331(f331(f109(f854(x57791,a840)),f331(f265(x57791),x57792)),f331(f302(x57791,x57792),x57793)),f184(f854(x57791,a840)))
% 51.10/50.82 [5839]~P76(x58391)+E(f331(f311(x58391,x58391,f86(x58391)),f331(f302(x58391,x58392),x58393)),f305(x58391,f331(f86(x58391),x58393),f331(f86(x58391),x58392)))
% 51.10/50.82 [5847]E(f331(f185(f848(x58471)),f161(x58471,x58472,x58473)),f331(f185(f848(x58471)),x58473))+P1(f331(f331(f333(x58471),x58472),f331(f163(x58471),x58473)))
% 51.10/50.82 [5868]P1(f331(x58681,x58682))+~P1(f331(f331(f333(x58683),x58682),f184(f854(x58683,a840))))
% 51.10/50.82 [5904]~P88(x59041)+E(f331(f331(f109(f854(x59041,a840)),f331(f302(x59041,x59042),x59043)),f331(f266(x59041),x59043)),f184(f854(x59041,a840)))
% 51.10/50.82 [5926]~P76(x59261)+E(f331(f311(x59261,x59261,f86(x59261)),f306(x59261,x59262,x59263)),f306(x59261,f331(f86(x59261),x59263),f331(f86(x59261),x59262)))
% 51.10/50.82 [5927]~P76(x59271)+E(f331(f311(x59271,x59271,f86(x59271)),f303(x59271,x59272,x59273)),f303(x59271,f331(f86(x59271),x59273),f331(f86(x59271),x59272)))
% 51.10/50.82 [5986]E(f165(x59861,f331(f331(f145(x59861),x59862),f120(x59861)),x59863),f331(f331(f145(x59861),x59862),f120(x59861)))+~P1(f331(f331(f333(a847),f2(a847)),x59863))
% 51.10/50.82 [5994]~P76(x59941)+E(f331(f311(x59941,x59941,f86(x59941)),f305(x59941,x59942,x59943)),f331(f302(x59941,f331(f86(x59941),x59943)),f331(f86(x59941),x59942)))
% 51.10/50.82 [6014]~P6(x60141)+E(f57(x60141,f331(f86(x60141),f57(x60141,x60142,x60143)),x60143),f57(x60141,f331(f86(x60141),x60142),x60143))
% 51.10/50.82 [6119]~P1(f331(f68(f853(x61192,x61191)),x61193))+P1(f331(f68(x61191),f331(f267(x61192,x61191),x61193)))
% 51.10/50.82 [6120]~P1(f331(f68(f853(x61201,x61202)),x61203))+P1(f331(f68(x61201),f331(f269(x61201,x61202),x61203)))
% 51.10/50.82 [6125]~P88(x61251)+E(f331(f331(f109(f854(x61251,a840)),f306(x61251,x61252,x61253)),f331(f266(x61251),x61253)),f184(f854(x61251,a840)))
% 51.10/50.82 [6126]~P88(x61261)+E(f331(f331(f109(f854(x61261,a840)),f305(x61261,x61262,x61263)),f331(f304(x61261),x61263)),f184(f854(x61261,a840)))
% 51.10/50.82 [6127]~P88(x61271)+E(f331(f331(f109(f854(x61271,a840)),f303(x61271,x61272,x61273)),f331(f304(x61271),x61273)),f184(f854(x61271,a840)))
% 51.10/50.82 [6196]E(f331(f331(f155(x61961),x61962),f729(x61962,x61963,x61961)),x61963)+~P1(f331(f331(f333(x61961),x61963),f331(f163(x61961),x61962)))
% 51.10/50.82 [6347]E(x63471,f120(x63472))+~E(f331(f331(f331(f178(f848(x63472),f848(x63472)),x63473),f159(x63472)),x63471),f120(x63472))
% 51.10/50.82 [6426]P37(x64261,x64262,f805(x64263,x64262,x64261),x64263)+~P1(f331(f331(f191(x64261),x64262),x64263))
% 51.10/50.82 [6427]P37(x64271,x64272,f406(x64273,x64272,x64271),x64273)+~P1(f331(f331(f191(x64271),x64272),x64273))
% 51.10/50.82 [6456]~P1(f331(f68(f853(x64562,x64561)),x64563))+P1(f331(f68(f853(x64561,x64562)),f331(f286(x64562,x64561),x64563)))
% 51.10/50.82 [6478]E(x64781,x64782)+~E(f290(a847,f287(a847),x64783,x64781),f331(f331(f310(a847),x64782),f184(f854(a847,a840))))
% 51.10/50.82 [6479]E(x64791,x64792)+~E(f290(a847,f287(a847),x64791,x64792),f331(f331(f310(a847),x64793),f184(f854(a847,a840))))
% 51.10/50.82 [6614]P52(x66141,x66142,x66143)+P1(f331(f331(f333(x66141),f648(x66143,x66142,x66141)),x66142))
% 51.10/50.82 [6615]P52(x66151,x66152,x66153)+P1(f331(f331(f333(x66151),f647(x66153,x66152,x66151)),x66152))
% 51.10/50.82 [6627]P1(f331(f320(x66271,x66272),x66273))+P1(f331(f331(x66272,f806(x66273,x66272,x66271)),x66273))
% 51.10/50.82 [6628]P1(f331(f320(x66281,x66282),x66283))+P1(f331(f331(x66282,f813(x66283,x66282,x66281)),x66283))
% 51.10/50.82 [6659]E(f331(f185(f848(x66591)),f161(x66591,x66592,x66593)),f331(f331(f3(a847),f331(f185(f848(x66591)),x66593)),f85(a847)))+~P1(f331(f331(f333(x66591),x66592),f331(f163(x66591),x66593)))
% 51.10/50.82 [6699]P1(f331(f253(x66991,x66992),x66993))+P1(f331(f331(f333(x66991),f581(x66993,x66992,x66991)),x66993))
% 51.10/50.82 [6711]~P1(f331(f68(f853(x67112,x67111)),f331(f286(x67111,x67112),x67113)))+P1(f331(f68(f853(x67111,x67112)),x67113))
% 51.10/50.82 [6772]~P1(f331(f331(f333(x67721),x67722),f331(f163(x67721),f121(x67721,x67723))))+P1(f331(f331(f333(x67721),x67722),f331(f163(x67721),x67723)))
% 51.10/50.82 [6779]P30(x67791,x67792,x67793)+P1(f331(f331(f333(f846(x67791)),f597(x67793,x67792,x67791)),x67793))
% 51.10/50.82 [6808]E(f331(f131(x68081,x68082),x68083),x68083)+P1(f331(f331(f333(x68081),f759(x68083,x68082,x68081)),f331(f163(x68081),x68083)))
% 51.10/50.82 [6825]E(f331(f131(x68251,x68252),x68253),f120(x68251))+P1(f331(f331(f333(x68251),f745(x68253,x68252,x68251)),f331(f163(x68251),x68253)))
% 51.10/50.82 [6853]E(f167(x68531,x68532,x68533),x68533)+P1(f331(f331(f333(x68531),f768(x68533,x68532,x68531)),f331(f163(x68531),x68533)))
% 51.10/50.82 [6974]P1(f331(f331(f333(x69741),x69742),f695(x69743,x69742,x69741)))+~P1(f331(f331(f333(x69741),x69742),f49(f854(x69741,a840),x69743)))
% 51.10/50.82 [6976]~P68(x69761)+E(f331(f331(f87(x69761),f331(f331(f8(a847,x69761),x69762),f331(f265(a847),x69763))),f331(x69762,x69763)),f331(f331(f8(a847,x69761),x69762),f331(f265(a847),f331(a119,x69763))))
% 51.10/50.82 [7080]~P1(f331(f331(f333(x70801),x70802),f669(x70802,x70803,x70801)))+P1(f331(f331(f333(x70801),x70802),f50(f854(x70801,a840),x70803)))
% 51.10/50.82 [7109]~P68(x71091)+E(f331(f331(f87(x71091),f331(f331(f8(a847,x71091),x71092),f331(f301(a847),x71093))),f331(x71092,f331(a119,x71093))),f331(f331(f8(a847,x71091),x71092),f331(f301(a847),f331(a119,x71093))))
% 51.10/50.82 [7261]P1(f331(f331(f333(f848(x72611)),x72612),f153(x72611,x72613)))+P1(f331(f331(f333(x72611),f749(x72613,x72612,x72611)),f331(f163(x72611),x72612)))
% 51.10/50.82 [7278]~P1(f331(f331(f333(f848(x72781)),x72782),f153(x72781,f321(x72781,x72783))))+P1(f331(f331(f333(f848(x72781)),x72782),f321(f848(x72781),f150(x72781,x72783))))
% 51.10/50.82 [7306]~P1(f331(f331(f333(f848(x73061)),x73062),f321(f848(x73061),f150(x73061,x73063))))+P1(f331(f331(f333(f848(x73061)),x73062),f153(x73061,f321(x73061,x73063))))
% 51.10/50.82 [7346]E(f331(f331(f331(f178(f848(x73461),f848(x73461)),x73462),f159(x73461)),x73463),x73463)+~P1(f331(f331(f240(a847),f331(f185(f848(x73461)),x73463)),f85(a847)))
% 51.10/50.82 [7399]~P27(x73991,x73992,x73993,f247(f854(x73991,a840)))+P27(f848(x73991),f848(x73992),f331(f147(x73991,x73992),x73993),f247(f854(f848(x73991),a840)))
% 51.10/50.82 [7400]~P27(x74001,x74002,x74003,f247(f854(x74001,a840)))+P27(f848(x74001),f848(x74002),f331(f147(x74001,x74002),x74003),f247(f854(f848(x74001),a840)))
% 51.10/50.82 [7437]E(f134(x74371,x74372,x74373),f120(x74371))+~P1(f331(x74372,f331(f136(x74371),f134(x74371,x74372,x74373))))
% 51.10/50.82 [7558]E(x75581,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x75582)),x75583)),f331(f258(a847,a847),x75582)))+~P1(f331(f60(x75581,x75583),x75582))
% 51.10/50.82 [7565]P27(x75651,x75652,x75653,f247(f854(x75651,a840)))+~P27(f848(x75651),f848(x75652),f331(f147(x75651,x75652),x75653),f247(f854(f848(x75651),a840)))
% 51.10/50.82 [7566]P27(x75661,x75662,x75663,f247(f854(x75661,a840)))+~P27(f848(x75661),f848(x75662),f331(f147(x75661,x75662),x75663),f247(f854(f848(x75661),a840)))
% 51.10/50.82 [7609]P1(f331(f331(f333(f854(x76091,a840)),f669(x76092,x76093,x76091)),x76093))+P1(f331(f331(f333(x76091),x76092),f50(f854(x76091,a840),x76093)))
% 51.10/50.82 [7698]P1(f331(f331(f333(f848(x76981)),x76982),f153(x76981,x76983)))+~P1(f331(f331(f333(x76981),f749(x76983,x76982,x76981)),x76983))
% 51.10/50.82 [7829]E(x78291,x78292)+~E(f331(f331(f9(x78293,f854(x78293,a840),a840),f333(x78293)),x78291),f331(f331(f9(x78293,f854(x78293,a840),a840),f333(x78293)),x78292))
% 51.10/50.82 [7835]~P1(f331(f331(f333(f853(x78351,x78351)),x78353),f268(x78351,x78352)))+P1(f331(f331(f333(x78351),f417(x78352,x78353,x78351)),x78352))
% 51.10/50.82 [7837]~P1(f331(f331(f333(x78371),x78373),f49(f854(x78371,a840),x78372)))+P1(f331(f331(f333(f854(x78371,a840)),f695(x78372,x78373,x78371)),x78372))
% 51.10/50.82 [8097]E(f331(f236(f851(f848(a838)),f848(a838),f314(x80971,x80972,f331(f331(f87(a1),x80973),f85(a1))),f234(f848(a838))),f331(x80971,x80973)),f314(x80971,x80972,x80973))+P1(f331(f331(f241(a1),x80972),x80973))
% 51.10/50.82 [8197]E(x81971,f120(x81972))+P1(f331(f331(f333(x81972),f331(f248(x81972,f853(a106,a106)),f331(f278(x81972,x81971),x81973))),f331(f163(x81972),x81971)))
% 51.10/50.82 [8296]~P3(x82961)+E(f331(f137(x82961,x82961,f331(f9(x82961,x82961,x82961),f87(x82961)),x82962),f331(f160(x82961),x82963)),f331(f137(x82961,x82961,f87(x82961),x82962),x82963))
% 51.10/50.82 [8754]~P102(x87541)+E(f331(f163(x87541),f144(x87541,x87541,f7(x87541),x87542,x87543)),f331(f331(f310(x87541),x87542),f331(f163(x87541),x87543)))
% 51.10/50.82 [8763]P1(f331(f331(f241(a847),f2(a847)),f650(x87631,x87632,x87633)))+~P1(f331(f331(f333(f853(x87633,x87633)),x87632),f331(f331(f289(x87633,x87633,x87633),x87631),f308(x87633,x87631))))
% 51.10/50.82 [9022]~P54(x90221,x90222)+~P1(f331(f331(f333(f853(x90221,x90221)),f331(f331(f249(x90221,x90221),x90223),x90223)),f331(f331(f289(x90221,x90221,x90221),x90222),f308(x90221,x90222))))
% 51.10/50.82 [9132]~E(f331(f331(f109(f854(f853(x91321,x91321),a840)),f331(f286(x91321,x91321),x91322)),f308(x91321,x91322)),f184(f854(f853(x91321,x91321),a840)))+~P1(f331(f331(f333(f853(x91321,x91321)),f331(f331(f249(x91321,x91321),x91323),x91323)),f331(f331(f289(x91321,x91321,x91321),x91322),f308(x91321,x91322))))
% 51.10/50.82 [9307]~P1(f331(f68(x93071),x93072))+P1(f331(f331(f240(a847),f331(f47(x93071),f331(f331(f3(f854(x93071,a840)),x93072),f331(f331(f310(x93071),x93073),f184(f854(x93071,a840)))))),f331(f47(x93071),x93072)))
% 51.10/50.82 [4913]~E(x49133,f120(x49131))+E(f139(x49131,f331(f331(f145(x49131),x49132),x49133)),x49132)
% 51.10/50.82 [4914]~E(x49143,f120(x49141))+E(f139(x49141,f331(f331(f145(x49141),x49142),x49143)),x49142)
% 51.10/50.82 [4923]~E(x49233,f120(x49231))+E(f121(x49231,f331(f331(f145(x49231),x49232),x49233)),f120(x49231))
% 51.10/50.82 [4951]E(x49511,f120(x49512))+E(f139(x49512,f331(f331(f145(x49512),x49513),x49511)),f139(x49512,x49511))
% 51.10/50.82 [4952]E(x49521,f120(x49522))+E(f139(x49522,f331(f331(f145(x49522),x49523),x49521)),f139(x49522,x49521))
% 51.10/50.82 [4953]E(x49531,f120(x49532))+E(f139(x49532,f331(f331(f130(x49532),x49533),x49531)),f139(x49532,x49531))
% 51.10/50.82 [4954]E(x49541,f120(x49542))+E(f139(x49542,f331(f331(f130(x49542),x49543),x49541)),f139(x49542,x49541))
% 51.10/50.82 [4960]~E(x49603,f120(x49601))+E(f139(x49601,f331(f331(f130(x49601),x49602),x49603)),f139(x49601,x49602))
% 51.10/50.82 [4961]~E(x49613,f120(x49611))+E(f139(x49611,f331(f331(f130(x49611),x49612),x49613)),f139(x49611,x49612))
% 51.10/50.82 [4962]~E(x49623,f120(x49621))+E(f121(x49621,f331(f331(f130(x49621),x49622),x49623)),f121(x49621,x49622))
% 51.10/50.82 [4991]E(x49911,f120(x49912))+E(f331(f136(x49912),f331(f331(f130(x49912),x49911),x49913)),f331(f136(x49912),x49911))
% 51.10/50.82 [4992]E(x49921,f120(x49922))+E(f331(f136(x49922),f331(f331(f130(x49922),x49921),x49923)),f331(f136(x49922),x49921))
% 51.10/50.82 [5023]~E(x50232,f120(x50231))+E(f331(f136(x50231),f331(f331(f130(x50231),x50232),x50233)),f331(f136(x50231),x50233))
% 51.10/50.82 [5076]~P102(x50761)+E(f331(f331(f244(x50761),x50762),f331(f331(f239(x50761),x50762),x50763)),x50762)
% 51.10/50.82 [5077]~P102(x50771)+E(f331(f331(f239(x50771),x50772),f331(f331(f244(x50771),x50772),x50773)),x50772)
% 51.10/50.82 [5078]~P97(x50781)+E(f331(f331(f108(x50781),x50782),f331(f331(f109(x50781),x50782),x50783)),x50782)
% 51.10/50.82 [5079]~P97(x50791)+E(f331(f331(f109(x50791),x50792),f331(f331(f108(x50791),x50792),x50793)),x50792)
% 51.10/50.82 [5097]~P5(x50971)+E(f57(x50971,f331(f331(f88(x50971),x50972),x50973),x50973),f2(x50971))
% 51.10/50.82 [5098]~P5(x50981)+E(f57(x50981,f331(f331(f88(x50981),x50982),x50983),x50982),f2(x50981))
% 51.10/50.82 [5164]~P4(x51641)+E(f331(f86(x51641),f331(f331(f3(x51641),x51642),x51643)),f331(f331(f3(x51641),x51643),x51642))
% 51.10/50.82 [5225]E(x52251,f120(x52252))+E(f121(x52252,f331(f331(f145(x52252),x52253),x52251)),f331(f331(f145(x52252),x52253),f121(x52252,x52251)))
% 51.10/50.82 [5226]E(x52261,f120(x52262))+E(f121(x52262,f331(f331(f130(x52262),x52263),x52261)),f331(f331(f130(x52262),x52263),f121(x52262,x52261)))
% 51.10/50.82 [5227]~P7(x52271)+E(f50(x52271,f331(f331(f310(x52271),x52272),x52273)),f331(f331(f109(x52271),x52272),f50(x52271,x52273)))
% 51.10/50.82 [5228]~P7(x52281)+E(f49(x52281,f331(f331(f310(x52281),x52282),x52283)),f331(f331(f108(x52281),x52282),f49(x52281,x52283)))
% 51.10/50.82 [5271]~P94(x52711)+E(f331(f331(f88(x52711),x52712),f331(f331(f88(x52711),x52712),x52713)),f331(f331(f88(x52711),x52712),x52713))
% 51.10/50.82 [5272]~P102(x52721)+E(f331(f331(f244(x52721),x52722),f331(f331(f244(x52721),x52722),x52723)),f331(f331(f244(x52721),x52722),x52723))
% 51.10/50.82 [5273]~P102(x52731)+E(f331(f331(f244(x52731),x52732),f331(f331(f244(x52731),x52732),x52733)),f331(f331(f244(x52731),x52732),x52733))
% 51.10/50.82 [5274]~P102(x52741)+E(f331(f331(f239(x52741),x52742),f331(f331(f239(x52741),x52742),x52743)),f331(f331(f239(x52741),x52742),x52743))
% 51.10/50.82 [5275]~P102(x52751)+E(f331(f331(f239(x52751),x52752),f331(f331(f239(x52751),x52752),x52753)),f331(f331(f239(x52751),x52752),x52753))
% 51.10/50.82 [5276]~P97(x52761)+E(f331(f331(f108(x52761),x52762),f331(f331(f108(x52761),x52762),x52763)),f331(f331(f108(x52761),x52762),x52763))
% 51.10/50.82 [5277]~P100(x52771)+E(f331(f331(f108(x52771),x52772),f331(f331(f108(x52771),x52772),x52773)),f331(f331(f108(x52771),x52772),x52773))
% 51.10/50.82 [5278]~P100(x52781)+E(f331(f331(f108(x52781),x52782),f331(f331(f108(x52781),x52782),x52783)),f331(f331(f108(x52781),x52782),x52783))
% 51.10/50.82 [5279]~P97(x52791)+E(f331(f331(f109(x52791),x52792),f331(f331(f109(x52791),x52792),x52793)),f331(f331(f109(x52791),x52792),x52793))
% 51.10/50.82 [5280]~P101(x52801)+E(f331(f331(f109(x52801),x52802),f331(f331(f109(x52801),x52802),x52803)),f331(f331(f109(x52801),x52802),x52803))
% 51.10/50.82 [5281]~P101(x52811)+E(f331(f331(f109(x52811),x52812),f331(f331(f109(x52811),x52812),x52813)),f331(f331(f109(x52811),x52812),x52813))
% 51.10/50.82 [5288]~P5(x52881)+E(f57(x52881,f331(f331(f87(x52881),x52882),x52883),x52883),f57(x52881,x52882,x52883))
% 51.10/50.82 [5289]~P5(x52891)+E(f57(x52891,f331(f331(f87(x52891),x52892),x52893),x52892),f57(x52891,x52893,x52892))
% 51.10/50.82 [5296]~P121(x52961)+E(f331(f331(f88(x52961),x52962),f331(f86(x52961),x52963)),f331(f86(x52961),f331(f331(f88(x52961),x52962),x52963)))
% 51.10/50.82 [5297]~P58(x52971)+E(f331(f331(f291(x52971),x52972),f331(f86(x52971),x52973)),f331(f86(x52971),f331(f331(f291(x52971),x52972),x52973)))
% 51.10/50.82 [5298]~P71(x52981)+E(f331(f331(f87(x52981),x52982),f331(f157(x52981),x52983)),f331(f157(x52981),f331(f331(f145(x52981),x52982),x52983)))
% 51.10/50.82 [5329]~P121(x53291)+E(f331(f331(f88(x53291),f331(f86(x53291),x53292)),x53293),f331(f331(f88(x53291),x53292),f331(f86(x53291),x53293)))
% 51.10/50.82 [5335]~P10(x53351,x53352,x53353)+E(f49(f854(x53351,a840),f331(f331(f66(x53351),x53352),x53353)),x53352)
% 51.10/50.82 [5395]~P87(x53951)+E(f331(f331(f88(x53951),x53952),f331(f331(f250(x53951),x53952),x53953)),f331(f331(f250(x53951),x53952),f331(a119,x53953)))
% 51.10/50.82 [5396]~P107(x53961)+E(f331(f331(f88(x53961),x53962),f331(f331(f250(x53961),x53962),x53963)),f331(f331(f250(x53961),x53962),f331(a119,x53963)))
% 51.10/50.82 [5397]~P87(x53971)+E(f331(f331(f88(x53971),x53972),f331(f331(f250(x53971),x53972),x53973)),f331(f331(f250(x53971),x53972),f331(a119,x53973)))
% 51.10/50.82 [5407]~P69(x54071)+E(f331(f331(f87(x54071),f331(f86(x54071),x54072)),f331(f331(f87(x54071),x54072),x54073)),x54073)
% 51.10/50.82 [5428]~P84(x54281)+E(f331(f331(f250(x54281),f331(f107(x54281),x54282)),x54283),f331(f107(x54281),f331(f331(f250(a847),x54282),x54283)))
% 51.10/50.82 [5429]~P133(x54291)+E(f331(f331(f250(x54291),f331(f110(x54291),x54292)),x54293),f331(f110(x54291),f331(f331(f250(a1),x54292),x54293)))
% 51.10/50.82 [5434]~P78(x54341)+E(f331(f82(x54341),f331(f331(f3(x54341),x54342),x54343)),f331(f82(x54341),f331(f331(f3(x54341),x54343),x54342)))
% 51.10/50.82 [5436]~P86(x54361)+E(f331(f331(f88(x54361),f89(x54361,x54362)),f89(x54361,x54363)),f89(x54361,f331(f331(f88(x54361),x54362),x54363)))
% 51.10/50.82 [5440]E(x54401,f120(x54402))+E(f331(f331(f130(x54402),f331(f162(x54402),x54401)),x54403),f331(f162(x54402),f331(f331(f130(x54402),x54401),x54403)))
% 51.10/50.82 [5446]~E(x54462,f331(a119,f331(f331(f87(a847),x54461),x54463)))+P1(f331(f331(f241(a847),x54461),x54462))
% 51.10/50.82 [5447]~P121(x54471)+E(f331(f331(f88(x54471),f331(f86(x54471),x54472)),x54473),f331(f86(x54471),f331(f331(f88(x54471),x54472),x54473)))
% 51.10/50.82 [5448]~P114(x54481)+E(f331(f331(f291(x54481),f331(f86(x54481),x54482)),x54483),f331(f86(x54481),f331(f331(f291(x54481),x54482),x54483)))
% 51.10/50.82 [5449]~P86(x54491)+E(f331(f331(f250(x54491),f331(f82(x54491),x54492)),x54493),f331(f82(x54491),f331(f331(f250(x54491),x54492),x54493)))
% 51.10/50.82 [5545]E(f370(x55451,x55452,x55453),f371(x55451,x55452,x55453))+E(f331(f331(f109(f854(x55453,a840)),x55452),x55451),f184(f854(x55453,a840)))
% 51.10/50.82 [5559]~P70(x55592)+E(f331(f331(f11(x55591,x55592),f331(f18(x55592,x55591),f85(x55592))),x55593),f85(x55592))
% 51.10/50.82 [5560]~P68(x55602)+E(f331(f331(f8(x55601,x55602),f331(f18(x55602,x55601),f2(x55602))),x55603),f2(x55602))
% 51.10/50.82 [5562]~P84(x55621)+E(f331(f331(f87(x55621),f331(f107(x55621),x55622)),f331(f107(x55621),x55623)),f331(f107(x55621),f331(f331(f87(a847),x55622),x55623)))
% 51.10/50.82 [5563]~P84(x55631)+E(f331(f331(f88(x55631),f331(f107(x55631),x55632)),f331(f107(x55631),x55633)),f331(f107(x55631),f331(f331(f88(a847),x55632),x55633)))
% 51.10/50.82 [5564]~P133(x55641)+E(f331(f331(f87(x55641),f331(f110(x55641),x55642)),f331(f110(x55641),x55643)),f331(f110(x55641),f331(f331(f87(a1),x55642),x55643)))
% 51.10/50.82 [5565]~P133(x55651)+E(f331(f331(f88(x55651),f331(f110(x55651),x55652)),f331(f110(x55651),x55653)),f331(f110(x55651),f331(f331(f88(a1),x55652),x55653)))
% 51.10/50.82 [5566]~P133(x55661)+E(f331(f331(f3(x55661),f331(f110(x55661),x55662)),f331(f110(x55661),x55663)),f331(f110(x55661),f331(f331(f3(a1),x55662),x55663)))
% 51.10/50.82 [5567]~P91(x55671)+E(f331(f331(f87(x55671),f331(f111(x55671),x55672)),f331(f111(x55671),x55673)),f331(f111(x55671),f331(f331(f87(a1),x55672),x55673)))
% 51.10/50.82 [5568]~P91(x55681)+E(f331(f331(f88(x55681),f331(f111(x55681),x55682)),f331(f111(x55681),x55683)),f331(f111(x55681),f331(f331(f88(a1),x55682),x55683)))
% 51.10/50.82 [5569]~P91(x55691)+E(f331(f331(f3(x55691),f331(f111(x55691),x55692)),f331(f111(x55691),x55693)),f331(f111(x55691),f331(f331(f3(a1),x55692),x55693)))
% 51.10/50.82 [5570]~P91(x55701)+E(f331(f331(f87(x55701),f331(f111(x55701),x55702)),f331(f111(x55701),x55703)),f331(f111(x55701),f331(f331(f87(a1),x55702),x55703)))
% 51.10/50.82 [5571]~P91(x55711)+E(f331(f331(f88(x55711),f331(f111(x55711),x55712)),f331(f111(x55711),x55713)),f331(f111(x55711),f331(f331(f88(a1),x55712),x55713)))
% 51.10/50.82 [5618]~E(x56183,x56182)+P1(f331(f331(f240(f854(x56181,a840)),x56182),x56183))
% 51.10/50.82 [5619]~E(x56192,x56193)+P1(f331(f331(f240(f854(x56191,a840)),x56192),x56193))
% 51.10/50.82 [5620]~E(x56202,x56203)+P1(f331(f331(f240(f854(x56201,a840)),x56202),x56203))
% 51.10/50.82 [5621]~E(x56212,x56213)+P1(f331(f331(f240(f854(x56211,a840)),x56212),x56213))
% 51.10/50.82 [5622]~E(x56222,x56223)+P1(f331(f331(f240(f854(x56221,a840)),x56222),x56223))
% 51.10/50.82 [5623]~E(x56232,x56233)+P1(f331(f331(f240(f854(x56231,a840)),x56232),x56233))
% 51.10/50.82 [5624]~E(x56242,x56243)+P1(f331(f331(f240(f854(x56241,a840)),x56242),x56243))
% 51.10/50.82 [5629]~P69(x56291)+E(f331(f331(f87(x56291),f331(f86(x56291),x56292)),f331(f86(x56291),x56293)),f331(f86(x56291),f331(f331(f87(x56291),x56293),x56292)))
% 51.10/50.82 [5630]~P4(x56301)+E(f331(f331(f87(x56301),f331(f86(x56301),x56302)),f331(f86(x56301),x56303)),f331(f86(x56301),f331(f331(f87(x56301),x56302),x56303)))
% 51.10/50.82 [5631]~P67(x56311)+E(f331(f331(f239(x56311),f331(f86(x56311),x56312)),f331(f86(x56311),x56313)),f331(f86(x56311),f331(f331(f244(x56311),x56312),x56313)))
% 51.10/50.82 [5632]~P67(x56321)+E(f331(f331(f244(x56321),f331(f86(x56321),x56322)),f331(f86(x56321),x56323)),f331(f86(x56321),f331(f331(f239(x56321),x56322),x56323)))
% 51.10/50.82 [5633]~P93(x56331)+E(f331(f331(f109(x56331),f331(f86(x56331),x56332)),f331(f86(x56331),x56333)),f331(f86(x56331),f331(f331(f108(x56331),x56332),x56333)))
% 51.10/50.82 [5634]~P93(x56341)+E(f331(f331(f108(x56341),f331(f86(x56341),x56342)),f331(f86(x56341),x56343)),f331(f86(x56341),f331(f331(f109(x56341),x56342),x56343)))
% 51.10/50.82 [5635]~P86(x56351)+E(f331(f331(f88(x56351),f331(f82(x56351),x56352)),f331(f82(x56351),x56353)),f331(f82(x56351),f331(f331(f88(x56351),x56352),x56353)))
% 51.10/50.82 [5636]~P60(x56361)+E(f331(f331(f291(x56361),f331(f82(x56361),x56362)),f331(f82(x56361),x56363)),f331(f82(x56361),f331(f331(f291(x56361),x56362),x56363)))
% 51.10/50.82 [5637]~P71(x56371)+E(f331(f331(f87(x56371),f331(f157(x56371),x56372)),f331(f157(x56371),x56373)),f331(f157(x56371),f331(f331(f130(x56371),x56372),x56373)))
% 51.10/50.82 [5638]E(x56381,f184(f854(x56382,a840)))+~E(f331(f331(f108(f854(x56382,a840)),x56383),x56381),f184(f854(x56382,a840)))
% 51.10/50.82 [5639]E(x56391,f184(f854(x56392,a840)))+~E(f331(f331(f108(f854(x56392,a840)),x56391),x56393),f184(f854(x56392,a840)))
% 51.10/50.82 [5640]~P141(x56401,x56403,x56402)+P1(f331(x56401,f331(f331(f48(a1),x56402),x56403)))
% 51.10/50.82 [5701]~P1(f331(f68(x57011),x57013))+P1(f331(f68(x57011),f331(f331(f310(x57011),x57012),x57013)))
% 51.10/50.82 [5702]~P1(f331(f68(x57021),x57023))+P1(f331(f68(x57021),f331(f331(f310(x57021),x57022),x57023)))
% 51.10/50.82 [5703]~P1(f331(f132(x57031),x57033))+P1(f331(f132(x57031),f331(f331(f164(x57031),x57032),x57033)))
% 51.10/50.82 [5704]~P1(f331(f132(x57041),x57043))+P1(f331(f132(x57041),f331(f331(f133(x57041),x57042),x57043)))
% 51.10/50.82 [5735]~P102(x57351)+P1(f331(f331(f240(x57351),x57352),f331(f331(f239(x57351),x57353),x57352)))
% 51.10/50.82 [5736]~P102(x57361)+P1(f331(f331(f240(x57361),x57362),f331(f331(f239(x57361),x57362),x57363)))
% 51.10/50.82 [5737]~P97(x57371)+P1(f331(f331(f240(x57371),x57372),f331(f331(f108(x57371),x57373),x57372)))
% 51.10/50.82 [5738]~P100(x57381)+P1(f331(f331(f240(x57381),x57382),f331(f331(f108(x57381),x57383),x57382)))
% 51.10/50.82 [5739]~P97(x57391)+P1(f331(f331(f240(x57391),x57392),f331(f331(f108(x57391),x57392),x57393)))
% 51.10/50.82 [5740]~P100(x57401)+P1(f331(f331(f240(x57401),x57402),f331(f331(f108(x57401),x57402),x57403)))
% 51.10/50.82 [5741]~P87(x57411)+P1(f331(f331(f287(x57411),x57412),f331(f331(f88(x57411),x57413),x57412)))
% 51.10/50.82 [5742]~P87(x57421)+P1(f331(f331(f287(x57421),x57422),f331(f331(f88(x57421),x57422),x57423)))
% 51.10/50.82 [5756]~E(x57561,f2(a847))+E(f331(f331(f48(a847),f331(f331(f88(a847),x57561),x57562)),f331(f331(f88(a847),x57561),x57563)),f2(a847))
% 51.10/50.82 [5819]P1(f331(x58191,x58192))+P1(f331(f331(f191(f37(x58191,x58193)),x58192),x58192))
% 51.10/50.82 [5820]P1(f331(x58201,x58202))+P1(f331(f331(f191(f37(x58201,x58203)),x58202),x58202))
% 51.10/50.82 [5832]~P91(x58321)+E(f331(f331(f3(x58321),f331(f111(x58321),x58322)),f331(f111(x58321),x58323)),f331(f111(x58321),f331(f331(f87(a1),x58322),f331(f86(a1),x58323))))
% 51.10/50.82 [5888]E(x58881,f2(a847))+E(f331(f331(f48(a847),f331(f331(f88(a847),x58881),x58882)),f331(f331(f88(a847),x58881),x58883)),f331(f331(f48(a847),x58882),x58883))
% 51.10/50.82 [5924]E(f146(x59241,f331(f331(f145(x59241),x59242),x59243)),f331(f331(f145(x59241),x59242),f146(x59241,x59243)))+P1(f331(f331(f333(x59241),x59242),f331(f163(x59241),x59243)))
% 51.10/50.82 [5958]P141(x59581,x59582,x59583)+~P1(f331(x59581,f331(f331(f48(a1),x59583),x59582)))
% 51.10/50.82 [6035]E(x60351,f120(x60352))+E(f331(f331(f145(x60352),f331(f136(x60352),x60351)),f331(f331(f164(x60352),x60353),f331(f162(x60352),x60351))),f331(f331(f164(x60352),f331(a119,x60353)),x60351))
% 51.10/50.82 [6043]E(f331(f331(f3(f854(x60431,a840)),x60432),x60433),x60432)+~E(f331(f331(f109(f854(x60431,a840)),x60432),x60433),f184(f854(x60431,a840)))
% 51.10/50.82 [6056]E(f146(x60561,f331(f331(f145(x60561),x60562),x60563)),f146(x60561,x60563))+~P1(f331(f331(f333(x60561),x60562),f331(f163(x60561),x60563)))
% 51.10/50.82 [6087]~P1(f331(f331(f241(a847),x60871),x60873))+P1(f331(f331(f241(a847),x60871),f331(f331(f87(a847),x60872),x60873)))
% 51.10/50.82 [6088]~P1(f331(f331(f241(a847),x60881),x60883))+P1(f331(f331(f241(a847),x60881),f331(f331(f87(a847),x60882),x60883)))
% 51.10/50.82 [6089]~P1(f331(f331(f241(a847),x60891),x60892))+P1(f331(f331(f241(a847),x60891),f331(f331(f87(a847),x60892),x60893)))
% 51.10/50.82 [6090]~P1(f331(f331(f241(a847),x60901),x60902))+P1(f331(f331(f241(a847),x60901),f331(f331(f87(a847),x60902),x60903)))
% 51.10/50.82 [6091]~P1(f331(f331(f240(a847),x60911),x60913))+P1(f331(f331(f240(a847),x60911),f331(f331(f87(a847),x60912),x60913)))
% 51.10/50.82 [6092]~P1(f331(f331(f240(a847),x60921),x60923))+P1(f331(f331(f240(a847),x60921),f331(f331(f87(a847),x60922),x60923)))
% 51.10/50.82 [6093]~P1(f331(f331(f240(a847),x60931),x60932))+P1(f331(f331(f240(a847),x60931),f331(f331(f87(a847),x60932),x60933)))
% 51.10/50.82 [6094]~P1(f331(f331(f240(a847),x60941),x60942))+P1(f331(f331(f240(a847),x60941),f331(f331(f87(a847),x60942),x60943)))
% 51.10/50.82 [6133]P1(f331(f68(x61331),x61332))+~P1(f331(f68(x61331),f331(f331(f310(x61331),x61333),x61332)))
% 51.10/50.82 [6134]P1(f331(f132(x61341),x61342))+~P1(f331(f132(x61341),f331(f331(f145(x61341),x61343),x61342)))
% 51.10/50.82 [6135]P1(f331(f132(x61351),x61352))+~P1(f331(f132(x61351),f331(f331(f130(x61351),x61353),x61352)))
% 51.10/50.82 [6136]P1(f331(f132(x61361),x61362))+~P1(f331(f132(x61361),f331(f331(f130(x61361),x61362),x61363)))
% 51.10/50.82 [6181]~E(f57(a1,x61812,x61811),f57(a1,x61813,x61811))+P1(f331(f331(f287(a1),x61811),f331(f331(f3(a1),x61812),x61813)))
% 51.10/50.82 [6186]~P87(x61861)+E(f331(f331(f87(x61861),x61862),f331(f331(f88(x61861),x61863),x61862)),f331(f331(f88(x61861),f331(f331(f87(x61861),x61863),f85(x61861))),x61862))
% 51.10/50.82 [6235]~E(x62351,x62352)+~P1(f331(f331(f241(f854(x62353,a840)),x62351),x62352))
% 51.10/50.82 [6281]P1(f331(f331(f333(x62811),x62812),x62813))+P1(f331(f331(f333(x62811),x62812),f331(f86(f854(x62811,a840)),x62813)))
% 51.10/50.82 [6282]P1(f331(f331(f333(x62821),x62822),x62823))+P1(f331(f331(f333(x62821),x62822),f331(f86(f854(x62821,a840)),x62823)))
% 51.10/50.82 [6289]E(f139(x62891,f331(f331(f133(x62891),x62892),x62893)),f139(x62891,x62893))+~P1(f331(f331(f241(a847),x62892),f331(f185(f848(x62891)),x62893)))
% 51.10/50.82 [6290]E(f331(f331(f164(x62901),x62902),f121(x62901,x62903)),f331(f331(f164(x62901),x62902),x62903))+~P1(f331(f331(f241(a847),x62902),f331(f185(f848(x62901)),x62903)))
% 51.10/50.82 [6349]E(f331(f331(f331(f178(f848(x63491),f848(x63491)),x63492),f159(x63491)),x63493),x63493)+~E(f57(a847,x63492,f331(f185(f848(x63491)),x63493)),f2(a847))
% 51.10/50.82 [6358]~P10(x63581,x63583,x63582)+E(f331(f331(f289(x63581,x63581,x63581),f331(f286(x63581,x63581),x63582)),x63582),x63582)
% 51.10/50.82 [6401]~E(f331(f331(f108(f854(x64011,a840)),x64012),x64013),x64013)+P1(f331(f331(f240(f854(x64011,a840)),x64012),x64013))
% 51.10/50.82 [6406]~P51(x64061,x64061,x64063)+P51(x64061,x64061,f331(f331(f178(f853(x64061,x64061),a840),x64062),x64063))
% 51.10/50.82 [6408]~P1(f331(f331(f333(x64081),x64083),f331(f163(x64081),x64082)))+P1(f331(f331(f241(a847),f2(a847)),f331(f185(f848(x64081)),x64082)))
% 51.10/50.82 [6425]~E(x64252,x64253)+P1(f331(f331(f333(x64251),x64252),f331(f331(f310(x64251),x64253),f184(f854(x64251,a840)))))
% 51.10/50.82 [6438]~P78(x64381)+E(f331(f82(x64381),f331(f331(f87(x64381),f331(f82(x64381),x64382)),f331(f82(x64381),x64383))),f331(f331(f87(x64381),f331(f82(x64381),x64382)),f331(f82(x64381),x64383)))
% 51.10/50.82 [6449]E(f331(f331(f48(a847),f331(f331(f88(a847),x64491),x64492)),f331(f331(f88(a847),x64491),x64493)),f331(f331(f48(a847),x64492),x64493))+~P1(f331(f331(f241(a847),f2(a847)),x64491))
% 51.10/50.82 [6476]E(f57(a1,x64761,x64762),f57(a1,x64763,x64762))+~P1(f331(f331(f287(a1),x64762),f331(f331(f3(a1),x64761),x64763)))
% 51.10/50.82 [6589]~P1(f331(f68(x65891),x65893))+E(f331(f331(f71(x65891,f854(x65891,a840),f310(x65891)),x65892),x65893),f331(f331(f108(f854(x65891,a840)),x65893),x65892))
% 51.10/50.82 [6652]E(f331(f331(f108(f854(x66521,a840)),x66522),x66523),x66522)+~P1(f331(f331(f240(f854(x66521,a840)),x66523),x66522))
% 51.10/50.82 [6653]E(f331(f331(f108(f854(x66531,a840)),x66532),x66533),x66533)+~P1(f331(f331(f240(f854(x66531,a840)),x66532),x66533))
% 51.10/50.82 [6654]E(f331(f331(f108(f854(x66541,a840)),x66542),x66543),x66543)+~P1(f331(f331(f240(f854(x66541,a840)),x66542),x66543))
% 51.10/50.82 [6655]E(f331(f331(f109(f854(x66551,a840)),x66552),x66553),x66553)+~P1(f331(f331(f240(f854(x66551,a840)),x66553),x66552))
% 51.10/50.82 [6656]E(f331(f331(f109(f854(x66561,a840)),x66562),x66563),x66562)+~P1(f331(f331(f240(f854(x66561,a840)),x66562),x66563))
% 51.10/50.82 [6709]~P1(f331(f132(x67091),x67092))+E(f331(f331(f3(f854(x67091,a840)),f331(f163(x67091),x67092)),f331(f331(f310(x67091),x67093),f184(f854(x67091,a840)))),f331(f163(x67091),f161(x67091,x67093,x67092)))
% 51.10/50.82 [6767]P34(x67671,x67672)+~P34(x67671,f331(f331(f178(f853(x67671,x67671),a840),x67673),x67672))
% 51.10/50.82 [6783]~E(x67831,f2(a847))+P1(f331(f331(f287(a847),f331(f331(f88(a847),x67831),x67832)),f331(f331(f88(a847),x67831),x67833)))
% 51.10/50.82 [6837]P1(f331(f61(x68371,x68372),f331(a63,x68373)))+~P1(f331(f61(f331(f86(a1),x68371),f331(f86(a1),x68372)),x68373))
% 51.10/50.82 [6842]E(f331(f331(f3(f854(x68421,a840)),f331(f331(f310(x68421),x68422),x68423)),f331(f331(f310(x68421),x68422),f184(f854(x68421,a840)))),x68423)+P1(f331(f331(f333(x68421),x68422),x68423))
% 51.10/50.82 [6861]E(f331(f331(f109(f854(x68611,a840)),f331(f163(x68611),x68612)),f331(f163(x68611),x68613)),f184(f854(x68611,a840)))+~P1(f331(f132(x68611),f331(f331(f130(x68611),x68612),x68613)))
% 51.10/50.82 [6878]~P1(f331(f331(f333(x68781),x68782),f331(f163(x68781),x68783)))+~P1(f331(f132(x68781),f331(f331(f145(x68781),x68782),x68783)))
% 51.10/50.82 [6955]E(f331(f331(f109(f854(x69551,a840)),x69552),x69553),f184(f854(x69551,a840)))+P1(f331(f331(f333(x69551),f370(x69553,x69552,x69551)),x69552))
% 51.10/50.82 [6956]E(f331(f331(f109(f854(x69561,a840)),x69562),x69563),f184(f854(x69561,a840)))+P1(f331(f331(f333(x69561),f371(x69563,x69562,x69561)),x69563))
% 51.10/50.82 [6960]E(f121(x69601,f331(f331(f164(x69601),x69602),x69603)),f331(f331(f164(x69601),f331(f331(f3(a847),x69602),f85(a847))),x69603))+~P1(f331(f331(f240(a847),x69602),f331(f185(f848(x69601)),x69603)))
% 51.10/50.82 [7042]P1(f331(f331(f241(a847),f2(a847)),x70421))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x70422),x70421)),f331(f331(f88(a847),x70423),x70421)))
% 51.10/50.82 [7043]P1(f331(f331(f241(a847),f2(a847)),x70431))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x70431),x70432)),f331(f331(f88(a847),x70431),x70433)))
% 51.10/50.82 [7044]~P1(f331(f331(f333(x70441),x70442),x70443))+~P1(f331(f331(f333(x70441),x70442),f331(f86(f854(x70441,a840)),x70443)))
% 51.10/50.82 [7045]~P1(f331(f331(f333(x70451),x70452),x70453))+~P1(f331(f331(f333(x70451),x70452),f331(f86(f854(x70451,a840)),x70453)))
% 51.10/50.82 [7046]~P1(f331(f331(f333(x70461),x70462),x70463))+~P1(f331(f331(f333(x70461),x70462),f331(f86(f854(x70461,a840)),x70463)))
% 51.10/50.82 [7050]~P1(f331(f331(f241(f854(x70501,a840)),x70502),x70503))+P1(f331(f331(f240(f854(x70501,a840)),x70502),x70503))
% 51.10/50.82 [7051]~P1(f331(f331(f241(f854(x70511,a840)),x70512),x70513))+P1(f331(f331(f240(f854(x70511,a840)),x70512),x70513))
% 51.10/50.82 [7052]~P1(f331(f331(f241(f854(x70521,a840)),x70522),x70523))+P1(f331(f331(f240(f854(x70521,a840)),x70522),x70523))
% 51.10/50.82 [7155]~P1(f331(f331(f241(a847),x71552),x71553))+P1(f331(f331(f241(a847),f331(f331(f87(a847),x71551),x71552)),f331(f331(f87(a847),x71551),x71553)))
% 51.10/50.82 [7156]~P1(f331(f331(f241(a847),x71561),x71563))+P1(f331(f331(f241(a847),f331(f331(f87(a847),x71561),x71562)),f331(f331(f87(a847),x71563),x71562)))
% 51.10/50.82 [7157]~P1(f331(f331(f241(a1),x71571),x71573))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x71571),x71572)),f331(f331(f87(a1),x71573),x71572)))
% 51.10/50.82 [7160]~P1(f331(f331(f240(a847),x71602),x71603))+P1(f331(f331(f240(a847),f331(f331(f87(a847),x71601),x71602)),f331(f331(f87(a847),x71601),x71603)))
% 51.10/50.82 [7161]~P1(f331(f331(f240(a847),x71611),x71613))+P1(f331(f331(f240(a847),f331(f331(f87(a847),x71611),x71612)),f331(f331(f87(a847),x71613),x71612)))
% 51.10/50.82 [7162]~P1(f331(f331(f240(a847),x71622),x71623))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x71621),x71622)),f331(f331(f88(a847),x71621),x71623)))
% 51.10/50.82 [7163]~P1(f331(f331(f240(a847),x71632),x71633))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x71631),x71632)),f331(f331(f88(a847),x71631),x71633)))
% 51.10/50.82 [7164]~P1(f331(f331(f240(a847),x71641),x71643))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x71641),x71642)),f331(f331(f88(a847),x71643),x71642)))
% 51.10/50.82 [7165]~P1(f331(f331(f240(a847),x71651),x71653))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x71651),x71652)),f331(f331(f88(a847),x71653),x71652)))
% 51.10/50.82 [7166]~P1(f331(f331(f240(a847),x71661),x71663))+P1(f331(f331(f240(a847),f331(f331(f48(a847),x71661),x71662)),f331(f331(f48(a847),x71663),x71662)))
% 51.10/50.82 [7167]~P1(f331(f331(f240(a847),x71673),x71672))+P1(f331(f331(f240(a847),f331(f331(f3(a847),x71671),x71672)),f331(f331(f3(a847),x71671),x71673)))
% 51.10/50.82 [7168]~P1(f331(f331(f240(a847),x71681),x71683))+P1(f331(f331(f240(a847),f331(f331(f3(a847),x71681),x71682)),f331(f331(f3(a847),x71683),x71682)))
% 51.10/50.82 [7169]~P1(f331(f331(f240(a1),x71692),x71693))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x71691),x71692)),f331(f331(f87(a1),x71691),x71693)))
% 51.10/50.82 [7172]~P1(f331(f331(f287(a847),x71722),x71723))+P1(f331(f331(f287(a847),f331(f331(f88(a847),x71721),x71722)),f331(f331(f88(a847),x71721),x71723)))
% 51.10/50.82 [7259]E(x72591,x72592)+~P1(f331(f331(f333(x72593),x72591),f331(f331(f310(x72593),x72592),f184(f854(x72593,a840)))))
% 51.10/50.82 [7260]E(x72601,x72602)+~P1(f331(f331(f333(x72603),x72601),f331(f331(f310(x72603),x72602),f184(f854(x72603,a840)))))
% 51.10/50.82 [7262]~E(f331(f331(f109(f854(x72621,a840)),x72622),x72623),f184(f854(x72621,a840)))+P1(f331(f331(f240(f854(x72621,a840)),x72622),f331(f86(f854(x72621,a840)),x72623)))
% 51.10/50.82 [7268]P1(f331(f331(f333(f854(x72681,a840)),x72682),f331(f309(x72681),x72683)))+~P1(f331(f331(f240(f854(x72681,a840)),x72682),x72683))
% 51.10/50.82 [7269]P1(f331(f331(f333(f854(x72691,a840)),x72692),f331(f309(x72691),x72693)))+~P1(f331(f331(f240(f854(x72691,a840)),x72692),x72693))
% 51.10/50.82 [7326]E(f331(f331(f145(x73261),f331(f331(f155(x73261),x73262),x73263)),f331(f331(f133(x73261),f331(a119,x73263)),x73262)),f331(f331(f133(x73261),x73263),x73262))+~P1(f331(f331(f241(a847),x73263),f331(f185(f848(x73261)),x73262)))
% 51.10/50.82 [7356]P1(f331(f331(f333(f853(x73561,x73561)),x73562),f308(x73561,x73563)))+~P1(f331(f331(f333(f853(x73561,x73561)),x73562),x73563))
% 51.10/50.82 [7365]~P1(f331(f331(f333(f854(x73651,a840)),x73652),f331(f309(x73651),x73653)))+P1(f331(f331(f240(f854(x73651,a840)),x73652),x73653))
% 51.10/50.82 [7366]~P1(f331(f331(f333(f854(x73661,a840)),x73662),f331(f309(x73661),x73663)))+P1(f331(f331(f240(f854(x73661,a840)),x73662),x73663))
% 51.10/50.82 [7408]P1(f331(f331(f240(f854(x74081,a840)),x74082),f49(f854(x74081,a840),x74083)))+~P1(f331(f331(f333(f854(x74081,a840)),x74082),x74083))
% 51.10/50.82 [7436]~P133(x74361)+E(f331(f331(f88(x74361),f331(f331(f250(x74361),f331(f86(x74361),f85(x74361))),x74362)),f331(f331(f250(x74361),x74363),x74362)),f331(f331(f250(x74361),f331(f86(x74361),x74363)),x74362))
% 51.10/50.82 [7459]E(f331(f331(f155(x74591),x74592),f331(f331(f3(a847),f331(f185(f848(x74591)),x74592)),f331(a119,x74593))),f331(f331(f155(x74591),f331(f160(x74591),x74592)),x74593))+~P1(f331(f331(f241(a847),x74593),f331(f185(f848(x74591)),x74592)))
% 51.10/50.82 [7476]~E(f331(f331(f109(f854(x74761,a840)),f663(x74763,x74762,x74761)),x74763),f184(f854(x74761,a840)))+E(f331(f331(f109(f854(x74761,a840)),f49(f854(x74761,a840),x74762)),x74763),f184(f854(x74761,a840)))
% 51.10/50.82 [7540]~P1(f331(f331(f333(x75403),x75402),f331(f163(x75403),x75401)))+P1(f331(f331(f241(a847),f729(x75401,x75402,x75403)),f331(f185(f848(x75403)),x75401)))
% 51.10/50.82 [7548]P1(f331(f331(f333(x75481),f331(f331(f155(x75481),x75482),x75483)),f331(f163(x75481),x75482)))+~P1(f331(f331(f241(a847),x75483),f331(f185(f848(x75481)),x75482)))
% 51.10/50.82 [7657]P1(f331(f331(f240(f854(f848(x76571),a840)),f153(x76571,x76572)),f153(x76571,x76573)))+~P1(f331(f331(f240(f854(x76571,a840)),x76572),x76573))
% 51.10/50.82 [7686]E(f331(f331(f109(f854(x76861,a840)),f49(f854(x76861,a840),x76862)),x76863),f184(f854(x76861,a840)))+P1(f331(f331(f333(f854(x76861,a840)),f663(x76863,x76862,x76861)),x76862))
% 51.10/50.82 [7688]~P1(f331(f331(f333(f854(x76881,a840)),x76883),x76882))+P1(f331(f331(f240(f854(x76881,a840)),f50(f854(x76881,a840),x76882)),x76883))
% 51.10/50.82 [7690]E(f331(f331(f109(f854(x76901,a840)),x76902),x76903),f184(f854(x76901,a840)))+~P1(f331(f331(f240(f854(x76901,a840)),x76902),f331(f86(f854(x76901,a840)),x76903)))
% 51.10/50.82 [7743]E(f331(f331(f3(a847),f331(f331(f87(a847),f331(f157(a847),x77431)),x77432)),f331(f331(f155(a847),x77431),x77433)),f331(f157(a847),f331(f331(f152(a847,x77431),x77433),x77432)))+~P1(f331(f331(f241(a847),x77433),f331(f185(f848(a847)),x77431)))
% 51.10/50.82 [7793]P1(f331(f331(f241(a847),x77931),x77932))+~P1(f331(f331(f241(a847),f331(f331(f87(a847),x77933),x77931)),f331(f331(f87(a847),x77933),x77932)))
% 51.10/50.82 [7794]P1(f331(f331(f241(a847),x77941),x77942))+~P1(f331(f331(f241(a847),f331(f331(f88(a847),x77943),x77941)),f331(f331(f88(a847),x77943),x77942)))
% 51.10/50.82 [7795]P1(f331(f331(f241(a847),x77951),x77952))+~P1(f331(f331(f241(a847),f331(f331(f88(a847),x77951),x77953)),f331(f331(f88(a847),x77952),x77953)))
% 51.10/50.82 [7798]P1(f331(f331(f240(a847),x77981),x77982))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x77983),x77981)),f331(f331(f87(a847),x77983),x77982)))
% 51.10/50.82 [7827]P1(f331(f331(f241(a847),f2(a847)),x78271))+~P1(f331(f331(f241(a847),f331(f331(f88(a847),x78272),x78271)),f331(f331(f88(a847),x78273),x78271)))
% 51.10/50.82 [7828]P1(f331(f331(f241(a847),f2(a847)),x78281))+~P1(f331(f331(f241(a847),f331(f331(f88(a847),x78281),x78282)),f331(f331(f88(a847),x78281),x78283)))
% 51.10/50.82 [7901]E(f252(x79011,x79012,x79013),x79012)+~P1(f331(f331(f240(f854(x79011,a840)),x79013),f331(f331(f310(x79011),x79012),f184(f854(x79011,a840)))))
% 51.10/50.82 [7980]E(f331(f331(f130(x79801),f331(f331(f164(x79801),x79802),x79803)),f331(f331(f145(x79801),f331(f331(f155(x79801),x79803),x79802)),f120(x79801))),f331(f331(f164(x79801),f331(a119,x79802)),x79803))+~P1(f331(f331(f241(a847),x79802),f331(f185(f848(x79801)),x79803)))
% 51.10/50.82 [8049]P1(f331(f331(f240(f854(f854(x80491,a840),a840)),f253(x80491,x80492)),f253(x80491,x80493)))+~P1(f331(f331(f240(f854(x80491,a840)),x80492),x80493))
% 51.10/50.82 [8088]~P1(f331(f132(x80881),x80883))+P1(f331(f132(x80881),f331(f331(f331(f178(f848(x80881),f848(x80881)),x80882),f159(x80881)),x80883)))
% 51.10/50.82 [8093]~P1(f331(f331(f241(a847),x80932),x80933))+P1(f331(f331(f241(a847),f331(f331(f88(a847),f331(a119,x80931)),x80932)),f331(f331(f88(a847),f331(a119,x80931)),x80933)))
% 51.10/50.82 [8094]~P1(f331(f331(f240(a847),x80942),x80943))+P1(f331(f331(f240(a847),f331(f331(f88(a847),f331(a119,x80941)),x80942)),f331(f331(f88(a847),f331(a119,x80941)),x80943)))
% 51.10/50.82 [8116]P1(f331(f331(f240(f854(f854(x81161,a840),a840)),f331(f309(x81161),x81162)),f331(f309(x81161),x81163)))+~P1(f331(f331(f240(f854(x81161,a840)),x81162),x81163))
% 51.10/50.82 [8274]~P1(f331(f331(f240(f854(x82741,a840)),x82743),x82742))+P1(f331(f331(f240(f854(x82741,a840)),f331(f86(f854(x82741,a840)),x82742)),f331(f86(f854(x82741,a840)),x82743)))
% 51.10/50.82 [8275]~P1(f331(f331(f240(f854(x82751,a840)),x82753),x82752))+P1(f331(f331(f240(f854(x82751,a840)),f331(f86(f854(x82751,a840)),x82752)),f331(f86(f854(x82751,a840)),x82753)))
% 51.10/50.82 [8313]E(f331(f311(a847,a847,f331(f331(f9(a847,a847,a847),f3(a847)),x83131)),f331(f302(a847,x83132),x83133)),f331(f302(a847,f331(f331(f3(a847),x83132),x83131)),f331(f331(f3(a847),x83133),x83131)))+~P1(f331(f331(f241(a847),x83131),x83133))
% 51.10/50.82 [8338]~P71(x83381)+E(f331(f331(f87(x83381),x83382),f331(f137(x83381,x83381,f87(x83381),f2(x83381)),x83383)),f331(f137(x83381,x83381,f87(x83381),x83382),x83383))
% 51.10/50.82 [8420]~P78(x84201)+P1(f331(f331(f240(x84201),f331(f82(x84201),f331(f331(f87(x84201),x84202),x84203))),f331(f331(f87(x84201),f331(f82(x84201),x84202)),f331(f82(x84201),x84203))))
% 51.10/50.82 [8421]~P78(x84211)+P1(f331(f331(f240(x84211),f331(f82(x84211),f331(f331(f3(x84211),x84212),x84213))),f331(f331(f87(x84211),f331(f82(x84211),x84212)),f331(f82(x84211),x84213))))
% 51.10/50.82 [8431]E(f331(f331(f87(a1),f331(f331(f88(a1),x84311),f57(a1,f331(f331(f48(a1),x84312),x84311),x84313))),f57(a1,x84312,x84311)),f57(a1,x84312,f331(f331(f88(a1),x84311),x84313)))+~P1(f331(f331(f241(a1),f2(a1)),x84313))
% 51.10/50.82 [8437]E(f331(f331(f130(x84371),f331(f331(f164(x84371),x84372),x84373)),f331(f331(f145(x84371),f331(f136(x84371),f331(f331(f133(x84371),x84372),x84373))),f120(x84371))),f331(f331(f164(x84371),f331(a119,x84372)),x84373))+~P1(f331(f331(f241(a847),x84372),f331(f185(f848(x84371)),x84373)))
% 51.10/50.82 [8456]E(f331(f273(x84561,f331(f331(f147(x84561,f853(a106,x84561)),f331(f249(a106,x84561),f85(a106))),x84562)),f331(a5,x84563)),f331(f331(f155(x84561),x84562),x84563))+~P1(f331(f331(f241(a847),x84563),f331(f185(f848(x84561)),x84562)))
% 51.10/50.82 [8513]P1(f331(f331(f333(f853(x85131,x85131)),x85132),f331(f331(f289(x85131,x85131,x85131),x85133),f308(x85131,x85133))))+~P1(f331(f331(f333(f853(x85131,x85131)),x85132),x85133))
% 51.10/50.82 [8529]P1(f331(f331(f241(a847),x85291),x85292))+~P1(f331(f331(f241(a847),f331(f331(f88(a847),f331(a119,x85293)),x85291)),f331(f331(f88(a847),f331(a119,x85293)),x85292)))
% 51.10/50.82 [8530]P1(f331(f331(f240(a847),x85301),x85302))+~P1(f331(f331(f240(a847),f331(f331(f88(a847),f331(a119,x85303)),x85301)),f331(f331(f88(a847),f331(a119,x85303)),x85302)))
% 51.10/50.82 [8541]P1(f331(f331(f240(f854(x85411,a840)),x85412),x85413))+~P1(f331(f331(f240(f854(x85411,a840)),f331(f86(f854(x85411,a840)),x85413)),f331(f86(f854(x85411,a840)),x85412)))
% 51.10/50.82 [8560]P1(f331(f132(x85601),x85602))+~P1(f331(f132(x85601),f331(f331(f331(f178(f848(x85601),f848(x85601)),x85603),f159(x85601)),x85602)))
% 51.10/50.82 [8626]E(f331(f285(x86261,x86261,f308(x86261,x86262)),x86263),x86263)+~P1(f331(f331(f240(f854(x86261,a840)),f331(f285(x86261,x86261,x86262),x86263)),x86263))
% 51.10/50.82 [8628]E(f331(f311(f853(x86281,x86282),x86282,f258(x86281,x86282)),f331(f163(f853(x86281,x86282)),x86283)),f176(x86281,x86282,f171(x86281,x86282,x86283)))+~P1(f331(f132(x86281),f331(f331(f147(f853(x86281,x86282),x86281),f248(x86281,x86282)),x86283)))
% 51.10/50.82 [8667]~P102(x86671)+P16(x86671,f331(f131(x86671,f331(f331(f9(x86671,x86671,a840),a328),f331(x86672,x86673))),x86673))
% 51.10/50.82 [8672]~P1(f331(f331(f240(a847),x86721),x86722))+P1(f331(f331(f240(a847),x86721),f331(f137(a847,a847,f87(a847),x86722),x86723)))
% 51.10/50.82 [8743]~P1(f331(f331(f333(f853(x87431,x87431)),x87432),f308(x87431,x87433)))+P1(f331(f331(f333(f853(x87431,x87431)),x87432),f331(f331(f178(f853(x87431,x87431),a840),f649(x87433,x87432,x87431)),x87433)))
% 51.10/50.82 [8812]~P71(x88121)+E(f331(f331(f87(x88121),x88122),f331(f137(x88121,x88121,f331(f9(x88121,x88121,x88121),f87(x88121)),f2(x88121)),f331(f160(x88121),x88123))),f331(f137(x88121,x88121,f87(x88121),x88122),x88123))
% 51.10/50.82 [9067]P51(x90671,x90672,x90673)+P1(f331(f331(f333(f853(x90671,x90672)),f331(f331(f249(x90671,x90672),f639(x90673,x90672,x90671)),f616(x90673,x90672,x90671))),x90673))
% 51.10/50.82 [9068]P51(x90681,x90682,x90683)+P1(f331(f331(f333(f853(x90681,x90682)),f331(f331(f249(x90681,x90682),f639(x90683,x90682,x90681)),f646(x90683,x90682,x90681))),x90683))
% 51.10/50.82 [9122]~P1(f331(f331(f333(f853(x91221,x91221)),x91222),f331(f331(f289(x91221,x91221,x91221),x91223),f308(x91221,x91223))))+P1(f331(f331(f333(f853(x91221,x91221)),x91222),f331(f331(f178(f853(x91221,x91221),a840),f650(x91223,x91222,x91221)),x91223)))
% 51.10/50.82 [9123]~P1(f331(x91231,f331(f331(f155(x91232),x91233),f331(f185(f848(x91232)),f167(x91232,x91231,x91233)))))+~P1(f331(f331(f241(a847),f331(f185(f848(x91232)),f167(x91232,x91231,x91233))),f331(f185(f848(x91232)),x91233)))
% 51.10/50.82 [9199]~P1(f331(f331(f240(f854(x91991,a840)),x91992),x91993))+P1(f331(f331(f240(f854(x91991,a840)),f331(f331(f9(x91991,f854(x91991,a840),a840),f333(x91991)),x91992)),f331(f331(f9(x91991,f854(x91991,a840),a840),f333(x91991)),x91993)))
% 51.10/50.82 [9256]~P1(f331(f331(f333(f853(f854(x92561,a840),f854(x92561,a840))),f331(f331(f249(f854(x92561,a840),f854(x92561,a840)),x92562),x92563)),f307(x92561)))+P1(f331(f331(f241(f854(x92561,a840)),x92562),x92563))
% 51.10/50.82 [9282]P52(x92821,x92822,x92823)+~P1(f331(f331(f333(f853(x92821,x92821)),f331(f331(f249(x92821,x92821),f648(x92823,x92822,x92821)),f647(x92823,x92822,x92821))),x92823))
% 51.10/50.82 [9283]P52(x92831,x92832,x92833)+~P1(f331(f331(f333(f853(x92831,x92831)),f331(f331(f249(x92831,x92831),f647(x92833,x92832,x92831)),f648(x92833,x92832,x92831))),x92833))
% 51.10/50.82 [9317]~P1(f331(f331(f333(f853(f848(x93171),f848(x93171))),f331(f331(f249(f848(x93171),f848(x93171)),x93172),x93172)),f142(x93171,x93173)))+P1(f331(f331(f333(f853(x93171,x93171)),f331(f331(f249(x93171,x93171),f755(x93172,x93173,x93171)),f755(x93172,x93173,x93171))),x93173))
% 51.10/50.82 [9362]P1(f331(f331(f240(f854(x93621,a840)),x93622),x93623))+~P1(f331(f331(f240(f854(x93621,a840)),f331(f331(f9(x93621,f854(x93621,a840),a840),f333(x93621)),x93622)),f331(f331(f9(x93621,f854(x93621,a840),a840),f333(x93621)),x93623)))
% 51.10/50.82 [9452]E(f331(f331(f3(a847),f331(f331(f8(a847,a847),x94521),f331(f265(a847),x94522))),f331(f331(f8(a847,a847),x94523),f331(f265(a847),x94522))),f331(f331(f8(a847,a847),f331(f331(f20(a847,a847,a847),f331(f331(f10(a847,f854(a847,a847),a847),f3(a847)),x94521)),x94523)),f331(f265(a847),x94522)))+~P1(f331(f331(f240(a847),f331(x94523,f508(x94522,x94521,x94523))),f331(x94521,f508(x94522,x94521,x94523))))
% 51.10/50.82 [9743]E(f331(f264(f853(x97431,x97432)),f331(f259(x97431,x97432,a840),f331(f331(f9(x97431,f854(x97432,f851(x97432)),f854(x97432,a840)),f331(f331(f10(f854(f851(x97432),a840),f854(f854(x97432,f851(x97432)),f854(x97432,a840)),x97431),f10(f851(x97432),a840,x97432)),f331(f331(f10(f851(x97432),f854(f851(x97432),a840),x97431),a328),f171(x97431,x97432,x97433)))),f234(x97432)))),f331(f163(f853(x97431,x97432)),x97433))+~P1(f331(f132(x97431),f331(f331(f147(f853(x97431,x97432),x97431),f248(x97431,x97432)),x97433)))
% 51.10/50.82 [5481]~P69(x54811)+E(f331(f331(f87(x54811),f331(f331(f3(x54811),x54812),x54813)),x54813),x54812)
% 51.10/50.82 [5482]~P69(x54821)+E(f331(f331(f3(x54821),f331(f331(f87(x54821),x54822),x54823)),x54823),x54822)
% 51.10/50.82 [5710]~P69(x57101)+E(f331(f331(f87(x57101),x57102),f331(f331(f87(x57101),f331(f86(x57101),x57102)),x57103)),x57103)
% 51.10/50.82 [5794]~P74(x57941)+E(f331(f331(f88(x57941),f331(f331(f250(x57941),x57942),x57943)),x57942),f331(f331(f250(x57941),x57942),f331(a119,x57943)))
% 51.10/50.82 [5795]~P87(x57951)+E(f331(f331(f88(x57951),f331(f331(f250(x57951),x57952),x57953)),x57952),f331(f331(f250(x57951),x57952),f331(a119,x57953)))
% 51.10/50.82 [6011]~P86(x60111)+E(f331(f82(x60111),f331(f331(f250(x60111),f331(f86(x60111),x60112)),x60113)),f331(f82(x60111),f331(f331(f250(x60111),x60112),x60113)))
% 51.10/50.82 [6064]~P74(x60641)+E(f331(f331(f88(x60641),f331(f331(f250(x60641),x60642),x60643)),x60642),f331(f331(f88(x60641),x60642),f331(f331(f250(x60641),x60642),x60643)))
% 51.10/50.82 [6124]E(f331(f331(f3(a106),f331(f331(f87(a106),x61241),x61242)),x61243),f277(x61241,x61242,x61243))+~P1(f331(f331(f241(a106),x61242),x61243))
% 51.10/50.82 [6146]~E(f331(f331(f133(x61461),x61463),x61462),f120(x61461))+P1(f331(f331(f240(a847),f331(f185(f848(x61461)),x61462)),x61463))
% 51.10/50.82 [6287]E(f331(f331(f88(a847),f331(f111(a847),x62871)),f331(f331(f88(a847),f331(f111(a847),x62872)),x62873)),f2(a847))+~P1(f331(f331(f241(a1),x62871),a90))
% 51.10/50.82 [6303]~P58(x63031)+E(f331(f331(f250(x63031),f331(f331(f291(x63031),f85(x63031)),x63032)),x63033),f331(f331(f291(x63031),f85(x63031)),f331(f331(f250(x63031),x63032),x63033)))
% 51.10/50.82 [6387]E(f331(f331(f3(a847),f331(f331(f87(a847),x63871),x63872)),x63873),f331(f331(f87(a847),x63871),f331(f331(f3(a847),x63872),x63873)))+~P1(f331(f331(f240(a847),x63873),x63872))
% 51.10/50.82 [6388]E(f331(f331(f3(a847),f331(f331(f87(a847),x63881),x63882)),x63883),f331(f331(f3(a847),x63881),f331(f331(f3(a847),x63883),x63882)))+~P1(f331(f331(f240(a847),x63882),x63883))
% 51.10/50.82 [6389]E(f331(f331(f3(a847),f331(f331(f87(a847),x63891),x63892)),x63893),f331(f331(f87(a847),x63891),f331(f331(f3(a847),x63892),x63893)))+~P1(f331(f331(f240(a847),x63893),x63892))
% 51.10/50.82 [6429]~P102(x64291)+P1(f331(f331(f240(x64291),f331(f331(f244(x64291),x64292),x64293)),x64293))
% 51.10/50.82 [6430]~P102(x64301)+P1(f331(f331(f240(x64301),f331(f331(f244(x64301),x64302),x64303)),x64302))
% 51.10/50.82 [6431]~P97(x64311)+P1(f331(f331(f240(x64311),f331(f331(f109(x64311),x64312),x64313)),x64313))
% 51.10/50.82 [6432]~P101(x64321)+P1(f331(f331(f240(x64321),f331(f331(f109(x64321),x64322),x64323)),x64323))
% 51.10/50.82 [6433]~P97(x64331)+P1(f331(f331(f240(x64331),f331(f331(f109(x64331),x64332),x64333)),x64332))
% 51.10/50.82 [6434]~P101(x64341)+P1(f331(f331(f240(x64341),f331(f331(f109(x64341),x64342),x64343)),x64342))
% 51.10/50.82 [6448]E(f331(f331(f48(a1),f331(f331(f48(a1),x64481),x64482)),x64483),f331(f331(f48(a1),x64481),f331(f331(f88(a1),x64482),x64483)))+~P1(f331(f331(f241(a1),f2(a1)),x64483))
% 51.10/50.82 [6501]~P87(x65011)+E(f331(f331(f87(x65011),f331(f331(f88(x65011),x65012),x65013)),x65013),f331(f331(f88(x65011),f331(f331(f87(x65011),x65012),f85(x65011))),x65013))
% 51.10/50.82 [6502]~P91(x65021)+E(f331(f331(f88(x65021),f331(f86(x65021),f331(f111(x65021),x65022))),x65023),f331(f331(f88(x65021),f331(f111(x65021),f331(f86(a1),x65022))),x65023))
% 51.10/50.82 [6574]~P71(x65741)+E(f331(f157(x65741),f331(f331(f147(x65742,x65741),f331(f18(x65741,x65742),f2(x65741))),x65743)),f2(x65741))
% 51.10/50.82 [6593]E(f331(f331(f87(a847),f331(f111(a847),x65931)),f331(f331(f87(a847),f331(f111(a847),x65932)),x65933)),f331(f331(f87(a847),f331(f111(a847),x65932)),x65933))+~P1(f331(a190,f331(f111(a1),x65931)))
% 51.10/50.82 [6608]~P7(x66081)+E(f50(x66081,f331(f331(f310(x66081),x66082),f331(f331(f310(x66081),x66083),f184(f854(x66081,a840))))),f331(f331(f109(x66081),x66082),x66083))
% 51.10/50.82 [6609]~P7(x66091)+E(f49(x66091,f331(f331(f310(x66091),x66092),f331(f331(f310(x66091),x66093),f184(f854(x66091,a840))))),f331(f331(f108(x66091),x66092),x66093))
% 51.10/50.82 [6634]E(f331(f331(f164(x66341),x66342),x66343),x66343)+~P1(f331(f331(f240(a847),f331(f185(f848(x66341)),x66343)),x66342))
% 51.10/50.82 [6645]E(f331(f331(f133(x66451),x66452),x66453),f120(x66451))+~P1(f331(f331(f240(a847),f331(f185(f848(x66451)),x66453)),x66452))
% 51.10/50.82 [6646]E(f331(f331(f133(x66461),x66462),x66463),f120(x66461))+~P1(f331(f331(f240(a847),f331(f185(f848(x66461)),x66463)),x66462))
% 51.10/50.82 [6657]E(f331(f331(f3(a847),f331(f331(f87(a847),x66571),x66572)),x66573),f331(f331(f87(a847),f331(f331(f3(a847),x66571),x66573)),x66572))+~P1(f331(f331(f240(a847),x66573),x66571))
% 51.10/50.82 [6658]E(f331(f331(f3(a847),f331(f331(f87(a847),x66581),x66582)),x66583),f331(f331(f87(a847),f331(f331(f3(a847),x66581),x66583)),x66582))+~P1(f331(f331(f240(a847),x66583),x66581))
% 51.10/50.82 [6672]~P1(f331(f331(f241(a847),x66721),x66723))+P1(f331(f331(f241(a847),f331(f331(f3(a847),x66721),x66722)),x66723))
% 51.10/50.82 [6700]~P102(x67001)+E(f161(x67001,x67002,f331(f331(f143(x67001,x67001,f7(x67001)),x67002),x67003)),x67003)
% 51.10/50.82 [6797]E(f331(f331(f3(a847),f331(f331(f87(a847),x67971),x67972)),f331(a119,x67973)),f331(f331(f3(a847),x67971),f331(a119,f331(f331(f3(a847),x67973),x67972))))+~P1(f331(f331(f240(a847),x67972),x67973))
% 51.10/50.82 [6798]~P86(x67981)+P1(f331(f331(f240(x67981),f2(x67981)),f331(f331(f250(x67981),f331(f82(x67981),x67982)),x67983)))
% 51.10/50.82 [6849]P26(x68491,x68492,x68493)+~P1(f331(f331(f240(f854(f846(x68491),a840)),x68493),x68492))
% 51.10/50.82 [6890]~P1(f331(f68(x68901),x68902))+P1(f331(f68(x68901),f331(f331(f3(f854(x68901,a840)),x68902),x68903)))
% 51.10/50.82 [6891]~P1(f331(f68(x68911),x68913))+P1(f331(f68(x68911),f331(f331(f109(f854(x68911,a840)),x68912),x68913)))
% 51.10/50.82 [6892]~P1(f331(f68(x68921),x68922))+P1(f331(f68(x68921),f331(f331(f109(f854(x68921,a840)),x68922),x68923)))
% 51.10/50.82 [7031]~P34(x70311,x70313)+P34(x70311,f331(f331(f109(f854(f853(x70311,x70311),a840)),x70312),x70313))
% 51.10/50.82 [7032]~P34(x70321,x70322)+P34(x70321,f331(f331(f109(f854(f853(x70321,x70321),a840)),x70322),x70323))
% 51.10/50.82 [7150]~P97(x71501)+E(f12(x71501,f331(f163(x71501),f331(f331(f145(x71501),x71502),x71503))),f331(f137(x71501,x71501,f109(x71501),x71502),x71503))
% 51.10/50.82 [7151]~P97(x71511)+E(f15(x71511,f331(f163(x71511),f331(f331(f145(x71511),x71512),x71513))),f331(f137(x71511,x71511,f108(x71511),x71512),x71513))
% 51.10/50.82 [7152]~P102(x71521)+E(f16(x71521,f331(f163(x71521),f331(f331(f145(x71521),x71522),x71523))),f331(f137(x71521,x71521,f239(x71521),x71522),x71523))
% 51.10/50.82 [7153]~P102(x71531)+E(f17(x71531,f331(f163(x71531),f331(f331(f145(x71531),x71532),x71533))),f331(f137(x71531,x71531,f244(x71531),x71532),x71533))
% 51.10/50.82 [7154]~P1(f331(f331(f287(a1),x71541),x71542))+P1(f331(f331(f287(a1),x71541),f331(f331(f87(a1),x71542),f331(f331(f88(a1),x71541),x71543))))
% 51.10/50.82 [7224]~P1(f331(f68(x72241),x72242))+P1(f331(f331(f240(a847),f331(f47(x72241),x72242)),f331(f47(x72241),f331(f331(f310(x72241),x72243),x72242))))
% 51.10/50.82 [7231]E(f331(f331(f108(f854(a847,a840)),f331(f302(a847,x72311),x72312)),f331(f302(a847,x72312),f331(f331(f87(a847),x72312),x72313))),f331(f302(a847,x72311),f331(f331(f87(a847),x72312),x72313)))+~P1(f331(f331(f240(a847),x72311),x72312))
% 51.10/50.82 [7241]P1(f331(f331(f241(a847),x72411),x72412))+~P1(f331(f331(f241(a847),f331(f331(f87(a847),x72411),x72413)),x72412))
% 51.10/50.82 [7242]P1(f331(f331(f240(a847),x72421),x72422))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x72423),x72421)),x72422))
% 51.10/50.82 [7243]P1(f331(f331(f240(a847),x72431),x72432))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x72431),x72433)),x72432))
% 51.10/50.82 [7244]P1(f331(f331(f240(a847),x72441),x72442))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x72443),x72441)),x72442))
% 51.10/50.82 [7245]P1(f331(f331(f240(a847),x72451),x72452))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x72451),x72453)),x72452))
% 51.10/50.82 [7287]~P102(x72871)+E(f13(x72871,f239(x72871),f331(f163(x72871),f331(f331(f145(x72871),x72872),x72873))),f331(f137(x72871,x72871,f239(x72871),x72872),x72873))
% 51.10/50.82 [7288]~P102(x72881)+E(f14(x72881,f244(x72881),f331(f163(x72881),f331(f331(f145(x72881),x72882),x72883))),f331(f137(x72881,x72881,f244(x72881),x72882),x72883))
% 51.10/50.82 [7292]~E(x72922,f184(f854(f853(x72921,x72921),a840)))+P1(f331(f331(f240(f854(f853(x72921,x72921),a840)),x72922),x72923))
% 51.10/50.82 [7401]E(f331(f331(f108(f854(x74011,a840)),x74012),f331(f331(f3(f854(x74011,a840)),x74013),x74012)),x74013)+~P1(f331(f331(f240(f854(x74011,a840)),x74012),x74013))
% 51.10/50.82 [7404]~P1(f331(f331(f241(a847),x74041),f331(f331(f3(a847),x74043),x74042)))+P1(f331(f331(f241(a847),f331(f331(f87(a847),x74041),x74042)),x74043))
% 51.10/50.82 [7405]~P1(f331(f331(f240(a847),x74051),f331(f331(f87(a847),x74053),x74052)))+P1(f331(f331(f240(a847),f331(f331(f3(a847),x74051),x74052)),x74053))
% 51.10/50.82 [7466]E(x74661,f120(x74662))+E(f331(f136(x74662),f331(f331(f331(f178(f848(x74662),f848(x74662)),x74663),f159(x74662)),x74661)),f331(f331(f155(x74662),x74661),f57(a847,x74663,f331(f185(f848(x74662)),x74661))))
% 51.10/50.82 [7475]E(f331(f331(f310(x74751),x74752),f331(f331(f3(f854(x74751,a840)),x74753),f331(f331(f310(x74751),x74752),f184(f854(x74751,a840))))),x74753)+~P1(f331(f331(f333(x74751),x74752),x74753))
% 51.10/50.82 [7639]P1(f331(f331(f241(a847),x76391),f331(f331(f3(a847),x76392),x76393)))+~P1(f331(f331(f241(a847),f331(f331(f87(a847),x76391),x76393)),x76392))
% 51.10/50.82 [7640]P1(f331(f331(f240(a847),x76401),f331(f331(f87(a847),x76402),x76403)))+~P1(f331(f331(f240(a847),f331(f331(f3(a847),x76401),x76403)),x76402))
% 51.10/50.82 [7660]P1(f331(f68(x76601),x76602))+~P1(f331(f68(x76601),f331(f331(f108(f854(x76601,a840)),x76603),x76602)))
% 51.10/50.82 [7661]P1(f331(f68(x76611),x76612))+~P1(f331(f68(x76611),f331(f331(f108(f854(x76611,a840)),x76612),x76613)))
% 51.10/50.82 [7742]~P42(x77421,x77423)+P1(f331(f331(f333(f853(x77421,x77421)),f331(f331(f249(x77421,x77421),x77422),x77422)),x77423))
% 51.10/50.82 [7792]P1(f331(f331(f287(a1),x77921),x77922))+~P1(f331(f331(f287(a1),x77921),f331(f331(f87(a1),x77922),f331(f331(f88(a1),x77921),x77923))))
% 51.10/50.82 [7872]E(f331(f331(f155(a847),f135(a847,f331(f302(a847,x78721),x78722))),x78723),f331(f331(f87(a847),x78721),x78723))+~P1(f331(f331(f241(a847),f331(f331(f87(a847),x78721),x78723)),x78722))
% 51.10/50.82 [7941]~P1(f331(f331(f191(f331(a29,x79411)),x79412),x79413))+P1(f331(f331(f191(f331(f238(a841),f331(a32,x79411))),x79412),x79413))
% 51.10/50.82 [7942]~P1(f331(f331(f191(f331(a29,x79421)),x79422),x79423))+P1(f331(f331(f191(f331(f238(a841),f331(a32,x79421))),x79422),x79423))
% 51.10/50.82 [7946]E(f331(f331(f164(a847),x79461),f135(a847,f331(f302(a847,x79462),x79463))),f135(a847,f331(f302(a847,x79462),f331(f331(f87(a847),x79462),x79461))))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x79462),x79461)),x79463))
% 51.10/50.82 [7995]~P91(x79951)+E(f331(f331(f250(x79951),x79952),f331(f111(a847),f331(f331(f87(a1),x79953),x79953))),f331(f331(f93(x79951,x79951),f331(f331(f250(x79951),x79952),f331(f111(a847),x79953))),f331(f331(f20(x79951,x79951,x79951),f88(x79951)),f7(x79951))))
% 51.10/50.82 [8195]P1(f331(f331(f191(f331(a29,x81951)),x81952),x81953))+~P1(f331(f331(f191(f331(f238(a841),f331(a32,x81951))),x81952),x81953))
% 51.10/50.82 [8196]P1(f331(f331(f191(f331(a29,x81961)),x81962),x81963))+~P1(f331(f331(f191(f331(f238(a841),f331(a32,x81961))),x81962),x81963))
% 51.10/50.82 [8254]E(f331(f331(f130(x82541),f331(f331(f164(x82541),x82542),x82543)),f331(f331(f145(x82541),f331(f331(f155(x82541),x82543),x82542)),f331(f331(f133(x82541),f331(a119,x82542)),x82543))),x82543)+~P1(f331(f331(f241(a847),x82542),f331(f185(f848(x82541)),x82543)))
% 51.10/50.82 [8261]P1(f331(f331(f240(f854(x82611,a840)),f320(x82611,x82612)),f320(x82611,x82613)))+~P1(f331(f331(f240(f854(x82611,f854(x82611,a840))),x82613),x82612))
% 51.10/50.82 [8262]~P52(x82621,x82622,x82623)+P52(x82621,x82622,f331(f331(f3(f854(f853(x82621,x82621),a840)),x82623),f308(x82621,f184(f854(f853(x82621,x82621),a840)))))
% 51.10/50.82 [8284]P1(f331(f331(f240(f854(x82841,a840)),f321(x82841,x82842)),f321(x82841,x82843)))+~P1(f331(f331(f240(f854(f853(x82841,x82841),a840)),x82843),x82842))
% 51.10/50.82 [8291]~P119(x82911)+P1(f331(f331(f240(x82911),f2(x82911)),f331(f331(f87(x82911),f331(f331(f88(x82911),x82912),x82912)),f331(f331(f88(x82911),x82913),x82913))))
% 51.10/50.82 [8322]~P91(x83221)+E(f331(f331(f250(x83221),f331(f111(x83221),x83222)),f331(f111(a847),f331(f331(f87(a1),x83223),x83223))),f331(f331(f93(x83221,x83221),f331(f331(f250(x83221),f331(f111(x83221),x83222)),f331(f111(a847),x83223))),f331(f331(f20(x83221,x83221,x83221),f88(x83221)),f7(x83221))))
% 51.10/50.82 [8327]P1(f331(f331(f240(f854(x83271,a840)),f331(f284(x83271),x83272)),f331(f284(x83271),x83273)))+~P1(f331(f331(f240(f854(f853(x83271,x83271),a840)),x83272),x83273))
% 51.10/50.82 [8358]~P46(x83581,x83582)+~P1(f331(f331(f333(f853(x83581,x83581)),f331(f331(f249(x83581,x83581),x83583),x83583)),x83582))
% 51.10/50.82 [8359]~P34(x83591,x83592)+~P1(f331(f331(f333(f853(x83591,x83591)),f331(f331(f249(x83591,x83591),x83593),x83593)),x83592))
% 51.10/50.82 [8360]~P34(x83601,x83602)+~P1(f331(f331(f333(f853(x83601,x83601)),f331(f331(f249(x83601,x83601),x83603),x83603)),x83602))
% 51.10/50.82 [8401]~E(x84012,x84013)+P1(f331(f331(f333(f853(x84011,x84011)),f331(f331(f249(x84011,x84011),x84012),x84013)),f308(x84011,f184(f854(f853(x84011,x84011),a840)))))
% 51.10/50.82 [8422]P1(f331(f331(f240(f854(x84221,a840)),f50(f854(x84221,a840),x84222)),f50(f854(x84221,a840),x84223)))+~P1(f331(f331(f240(f854(f854(x84221,a840),a840)),x84223),x84222))
% 51.10/50.82 [8423]P1(f331(f331(f240(f854(x84231,a840)),f49(f854(x84231,a840),x84232)),f49(f854(x84231,a840),x84233)))+~P1(f331(f331(f240(f854(f854(x84231,a840),a840)),x84232),x84233))
% 51.10/50.82 [8475]~P10(x84751,x84753,x84752)+P1(f331(f331(f240(f854(f853(x84751,x84751),a840)),x84752),f331(f331(f256(x84751,x84751),x84753),f331(f18(f854(x84751,a840),x84751),x84753))))
% 51.10/50.82 [8476]~P45(x84761,x84763,x84762)+P1(f331(f331(f240(f854(f853(x84761,x84761),a840)),x84762),f331(f331(f256(x84761,x84761),x84763),f331(f18(f854(x84761,a840),x84761),x84763))))
% 51.10/50.82 [8514]~P78(x85141)+P1(f331(f331(f240(x85141),f331(f331(f3(x85141),f331(f82(x85141),x85142)),f331(f82(x85141),x85143))),f331(f82(x85141),f331(f331(f3(x85141),x85143),x85142))))
% 51.10/50.82 [8515]~P78(x85151)+P1(f331(f331(f240(x85151),f331(f331(f3(x85151),f331(f82(x85151),x85152)),f331(f82(x85151),x85153))),f331(f82(x85151),f331(f331(f3(x85151),x85152),x85153))))
% 51.10/50.82 [8539]P1(f331(f331(f240(f854(f853(x85391,x85391),a840)),f308(x85391,x85392)),f308(x85391,x85393)))+~P1(f331(f331(f240(f854(f853(x85391,x85391),a840)),x85392),x85393))
% 51.10/50.82 [8686]P52(x86861,x86862,x86863)+~P52(x86861,x86862,f331(f331(f3(f854(f853(x86861,x86861),a840)),x86863),f308(x86861,f184(f854(f853(x86861,x86861),a840)))))
% 51.10/50.82 [8705]P1(f331(f331(f240(f854(f853(f848(x87051),f848(x87051)),a840)),f151(x87051,x87052)),f151(x87051,x87053)))+~P1(f331(f331(f240(f854(f853(x87051,x87051),a840)),x87052),x87053))
% 51.10/50.82 [8706]P1(f331(f331(f240(f854(f853(f848(x87061),f848(x87061)),a840)),f150(x87061,x87062)),f150(x87061,x87063)))+~P1(f331(f331(f240(f854(f853(x87061,x87061),a840)),x87062),x87063))
% 51.10/50.82 [8723]~P45(x87231,x87233,x87232)+P1(f331(f331(f240(f854(f853(x87231,x87231),a840)),x87232),f331(f331(f289(x87231,x87231,x87231),f331(f286(x87231,x87231),x87232)),x87232)))
% 51.10/50.82 [8764]~P1(f331(f132(x87641),x87642))+E(f331(f131(x87641,f331(f331(f9(x87641,f854(x87641,a840),a840),f333(x87641)),f331(f163(x87641),f165(x87641,x87642,x87643)))),x87642),f165(x87641,x87642,x87643))
% 51.10/50.82 [8810]E(x88101,x88102)+~P1(f331(f331(f333(f853(x88103,x88103)),f331(f331(f249(x88103,x88103),x88101),x88102)),f308(x88103,f184(f854(f853(x88103,x88103),a840)))))
% 51.10/50.82 [8890]P1(f331(f331(f333(x88901),x88902),f321(x88901,x88903)))+P1(f331(f331(f333(f853(x88901,x88901)),f331(f331(f249(x88901,x88901),f366(x88903,x88902,x88901)),x88902)),x88903))
% 51.10/50.82 [8891]P1(f331(f331(f333(x88911),x88912),f321(x88911,x88913)))+P1(f331(f331(f333(f853(x88911,x88911)),f331(f331(f249(x88911,x88911),f618(x88913,x88912,x88911)),x88912)),x88913))
% 51.10/50.82 [8892]P1(f331(f331(f333(x88921),x88922),f321(x88921,x88923)))+P1(f331(f331(f333(f853(x88921,x88921)),f331(f331(f249(x88921,x88921),f620(x88923,x88922,x88921)),x88922)),x88923))
% 51.10/50.82 [8993]P1(f331(x89933,x89932))+E(f331(f264(x89931),f331(f331(f20(x89931,a840,a840),f331(f331(f10(a840,f854(a840,a840),x89931),a329),f331(a328,x89932))),x89933)),f184(f854(x89931,a840)))
% 51.10/50.82 [9013]~P78(x90131)+P1(f331(f331(f240(x90131),f331(f82(x90131),f331(f331(f3(x90131),f331(f82(x90131),x90132)),f331(f82(x90131),x90133)))),f331(f82(x90131),f331(f331(f3(x90131),x90132),x90133))))
% 51.10/50.82 [9026]~P1(f331(x90263,x90262))+E(f331(f264(x90261),f331(f331(f20(x90261,a840,a840),f331(f331(f10(a840,f854(a840,a840),x90261),a329),f331(a328,x90262))),x90263)),f331(f331(f310(x90261),x90262),f184(f854(x90261,a840))))
% 51.10/50.82 [9032]~P1(f331(f331(f333(f854(x90321,a840)),x90323),f331(f309(x90321),x90322)))+P1(f331(f253(x90321,f331(f331(f9(x90321,f854(x90321,a840),a840),f333(x90321)),x90322)),x90323))
% 51.10/50.82 [9066]P34(x90661,x90662)+P1(f331(f331(f333(f853(x90661,x90661)),f331(f331(f249(x90661,x90661),f331(f574(x90662,x90661),f331(a119,x90663))),f331(f574(x90662,x90661),x90663))),x90662))
% 51.10/50.82 [9191]P1(f331(f331(f333(f854(x91911,a840)),x91912),f331(f309(x91911),x91913)))+~P1(f331(f253(x91911,f331(f331(f9(x91911,f854(x91911,a840),a840),f333(x91911)),x91913)),x91912))
% 51.10/50.82 [9252]P1(f331(f331(f333(x92521),f331(f273(x92521,x92522),x92523)),f331(f163(x92521),f331(f331(f147(f853(a106,x92521),x92521),f258(a106,x92521)),x92522))))+~P1(f331(f331(f241(a106),x92523),f331(f157(a106),f331(f331(f147(f853(a106,x92521),a106),f248(a106,x92521)),x92522))))
% 51.10/50.82 [9300]P1(f331(f331(f240(f854(f853(f848(x93001),f848(x93001)),a840)),f151(x93001,x93002)),f331(f331(f256(f848(x93001),f848(x93001)),f153(x93001,x93003)),f331(f18(f854(f848(x93001),a840),f848(x93001)),f153(x93001,x93003)))))+~P1(f331(f331(f240(f854(f853(x93001,x93001),a840)),x93002),f331(f331(f256(x93001,x93001),x93003),f331(f18(f854(x93001,a840),x93001),x93003))))
% 51.10/50.82 [9320]P1(f331(f331(f333(x93201),f331(f248(x93201,f853(a106,a106)),f331(f271(x93201,x93202),x93203))),f331(f163(x93201),f331(f331(f147(f853(a106,x93201),x93201),f258(a106,x93201)),x93202))))+~P1(f331(f331(f241(a106),f2(a106)),f331(f157(a106),f331(f331(f147(f853(a106,x93201),a106),f248(a106,x93201)),x93202))))
% 51.10/50.82 [9335]~P1(f331(f331(f240(f854(f853(x93351,x93351),a840)),x93352),f331(f331(f256(x93351,x93351),x93353),f331(f18(f854(x93351,a840),x93351),x93353))))+P1(f331(f331(f240(f854(f853(x93351,x93351),a840)),f331(f331(f289(x93351,x93351,x93351),x93352),f308(x93351,x93352))),f331(f331(f256(x93351,x93351),x93353),f331(f18(f854(x93351,a840),x93351),x93353))))
% 51.10/50.82 [9628]~P34(x96281,x96282)+~P1(f331(f331(f333(f853(x96281,x96281)),f331(f331(f249(x96281,x96281),f331(x96283,f331(a119,f575(x96282,x96281,x96283)))),f331(x96283,f575(x96282,x96281,x96283)))),x96282))
% 51.10/50.82 [9629]~P34(x96291,x96292)+~P1(f331(f331(f333(f853(x96291,x96291)),f331(f331(f249(x96291,x96291),f331(x96293,f331(a119,f631(x96293,x96292,x96291)))),f331(x96293,f631(x96293,x96292,x96291)))),x96292))
% 51.10/50.82 [9889]P1(f331(f331(f240(f854(f853(f854(x98891,a840),f854(x98891,a840)),a840)),f331(f331(f289(f854(x98891,a840),f854(x98891,a840),f854(x98891,a840)),f325(x98891,x98892)),f331(f331(f108(f854(f853(f854(x98891,a840),f854(x98891,a840)),a840)),f325(x98891,x98893)),f331(f331(f310(f853(f854(x98891,a840),f854(x98891,a840))),f331(f331(f249(f854(x98891,a840),f854(x98891,a840)),f184(f854(x98891,a840))),f184(f854(x98891,a840)))),f184(f854(f853(f854(x98891,a840),f854(x98891,a840)),a840)))))),f325(x98891,x98892)))+~P1(f331(f331(f240(f854(f853(x98891,x98891),a840)),f331(f331(f289(x98891,x98891,x98891),x98892),x98893)),x98892))
% 51.10/50.82 [9890]P1(f331(f331(f240(f854(f853(f854(x98901,a840),f854(x98901,a840)),a840)),f331(f331(f289(f854(x98901,a840),f854(x98901,a840),f854(x98901,a840)),f323(x98901,x98902)),f331(f331(f108(f854(f853(f854(x98901,a840),f854(x98901,a840)),a840)),f323(x98901,x98903)),f331(f331(f310(f853(f854(x98901,a840),f854(x98901,a840))),f331(f331(f249(f854(x98901,a840),f854(x98901,a840)),f184(f854(x98901,a840))),f184(f854(x98901,a840)))),f184(f854(f853(f854(x98901,a840),f854(x98901,a840)),a840)))))),f323(x98901,x98902)))+~P1(f331(f331(f240(f854(f853(x98901,x98901),a840)),f331(f331(f289(x98901,x98901,x98901),x98902),x98903)),x98902))
% 51.10/50.82 [7149]~P1(f331(f331(f240(a847),x71492),x71491))+E(f331(f331(f3(a847),f331(a119,f331(f331(f3(a847),x71491),x71492))),x71493),f331(f331(f3(a847),f331(a119,x71491)),f331(f331(f87(a847),x71492),x71493)))
% 51.10/50.82 [7189]~P5(x71891)+E(f331(f331(f87(x71891),f57(x71891,x71892,x71893)),f331(f331(f88(x71891),f331(f331(f48(x71891),x71892),x71893)),x71893)),x71892)
% 51.10/50.82 [7409]E(f331(f331(f88(a847),f331(f111(a847),x74091)),f331(f331(f88(a847),f331(f111(a847),x74092)),x74093)),f331(f331(f88(a847),f331(f111(a847),f331(f331(f88(a1),x74091),x74092))),x74093))+P1(f331(f331(f241(a1),x74091),a90))
% 51.10/50.82 [7883]~P1(f331(f331(f240(a847),x78833),x78832))+P1(f331(f331(f240(a847),x78831),f331(f331(f3(a847),f331(f331(f87(a847),x78832),x78831)),x78833)))
% 51.10/50.82 [8078]~P1(f331(f331(f240(a847),x80781),x80782))+E(f331(f331(f130(a847),f135(a847,f331(f302(a847,x80781),x80782))),f135(a847,f331(f302(a847,x80782),f331(f331(f87(a847),x80782),x80783)))),f135(a847,f331(f302(a847,x80781),f331(f331(f87(a847),x80782),x80783))))
% 51.10/50.82 [8335]~P1(f331(f68(x83351),x83352))+E(f331(a119,f331(f47(x83351),f331(f331(f3(f854(x83351,a840)),x83352),f331(f331(f310(x83351),x83353),f184(f854(x83351,a840)))))),f331(f47(x83351),f331(f331(f310(x83351),x83353),x83352)))
% 51.10/50.82 [8379]~P1(f331(f68(x83791),x83792))+E(f331(f331(f87(a847),f85(a847)),f331(f47(x83791),f331(f331(f3(f854(x83791,a840)),x83792),f331(f331(f310(x83791),x83793),f184(f854(x83791,a840)))))),f331(f47(x83791),f331(f331(f310(x83791),x83793),x83792)))
% 51.10/50.82 [8548]E(f331(f331(f3(a847),f331(f47(x85481),x85482)),f331(f47(x85481),f331(f331(f109(f854(x85481,a840)),x85482),x85483))),f331(f47(x85481),f331(f331(f3(f854(x85481,a840)),x85482),x85483)))+~P1(f331(f68(x85481),f331(f331(f109(f854(x85481,a840)),x85482),x85483)))
% 51.10/50.82 [8761]~P8(f331(x87612,f397(x87612,x87613,x87611)))+E(f331(f107(a1),f331(f331(f11(x87611,a847),f331(f331(f10(a1,a847,x87611),a112),x87612)),x87613)),f331(f331(f11(x87611,a1),x87612),x87613))
% 51.10/50.82 [8762]~P8(f331(x87622,f503(x87622,x87623,x87621)))+E(f331(f107(a1),f331(f331(f8(x87621,a847),f331(f331(f10(a1,a847,x87621),a112),x87622)),x87623)),f331(f331(f8(x87621,a1),x87622),x87623))
% 51.10/50.82 [8794]~P1(f331(f68(x87941),x87943))+P1(f331(f331(f240(a847),f331(f331(f3(a847),f331(f47(x87941),x87942)),f331(f47(x87941),x87943))),f331(f47(x87941),f331(f331(f3(f854(x87941,a840)),x87942),x87943))))
% 51.10/50.82 [8818]P1(f331(f331(f333(x88181),f397(x88182,x88183,x88181)),x88183))+E(f331(f107(a1),f331(f331(f11(x88181,a847),f331(f331(f10(a1,a847,x88181),a112),x88182)),x88183)),f331(f331(f11(x88181,a1),x88182),x88183))
% 51.10/50.82 [8819]P1(f331(f331(f333(x88191),f503(x88192,x88193,x88191)),x88193))+E(f331(f107(a1),f331(f331(f8(x88191,a847),f331(f331(f10(a1,a847,x88191),a112),x88192)),x88193)),f331(f331(f8(x88191,a1),x88192),x88193))
% 51.10/50.82 [8884]E(f92(x88841,f331(f331(f9(x88841,f854(x88841,a840),a840),f333(x88841)),f331(f331(f3(f854(x88841,a840)),x88842),f331(f331(f310(x88841),x88843),f184(f854(x88841,a840)))))),f252(x88841,x88843,x88842))+P1(f331(f331(f240(f854(x88841,a840)),x88842),f331(f331(f310(x88841),x88843),f184(f854(x88841,a840)))))
% 51.10/50.82 [9192]E(f331(f331(f147(f848(x91921),x91921),f331(f331(f9(f848(x91921),a847,x91921),f155(x91921)),x91922)),f331(f131(f848(x91921),f331(f331(f10(a847,a840,f848(x91921)),f331(f241(a847),x91922)),f185(f848(x91921)))),x91923)),f331(f331(f155(f848(x91921)),f169(x91921,x91923)),x91922))+~P1(f331(f331(f241(a847),x91922),f331(f185(f848(f848(x91921))),f169(x91921,x91923))))
% 51.10/50.82 [9497]~P1(f331(f331(f333(f853(x94971,x94971)),x94972),f308(x94971,x94973)))+P1(f331(f331(f333(f853(x94971,x94971)),x94972),f331(f331(f51(a847,f854(f853(x94971,x94971),a840)),f247(f854(a847,a840))),f331(f331(f9(a847,f854(f853(x94971,x94971),a840),f854(f853(x94971,x94971),a840)),f178(f853(x94971,x94971),a840)),x94973))))
% 51.10/50.82 [9553]~P1(f331(f331(f240(f854(x95531,a840)),f331(f331(f51(a847,f854(x95531,a840)),f331(f302(a847,f2(a847)),f519(x95533,x95532,x95531))),x95532)),x95533))+P1(f331(f331(f240(f854(x95531,a840)),f331(f331(f51(a847,f854(x95531,a840)),f247(f854(a847,a840))),x95532)),x95533))
% 51.10/50.82 [9605]~P1(f331(f331(f241(a1),f2(a1)),x96053))+P1(f331(f331(f241(a1),x96051),f331(f331(f87(a1),x96052),f331(f331(f88(a1),f331(f331(f87(a1),f331(f82(a1),f331(f331(f3(a1),x96052),x96051))),f85(a1))),x96053))))
% 51.10/50.82 [9615]~P34(x96151,f331(f331(f108(f854(f853(x96151,x96151),a840)),x96152),x96153))+P34(x96151,f331(f331(f108(f854(f853(x96151,x96151),a840)),f331(f331(f108(f854(f853(x96151,x96151),a840)),f331(f331(f289(x96151,x96151,x96151),x96152),x96152)),f331(f331(f289(x96151,x96151,x96151),x96153),x96152))),x96153))
% 51.10/50.82 [9681]P34(x96811,f331(f331(f108(f854(f853(x96811,x96811),a840)),x96812),x96813))+~P34(x96811,f331(f331(f108(f854(f853(x96811,x96811),a840)),f331(f331(f108(f854(f853(x96811,x96811),a840)),f331(f331(f289(x96811,x96811,x96811),x96812),x96812)),f331(f331(f289(x96811,x96811,x96811),x96813),x96812))),x96813))
% 51.10/50.82 [9274]~P133(x92741)+E(f331(f110(x92741),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x92742),x92743)),f184(f854(f853(a847,a847),a840)))))),f331(f331(f3(x92741),f331(f107(x92741),x92742)),f331(f107(x92741),x92743)))
% 51.10/50.82 [9353]P1(f331(x93533,x93532))+E(f331(f264(x93531),f331(f331(f20(x93531,a840,a840),f331(f331(f10(a840,f854(a840,a840),x93531),a329),f331(f331(f9(x93531,x93531,a840),a328),x93532))),x93533)),f184(f854(x93531,a840)))
% 51.10/50.82 [9355]~P1(f331(x93553,x93552))+E(f331(f264(x93551),f331(f331(f20(x93551,a840,a840),f331(f331(f10(a840,f854(a840,a840),x93551),a329),f331(f331(f9(x93551,x93551,a840),a328),x93552))),x93553)),f331(f331(f310(x93551),x93552),f184(f854(x93551,a840))))
% 51.10/50.82 [9673]~P1(f331(f68(x96731),x96733))+E(f331(f331(f71(x96731,f854(x96731,a840),f331(f331(f10(f854(x96731,a840),f854(f854(x96731,a840),f854(x96731,a840)),x96731),f331(f9(f854(x96731,a840),f854(x96731,a840),f854(x96731,a840)),f3(f854(x96731,a840)))),f331(f331(f9(x96731,f854(x96731,a840),f854(x96731,a840)),f310(x96731)),f184(f854(x96731,a840))))),x96732),x96733),f331(f331(f3(f854(x96731,a840)),x96732),x96733))
% 51.10/50.82 [9707]~P1(f331(f331(f241(a1),f2(a1)),x97073))+P1(f331(f331(f241(a1),f331(f331(f3(a1),x97071),f331(f331(f88(a1),f331(f331(f87(a1),f331(f82(a1),f331(f331(f3(a1),x97071),x97072))),f85(a1))),x97073))),x97072))
% 51.10/50.82 [9959]~P1(f331(f331(f333(x99591),x99593),f321(x99591,x99592)))+P1(f331(f320(x99591,f331(f331(f9(x99591,f854(f853(x99591,x99591),a840),f854(x99591,a840)),f331(f331(f10(f854(x99591,f854(f854(f853(x99591,x99591),a840),a840)),f854(f854(f853(x99591,x99591),a840),f854(x99591,a840)),x99591),f9(x99591,f854(f853(x99591,x99591),a840),a840)),f331(f331(f10(f854(x99591,f853(x99591,x99591)),f854(x99591,f854(f854(f853(x99591,x99591),a840),a840)),x99591),f331(f10(f853(x99591,x99591),f854(f854(f853(x99591,x99591),a840),a840),x99591),f333(f853(x99591,x99591)))),f249(x99591,x99591)))),x99592)),x99593))
% 51.10/50.82 [9971]P1(f331(f331(f333(x99711),x99712),f321(x99711,x99713)))+~P1(f331(f320(x99711,f331(f331(f9(x99711,f854(f853(x99711,x99711),a840),f854(x99711,a840)),f331(f331(f10(f854(x99711,f854(f854(f853(x99711,x99711),a840),a840)),f854(f854(f853(x99711,x99711),a840),f854(x99711,a840)),x99711),f9(x99711,f854(f853(x99711,x99711),a840),a840)),f331(f331(f10(f854(x99711,f853(x99711,x99711)),f854(x99711,f854(f854(f853(x99711,x99711),a840),a840)),x99711),f331(f10(f853(x99711,x99711),f854(f854(f853(x99711,x99711),a840),a840),x99711),f333(f853(x99711,x99711)))),f249(x99711,x99711)))),x99713)),x99712))
% 51.10/50.82 [9551]~P1(f331(f68(x95511),f331(f264(x95511),x95513)))+P1(f331(f68(x95511),f331(f264(x95511),f331(f331(f20(x95511,a840,a840),f331(f331(f10(a840,f854(a840,a840),x95511),a329),x95512)),x95513))))
% 51.10/50.82 [9552]~P1(f331(f68(x95521),f331(f264(x95521),x95522)))+P1(f331(f68(x95521),f331(f264(x95521),f331(f331(f20(x95521,a840,a840),f331(f331(f10(a840,f854(a840,a840),x95521),a329),x95522)),x95523))))
% 51.10/50.82 [9640]P1(f331(f68(x96401),f331(f264(x96401),x96402)))+~P1(f331(f68(x96401),f331(f264(x96401),f331(f331(f20(x96401,a840,a840),f331(f331(f10(a840,f854(a840,a840),x96401),a330),x96403)),x96402))))
% 51.10/50.82 [9641]P1(f331(f68(x96411),f331(f264(x96411),x96412)))+~P1(f331(f68(x96411),f331(f264(x96411),f331(f331(f20(x96411,a840,a840),f331(f331(f10(a840,f854(a840,a840),x96411),a330),x96412)),x96413))))
% 51.10/50.82 [9944]~P1(f331(f68(x99441),x99442))+P1(f331(f68(f848(x99441)),f331(f264(f848(x99441)),f331(f331(f20(f848(x99441),a840,a840),f331(f331(f10(a840,f854(a840,a840),f848(x99441)),a329),f331(f331(f9(f848(x99441),f854(x99441,a840),a840),f331(f331(f10(f854(x99441,a840),f854(f854(x99441,a840),a840),f848(x99441)),f240(f854(x99441,a840))),f163(x99441))),x99442))),f331(f331(f9(f848(x99441),a847,a840),f331(f331(f10(a847,f854(a847,a840),f848(x99441)),a328),f185(f848(x99441)))),x99443)))))
% 51.10/50.82 [9945]~P1(f331(f68(x99451),x99452))+P1(f331(f68(f848(x99451)),f331(f264(f848(x99451)),f331(f331(f20(f848(x99451),a840,a840),f331(f331(f10(a840,f854(a840,a840),f848(x99451)),a329),f331(f331(f9(f848(x99451),f854(x99451,a840),a840),f331(f331(f10(f854(x99451,a840),f854(f854(x99451,a840),a840),f848(x99451)),f240(f854(x99451,a840))),f163(x99451))),x99452))),f331(f331(f9(f848(x99451),a847,a840),f331(f331(f10(a847,f854(a847,a840),f848(x99451)),f240(a847)),f185(f848(x99451)))),x99453)))))
% 51.10/50.82 [9654]~P87(x96541)+E(f331(f331(f250(x96541),x96542),f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x96543)),f331(f331(f88(x96541),f331(f331(f250(x96541),x96542),x96543)),f331(f331(f250(x96541),x96542),x96543)))
% 51.10/50.82 [9686]~P74(x96861)+E(f331(f331(f250(x96861),f331(f331(f250(x96861),x96862),x96863)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f250(x96861),x96862),f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x96863)))
% 51.10/50.82 [9747]~P133(x97471)+E(f331(f331(f250(x97471),f331(f86(x97471),x97472)),f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97473)),f331(f331(f250(x97471),x97472),f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97473)))
% 51.10/50.82 [9894]~P86(x98941)+P1(f331(f331(f240(x98941),f2(x98941)),f331(f331(f87(x98941),f331(f331(f250(x98941),x98942),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x98941),x98943),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))))
% 51.10/50.82 [9757]~P87(x97571)+E(f331(f331(f250(x97571),x97572),f331(a119,f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97573))),f331(f331(f88(x97571),x97572),f331(f331(f88(x97571),f331(f331(f250(x97571),x97572),x97573)),f331(f331(f250(x97571),x97572),x97573))))
% 51.10/50.82 [9809]~P74(x98091)+E(f331(f331(f88(x98091),x98092),f331(f331(f250(x98091),f331(f331(f250(x98091),x98092),x98093)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x98091),x98092),f331(a119,f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98093))))
% 51.10/50.82 [9854]~P86(x98541)+P1(f331(f331(f240(x98541),f2(x98541)),f331(f331(f250(x98541),x98542),f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x98543))))
% 51.10/50.82 [9923]~P91(x99231)+E(f331(f331(f87(x99231),f331(f331(f87(x99231),f331(f331(f250(x99231),x99232),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x99231),x99233),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f331(f331(f88(x99231),f331(f331(f88(x99231),f331(f111(x99231),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x99232)),x99233)),f331(f331(f250(x99231),f331(f331(f87(x99231),x99232),x99233)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9924]~P91(x99241)+E(f331(f331(f3(x99241),f331(f331(f87(x99241),f331(f331(f250(x99241),x99242),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x99241),x99243),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f331(f331(f88(x99241),f331(f331(f88(x99241),f331(f111(x99241),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x99242)),x99243)),f331(f331(f250(x99241),f331(f331(f3(x99241),x99242),x99243)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [4549]E(x45491,x45492)+~E(f30(x45493,x45491),f30(x45494,x45492))
% 51.10/50.82 [4550]E(x45501,x45502)+~E(f30(x45501,x45503),f30(x45502,x45504))
% 51.10/50.82 [4551]E(x45511,x45512)+~E(f38(x45513,x45511),f38(x45514,x45512))
% 51.10/50.82 [4552]E(x45521,x45522)+~E(f38(x45521,x45523),f38(x45522,x45524))
% 51.10/50.82 [4553]E(x45531,x45532)+~E(f37(x45533,x45531),f37(x45534,x45532))
% 51.10/50.82 [4554]E(x45541,x45542)+~E(f37(x45541,x45543),f37(x45542,x45544))
% 51.10/50.82 [5674]P37(f37(x56741,x56743),x56742,x56744,x56742)+P1(f331(x56741,x56742))
% 51.10/50.82 [5675]P37(f37(x56751,x56753),x56752,x56754,x56752)+P1(f331(x56751,x56752))
% 51.10/50.82 [6836]~P37(x68361,x68362,x68363,x68364)+P37(x68361,x68362,f331(a119,x68363),x68364)
% 51.10/50.82 [7680]P27(x76801,x76802,x76803,x76804)+~E(f444(x76804,x76803,x76802,x76801),f446(x76804,x76803,x76802,x76801))
% 51.10/50.82 [8181]~P27(x81811,f851(x81812),x81814,f174(x81811,x81812,x81814))+P27(x81811,f851(x81812),f175(x81811,x81812,x81813,x81814),f174(x81811,x81812,x81814))
% 51.10/50.82 [8395]~P27(x83951,f851(x83952),f175(x83951,x83952,x83954,x83953),f174(x83951,x83952,x83953))+P27(x83951,f851(x83952),x83953,f174(x83951,x83952,x83953))
% 51.10/50.82 [4919]~P19(x49193,x49191,x49194)+E(f331(f331(x49191,x49192),x49192),x49192)
% 51.10/50.82 [5197]~E(x51974,f184(f854(x51971,a840)))+E(f331(f311(x51971,x51972,x51973),x51974),f184(f854(x51972,a840)))
% 51.10/50.82 [5198]~E(x51984,f184(f854(x51981,a840)))+E(f331(f311(x51981,x51982,x51983),x51984),f184(f854(x51982,a840)))
% 51.10/50.82 [5462]~E(f331(f311(x54622,x54623,x54624),x54621),f184(f854(x54623,a840)))+E(x54621,f184(f854(x54622,a840)))
% 51.10/50.82 [5463]~E(f331(f311(x54632,x54633,x54634),x54631),f184(f854(x54633,a840)))+E(x54631,f184(f854(x54632,a840)))
% 51.10/50.82 [5757]~P102(x57572)+E(f331(f331(f143(x57571,x57572,x57573),x57574),f120(x57571)),f331(f331(f145(x57571),x57574),f120(x57571)))
% 51.10/50.82 [5792]E(f331(x57921,x57922),f187(x57923))+P1(f331(f331(f333(x57924),x57922),f174(x57924,x57923,x57921)))
% 51.10/50.82 [6118]~E(x61181,f184(f854(x61182,a840)))+~P1(f331(f69(x61182,x61183,x61181),x61184))
% 51.10/50.82 [6139]~P55(x61391,x61393,x61394,x61392)+P1(f331(f68(x61391),x61392))
% 51.10/50.82 [6140]~P55(x61401,x61403,x61402,x61404)+P1(f331(f68(x61401),x61402))
% 51.10/50.82 [6147]~P55(x61472,x61473,x61474,x61471)+~E(x61471,f184(f854(x61472,a840)))
% 51.10/50.82 [6179]~P88(x61791)+E(f331(f331(f109(f854(x61791,a840)),f331(f302(x61791,x61792),x61793)),f303(x61791,x61793,x61794)),f184(f854(x61791,a840)))
% 51.10/50.82 [6208]~P1(f331(f331(x62083,x62084),x62082))+P1(f331(f331(f333(x62081),x62082),f295(x62081,x62083,x62084)))
% 51.10/50.82 [6209]~P1(f331(f331(x62093,x62094),x62092))+P1(f331(f331(f333(x62091),x62092),f294(x62091,x62093,x62094)))
% 51.10/50.82 [6210]~P1(f331(f331(x62103,x62102),x62104))+P1(f331(f331(f333(x62101),x62102),f298(x62101,x62103,x62104)))
% 51.10/50.82 [6211]~P1(f331(f331(x62113,x62112),x62114))+P1(f331(f331(f333(x62111),x62112),f296(x62111,x62113,x62114)))
% 51.10/50.82 [6362]~P88(x63621)+E(f331(f331(f109(f854(x63621,a840)),f306(x63621,x63622,x63623)),f303(x63621,x63623,x63624)),f184(f854(x63621,a840)))
% 51.10/50.82 [6363]~P88(x63631)+E(f331(f331(f109(f854(x63631,a840)),f305(x63631,x63632,x63633)),f306(x63631,x63633,x63634)),f184(f854(x63631,a840)))
% 51.10/50.82 [6364]~P88(x63641)+E(f331(f331(f109(f854(x63641,a840)),f305(x63641,x63642,x63643)),f305(x63641,x63643,x63644)),f184(f854(x63641,a840)))
% 51.10/50.82 [6365]~P88(x63651)+E(f331(f331(f109(f854(x63651,a840)),f303(x63651,x63652,x63653)),f306(x63651,x63653,x63654)),f184(f854(x63651,a840)))
% 51.10/50.82 [6366]~P88(x63661)+E(f331(f331(f109(f854(x63661,a840)),f303(x63661,x63662,x63663)),f305(x63661,x63663,x63664)),f184(f854(x63661,a840)))
% 51.10/50.82 [6404]P1(f331(f331(x64041,x64042),f582(x64042,x64041)))+~P1(f331(f254(x64043,x64044,x64041),x64042))
% 51.10/50.82 [6457]~E(f331(x64571,x64572),f187(x64573))+~P1(f331(f331(f333(x64574),x64572),f174(x64574,x64573,x64571)))
% 51.10/50.82 [6539]~P84(x65391)+E(f186(x65391,x65392,f331(a119,x65393),x65394),f186(x65391,x65392,x65393,f331(x65392,x65394)))
% 51.10/50.82 [6602]~P1(f331(f331(f333(x66024),x66023),f295(x66024,x66021,x66022)))+P1(f331(f331(x66021,x66022),x66023))
% 51.10/50.82 [6603]~P1(f331(f331(f333(x66034),x66033),f294(x66034,x66031,x66032)))+P1(f331(f331(x66031,x66032),x66033))
% 51.10/50.82 [6604]~P1(f331(f331(f333(x66044),x66042),f298(x66044,x66041,x66043)))+P1(f331(f331(x66041,x66042),x66043))
% 51.10/50.82 [6605]~P1(f331(f331(f333(x66054),x66052),f296(x66054,x66051,x66053)))+P1(f331(f331(x66051,x66052),x66053))
% 51.10/50.82 [6687]E(f331(f47(f855(x66871,x66872)),f319(x66871,x66872,x66873,x66874)),f2(a847))+P1(f331(f68(x66872),x66874))
% 51.10/50.82 [6688]E(f331(f47(f855(x66881,x66882)),f319(x66881,x66882,x66883,x66884)),f2(a847))+P1(f331(f68(x66881),x66883))
% 51.10/50.82 [6898]~P17(x68984,x68981,x68982)+E(f331(f80(x68981,x68981,x68981,f331(x68982,x68983)),f331(x68982,x68983)),f331(x68982,x68983))
% 51.10/50.82 [7136]E(f280(x71361,x71362,x71363,x71364),f331(f249(f854(a106,f854(a840,f851(f849(x71361)))),f853(a106,a106)),f53(x71361)))+~P1(f331(f331(f240(a106),x71363),f2(a106)))
% 51.10/50.82 [7200]~P37(f331(a29,x72001),x72002,f331(a119,x72003),x72004)+P37(f331(f238(a841),f331(a32,x72001)),x72002,x72003,x72004)
% 51.10/50.82 [7236]P37(f331(a29,x72361),x72362,f331(a119,x72363),x72364)+~P37(f331(f238(a841),f331(a32,x72361)),x72362,x72363,x72364)
% 51.10/50.82 [7237]P37(f331(a29,x72371),x72372,f331(a119,x72373),x72374)+~P37(f331(f238(a841),f331(a32,x72371)),x72372,x72373,x72374)
% 51.10/50.82 [7538]~P37(f331(a29,x75384),x75383,x75382,x75381)+E(f331(a119,f781(x75381,x75382,x75383,x75384)),x75382)
% 51.10/50.82 [7808]~E(x78082,x78083)+P1(f331(f331(f333(f853(x78081,x78081)),f331(f331(f249(x78081,x78081),x78082),x78083)),f308(x78081,x78084)))
% 51.10/50.82 [7834]~P27(x78341,x78342,x78343,f247(f854(x78341,a840)))+E(f331(f84(x78341,x78342,f247(f854(x78341,a840)),x78343),f331(x78343,x78344)),x78344)
% 51.10/50.82 [7926]~P1(f331(f331(f333(f848(x79261)),f331(f331(f145(x79261),x79264),x79262)),f153(x79261,x79263)))+P1(f331(f331(f333(f848(x79261)),x79262),f153(x79261,x79263)))
% 51.10/50.82 [7927]~P1(f331(f331(f333(f848(x79271)),f331(f331(f130(x79271),x79274),x79272)),f153(x79271,x79273)))+P1(f331(f331(f333(f848(x79271)),x79272),f153(x79271,x79273)))
% 51.10/50.82 [7928]~P1(f331(f331(f333(f848(x79281)),f331(f331(f130(x79281),x79282),x79284)),f153(x79281,x79283)))+P1(f331(f331(f333(f848(x79281)),x79282),f153(x79281,x79283)))
% 51.10/50.82 [8002]~P37(f331(a29,x80021),x80022,x80024,x80023)+P37(f331(f238(a841),f331(a32,x80021)),x80022,f781(x80023,x80024,x80022,x80021),x80023)
% 51.10/50.82 [8039]P27(x80394,x80393,x80391,x80392)+E(f331(x80391,f444(x80392,x80391,x80393,x80394)),f331(x80391,f446(x80392,x80391,x80393,x80394)))
% 51.10/50.82 [8048]E(f175(x80481,x80482,x80483,x80484),f175(x80481,x80482,x80484,x80483))+~E(f331(f331(f109(f854(x80481,a840)),f174(x80481,x80482,x80483)),f174(x80481,x80482,x80484)),f184(f854(x80481,a840)))
% 51.10/50.82 [8145]~P27(x81452,x81451,x81454,x81453)+P27(x81451,x81452,f84(x81452,x81451,x81453,x81454),f331(f311(x81452,x81451,x81454),x81453))
% 51.10/50.82 [8282]P34(f853(x82822,x82824),f283(x82822,x82824,x82821,x82823))+P1(f331(x82821,f573(x82822,x82823,x82824,x82821)))
% 51.10/50.82 [8402]E(x84021,x84022)+~P1(f331(f331(f333(f853(x84023,x84023)),f331(f331(f249(x84023,x84023),x84021),x84022)),f268(x84023,x84024)))
% 51.10/50.82 [8465]~P1(f331(f68(f855(x84653,x84651)),f319(x84653,x84651,x84654,x84652)))+P1(f331(f68(x84651),x84652))
% 51.10/50.82 [8466]~P1(f331(f68(f855(x84661,x84663)),f319(x84661,x84663,x84662,x84664)))+P1(f331(f68(x84661),x84662))
% 51.10/50.82 [8467]~P1(f331(f68(f855(x84673,x84671)),f319(x84673,x84671,x84674,x84672)))+P1(f331(f68(x84671),x84672))
% 51.10/50.82 [8468]~P1(f331(f68(f855(x84681,x84683)),f319(x84681,x84683,x84682,x84684)))+P1(f331(f68(x84681),x84682))
% 51.10/50.82 [8630]P34(f853(x86301,x86302),f283(x86301,x86302,x86303,x86304))+~P34(x86302,f331(x86304,f573(x86301,x86304,x86302,x86303)))
% 51.10/50.82 [9126]E(f331(f331(f152(x91261,x91262),f736(x91263,x91264,x91262,x91261)),f737(x91263,x91264,x91262,x91261)),x91264)+~P1(f331(f331(f333(f853(f848(x91261),f848(x91261))),f331(f331(f249(f848(x91261),f848(x91261)),x91262),x91264)),f150(x91261,x91263)))
% 51.10/50.82 [9130]~P1(f331(f331(f333(f853(f848(x91301),f848(x91301))),f331(f331(f249(f848(x91301),f848(x91301)),x91302),x91303)),f140(x91301,x91304)))+P1(f331(f331(f333(f853(f848(x91301),f848(x91301))),f331(f331(f249(f848(x91301),f848(x91301)),x91302),x91303)),f142(x91301,x91304)))
% 51.10/50.82 [9227]P1(f331(f68(x92271),x92272))+~P1(f331(f331(f333(f853(f854(x92271,a840),f854(x92271,a840))),f331(f331(f249(f854(x92271,a840),f854(x92271,a840)),x92273),x92272)),f323(x92271,x92274)))
% 51.10/50.82 [9228]P1(f331(f68(x92281),x92282))+~P1(f331(f331(f333(f853(f854(x92281,a840),f854(x92281,a840))),f331(f331(f249(f854(x92281,a840),f854(x92281,a840)),x92282),x92283)),f323(x92281,x92284)))
% 51.10/50.82 [9231]~E(x92311,f184(f854(x92312,a840)))+~P1(f331(f331(f333(f853(f854(x92312,a840),f854(x92312,a840))),f331(f331(f249(f854(x92312,a840),f854(x92312,a840)),x92313),x92311)),f323(x92312,x92314)))
% 51.10/50.82 [9865]P14(x98651,x98652,x98653,x98654)+~P1(f331(f331(f259(x98651,x98651,a840),f331(f331(f9(x98651,f854(x98651,x98652),f854(x98651,a840)),f331(f331(f10(f854(x98652,a840),f854(f854(x98651,x98652),f854(x98651,a840)),x98651),f10(x98652,a840,x98651)),f331(f331(f10(x98652,f854(x98652,a840),x98651),a328),x98654))),x98654)),f589(x98654,x98653,x98652,x98651)))
% 51.10/50.82 [4821]~E(x48214,f120(x48211))+E(f331(f331(f147(x48211,x48212),x48213),x48214),f120(x48212))
% 51.10/50.82 [4822]~E(x48224,f120(x48221))+E(f331(f331(f147(x48221,x48222),x48223),x48224),f120(x48222))
% 51.10/50.82 [4823]~E(x48234,f187(x48231))+E(f331(f331(f203(x48231,x48232),x48233),x48234),f187(x48232))
% 51.10/50.82 [4824]~E(x48242,f120(x48241))+E(f331(f331(f152(x48241,x48242),x48243),x48244),f120(x48241))
% 51.10/50.82 [5057]E(x50571,f120(x50572))+~E(f331(f331(f147(x50572,x50573),x50574),x50571),f120(x50573))
% 51.10/50.82 [5058]E(x50581,f187(x50582))+~E(f331(f331(f203(x50582,x50583),x50584),x50581),f187(x50583))
% 51.10/50.82 [5059]E(x50591,f120(x50592))+~E(f331(f331(f147(x50592,x50593),x50594),x50591),f120(x50593))
% 51.10/50.82 [5060]E(x50601,f120(x50602))+~E(f331(f331(f152(x50602,x50601),x50603),x50604),f120(x50602))
% 51.10/50.82 [5090]E(x50901,x50902)+~E(f331(f331(f130(x50903),x50904),x50901),f331(f331(f130(x50903),x50904),x50902))
% 51.10/50.82 [5091]E(x50911,x50912)+~E(f331(f331(f130(x50913),x50911),x50914),f331(f331(f130(x50913),x50912),x50914))
% 51.10/50.82 [5233]P1(f331(x52333,x52332))+E(f161(x52331,x52332,f331(f131(x52331,x52333),x52334)),f331(f131(x52331,x52333),x52334))
% 51.10/50.82 [5244]E(x52441,x52442)+~E(f135(a847,f331(f302(a847,x52441),x52443)),f331(f331(f145(a847),x52442),x52444))
% 51.10/50.82 [5291]~P28(x52912,x52913)+P28(x52911,f331(f331(f81(x52912,x52911),x52913),x52914))
% 51.10/50.82 [5292]~P34(x52922,x52923)+P34(x52921,f331(f331(f288(x52922,x52921),x52923),x52924))
% 51.10/50.82 [5504]~E(x55041,f120(x55042))+~E(f331(f331(f130(x55042),x55043),f331(f331(f145(x55042),x55044),f120(x55042))),x55041)
% 51.10/50.82 [5538]E(f139(x55381,x55382),x55383)+~E(f331(f331(f130(x55381),x55384),f331(f331(f145(x55381),x55383),f120(x55381))),x55382)
% 51.10/50.82 [5539]E(f121(x55391,x55392),x55393)+~E(f331(f331(f130(x55391),x55393),f331(f331(f145(x55391),x55394),f120(x55391))),x55392)
% 51.10/50.82 [5647]~E(f135(a847,f331(f302(a847,x56471),x56472)),f331(f331(f145(a847),x56473),x56474))+P1(f331(f331(f241(a847),x56471),x56472))
% 51.10/50.82 [5746]~E(f331(f111(a847),x57464),f2(a847))+E(f331(f331(f155(x57461),f331(f331(f145(x57461),x57462),x57463)),f331(f111(a847),x57464)),x57462)
% 51.10/50.82 [5855]E(x58551,f331(f331(f130(x58552),f331(f160(x58552),x58553)),f331(f331(f145(x58552),x58554),f120(x58552))))+~E(f331(f160(x58552),x58551),f331(f331(f145(x58552),x58554),x58553))
% 51.10/50.82 [6039]~P88(x60391)+E(f331(f331(f109(f854(x60391,a840)),f331(f302(x60391,x60392),x60393)),f331(f302(x60391,x60393),x60394)),f184(f854(x60391,a840)))
% 51.10/50.82 [6075]~P68(x60751)+E(f331(f157(x60751),f331(f331(f147(a1,x60751),x60752),f168(x60753,x60754))),f331(f331(f8(a1,x60751),x60752),f331(f163(a1),f168(x60753,x60754))))
% 51.10/50.82 [6076]~P68(x60761)+E(f331(f331(f8(a1,x60761),x60762),f331(f163(a1),f168(x60763,x60764))),f331(f157(x60761),f331(f331(f147(a1,x60761),x60762),f168(x60763,x60764))))
% 51.10/50.82 [6223]~E(x62232,f331(f331(f130(x62231),f331(f160(x62231),x62234)),f331(f331(f145(x62231),x62233),f120(x62231))))+E(f331(f160(x62231),x62232),f331(f331(f145(x62231),x62233),x62234))
% 51.10/50.82 [6239]~P21(x62392,x62393,x62394,x62391)+E(f331(x62391,f184(f854(x62392,a840))),f39(x62393))
% 51.10/50.82 [6268]~P88(x62681)+E(f331(f331(f109(f854(x62681,a840)),f306(x62681,x62682,x62683)),f331(f302(x62681,x62683),x62684)),f184(f854(x62681,a840)))
% 51.10/50.82 [6354]~P37(x63541,x63542,x63544,x63543)+P1(f331(f331(f191(x63541),x63542),x63543))
% 51.10/50.82 [6355]~P37(x63551,x63552,x63554,x63553)+P1(f331(f331(f191(x63551),x63552),x63553))
% 51.10/50.82 [6488]E(x64881,f184(f854(x64882,a840)))+~E(f319(x64883,x64882,x64884,x64881),f184(f854(f855(x64883,x64882),a840)))
% 51.10/50.82 [6489]E(x64891,f184(f854(x64892,a840)))+~E(f319(x64892,x64893,x64891,x64894),f184(f854(f855(x64892,x64893),a840)))
% 51.10/50.82 [6568]~P1(f331(f255(x65683,x65684,x65681),x65682))+P1(f331(f331(x65681,f580(x65682,x65681)),x65682))
% 51.10/50.82 [6598]E(f331(f111(a847),x65981),f2(a847))+E(f331(f331(f155(x65982),f331(f331(f145(x65982),x65983),x65984)),f331(f111(a847),x65981)),f331(f331(f155(x65982),x65984),f331(f331(f3(a847),f331(f111(a847),x65981)),f85(a847))))
% 51.10/50.82 [6616]~P1(f331(f68(x66162),x66164))+P1(f331(f68(x66161),f331(f311(x66162,x66161,x66163),x66164)))
% 51.10/50.82 [6857]~P27(x68572,x68571,x68573,x68574)+E(f331(f47(x68571),f331(f311(x68572,x68571,x68573),x68574)),f331(f47(x68572),x68574))
% 51.10/50.82 [6877]E(f331(f311(x68771,x68772,x68773),f331(f312(x68771,x68772,x68773),x68774)),x68774)+~E(f331(f311(x68771,x68772,x68773),f247(f854(x68771,a840))),f247(f854(x68772,a840)))
% 51.10/50.82 [7301]~P27(x73011,x73012,x73013,f247(f854(x73011,a840)))+E(f331(f312(x73011,x73012,x73013),f331(f311(x73011,x73012,x73013),x73014)),x73014)
% 51.10/50.82 [7642]P1(f331(x76421,x76422))+~P1(f331(f331(f333(x76423),x76422),f331(f163(x76423),f167(x76423,x76421,x76424))))
% 51.10/50.82 [7752]~P1(f331(f331(f333(f848(x77521)),f331(f331(f145(x77521),x77522),x77524)),f153(x77521,x77523)))+P1(f331(f331(f333(x77521),x77522),x77523))
% 51.10/50.82 [7879]~P1(f331(f331(f333(x78791),x78792),f331(f163(x78791),f161(x78791,x78794,x78793))))+P1(f331(f331(f333(x78791),x78792),f331(f163(x78791),x78793)))
% 51.10/50.82 [7880]~P1(f331(f331(f333(x78801),x78802),f331(f163(x78801),f165(x78801,x78803,x78804))))+P1(f331(f331(f333(x78801),x78802),f331(f163(x78801),x78803)))
% 51.10/50.82 [7881]~P1(f331(f331(f333(x78811),x78812),f331(f163(x78811),f165(x78811,x78813,x78814))))+P1(f331(f331(f333(x78811),x78812),f331(f163(x78811),x78813)))
% 51.10/50.82 [7882]~P1(f331(f331(f333(x78821),x78822),f331(f163(x78821),f167(x78821,x78824,x78823))))+P1(f331(f331(f333(x78821),x78822),f331(f163(x78821),x78823)))
% 51.10/50.82 [8095]E(f331(f331(f155(x80951),f167(x80951,x80952,x80953)),x80954),f331(f331(f155(x80951),x80953),x80954))+~P1(f331(f331(f241(a847),x80954),f331(f185(f848(x80951)),f167(x80951,x80952,x80953))))
% 51.10/50.82 [8179]~P68(x81791)+E(f331(f331(f8(a847,x81791),f331(f331(f10(a847,x81791,a847),x81792),a119)),f331(f302(a847,x81793),x81794)),f331(f331(f8(a847,x81791),x81792),f331(f302(a847,f331(a119,x81793)),f331(a119,x81794))))
% 51.10/50.82 [8188]~P68(x81881)+E(f331(f331(f8(a847,x81881),f331(f331(f10(a847,x81881,a847),x81882),a119)),f303(a847,x81883,x81884)),f331(f331(f8(a847,x81881),x81882),f303(a847,f331(a119,x81883),f331(a119,x81884))))
% 51.10/50.82 [8320]~P27(x83201,x83203,x83204,f247(f854(x83201,a840)))+P27(x83201,f854(x83202,x83203),f331(f331(f10(x83203,f854(x83202,x83203),x83201),f18(x83203,x83202)),x83204),f247(f854(x83201,a840)))
% 51.10/50.82 [8411]~P27(x84112,x84111,x84114,x84113)+E(f331(f311(x84111,x84112,f84(x84112,x84111,x84113,x84114)),f331(f311(x84112,x84111,x84114),x84113)),x84113)
% 51.10/50.82 [8469]~P1(f331(f331(f333(f853(x84691,x84691)),f331(f331(f249(x84691,x84691),x84692),x84694)),f268(x84691,x84693)))+P1(f331(f331(f333(x84691),x84692),x84693))
% 51.10/50.82 [8544]E(f331(f331(f331(f79(x85441,f851(x85442)),f331(f18(f851(x85442),x85441),f187(x85442))),x85443),f331(f234(x85442),f514(x85443,x85444,x85442,x85441))),x85444)+~E(f174(x85441,x85442,x85444),f331(f331(f310(x85441),x85443),f184(f854(x85441,a840))))
% 51.10/50.82 [8663]~E(f331(f331(f8(x86631,a847),x86634),x86633),f331(a119,x86632))+P1(f331(f331(f333(x86631),f605(x86632,x86633,x86634,x86631)),x86633))
% 51.10/50.82 [8679]~E(f331(f331(f8(x86794,a847),x86791),x86793),f331(a119,x86792))+P1(f331(f331(f241(a847),f2(a847)),f331(x86791,f605(x86792,x86793,x86791,x86794))))
% 51.10/50.82 [8689]~P1(f331(f68(x86892),x86894))+P1(f331(f331(f240(a847),f331(f47(x86891),f331(f311(x86892,x86891,x86893),x86894))),f331(f47(x86892),x86894)))
% 51.10/50.82 [8690]E(f331(f331(f249(x86901,x86902),f703(x86903,x86904,x86902,x86901)),f704(x86903,x86904,x86902,x86901)),x86904)+~P1(f331(f331(f333(f853(x86901,x86902)),x86904),f331(f286(x86902,x86901),x86903)))
% 51.10/50.82 [8699]P27(x86991,x86992,x86993,x86994)+P1(f331(f331(f333(x86991),f444(x86994,x86993,x86992,x86991)),x86994))
% 51.10/50.82 [8700]P27(x87001,x87002,x87003,x87004)+P1(f331(f331(f333(x87001),f446(x87004,x87003,x87002,x87001)),x87004))
% 51.10/50.82 [8753]P14(x87531,x87532,x87533,x87534)+P1(f331(f331(f333(f853(x87531,x87531)),f589(x87534,x87533,x87532,x87531)),x87533))
% 51.10/50.82 [8800]P1(f331(x88001,x88002))+~P1(f331(x88001,f331(f331(f249(x88003,x88004),f822(x88004,x88003,x88001)),f823(x88004,x88003,x88001))))
% 51.10/50.82 [8813]E(f331(f185(f848(x88131)),x88132),f331(f185(f848(x88131)),x88133))+~P1(f331(f331(f333(f853(f848(x88131),f848(x88131))),f331(f331(f249(f848(x88131),f848(x88131)),x88132),x88133)),f140(x88131,x88134)))
% 51.10/50.82 [8814]E(f331(f185(f848(x88141)),x88142),f331(f185(f848(x88141)),x88143))+~P1(f331(f331(f333(f853(f848(x88141),f848(x88141))),f331(f331(f249(f848(x88141),f848(x88141)),x88142),x88143)),f151(x88141,x88144)))
% 51.10/50.82 [8815]E(f331(f185(f848(x88151)),x88152),f331(f185(f848(x88151)),x88153))+~P1(f331(f331(f333(f853(f848(x88151),f848(x88151))),f331(f331(f249(f848(x88151),f848(x88151)),x88152),x88153)),f151(x88151,x88154)))
% 51.10/50.82 [8816]E(f331(f185(f848(x88161)),x88162),f331(f185(f848(x88161)),x88163))+~P1(f331(f331(f333(f853(f848(x88161),f848(x88161))),f331(f331(f249(f848(x88161),f848(x88161)),x88162),x88163)),f151(x88161,x88164)))
% 51.10/50.82 [8817]E(f331(f185(f848(x88171)),x88172),f331(f185(f848(x88171)),x88173))+~P1(f331(f331(f333(f853(f848(x88171),f848(x88171))),f331(f331(f249(f848(x88171),f848(x88171)),x88172),x88173)),f150(x88171,x88174)))
% 51.10/50.82 [8888]P1(f331(f331(f240(a847),f148(x88881,x88882,x88883)),f148(x88881,x88884,x88883)))+P1(f331(f331(f333(x88881),f758(x88884,x88882,x88883,x88881)),f331(f163(x88881),x88883)))
% 51.10/50.82 [8889]E(f331(f185(f848(x88891)),x88892),f331(f185(f848(x88891)),x88893))+~P1(f331(f331(f333(f853(f848(x88891),f848(x88891))),f331(f331(f249(f848(x88891),f848(x88891)),x88892),x88893)),f308(f848(x88891),f150(x88891,x88894))))
% 51.10/50.82 [8998]P1(f331(f331(f287(a847),x89981),x89982))+P1(f331(f331(f240(f854(a847,a840)),f290(a847,f287(a847),x89981,x89982)),f290(a847,f287(a847),x89983,x89984)))
% 51.10/50.82 [9106]~P27(x91061,x91062,x91063,x91064)+~P1(f331(f331(f241(a847),f331(f47(x91062),f331(f311(x91061,x91062,x91063),x91064))),f331(f47(x91061),x91064)))
% 51.10/50.82 [9136]~P1(f331(f331(f333(f853(f848(x91361),f848(x91361))),f331(f331(f249(f848(x91361),f848(x91361)),x91362),x91363)),f150(x91361,x91364)))+P1(f331(f331(f333(f853(f848(x91361),f848(x91361))),f331(f331(f249(f848(x91361),f848(x91361)),x91362),x91363)),f151(x91361,f308(x91361,x91364))))
% 51.10/50.82 [9139]~P1(f331(f331(f333(f853(f848(x91391),f848(x91391))),f331(f331(f249(f848(x91391),f848(x91391)),x91392),x91393)),f151(x91391,x91394)))+P1(f331(f331(f333(f853(f848(x91391),f848(x91391))),f331(f331(f249(f848(x91391),f848(x91391)),x91392),x91393)),f308(f848(x91391),f150(x91391,x91394))))
% 51.10/50.82 [9154]P1(f331(f331(f333(f853(x91541,x91541)),f331(f331(f249(x91541,x91541),x91542),x91543)),f308(x91541,x91544)))+~P1(f331(f331(f333(f853(x91541,x91541)),f331(f331(f249(x91541,x91541),x91542),x91543)),f331(f331(f289(x91541,x91541,x91541),x91544),f308(x91541,x91544))))
% 51.10/50.82 [9223]P1(f331(f331(f287(a847),x92231),x92232))+~P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x92233,x92234)),f290(a847,f287(a847),x92231,x92232)))
% 51.10/50.82 [9336]E(f331(f331(f130(x93361),f741(x93362,x93363,x93364,x93361)),f331(f331(f145(x93361),f742(x93362,x93363,x93364,x93361)),f744(x93362,x93363,x93364,x93361))),x93364)+~P1(f331(f331(f333(f853(f848(x93361),f848(x93361))),f331(f331(f249(f848(x93361),f848(x93361)),x93364),x93363)),f150(x93361,x93362)))
% 51.10/50.82 [9337]E(f331(f331(f130(x93371),f741(x93372,x93373,x93374,x93371)),f331(f331(f145(x93371),f743(x93372,x93373,x93374,x93371)),f744(x93372,x93373,x93374,x93371))),x93373)+~P1(f331(f331(f333(f853(f848(x93371),f848(x93371))),f331(f331(f249(f848(x93371),f848(x93371)),x93374),x93373)),f150(x93371,x93372)))
% 51.10/50.82 [9412]P1(f331(f331(f333(f853(x94121,x94121)),f331(f331(f249(x94121,x94121),x94122),f679(x94123,x94124,x94122,x94121))),f308(x94121,x94123)))+~P1(f331(f331(f333(f853(x94121,x94121)),f331(f331(f249(x94121,x94121),x94122),x94124)),f331(f331(f289(x94121,x94121,x94121),x94123),f308(x94121,x94123))))
% 51.10/50.82 [9480]P1(f331(f331(f240(a847),f148(x94801,x94802,x94803)),f148(x94801,x94804,x94803)))+~P1(f331(f331(f241(a847),f331(x94802,f758(x94804,x94802,x94803,x94801))),f331(x94804,f758(x94804,x94802,x94803,x94801))))
% 51.10/50.82 [9548]P1(f331(f331(f333(f853(x95481,x95481)),f331(f331(f249(x95481,x95481),f678(x95482,x95483,x95484,x95481)),x95483)),f308(x95481,x95482)))+~P1(f331(f331(f333(f853(x95481,x95481)),f331(f331(f249(x95481,x95481),x95484),x95483)),f331(f331(f289(x95481,x95481,x95481),x95482),f308(x95481,x95482))))
% 51.10/50.82 [5071]~E(x50712,x50713)+E(f161(x50711,x50712,f331(f331(f145(x50711),x50713),x50714)),x50714)
% 51.10/50.82 [5084]~E(x50842,f2(a847))+E(f331(f331(f164(x50841),x50842),f331(f331(f145(x50841),x50843),x50844)),f120(x50841))
% 51.10/50.82 [5190]P1(f331(x51902,x51903))+E(f167(x51901,x51902,f331(f331(f145(x51901),x51903),x51904)),f120(x51901))
% 51.10/50.82 [5255]~P83(x52552)+E(f331(f331(f86(f854(x52551,x52552)),x52553),x52554),f331(f86(x52552),f331(x52553,x52554)))
% 51.10/50.82 [5256]~P83(x52562)+E(f331(f331(f86(f854(x52561,x52562)),x52563),x52564),f331(f86(x52562),f331(x52563,x52564)))
% 51.10/50.82 [5268]~E(x52682,f2(a847))+E(f331(f331(f133(x52681),x52682),f331(f331(f145(x52681),x52683),x52684)),f331(f331(f145(x52681),x52683),x52684))
% 51.10/50.82 [5269]P1(f331(x52692,x52693))+E(f331(f131(x52691,x52692),f331(f331(f145(x52691),x52693),x52694)),f331(f131(x52691,x52692),x52694))
% 51.10/50.82 [5402]~E(x54022,x54024)+P1(f331(f331(f331(f310(x54021),x54022),x54023),x54024))
% 51.10/50.82 [5409]P1(f331(x54092,x54093))+E(f134(x54091,x54092,f331(f331(f145(x54091),x54093),x54094)),f331(f331(f145(x54091),x54093),x54094))
% 51.10/50.82 [5411]E(x54111,f120(x54112))+E(f139(x54113,f331(f331(f147(x54112,x54113),x54114),x54111)),f331(x54114,f139(x54112,x54111)))
% 51.10/50.82 [5422]~E(x54221,f70(x54222,x54224))+E(f331(x54221,f331(f331(f310(x54222),x54223),f184(f854(x54222,a840)))),x54223)
% 51.10/50.82 [5437]~E(f331(f111(a847),x54372),f2(a847))+E(f331(f331(f164(x54371),f331(f111(a847),x54372)),f331(f331(f145(x54371),x54373),x54374)),f120(x54371))
% 51.10/50.82 [5457]~P1(f331(x54572,x54573))+E(f134(x54571,x54572,f331(f331(f145(x54571),x54573),x54574)),f134(x54571,x54572,x54574))
% 51.10/50.82 [5458]E(x54581,f120(x54582))+E(f331(f136(x54583),f331(f331(f147(x54582,x54583),x54584),x54581)),f331(x54584,f331(f136(x54582),x54581)))
% 51.10/50.82 [5557]~P1(f331(x55573,x55574))+P1(f331(f331(f331(f310(x55571),x55572),x55573),x55574))
% 51.10/50.82 [5664]~E(f331(f111(a847),x56642),f2(a847))+E(f331(f331(f133(x56641),f331(f111(a847),x56642)),f331(f331(f145(x56641),x56643),x56644)),f331(f331(f145(x56641),x56643),x56644))
% 51.10/50.82 [5682]~P20(x56822,x56824,x56821)+E(f331(x56821,f331(f331(f310(x56822),x56823),f184(f854(x56822,a840)))),x56823)
% 51.10/50.82 [5706]~E(x57062,x57063)+P1(f331(f331(f333(x57061),x57062),f331(f331(f310(x57061),x57063),x57064)))
% 51.10/50.82 [5707]~E(x57072,x57073)+P1(f331(f331(f333(x57071),x57072),f331(f331(f310(x57071),x57073),x57074)))
% 51.10/50.82 [5711]~P87(x57111)+E(f331(f331(f87(x57111),x57112),f331(f331(f87(x57111),x57113),x57114)),f331(f331(f87(x57111),x57113),f331(f331(f87(x57111),x57112),x57114)))
% 51.10/50.82 [5712]~P87(x57121)+E(f331(f331(f88(x57121),x57122),f331(f331(f88(x57121),x57123),x57124)),f331(f331(f88(x57121),x57123),f331(f331(f88(x57121),x57122),x57124)))
% 51.10/50.82 [5713]~P102(x57131)+E(f331(f331(f244(x57131),x57132),f331(f331(f244(x57131),x57133),x57134)),f331(f331(f244(x57131),x57133),f331(f331(f244(x57131),x57132),x57134)))
% 51.10/50.82 [5714]~P102(x57141)+E(f331(f331(f244(x57141),x57142),f331(f331(f244(x57141),x57143),x57144)),f331(f331(f244(x57141),x57143),f331(f331(f244(x57141),x57142),x57144)))
% 51.10/50.82 [5715]~P102(x57151)+E(f331(f331(f239(x57151),x57152),f331(f331(f239(x57151),x57153),x57154)),f331(f331(f239(x57151),x57153),f331(f331(f239(x57151),x57152),x57154)))
% 51.10/50.82 [5716]~P102(x57161)+E(f331(f331(f239(x57161),x57162),f331(f331(f239(x57161),x57163),x57164)),f331(f331(f239(x57161),x57163),f331(f331(f239(x57161),x57162),x57164)))
% 51.10/50.82 [5717]~P97(x57171)+E(f331(f331(f108(x57171),x57172),f331(f331(f108(x57171),x57173),x57174)),f331(f331(f108(x57171),x57173),f331(f331(f108(x57171),x57172),x57174)))
% 51.10/50.82 [5718]~P100(x57181)+E(f331(f331(f108(x57181),x57182),f331(f331(f108(x57181),x57183),x57184)),f331(f331(f108(x57181),x57183),f331(f331(f108(x57181),x57182),x57184)))
% 51.10/50.82 [5719]~P100(x57191)+E(f331(f331(f108(x57191),x57192),f331(f331(f108(x57191),x57193),x57194)),f331(f331(f108(x57191),x57193),f331(f331(f108(x57191),x57192),x57194)))
% 51.10/50.82 [5720]~P97(x57201)+E(f331(f331(f109(x57201),x57202),f331(f331(f109(x57201),x57203),x57204)),f331(f331(f109(x57201),x57203),f331(f331(f109(x57201),x57202),x57204)))
% 51.10/50.82 [5721]~P101(x57211)+E(f331(f331(f109(x57211),x57212),f331(f331(f109(x57211),x57213),x57214)),f331(f331(f109(x57211),x57213),f331(f331(f109(x57211),x57212),x57214)))
% 51.10/50.82 [5722]~P101(x57221)+E(f331(f331(f109(x57221),x57222),f331(f331(f109(x57221),x57223),x57224)),f331(f331(f109(x57221),x57223),f331(f331(f109(x57221),x57222),x57224)))
% 51.10/50.82 [5729]E(x57291,x57292)+E(f161(x57293,x57291,f331(f331(f145(x57293),x57292),x57294)),f331(f331(f145(x57293),x57292),f161(x57293,x57291,x57294)))
% 51.10/50.82 [5744]~P1(f331(x57442,x57443))+E(f331(f131(x57441,x57442),f331(f331(f145(x57441),x57443),x57444)),f331(f331(f145(x57441),x57443),f331(f131(x57441,x57442),x57444)))
% 51.10/50.82 [5831]~E(x58314,f184(f854(x58311,a840)))+E(f331(f311(x58311,x58312,f331(f18(x58312,x58311),x58313)),x58314),f184(f854(x58312,a840)))
% 51.10/50.82 [5876]~P1(f331(x58762,x58763))+E(f167(x58761,x58762,f331(f331(f145(x58761),x58763),x58764)),f331(f331(f145(x58761),x58763),f167(x58761,x58762,x58764)))
% 51.10/50.82 [5929]P26(x59291,x59292,x59293)+~P26(x59291,x59292,f331(f331(f310(f846(x59291)),x59294),x59293))
% 51.10/50.82 [5942]E(x59421,f184(f854(x59422,a840)))+E(f331(f331(f51(x59422,f854(x59423,a840)),x59421),f331(f18(f854(x59423,a840),x59422),x59424)),x59424)
% 51.10/50.82 [5943]E(x59431,f184(f854(x59432,a840)))+E(f331(f331(f52(x59432,f854(x59433,a840)),x59431),f331(f18(f854(x59433,a840),x59432),x59434)),x59434)
% 51.10/50.82 [5952]~E(x59524,f184(f854(x59522,a840)))+E(f331(f331(f256(x59521,x59522),x59523),f331(f18(f854(x59522,a840),x59521),x59524)),f184(f854(f853(x59521,x59522),a840)))
% 51.10/50.82 [5953]~E(x59533,f184(f854(x59531,a840)))+E(f331(f331(f256(x59531,x59532),x59533),f331(f18(f854(x59532,a840),x59531),x59534)),f184(f854(f853(x59531,x59532),a840)))
% 51.10/50.82 [6004]E(x60041,f2(a847))+E(f331(f331(f133(x60042),x60041),f331(f331(f145(x60042),x60043),x60044)),f331(f331(f133(x60042),f331(f331(f3(a847),x60041),f85(a847))),x60044))
% 51.10/50.82 [6031]E(x60311,f184(f854(x60312,a840)))+E(f331(f311(x60312,x60313,f331(f18(x60313,x60312),x60314)),x60311),f331(f331(f310(x60313),x60314),f184(f854(x60313,a840))))
% 51.10/50.82 [6034]E(f331(f312(x60341,x60342,f331(f18(x60342,x60341),x60343)),x60344),f184(f854(x60341,a840)))+P1(f331(f331(f333(x60342),x60343),x60344))
% 51.10/50.82 [6102]~E(x61023,f184(f854(x61021,a840)))+E(f331(f331(f51(x61021,f854(x61022,a840)),x61023),f331(f18(f854(x61022,a840),x61021),x61024)),f184(f854(x61022,a840)))
% 51.10/50.82 [6103]~E(x61033,f184(f854(x61031,a840)))+E(f331(f331(f52(x61031,f854(x61032,a840)),x61033),f331(f18(f854(x61032,a840),x61031),x61034)),f247(f854(x61032,a840)))
% 51.10/50.82 [6105]~P5(x61051)+E(f57(x61051,f331(f331(f88(x61051),x61052),x61053),f331(f331(f88(x61051),x61052),x61054)),f331(f331(f88(x61051),x61052),f57(x61051,x61053,x61054)))
% 51.10/50.82 [6278]E(f331(f312(x62781,x62782,f331(f18(x62782,x62781),x62783)),x62784),f247(f854(x62781,a840)))+~P1(f331(f331(f333(x62782),x62783),x62784))
% 51.10/50.82 [6299]~P1(f331(f331(f333(x62991),x62992),x62994))+P1(f331(f331(f333(x62991),x62992),f331(f331(f310(x62991),x62993),x62994)))
% 51.10/50.82 [6300]~P1(f331(f331(f333(x63001),x63002),x63004))+P1(f331(f331(f333(x63001),x63002),f331(f331(f310(x63001),x63003),x63004)))
% 51.10/50.82 [6301]~P1(f331(f331(f333(x63011),x63012),x63014))+P1(f331(f331(f333(x63011),x63012),f331(f331(f310(x63011),x63013),x63014)))
% 51.10/50.82 [6314]~E(x63143,f331(f331(f3(a847),f331(f185(f848(x63141)),x63142)),f85(a847)))+E(f121(x63141,f331(f331(f152(x63141,x63142),x63143),x63144)),f121(x63141,x63142))
% 51.10/50.82 [6339]~P102(x63391)+E(f331(f331(f109(f854(x63391,a840)),f331(f301(x63391),x63392)),f303(x63391,x63393,x63394)),f303(x63391,x63393,f331(f331(f244(x63391),x63392),x63394)))
% 51.10/50.82 [6340]~P102(x63401)+E(f331(f331(f109(f854(x63401,a840)),f331(f266(x63401),x63402)),f303(x63401,x63403,x63404)),f303(x63401,f331(f331(f239(x63401),x63402),x63403),x63404))
% 51.10/50.82 [6356]E(f331(f331(f109(f854(x63561,a840)),x63562),f331(f331(f310(x63561),x63563),x63564)),f331(f331(f109(f854(x63561,a840)),x63562),x63564))+P1(f331(f331(f333(x63561),x63563),x63562))
% 51.10/50.82 [6357]E(f331(f331(f109(f854(x63571,a840)),x63572),f331(f331(f310(x63571),x63573),x63574)),f331(f331(f109(f854(x63571,a840)),x63572),x63574))+P1(f331(f331(f333(x63571),x63573),x63572))
% 51.10/50.82 [6369]E(f161(x63691,x63692,f331(f331(f130(x63691),x63693),x63694)),f331(f331(f130(x63691),x63693),f161(x63691,x63692,x63694)))+P1(f331(f331(f333(x63691),x63692),f331(f163(x63691),x63693)))
% 51.10/50.82 [6374]~P74(x63741)+E(f331(f331(f88(x63741),f331(f331(f250(x63741),x63742),x63743)),f331(f331(f250(x63741),x63742),x63744)),f331(f331(f250(x63741),x63742),f331(f331(f87(a847),x63743),x63744)))
% 51.10/50.82 [6375]~P87(x63751)+E(f331(f331(f88(x63751),f331(f331(f250(x63751),x63752),x63753)),f331(f331(f250(x63751),x63752),x63754)),f331(f331(f250(x63751),x63752),f331(f331(f87(a847),x63753),x63754)))
% 51.10/50.82 [6411]~P87(x64111)+E(f331(f331(f87(x64111),f331(f331(f88(x64111),x64112),x64113)),f331(f331(f88(x64111),x64112),x64114)),f331(f331(f88(x64111),x64112),f331(f331(f87(x64111),x64113),x64114)))
% 51.10/50.82 [6412]~P102(x64121)+E(f331(f331(f239(x64121),f331(f331(f244(x64121),x64122),x64123)),f331(f331(f244(x64121),x64122),x64124)),f331(f331(f244(x64121),x64122),f331(f331(f239(x64121),x64123),x64124)))
% 51.10/50.82 [6413]~P102(x64131)+E(f331(f331(f244(x64131),f331(f331(f239(x64131),x64132),x64133)),f331(f331(f239(x64131),x64132),x64134)),f331(f331(f239(x64131),x64132),f331(f331(f244(x64131),x64133),x64134)))
% 51.10/50.82 [6414]~P98(x64141)+E(f331(f331(f109(x64141),f331(f331(f108(x64141),x64142),x64143)),f331(f331(f108(x64141),x64142),x64144)),f331(f331(f108(x64141),x64142),f331(f331(f109(x64141),x64143),x64144)))
% 51.10/50.82 [6415]~P98(x64151)+E(f331(f331(f108(x64151),f331(f331(f109(x64151),x64152),x64153)),f331(f331(f109(x64151),x64152),x64154)),f331(f331(f109(x64151),x64152),f331(f331(f108(x64151),x64153),x64154)))
% 51.10/50.82 [6451]~P5(x64511)+E(f57(x64511,f331(f331(f88(x64511),x64512),x64513),f331(f331(f88(x64511),x64514),x64513)),f331(f331(f88(x64511),f57(x64511,x64512,x64514)),x64513))
% 51.10/50.82 [6454]~E(f331(f185(f848(x64541)),x64543),f331(f185(f848(x64542)),x64544))+E(f331(f331(f147(f853(x64541,x64542),x64542),f258(x64541,x64542)),f331(f331(f172(x64541,x64542),x64543),x64544)),x64544)
% 51.10/50.82 [6455]~E(f331(f185(f848(x64551)),x64553),f331(f185(f848(x64552)),x64554))+E(f331(f331(f147(f853(x64551,x64552),x64551),f248(x64551,x64552)),f331(f331(f172(x64551,x64552),x64553),x64554)),x64553)
% 51.10/50.82 [6465]~P5(x64651)+E(f57(x64651,f331(f331(f87(x64651),x64652),f57(x64651,x64653,x64654)),x64654),f57(x64651,f331(f331(f87(x64651),x64652),x64653),x64654))
% 51.10/50.82 [6466]~P5(x64661)+E(f57(x64661,f331(f331(f88(x64661),x64662),f57(x64661,x64663,x64664)),x64664),f57(x64661,f331(f331(f88(x64661),x64662),x64663),x64664))
% 51.10/50.82 [6467]~P6(x64671)+E(f57(x64671,f331(f331(f3(x64671),x64672),f57(x64671,x64673,x64674)),x64674),f57(x64671,f331(f331(f3(x64671),x64672),x64673),x64674))
% 51.10/50.82 [6468]~P5(x64681)+E(f57(x64681,f331(f331(f87(x64681),x64682),f57(x64681,x64683,x64684)),x64684),f57(x64681,f331(f331(f87(x64681),x64682),x64683),x64684))
% 51.10/50.82 [6551]~P102(x65511)+E(f331(f331(f109(f854(x65511,a840)),f303(x65511,x65512,x65513)),f331(f301(x65511),x65514)),f303(x65511,x65512,f331(f331(f244(x65511),x65513),x65514)))
% 51.10/50.82 [6552]~P102(x65521)+E(f331(f331(f109(f854(x65521,a840)),f303(x65521,x65522,x65523)),f331(f266(x65521),x65524)),f303(x65521,f331(f331(f239(x65521),x65522),x65524),x65523))
% 51.10/50.82 [6555]~E(f331(f185(f848(x65551)),x65553),f331(f185(f848(x65552)),x65554))+E(f331(f331(f172(x65551,x65552),f331(f160(x65551),x65553)),f331(f160(x65552),x65554)),f331(f160(f853(x65551,x65552)),f331(f331(f172(x65551,x65552),x65553),x65554)))
% 51.10/50.82 [6564]E(x65641,f331(f331(f3(a847),f331(f185(f848(x65642)),x65643)),f85(a847)))+E(f121(x65642,f331(f331(f152(x65642,x65643),x65641),x65644)),f331(f331(f152(x65642,f121(x65642,x65643)),x65641),x65644))
% 51.10/50.82 [6581]~P1(f331(f132(x65812),x65814))+P1(f331(f132(f853(x65811,x65812)),f331(f331(f172(x65811,x65812),x65813),x65814)))
% 51.10/50.82 [6582]~P1(f331(f132(x65821),x65823))+P1(f331(f132(f853(x65821,x65822)),f331(f331(f172(x65821,x65822),x65823),x65824)))
% 51.10/50.82 [6680]E(x66801,f331(f331(f331(a193,x66802),x66803),f331(x66804,x66802)))+~P1(f331(f331(f191(f30(x66803,x66804)),x66802),x66801))
% 51.10/50.82 [6860]E(f331(f331(f48(a847),x68601),x68602),x68603)+~P1(f331(f60(x68601,x68602),f331(f331(f249(a847,a847),x68603),x68604)))
% 51.10/50.82 [6886]E(f57(a847,x68861,x68862),x68863)+~P1(f331(f60(x68861,x68862),f331(f331(f249(a847,a847),x68864),x68863)))
% 51.10/50.82 [6889]P1(f331(f132(x68891),x68892))+~P1(f331(f132(x68893),f331(f331(f147(x68891,x68893),x68894),x68892)))
% 51.10/50.82 [6897]~P26(x68971,x68972,f331(f331(f310(f846(x68971)),x68973),x68974))+P26(x68971,x68972,f331(f331(f310(f846(x68971)),x68973),f184(f854(f846(x68971),a840))))
% 51.10/50.82 [6969]E(f161(x69691,x69692,f331(f331(f130(x69691),x69693),x69694)),f331(f331(f130(x69691),f161(x69691,x69692,x69693)),x69694))+~P1(f331(f331(f333(x69691),x69692),f331(f163(x69691),x69693)))
% 51.10/50.82 [7037]E(f331(f111(a847),x70371),f2(a847))+E(f331(f331(f133(x70372),f331(f111(a847),x70371)),f331(f331(f145(x70372),x70373),x70374)),f331(f331(f133(x70372),f331(f331(f3(a847),f331(f111(a847),x70371)),f85(a847))),x70374))
% 51.10/50.82 [7063]~P5(x70631)+E(f57(x70631,f331(f331(f87(x70631),f57(x70631,x70632,x70633)),x70634),x70633),f57(x70631,f331(f331(f87(x70631),x70632),x70634),x70633))
% 51.10/50.82 [7064]~P5(x70641)+E(f57(x70641,f331(f331(f88(x70641),f57(x70641,x70642,x70643)),x70644),x70643),f57(x70641,f331(f331(f88(x70641),x70642),x70644),x70643))
% 51.10/50.82 [7065]~P6(x70651)+E(f57(x70651,f331(f331(f3(x70651),f57(x70651,x70652,x70653)),x70654),x70653),f57(x70651,f331(f331(f3(x70651),x70652),x70654),x70653))
% 51.10/50.82 [7066]~P5(x70661)+E(f57(x70661,f331(f331(f87(x70661),f57(x70661,x70662,x70663)),x70664),x70663),f57(x70661,f331(f331(f87(x70661),x70662),x70664),x70663))
% 51.10/50.82 [7067]~P5(x70671)+E(f57(x70671,f331(f331(f88(x70671),f57(x70671,x70672,x70673)),x70674),x70673),f57(x70671,f331(f331(f88(x70671),x70672),x70674),x70673))
% 51.10/50.82 [7271]~E(x72711,f331(f331(f145(x72712),x72713),x72714))+~P1(f331(f331(f240(a847),f331(f185(f848(x72712)),x72711)),f331(f185(f848(x72712)),x72714)))
% 51.10/50.82 [7444]~E(f171(x74441,x74442,x74443),f171(x74441,x74442,x74444))+E(f331(f311(f853(x74441,x74442),x74441,f248(x74441,x74442)),f331(f163(f853(x74441,x74442)),x74443)),f331(f311(f853(x74441,x74442),x74441,f248(x74441,x74442)),f331(f163(f853(x74441,x74442)),x74444)))
% 51.10/50.82 [7487]P27(x74871,x74872,x74873,f331(f163(x74871),x74874))+~P1(f331(f132(x74872),f331(f331(f147(x74871,x74872),x74873),x74874)))
% 51.10/50.82 [7564]~P1(f331(f331(f240(f854(x75641,a840)),x75642),x75644))+P1(f331(f331(f240(f854(x75641,a840)),x75642),f331(f331(f310(x75641),x75643),x75644)))
% 51.10/50.82 [7599]~P5(x75991)+E(f57(x75991,f331(f331(f87(x75991),f57(x75991,x75992,x75993)),f57(x75991,x75994,x75993)),x75993),f57(x75991,f331(f331(f87(x75991),x75992),x75994),x75993))
% 51.10/50.82 [7600]~P5(x76001)+E(f57(x76001,f331(f331(f88(x76001),f57(x76001,x76002,x76003)),f57(x76001,x76004,x76003)),x76003),f57(x76001,f331(f331(f88(x76001),x76002),x76004),x76003))
% 51.10/50.82 [7601]~P6(x76011)+E(f57(x76011,f331(f331(f3(x76011),f57(x76011,x76012,x76013)),f57(x76011,x76014,x76013)),x76013),f57(x76011,f331(f331(f3(x76011),x76012),x76014),x76013))
% 51.10/50.82 [7702]~E(f331(x77024,f407(x77024,x77023,x77021,x77022)),f184(f854(x77022,a840)))+E(f331(f331(f51(x77021,f854(x77022,a840)),x77023),x77024),f184(f854(x77022,a840)))
% 51.10/50.82 [7703]~E(f331(x77034,f637(x77034,x77033,x77031,x77032)),f247(f854(x77032,a840)))+E(f331(f331(f52(x77031,f854(x77032,a840)),x77033),x77034),f247(f854(x77032,a840)))
% 51.10/50.82 [7704]~E(f331(x77044,f413(x77044,x77043,x77042,x77041)),f184(f854(x77042,a840)))+E(f331(f331(f51(x77041,f854(x77042,a840)),x77043),x77044),f184(f854(x77042,a840)))
% 51.10/50.82 [7705]~E(f331(x77054,f638(x77054,x77053,x77052,x77051)),f247(f854(x77052,a840)))+E(f331(f331(f52(x77051,f854(x77052,a840)),x77053),x77054),f247(f854(x77052,a840)))
% 51.10/50.82 [8096]P1(f331(x80961,x80962))+~P1(f331(f331(f333(x80963),x80962),f331(f331(f109(f854(x80963,a840)),x80964),f331(f264(x80963),x80961))))
% 51.10/50.82 [8135]~P1(f331(f331(f240(f854(x81351,a840)),x81353),x81354))+P1(f331(f331(f240(f854(x81351,a840)),f331(f331(f310(x81351),x81352),x81353)),f331(f331(f310(x81351),x81352),x81354)))
% 51.10/50.82 [8177]P1(f331(f331(f333(x81771),x81772),x81773))+~P1(f331(f331(f333(x81771),x81772),f331(f331(f109(f854(x81771,a840)),x81773),f331(f264(x81771),x81774))))
% 51.10/50.82 [8304]P1(f331(f331(f191(x83041),x83042),f502(x83043,x83042,x83044,x83041)))+~P1(f331(f331(f191(f38(x83041,x83044)),x83042),x83043))
% 51.10/50.82 [8305]P1(f331(f331(f191(x83051),x83052),f588(x83053,x83052,x83054,x83051)))+~P1(f331(f331(f191(f38(x83051,x83054)),x83052),x83053))
% 51.10/50.82 [8425]~P1(f331(f331(f241(a847),f331(x84254,x84252)),f331(x84254,x84253)))+P1(f331(f331(f333(f853(x84251,x84251)),f331(f331(f249(x84251,x84251),x84252),x84253)),f331(f331(f288(a847,x84251),a245),x84254)))
% 51.10/50.82 [8570]P27(f848(x85701),f848(x85702),f331(f147(x85701,x85702),x85703),x85704)+~P27(x85701,x85702,x85703,f49(f854(x85701,a840),f331(f311(f848(x85701),f854(x85701,a840),f163(x85701)),x85704)))
% 51.10/50.82 [8680]E(f331(f331(f51(x86801,f854(x86802,a840)),x86803),x86804),f184(f854(x86802,a840)))+P1(f331(f331(f333(x86801),f407(x86804,x86803,x86801,x86802)),x86803))
% 51.10/50.82 [8681]E(f331(f331(f52(x86811,f854(x86812,a840)),x86813),x86814),f247(f854(x86812,a840)))+P1(f331(f331(f333(x86811),f637(x86814,x86813,x86811,x86812)),x86813))
% 51.10/50.82 [8682]E(f331(f331(f51(x86821,f854(x86822,a840)),x86823),x86824),f184(f854(x86822,a840)))+P1(f331(f331(f333(x86821),f413(x86824,x86823,x86822,x86821)),x86823))
% 51.10/50.82 [8683]E(f331(f331(f52(x86831,f854(x86832,a840)),x86833),x86834),f247(f854(x86832,a840)))+P1(f331(f331(f333(x86831),f638(x86834,x86833,x86832,x86831)),x86833))
% 51.10/50.82 [8718]P1(f331(f331(f241(a847),f331(x87181,x87182)),f331(x87181,x87183)))+~P1(f331(f331(f333(f853(x87184,x87184)),f331(f331(f249(x87184,x87184),x87182),x87183)),f331(f331(f288(a847,x87184),a245),x87181)))
% 51.10/50.82 [8767]P1(f331(f331(f191(x87671),f502(x87672,x87673,x87671,x87674)),x87672))+~P1(f331(f331(f191(f38(x87674,x87671)),x87673),x87672))
% 51.10/50.82 [8768]P1(f331(f331(f191(x87681),f588(x87682,x87683,x87681,x87684)),x87682))+~P1(f331(f331(f191(f38(x87684,x87681)),x87683),x87682))
% 51.10/50.82 [8877]P1(f331(f331(f333(x88771),f375(x88772,x88773,x88774,x88771)),x88773))+~P1(f331(f331(f333(f854(x88771,a840)),x88774),f331(f331(f66(x88771),x88773),x88772)))
% 51.10/50.82 [8880]E(x88801,x88802)+~P1(f331(f331(f333(f853(x88803,x88803)),f331(f331(f249(x88803,x88803),x88801),x88802)),f331(f331(f178(f853(x88803,x88803),a840),f2(a847)),x88804)))
% 51.10/50.82 [8952]E(f331(f285(x89521,x89521,x89522),f331(f331(f310(x89521),f375(x89522,x89523,x89524,x89521)),f184(f854(x89521,a840)))),x89524)+~P1(f331(f331(f333(f854(x89521,a840)),x89524),f331(f331(f66(x89521),x89523),x89522)))
% 51.10/50.82 [8961]~P1(f331(f331(f333(f853(x89611,x89611)),f331(f331(f249(x89611,x89611),x89613),x89612)),f308(x89611,x89614)))+P1(f331(f331(f333(f853(x89611,x89611)),f331(f331(f249(x89611,x89611),x89612),x89613)),f308(x89611,f331(f286(x89611,x89611),x89614))))
% 51.10/50.82 [8972]~P5(x89721)+E(f331(f331(f87(x89721),f331(f331(f87(x89721),f331(f331(f88(x89721),x89722),f331(f331(f48(x89721),x89723),x89722))),f57(x89721,x89723,x89722))),x89724),f331(f331(f87(x89721),x89723),x89724))
% 51.10/50.82 [8980]~P1(f331(f331(f333(x89801),x89803),x89804))+P1(f331(f331(f333(f854(x89801,a840)),f331(f285(x89801,x89801,x89802),f331(f331(f310(x89801),x89803),f184(f854(x89801,a840))))),f331(f331(f66(x89801),x89804),x89802)))
% 51.10/50.82 [8990]P1(f331(f331(f333(f853(x89901,x89901)),f331(f331(f249(x89901,x89901),x89902),x89903)),f308(x89901,x89904)))+~P1(f331(f331(f333(f853(x89901,x89901)),f331(f331(f249(x89901,x89901),x89903),x89902)),f308(x89901,f331(f286(x89901,x89901),x89904))))
% 51.10/50.82 [9074]E(f331(f331(f152(x90741,f331(f160(x90741),x90742)),f331(f331(f3(a847),f331(f331(f3(a847),f331(f185(f848(x90741)),x90742)),x90743)),f85(a847))),x90744),f331(f160(x90741),f331(f331(f152(x90741,x90742),x90743),x90744)))+~P1(f331(f331(f241(a847),x90743),f331(f185(f848(x90741)),x90742)))
% 51.10/50.82 [9110]~P27(x91102,x91101,x91103,f247(f854(x91102,a840)))+P1(f331(f331(f240(f854(x91101,a840)),f331(f311(x91102,x91101,x91103),f331(f86(f854(x91102,a840)),x91104))),f331(f86(f854(x91101,a840)),f331(f311(x91102,x91101,x91103),x91104))))
% 51.10/50.82 [9118]~P7(x91181)+E(f331(f137(x91181,x91182,f331(f9(x91182,x91181,x91181),f331(f331(f10(x91181,f854(x91181,x91181),x91182),f108(x91181)),x91183)),f184(x91181)),x91184),f331(f331(f51(x91182,x91181),f331(f163(x91182),x91184)),x91183))
% 51.10/50.82 [9119]~P7(x91191)+E(f331(f137(x91191,x91192,f331(f9(x91192,x91191,x91191),f331(f331(f10(x91191,f854(x91191,x91191),x91192),f109(x91191)),x91193)),f247(x91191)),x91194),f331(f331(f52(x91192,x91191),f331(f163(x91192),x91194)),x91193))
% 51.10/50.82 [9185]~P1(f331(f331(f333(f853(f848(x91854),f848(x91854))),f331(f331(f249(f848(x91854),f848(x91854)),x91853),x91852)),f150(x91854,x91851)))+P1(f331(f331(f241(a847),f736(x91851,x91852,x91853,x91854)),f331(f185(f848(x91854)),x91853)))
% 51.10/50.82 [9186]~P5(x91861)+E(f331(f331(f87(x91861),f331(f331(f87(x91861),f331(f331(f88(x91861),f331(f331(f48(x91861),x91862),x91863)),x91863)),f57(x91861,x91862,x91863))),x91864),f331(f331(f87(x91861),x91862),x91864))
% 51.10/50.82 [9215]~P1(f331(f331(f333(f853(f848(x92151),f848(x92151))),f331(f331(f249(f848(x92151),f848(x92151)),x92152),x92153)),f331(f286(f848(x92151),f848(x92151)),f150(x92151,x92154))))+P1(f331(f331(f333(f853(f848(x92151),f848(x92151))),f331(f331(f249(f848(x92151),f848(x92151)),x92152),x92153)),f150(x92151,f331(f286(x92151,x92151),x92154))))
% 51.10/50.82 [9216]P1(f331(f331(f333(f853(f848(x92161),f848(x92161))),f331(f331(f249(f848(x92161),f848(x92161)),x92162),x92163)),f331(f286(f848(x92161),f848(x92161)),f150(x92161,x92164))))+~P1(f331(f331(f333(f853(f848(x92161),f848(x92161))),f331(f331(f249(f848(x92161),f848(x92161)),x92162),x92163)),f150(x92161,f331(f286(x92161,x92161),x92164))))
% 51.10/50.82 [9254]~P1(f331(f331(f333(x92541),x92543),f331(f269(x92541,x92542),x92544)))+P1(f331(f331(f333(f853(x92541,x92542)),f331(f331(f249(x92541,x92542),x92543),f583(x92544,x92542,x92543,x92541))),x92544))
% 51.10/50.82 [9255]~P1(f331(f331(f333(x92551),x92553),f331(f269(x92551,x92552),x92554)))+P1(f331(f331(f333(f853(x92551,x92552)),f331(f331(f249(x92551,x92552),x92553),f584(x92554,x92552,x92553,x92551))),x92554))
% 51.10/50.82 [9382]~P1(f331(f68(f851(x93821)),f331(f311(x93822,f851(x93821),x93823),f247(f854(x93822,a840)))))+P1(f331(f68(f851(x93821)),f331(f311(x93822,f851(x93821),f175(x93822,x93821,x93823,f171(x93822,x93821,x93824))),f247(f854(x93822,a840)))))
% 51.10/50.82 [9407]~P1(f331(f331(f333(f853(x94071,x94071)),f331(f331(f249(x94071,x94071),x94072),x94074)),f331(f331(f289(x94071,x94071,x94071),x94073),f308(x94071,x94073))))+P1(f331(f331(f333(f853(x94071,x94071)),f331(f331(f249(x94071,x94071),x94072),f678(x94073,x94074,x94072,x94071))),x94073))
% 51.10/50.82 [9574]~P1(f331(f331(f333(f853(x95742,x95741)),x95744),f331(f286(x95741,x95742),x95743)))+P1(f331(f331(f333(f853(x95741,x95742)),f331(f331(f249(x95741,x95742),f704(x95743,x95744,x95741,x95742)),f703(x95743,x95744,x95741,x95742))),x95743))
% 51.10/50.82 [9598]~P1(f331(f331(f333(f853(f848(x95981),f848(x95981))),f331(f331(f249(f848(x95981),f848(x95981)),x95984),x95983)),f150(x95981,x95982)))+P1(f331(f331(f333(f853(x95981,x95981)),f331(f331(f249(x95981,x95981),f742(x95982,x95983,x95984,x95981)),f743(x95982,x95983,x95984,x95981))),x95982))
% 51.10/50.82 [9675]~P1(f331(f331(f333(f853(f848(x96751),f848(x96751))),f331(f331(f249(f848(x96751),f848(x96751)),x96752),x96754)),f150(x96751,x96753)))+P1(f331(f331(f333(f853(x96751,x96751)),f331(f331(f249(x96751,x96751),f331(f331(f155(x96751),x96752),f736(x96753,x96754,x96752,x96751))),f737(x96753,x96754,x96752,x96751))),x96753))
% 51.10/50.82 [9697]~P1(f331(f68(x96972),x96974))+E(f331(f331(f331(f72(f854(x96971,a840),x96972,f108(f854(x96971,a840))),f331(f331(f9(x96972,f854(x96971,a840),f854(x96971,a840)),f331(f331(f10(x96971,f854(f854(x96971,a840),f854(x96971,a840)),x96972),f310(x96971)),x96973)),f184(f854(x96971,a840)))),f184(f854(x96971,a840))),x96974),f331(f311(x96972,x96971,x96973),x96974))
% 51.10/50.82 [9817]~P27(x98171,x98172,x98173,f247(f854(x98171,a840)))+P1(f331(f331(f240(f854(x98171,a840)),f331(f312(x98171,x98172,x98173),f331(f331(f310(x98172),x98174),f184(f854(x98172,a840))))),f331(f331(f310(x98171),f92(x98171,f331(f331(f9(x98171,x98172,a840),f331(f331(f10(x98172,f854(x98172,a840),x98171),a328),x98173)),x98174))),f184(f854(x98171,a840)))))
% 51.10/50.82 [5467]~E(f331(f331(f130(x54671),x54672),x54674),x54673)+E(f331(f331(f164(x54671),f331(f185(f848(x54671)),x54672)),x54673),x54672)
% 51.10/50.82 [5468]~E(f331(f331(f130(x54682),x54683),x54681),x54684)+E(x54681,f331(f331(f133(x54682),f331(f185(f848(x54682)),x54683)),x54684))
% 51.10/50.82 [5479]~E(x54794,f2(a847))+E(f331(f331(f155(x54791),f331(f331(f145(x54791),x54792),x54793)),x54794),x54792)
% 51.10/50.82 [6015]~P87(x60151)+E(f331(f331(f250(x60151),f331(f331(f250(x60151),x60152),x60153)),x60154),f331(f331(f250(x60151),x60152),f331(f331(f88(a847),x60153),x60154)))
% 51.10/50.82 [6016]~P74(x60161)+E(f331(f331(f250(x60161),f331(f331(f250(x60161),x60162),x60163)),x60164),f331(f331(f250(x60161),x60162),f331(f331(f88(a847),x60163),x60164)))
% 51.10/50.82 [6032]E(x60321,f2(a847))+E(f331(f331(f155(x60322),f331(f331(f145(x60322),x60323),x60324)),x60321),f331(f331(f155(x60322),x60324),f331(f331(f3(a847),x60321),f85(a847))))
% 51.10/50.82 [6057]~P87(x60571)+E(f331(f331(f87(x60571),f331(f331(f87(x60571),x60572),x60573)),x60574),f331(f331(f87(x60571),x60572),f331(f331(f87(x60571),x60573),x60574)))
% 51.10/50.82 [6058]~P87(x60581)+E(f331(f331(f88(x60581),f331(f331(f88(x60581),x60582),x60583)),x60584),f331(f331(f88(x60581),x60582),f331(f331(f88(x60581),x60583),x60584)))
% 51.10/50.82 [6059]~P114(x60591)+E(f331(f331(f291(x60591),f331(f331(f88(x60591),x60592),x60593)),x60594),f331(f331(f88(x60591),x60592),f331(f331(f291(x60591),x60593),x60594)))
% 51.10/50.82 [6060]~P3(x60601)+E(f331(f331(f87(x60601),f331(f331(f87(x60601),x60602),x60603)),x60604),f331(f331(f87(x60601),x60602),f331(f331(f87(x60601),x60603),x60604)))
% 51.10/50.82 [6061]~P87(x60611)+E(f331(f331(f87(x60611),f331(f331(f87(x60611),x60612),x60613)),x60614),f331(f331(f87(x60611),x60612),f331(f331(f87(x60611),x60613),x60614)))
% 51.10/50.82 [6062]~P87(x60621)+E(f331(f331(f88(x60621),f331(f331(f88(x60621),x60622),x60623)),x60624),f331(f331(f88(x60621),x60622),f331(f331(f88(x60621),x60623),x60624)))
% 51.10/50.82 [6063]~P64(x60631)+E(f331(f331(f88(x60631),f331(f331(f88(x60631),x60632),x60633)),x60634),f331(f331(f88(x60631),x60632),f331(f331(f88(x60631),x60633),x60634)))
% 51.10/50.82 [6065]~P102(x60651)+E(f331(f331(f244(x60651),f331(f331(f244(x60651),x60652),x60653)),x60654),f331(f331(f244(x60651),x60652),f331(f331(f244(x60651),x60653),x60654)))
% 51.10/50.82 [6066]~P102(x60661)+E(f331(f331(f244(x60661),f331(f331(f244(x60661),x60662),x60663)),x60664),f331(f331(f244(x60661),x60662),f331(f331(f244(x60661),x60663),x60664)))
% 51.10/50.82 [6067]~P102(x60671)+E(f331(f331(f239(x60671),f331(f331(f239(x60671),x60672),x60673)),x60674),f331(f331(f239(x60671),x60672),f331(f331(f239(x60671),x60673),x60674)))
% 51.10/50.82 [6068]~P102(x60681)+E(f331(f331(f239(x60681),f331(f331(f239(x60681),x60682),x60683)),x60684),f331(f331(f239(x60681),x60682),f331(f331(f239(x60681),x60683),x60684)))
% 51.10/50.82 [6069]~P97(x60691)+E(f331(f331(f108(x60691),f331(f331(f108(x60691),x60692),x60693)),x60694),f331(f331(f108(x60691),x60692),f331(f331(f108(x60691),x60693),x60694)))
% 51.10/50.82 [6070]~P100(x60701)+E(f331(f331(f108(x60701),f331(f331(f108(x60701),x60702),x60703)),x60704),f331(f331(f108(x60701),x60702),f331(f331(f108(x60701),x60703),x60704)))
% 51.10/50.82 [6071]~P100(x60711)+E(f331(f331(f108(x60711),f331(f331(f108(x60711),x60712),x60713)),x60714),f331(f331(f108(x60711),x60712),f331(f331(f108(x60711),x60713),x60714)))
% 51.10/50.82 [6072]~P97(x60721)+E(f331(f331(f109(x60721),f331(f331(f109(x60721),x60722),x60723)),x60724),f331(f331(f109(x60721),x60722),f331(f331(f109(x60721),x60723),x60724)))
% 51.10/50.82 [6073]~P101(x60731)+E(f331(f331(f109(x60731),f331(f331(f109(x60731),x60732),x60733)),x60734),f331(f331(f109(x60731),x60732),f331(f331(f109(x60731),x60733),x60734)))
% 51.10/50.82 [6074]~P101(x60741)+E(f331(f331(f109(x60741),f331(f331(f109(x60741),x60742),x60743)),x60744),f331(f331(f109(x60741),x60742),f331(f331(f109(x60741),x60743),x60744)))
% 51.10/50.82 [6085]~P5(x60851)+E(f57(x60851,f331(f331(f87(x60851),x60852),f331(f331(f88(x60851),x60853),x60854)),x60854),f57(x60851,x60852,x60854))
% 51.10/50.82 [6086]~P5(x60861)+E(f57(x60861,f331(f331(f87(x60861),x60862),f331(f331(f88(x60861),x60863),x60864)),x60863),f57(x60861,x60862,x60863))
% 51.10/50.82 [6224]E(f331(f331(f155(x62241),f331(f331(f164(x62241),x62242),x62243)),x62244),f331(f331(f155(x62241),x62243),x62244))+~P1(f331(f331(f241(a847),x62244),x62242))
% 51.10/50.82 [6409]~P87(x64091)+E(f331(f331(f87(x64091),f331(f331(f87(x64091),x64092),x64093)),x64094),f331(f331(f87(x64091),f331(f331(f87(x64091),x64092),x64094)),x64093))
% 51.10/50.82 [6410]~P87(x64101)+E(f331(f331(f88(x64101),f331(f331(f88(x64101),x64102),x64103)),x64104),f331(f331(f88(x64101),f331(f331(f88(x64101),x64102),x64104)),x64103))
% 51.10/50.82 [6471]~P84(x64712)+E(f331(f331(f8(x64711,x64712),f331(f18(x64712,x64711),x64713)),x64714),f331(f331(f88(x64712),f331(f107(x64712),f331(f47(x64711),x64714))),x64713))
% 51.10/50.82 [6648]E(f331(f331(f109(f854(x66481,a840)),f331(f331(f310(x66481),x66482),x66483)),x66484),f331(f331(f109(f854(x66481,a840)),x66483),x66484))+P1(f331(f331(f333(x66481),x66482),x66484))
% 51.10/50.82 [6649]E(f331(f331(f109(f854(x66491,a840)),f331(f331(f310(x66491),x66492),x66493)),x66494),f331(f331(f109(f854(x66491,a840)),x66493),x66494))+P1(f331(f331(f333(x66491),x66492),x66494))
% 51.10/50.82 [6723]~P66(x67231)+E(f331(f331(f244(x67231),f331(f331(f87(x67231),x67232),x67233)),f331(f331(f87(x67231),x67234),x67233)),f331(f331(f87(x67231),f331(f331(f244(x67231),x67232),x67234)),x67233))
% 51.10/50.82 [6724]~P66(x67241)+E(f331(f331(f239(x67241),f331(f331(f87(x67241),x67242),x67243)),f331(f331(f87(x67241),x67244),x67243)),f331(f331(f87(x67241),f331(f331(f239(x67241),x67242),x67244)),x67243))
% 51.10/50.82 [6725]~P87(x67251)+E(f331(f331(f87(x67251),f331(f331(f88(x67251),x67252),x67253)),f331(f331(f88(x67251),x67254),x67253)),f331(f331(f88(x67251),f331(f331(f87(x67251),x67252),x67254)),x67253))
% 51.10/50.82 [6726]~P111(x67261)+E(f331(f331(f87(x67261),f331(f331(f88(x67261),x67262),x67263)),f331(f331(f88(x67261),x67264),x67263)),f331(f331(f88(x67261),f331(f331(f87(x67261),x67262),x67264)),x67263))
% 51.10/50.82 [6727]~P76(x67271)+E(f331(f331(f244(x67271),f331(f331(f3(x67271),x67272),x67273)),f331(f331(f3(x67271),x67274),x67273)),f331(f331(f3(x67271),f331(f331(f244(x67271),x67272),x67274)),x67273))
% 51.10/50.82 [6728]~P76(x67281)+E(f331(f331(f239(x67281),f331(f331(f3(x67281),x67282),x67283)),f331(f331(f3(x67281),x67284),x67283)),f331(f331(f3(x67281),f331(f331(f239(x67281),x67282),x67284)),x67283))
% 51.10/50.82 [6729]~P87(x67291)+E(f331(f331(f88(x67291),f331(f331(f250(x67291),x67292),x67293)),f331(f331(f250(x67291),x67294),x67293)),f331(f331(f250(x67291),f331(f331(f88(x67291),x67292),x67294)),x67293))
% 51.10/50.82 [6730]~P70(x67301)+E(f331(f331(f88(x67301),f331(f331(f250(x67301),x67302),x67303)),f331(f331(f250(x67301),x67304),x67303)),f331(f331(f250(x67301),f331(f331(f88(x67301),x67302),x67304)),x67303))
% 51.10/50.82 [6731]~P58(x67311)+E(f331(f331(f291(x67311),f331(f331(f250(x67311),x67312),x67313)),f331(f331(f250(x67311),x67314),x67313)),f331(f331(f250(x67311),f331(f331(f291(x67311),x67312),x67314)),x67313))
% 51.10/50.82 [6732]~P114(x67321)+E(f331(f331(f87(x67321),f331(f331(f291(x67321),x67322),x67323)),f331(f331(f291(x67321),x67324),x67323)),f331(f331(f291(x67321),f331(f331(f87(x67321),x67322),x67324)),x67323))
% 51.10/50.82 [6733]~P114(x67331)+E(f331(f331(f3(x67331),f331(f331(f291(x67331),x67332),x67333)),f331(f331(f291(x67331),x67334),x67333)),f331(f331(f291(x67331),f331(f331(f3(x67331),x67332),x67334)),x67333))
% 51.10/50.82 [6734]~P102(x67341)+E(f331(f331(f239(x67341),f331(f331(f244(x67341),x67342),x67343)),f331(f331(f244(x67341),x67344),x67343)),f331(f331(f244(x67341),f331(f331(f239(x67341),x67342),x67344)),x67343))
% 51.10/50.82 [6735]~P102(x67351)+E(f331(f331(f244(x67351),f331(f331(f239(x67351),x67352),x67353)),f331(f331(f239(x67351),x67354),x67353)),f331(f331(f239(x67351),f331(f331(f244(x67351),x67352),x67354)),x67353))
% 51.10/50.82 [6736]~P98(x67361)+E(f331(f331(f109(x67361),f331(f331(f108(x67361),x67362),x67363)),f331(f331(f108(x67361),x67364),x67363)),f331(f331(f108(x67361),f331(f331(f109(x67361),x67362),x67364)),x67363))
% 51.10/50.82 [6737]~P98(x67371)+E(f331(f331(f108(x67371),f331(f331(f109(x67371),x67372),x67373)),f331(f331(f109(x67371),x67374),x67373)),f331(f331(f109(x67371),f331(f331(f108(x67371),x67372),x67374)),x67373))
% 51.10/50.82 [6738]~P87(x67381)+E(f331(f331(f87(x67381),f331(f331(f88(x67381),x67382),x67383)),f331(f331(f88(x67381),x67384),x67383)),f331(f331(f88(x67381),f331(f331(f87(x67381),x67382),x67384)),x67383))
% 51.10/50.82 [6773]E(f331(f331(f152(x67731,x67732),x67733),x67734),x67732)+~P1(f331(f331(f240(a847),f331(f185(f848(x67731)),x67732)),x67733))
% 51.10/50.82 [6799]~P1(f331(x67993,x67994))+P1(f331(f331(f331(f108(f854(x67991,a840)),x67992),x67993),x67994))
% 51.10/50.82 [6800]~P1(f331(x68003,x68004))+P1(f331(f331(f331(f108(f854(x68001,a840)),x68002),x68003),x68004))
% 51.10/50.82 [6801]~P1(f331(x68012,x68014))+P1(f331(f331(f331(f108(f854(x68011,a840)),x68012),x68013),x68014))
% 51.10/50.82 [6802]~P1(f331(x68022,x68024))+P1(f331(f331(f331(f108(f854(x68021,a840)),x68022),x68023),x68024))
% 51.10/50.82 [6824]E(f331(f331(f155(x68241),f331(f331(f130(x68241),x68242),x68243)),x68244),f331(f331(f155(x68241),x68242),x68244))+~P1(f331(f331(f241(a847),x68244),f331(f185(f848(x68241)),x68242)))
% 51.10/50.82 [6833]E(f331(f331(f3(f854(x68331,a840)),f331(f331(f310(x68331),x68332),x68333)),x68334),f331(f331(f3(f854(x68331,a840)),x68333),x68334))+~P1(f331(f331(f333(x68331),x68332),x68334))
% 51.10/50.82 [6834]E(f331(f331(f3(f854(x68341,a840)),f331(f331(f310(x68341),x68342),x68343)),x68344),f331(f331(f3(f854(x68341,a840)),x68343),x68344))+~P1(f331(f331(f333(x68341),x68342),x68344))
% 51.10/50.82 [6875]~E(f135(a847,f331(f302(a847,x68751),x68752)),f331(f331(f145(a847),x68754),x68753))+E(f135(a847,f331(f302(a847,f331(f331(f87(a847),x68751),f85(a847))),x68752)),x68753)
% 51.10/50.82 [6944]E(x69441,f2(a847))+E(f331(f331(f145(x69442),x69443),f331(f331(f164(x69442),f331(f331(f3(a847),x69441),f85(a847))),x69444)),f331(f331(f164(x69442),x69441),f331(f331(f145(x69442),x69443),x69444)))
% 51.10/50.82 [7048]E(f331(f331(f155(x70481),x70482),f331(f331(f3(a847),x70483),f331(f185(f848(x70481)),x70484))),f331(f331(f155(x70481),f331(f331(f130(x70481),x70484),x70482)),x70483))+P1(f331(f331(f241(a847),x70483),f331(f185(f848(x70481)),x70484)))
% 51.10/50.82 [7075]E(f331(f331(f109(f854(x70751,a840)),x70752),f331(f331(f310(x70751),x70753),x70754)),f331(f331(f310(x70751),x70753),f331(f331(f109(f854(x70751,a840)),x70752),x70754)))+~P1(f331(f331(f333(x70751),x70753),x70752))
% 51.10/50.82 [7076]E(f331(f331(f109(f854(x70761,a840)),x70762),f331(f331(f310(x70761),x70763),x70764)),f331(f331(f310(x70761),x70763),f331(f331(f109(f854(x70761,a840)),x70762),x70764)))+~P1(f331(f331(f333(x70761),x70763),x70762))
% 51.10/50.82 [7110]E(f331(f331(f155(x71101),f331(f331(f152(x71101,x71102),x71103),x71104)),x71103),x71104)+~P1(f331(f331(f241(a847),x71103),f331(f185(f848(x71101)),x71102)))
% 51.10/50.82 [7131]E(x71311,f184(f854(x71312,a840)))+E(f331(f311(f853(x71313,x71312),x71313,f248(x71313,x71312)),f331(f331(f256(x71313,x71312),x71314),f331(f18(f854(x71312,a840),x71313),x71311))),x71314)
% 51.10/50.82 [7132]E(x71321,f184(f854(x71322,a840)))+E(f331(f311(f853(x71322,x71323),x71323,f258(x71322,x71323)),f331(f331(f256(x71322,x71323),x71321),f331(f18(f854(x71323,a840),x71322),x71324))),x71324)
% 51.10/50.82 [7214]E(f331(f331(f3(f854(x72141,a840)),f331(f331(f310(x72141),x72142),x72143)),x72144),f331(f331(f310(x72141),x72142),f331(f331(f3(f854(x72141,a840)),x72143),x72144)))+P1(f331(f331(f333(x72141),x72142),x72144))
% 51.10/50.82 [7255]~E(x72554,f184(f854(x72552,a840)))+E(f331(f311(f853(x72551,x72552),x72551,f248(x72551,x72552)),f331(f331(f256(x72551,x72552),x72553),f331(f18(f854(x72552,a840),x72551),x72554))),f184(f854(x72551,a840)))
% 51.10/50.82 [7256]~E(x72563,f184(f854(x72561,a840)))+E(f331(f311(f853(x72561,x72562),x72562,f258(x72561,x72562)),f331(f331(f256(x72561,x72562),x72563),f331(f18(f854(x72562,a840),x72561),x72564))),f184(f854(x72562,a840)))
% 51.10/50.82 [7313]~P1(f331(f331(f333(x73131),x73132),x73134))+P1(f331(f331(f333(x73131),x73132),f331(f331(f108(f854(x73131,a840)),x73133),x73134)))
% 51.10/50.82 [7314]~P1(f331(f331(f333(x73141),x73142),x73144))+P1(f331(f331(f333(x73141),x73142),f331(f331(f108(f854(x73141,a840)),x73143),x73144)))
% 51.10/50.82 [7315]~P1(f331(f331(f333(x73151),x73152),x73154))+P1(f331(f331(f333(x73151),x73152),f331(f331(f108(f854(x73151,a840)),x73153),x73154)))
% 51.10/50.82 [7316]~P1(f331(f331(f333(x73161),x73162),x73163))+P1(f331(f331(f333(x73161),x73162),f331(f331(f108(f854(x73161,a840)),x73163),x73164)))
% 51.10/50.82 [7317]~P1(f331(f331(f333(x73171),x73172),x73173))+P1(f331(f331(f333(x73171),x73172),f331(f331(f108(f854(x73171,a840)),x73173),x73174)))
% 51.10/50.82 [7318]~P1(f331(f331(f333(x73181),x73182),x73183))+P1(f331(f331(f333(x73181),x73182),f331(f331(f108(f854(x73181,a840)),x73183),x73184)))
% 51.10/50.82 [7339]E(f331(f331(f109(f854(x73391,a840)),f331(f331(f310(x73391),x73392),x73393)),x73394),f331(f331(f310(x73391),x73392),f331(f331(f109(f854(x73391,a840)),x73393),x73394)))+~P1(f331(f331(f333(x73391),x73392),x73394))
% 51.10/50.82 [7340]E(f331(f331(f109(f854(x73401,a840)),f331(f331(f310(x73401),x73402),x73403)),x73404),f331(f331(f310(x73401),x73402),f331(f331(f109(f854(x73401,a840)),x73403),x73404)))+~P1(f331(f331(f333(x73401),x73402),x73404))
% 51.10/50.82 [7618]P1(f331(x76181,x76182))+~P1(f331(f331(f331(f109(f854(x76183,a840)),x76184),x76181),x76182))
% 51.10/50.82 [7619]P1(f331(x76191,x76192))+~P1(f331(f331(f331(f109(f854(x76193,a840)),x76191),x76194),x76192))
% 51.10/50.82 [7620]P1(f331(x76201,x76202))+~P1(f331(f331(f331(f109(f854(x76203,a840)),x76204),x76201),x76202))
% 51.10/50.82 [7621]P1(f331(x76211,x76212))+~P1(f331(f331(f331(f109(f854(x76213,a840)),x76211),x76214),x76212))
% 51.10/50.82 [7624]E(f331(f331(f8(x76241,a847),x76242),f331(f331(f3(f854(x76241,a840)),x76243),f331(f331(f310(x76241),x76244),f184(f854(x76241,a840))))),f331(f331(f8(x76241,a847),x76242),x76243))+P1(f331(f331(f333(x76241),x76244),x76243))
% 51.10/50.82 [7630]~P68(x76301)+E(f331(f157(x76301),f331(f331(f147(a847,x76301),x76302),f135(a847,f331(f302(a847,x76303),x76304)))),f331(f331(f8(a847,x76301),x76302),f331(f163(a847),f135(a847,f331(f302(a847,x76303),x76304)))))
% 51.10/50.82 [7631]~P68(x76311)+E(f331(f331(f8(a847,x76311),x76312),f331(f163(a847),f135(a847,f331(f302(a847,x76313),x76314)))),f331(f157(x76311),f331(f331(f147(a847,x76311),x76312),f135(a847,f331(f302(a847,x76313),x76314)))))
% 51.10/50.82 [7745]~E(x77453,x77454)+P1(f331(f69(x77451,x77452,f331(f331(f310(x77451),x77453),f184(f854(x77451,a840)))),x77454))
% 51.10/50.82 [7841]P1(f331(f331(f333(x78411),x78412),f331(f163(x78411),x78413)))+~P1(f331(f331(f333(x78411),x78412),f331(f163(x78411),f331(f331(f164(x78411),x78414),x78413))))
% 51.10/50.82 [7842]P1(f331(f331(f333(x78421),x78422),f331(f163(x78421),x78423)))+~P1(f331(f331(f333(x78421),x78422),f331(f163(x78421),f331(f331(f133(x78421),x78424),x78423))))
% 51.10/50.82 [7913]P1(f331(f331(f333(x79131),x79132),x79133))+~P1(f331(f331(f333(x79131),x79132),f331(f331(f109(f854(x79131,a840)),x79134),x79133)))
% 51.10/50.82 [7914]P1(f331(f331(f333(x79141),x79142),x79143))+~P1(f331(f331(f333(x79141),x79142),f331(f331(f3(f854(x79141,a840)),x79143),x79144)))
% 51.10/50.82 [7915]P1(f331(f331(f333(x79151),x79152),x79153))+~P1(f331(f331(f333(x79151),x79152),f331(f331(f3(f854(x79151,a840)),x79153),x79154)))
% 51.10/50.82 [7916]P1(f331(f331(f333(x79161),x79162),x79163))+~P1(f331(f331(f333(x79161),x79162),f331(f331(f3(f854(x79161,a840)),x79163),x79164)))
% 51.10/50.82 [7917]P1(f331(f331(f333(x79171),x79172),x79173))+~P1(f331(f331(f333(x79171),x79172),f331(f331(f109(f854(x79171,a840)),x79174),x79173)))
% 51.10/50.82 [7918]P1(f331(f331(f333(x79181),x79182),x79183))+~P1(f331(f331(f333(x79181),x79182),f331(f331(f109(f854(x79181,a840)),x79184),x79183)))
% 51.10/50.82 [7919]P1(f331(f331(f333(x79191),x79192),x79193))+~P1(f331(f331(f333(x79191),x79192),f331(f331(f109(f854(x79191,a840)),x79193),x79194)))
% 51.10/50.82 [7920]P1(f331(f331(f333(x79201),x79202),x79203))+~P1(f331(f331(f333(x79201),x79202),f331(f331(f109(f854(x79201,a840)),x79203),x79204)))
% 51.10/50.82 [7921]P1(f331(f331(f333(x79211),x79212),x79213))+~P1(f331(f331(f333(x79211),x79212),f331(f331(f109(f854(x79211,a840)),x79213),x79214)))
% 51.10/50.82 [7938]E(f331(f331(f130(x79381),f331(f331(f164(x79381),x79382),x79383)),f331(f331(f145(x79381),x79384),f331(f331(f133(x79381),f331(a119,x79382)),x79383))),f331(f331(f152(x79381,x79383),x79382),x79384))+~P1(f331(f331(f241(a847),x79382),f331(f185(f848(x79381)),x79383)))
% 51.10/50.82 [7961]P1(f331(f331(f333(x79611),x79612),x79613))+~P1(f331(f331(f240(f854(x79611,a840)),f331(f331(f310(x79611),x79612),x79614)),x79613))
% 51.10/50.82 [7989]~P1(f331(f331(f333(x79891),x79892),x79893))+~P1(f331(f331(f333(x79891),x79892),f331(f331(f3(f854(x79891,a840)),x79894),x79893)))
% 51.10/50.82 [7990]~P1(f331(f331(f333(x79901),x79902),x79903))+~P1(f331(f331(f333(x79901),x79902),f331(f331(f3(f854(x79901,a840)),x79904),x79903)))
% 51.10/50.82 [7991]~P1(f331(f331(f333(x79911),x79912),x79913))+~P1(f331(f331(f333(x79911),x79912),f331(f331(f3(f854(x79911,a840)),x79914),x79913)))
% 51.10/50.82 [8024]~P1(f331(f331(f241(a847),x80244),f331(f185(f848(x80241)),x80243)))+P1(f331(f331(f333(x80241),x80242),f331(f163(x80241),f331(f331(f152(x80241,x80243),x80244),x80242))))
% 51.10/50.82 [8065]E(f331(f111(a847),x80651),f2(a847))+E(f331(f331(f145(x80652),x80653),f331(f331(f164(x80652),f331(f331(f3(a847),f331(f111(a847),x80651)),f85(a847))),x80654)),f331(f331(f164(x80652),f331(f111(a847),x80651)),f331(f331(f145(x80652),x80653),x80654)))
% 51.10/50.82 [8074]E(f331(f331(f155(x80741),f331(f331(f133(x80741),x80742),x80743)),x80744),f331(f331(f155(x80741),x80743),f331(f331(f87(a847),x80742),x80744)))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x80742),x80744)),f331(f185(f848(x80741)),x80743)))
% 51.10/50.82 [8083]~P84(x80832)+E(f331(f331(f8(x80831,x80832),f331(f331(f10(a847,x80832,x80831),f107(x80832)),x80833)),x80834),f331(f107(x80832),f331(f331(f8(x80831,a847),x80833),x80834)))
% 51.10/50.82 [8084]~P133(x80842)+E(f331(f331(f8(x80841,x80842),f331(f331(f10(a1,x80842,x80841),f110(x80842)),x80843)),x80844),f331(f110(x80842),f331(f331(f8(x80841,a1),x80843),x80844)))
% 51.10/50.82 [8137]~P61(x81372)+E(f331(f331(f11(x81371,x81372),f331(f331(f10(x81372,x81372,x81371),f82(x81372)),x81373)),x81374),f331(f82(x81372),f331(f331(f11(x81371,x81372),x81373),x81374)))
% 51.10/50.82 [8138]~P4(x81382)+E(f331(f331(f8(x81381,x81382),f331(f331(f10(x81382,x81382,x81381),f86(x81382)),x81383)),x81384),f331(f86(x81382),f331(f331(f8(x81381,x81382),x81383),x81384)))
% 51.10/50.82 [8140]E(f331(f331(f8(x81401,a847),x81402),f331(f331(f3(f854(x81401,a840)),x81403),f331(f331(f310(x81401),x81404),f184(f854(x81401,a840))))),f331(f331(f3(a847),f331(f331(f8(x81401,a847),x81402),x81403)),f331(x81402,x81404)))+~P1(f331(f331(f333(x81401),x81404),x81403))
% 51.10/50.82 [8159]P1(f331(f331(f240(f854(x81591,a840)),x81592),x81593))+~P1(f331(f331(f240(f854(x81591,a840)),f331(f331(f310(x81591),x81594),x81592)),x81593))
% 51.10/50.82 [8367]P34(x83671,x83672)+~P34(x83671,f331(f331(f310(f853(x83671,x83671)),f331(f331(f249(x83671,x83671),x83673),x83674)),x83672))
% 51.10/50.82 [8368]P54(x83681,x83682)+~P54(x83681,f331(f331(f310(f853(x83681,x83681)),f331(f331(f249(x83681,x83681),x83683),x83684)),x83682))
% 51.10/50.82 [8376]~P102(x83761)+E(f331(f331(f143(x83761,x83761,f7(x83761)),x83762),f331(f331(f143(x83761,x83761,f7(x83761)),x83763),x83764)),f331(f331(f143(x83761,x83761,f7(x83761)),x83763),f331(f331(f143(x83761,x83761,f7(x83761)),x83762),x83764)))
% 51.10/50.82 [8386]E(x83861,x83862)+~P1(f331(f69(x83863,x83864,f331(f331(f310(x83863),x83861),f184(f854(x83863,a840)))),x83862))
% 51.10/50.82 [8392]E(f331(f171(x83921,x83922,x83923),x83924),f187(x83922))+P1(f331(f331(f333(x83921),x83924),f331(f311(f853(x83921,x83922),x83921,f248(x83921,x83922)),f331(f163(f853(x83921,x83922)),x83923))))
% 51.10/50.82 [8398]E(f331(f331(f130(x83981),f331(f331(f164(x83981),x83982),x83983)),f331(f331(f164(x83981),x83984),f331(f331(f133(x83981),x83982),x83983))),f331(f331(f164(x83981),f331(f331(f87(a847),x83982),x83984)),x83983))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x83982),x83984)),f331(f185(f848(x83981)),x83983)))
% 51.10/50.82 [8438]P1(f331(f68(x84381),x84382))+~E(x84382,f331(f311(a847,x84381,x84383),f331(f264(a847),f331(f331(f9(a847,a847,a840),f241(a847)),x84384))))
% 51.10/50.82 [8439]P1(f331(f68(x84391),x84392))+~E(x84392,f331(f311(a847,x84391,x84393),f331(f264(a847),f331(f331(f9(a847,a847,a840),f241(a847)),x84394))))
% 51.10/50.82 [8459]~P82(x84591)+E(f331(f137(x84591,x84591,f87(x84591),f331(f331(f87(x84591),x84592),x84593)),x84594),f331(f331(f87(x84591),x84592),f331(f137(x84591,x84591,f87(x84591),x84593),x84594)))
% 51.10/50.82 [8491]P1(f331(f331(f240(f854(x84911,a840)),f331(f269(x84911,x84912),x84913)),f331(f269(x84911,x84912),x84914)))+~P1(f331(f331(f240(f854(f853(x84911,x84912),a840)),x84913),x84914))
% 51.10/50.82 [8502]~P1(f331(f331(f240(a847),x85022),x85024))+P1(f331(f331(f240(f854(x85021,a840)),f331(f163(x85021),f331(f331(f164(x85021),x85022),x85023))),f331(f163(x85021),f331(f331(f164(x85021),x85024),x85023))))
% 51.10/50.82 [8503]~P1(f331(f331(f240(a847),x85034),x85032))+P1(f331(f331(f240(f854(x85031,a840)),f331(f163(x85031),f331(f331(f133(x85031),x85032),x85033))),f331(f163(x85031),f331(f331(f133(x85031),x85034),x85033))))
% 51.10/50.82 [8546]~P1(f331(f68(x85461),f331(f331(f3(f854(x85461,a840)),x85462),x85464)))+P1(f331(f68(x85461),f331(f331(f3(f854(x85461,a840)),x85462),f331(f331(f310(x85461),x85463),x85464))))
% 51.10/50.82 [8580]P1(f331(f331(f333(f853(x85801,x85801)),x85802),f308(x85801,x85803)))+~P1(f331(f331(f333(f853(x85801,x85801)),x85802),f331(f331(f178(f853(x85801,x85801),a840),x85804),x85803)))
% 51.10/50.82 [8581]P1(f331(f331(f333(f853(x85811,x85811)),x85812),f308(x85811,x85813)))+~P1(f331(f331(f333(f853(x85811,x85811)),x85812),f331(f331(f178(f853(x85811,x85811),a840),x85814),x85813)))
% 51.10/50.82 [8656]~P1(f331(f68(x86561),f331(f331(f3(f854(x86561,a840)),x86562),f331(f331(f310(x86561),x86564),x86563))))+P1(f331(f68(x86561),f331(f331(f3(f854(x86561,a840)),x86562),x86563)))
% 51.10/50.82 [8722]P1(f331(f331(f333(f853(x87221,x87222)),f331(f331(f249(x87221,x87222),x87223),x87224)),f184(f854(f853(x87221,x87222),a840))))+~P1(f331(f331(f184(f854(x87221,f854(x87222,a840))),x87223),x87224))
% 51.10/50.82 [8799]~E(f331(f171(x87991,x87992,x87993),x87994),f187(x87992))+~P1(f331(f331(f333(x87991),x87994),f331(f311(f853(x87991,x87992),x87991,f248(x87991,x87992)),f331(f163(f853(x87991,x87992)),x87993))))
% 51.10/50.82 [8836]~P102(x88361)+P1(f331(f331(f240(x88361),f331(f331(f239(x88361),x88362),f331(f331(f244(x88361),x88363),x88364))),f331(f331(f244(x88361),f331(f331(f239(x88361),x88362),x88363)),f331(f331(f239(x88361),x88362),x88364))))
% 51.10/50.82 [8837]~P97(x88371)+P1(f331(f331(f240(x88371),f331(f331(f108(x88371),x88372),f331(f331(f109(x88371),x88373),x88374))),f331(f331(f109(x88371),f331(f331(f108(x88371),x88372),x88373)),f331(f331(f108(x88371),x88372),x88374))))
% 51.10/50.82 [8855]~P1(f331(f331(f333(f853(x88551,x88552)),f331(f331(f249(x88551,x88552),x88553),x88554)),f184(f854(f853(x88551,x88552),a840))))+P1(f331(f331(f184(f854(x88551,f854(x88552,a840))),x88553),x88554))
% 51.10/50.82 [8975]E(x89751,x89752)+~P1(f331(f331(f333(f853(x89753,x89753)),f331(f331(f249(x89753,x89753),x89751),x89752)),f331(f163(f853(x89753,x89753)),f331(f331(f172(x89753,x89753),x89754),x89754))))
% 51.10/50.82 [9007]~P1(f331(f331(f333(f853(x90071,x90071)),f331(f331(f249(x90071,x90071),x90073),x90072)),f308(x90071,x90074)))+~P34(x90071,f331(f331(f310(f853(x90071,x90071)),f331(f331(f249(x90071,x90071),x90072),x90073)),x90074))
% 51.10/50.82 [9008]~P1(f331(f331(f333(f853(x90081,x90081)),f331(f331(f249(x90081,x90081),x90083),x90082)),f308(x90081,x90084)))+~P54(x90081,f331(f331(f310(f853(x90081,x90081)),f331(f331(f249(x90081,x90081),x90082),x90083)),x90084))
% 51.10/50.82 [9021]P1(f331(f331(f333(x90211),x90212),f331(f163(x90211),x90213)))+~P1(f331(f331(f333(f853(x90211,x90211)),f331(f331(f249(x90211,x90211),x90212),x90214)),f331(f163(f853(x90211,x90211)),f331(f331(f172(x90211,x90211),x90213),x90213))))
% 51.10/50.82 [9052]~P102(x90521)+P1(f331(f331(f240(x90521),f331(f331(f239(x90521),f331(f331(f244(x90521),x90522),x90523)),f331(f331(f244(x90521),x90522),x90524))),f331(f331(f244(x90521),x90522),f331(f331(f239(x90521),x90523),x90524))))
% 51.10/50.82 [9053]~P97(x90531)+P1(f331(f331(f240(x90531),f331(f331(f108(x90531),f331(f331(f109(x90531),x90532),x90533)),f331(f331(f109(x90531),x90532),x90534))),f331(f331(f109(x90531),x90532),f331(f331(f108(x90531),x90533),x90534))))
% 51.10/50.82 [9087]P1(f331(f331(f333(f853(x90871,x90871)),f331(f331(f249(x90871,x90871),x90872),x90873)),f331(f331(f289(x90871,x90871,x90871),x90874),f308(x90871,x90874))))+~P1(f331(f331(f333(f853(x90871,x90871)),f331(f331(f249(x90871,x90871),x90872),x90873)),x90874))
% 51.10/50.82 [9115]~E(f331(f311(x91152,x91151,x91153),f247(f854(x91152,a840))),f247(f854(x91151,a840)))+P1(f331(f331(f240(f854(x91151,a840)),f331(f86(f854(x91151,a840)),f331(f311(x91152,x91151,x91153),x91154))),f331(f311(x91152,x91151,x91153),f331(f86(f854(x91152,a840)),x91154))))
% 51.10/50.82 [9422]P1(f331(f331(f333(f853(x94221,x94221)),f331(f331(f249(x94221,x94221),x94222),x94223)),f331(f286(x94221,x94221),f331(f331(f289(x94221,x94221,x94221),x94224),f308(x94221,x94224)))))+~P1(f331(f331(f333(f853(x94221,x94221)),f331(f331(f249(x94221,x94221),x94222),x94223)),f331(f331(f289(x94221,x94221,x94221),f331(f286(x94221,x94221),x94224)),f308(x94221,f331(f286(x94221,x94221),x94224)))))
% 51.10/50.82 [9423]~P1(f331(f331(f333(f853(x94231,x94231)),f331(f331(f249(x94231,x94231),x94232),x94233)),f331(f286(x94231,x94231),f331(f331(f289(x94231,x94231,x94231),x94234),f308(x94231,x94234)))))+P1(f331(f331(f333(f853(x94231,x94231)),f331(f331(f249(x94231,x94231),x94232),x94233)),f331(f331(f289(x94231,x94231,x94231),f331(f286(x94231,x94231),x94234)),f308(x94231,f331(f286(x94231,x94231),x94234)))))
% 51.10/50.82 [9449]~P1(f331(f331(f333(x94492),x94494),f331(f267(x94491,x94492),x94493)))+P1(f331(f331(f333(f853(x94491,x94492)),f331(f331(f249(x94491,x94492),f577(x94493,x94491,x94494,x94492)),x94494)),x94493))
% 51.10/50.82 [9450]~P1(f331(f331(f333(x94502),x94504),f331(f267(x94501,x94502),x94503)))+P1(f331(f331(f333(f853(x94501,x94502)),f331(f331(f249(x94501,x94502),f578(x94503,x94501,x94504,x94502)),x94504)),x94503))
% 51.10/50.82 [9470]~P1(f331(f331(f333(x94701),x94704),f331(f331(f108(f854(x94701,a840)),x94702),x94703)))+P1(f331(f331(f331(f108(f854(x94701,a840)),f331(f331(f9(x94701,f854(x94701,a840),a840),f333(x94701)),x94702)),f331(f331(f9(x94701,f854(x94701,a840),a840),f333(x94701)),x94703)),x94704))
% 51.10/50.82 [9471]~P1(f331(f331(f333(x94711),x94714),f331(f331(f109(f854(x94711,a840)),x94712),x94713)))+P1(f331(f331(f331(f109(f854(x94711,a840)),f331(f331(f9(x94711,f854(x94711,a840),a840),f333(x94711)),x94712)),f331(f331(f9(x94711,f854(x94711,a840),a840),f333(x94711)),x94713)),x94714))
% 51.10/50.82 [9546]~P1(f331(f331(f333(f853(x95461,x95461)),f331(f331(f249(x95461,x95461),x95464),x95463)),f331(f331(f289(x95461,x95461,x95461),x95462),f308(x95461,x95462))))+P1(f331(f331(f333(f853(x95461,x95461)),f331(f331(f249(x95461,x95461),f679(x95462,x95463,x95464,x95461)),x95463)),x95462))
% 51.10/50.82 [9586]P1(f331(f331(f333(x95861),x95862),f331(f331(f108(f854(x95861,a840)),x95863),x95864)))+~P1(f331(f331(f331(f108(f854(x95861,a840)),f331(f331(f9(x95861,f854(x95861,a840),a840),f333(x95861)),x95863)),f331(f331(f9(x95861,f854(x95861,a840),a840),f333(x95861)),x95864)),x95862))
% 51.10/50.82 [9587]P1(f331(f331(f333(x95871),x95872),f331(f331(f109(f854(x95871,a840)),x95873),x95874)))+~P1(f331(f331(f331(f109(f854(x95871,a840)),f331(f331(f9(x95871,f854(x95871,a840),a840),f333(x95871)),x95873)),f331(f331(f9(x95871,f854(x95871,a840),a840),f333(x95871)),x95874)),x95872))
% 51.10/50.82 [9870]P32(x98701,f331(f331(f9(x98701,f854(f853(x98701,x98701),a840),f854(x98701,a840)),f331(f331(f10(f854(x98701,f854(f854(f853(x98701,x98701),a840),a840)),f854(f854(f853(x98701,x98701),a840),f854(x98701,a840)),x98701),f9(x98701,f854(f853(x98701,x98701),a840),a840)),f331(f331(f10(f854(x98701,f853(x98701,x98701)),f854(x98701,f854(f854(f853(x98701,x98701),a840),a840)),x98701),f331(f10(f853(x98701,x98701),f854(f854(f853(x98701,x98701),a840),a840),x98701),f333(f853(x98701,x98701)))),f249(x98701,x98701)))),x98702),x98703,x98704)+~P1(f331(f331(f333(f853(f848(x98701),f848(x98701))),f331(f331(f249(f848(x98701),f848(x98701)),x98703),x98704)),f151(x98701,x98702)))
% 51.10/50.82 [9874]P55(x98741,f331(f331(f9(x98741,f854(f853(x98741,x98741),a840),f854(x98741,a840)),f331(f331(f10(f854(x98741,f854(f854(f853(x98741,x98741),a840),a840)),f854(f854(f853(x98741,x98741),a840),f854(x98741,a840)),x98741),f9(x98741,f854(f853(x98741,x98741),a840),a840)),f331(f331(f10(f854(x98741,f853(x98741,x98741)),f854(x98741,f854(f854(f853(x98741,x98741),a840),a840)),x98741),f331(f10(f853(x98741,x98741),f854(f854(f853(x98741,x98741),a840),a840),x98741),f333(f853(x98741,x98741)))),f249(x98741,x98741)))),x98742),x98743,x98744)+~P1(f331(f331(f333(f853(f854(x98741,a840),f854(x98741,a840))),f331(f331(f249(f854(x98741,a840),f854(x98741,a840)),x98743),x98744)),f323(x98741,x98742)))
% 51.10/50.82 [9903]E(x99031,x99032)+~E(f331(f331(f9(x99033,f854(f853(x99033,x99034),a840),f854(x99034,a840)),f331(f331(f10(f854(x99034,f854(f854(f853(x99033,x99034),a840),a840)),f854(f854(f853(x99033,x99034),a840),f854(x99034,a840)),x99033),f9(x99034,f854(f853(x99033,x99034),a840),a840)),f331(f331(f10(f854(x99034,f853(x99033,x99034)),f854(x99034,f854(f854(f853(x99033,x99034),a840),a840)),x99033),f331(f10(f853(x99033,x99034),f854(f854(f853(x99033,x99034),a840),a840),x99034),f333(f853(x99033,x99034)))),f249(x99033,x99034)))),x99031),f331(f331(f9(x99033,f854(f853(x99033,x99034),a840),f854(x99034,a840)),f331(f331(f10(f854(x99034,f854(f854(f853(x99033,x99034),a840),a840)),f854(f854(f853(x99033,x99034),a840),f854(x99034,a840)),x99033),f9(x99034,f854(f853(x99033,x99034),a840),a840)),f331(f331(f10(f854(x99034,f853(x99033,x99034)),f854(x99034,f854(f854(f853(x99033,x99034),a840),a840)),x99033),f331(f10(f853(x99033,x99034),f854(f854(f853(x99033,x99034),a840),a840),x99034),f333(f853(x99033,x99034)))),f249(x99033,x99034)))),x99032))
% 51.10/50.82 [9906]~P32(x99061,f331(f331(f9(x99061,f854(f853(x99061,x99061),a840),f854(x99061,a840)),f331(f331(f10(f854(x99061,f854(f854(f853(x99061,x99061),a840),a840)),f854(f854(f853(x99061,x99061),a840),f854(x99061,a840)),x99061),f9(x99061,f854(f853(x99061,x99061),a840),a840)),f331(f331(f10(f854(x99061,f853(x99061,x99061)),f854(x99061,f854(f854(f853(x99061,x99061),a840),a840)),x99061),f331(f10(f853(x99061,x99061),f854(f854(f853(x99061,x99061),a840),a840),x99061),f333(f853(x99061,x99061)))),f249(x99061,x99061)))),x99064),x99062,x99063)+P1(f331(f331(f333(f853(f848(x99061),f848(x99061))),f331(f331(f249(f848(x99061),f848(x99061)),x99062),x99063)),f151(x99061,x99064)))
% 51.10/50.82 [9907]~P55(x99071,f331(f331(f9(x99071,f854(f853(x99071,x99071),a840),f854(x99071,a840)),f331(f331(f10(f854(x99071,f854(f854(f853(x99071,x99071),a840),a840)),f854(f854(f853(x99071,x99071),a840),f854(x99071,a840)),x99071),f9(x99071,f854(f853(x99071,x99071),a840),a840)),f331(f331(f10(f854(x99071,f853(x99071,x99071)),f854(x99071,f854(f854(f853(x99071,x99071),a840),a840)),x99071),f331(f10(f853(x99071,x99071),f854(f854(f853(x99071,x99071),a840),a840),x99071),f333(f853(x99071,x99071)))),f249(x99071,x99071)))),x99074),x99072,x99073)+P1(f331(f331(f333(f853(f854(x99071,a840),f854(x99071,a840))),f331(f331(f249(f854(x99071,a840),f854(x99071,a840)),x99072),x99073)),f323(x99071,x99074)))
% 51.10/50.82 [7388]~P91(x73881)+E(f331(f331(f87(x73881),f331(f111(x73881),x73882)),f331(f331(f87(x73881),f331(f111(x73881),x73883)),x73884)),f331(f331(f87(x73881),f331(f111(x73881),f331(f331(f87(a1),x73882),x73883))),x73884))
% 51.10/50.82 [7389]~P91(x73891)+E(f331(f331(f87(x73891),f331(f111(x73891),x73892)),f331(f331(f3(x73891),f331(f111(x73891),x73893)),x73894)),f331(f331(f3(x73891),f331(f111(x73891),f331(f331(f87(a1),x73892),x73893))),x73894))
% 51.10/50.82 [7390]~P91(x73901)+E(f331(f331(f88(x73901),f331(f111(x73901),x73902)),f331(f331(f88(x73901),f331(f111(x73901),x73903)),x73904)),f331(f331(f88(x73901),f331(f111(x73901),f331(f331(f88(a1),x73902),x73903))),x73904))
% 51.10/50.82 [7438]~P84(x74381)+E(f331(f157(x74381),f331(f331(f147(x74382,x74381),f331(f18(x74381,x74382),x74383)),x74384)),f331(f331(f88(x74381),f331(f107(x74381),f331(f185(f848(x74382)),x74384))),x74383))
% 51.10/50.82 [7674]E(f331(f273(x76741,f331(f331(f145(f853(a106,x76741)),x76742),x76743)),x76744),f331(f258(a106,x76741),x76742))+~P1(f331(f331(f241(a106),x76744),f331(f248(a106,x76741),x76742)))
% 51.10/50.82 [7722]~P91(x77221)+E(f331(f331(f87(x77221),f331(f111(x77221),x77222)),f331(f331(f3(x77221),x77223),f331(f111(x77221),x77224))),f331(f331(f87(x77221),f331(f111(x77221),f331(f331(f87(a1),x77222),f331(f86(a1),x77224)))),x77223))
% 51.10/50.82 [7853]E(f331(f273(x78531,x78532),f331(f331(f3(a106),x78533),f331(f248(a106,x78531),x78534))),f331(f273(x78531,f331(f331(f145(f853(a106,x78531)),x78534),x78532)),x78533))+P1(f331(f331(f241(a106),x78533),f331(f248(a106,x78531),x78534)))
% 51.10/50.82 [8286]~P1(f331(f331(f333(x82861),x82862),f331(f163(x82861),f121(x82861,x82864))))+P1(f331(f331(f333(x82861),x82862),f331(f163(x82861),f121(x82861,f331(f331(f130(x82861),x82863),x82864)))))
% 51.10/50.82 [8287]~P1(f331(f331(f333(x82871),x82872),f331(f163(x82871),f121(x82871,x82873))))+P1(f331(f331(f333(x82871),x82872),f331(f163(x82871),f121(x82871,f331(f331(f130(x82871),x82873),x82874)))))
% 51.10/50.82 [8309]E(f331(f331(f108(f854(x83091,a840)),f331(f331(f109(f854(x83091,a840)),x83092),x83093)),x83094),f331(f331(f109(f854(x83091,a840)),x83092),f331(f331(f108(f854(x83091,a840)),x83093),x83094)))+~P1(f331(f331(f240(f854(x83091,a840)),x83094),x83092))
% 51.10/50.82 [8594]~E(f331(f331(f108(f854(x85941,a840)),f331(f331(f109(f854(x85941,a840)),x85943),x85944)),x85942),f331(f331(f109(f854(x85941,a840)),x85943),f331(f331(f108(f854(x85941,a840)),x85944),x85942)))+P1(f331(f331(f240(f854(x85941,a840)),x85942),x85943))
% 51.10/50.82 [8842]~P1(f331(f331(f240(f854(x88421,a840)),x88422),f331(f331(f108(f854(x88421,a840)),x88423),x88424)))+P1(f331(f331(f240(f854(x88421,a840)),f331(f331(f3(f854(x88421,a840)),x88422),x88423)),x88424))
% 51.10/50.82 [8959]P1(f331(f331(f240(f854(x89591,a840)),x89592),f331(f331(f108(f854(x89591,a840)),x89593),x89594)))+~P1(f331(f331(f240(f854(x89591,a840)),f331(f331(f3(f854(x89591,a840)),x89592),x89593)),x89594))
% 51.10/50.82 [9034]~P78(x90341)+E(f331(f82(x90341),f331(f331(f8(x90342,x90341),f331(f331(f10(x90341,x90341,x90342),f82(x90341)),x90343)),x90344)),f331(f331(f8(x90342,x90341),f331(f331(f10(x90341,x90341,x90342),f82(x90341)),x90343)),x90344))
% 51.10/50.82 [9178]~P78(x91781)+P1(f331(f331(f240(x91781),f2(x91781)),f331(f331(f8(x91782,x91781),f331(f331(f10(x91781,x91781,x91782),f82(x91781)),x91783)),x91784)))
% 51.10/50.82 [9181]~P4(x91811)+E(f331(f157(x91811),f331(f331(f147(x91812,x91811),f331(f80(x91811,x91811,x91812,f86(x91811)),x91813)),x91814)),f331(f86(x91811),f331(f157(x91811),f331(f331(f147(x91812,x91811),x91813),x91814))))
% 51.10/50.82 [9319]~P78(x93191)+P1(f331(f331(f240(x93191),f331(f82(x93191),f331(f331(f8(x93192,x93191),x93193),x93194))),f331(f331(f8(x93192,x93191),f331(f331(f10(x93191,x93191,x93192),f82(x93191)),x93193)),x93194)))
% 51.10/50.82 [9347]~E(f331(f331(f87(a847),x93471),x93474),f331(f331(f87(a847),x93473),x93472))+P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),f331(f331(f249(a847,a847),x93471),x93472)),f331(f331(f249(a847,a847),x93473),x93474))),a116))
% 51.10/50.82 [9348]~P1(f331(f331(f241(a847),x93481),x93483))+P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),f331(f331(f249(a847,a847),x93481),x93482)),f331(f331(f249(a847,a847),x93483),x93484))),a45))
% 51.10/50.82 [9349]~P1(f331(f331(f241(a847),x93491),x93493))+P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),f331(f331(f249(a847,a847),x93491),x93492)),f331(f331(f249(a847,a847),x93493),x93494))),a77))
% 51.10/50.82 [9493]E(f331(f331(f87(a847),x94931),x94932),f331(f331(f87(a847),x94933),x94934))+~P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),f331(f331(f249(a847,a847),x94931),x94934)),f331(f331(f249(a847,a847),x94933),x94932))),a116))
% 51.10/50.82 [9539]~P1(f331(f331(f333(x95392),x95394),f331(f331(f51(x95391,f854(x95392,a840)),f247(f854(x95391,a840))),x95393)))+P1(f331(f331(f331(f51(x95391,f854(x95392,a840)),f247(f854(x95391,a840))),f331(f331(f10(f854(x95392,a840),f854(x95392,a840),x95391),f331(f9(x95392,f854(x95392,a840),a840),f333(x95392))),x95393)),x95394))
% 51.10/50.82 [9540]~P1(f331(f331(f333(x95402),x95404),f331(f331(f52(x95401,f854(x95402,a840)),f247(f854(x95401,a840))),x95403)))+P1(f331(f331(f331(f52(x95401,f854(x95402,a840)),f247(f854(x95401,a840))),f331(f331(f10(f854(x95402,a840),f854(x95402,a840),x95401),f331(f9(x95402,f854(x95402,a840),a840),f333(x95402))),x95403)),x95404))
% 51.10/50.82 [9611]~P1(f331(f61(x96111,x96112),f331(f331(f249(a1,a1),x96114),x96113)))+P1(f331(f61(f331(f86(a1),x96111),x96112),f331(f331(f249(a1,a1),f331(f331(f331(f103(a1),f331(f331(a328,x96113),f2(a1))),f331(f86(a1),x96114)),f331(f331(f3(a1),f331(f86(a1),x96114)),f85(a1)))),f331(f331(f331(f103(a1),f331(f331(a328,x96113),f2(a1))),f2(a1)),f331(f331(f3(a1),x96112),x96113)))))
% 51.10/50.82 [9620]P1(f331(f331(f333(x96201),x96202),f331(f331(f51(x96203,f854(x96201,a840)),f247(f854(x96203,a840))),x96204)))+~P1(f331(f331(f331(f51(x96203,f854(x96201,a840)),f247(f854(x96203,a840))),f331(f331(f10(f854(x96201,a840),f854(x96201,a840),x96203),f331(f9(x96201,f854(x96201,a840),a840),f333(x96201))),x96204)),x96202))
% 51.10/50.82 [9621]P1(f331(f331(f333(x96211),x96212),f331(f331(f52(x96213,f854(x96211,a840)),f247(f854(x96213,a840))),x96214)))+~P1(f331(f331(f331(f52(x96213,f854(x96211,a840)),f247(f854(x96213,a840))),f331(f331(f10(f854(x96211,a840),f854(x96211,a840),x96213),f331(f9(x96211,f854(x96211,a840),a840),f333(x96211))),x96214)),x96212))
% 51.10/50.82 [9632]E(f331(f331(f51(a847,f854(x96321,a840)),f247(f854(a847,a840))),x96322),f331(f331(f51(a847,f854(x96321,a840)),f247(f854(a847,a840))),x96323))+~E(f331(f331(f51(a847,f854(x96321,a840)),f331(f302(a847,f2(a847)),f520(x96322,x96324,x96323,x96321))),x96323),f331(f331(f51(a847,f854(x96321,a840)),f331(f302(a847,f2(a847)),f331(f331(f87(a847),f520(x96322,x96324,x96323,x96321)),x96324))),x96322))
% 51.10/50.82 [9969]~P1(f331(f331(f240(f854(f853(x99691,x99692),a840)),x99693),x99694))+P1(f331(f331(f240(f854(x99691,f854(x99692,a840))),f331(f331(f9(x99691,f854(f853(x99691,x99692),a840),f854(x99692,a840)),f331(f331(f10(f854(x99692,f854(f854(f853(x99691,x99692),a840),a840)),f854(f854(f853(x99691,x99692),a840),f854(x99692,a840)),x99691),f9(x99692,f854(f853(x99691,x99692),a840),a840)),f331(f331(f10(f854(x99692,f853(x99691,x99692)),f854(x99692,f854(f854(f853(x99691,x99692),a840),a840)),x99691),f331(f10(f853(x99691,x99692),f854(f854(f853(x99691,x99692),a840),a840),x99692),f333(f853(x99691,x99692)))),f249(x99691,x99692)))),x99693)),f331(f331(f9(x99691,f854(f853(x99691,x99692),a840),f854(x99692,a840)),f331(f331(f10(f854(x99692,f854(f854(f853(x99691,x99692),a840),a840)),f854(f854(f853(x99691,x99692),a840),f854(x99692,a840)),x99691),f9(x99692,f854(f853(x99691,x99692),a840),a840)),f331(f331(f10(f854(x99692,f853(x99691,x99692)),f854(x99692,f854(f854(f853(x99691,x99692),a840),a840)),x99691),f331(f10(f853(x99691,x99692),f854(f854(f853(x99691,x99692),a840),a840),x99692),f333(f853(x99691,x99692)))),f249(x99691,x99692)))),x99694)))
% 51.10/50.82 [9985]P1(f331(f331(f240(f854(f853(x99851,x99852),a840)),x99853),x99854))+~P1(f331(f331(f240(f854(x99851,f854(x99852,a840))),f331(f331(f9(x99851,f854(f853(x99851,x99852),a840),f854(x99852,a840)),f331(f331(f10(f854(x99852,f854(f854(f853(x99851,x99852),a840),a840)),f854(f854(f853(x99851,x99852),a840),f854(x99852,a840)),x99851),f9(x99852,f854(f853(x99851,x99852),a840),a840)),f331(f331(f10(f854(x99852,f853(x99851,x99852)),f854(x99852,f854(f854(f853(x99851,x99852),a840),a840)),x99851),f331(f10(f853(x99851,x99852),f854(f854(f853(x99851,x99852),a840),a840),x99852),f333(f853(x99851,x99852)))),f249(x99851,x99852)))),x99853)),f331(f331(f9(x99851,f854(f853(x99851,x99852),a840),f854(x99852,a840)),f331(f331(f10(f854(x99852,f854(f854(f853(x99851,x99852),a840),a840)),f854(f854(f853(x99851,x99852),a840),f854(x99852,a840)),x99851),f9(x99852,f854(f853(x99851,x99852),a840),a840)),f331(f331(f10(f854(x99852,f853(x99851,x99852)),f854(x99852,f854(f854(f853(x99851,x99852),a840),a840)),x99851),f331(f10(f853(x99851,x99852),f854(f854(f853(x99851,x99852),a840),a840),x99852),f333(f853(x99851,x99852)))),f249(x99851,x99852)))),x99854)))
% 51.10/50.82 [9079]~P1(f331(f331(f333(f853(x90791,x90791)),x90792),f308(x90791,x90794)))+P1(f331(f331(f333(f853(x90791,x90791)),x90792),f308(x90791,f331(f331(f108(f854(f853(x90791,x90791),a840)),x90793),x90794))))
% 51.10/50.82 [9080]~P1(f331(f331(f333(f853(x90801,x90801)),x90802),f308(x90801,x90803)))+P1(f331(f331(f333(f853(x90801,x90801)),x90802),f308(x90801,f331(f331(f108(f854(f853(x90801,x90801),a840)),x90803),x90804))))
% 51.10/50.82 [9413]~E(f331(f163(x94131),x94134),f174(x94131,x94132,x94133))+E(f171(x94131,x94132,f331(f331(f147(x94131,f853(x94131,x94132)),f331(f331(f20(x94131,x94132,f853(x94131,x94132)),f249(x94131,x94132)),f331(f331(f10(f851(x94132),x94132,x94131),f238(x94132)),x94133))),x94134)),x94133)
% 51.10/50.82 [9715]~P1(f331(f331(f241(a847),f331(f331(f87(a847),x97151),x97154)),f331(f331(f87(a847),x97153),x97152)))+P1(f331(f331(f241(a1),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x97151),x97152)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x97153),x97154)),f184(f854(f853(a847,a847),a840)))))))
% 51.10/50.82 [9716]~P1(f331(f331(f240(a847),f331(f331(f87(a847),x97161),x97164)),f331(f331(f87(a847),x97163),x97162)))+P1(f331(f331(f240(a1),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x97161),x97162)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x97163),x97164)),f184(f854(f853(a847,a847),a840)))))))
% 51.10/50.82 [9807]P1(f331(f331(f241(a847),f331(f331(f87(a847),x98071),x98072)),f331(f331(f87(a847),x98073),x98074)))+~P1(f331(f331(f241(a1),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x98071),x98074)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x98073),x98072)),f184(f854(f853(a847,a847),a840)))))))
% 51.10/50.82 [9808]P1(f331(f331(f240(a847),f331(f331(f87(a847),x98081),x98082)),f331(f331(f87(a847),x98083),x98084)))+~P1(f331(f331(f240(a1),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x98081),x98084)),f184(f854(f853(a847,a847),a840)))))),f331(a96,f331(f285(f853(a847,a847),f853(a847,a847),a116),f331(f331(f310(f853(a847,a847)),f331(f331(f249(a847,a847),x98083),x98082)),f184(f854(f853(a847,a847),a840)))))))
% 51.10/50.82 [9856]P1(f331(f331(f240(f854(x98561,a840)),f331(f331(f51(a847,f854(x98561,a840)),f247(f854(a847,a840))),x98562)),f331(f331(f51(a847,f854(x98561,a840)),f247(f854(a847,a840))),x98563)))+~P1(f331(f331(f240(f854(x98561,a840)),f331(f331(f51(a847,f854(x98561,a840)),f331(f302(a847,f2(a847)),f521(x98563,x98564,x98562,x98561))),x98562)),f331(f331(f51(a847,f854(x98561,a840)),f331(f302(a847,f2(a847)),f331(f331(f87(a847),f521(x98563,x98564,x98562,x98561)),x98564))),x98563)))
% 51.10/50.82 [9909]P1(f331(f331(f240(a106),x99094),f2(a106)))+E(f331(f331(f261(f853(a106,a106),f853(x99091,f854(a850,a838)),f853(a106,a106),f853(f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106))),f331(x99092,x99093)),f331(f331(f10(f854(f854(a106,f854(a840,f851(f849(x99091)))),f854(f853(a106,a106),f853(f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106)))),f854(f853(a106,a106),f853(f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106))),f853(x99091,f854(a850,a838))),f331(f261(f853(a106,a106),f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106),f853(f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106))),f280(x99091,x99092,f331(f331(f3(a106),x99094),f85(a106)),x99093))),f331(f331(f10(f854(f854(a106,f854(a840,f851(f849(x99091)))),f854(a106,f854(a840,f851(f849(x99091))))),f854(f854(a106,f854(a840,f851(f849(x99091)))),f854(f853(a106,a106),f853(f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106)))),f853(x99091,f854(a850,a838))),f331(f10(f854(a106,f854(a840,f851(f849(x99091)))),f854(f853(a106,a106),f853(f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106))),f854(a106,f854(a840,f851(f849(x99091))))),f249(f854(a106,f854(a840,f851(f849(x99091)))),f853(a106,a106)))),f331(f331(f10(f854(a106,f854(a840,f851(f849(x99091)))),f854(f854(a106,f854(a840,f851(f849(x99091)))),f854(a106,f854(a840,f851(f849(x99091))))),f853(x99091,f854(a850,a838))),f56(x99091)),f331(f331(f10(x99091,f854(a106,f854(a840,f851(f849(x99091)))),f853(x99091,f854(a850,a838))),f54(x99091)),f248(x99091,f854(a850,a838))))))),f280(x99091,x99092,x99094,x99093))
% 51.10/50.82 [9960]~P1(f331(f331(f333(x99602),x99604),f331(f267(x99601,x99602),x99603)))+P1(f331(f255(x99601,x99602,f331(f331(f9(x99601,f854(f853(x99601,x99602),a840),f854(x99602,a840)),f331(f331(f10(f854(x99602,f854(f854(f853(x99601,x99602),a840),a840)),f854(f854(f853(x99601,x99602),a840),f854(x99602,a840)),x99601),f9(x99602,f854(f853(x99601,x99602),a840),a840)),f331(f331(f10(f854(x99602,f853(x99601,x99602)),f854(x99602,f854(f854(f853(x99601,x99602),a840),a840)),x99601),f331(f10(f853(x99601,x99602),f854(f854(f853(x99601,x99602),a840),a840),x99602),f333(f853(x99601,x99602)))),f249(x99601,x99602)))),x99603)),x99604))
% 51.10/50.82 [9961]~P1(f331(f331(f333(x99611),x99614),f331(f269(x99611,x99612),x99613)))+P1(f331(f254(x99611,x99612,f331(f331(f9(x99611,f854(f853(x99611,x99612),a840),f854(x99612,a840)),f331(f331(f10(f854(x99612,f854(f854(f853(x99611,x99612),a840),a840)),f854(f854(f853(x99611,x99612),a840),f854(x99612,a840)),x99611),f9(x99612,f854(f853(x99611,x99612),a840),a840)),f331(f331(f10(f854(x99612,f853(x99611,x99612)),f854(x99612,f854(f854(f853(x99611,x99612),a840),a840)),x99611),f331(f10(f853(x99611,x99612),f854(f854(f853(x99611,x99612),a840),a840),x99612),f333(f853(x99611,x99612)))),f249(x99611,x99612)))),x99613)),x99614))
% 51.10/50.82 [9972]P1(f331(f331(f333(x99721),x99722),f331(f267(x99723,x99721),x99724)))+~P1(f331(f255(x99723,x99721,f331(f331(f9(x99723,f854(f853(x99723,x99721),a840),f854(x99721,a840)),f331(f331(f10(f854(x99721,f854(f854(f853(x99723,x99721),a840),a840)),f854(f854(f853(x99723,x99721),a840),f854(x99721,a840)),x99723),f9(x99721,f854(f853(x99723,x99721),a840),a840)),f331(f331(f10(f854(x99721,f853(x99723,x99721)),f854(x99721,f854(f854(f853(x99723,x99721),a840),a840)),x99723),f331(f10(f853(x99723,x99721),f854(f854(f853(x99723,x99721),a840),a840),x99721),f333(f853(x99723,x99721)))),f249(x99723,x99721)))),x99724)),x99722))
% 51.10/50.82 [9973]P1(f331(f331(f333(x99731),x99732),f331(f269(x99731,x99733),x99734)))+~P1(f331(f254(x99731,x99733,f331(f331(f9(x99731,f854(f853(x99731,x99733),a840),f854(x99733,a840)),f331(f331(f10(f854(x99733,f854(f854(f853(x99731,x99733),a840),a840)),f854(f854(f853(x99731,x99733),a840),f854(x99733,a840)),x99731),f9(x99733,f854(f853(x99731,x99733),a840),a840)),f331(f331(f10(f854(x99733,f853(x99731,x99733)),f854(x99733,f854(f854(f853(x99731,x99733),a840),a840)),x99731),f331(f10(f853(x99731,x99733),f854(f854(f853(x99731,x99733),a840),a840),x99733),f333(f853(x99731,x99733)))),f249(x99731,x99733)))),x99734)),x99732))
% 51.10/50.82 [9729]~P87(x97291)+E(f331(f331(f88(x97291),f331(f331(f87(x97291),f85(x97291)),f85(x97291))),f331(f331(f8(a847,x97291),f331(f331(f10(x97291,x97291,a847),f331(f87(x97291),x97292)),f331(f331(f9(a847,x97291,x97291),f331(f331(f10(x97291,f854(x97291,x97291),a847),f88(x97291)),f107(x97291))),x97293))),f331(f265(a847),x97294))),f331(f331(f88(x97291),f331(f107(x97291),x97294)),f331(f331(f87(x97291),x97292),f331(f331(f87(x97291),x97292),f331(f331(f88(x97291),f331(f107(x97291),f331(f331(f3(a847),x97294),f85(a847)))),x97293)))))
% 51.10/50.82 [9877]P1(f331(x98771,f576(x98772,x98773,x98774,x98771)))+P34(x98772,f331(f264(f853(x98772,x98772)),f331(f259(x98772,x98772,a840),f331(f331(f10(f854(x98772,a840),f854(x98772,a840),x98772),f331(f20(x98772,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98772),a329),x98771))),f331(f331(f9(x98772,f854(x98772,x98772),f854(x98772,a840)),f331(f331(f10(f854(x98772,a840),f854(f854(x98772,x98772),f854(x98772,a840)),x98772),f10(x98772,a840,x98772)),a328)),x98773)))))
% 51.10/50.82 [9891]~P1(f331(f331(f241(a847),f331(x98914,f331(x98913,f576(x98911,x98913,x98914,x98912)))),f331(x98914,f576(x98911,x98913,x98914,x98912))))+P34(x98911,f331(f264(f853(x98911,x98911)),f331(f259(x98911,x98911,a840),f331(f331(f10(f854(x98911,a840),f854(x98911,a840),x98911),f331(f20(x98911,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98911),a329),x98912))),f331(f331(f9(x98911,f854(x98911,x98911),f854(x98911,a840)),f331(f331(f10(f854(x98911,a840),f854(f854(x98911,x98911),f854(x98911,a840)),x98911),f10(x98911,a840,x98911)),a328)),x98913)))))
% 51.10/50.82 [9998]~P1(f331(f331(f333(f853(x99981,x99981)),f331(f331(f249(x99981,x99981),x99983),x99984)),f331(f331(f108(f854(f853(x99981,x99981),a840)),x99982),f308(x99981,f184(f854(f853(x99981,x99981),a840))))))+P1(f331(f331(f331(f331(f108(f854(x99981,f854(x99981,a840))),f331(f331(f9(x99981,f854(f853(x99981,x99981),a840),f854(x99981,a840)),f331(f331(f10(f854(x99981,f854(f854(f853(x99981,x99981),a840),a840)),f854(f854(f853(x99981,x99981),a840),f854(x99981,a840)),x99981),f9(x99981,f854(f853(x99981,x99981),a840),a840)),f331(f331(f10(f854(x99981,f853(x99981,x99981)),f854(x99981,f854(f854(f853(x99981,x99981),a840),a840)),x99981),f331(f10(f853(x99981,x99981),f854(f854(f853(x99981,x99981),a840),a840),x99981),f333(f853(x99981,x99981)))),f249(x99981,x99981)))),x99982)),a328),x99983),x99984))
% 51.10/50.82 [10007]P1(f331(f331(f333(f853(x100071,x100071)),f331(f331(f249(x100071,x100071),x100072),x100073)),f331(f331(f108(f854(f853(x100071,x100071),a840)),x100074),f308(x100071,f184(f854(f853(x100071,x100071),a840))))))+~P1(f331(f331(f331(f331(f108(f854(x100071,f854(x100071,a840))),f331(f331(f9(x100071,f854(f853(x100071,x100071),a840),f854(x100071,a840)),f331(f331(f10(f854(x100071,f854(f854(f853(x100071,x100071),a840),a840)),f854(f854(f853(x100071,x100071),a840),f854(x100071,a840)),x100071),f9(x100071,f854(f853(x100071,x100071),a840),a840)),f331(f331(f10(f854(x100071,f853(x100071,x100071)),f854(x100071,f854(f854(f853(x100071,x100071),a840),a840)),x100071),f331(f10(f853(x100071,x100071),f854(f854(f853(x100071,x100071),a840),a840),x100071),f333(f853(x100071,x100071)))),f249(x100071,x100071)))),x100074)),a328),x100072),x100073))
% 51.10/50.82 [9957]E(f331(f331(f145(f848(x99571)),f331(f331(f145(x99571),x99572),f331(f137(f848(x99571),f848(x99571),f130(x99571),f120(x99571)),f331(f331(f147(f848(x99571),f848(x99571)),f149(f848(x99571),x99571,f120(x99571),f331(f331(f10(f848(x99571),f854(f848(x99571),f848(x99571)),x99571),f18(f848(x99571),f848(x99571))),f331(f331(f9(x99571,f848(x99571),f848(x99571)),f145(x99571)),f120(x99571))))),x99573)))),f169(x99571,f331(f331(f145(f848(x99571)),x99574),f331(f137(f848(f848(x99571)),f848(f848(x99571)),f130(f848(x99571)),f120(f848(x99571))),f331(f331(f147(f848(x99571),f848(f848(x99571))),f149(f848(f848(x99571)),x99571,f120(f848(x99571)),f331(f18(f854(f848(x99571),f848(f848(x99571))),x99571),f331(f331(f9(f848(x99571),f848(f848(x99571)),f848(f848(x99571))),f145(f848(x99571))),f120(f848(x99571)))))),x99573))))),f169(x99571,f331(f331(f145(f848(x99571)),f331(f331(f145(x99571),x99572),x99574)),x99573)))+~P1(f331(f320(f848(f848(x99571)),f170(x99571)),f331(f331(f145(f848(x99571)),f331(f331(f145(x99571),x99572),x99574)),x99573)))
% 51.10/50.82 [9997]~P1(f331(f68(x99972),f331(f264(x99972),x99974)))+P1(f331(f68(x99971),f331(f264(x99971),f331(f331(f10(f854(x99972,a840),a840,x99971),f94(x99972)),f331(f331(f9(x99971,f854(x99972,a840),f854(x99972,a840)),f331(f331(f10(f854(x99972,f854(a840,a840)),f854(f854(x99972,a840),f854(x99972,a840)),x99971),f20(x99972,a840,a840)),f331(f331(f10(f854(x99972,a840),f854(x99972,f854(a840,a840)),x99971),f331(f10(a840,f854(a840,a840),x99972),a329)),f331(f331(f9(x99971,f854(x99972,x99971),f854(x99972,a840)),f331(f331(f10(f854(x99971,a840),f854(f854(x99972,x99971),f854(x99972,a840)),x99971),f10(x99971,a840,x99972)),a328)),x99973)))),x99974)))))
% 51.10/50.82 [8954]~P37(f38(x89541,x89545),x89542,x89543,x89544)+P37(x89541,x89542,x89543,f488(x89544,x89543,x89542,x89545,x89541))
% 51.10/50.82 [8955]~P37(f38(x89551,x89555),x89552,x89553,x89554)+P37(x89551,x89552,x89553,f625(x89554,x89553,x89552,x89555,x89551))
% 51.10/50.82 [8956]~P37(f38(x89565,x89561),x89564,x89563,x89562)+P37(x89561,f488(x89562,x89563,x89564,x89561,x89565),x89563,x89562)
% 51.10/50.82 [8957]~P37(f38(x89575,x89571),x89574,x89573,x89572)+P37(x89571,f625(x89572,x89573,x89574,x89571,x89575),x89573,x89572)
% 51.10/50.82 [5491]E(f331(f331(f310(x54911),x54912),f174(x54911,x54913,x54914)),f174(x54911,x54913,x54914))+~E(f331(x54914,x54912),f331(f234(x54913),x54915))
% 51.10/50.82 [5907]P1(f331(f255(x59071,x59072,x59073),x59074))+~P1(f331(f331(x59073,x59075),x59074))
% 51.10/50.82 [5908]P1(f331(f255(x59081,x59082,x59083),x59084))+~P1(f331(f331(x59083,x59085),x59084))
% 51.10/50.82 [5909]P1(f331(f254(x59091,x59092,x59093),x59094))+~P1(f331(f331(x59093,x59094),x59095))
% 51.10/50.82 [5910]P1(f331(f254(x59101,x59102,x59103),x59104))+~P1(f331(f331(x59103,x59104),x59105))
% 51.10/50.82 [5913]~E(f331(x59134,x59132),f331(f234(x59133),x59135))+P1(f331(f331(f333(x59131),x59132),f174(x59131,x59133,x59134)))
% 51.10/50.82 [5914]~E(f331(x59144,x59145),f331(f234(x59141),x59142))+P1(f331(f331(f333(x59141),x59142),f176(x59143,x59141,x59144)))
% 51.10/50.82 [6399]~E(x63995,f2(a106))+E(f331(f200(x63991,x63992,x63993,x63994),x63995),f122(x63992))
% 51.10/50.82 [6400]~E(x64005,f2(a106))+E(f331(f198(x64001,x64002,x64003,x64004),x64005),f129(x64002))
% 51.10/50.82 [6495]~P37(f30(x64953,x64954),x64952,x64955,x64951)+E(x64951,f331(f331(f331(a193,x64952),x64953),f331(x64954,x64952)))
% 51.10/50.82 [6540]~E(x65403,f2(a106))+E(f331(f276(x65401,x65402,x65403,x65404),x65405),f331(f249(x65401,x65402),x65405))
% 51.10/50.82 [6618]~E(f331(x66184,x66185),f187(x66182))+E(f331(f236(f851(x66181),x66182,f187(x66181),x66183),f331(x66184,x66185)),f187(x66181))
% 51.10/50.82 [6619]~E(f331(x66194,x66195),f187(x66192))+E(f331(f236(f851(x66191),x66192,f187(x66191),x66193),f331(x66194,x66195)),f187(x66191))
% 51.10/50.82 [7266]E(f331(x72661,x72662),f187(x72663))+~E(f331(f175(x72664,x72663,x72665,x72661),x72662),f187(x72663))
% 51.10/50.82 [7267]E(f331(x72671,x72672),f187(x72673))+~E(f331(f175(x72674,x72673,x72671,x72675),x72672),f187(x72673))
% 51.10/50.82 [7307]E(f331(f175(x73071,x73072,x73073,x73074),x73075),f331(x73073,x73075))+P1(f331(f331(f333(x73071),x73075),f174(x73071,x73072,x73074)))
% 51.10/50.82 [7308]E(f331(f175(x73081,x73082,x73083,x73084),x73085),f331(x73084,x73085))+P1(f331(f331(f333(x73081),x73085),f174(x73081,x73082,x73083)))
% 51.10/50.82 [7635]~P22(x76354,x76351,x76352,x76355)+E(f331(f80(x76351,x76351,x76351,f331(x76352,x76353)),f331(x76352,x76353)),f331(x76352,x76353))
% 51.10/50.82 [7678]E(f331(f175(x76781,x76782,x76783,x76784),x76785),f331(x76784,x76785))+~P1(f331(f331(f333(x76781),x76785),f174(x76781,x76782,x76784)))
% 51.10/50.82 [8025]~P18(x80255,x80251,x80252)+E(f331(f80(x80251,x80251,x80251,f331(x80252,x80253)),f331(x80252,x80254)),f331(f80(x80251,x80251,x80251,f331(x80252,x80254)),f331(x80252,x80253)))
% 51.10/50.82 [8347]P1(f331(f331(f333(f853(x83471,x83471)),f331(f331(f249(x83471,x83471),x83472),x83473)),f326(x83471,x83474,x83475)))+~P1(f331(f331(f241(a847),f331(x83474,x83472)),f331(x83474,x83473)))
% 51.10/50.82 [8445]~P1(f331(f331(f333(x84454),x84453),f299(x84454,x84451,x84452,x84455)))+P1(f331(f331(x84451,x84452),x84453))
% 51.10/50.82 [8446]~P1(f331(f331(f333(x84464),x84463),f290(x84464,x84461,x84462,x84465)))+P1(f331(f331(x84461,x84462),x84463))
% 51.10/50.82 [8447]~P1(f331(f331(f333(x84474),x84472),f299(x84474,x84471,x84475,x84473)))+P1(f331(f331(x84471,x84472),x84473))
% 51.10/50.82 [8448]~P1(f331(f331(f333(x84484),x84482),f290(x84484,x84481,x84485,x84483)))+P1(f331(f331(x84481,x84482),x84483))
% 51.10/50.82 [8571]~P53(x85712,x85711,x85715,x85713,x85714)+E(f331(f311(x85711,x85712,x85713),x85714),f247(f854(x85712,a840)))
% 51.10/50.82 [9338]P1(f331(f331(f333(f853(f848(x93381),f848(x93381))),f331(f331(f249(f848(x93381),f848(x93381)),f331(f331(f145(x93381),x93382),x93383)),f331(f331(f145(x93381),x93382),x93384))),f150(x93381,x93385)))+~P1(f331(f331(f333(f853(f848(x93381),f848(x93381))),f331(f331(f249(f848(x93381),f848(x93381)),x93383),x93384)),f150(x93381,x93385)))
% 51.10/50.82 [9339]P1(f331(f331(f333(f853(f848(x93391),f848(x93391))),f331(f331(f249(f848(x93391),f848(x93391)),f331(f331(f130(x93391),x93392),x93393)),f331(f331(f130(x93391),x93392),x93394))),f142(x93391,x93395)))+~P1(f331(f331(f333(f853(f848(x93391),f848(x93391))),f331(f331(f249(f848(x93391),f848(x93391)),x93393),x93394)),f142(x93391,x93395)))
% 51.10/50.82 [9521]E(f331(f331(f145(x95211),f716(x95212,x95213,x95214,x95215,x95211)),f717(x95212,x95213,x95214,x95215,x95211)),x95215)+~P1(f331(f331(f333(f853(f848(x95211),f848(x95211))),f331(f331(f249(f848(x95211),f848(x95211)),x95215),f331(f331(f145(x95211),x95214),x95213))),f151(x95211,x95212)))
% 51.10/50.82 [9549]E(f331(f331(f145(x95491),f718(x95492,x95493,x95494,x95495,x95491)),f719(x95492,x95493,x95494,x95495,x95491)),x95493)+~P1(f331(f331(f333(f853(f848(x95491),f848(x95491))),f331(f331(f249(f848(x95491),f848(x95491)),f331(f331(f145(x95491),x95495),x95494)),x95493)),f151(x95491,x95492)))
% 51.10/50.82 [9687]~P1(f331(f331(f333(f853(f848(x96871),f848(x96871))),f331(f331(f249(f848(x96871),f848(x96871)),f331(f331(f145(x96871),x96875),x96872)),x96874)),f151(x96871,x96873)))+P1(f331(f331(f333(f853(f848(x96871),f848(x96871))),f331(f331(f249(f848(x96871),f848(x96871)),x96872),f719(x96873,x96874,x96872,x96875,x96871))),f151(x96871,x96873)))
% 51.10/50.82 [9772]~P1(f331(f331(f333(f853(f848(x97721),f848(x97721))),f331(f331(f249(f848(x97721),f848(x97721)),x97725),f331(f331(f145(x97721),x97724),x97723))),f151(x97721,x97722)))+P1(f331(f331(f333(f853(f848(x97721),f848(x97721))),f331(f331(f249(f848(x97721),f848(x97721)),f717(x97722,x97723,x97724,x97725,x97721)),x97723)),f151(x97721,x97722)))
% 51.10/50.82 [9951]P1(f331(f331(f333(f853(x99511,x99511)),f331(f331(f249(x99511,x99511),f331(x99512,f331(f331(f87(a847),x99513),x99514))),f331(x99512,x99513))),f308(x99511,x99515)))+~P1(f331(f331(f333(f853(x99511,x99511)),f331(f331(f249(x99511,x99511),f331(x99512,f331(a119,f643(x99514,x99513,x99515,x99512,x99511)))),f331(x99512,f643(x99514,x99513,x99515,x99512,x99511)))),f308(x99511,x99515)))
% 51.10/50.82 [9975]E(x99751,f2(a106))+E(f331(f236(f853(f848(x99752),x99753),f853(x99752,x99753),f331(f331(f249(f848(x99752),x99753),f120(x99752)),x99754),f331(f259(x99752,x99753,f853(f848(x99752),x99753)),f331(f331(f9(x99752,f854(x99753,f853(f848(x99752),x99753)),f854(x99753,f853(f848(x99752),x99753))),f331(f331(f10(f854(f853(f848(x99752),x99753),f853(f848(x99752),x99753)),f854(f854(x99753,f853(f848(x99752),x99753)),f854(x99753,f853(f848(x99752),x99753))),x99752),f10(f853(f848(x99752),x99753),f853(f848(x99752),x99753),x99753)),f331(f331(f10(f854(f848(x99752),f854(x99753,f853(f848(x99752),x99753))),f854(f853(f848(x99752),x99753),f853(f848(x99752),x99753)),x99752),f259(f848(x99752),x99753,f853(f848(x99752),x99753))),f331(f331(f10(f854(f848(x99752),f848(x99752)),f854(f848(x99752),f854(x99753,f853(f848(x99752),x99753))),x99752),f331(f10(f848(x99752),f854(x99753,f853(f848(x99752),x99753)),f848(x99752)),f249(f848(x99752),x99753))),f145(x99752))))),f124(x99753,x99752,x99755,f331(f331(f3(a106),x99751),f85(a106)))))),f331(x99755,x99754)),f331(f124(x99753,x99752,x99755,x99751),x99754))
% 51.10/50.82 [5092]E(x50921,x50922)+~E(f331(f331(f145(x50923),x50924),x50921),f331(f331(f145(x50923),x50925),x50922))
% 51.10/50.82 [5093]E(x50931,x50932)+~E(f331(f331(f145(x50933),x50931),x50934),f331(f331(f145(x50933),x50932),x50935))
% 51.10/50.82 [5287]~E(f331(f331(f133(x52871),x52873),x52872),f331(f331(f145(x52871),x52874),x52875))+E(f331(f331(f155(x52871),x52872),x52873),x52874)
% 51.10/50.82 [5421]~P17(x54214,x54215,x54211)+E(f331(f331(x54211,x54212),f331(f331(x54211,x54212),x54213)),f331(f331(x54211,x54212),x54213))
% 51.10/50.82 [5790]~E(f331(x57903,x57904),f331(f234(x57902),x57905))+E(f331(f331(f331(f79(x57901,f851(x57902)),x57903),x57904),f331(f234(x57902),x57905)),x57903)
% 51.10/50.82 [6042]~P102(x60422)+~E(f331(f331(f143(x60421,x60422,x60423),x60424),x60425),f120(x60421))
% 51.10/50.82 [6441]E(x64411,x64412)+~E(f331(f331(f130(x64413),x64414),f331(f331(f145(x64413),x64411),f120(x64413))),f331(f331(f130(x64413),x64415),f331(f331(f145(x64413),x64412),f120(x64413))))
% 51.10/50.82 [6442]E(x64421,x64422)+~E(f331(f331(f130(x64423),x64421),f331(f331(f145(x64423),x64424),f120(x64423))),f331(f331(f130(x64423),x64422),f331(f331(f145(x64423),x64425),f120(x64423))))
% 51.10/50.82 [6701]E(f331(f177(x67011,x67012,x67013,x67014),x67015),f187(x67012))+P1(f331(f331(f333(x67011),x67015),x67014))
% 51.10/50.82 [6702]E(f331(f177(x67021,x67022,x67023,x67024),x67025),f187(x67022))+P1(f331(f331(f333(x67021),x67025),x67024))
% 51.10/50.82 [6771]E(f331(f331(f310(x67711),f331(x67712,x67713)),f331(f311(x67714,x67711,x67712),x67715)),f331(f311(x67714,x67711,x67712),x67715))+~P1(f331(f331(f333(x67714),x67713),x67715))
% 51.10/50.82 [6780]~P1(f331(x67804,f331(x67803,x67805)))+P1(f331(f331(f312(x67801,x67802,x67803),x67804),x67805))
% 51.10/50.82 [6785]~E(x67854,f2(a106))+E(f331(f124(x67851,x67852,x67853,x67854),x67855),f331(f331(f249(f848(x67852),x67851),f120(x67852)),x67855))
% 51.10/50.82 [6879]~E(f331(f311(x68791,x68792,x68793),x68794),x68795)+E(f331(f311(f854(x68791,a840),f854(x68792,a840),f311(x68791,x68792,x68793)),f331(f309(x68791),x68794)),f331(f309(x68792),x68795))
% 51.10/50.82 [6909]E(f331(f177(x69091,x69092,x69093,x69094),x69095),f331(x69093,x69095))+~P1(f331(f331(f333(x69091),x69095),x69094))
% 51.10/50.82 [6910]E(f331(f177(x69101,x69102,x69103,x69104),x69105),f331(x69103,x69105))+~P1(f331(f331(f333(x69101),x69105),x69104))
% 51.10/50.82 [7223]P27(x72231,x72232,x72233,x72234)+~P27(x72231,x72232,x72233,f331(f331(f310(x72231),x72235),x72234))
% 51.10/50.82 [7294]P1(f331(x72941,x72942))+~P1(f331(f331(f99(x72943,x72944,x72941),x72945),x72942))
% 51.10/50.82 [7345]~P1(f331(f331(f333(x73454),x73453),x73455))+P1(f331(f331(f333(x73451),f331(x73452,x73453)),f331(f311(x73454,x73451,x73452),x73455)))
% 51.10/50.82 [7397]P1(f331(x73971,f331(x73972,x73973)))+~P1(f331(f331(f312(x73974,x73975,x73972),x73971),x73973))
% 51.10/50.82 [7398]P1(f331(f331(x73981,x73982),x73983))+~P1(f331(f331(f99(x73984,x73981,x73985),x73982),x73983))
% 51.10/50.82 [7467]~P1(f331(f331(f333(x74673),f331(x74674,x74672)),x74675))+P1(f331(f331(f333(x74671),x74672),f331(f312(x74671,x74673,x74674),x74675)))
% 51.10/50.82 [7468]~P1(f331(f331(f333(x74683),f331(x74684,x74682)),x74685))+P1(f331(f331(f333(x74681),x74682),f331(f312(x74681,x74683,x74684),x74685)))
% 51.10/50.82 [7866]~P1(f331(f331(f333(x78665),x78663),f331(f312(x78665,x78661,x78662),x78664)))+P1(f331(f331(f333(x78661),f331(x78662,x78663)),x78664))
% 51.10/50.82 [7867]~P1(f331(f331(f333(x78675),x78673),f331(f312(x78675,x78671,x78672),x78674)))+P1(f331(f331(f333(x78671),f331(x78672,x78673)),x78674))
% 51.10/50.82 [8085]~E(x80853,f331(f331(f331(f79(x80851,f851(x80852)),f331(f18(f851(x80852),x80851),f187(x80852))),x80854),f331(f234(x80852),x80855)))+E(f174(x80851,x80852,x80853),f331(f331(f310(x80851),x80854),f184(f854(x80851,a840))))
% 51.10/50.82 [8164]~P18(x81642,x81641,x81643)+E(f331(f137(x81641,x81642,f331(f9(x81642,x81641,x81641),x81643),x81644),f146(x81642,x81645)),f331(f331(f71(x81642,x81641,x81643),x81644),f331(f163(x81642),x81645)))
% 51.10/50.82 [8182]E(f331(x81821,f350(x81822,x81821,x81823,x81824)),x81824)+~P1(f331(f331(f333(x81825),x81824),f331(f311(x81823,x81825,x81821),x81822)))
% 51.10/50.82 [8489]~E(x84892,f331(f331(f145(x84891),x84894),x84895))+P1(f331(f331(f333(f853(f848(x84891),f848(x84891))),f331(f331(f249(f848(x84891),f848(x84891)),f120(x84891)),x84892)),f142(x84891,x84893)))
% 51.10/50.82 [8540]P1(f331(f331(f240(f854(x85401,a840)),f331(f331(f52(x85402,f854(x85401,a840)),x85403),x85404)),f331(x85404,x85405)))+~P1(f331(f331(f333(x85402),x85405),x85403))
% 51.10/50.82 [8587]~P53(x85871,x85872,x85873,x85875,x85874)+E(f331(f311(x85871,x85872,x85873),f247(f854(x85871,a840))),x85874)
% 51.10/50.82 [8776]E(f331(f331(f331(f79(x87761,f851(x87762)),f177(x87761,x87762,x87763,x87764)),x87765),f187(x87762)),f177(x87761,x87762,x87763,x87764))+P1(f331(f331(f333(x87761),x87765),x87764))
% 51.10/50.82 [8779]E(f331(x87791,f705(x87792,x87793,x87791,x87794,x87795)),x87792)+~E(f331(f331(f203(x87795,x87794),x87791),x87793),f331(f234(x87794),x87792))
% 51.10/50.82 [8782]E(f331(f234(x87821),f705(x87822,x87823,x87824,x87825,x87821)),x87823)+~E(f331(f331(f203(x87821,x87825),x87824),x87823),f331(f234(x87825),x87822))
% 51.10/50.82 [8864]E(f331(f185(f848(x88641)),x88642),x88643)+~P1(f331(f331(f333(f853(f848(x88641),f848(x88641))),f331(f331(f249(f848(x88641),f848(x88641)),x88644),x88642)),f331(f138(x88641,x88645),x88643)))
% 51.10/50.82 [8865]E(f331(f185(f848(x88651)),x88652),x88653)+~P1(f331(f331(f333(f853(f848(x88651),f848(x88651))),f331(f331(f249(f848(x88651),f848(x88651)),x88652),x88654)),f331(f138(x88651,x88655),x88653)))
% 51.10/50.82 [8926]P1(f331(f331(f333(x89261),f350(x89262,x89263,x89261,x89264)),x89262))+~P1(f331(f331(f333(x89265),x89264),f331(f311(x89261,x89265,x89263),x89262)))
% 51.10/50.82 [9077]E(f331(f311(x90771,x90772,x90773),f352(x90774,x90773,x90771,x90775,x90772)),x90775)+~P1(f331(f331(f240(f854(x90772,a840)),x90775),f331(f311(x90771,x90772,x90773),x90774)))
% 51.10/50.82 [9310]E(f331(x93101,f517(x93102,x93101,x93103,x93104,x93105)),f331(f234(x93105),x93104))+~P1(f331(f331(f333(x93105),x93104),f176(x93103,x93105,f177(x93103,x93105,x93101,x93102))))
% 51.10/50.82 [9354]P1(f331(f331(f333(f853(f848(x93541),f848(x93541))),f331(f331(f249(f848(x93541),f848(x93541)),f331(f331(f145(x93541),x93542),x93543)),f331(f331(f145(x93541),x93542),x93544))),f308(f848(x93541),f150(x93541,x93545))))+~P1(f331(f331(f333(f853(f848(x93541),f848(x93541))),f331(f331(f249(f848(x93541),f848(x93541)),x93543),x93544)),f308(f848(x93541),f150(x93541,x93545))))
% 51.10/50.82 [9384]~E(f331(x93843,f706(x93845,x93844,x93843,x93842,x93841)),f331(x93845,f706(x93845,x93844,x93843,x93842,x93841)))+E(f331(f331(f147(x93841,x93842),x93843),x93844),f331(f331(f147(x93841,x93842),x93845),x93844))
% 51.10/50.82 [9466]E(f331(f331(f147(x94661,x94662),x94663),x94664),f331(f331(f147(x94661,x94662),x94665),x94664))+P1(f331(f331(f333(x94661),f706(x94663,x94664,x94665,x94662,x94661)),f331(f163(x94661),x94664)))
% 51.10/50.82 [9494]~P1(f331(f331(f333(x94945),x94944),f331(f285(x94941,x94945,x94943),x94942)))+P1(f331(f331(f333(x94941),f356(x94942,x94943,x94941,x94944,x94945)),x94942))
% 51.10/50.82 [9495]~P1(f331(f331(f333(x94955),x94954),f331(f285(x94951,x94955,x94953),x94952)))+P1(f331(f331(f333(x94951),f361(x94952,x94953,x94951,x94954,x94955)),x94952))
% 51.10/50.82 [9519]~P1(f331(f331(f240(f854(x95195,a840)),x95194),f331(f311(x95191,x95195,x95193),x95192)))+P1(f331(f331(f240(f854(x95191,a840)),f352(x95192,x95193,x95191,x95194,x95195)),x95192))
% 51.10/50.82 [9566]~P1(f331(f331(f333(x95665),x95664),f176(x95661,x95665,f177(x95661,x95665,x95663,x95662))))+P1(f331(f331(f333(x95661),f517(x95662,x95663,x95661,x95664,x95665)),x95662))
% 51.10/50.82 [5300]~E(f331(x53003,x53004),x53005)+E(f331(f331(f331(f79(x53001,x53002),x53003),x53004),x53005),x53003)
% 51.10/50.82 [5301]~E(f331(x53013,x53014),x53015)+E(f331(f331(f331(f79(x53011,x53012),x53013),x53014),x53015),x53013)
% 51.10/50.82 [5755]E(f331(x57551,x57552),x57553)+~E(f331(f331(f331(f79(x57554,x57555),x57551),x57552),x57553),x57551)
% 51.10/50.82 [5844]E(x58441,x58442)+~E(f331(f258(x58443,x58444),f331(f331(f249(x58443,x58444),x58445),x58441)),x58442)
% 51.10/50.82 [5845]E(x58451,x58452)+~E(f331(f248(x58453,x58454),f331(f331(f249(x58453,x58454),x58451),x58455)),x58452)
% 51.10/50.82 [6528]E(f331(f311(x65281,x65282,f331(f18(x65282,x65281),x65283)),x65284),f331(f331(f310(x65282),x65283),f184(f854(x65282,a840))))+~P1(f331(f331(f333(x65281),x65285),x65284))
% 51.10/50.82 [6601]E(f331(f331(f108(f854(x66011,a840)),f331(f163(x66011),x66012)),f331(f163(x66011),x66013)),f331(f163(x66011),x66014))+~E(f158(x66011,x66015,x66014),f331(f331(f249(f848(x66011),f848(x66011)),x66012),x66013))
% 51.10/50.82 [6708]~P102(x67082)+E(f331(f185(f848(x67081)),f331(f331(f143(x67081,x67082,x67083),x67084),x67085)),f331(a119,f331(f185(f848(x67081)),x67085)))
% 51.10/50.82 [6722]~P102(x67222)+E(f331(f163(x67221),f331(f331(f143(x67221,x67222,x67223),x67224),x67225)),f331(f331(f310(x67221),x67224),f331(f163(x67221),x67225)))
% 51.10/50.82 [7000]~P87(x70001)+E(f331(f331(f87(x70001),f331(f331(f87(x70001),x70002),x70003)),f331(f331(f87(x70001),x70004),x70005)),f331(f331(f87(x70001),f331(f331(f87(x70001),x70002),x70004)),f331(f331(f87(x70001),x70003),x70005)))
% 51.10/50.82 [7001]~P87(x70011)+E(f331(f331(f88(x70011),f331(f331(f88(x70011),x70012),x70013)),f331(f331(f88(x70011),x70014),x70015)),f331(f331(f88(x70011),f331(f331(f88(x70011),x70012),x70014)),f331(f331(f88(x70011),x70013),x70015)))
% 51.10/50.82 [7002]~P58(x70021)+E(f331(f331(f291(x70021),f331(f331(f88(x70021),x70022),x70023)),f331(f331(f88(x70021),x70024),x70025)),f331(f331(f88(x70021),f331(f331(f291(x70021),x70022),x70024)),f331(f331(f291(x70021),x70023),x70025)))
% 51.10/50.82 [7016]~P102(x70161)+E(f306(x70161,f331(f331(f239(x70161),x70162),x70163),f331(f331(f244(x70161),x70164),x70165)),f331(f331(f109(f854(x70161,a840)),f306(x70161,x70162,x70164)),f306(x70161,x70163,x70165)))
% 51.10/50.82 [7017]~P102(x70171)+E(f305(x70171,f331(f331(f239(x70171),x70172),x70173),f331(f331(f244(x70171),x70174),x70175)),f331(f331(f109(f854(x70171,a840)),f305(x70171,x70172,x70174)),f305(x70171,x70173,x70175)))
% 51.10/50.82 [7018]~P102(x70181)+E(f303(x70181,f331(f331(f239(x70181),x70182),x70183),f331(f331(f244(x70181),x70184),x70185)),f331(f331(f109(f854(x70181,a840)),f303(x70181,x70182,x70184)),f303(x70181,x70183,x70185)))
% 51.10/50.82 [7019]~P102(x70191)+E(f331(f331(f109(f854(x70191,a840)),f331(f302(x70191,x70192),x70193)),f331(f302(x70191,x70194),x70195)),f331(f302(x70191,f331(f331(f239(x70191),x70192),x70194)),f331(f331(f244(x70191),x70193),x70195)))
% 51.10/50.82 [7137]~P1(f331(x71371,f815(x71373,x71372,x71371)))+P1(f331(x71371,f331(f331(f249(x71372,x71373),x71374),x71375)))
% 51.10/50.82 [7235]~E(f331(x72353,x72354),f187(x72352))+E(f176(x72351,x72352,f331(f331(f331(f79(x72351,f851(x72352)),x72353),x72354),f331(f234(x72352),x72355))),f331(f331(f310(x72352),x72355),f176(x72351,x72352,x72353)))
% 51.10/50.82 [7258]~E(x72582,f331(x72584,x72585))+P1(f331(f331(f333(x72581),x72582),f331(f311(x72583,x72581,x72584),f247(f854(x72583,a840)))))
% 51.10/50.82 [7319]~E(f331(x73193,x73194),f187(x73192))+E(f331(f331(f3(f854(x73191,a840)),f174(x73191,x73192,x73193)),f331(f331(f310(x73191),x73194),x73195)),f331(f331(f3(f854(x73191,a840)),f174(x73191,x73192,x73193)),x73195))
% 51.10/50.82 [7341]~P17(x73413,x73412,x73414)+P17(x73411,x73412,f331(f331(f10(x73413,f854(x73412,x73412),x73411),x73414),x73415))
% 51.10/50.82 [7342]~P18(x73423,x73422,x73424)+P18(x73421,x73422,f331(f331(f10(x73423,f854(x73422,x73422),x73421),x73424),x73425))
% 51.10/50.82 [7484]~P27(x74841,x74842,x74843,x74844)+P27(x74841,x74842,x74843,f331(f331(f3(f854(x74841,a840)),x74844),x74845))
% 51.10/50.82 [7643]~P1(f331(f331(x76433,x76434),x76435))+P1(f331(f331(f259(x76431,x76432,a840),x76433),f331(f331(f249(x76431,x76432),x76434),x76435)))
% 51.10/50.82 [7644]~P1(f331(f331(x76443,x76444),x76445))+P1(f331(f331(f259(x76441,x76442,a840),x76443),f331(f331(f249(x76441,x76442),x76444),x76445)))
% 51.10/50.82 [7778]P27(x77781,x77782,x77783,x77784)+~P27(x77781,x77782,x77783,f331(f331(f108(f854(x77781,a840)),x77785),x77784))
% 51.10/50.82 [7779]P27(x77791,x77792,x77793,x77794)+~P27(x77791,x77792,x77793,f331(f331(f108(f854(x77791,a840)),x77794),x77795))
% 51.10/50.82 [7984]~P29(x79841,f331(a119,x79842),f331(f331(f331(f98(x79841),x79843),f331(a29,x79844)),x79845))+P29(x79841,x79842,f331(f331(f331(f98(x79841),x79843),f331(f238(a841),f331(a32,x79844))),x79845))
% 51.10/50.82 [8112]P29(x81121,f331(a119,x81122),f331(f331(f331(f98(x81121),x81123),f331(a29,x81124)),x81125))+~P29(x81121,x81122,f331(f331(f331(f98(x81121),x81123),f331(f238(a841),f331(a32,x81124))),x81125))
% 51.10/50.82 [8141]~P17(x81412,x81411,x81413)+E(f331(f137(x81411,x81412,f331(f9(x81412,x81411,x81411),x81413),x81414),x81415),f331(f331(f71(x81412,x81411,x81413),x81414),f331(f163(x81412),x81415)))
% 51.10/50.82 [8192]P1(f331(f331(x81921,x81922),x81923))+~P1(f331(f331(f259(x81924,x81925,a840),x81921),f331(f331(f249(x81924,x81925),x81922),x81923)))
% 51.10/50.82 [8264]P37(x82644,f831(x82645,x82644,x82643,x82642),x82642,f344(x82645,x82644,x82643,x82642))+P29(x82641,x82642,f331(f331(f331(f98(x82641),x82643),x82644),x82645))
% 51.10/50.82 [8279]~E(f331(f171(x82791,x82792,x82795),x82793),f331(f234(x82792),x82794))+P1(f331(f331(f333(f853(x82791,x82792)),f331(f331(f249(x82791,x82792),x82793),x82794)),f331(f163(f853(x82791,x82792)),x82795)))
% 51.10/50.82 [8280]~E(f331(f171(x82801,x82802,x82805),x82803),f331(f234(x82802),x82804))+P1(f331(f331(f333(f853(x82801,x82802)),f331(f331(f249(x82801,x82802),x82803),x82804)),f331(f163(f853(x82801,x82802)),x82805)))
% 51.10/50.82 [8640]P1(f331(f331(f240(f854(x86401,a840)),f331(f311(x86402,x86401,x86403),x86404)),f331(f311(x86402,x86401,x86403),x86405)))+~P1(f331(f331(f240(f854(x86402,a840)),x86404),x86405))
% 51.10/50.82 [8641]P1(f331(f331(f240(f854(x86411,a840)),f331(f312(x86411,x86412,x86413),x86414)),f331(f312(x86411,x86412,x86413),x86415)))+~P1(f331(f331(f240(f854(x86412,a840)),x86414),x86415))
% 51.10/50.82 [8712]E(x87121,f2(a106))+E(f331(f331(f261(x87122,x87123,x87122,f853(x87123,x87122)),f331(x87124,x87125)),f276(x87123,x87122,f331(f331(f3(a106),x87121),f85(a106)),x87124)),f331(f276(x87123,x87122,x87121,x87124),x87125))
% 51.10/50.82 [8798]P1(f331(f331(f257(x87981,x87982,a840,x87983),x87984),x87985))+~P1(f331(x87983,f331(f331(f249(x87981,x87982),x87984),x87985)))
% 51.10/50.82 [8994]P29(x89941,x89942,f331(f331(f331(f98(x89941),x89943),x89944),x89945))+P1(f331(f331(x89943,f827(x89945,x89944,x89943,x89942)),f831(x89945,x89944,x89943,x89942)))
% 51.10/50.82 [9004]~P1(f331(f331(f191(x90043),f331(f331(f331(a193,x90044),f40(x90041)),f331(x90042,x90044))),x90045))+P1(f331(f331(f191(f34(x90041,x90042,x90043)),x90044),f331(f331(f331(a193,x90045),f40(x90041)),f331(f331(a196,x90044),x90041))))
% 51.10/50.82 [9055]~P1(f331(f331(f257(x90552,x90553,a840,x90551),x90554),x90555))+P1(f331(x90551,f331(f331(f249(x90552,x90553),x90554),x90555)))
% 51.10/50.82 [9056]~P1(f331(f331(f257(x90562,x90563,a840,x90561),x90564),x90565))+P1(f331(x90561,f331(f331(f249(x90562,x90563),x90564),x90565)))
% 51.10/50.82 [9164]E(f331(f234(x91641),f713(x91642,x91643,x91644,x91641,x91645)),f331(f171(x91645,x91641,x91642),x91644))+~P1(f331(f331(f333(f853(x91645,x91641)),f331(f331(f249(x91645,x91641),x91644),x91643)),f331(f163(f853(x91645,x91641)),x91642)))
% 51.10/50.82 [9207]P29(x92071,x92072,f331(f331(f331(f98(x92071),x92073),x92074),x92075))+~P1(f331(f331(x92075,f827(x92075,x92074,x92073,x92072)),f344(x92075,x92074,x92073,x92072)))
% 51.10/50.82 [9275]~P26(x92751,x92752,f331(f331(f310(f846(x92751)),f331(f331(f331(f98(x92751),x92753),f331(f238(a841),f331(a32,x92754))),x92755)),f184(f854(f846(x92751),a840))))+P26(x92751,x92752,f331(f331(f310(f846(x92751)),f331(f331(f331(f98(x92751),x92753),f331(a29,x92754)),x92755)),f184(f854(f846(x92751),a840))))
% 51.10/50.82 [9302]~P1(f331(f68(x93023),f331(f311(x93022,x93023,x93025),f247(f854(x93022,a840)))))+P1(f331(f68(x93021),f331(f311(x93022,x93021,f331(f331(f10(x93023,x93021,x93022),x93024),x93025)),f247(f854(x93022,a840)))))
% 51.10/50.82 [9324]P1(f331(f331(f240(f854(f854(x93241,a840),a840)),f331(f311(f854(x93242,a840),f854(x93241,a840),f311(x93242,x93241,x93243)),f331(f309(x93242),x93244))),f331(f309(x93241),x93245)))+~P1(f331(f331(f240(f854(x93241,a840)),f331(f311(x93242,x93241,x93243),x93244)),x93245))
% 51.10/50.82 [9334]~P1(f331(f68(f851(x93341)),f331(f311(x93342,f851(x93341),x93343),f247(f854(x93342,a840)))))+P1(f331(f68(f851(x93341)),f331(f311(x93342,f851(x93341),f331(f331(f331(f79(x93342,f851(x93341)),x93343),x93344),f331(f234(x93341),x93345))),f247(f854(x93342,a840)))))
% 51.10/50.82 [9365]P1(f331(f331(f191(x93651),f331(f331(f331(a193,x93652),f40(x93653)),f331(x93654,x93652))),f385(x93655,x93652,x93651,x93654,x93653)))+~P1(f331(f331(f191(f34(x93653,x93654,x93651)),x93652),x93655))
% 51.10/50.82 [9393]E(x93931,x93932)+~P1(f331(f73(x93933,x93934,x93935,x93931,f184(f854(x93933,a840))),x93932))
% 51.10/50.82 [9408]E(f331(f331(f249(x94081,x94082),f553(x94083,x94084,x94085,x94082,x94081)),f554(x94083,x94084,x94085,x94082,x94081)),x94085)+~P1(f331(f331(f333(f853(x94081,x94082)),x94085),f331(f331(f256(x94081,x94082),x94084),x94083)))
% 51.10/50.82 [9419]P1(f331(f331(f191(x94191),f331(f331(f331(a193,x94192),f40(x94193)),f331(x94194,x94192))),f818(x94195,x94192,x94191,x94194,x94193)))+~P1(f331(f331(f191(f34(x94193,x94194,x94191)),x94192),f331(f331(f331(a193,x94195),f40(x94193)),f331(f331(a196,x94192),x94193))))
% 51.10/50.82 [9425]~P1(f331(f331(f191(f331(a29,x94252)),f331(f331(f331(a193,f331(f331(a194,x94254),a195)),f40(a27)),f331(x94253,x94254))),x94255))+P1(f331(f331(f191(f33(x94251,x94252,x94253)),x94254),f331(f331(f331(a193,f331(f331(a194,x94255),f331(a196,x94254))),x94251),f331(f331(a196,x94255),a28))))
% 51.10/50.82 [9459]P1(f331(f331(f191(f331(a29,x94591)),f331(f331(f331(a193,f331(f331(a194,x94592),a195)),f40(a27)),f331(x94593,x94592))),f372(x94594,x94592,x94593,x94591,x94595)))+~P1(f331(f331(f191(f33(x94595,x94591,x94593)),x94592),x94594))
% 51.10/50.82 [9499]P1(f331(f331(f333(x94991),f553(x94992,x94993,x94994,x94995,x94991)),x94993))+~P1(f331(f331(f333(f853(x94991,x94995)),x94994),f331(f331(f256(x94991,x94995),x94993),x94992)))
% 51.10/50.82 [9525]E(f331(f331(f331(a193,f385(x95251,x95252,x95253,x95254,x95255)),f40(x95255)),f331(f331(a196,x95252),x95255)),x95251)+~P1(f331(f331(f191(f34(x95255,x95254,x95253)),x95252),x95251))
% 51.10/50.82 [9550]E(f331(f331(f331(a193,f818(x95501,x95502,x95503,x95504,x95505)),f40(x95505)),f331(f331(a196,x95502),x95505)),f331(f331(f331(a193,x95501),f40(x95505)),f331(f331(a196,x95502),x95505)))+~P1(f331(f331(f191(f34(x95505,x95504,x95503)),x95502),f331(f331(f331(a193,x95501),f40(x95505)),f331(f331(a196,x95502),x95505))))
% 51.10/50.82 [9575]P1(f331(f331(f191(f331(a29,x95751)),f331(f331(f331(a193,f331(f331(a194,x95752),a195)),f40(a27)),f331(x95753,x95752))),f797(x95754,x95752,x95753,x95751,x95755)))+~P1(f331(f331(f191(f33(x95755,x95751,x95753)),x95752),f331(f331(f331(a193,f331(f331(a194,x95754),f331(a196,x95752))),x95755),f331(f331(a196,x95754),a28))))
% 51.10/50.82 [9602]P26(x96025,x96024,f331(f331(f310(f846(x96025)),f331(f331(f331(f98(x96025),x96021),x96023),x96022)),f184(f854(f846(x96025),a840))))+P1(f331(f331(x96021,f832(x96022,x96023,x96024,x96025,x96021)),f833(x96022,x96023,x96024,x96025,x96021)))
% 51.10/50.82 [9644]P1(f331(f331(f333(x96441),f554(x96442,x96443,x96444,x96441,x96445)),f331(x96442,f553(x96442,x96443,x96444,x96441,x96445))))+~P1(f331(f331(f333(f853(x96445,x96441)),x96444),f331(f331(f256(x96445,x96441),x96443),x96442)))
% 51.10/50.82 [9663]P1(f331(f331(f333(f853(x96631,x96631)),f331(f331(f249(x96631,x96631),x96632),f686(x96633,x96634,x96635,x96632,x96631))),x96633))+~P1(f331(f331(f333(f853(x96631,x96631)),f331(f331(f249(x96631,x96631),x96632),x96635)),f331(f331(f178(f853(x96631,x96631),a840),f331(a119,x96634)),x96633)))
% 51.10/50.82 [9664]P1(f331(f331(f333(f853(x96641,x96641)),f331(f331(f249(x96641,x96641),x96642),f687(x96643,x96644,x96645,x96642,x96641))),x96643))+~P1(f331(f331(f333(f853(x96641,x96641)),f331(f331(f249(x96641,x96641),x96642),x96645)),f331(f331(f178(f853(x96641,x96641),a840),f331(a119,x96644)),x96643)))
% 51.10/50.82 [9682]~P1(f331(f331(f333(f853(f848(x96821),f848(x96821))),f331(f331(f249(f848(x96821),f848(x96821)),f331(f331(f145(x96821),x96822),x96825)),x96824)),f151(x96821,x96823)))+P1(f331(f331(f333(f853(x96821,x96821)),f331(f331(f249(x96821,x96821),x96822),f718(x96823,x96824,x96825,x96822,x96821))),x96823))
% 51.10/50.82 [9684]~P26(x96841,x96842,f331(f331(f310(f846(x96841)),f331(f331(f331(f98(x96841),f99(x96841,x96843,x96844)),x96845),x96843)),f184(f854(f846(x96841),a840))))+P26(x96841,x96842,f331(f331(f310(f846(x96841)),f331(f331(f331(f98(x96841),x96843),f37(x96844,x96845)),f99(x96841,x96843,f331(f80(a840,a840,a845,a327),x96844)))),f184(f854(f846(x96841),a840))))
% 51.10/50.82 [9685]~P30(x96851,x96852,f331(f331(f310(f846(x96851)),f331(f331(f331(f98(x96851),f99(x96851,x96853,x96854)),x96855),x96853)),f184(f854(f846(x96851),a840))))+P30(x96851,x96852,f331(f331(f310(f846(x96851)),f331(f331(f331(f98(x96851),x96853),f37(x96854,x96855)),f99(x96851,x96853,f331(f80(a840,a840,a845,a327),x96854)))),f184(f854(f846(x96851),a840))))
% 51.10/50.82 [9804]E(f331(f331(f331(a193,f331(f331(a194,f372(x98041,x98042,x98043,x98044,x98045)),f331(a196,x98042))),x98045),f331(f331(a196,f372(x98041,x98042,x98043,x98044,x98045)),a28)),x98041)+~P1(f331(f331(f191(f33(x98045,x98044,x98043)),x98042),x98041))
% 51.10/50.82 [9816]E(f331(f331(f331(a193,f331(f331(a194,f797(x98161,x98162,x98163,x98164,x98165)),f331(a196,x98162))),x98165),f331(f331(a196,f797(x98161,x98162,x98163,x98164,x98165)),a28)),f331(f331(f331(a193,f331(f331(a194,x98161),f331(a196,x98162))),x98165),f331(f331(a196,x98161),a28)))+~P1(f331(f331(f191(f33(x98165,x98164,x98163)),x98162),f331(f331(f331(a193,f331(f331(a194,x98161),f331(a196,x98162))),x98165),f331(f331(a196,x98161),a28))))
% 51.10/50.82 [9976]P26(x99761,x99762,f331(f331(f310(f846(x99761)),f331(f331(f331(f98(x99761),x99763),x99764),x99765)),f184(f854(f846(x99761),a840))))+~P26(x99761,x99762,f331(f331(f310(f846(x99761)),f331(f331(f331(f98(x99761),f331(f18(f854(a845,a840),x99761),f331(f331(f9(a845,a845,a840),a328),f833(x99765,x99764,x99762,x99761,x99763)))),x99764),f331(f18(f854(a845,a840),x99761),f331(x99765,f832(x99765,x99764,x99762,x99761,x99763))))),f184(f854(f846(x99761),a840))))
% 51.10/50.82 [6194]P1(f331(x61942,x61944))+E(f167(x61941,x61942,f331(f331(f130(x61941),x61943),f331(f331(f145(x61941),x61944),x61945))),f167(x61941,x61942,x61943))
% 51.10/50.82 [6243]~P72(x62432)+E(f331(f331(f331(f3(f854(x62431,x62432)),x62433),x62434),x62435),f331(f331(f3(x62432),f331(x62433,x62435)),f331(x62434,x62435)))
% 51.10/50.82 [6244]~P72(x62442)+E(f331(f331(f331(f3(f854(x62441,x62442)),x62443),x62444),x62445),f331(f331(f3(x62442),f331(x62443,x62445)),f331(x62444,x62445)))
% 51.10/50.82 [6245]~P97(x62452)+E(f331(f331(f331(f108(f854(x62451,x62452)),x62453),x62454),x62455),f331(f331(f108(x62452),f331(x62453,x62455)),f331(x62454,x62455)))
% 51.10/50.82 [6246]~P97(x62462)+E(f331(f331(f331(f108(f854(x62461,x62462)),x62463),x62464),x62465),f331(f331(f108(x62462),f331(x62463,x62465)),f331(x62464,x62465)))
% 51.10/50.82 [6247]~P97(x62472)+E(f331(f331(f331(f109(f854(x62471,x62472)),x62473),x62474),x62475),f331(f331(f109(x62472),f331(x62473,x62475)),f331(x62474,x62475)))
% 51.10/50.82 [6248]~P97(x62482)+E(f331(f331(f331(f109(f854(x62481,x62482)),x62483),x62484),x62485),f331(f331(f109(x62482),f331(x62483,x62485)),f331(x62484,x62485)))
% 51.10/50.82 [6269]E(x62691,x62692)+E(f331(f331(f155(x62693),f331(f331(f152(x62693,x62694),x62691),x62695)),x62692),f331(f331(f155(x62693),x62694),x62692))
% 51.10/50.82 [6545]~E(x65454,f184(f854(x65453,a840)))+E(f331(f331(f3(f854(x65451,a840)),x65452),f331(f331(f51(x65453,f854(x65451,a840)),x65454),x65455)),x65452)
% 51.10/50.82 [6546]~E(x65464,f184(f854(x65463,a840)))+E(f331(f331(f108(f854(x65461,a840)),x65462),f331(f331(f51(x65463,f854(x65461,a840)),x65464),x65465)),x65462)
% 51.10/50.82 [6547]~E(x65474,f184(f854(x65473,a840)))+E(f331(f331(f109(f854(x65471,a840)),x65472),f331(f331(f52(x65473,f854(x65471,a840)),x65474),x65475)),x65472)
% 51.10/50.82 [6560]~E(x65604,f184(f854(x65603,a840)))+E(f331(f331(f310(x65601),x65602),f331(f331(f51(x65603,f854(x65601,a840)),x65604),x65605)),f331(f331(f310(x65601),x65602),f184(f854(x65601,a840))))
% 51.10/50.82 [6999]~P87(x69991)+E(f331(f331(f88(x69991),f331(f331(f88(x69991),x69992),x69993)),f331(f331(f88(x69991),x69994),x69995)),f331(f331(f88(x69991),x69992),f331(f331(f88(x69991),x69993),f331(f331(f88(x69991),x69994),x69995))))
% 51.10/50.82 [7386]E(f331(f331(f155(x73861),f331(f331(f147(x73862,x73861),x73863),x73864)),x73865),f331(x73863,f331(f331(f155(x73862),x73864),x73865)))+~P1(f331(f331(f241(a847),x73865),f331(f185(f848(x73862)),x73864)))
% 51.10/50.82 [7456]E(f331(f331(f108(f854(x74561,a840)),f331(x74562,x74563)),f331(f331(f51(x74564,f854(x74561,a840)),x74565),x74562)),f331(f331(f51(x74564,f854(x74561,a840)),x74565),x74562))+~P1(f331(f331(f333(x74564),x74563),x74565))
% 51.10/50.82 [7457]E(f331(f331(f109(f854(x74571,a840)),f331(x74572,x74573)),f331(f331(f52(x74574,f854(x74571,a840)),x74575),x74572)),f331(f331(f52(x74574,f854(x74571,a840)),x74575),x74572))+~P1(f331(f331(f333(x74574),x74573),x74575))
% 51.10/50.82 [8060]~E(x80603,f184(f854(x80601,a840)))+E(f331(f331(f51(x80601,f854(x80602,a840)),x80603),f331(f331(f10(f854(x80602,a840),f854(x80602,a840),x80601),f331(f310(x80602),x80604)),x80605)),f184(f854(x80602,a840)))
% 51.10/50.82 [8066]~P1(f331(f331(f333(x80664),x80663),x80665))+P1(f331(f331(f240(f854(x80661,a840)),f331(x80662,x80663)),f331(f331(f51(x80664,f854(x80661,a840)),x80665),x80662)))
% 51.10/50.82 [8191]~E(f331(x81914,x81912),x81915)+P1(f331(f331(f333(x81911),x81912),f331(f312(x81911,x81913,x81914),f331(f331(f310(x81913),x81915),f184(f854(x81913,a840))))))
% 51.10/50.82 [8238]~P51(x82381,x82382,f331(f286(x82382,x82381),x82383))+E(f331(f331(f109(f854(x82381,a840)),f331(f285(x82382,x82381,x82383),x82384)),f331(f285(x82382,x82381,x82383),x82385)),f331(f285(x82382,x82381,x82383),f331(f331(f109(f854(x82382,a840)),x82384),x82385)))
% 51.10/50.82 [8263]E(x82631,f2(a106))+E(f123(x82632,x82633,f331(x82634,f331(f331(f3(a106),x82631),f85(a106))),f331(f331(f9(x82632,a106,f849(x82633)),x82635),x82631)),f331(f200(x82632,x82633,x82634,x82635),x82631))
% 51.10/50.82 [8356]E(x83561,f184(f854(x83562,a840)))+E(f331(f331(f51(x83562,f854(x83563,a840)),x83561),f331(f331(f10(f854(x83563,a840),f854(x83563,a840),x83562),f331(f310(x83563),x83564)),x83565)),f331(f331(f310(x83563),x83564),f331(f331(f51(x83562,f854(x83563,a840)),x83561),x83565)))
% 51.10/50.82 [8357]E(x83571,f184(f854(x83572,a840)))+E(f331(f331(f51(x83572,f854(x83573,a840)),x83571),f331(f331(f10(f854(x83573,a840),f854(x83573,a840),x83572),f331(f310(x83573),x83574)),x83575)),f331(f331(f310(x83573),x83574),f331(f331(f51(x83572,f854(x83573,a840)),x83571),x83575)))
% 51.10/50.82 [8412]~P27(x84122,x84121,x84123,f247(f854(x84122,a840)))+E(f331(f331(f3(f854(x84121,a840)),f331(f311(x84122,x84121,x84123),x84124)),f331(f311(x84122,x84121,x84123),x84125)),f331(f311(x84122,x84121,x84123),f331(f331(f3(f854(x84122,a840)),x84124),x84125)))
% 51.10/50.82 [8413]~P27(x84132,x84131,x84133,f247(f854(x84132,a840)))+E(f331(f331(f109(f854(x84131,a840)),f331(f311(x84132,x84131,x84133),x84134)),f331(f311(x84132,x84131,x84133),x84135)),f331(f311(x84132,x84131,x84133),f331(f331(f109(f854(x84132,a840)),x84134),x84135)))
% 51.10/50.82 [8477]~P1(f331(f331(f74(x84771,x84772,x84775),x84773),x84774))+P1(f331(f331(f333(f853(x84771,x84772)),f331(f331(f249(x84771,x84772),x84773),x84774)),x84775))
% 51.10/50.82 [8504]P1(f331(f331(f333(x85041),x85042),f331(f267(x85043,x85041),x85044)))+~P1(f331(f331(f333(f853(x85043,x85041)),f331(f331(f249(x85043,x85041),x85045),x85042)),x85044))
% 51.10/50.82 [8505]P1(f331(f331(f333(x85051),x85052),f331(f267(x85053,x85051),x85054)))+~P1(f331(f331(f333(f853(x85053,x85051)),f331(f331(f249(x85053,x85051),x85055),x85052)),x85054))
% 51.10/50.82 [8506]P1(f331(f331(f333(x85061),x85062),f331(f269(x85061,x85063),x85064)))+~P1(f331(f331(f333(f853(x85061,x85063)),f331(f331(f249(x85061,x85063),x85062),x85065)),x85064))
% 51.10/50.82 [8507]P1(f331(f331(f333(x85071),x85072),f331(f269(x85071,x85073),x85074)))+~P1(f331(f331(f333(f853(x85071,x85073)),f331(f331(f249(x85071,x85073),x85072),x85075)),x85074))
% 51.10/50.82 [8629]P1(f331(f331(f74(x86291,x86292,x86293),x86294),x86295))+~P1(f331(f331(f333(f853(x86291,x86292)),f331(f331(f249(x86291,x86292),x86294),x86295)),x86293))
% 51.10/50.82 [8662]E(f331(x86621,x86622),x86623)+~P1(f331(f331(f333(x86624),x86622),f331(f312(x86624,x86625,x86621),f331(f331(f310(x86625),x86623),f184(f854(x86625,a840))))))
% 51.10/50.82 [8860]P1(f331(f331(f333(f853(x88601,x88602)),f331(f331(f249(x88601,x88602),x88603),x88604)),f331(f286(x88602,x88601),x88605)))+~P1(f331(f331(f333(f853(x88602,x88601)),f331(f331(f249(x88602,x88601),x88604),x88603)),x88605))
% 51.10/50.82 [8861]P1(f331(f331(f333(f853(x88611,x88612)),f331(f331(f249(x88611,x88612),x88613),x88614)),f331(f286(x88612,x88611),x88615)))+~P1(f331(f331(f333(f853(x88612,x88611)),f331(f331(f249(x88612,x88611),x88614),x88613)),x88615))
% 51.10/50.82 [8879]~P1(f331(f331(x88791,x88795),x88794))+P1(f331(f331(x88791,f331(f258(x88792,x88793),f331(f331(f249(x88792,x88793),x88794),x88795))),f331(f248(x88792,x88793),f331(f331(f249(x88792,x88793),x88794),x88795))))
% 51.10/50.82 [8905]~P1(f331(f331(f333(f853(x89052,x89051)),f331(f331(f249(x89052,x89051),x89054),x89053)),f331(f286(x89051,x89052),x89055)))+P1(f331(f331(f333(f853(x89051,x89052)),f331(f331(f249(x89051,x89052),x89053),x89054)),x89055))
% 51.10/50.82 [8906]~P1(f331(f331(f333(f853(x89062,x89061)),f331(f331(f249(x89062,x89061),x89064),x89063)),f331(f286(x89061,x89062),x89065)))+P1(f331(f331(f333(f853(x89061,x89062)),f331(f331(f249(x89061,x89062),x89063),x89064)),x89065))
% 51.10/50.82 [8934]~P1(f331(f331(f333(f853(x89343,x89341)),f331(f331(f249(x89343,x89341),x89345),x89342)),x89344))+P1(f331(f331(f333(x89341),x89342),f331(f285(x89343,x89341,x89344),f331(f331(f310(x89343),x89345),f184(f854(x89343,a840))))))
% 51.10/50.82 [8977]P1(f331(f331(f333(f853(x89771,x89772)),f331(f331(f249(x89771,x89772),x89773),x89774)),x89775))+~P1(f331(f331(f333(x89772),x89774),f331(f285(x89771,x89772,x89775),f331(f331(f310(x89771),x89773),f184(f854(x89771,a840))))))
% 51.10/50.82 [8997]E(f331(f331(f331(f79(x89971,f851(x89972)),f177(x89971,x89972,x89973,x89974)),x89975),f187(x89972)),f177(x89971,x89972,x89973,f331(f331(f3(f854(x89971,a840)),x89974),f331(f331(f310(x89971),x89975),f184(f854(x89971,a840))))))+~P1(f331(f331(f333(x89971),x89975),x89974))
% 51.10/50.82 [9062]~P68(x90621)+E(f331(f331(f8(a847,x90621),x90622),f303(a847,f331(f331(f87(a847),x90623),x90624),f331(f331(f87(a847),x90625),x90624))),f331(f331(f8(a847,x90621),f331(f331(f10(a847,x90621,a847),x90622),f331(f331(f9(a847,a847,a847),f87(a847)),x90624))),f303(a847,x90623,x90625)))
% 51.10/50.82 [9081]~P68(x90811)+E(f331(f331(f8(a847,x90811),x90812),f331(f302(a847,f331(f331(f87(a847),x90813),x90814)),f331(f331(f87(a847),x90815),x90814))),f331(f331(f8(a847,x90811),f331(f331(f10(a847,x90811,a847),x90812),f331(f331(f9(a847,a847,a847),f87(a847)),x90814))),f331(f302(a847,x90813),x90815)))
% 51.10/50.82 [9290]P1(f331(f331(f333(f853(f848(x92901),f848(x92901))),f331(f331(f249(f848(x92901),f848(x92901)),f331(f331(f145(x92901),x92902),x92903)),f331(f331(f145(x92901),x92904),x92903))),f150(x92901,x92905)))+~P1(f331(f331(f333(f853(x92901,x92901)),f331(f331(f249(x92901,x92901),x92902),x92904)),x92905))
% 51.10/50.82 [9391]P26(x93911,x93912,f331(f331(f310(f846(x93911)),f331(f331(f331(f98(x93911),x93913),f331(a29,x93914)),x93915)),f184(f854(f846(x93911),a840))))+~P26(x93911,f331(f331(f310(f846(x93911)),f331(f331(f331(f98(x93911),x93913),f331(a29,x93914)),x93915)),x93912),f331(f331(f310(f846(x93911)),f331(f331(f331(f98(x93911),x93913),f331(f238(a841),f331(a32,x93914))),x93915)),f184(f854(f846(x93911),a840))))
% 51.10/50.82 [9404]E(f331(f331(f310(x94041),f531(x94042,x94043,x94044,x94045,x94041)),f532(x94042,x94043,x94044,x94045,x94041)),f331(f331(f310(x94041),x94044),x94043))+~P1(f331(f69(x94041,x94045,f331(f331(f310(x94041),x94044),x94043)),x94042))
% 51.10/50.82 [9405]E(f331(f331(f310(x94051),f533(x94052,x94053,x94054,x94055,x94051)),f534(x94052,x94053,x94054,x94055,x94051)),f331(f331(f310(x94051),x94054),x94053))+~P1(f331(f69(x94051,x94055,f331(f331(f310(x94051),x94054),x94053)),x94052))
% 51.10/50.82 [9485]P1(f331(f331(f333(x94851),f640(x94852,x94853,x94854,x94855,x94851)),x94854))+P1(f331(f331(f331(f52(x94851,f854(x94855,a840)),x94854),x94853),x94852))
% 51.10/50.82 [9490]P1(f331(f331(f333(x94901),f641(x94902,x94903,x94901,x94904,x94905)),x94903))+P1(f331(f331(f333(x94905),x94904),f331(f331(f52(x94901,f854(x94905,a840)),x94903),x94902)))
% 51.10/50.82 [9498]P1(f331(f331(f333(x94981),f636(x94982,x94983,x94981,x94984,x94985)),x94983))+P1(f331(f331(f240(f854(x94985,a840)),x94984),f331(f331(f52(x94981,f854(x94985,a840)),x94983),x94982)))
% 51.10/50.82 [9501]P1(f331(f331(x95011,f402(x95012,x95011,x95013,x95014,x95015)),x95012))+~P1(f331(f331(f331(f51(x95015,f854(x95014,a840)),x95013),x95011),x95012))
% 51.10/50.82 [9503]P1(f331(f331(f333(x95031),f402(x95032,x95033,x95034,x95035,x95031)),x95034))+~P1(f331(f331(f331(f51(x95031,f854(x95035,a840)),x95034),x95033),x95032))
% 51.10/50.82 [9513]P1(f331(f331(f333(x95131),f412(x95132,x95133,x95131,x95134,x95135)),x95133))+~P1(f331(f331(f333(x95135),x95134),f331(f331(f51(x95131,f854(x95135,a840)),x95133),x95132)))
% 51.10/50.82 [9518]P1(f331(f331(f333(x95181),x95182),f331(x95183,f412(x95183,x95184,x95185,x95182,x95181))))+~P1(f331(f331(f333(x95181),x95182),f331(f331(f51(x95185,f854(x95181,a840)),x95184),x95183)))
% 51.10/50.82 [9606]~P1(f331(f331(x96064,f640(x96065,x96064,x96063,x96062,x96061)),x96065))+P1(f331(f331(f331(f52(x96061,f854(x96062,a840)),x96063),x96064),x96065))
% 51.10/50.82 [9609]~P1(f331(f331(f333(x96091),x96092),f331(x96095,f641(x96095,x96094,x96093,x96092,x96091))))+P1(f331(f331(f333(x96091),x96092),f331(f331(f52(x96093,f854(x96091,a840)),x96094),x96095)))
% 51.10/50.82 [9612]~P1(f331(f331(f240(f854(x96121,a840)),x96122),f331(x96125,f636(x96125,x96124,x96123,x96122,x96121))))+P1(f331(f331(f240(f854(x96121,a840)),x96122),f331(f331(f52(x96123,f854(x96121,a840)),x96124),x96125)))
% 51.10/50.82 [9667]~P1(f331(f331(f333(x96671),f531(x96675,x96674,x96673,x96672,x96671)),f532(x96675,x96674,x96673,x96672,x96671)))+~P1(f331(f69(x96671,x96672,f331(f331(f310(x96671),x96673),x96674)),x96675))
% 51.10/50.82 [9668]~P1(f331(f331(f333(x96681),f533(x96685,x96684,x96683,x96682,x96681)),f534(x96685,x96684,x96683,x96682,x96681)))+~P1(f331(f69(x96681,x96682,f331(f331(f310(x96681),x96683),x96684)),x96685))
% 51.10/50.82 [9669]~P1(f331(f331(f333(f853(x96691,x96691)),f331(f331(f249(x96691,x96691),x96692),x96695)),f331(f331(f178(f853(x96691,x96691),a840),f331(a119,x96694)),x96693)))+P1(f331(f331(f333(f853(x96691,x96691)),f331(f331(f249(x96691,x96691),x96692),f685(x96693,x96694,x96695,x96692,x96691))),f331(f331(f178(f853(x96691,x96691),a840),x96694),x96693)))
% 51.10/50.82 [9676]P1(f331(f73(x96761,x96761,x96762,f531(x96763,x96764,x96765,x96762,x96761),f532(x96763,x96764,x96765,x96762,x96761)),x96763))+~P1(f331(f69(x96761,x96762,f331(f331(f310(x96761),x96765),x96764)),x96763))
% 51.10/50.82 [9677]P1(f331(f73(x96771,x96771,x96772,f533(x96773,x96774,x96775,x96772,x96771),f534(x96773,x96774,x96775,x96772,x96771)),x96773))+~P1(f331(f69(x96771,x96772,f331(f331(f310(x96771),x96775),x96774)),x96773))
% 51.10/50.82 [9689]~P102(x96891)+P16(x96891,f331(f331(f147(x96892,x96891),x96893),f331(f131(x96892,f331(f331(f9(x96892,x96891,a840),f331(f331(f10(x96891,f854(x96891,a840),x96892),a328),x96893)),f331(x96894,x96895))),x96895)))
% 51.10/50.82 [9744]~P1(f331(f331(f333(x97442),x97445),f331(f285(x97441,x97442,x97444),x97443)))+P1(f331(f331(f333(f853(x97441,x97442)),f331(f331(f249(x97441,x97442),f356(x97443,x97444,x97441,x97445,x97442)),x97445)),x97444))
% 51.10/50.82 [9745]~P1(f331(f331(f333(x97452),x97455),f331(f285(x97451,x97452,x97454),x97453)))+P1(f331(f331(f333(f853(x97451,x97452)),f331(f331(f249(x97451,x97452),f361(x97453,x97454,x97451,x97455,x97452)),x97455)),x97454))
% 51.10/50.82 [9765]~P1(f331(f331(f333(f853(x97651,x97651)),f331(f331(f249(x97651,x97651),x97655),x97654)),f331(f331(f178(f853(x97651,x97651),a840),f331(a119,x97653)),x97652)))+P1(f331(f331(f333(f853(x97651,x97651)),f331(f331(f249(x97651,x97651),f685(x97652,x97653,x97654,x97655,x97651)),x97654)),x97652))
% 51.10/50.82 [9768]~P1(f331(f331(f333(f853(x97681,x97681)),f331(f331(f249(x97681,x97681),x97685),x97684)),f331(f331(f178(f853(x97681,x97681),a840),f331(a119,x97683)),x97682)))+P1(f331(f331(f333(f853(x97681,x97681)),f331(f331(f249(x97681,x97681),f686(x97682,x97683,x97684,x97685,x97681)),x97684)),f331(f331(f178(f853(x97681,x97681),a840),x97683),x97682)))
% 51.10/50.82 [9769]~P1(f331(f331(f333(f853(x97691,x97691)),f331(f331(f249(x97691,x97691),x97695),x97694)),f331(f331(f178(f853(x97691,x97691),a840),f331(a119,x97693)),x97692)))+P1(f331(f331(f333(f853(x97691,x97691)),f331(f331(f249(x97691,x97691),f687(x97692,x97693,x97694,x97695,x97691)),x97694)),f331(f331(f178(f853(x97691,x97691),a840),x97693),x97692)))
% 51.10/50.82 [9770]~P1(f331(f331(f333(f853(f848(x97701),f848(x97701))),f331(f331(f249(f848(x97701),f848(x97701)),x97705),f331(f331(f145(x97701),x97704),x97703))),f151(x97701,x97702)))+P1(f331(f331(f333(f853(x97701,x97701)),f331(f331(f249(x97701,x97701),f716(x97702,x97703,x97704,x97705,x97701)),x97704)),x97702))
% 51.10/50.82 [6959]E(x69591,f187(x69592))+E(f174(x69593,x69592,f331(f331(f331(f79(x69593,f851(x69592)),x69594),x69595),x69591)),f331(f331(f310(x69593),x69595),f174(x69593,x69592,x69594)))
% 51.10/50.82 [7477]~E(x74773,f184(f854(x74772,a840)))+E(f331(f331(f108(f854(x74771,a840)),f331(f331(f51(x74772,f854(x74771,a840)),x74773),x74774)),x74775),x74775)
% 51.10/50.82 [7478]~E(x74783,f184(f854(x74782,a840)))+E(f331(f331(f109(f854(x74781,a840)),f331(f331(f52(x74782,f854(x74781,a840)),x74783),x74784)),x74785),x74785)
% 51.10/50.82 [7530]~P87(x75301)+E(f331(f331(f88(x75301),f331(f331(f88(x75301),x75302),x75303)),f331(f331(f88(x75301),x75304),x75305)),f331(f331(f88(x75301),x75304),f331(f331(f88(x75301),f331(f331(f88(x75301),x75302),x75303)),x75305)))
% 51.10/50.82 [7840]~E(x78405,f187(x78402))+E(f174(x78401,x78402,f331(f331(f331(f79(x78401,f851(x78402)),x78403),x78404),x78405)),f331(f331(f3(f854(x78401,a840)),f174(x78401,x78402,x78403)),f331(f331(f310(x78401),x78404),f184(f854(x78401,a840)))))
% 51.10/50.82 [7910]~E(x79103,f184(f854(x79102,a840)))+E(f331(f331(f3(f854(x79101,a840)),f331(f331(f52(x79102,f854(x79101,a840)),x79103),x79104)),x79105),f331(f331(f3(f854(x79101,a840)),f247(f854(x79101,a840))),x79105))
% 51.10/50.82 [8037]E(f331(f331(f152(x80371,f331(f331(f130(x80371),x80372),x80373)),x80374),x80375),f331(f331(f130(x80371),f331(f331(f152(x80371,x80372),x80374),x80375)),x80373))+~P1(f331(f331(f241(a847),x80374),f331(f185(f848(x80371)),x80372)))
% 51.10/50.82 [8038]E(f331(f331(f152(x80381,f331(f331(f130(x80381),x80382),x80383)),x80384),x80385),f331(f331(f130(x80381),f331(f331(f152(x80381,x80382),x80384),x80385)),x80383))+~P1(f331(f331(f241(a847),x80384),f331(f185(f848(x80381)),x80382)))
% 51.10/50.82 [8169]P1(f331(f331(f333(x81691),x81695),f331(f163(x81691),x81693)))+E(f331(f171(x81691,x81692,f331(f331(f172(x81691,x81692),x81693),f331(f331(f147(x81691,x81692),x81694),x81693))),x81695),f187(x81692))
% 51.10/50.82 [8278]~P1(f331(f331(f333(x82781),x82785),f331(f163(x82781),x82783)))+E(f331(f171(x82781,x82782,f331(f331(f172(x82781,x82782),x82783),f331(f331(f147(x82781,x82782),x82784),x82783))),x82785),f331(f234(x82782),f331(x82784,x82785)))
% 51.10/50.82 [8308]E(f331(f331(f155(x83081),f331(f331(f147(a847,x83081),x83082),f135(a847,f331(f302(a847,x83083),x83084)))),x83085),f331(x83082,f331(f331(f87(a847),x83083),x83085)))+~P1(f331(f331(f241(a847),x83085),f331(f331(f3(a847),x83084),x83083)))
% 51.10/50.82 [8321]E(x83211,f2(a106))+E(f126(x83212,x83213,f331(x83214,f331(f331(f3(a106),x83211),f85(a106))),f331(f331(f9(x83212,a106,f849(f851(x83213))),x83215),x83211)),f331(f198(x83212,x83213,x83214,x83215),x83211))
% 51.10/50.82 [8344]~E(x83443,f184(f854(x83441,a840)))+E(f331(f331(f51(x83441,f854(x83442,a840)),x83443),f331(f331(f10(f854(x83442,a840),f854(x83442,a840),x83441),f331(f108(f854(x83442,a840)),x83444)),x83445)),f184(f854(x83442,a840)))
% 51.10/50.82 [8345]~E(x83453,f184(f854(x83451,a840)))+E(f331(f331(f52(x83451,f854(x83452,a840)),x83453),f331(f331(f10(f854(x83452,a840),f854(x83452,a840),x83451),f331(f3(f854(x83452,a840)),x83454)),x83455)),f247(f854(x83452,a840)))
% 51.10/50.82 [8346]~E(x83463,f184(f854(x83461,a840)))+E(f331(f331(f52(x83461,f854(x83462,a840)),x83463),f331(f331(f10(f854(x83462,a840),f854(x83462,a840),x83461),f331(f109(f854(x83462,a840)),x83464)),x83465)),f247(f854(x83462,a840)))
% 51.10/50.82 [8351]~P136(x83512)+E(f331(f331(f8(x83511,x83512),f331(f331(f10(x83512,x83512,x83511),f331(f88(x83512),x83513)),x83514)),x83515),f331(f331(f88(x83512),x83513),f331(f331(f8(x83511,x83512),x83514),x83515)))
% 51.10/50.82 [8611]E(x86111,f184(f854(x86112,a840)))+E(f331(f331(f52(x86112,f854(x86113,a840)),x86111),f331(f331(f10(f854(x86113,a840),f854(x86113,a840),x86112),f331(f3(f854(x86113,a840)),x86114)),x86115)),f331(f331(f3(f854(x86113,a840)),x86114),f331(f331(f51(x86112,f854(x86113,a840)),x86111),x86115)))
% 51.10/50.82 [8612]E(x86121,f184(f854(x86122,a840)))+E(f331(f331(f51(x86122,f854(x86123,a840)),x86121),f331(f331(f10(f854(x86123,a840),f854(x86123,a840),x86122),f331(f108(f854(x86123,a840)),x86124)),x86125)),f331(f331(f108(f854(x86123,a840)),x86124),f331(f331(f51(x86122,f854(x86123,a840)),x86121),x86125)))
% 51.10/50.82 [8613]E(x86131,f184(f854(x86132,a840)))+E(f331(f331(f52(x86132,f854(x86133,a840)),x86131),f331(f331(f10(f854(x86133,a840),f854(x86133,a840),x86132),f331(f109(f854(x86133,a840)),x86134)),x86135)),f331(f331(f109(f854(x86133,a840)),x86134),f331(f331(f52(x86132,f854(x86133,a840)),x86131),x86135)))
% 51.10/50.82 [8614]E(x86141,f184(f854(x86142,a840)))+E(f331(f331(f51(x86142,f854(x86143,a840)),x86141),f331(f331(f10(f854(x86143,a840),f854(x86143,a840),x86142),f331(f108(f854(x86143,a840)),x86144)),x86145)),f331(f331(f108(f854(x86143,a840)),x86144),f331(f331(f51(x86142,f854(x86143,a840)),x86141),x86145)))
% 51.10/50.82 [8615]E(x86151,f184(f854(x86152,a840)))+E(f331(f331(f52(x86152,f854(x86153,a840)),x86151),f331(f331(f10(f854(x86153,a840),f854(x86153,a840),x86152),f331(f3(f854(x86153,a840)),x86154)),x86155)),f331(f331(f3(f854(x86153,a840)),x86154),f331(f331(f51(x86152,f854(x86153,a840)),x86151),x86155)))
% 51.10/50.82 [8616]E(x86161,f184(f854(x86162,a840)))+E(f331(f331(f52(x86162,f854(x86163,a840)),x86161),f331(f331(f10(f854(x86163,a840),f854(x86163,a840),x86162),f331(f109(f854(x86163,a840)),x86164)),x86165)),f331(f331(f109(f854(x86163,a840)),x86164),f331(f331(f52(x86162,f854(x86163,a840)),x86161),x86165)))
% 51.10/50.82 [9031]~P27(x90312,x90311,x90313,f331(f331(f108(f854(x90312,a840)),x90314),x90315))+E(f331(f331(f109(f854(x90311,a840)),f331(f311(x90312,x90311,x90313),f331(f331(f3(f854(x90312,a840)),x90314),x90315))),f331(f311(x90312,x90311,x90313),f331(f331(f3(f854(x90312,a840)),x90315),x90314))),f184(f854(x90311,a840)))
% 51.10/50.82 [9286]~P1(f331(f331(f240(f854(x92863,a840)),f331(f285(x92861,x92863,x92864),x92862)),x92865))+P1(f331(f331(f240(f854(x92861,a840)),x92862),f331(f86(f854(x92861,a840)),f331(f285(x92863,x92861,f331(f286(x92861,x92863),x92864)),f331(f86(f854(x92863,a840)),x92865)))))
% 51.10/50.82 [9309]~P27(x93091,x93092,x93093,f331(f331(f310(x93091),x93094),x93095))+~P1(f331(f331(f333(x93092),f331(x93093,x93094)),f331(f311(x93091,x93092,x93093),f331(f331(f3(f854(x93091,a840)),x93095),f331(f331(f310(x93091),x93094),f184(f854(x93091,a840)))))))
% 51.10/50.82 [9358]P1(f331(f331(f240(f854(x93581,a840)),f331(f285(x93582,x93581,x93583),x93584)),x93585))+~P1(f331(f331(f240(f854(x93582,a840)),x93584),f331(f86(f854(x93582,a840)),f331(f285(x93581,x93582,f331(f286(x93582,x93581),x93583)),f331(f86(f854(x93581,a840)),x93585)))))
% 51.10/50.82 [9435]~P78(x94351)+P1(f331(f331(f240(x94351),f331(f82(x94351),f331(f331(f3(x94351),f331(f331(f87(x94351),x94352),x94353)),f331(f331(f87(x94351),x94354),x94355)))),f331(f331(f87(x94351),f331(f82(x94351),f331(f331(f3(x94351),x94352),x94354))),f331(f82(x94351),f331(f331(f3(x94351),x94353),x94355)))))
% 51.10/50.82 [9531]P1(f331(f331(f333(x95311),f414(x95312,x95313,x95314,x95311,x95315)),x95314))+P1(f331(f331(f240(f854(x95315,a840)),f331(f331(f51(x95311,f854(x95315,a840)),x95314),x95313)),x95312))
% 51.10/50.82 [9709]~P1(f331(f331(f240(f854(x97091,a840)),f331(x97094,f414(x97095,x97094,x97093,x97092,x97091))),x97095))+P1(f331(f331(f240(f854(x97091,a840)),f331(f331(f51(x97092,f854(x97091,a840)),x97093),x97094)),x97095))
% 51.10/50.82 [8458]E(f331(f331(f130(x84581),x84582),f331(f331(f152(x84581,x84583),f331(f331(f3(a847),x84584),f331(f185(f848(x84581)),x84582))),x84585)),f331(f331(f152(x84581,f331(f331(f130(x84581),x84582),x84583)),x84584),x84585))+P1(f331(f331(f241(a847),x84584),f331(f185(f848(x84581)),x84582)))
% 51.10/50.82 [8483]~P135(x84831)+E(f331(f331(f87(x84831),f331(f331(f88(x84831),x84832),x84833)),f331(f331(f87(x84831),f331(f331(f88(x84831),x84834),x84833)),x84835)),f331(f331(f87(x84831),f331(f331(f88(x84831),f331(f331(f87(x84831),x84832),x84834)),x84833)),x84835))
% 51.10/50.82 [8987]~P136(x89871)+E(f331(f157(x89871),f331(f331(f147(x89872,x89871),f331(f331(f10(x89871,x89871,x89872),f331(f88(x89871),x89873)),x89874)),x89875)),f331(f331(f88(x89871),x89873),f331(f157(x89871),f331(f331(f147(x89872,x89871),x89874),x89875))))
% 51.10/50.82 [9366]~P136(x93662)+E(f331(f331(f8(x93661,x93662),f331(f331(f9(x93661,x93662,x93662),f331(f331(f10(x93662,f854(x93662,x93662),x93661),f88(x93662)),x93663)),x93664)),x93665),f331(f331(f88(x93662),f331(f331(f8(x93661,x93662),x93663),x93665)),x93664))
% 51.10/50.82 [9367]~P59(x93672)+E(f331(f331(f8(x93671,x93672),f331(f331(f9(x93671,x93672,x93672),f331(f331(f10(x93672,f854(x93672,x93672),x93671),f291(x93672)),x93673)),x93674)),x93675),f331(f331(f291(x93672),f331(f331(f8(x93671,x93672),x93673),x93675)),x93674))
% 51.10/50.82 [9374]~P70(x93742)+E(f331(f331(f11(x93741,x93742),f331(f331(f20(x93741,x93742,x93742),f331(f331(f10(x93742,f854(x93742,x93742),x93741),f88(x93742)),x93743)),x93744)),x93745),f331(f331(f88(x93742),f331(f331(f11(x93741,x93742),x93743),x93745)),f331(f331(f11(x93741,x93742),x93744),x93745)))
% 51.10/50.82 [9375]~P68(x93752)+E(f331(f331(f8(x93751,x93752),f331(f331(f20(x93751,x93752,x93752),f331(f331(f10(x93752,f854(x93752,x93752),x93751),f87(x93752)),x93753)),x93754)),x93755),f331(f331(f87(x93752),f331(f331(f8(x93751,x93752),x93753),x93755)),f331(f331(f8(x93751,x93752),x93754),x93755)))
% 51.10/50.82 [9376]~P4(x93762)+E(f331(f331(f8(x93761,x93762),f331(f331(f20(x93761,x93762,x93762),f331(f331(f10(x93762,f854(x93762,x93762),x93761),f3(x93762)),x93763)),x93764)),x93765),f331(f331(f3(x93762),f331(f331(f8(x93761,x93762),x93763),x93765)),f331(f331(f8(x93761,x93762),x93764),x93765)))
% 51.10/50.82 [9416]~E(x94163,f184(f854(x94161,a840)))+E(f331(f331(f51(x94161,f854(x94162,a840)),x94163),f331(f331(f9(x94161,f854(x94162,a840),f854(x94162,a840)),f331(f331(f10(f854(x94162,a840),f854(f854(x94162,a840),f854(x94162,a840)),x94161),f108(f854(x94162,a840))),x94164)),x94165)),f184(f854(x94162,a840)))
% 51.10/50.82 [9417]~E(x94173,f184(f854(x94171,a840)))+E(f331(f331(f52(x94171,f854(x94172,a840)),x94173),f331(f331(f9(x94171,f854(x94172,a840),f854(x94172,a840)),f331(f331(f10(f854(x94172,a840),f854(f854(x94172,a840),f854(x94172,a840)),x94171),f3(f854(x94172,a840))),x94174)),x94175)),f247(f854(x94172,a840)))
% 51.10/50.82 [9418]~E(x94183,f184(f854(x94181,a840)))+E(f331(f331(f52(x94181,f854(x94182,a840)),x94183),f331(f331(f9(x94181,f854(x94182,a840),f854(x94182,a840)),f331(f331(f10(f854(x94182,a840),f854(f854(x94182,a840),f854(x94182,a840)),x94181),f109(f854(x94182,a840))),x94184)),x94185)),f247(f854(x94182,a840)))
% 51.10/50.82 [9442]E(x94421,f184(f854(x94422,a840)))+E(f331(f331(f52(x94422,f854(x94423,a840)),x94421),f331(f331(f9(x94422,f854(x94423,a840),f854(x94423,a840)),f331(f331(f10(f854(x94423,a840),f854(f854(x94423,a840),f854(x94423,a840)),x94422),f3(f854(x94423,a840))),x94424)),x94425)),f331(f331(f3(f854(x94423,a840)),f331(f331(f52(x94422,f854(x94423,a840)),x94421),x94424)),x94425))
% 51.10/50.82 [9443]E(x94431,f184(f854(x94432,a840)))+E(f331(f331(f51(x94432,f854(x94433,a840)),x94431),f331(f331(f9(x94432,f854(x94433,a840),f854(x94433,a840)),f331(f331(f10(f854(x94433,a840),f854(f854(x94433,a840),f854(x94433,a840)),x94432),f108(f854(x94433,a840))),x94434)),x94435)),f331(f331(f108(f854(x94433,a840)),f331(f331(f51(x94432,f854(x94433,a840)),x94431),x94434)),x94435))
% 51.10/50.82 [9444]E(x94441,f184(f854(x94442,a840)))+E(f331(f331(f52(x94442,f854(x94443,a840)),x94441),f331(f331(f9(x94442,f854(x94443,a840),f854(x94443,a840)),f331(f331(f10(f854(x94443,a840),f854(f854(x94443,a840),f854(x94443,a840)),x94442),f109(f854(x94443,a840))),x94444)),x94445)),f331(f331(f109(f854(x94443,a840)),f331(f331(f52(x94442,f854(x94443,a840)),x94441),x94444)),x94445))
% 51.10/50.82 [9445]E(x94451,f184(f854(x94452,a840)))+E(f331(f331(f51(x94452,f854(x94453,a840)),x94451),f331(f331(f9(x94452,f854(x94453,a840),f854(x94453,a840)),f331(f331(f10(f854(x94453,a840),f854(f854(x94453,a840),f854(x94453,a840)),x94452),f108(f854(x94453,a840))),x94454)),x94455)),f331(f331(f108(f854(x94453,a840)),f331(f331(f51(x94452,f854(x94453,a840)),x94451),x94454)),x94455))
% 51.10/50.82 [9446]E(x94461,f184(f854(x94462,a840)))+E(f331(f331(f52(x94462,f854(x94463,a840)),x94461),f331(f331(f9(x94462,f854(x94463,a840),f854(x94463,a840)),f331(f331(f10(f854(x94463,a840),f854(f854(x94463,a840),f854(x94463,a840)),x94462),f3(f854(x94463,a840))),x94464)),x94465)),f331(f331(f3(f854(x94463,a840)),f331(f331(f52(x94462,f854(x94463,a840)),x94461),x94464)),x94465))
% 51.10/50.82 [9447]E(x94471,f184(f854(x94472,a840)))+E(f331(f331(f52(x94472,f854(x94473,a840)),x94471),f331(f331(f9(x94472,f854(x94473,a840),f854(x94473,a840)),f331(f331(f10(f854(x94473,a840),f854(f854(x94473,a840),f854(x94473,a840)),x94472),f109(f854(x94473,a840))),x94474)),x94475)),f331(f331(f109(f854(x94473,a840)),f331(f331(f52(x94472,f854(x94473,a840)),x94471),x94474)),x94475))
% 51.10/50.82 [9035]~P1(f331(f331(f240(a847),x90351),x90354))+E(f331(f331(f3(a847),f331(f331(f87(a847),f331(f331(f88(a847),x90351),x90352)),x90353)),f331(f331(f87(a847),f331(f331(f88(a847),x90354),x90352)),x90355)),f331(f331(f3(a847),x90353),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x90354),x90351)),x90352)),x90355)))
% 51.10/50.82 [9589]~P136(x95891)+E(f331(f157(x95891),f331(f331(f147(x95892,x95891),f331(f331(f9(x95892,x95891,x95891),f331(f331(f10(x95891,f854(x95891,x95891),x95892),f88(x95891)),x95893)),x95894)),x95895)),f331(f331(f88(x95891),f331(f157(x95891),f331(f331(f147(x95892,x95891),x95893),x95895))),x95894))
% 51.10/50.82 [9595]~P68(x95951)+E(f331(f157(x95951),f331(f331(f147(x95952,x95951),f331(f331(f20(x95952,x95951,x95951),f331(f331(f10(x95951,f854(x95951,x95951),x95952),f87(x95951)),x95953)),x95954)),x95955)),f331(f331(f87(x95951),f331(f157(x95951),f331(f331(f147(x95952,x95951),x95953),x95955))),f331(f157(x95951),f331(f331(f147(x95952,x95951),x95954),x95955))))
% 51.10/50.82 [9596]~P4(x95961)+E(f331(f157(x95961),f331(f331(f147(x95962,x95961),f331(f331(f20(x95962,x95961,x95961),f331(f331(f10(x95961,f854(x95961,x95961),x95962),f3(x95961)),x95963)),x95964)),x95965)),f331(f331(f3(x95961),f331(f157(x95961),f331(f331(f147(x95962,x95961),x95963),x95965))),f331(f157(x95961),f331(f331(f147(x95962,x95961),x95964),x95965))))
% 51.10/50.82 [9253]~P1(f331(f331(f240(a847),x92534),x92531))+E(f331(f331(f3(a847),f331(f331(f87(a847),f331(f331(f88(a847),x92531),x92532)),x92533)),f331(f331(f87(a847),f331(f331(f88(a847),x92534),x92532)),x92535)),f331(f331(f3(a847),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x92531),x92534)),x92532)),x92533)),x92535))
% 51.10/50.82 [10001]P26(x100011,x100012,f331(f311(a843,f846(x100011),f331(f331(f20(a843,f854(x100011,f854(a845,a840)),f846(x100011)),f331(f331(f20(a843,a841,f854(f854(x100011,f854(a845,a840)),f846(x100011))),f331(f331(f10(f854(x100011,f854(a845,a840)),f854(a841,f854(f854(x100011,f854(a845,a840)),f846(x100011))),a843),f98(x100011)),x100013)),a29)),x100014)),x100015))+~P26(x100011,f331(f331(f108(f854(f846(x100011),a840)),x100012),f331(f311(a843,f846(x100011),f331(f331(f20(a843,f854(x100011,f854(a845,a840)),f846(x100011)),f331(f331(f20(a843,a841,f854(f854(x100011,f854(a845,a840)),f846(x100011))),f331(f331(f10(f854(x100011,f854(a845,a840)),f854(a841,f854(f854(x100011,f854(a845,a840)),f846(x100011))),a843),f98(x100011)),x100013)),a29)),x100014)),x100015)),f331(f311(a843,f846(x100011),f331(f331(f20(a843,f854(x100011,f854(a845,a840)),f846(x100011)),f331(f331(f20(a843,a841,f854(f854(x100011,f854(a845,a840)),f846(x100011))),f331(f331(f10(f854(x100011,f854(a845,a840)),f854(a841,f854(f854(x100011,f854(a845,a840)),f846(x100011))),a843),f98(x100011)),x100013)),f331(f331(f10(f851(a841),a841,a843),f238(a841)),a32))),x100014)),x100015))
% 51.10/50.82 [10002]P30(x100021,x100022,f331(f311(a843,f846(x100021),f331(f331(f20(a843,f854(x100021,f854(a845,a840)),f846(x100021)),f331(f331(f20(a843,a841,f854(f854(x100021,f854(a845,a840)),f846(x100021))),f331(f331(f10(f854(x100021,f854(a845,a840)),f854(a841,f854(f854(x100021,f854(a845,a840)),f846(x100021))),a843),f98(x100021)),x100023)),a29)),x100024)),x100025))+~P30(x100021,f331(f331(f108(f854(f846(x100021),a840)),x100022),f331(f311(a843,f846(x100021),f331(f331(f20(a843,f854(x100021,f854(a845,a840)),f846(x100021)),f331(f331(f20(a843,a841,f854(f854(x100021,f854(a845,a840)),f846(x100021))),f331(f331(f10(f854(x100021,f854(a845,a840)),f854(a841,f854(f854(x100021,f854(a845,a840)),f846(x100021))),a843),f98(x100021)),x100023)),a29)),x100024)),x100025)),f331(f311(a843,f846(x100021),f331(f331(f20(a843,f854(x100021,f854(a845,a840)),f846(x100021)),f331(f331(f20(a843,a841,f854(f854(x100021,f854(a845,a840)),f846(x100021))),f331(f331(f10(f854(x100021,f854(a845,a840)),f854(a841,f854(f854(x100021,f854(a845,a840)),f846(x100021))),a843),f98(x100021)),x100023)),f331(f331(f10(f851(a841),a841,a843),f238(a841)),a32))),x100024)),x100025))
% 51.10/50.82 [5117]E(x51171,x51172)+~E(f33(x51173,x51174,x51171),f33(x51175,x51176,x51172))
% 51.10/50.82 [5118]E(x51181,x51182)+~E(f33(x51183,x51181,x51184),f33(x51185,x51182,x51186))
% 51.10/50.82 [5119]E(x51191,x51192)+~E(f33(x51191,x51193,x51194),f33(x51192,x51195,x51196))
% 51.10/50.82 [5120]E(x51201,x51202)+~E(f34(x51203,x51204,x51201),f34(x51205,x51206,x51202))
% 51.10/50.82 [5121]E(x51211,x51212)+~E(f34(x51213,x51211,x51214),f34(x51215,x51212,x51216))
% 51.10/50.82 [5122]E(x51221,x51222)+~E(f34(x51221,x51223,x51224),f34(x51222,x51225,x51226))
% 51.10/50.82 [5123]E(x51231,x51232)+~E(f35(x51233,x51234,x51231),f35(x51235,x51236,x51232))
% 51.10/50.82 [5124]E(x51241,x51242)+~E(f35(x51243,x51241,x51244),f35(x51245,x51242,x51246))
% 51.10/50.82 [5125]E(x51251,x51252)+~E(f35(x51251,x51253,x51254),f35(x51252,x51255,x51256))
% 51.10/50.82 [7145]E(x71451,x71452)+~E(f222(x71453,x71454,x71455,x71451),f222(x71453,x71454,x71456,x71452))
% 51.10/50.82 [7146]E(x71461,x71462)+~E(f222(x71463,x71464,x71461,x71465),f222(x71463,x71464,x71462,x71466))
% 51.10/50.82 [6590]E(f331(f175(x65901,x65902,x65903,x65904),x65905),f331(f234(x65902),x65906))+~E(f331(x65904,x65905),f331(f234(x65902),x65906))
% 51.10/50.82 [6591]E(f331(f175(x65911,x65912,x65913,x65914),x65915),f331(f234(x65912),x65916))+~E(f331(x65914,x65915),f331(f234(x65912),x65916))
% 51.10/50.82 [6742]E(f331(f236(f851(x67421),x67422,f187(x67421),x67423),f331(x67424,x67425)),f331(x67423,x67426))+~E(f331(x67424,x67425),f331(f234(x67422),x67426))
% 51.10/50.82 [8289]~P21(x82895,x82891,x82892,x82896)+E(f331(f80(x82891,x82891,x82891,f331(x82892,x82893)),f331(x82892,x82894)),f331(f80(x82891,x82891,x82891,f331(x82892,x82894)),f331(x82892,x82893)))
% 51.10/50.82 [8518]~P53(x85184,x85185,x85182,x85181,x85186)+E(f331(x85181,f331(x85182,x85183)),x85183)
% 51.10/50.82 [8660]P27(x86601,x86602,x86603,x86604)+~P27(x86601,x86605,f331(f80(x86602,x86605,x86601,x86606),x86603),x86604)
% 51.10/50.82 [8737]~P27(x87374,x87372,f331(f80(x87371,x87372,x87374,x87373),x87375),x87376)+P27(x87371,x87372,x87373,f331(f311(x87374,x87371,x87375),x87376))
% 51.10/50.82 [9377]P1(f331(f68(x93771),x93772))+~P1(f331(f73(x93771,x93773,x93774,x93775,x93772),x93776))
% 51.10/50.82 [9387]~P1(f331(f331(f333(x93874),x93873),f300(x93874,x93875,x93871,x93872,x93876)))+P1(f331(f331(x93871,x93872),x93873))
% 51.10/50.82 [9388]~P1(f331(f331(f333(x93884),x93883),f297(x93884,x93881,x93885,x93882,x93886)))+P1(f331(f331(x93881,x93882),x93883))
% 51.10/50.82 [9389]~P1(f331(f331(f333(x93894),x93892),f300(x93894,x93891,x93895,x93896,x93893)))+P1(f331(f331(x93891,x93892),x93893))
% 51.10/50.82 [9390]~P1(f331(f331(f333(x93904),x93902),f297(x93904,x93905,x93901,x93906,x93903)))+P1(f331(f331(x93901,x93902),x93903))
% 51.10/50.82 [9560]~P37(f34(x95603,x95604,x95601),x95602,x95605,x95606)+P37(x95601,f331(f331(f331(a193,x95602),f40(x95603)),f331(x95604,x95602)),x95605,f395(x95606,x95605,x95602,x95601,x95604,x95603))
% 51.10/50.82 [9573]~P37(f33(x95736,x95731,x95733),x95732,x95734,x95735)+P37(f331(a29,x95731),f331(f331(f331(a193,f331(f331(a194,x95732),a195)),f40(a27)),f331(x95733,x95732)),x95734,f672(x95735,x95734,x95732,x95733,x95731,x95736))
% 51.10/50.82 [5607]E(x56071,x56072)+~E(f331(f331(f249(x56073,x56074),x56075),x56071),f331(f331(f249(x56073,x56074),x56076),x56072))
% 51.10/50.82 [5608]E(x56081,x56082)+~E(f331(f331(f249(x56083,x56084),x56085),x56081),f331(f331(f249(x56083,x56084),x56086),x56082))
% 51.10/50.82 [5609]E(x56091,x56092)+~E(f331(f331(f249(x56093,x56094),x56091),x56095),f331(f331(f249(x56093,x56094),x56092),x56096))
% 51.10/50.82 [5610]E(x56101,x56102)+~E(f331(f331(f249(x56103,x56104),x56101),x56105),f331(f331(f249(x56103,x56104),x56102),x56106))
% 51.10/50.82 [5749]~P18(x57495,x57496,x57491)+E(f331(f331(x57491,x57492),f331(f331(x57491,x57493),x57494)),f331(f331(x57491,x57493),f331(f331(x57491,x57492),x57494)))
% 51.10/50.82 [7216]~P32(x72164,x72161,f331(f331(f145(x72164),x72162),x72165),f331(f331(f145(x72164),x72163),x72166))+P1(f331(f331(x72161,x72162),x72163))
% 51.10/50.82 [7596]P32(x75961,x75962,x75963,x75964)+~P32(x75961,x75962,f331(f331(f145(x75961),x75965),x75963),f331(f331(f145(x75961),x75966),x75964))
% 51.10/50.82 [8224]~P37(x82243,f331(f331(f331(a193,x82244),f40(x82241)),f331(x82242,x82244)),x82245,x82246)+P37(f34(x82241,x82242,x82243),x82244,x82245,f331(f331(f331(a193,x82246),f40(x82241)),f331(f331(a196,x82244),x82241)))
% 51.10/50.82 [8605]~P53(x86055,x86051,x86052,x86056,x86054)+P1(f331(f331(f333(x86051),f331(x86052,x86053)),x86054))
% 51.10/50.82 [8758]E(f331(f83(x87581,x87582,x87583,x87584,x87585),x87586),f331(x87583,x87586))+P1(f331(f331(f333(x87581),x87586),x87585))
% 51.10/50.82 [8759]E(f331(f83(x87591,x87592,x87593,x87594,x87595),x87596),f331(x87593,x87596))+P1(f331(f331(f333(x87591),x87596),x87595))
% 51.10/50.82 [8777]~E(x87773,f331(f331(f145(x87771),x87775),x87776))+P1(f331(f331(f333(f853(f848(x87771),f848(x87771))),f331(f331(f249(f848(x87771),f848(x87771)),x87772),f331(f331(f130(x87771),x87772),x87773))),f142(x87771,x87774)))
% 51.10/50.82 [8780]E(f331(f83(x87801,x87802,x87803,x87804,x87805),x87806),f331(x87804,x87806))+~P1(f331(f331(f333(x87801),x87806),x87805))
% 51.10/50.82 [8781]E(f331(f83(x87811,x87812,x87813,x87814,x87815),x87816),f331(x87814,x87816))+~P1(f331(f331(f333(x87811),x87816),x87815))
% 51.10/50.82 [8978]~P37(f331(a29,x89782),f331(f331(f331(a193,f331(f331(a194,x89784),a195)),f40(a27)),f331(x89783,x89784)),x89785,x89786)+P37(f33(x89781,x89782,x89783),x89784,x89785,f331(f331(f331(a193,f331(f331(a194,x89786),f331(a196,x89784))),x89781),f331(f331(a196,x89786),a28)))
% 51.10/50.82 [9457]~P25(x94574,x94572,x94575,x94573,x94576,x94571)+E(f331(x94571,f184(f854(x94572,a840))),x94573)
% 51.10/50.82 [9571]P37(x95711,f331(f331(f331(a193,x95712),f40(x95713)),f331(x95714,x95712)),x95715,f358(x95716,x95715,x95712,x95711,x95714,x95713))+~P37(f34(x95713,x95714,x95711),x95712,x95715,f331(f331(f331(a193,x95716),f40(x95713)),f331(f331(a196,x95712),x95713)))
% 51.10/50.82 [9599]P37(f331(a29,x95991),f331(f331(f331(a193,f331(f331(a194,x95992),a195)),f40(a27)),f331(x95993,x95992)),x95994,f560(x95995,x95994,x95992,x95993,x95991,x95996))+~P37(f33(x95996,x95991,x95993),x95992,x95994,f331(f331(f331(a193,f331(f331(a194,x95995),f331(a196,x95992))),x95996),f331(f331(a196,x95995),a28)))
% 51.10/50.82 [9670]~E(f331(x96704,f331(f248(x96701,x96703),x96705)),f331(x96706,f331(f248(x96701,x96703),x96705)))+E(f331(f260(x96701,x96702,x96703,x96703,x96704,f39(x96703)),x96705),f331(f260(x96701,x96702,x96703,x96703,x96706,f39(x96703)),x96705))
% 51.10/50.82 [9671]~E(f331(x96714,f331(f258(x96711,x96712),x96715)),f331(x96716,f331(f258(x96711,x96712),x96715)))+E(f331(f260(x96711,x96711,x96712,x96713,f39(x96711),x96714),x96715),f331(f260(x96711,x96711,x96712,x96713,f39(x96711),x96716),x96715))
% 51.10/50.82 [9732]~E(f331(f260(x97322,x97326,x97323,x97323,x97321,f39(x97323)),x97324),f331(f260(x97322,x97326,x97323,x97323,x97325,f39(x97323)),x97324))+E(f331(x97321,f331(f248(x97322,x97323),x97324)),f331(x97325,f331(f248(x97322,x97323),x97324)))
% 51.10/50.82 [9733]~E(f331(f260(x97332,x97332,x97333,x97336,f39(x97332),x97331),x97334),f331(f260(x97332,x97332,x97333,x97336,f39(x97332),x97335),x97334))+E(f331(x97331,f331(f258(x97332,x97333),x97334)),f331(x97335,f331(f258(x97332,x97333),x97334)))
% 51.10/50.82 [9794]~P37(f34(x97946,x97945,x97944),x97943,x97942,x97941)+E(f331(f331(f331(a193,f395(x97941,x97942,x97943,x97944,x97945,x97946)),f40(x97946)),f331(f331(a196,x97943),x97946)),x97941)
% 51.10/50.82 [9801]~P37(f34(x98016,x98015,x98014),x98013,x98012,f331(f331(f331(a193,x98011),f40(x98016)),f331(f331(a196,x98013),x98016)))+E(f331(f331(f331(a193,f358(x98011,x98012,x98013,x98014,x98015,x98016)),f40(x98016)),f331(f331(a196,x98013),x98016)),f331(f331(f331(a193,x98011),f40(x98016)),f331(f331(a196,x98013),x98016)))
% 51.10/50.82 [8692]P1(f331(f331(f333(x86921),x86922),x86923))+~P1(f331(f331(f333(f853(x86921,x86924)),f331(f331(f249(x86921,x86924),x86922),x86925)),f331(f331(f256(x86921,x86924),x86923),x86926)))
% 51.10/50.82 [8693]P1(f331(f331(f333(x86931),x86932),x86933))+~P1(f331(f331(f333(f853(x86931,x86934)),f331(f331(f249(x86931,x86934),x86932),x86935)),f331(f331(f256(x86931,x86934),x86933),x86936)))
% 51.10/50.82 [8694]P1(f331(f331(f333(x86941),x86942),x86943))+~P1(f331(f331(f333(f853(x86941,x86944)),f331(f331(f249(x86941,x86944),x86942),x86945)),f331(f331(f256(x86941,x86944),x86943),x86946)))
% 51.10/50.82 [8707]P1(f331(f331(f333(x87071),x87072),f331(x87073,x87074)))+~P1(f331(f331(f333(f853(x87075,x87071)),f331(f331(f249(x87075,x87071),x87074),x87072)),f331(f331(f256(x87075,x87071),x87076),x87073)))
% 51.10/50.82 [8708]P1(f331(f331(f333(x87081),x87082),f331(x87083,x87084)))+~P1(f331(f331(f333(f853(x87085,x87081)),f331(f331(f249(x87085,x87081),x87084),x87082)),f331(f331(f256(x87085,x87081),x87086),x87083)))
% 51.10/50.82 [8709]P1(f331(f331(f333(x87091),x87092),f331(x87093,x87094)))+~P1(f331(f331(f333(f853(x87095,x87091)),f331(f331(f249(x87095,x87091),x87094),x87092)),f331(f331(f256(x87095,x87091),x87096),x87093)))
% 51.10/50.82 [9011]P1(f331(f331(f333(x90111),x90114),f174(x90111,x90112,x90116)))+E(f175(x90111,x90112,f331(f331(f331(f79(x90111,f851(x90112)),x90113),x90114),f331(f234(x90112),x90115)),x90116),f331(f331(f331(f79(x90111,f851(x90112)),f175(x90111,x90112,x90113,x90116)),x90114),f331(f234(x90112),x90115)))
% 51.10/50.82 [9100]P1(f331(f331(f333(f853(x91001,x91001)),f331(f331(f249(x91001,x91001),f331(x91002,x91003)),f331(x91002,x91004))),x91005))+~P1(f331(f331(f333(f853(x91006,x91006)),f331(f331(f249(x91006,x91006),x91003),x91004)),f331(f331(f288(x91001,x91006),x91005),x91002)))
% 51.10/50.82 [9113]~P1(f331(f331(f333(f853(x91134,x91134)),f331(f331(f249(x91134,x91134),f331(x91136,x91132)),f331(x91136,x91133))),x91135))+P1(f331(f331(f333(f853(x91131,x91131)),f331(f331(f249(x91131,x91131),x91132),x91133)),f331(f331(f288(x91134,x91131),x91135),x91136)))
% 51.10/50.82 [9735]E(f331(f331(f249(x97351,x97352),f699(x97353,x97354,x97355,x97356,x97352,x97351)),f700(x97353,x97354,x97355,x97356,x97352,x97351)),x97356)+~P1(f331(f331(f333(f853(x97351,x97352)),x97356),f331(f331(f289(x97351,x97355,x97352),x97354),x97353)))
% 51.10/50.82 [9933]~P37(f33(x99336,x99335,x99334),x99333,x99332,x99331)+E(f331(f331(f331(a193,f331(f331(a194,f672(x99331,x99332,x99333,x99334,x99335,x99336)),f331(a196,x99333))),x99336),f331(f331(a196,f672(x99331,x99332,x99333,x99334,x99335,x99336)),a28)),x99331)
% 51.10/50.82 [9938]~P37(f33(x99386,x99385,x99384),x99383,x99382,f331(f331(f331(a193,f331(f331(a194,x99381),f331(a196,x99383))),x99386),f331(f331(a196,x99381),a28)))+E(f331(f331(f331(a193,f331(f331(a194,f560(x99381,x99382,x99383,x99384,x99385,x99386)),f331(a196,x99383))),x99386),f331(f331(a196,f560(x99381,x99382,x99383,x99384,x99385,x99386)),a28)),f331(f331(f331(a193,f331(f331(a194,x99381),f331(a196,x99383))),x99386),f331(f331(a196,x99381),a28)))
% 51.10/50.82 [9949]~P1(f331(f331(f333(f853(x99491,x99496)),x99495),f331(f331(f289(x99491,x99492,x99496),x99494),x99493)))+P1(f331(f331(f333(f853(x99491,x99492)),f331(f331(f249(x99491,x99492),f699(x99493,x99494,x99492,x99495,x99496,x99491)),f701(x99493,x99494,x99492,x99495,x99496,x99491))),x99494))
% 51.10/50.82 [9950]~P1(f331(f331(f333(f853(x99506,x99502)),x99505),f331(f331(f289(x99506,x99501,x99502),x99504),x99503)))+P1(f331(f331(f333(f853(x99501,x99502)),f331(f331(f249(x99501,x99502),f701(x99503,x99504,x99501,x99505,x99502,x99506)),f700(x99503,x99504,x99501,x99505,x99502,x99506))),x99503))
% 51.10/50.82 [6028]~E(x60286,x60284)+E(f331(f331(f331(f331(f79(x60281,x60282),x60283),x60284),x60285),x60286),x60285)
% 51.10/50.82 [6029]~E(x60296,x60294)+E(f331(f331(f331(f331(f79(x60291,x60292),x60293),x60294),x60295),x60296),x60295)
% 51.10/50.82 [6077]E(x60771,x60772)+E(f331(f331(f331(f331(f79(x60773,x60774),x60775),x60772),x60776),x60771),f331(x60775,x60771))
% 51.10/50.82 [6078]E(x60781,x60782)+E(f331(f331(f331(f331(f79(x60783,x60784),x60785),x60782),x60786),x60781),f331(x60785,x60781))
% 51.10/50.82 [6079]E(x60791,x60792)+E(f331(f331(f331(f331(f79(x60793,x60794),x60795),x60792),x60796),x60791),f331(x60795,x60791))
% 51.10/50.82 [7662]~P7(x76622)+E(f331(f331(f51(x76621,x76622),x76623),f331(f331(f9(x76621,x76624,x76622),x76625),x76626)),f331(f331(f331(f51(x76621,f854(x76624,x76622)),x76623),x76625),x76626))
% 51.10/50.82 [7663]~P7(x76632)+E(f331(f331(f52(x76631,x76632),x76633),f331(f331(f9(x76631,x76634,x76632),x76635),x76636)),f331(f331(f331(f52(x76631,f854(x76634,x76632)),x76633),x76635),x76636))
% 51.10/50.82 [8253]E(f331(f311(x82531,f851(x82532),f331(f331(f331(f79(x82531,f851(x82532)),x82533),x82534),f331(f234(x82532),x82535))),x82536),f331(f311(x82531,f851(x82532),x82533),x82536))+P1(f331(f331(f333(x82531),x82534),x82536))
% 51.10/50.82 [8440]E(f331(f331(f51(x84401,f854(x84402,a840)),x84403),f331(f331(f10(f854(x84402,a840),f854(x84402,a840),x84401),f331(f310(x84402),x84404)),x84405)),f331(f331(f310(x84402),x84404),f331(f331(f51(x84401,f854(x84402,a840)),x84403),x84405)))+~P1(f331(f331(f333(x84401),x84406),x84403))
% 51.10/50.82 [8441]E(f331(f331(f52(x84411,f854(x84412,a840)),x84413),f331(f331(f10(f854(x84412,a840),f854(x84412,a840),x84411),f331(f310(x84412),x84414)),x84415)),f331(f331(f310(x84412),x84414),f331(f331(f52(x84411,f854(x84412,a840)),x84413),x84415)))+~P1(f331(f331(f333(x84411),x84416),x84413))
% 51.10/50.82 [8821]~P7(x88212)+E(f331(f331(f51(x88211,x88212),x88213),f331(f331(f10(f854(x88214,x88212),x88212,x88211),f331(f51(x88214,x88212),x88215)),f331(f9(x88214,x88211,x88212),x88216))),f331(f331(f51(x88214,x88212),x88215),f331(f331(f10(f854(x88211,x88212),x88212,x88214),f331(f51(x88211,x88212),x88213)),x88216)))
% 51.10/50.82 [8822]~P7(x88222)+E(f331(f331(f52(x88221,x88222),x88223),f331(f331(f10(f854(x88224,x88222),x88222,x88221),f331(f52(x88224,x88222),x88225)),f331(f9(x88224,x88221,x88222),x88226))),f331(f331(f52(x88224,x88222),x88225),f331(f331(f10(f854(x88221,x88222),x88222,x88224),f331(f52(x88221,x88222),x88223)),x88226)))
% 51.10/50.82 [9017]P1(f331(f331(f333(x90171),x90172),f331(f163(x90171),x90173)))+~P1(f331(f331(f333(f853(x90174,x90171)),f331(f331(f249(x90174,x90171),x90175),x90172)),f331(f163(f853(x90174,x90171)),f331(f331(f172(x90174,x90171),x90176),x90173))))
% 51.10/50.82 [9018]P1(f331(f331(f333(x90181),x90182),f331(f163(x90181),x90183)))+~P1(f331(f331(f333(f853(x90181,x90184)),f331(f331(f249(x90181,x90184),x90182),x90185)),f331(f163(f853(x90181,x90184)),f331(f331(f172(x90181,x90184),x90183),x90186))))
% 51.10/50.82 [9019]P1(f331(f331(f333(x90191),x90192),f331(f163(x90191),x90193)))+~P1(f331(f331(f333(f853(x90194,x90191)),f331(f331(f249(x90194,x90191),x90195),x90192)),f331(f163(f853(x90194,x90191)),f331(f331(f172(x90194,x90191),x90196),x90193))))
% 51.10/50.82 [9020]P1(f331(f331(f333(x90201),x90202),f331(f163(x90201),x90203)))+~P1(f331(f331(f333(f853(x90201,x90204)),f331(f331(f249(x90201,x90204),x90202),x90205)),f331(f163(f853(x90201,x90204)),f331(f331(f172(x90201,x90204),x90203),x90206))))
% 51.10/50.82 [9111]P1(f331(f331(f240(f854(x91111,a840)),f331(f285(x91112,x91111,x91113),x91114)),x91115))+~P1(f331(f331(f240(f854(f853(x91112,x91111),a840)),x91113),f331(f331(f256(x91112,x91111),x91116),f331(f18(f854(x91111,a840),x91112),x91115))))
% 51.10/50.82 [9289]P1(f331(f331(f333(f853(f848(x92891),f848(x92891))),f331(f331(f249(f848(x92891),f848(x92891)),f331(f331(f145(x92891),x92892),x92893)),f331(f331(f145(x92891),x92894),x92895))),f142(x92891,x92896)))+~P1(f331(f331(f333(f853(x92891,x92891)),f331(f331(f249(x92891,x92891),x92892),x92894)),x92896))
% 51.10/50.82 [9731]E(f331(f331(f249(x97311,x97312),f606(x97313,x97314,x97315,x97312,x97311,x97316)),f609(x97313,x97314,x97315,x97312,x97311,x97316)),x97316)+P1(f331(f331(f333(x97315),x97314),f331(f331(f259(x97311,x97312,f854(x97315,a840)),x97313),x97316)))
% 51.10/50.82 [9736]E(f331(f331(f249(x97361,x97362),f607(x97363,x97364,x97362,x97361,x97365,x97366)),f608(x97363,x97364,x97362,x97361,x97365,x97366)),x97363)+~P1(f331(f331(f333(x97366),x97365),f331(f331(f259(x97361,x97362,f854(x97366,a840)),x97364),x97363)))
% 51.10/50.82 [9902]P1(f331(f331(f333(x99021),x99022),f331(f331(x99023,f607(x99024,x99023,x99025,x99026,x99022,x99021)),f608(x99024,x99023,x99025,x99026,x99022,x99021))))+~P1(f331(f331(f333(x99021),x99022),f331(f331(f259(x99026,x99025,f854(x99021,a840)),x99023),x99024)))
% 51.10/50.82 [9926]~P1(f331(f331(f333(x99261),x99262),f331(f331(x99265,f606(x99265,x99262,x99261,x99264,x99263,x99266)),f609(x99265,x99262,x99261,x99264,x99263,x99266))))+P1(f331(f331(f333(x99261),x99262),f331(f331(f259(x99263,x99264,f854(x99261,a840)),x99265),x99266)))
% 51.10/50.82 [7787]P1(f331(f331(f333(x77871),x77874),x77876))+E(f177(x77871,x77872,f331(f331(f331(f79(x77871,f851(x77872)),x77873),x77874),x77875),x77876),f177(x77871,x77872,x77873,x77876))
% 51.10/50.82 [7862]P1(f331(f331(f333(x78621),x78624),x78626))+E(f331(f311(x78621,x78622,f331(f331(f331(f79(x78621,x78622),x78623),x78624),x78625)),x78626),f331(f311(x78621,x78622,x78623),x78626))
% 51.10/50.82 [7890]P1(f331(f331(f333(x78901),x78904),f331(f163(x78901),x78906)))+E(f331(f331(f147(x78901,x78902),f331(f331(f331(f79(x78901,x78902),x78903),x78904),x78905)),x78906),f331(f331(f147(x78901,x78902),x78903),x78906))
% 51.10/50.82 [8337]E(x83371,x83372)+E(f331(f331(f152(x83373,f331(f331(f152(x83373,x83374),x83371),x83375)),x83372),x83376),f331(f331(f152(x83373,f331(f331(f152(x83373,x83374),x83372),x83376)),x83371),x83375))
% 51.10/50.82 [8827]~P1(f331(f331(f333(x88273),x88276),x88275))+E(f331(f331(f310(x88271),x88272),f331(f311(x88273,x88271,x88274),f331(f331(f3(f854(x88273,a840)),x88275),f331(f331(f310(x88273),x88276),f184(f854(x88273,a840)))))),f331(f311(x88273,x88271,f331(f331(f331(f79(x88273,x88271),x88274),x88276),x88272)),x88275))
% 51.10/50.82 [8655]~E(x86553,x86556)+E(f331(f171(x86551,x86552,f331(f331(f145(f853(x86551,x86552)),f331(f331(f249(x86551,x86552),x86553),x86554)),x86555)),x86556),f331(f234(x86552),x86554))
% 51.10/50.82 [8696]E(x86961,x86962)+E(f331(f171(x86963,x86964,f331(f331(f145(f853(x86963,x86964)),f331(f331(f249(x86963,x86964),x86961),x86965)),x86966)),x86962),f331(f171(x86963,x86964,x86966),x86962))
% 51.10/50.82 [8899]~P1(f331(f331(x88994,x88995),x88996))+P1(f331(f331(f331(f331(f108(f854(x88991,f854(x88992,a840))),x88993),x88994),x88995),x88996))
% 51.10/50.82 [8900]~P1(f331(f331(x89004,x89005),x89006))+P1(f331(f331(f331(f331(f108(f854(x89001,f854(x89002,a840))),x89003),x89004),x89005),x89006))
% 51.10/50.82 [8901]~P1(f331(f331(x89013,x89015),x89016))+P1(f331(f331(f331(f331(f108(f854(x89011,f854(x89012,a840))),x89013),x89014),x89015),x89016))
% 51.10/50.82 [8902]~P1(f331(f331(x89023,x89025),x89026))+P1(f331(f331(f331(f331(f108(f854(x89021,f854(x89022,a840))),x89023),x89024),x89025),x89026))
% 51.10/50.82 [8918]P1(f331(f331(f333(x89181),x89186),f331(f163(x89181),x89184)))+E(f331(f175(x89181,x89182,x89183,f171(x89181,x89182,f331(f160(f853(x89181,x89182)),f331(f331(f172(x89181,x89182),x89184),x89185)))),x89186),f331(x89183,x89186))
% 51.10/50.82 [9065]~E(f331(f185(f848(x90651)),x90654),f331(f185(f848(x90652)),x90655))+E(f175(x90651,x90652,x90653,f171(x90651,x90652,f331(f160(f853(x90651,x90652)),f331(f331(f172(x90651,x90652),x90654),f331(f331(f130(x90652),x90655),x90656))))),f175(x90651,x90652,x90653,f171(x90651,x90652,f331(f160(f853(x90651,x90652)),f331(f331(f172(x90651,x90652),x90654),x90655)))))
% 51.10/50.82 [9149]P1(f331(f331(x91491,x91492),x91493))+~P1(f331(f331(f331(f331(f109(f854(x91494,f854(x91495,a840))),x91496),x91491),x91492),x91493))
% 51.10/50.82 [9150]P1(f331(f331(x91501,x91502),x91503))+~P1(f331(f331(f331(f331(f109(f854(x91504,f854(x91505,a840))),x91501),x91506),x91502),x91503))
% 51.10/50.82 [9151]P1(f331(f331(x91511,x91512),x91513))+~P1(f331(f331(f331(f331(f109(f854(x91514,f854(x91515,a840))),x91516),x91511),x91512),x91513))
% 51.10/50.82 [9152]P1(f331(f331(x91521,x91522),x91523))+~P1(f331(f331(f331(f331(f109(f854(x91524,f854(x91525,a840))),x91521),x91526),x91522),x91523))
% 51.10/50.82 [9578]~P70(x95782)+E(f331(f331(f11(x95781,x95782),f331(f331(f9(x95781,f854(x95783,a840),x95782),f331(f331(f10(f854(x95783,x95782),f854(f854(x95783,a840),x95782),x95781),f11(x95783,x95782)),x95784)),x95785)),x95786),f331(f331(f11(f853(x95781,x95783),x95782),f331(f259(x95781,x95783,x95782),x95784)),f331(f331(f256(x95781,x95783),x95786),f331(f18(f854(x95783,a840),x95781),x95785))))
% 51.10/50.82 [9579]~P68(x95792)+E(f331(f331(f8(x95791,x95792),f331(f331(f9(x95791,f854(x95793,a840),x95792),f331(f331(f10(f854(x95793,x95792),f854(f854(x95793,a840),x95792),x95791),f8(x95793,x95792)),x95794)),x95795)),x95796),f331(f331(f8(f853(x95791,x95793),x95792),f331(f259(x95791,x95793,x95792),x95794)),f331(f331(f256(x95791,x95793),x95796),f331(f18(f854(x95793,a840),x95791),x95795))))
% 51.10/50.82 [9698]~P68(x96982)+E(f331(f331(f8(x96981,x96982),f331(f331(f9(x96981,f854(x96983,a840),x96982),f331(f331(f10(f854(x96983,x96982),f854(f854(x96983,a840),x96982),x96981),f8(x96983,x96982)),f331(f9(x96983,x96981,x96982),x96984))),x96985)),x96986),f331(f331(f8(x96983,x96982),f331(f331(f9(x96983,f854(x96981,a840),x96982),f331(f331(f10(f854(x96981,x96982),f854(f854(x96981,a840),x96982),x96983),f8(x96981,x96982)),x96984)),x96986)),x96985))
% 51.10/50.82 [9153]~E(f331(f185(f848(x91531)),x91534),f331(f185(f848(x91532)),x91536))+E(f175(x91531,x91532,x91533,f171(x91531,x91532,f331(f160(f853(x91531,x91532)),f331(f331(f172(x91531,x91532),f331(f331(f130(x91531),x91534),x91535)),x91536)))),f175(x91531,x91532,x91533,f171(x91531,x91532,f331(f160(f853(x91531,x91532)),f331(f331(f172(x91531,x91532),x91534),x91536)))))
% 51.10/50.82 [9421]~P1(f331(f331(f333(x94211),x94215),x94214))+E(f331(f331(f331(f79(x94211,f851(x94212)),f177(x94211,x94212,x94213,f331(f331(f3(f854(x94211,a840)),x94214),f331(f331(f310(x94211),x94215),f184(f854(x94211,a840)))))),x94215),x94216),f177(x94211,x94212,f331(f331(f331(f79(x94211,f851(x94212)),x94213),x94215),x94216),x94214))
% 51.10/50.82 [9475]~P1(f331(f331(f333(x94751),x94755),x94754))+E(f331(f331(f331(f79(x94751,f851(x94752)),f177(x94751,x94752,x94753,f331(f331(f3(f854(x94751,a840)),x94754),f331(f331(f310(x94751),x94755),f184(f854(x94751,a840)))))),x94755),x94756),f331(f331(f331(f79(x94751,f851(x94752)),f177(x94751,x94752,x94753,x94754)),x94755),x94756))
% 51.10/50.82 [9637]E(f175(x96371,x96372,x96373,f171(x96371,x96372,f331(f160(f853(x96371,x96372)),f331(f331(f172(x96371,x96372),f331(f331(f130(x96371),x96374),f331(f331(f145(x96371),x96375),f120(x96371)))),x96376)))),f331(f331(f331(f79(x96371,f851(x96372)),f175(x96371,x96372,x96373,f171(x96371,x96372,f331(f160(f853(x96371,x96372)),f331(f331(f172(x96371,x96372),x96374),x96376))))),x96375),f331(f234(x96372),f331(f331(f155(x96372),x96376),f331(f185(f848(x96371)),x96374)))))+~P1(f331(f331(f241(a847),f331(f185(f848(x96371)),x96374)),f331(f185(f848(x96372)),x96376)))
% 51.10/50.82 [10005]~P1(f331(f331(f333(f853(x100051,x100052)),f331(f331(f249(x100051,x100052),x100055),x100056)),f331(f331(f108(f854(f853(x100051,x100052),a840)),x100053),x100054)))+P1(f331(f331(f331(f331(f108(f854(x100051,f854(x100052,a840))),f331(f331(f9(x100051,f854(f853(x100051,x100052),a840),f854(x100052,a840)),f331(f331(f10(f854(x100052,f854(f854(f853(x100051,x100052),a840),a840)),f854(f854(f853(x100051,x100052),a840),f854(x100052,a840)),x100051),f9(x100052,f854(f853(x100051,x100052),a840),a840)),f331(f331(f10(f854(x100052,f853(x100051,x100052)),f854(x100052,f854(f854(f853(x100051,x100052),a840),a840)),x100051),f331(f10(f853(x100051,x100052),f854(f854(f853(x100051,x100052),a840),a840),x100052),f333(f853(x100051,x100052)))),f249(x100051,x100052)))),x100053)),f331(f331(f9(x100051,f854(f853(x100051,x100052),a840),f854(x100052,a840)),f331(f331(f10(f854(x100052,f854(f854(f853(x100051,x100052),a840),a840)),f854(f854(f853(x100051,x100052),a840),f854(x100052,a840)),x100051),f9(x100052,f854(f853(x100051,x100052),a840),a840)),f331(f331(f10(f854(x100052,f853(x100051,x100052)),f854(x100052,f854(f854(f853(x100051,x100052),a840),a840)),x100051),f331(f10(f853(x100051,x100052),f854(f854(f853(x100051,x100052),a840),a840),x100052),f333(f853(x100051,x100052)))),f249(x100051,x100052)))),x100054)),x100055),x100056))
% 51.10/50.82 [10006]~P1(f331(f331(f333(f853(x100061,x100062)),f331(f331(f249(x100061,x100062),x100065),x100066)),f331(f331(f109(f854(f853(x100061,x100062),a840)),x100063),x100064)))+P1(f331(f331(f331(f331(f109(f854(x100061,f854(x100062,a840))),f331(f331(f9(x100061,f854(f853(x100061,x100062),a840),f854(x100062,a840)),f331(f331(f10(f854(x100062,f854(f854(f853(x100061,x100062),a840),a840)),f854(f854(f853(x100061,x100062),a840),f854(x100062,a840)),x100061),f9(x100062,f854(f853(x100061,x100062),a840),a840)),f331(f331(f10(f854(x100062,f853(x100061,x100062)),f854(x100062,f854(f854(f853(x100061,x100062),a840),a840)),x100061),f331(f10(f853(x100061,x100062),f854(f854(f853(x100061,x100062),a840),a840),x100062),f333(f853(x100061,x100062)))),f249(x100061,x100062)))),x100063)),f331(f331(f9(x100061,f854(f853(x100061,x100062),a840),f854(x100062,a840)),f331(f331(f10(f854(x100062,f854(f854(f853(x100061,x100062),a840),a840)),f854(f854(f853(x100061,x100062),a840),f854(x100062,a840)),x100061),f9(x100062,f854(f853(x100061,x100062),a840),a840)),f331(f331(f10(f854(x100062,f853(x100061,x100062)),f854(x100062,f854(f854(f853(x100061,x100062),a840),a840)),x100061),f331(f10(f853(x100061,x100062),f854(f854(f853(x100061,x100062),a840),a840),x100062),f333(f853(x100061,x100062)))),f249(x100061,x100062)))),x100064)),x100065),x100066))
% 51.10/50.82 [10010]P1(f331(f331(f333(f853(x100101,x100102)),f331(f331(f249(x100101,x100102),x100103),x100104)),f331(f331(f108(f854(f853(x100101,x100102),a840)),x100105),x100106)))+~P1(f331(f331(f331(f331(f108(f854(x100101,f854(x100102,a840))),f331(f331(f9(x100101,f854(f853(x100101,x100102),a840),f854(x100102,a840)),f331(f331(f10(f854(x100102,f854(f854(f853(x100101,x100102),a840),a840)),f854(f854(f853(x100101,x100102),a840),f854(x100102,a840)),x100101),f9(x100102,f854(f853(x100101,x100102),a840),a840)),f331(f331(f10(f854(x100102,f853(x100101,x100102)),f854(x100102,f854(f854(f853(x100101,x100102),a840),a840)),x100101),f331(f10(f853(x100101,x100102),f854(f854(f853(x100101,x100102),a840),a840),x100102),f333(f853(x100101,x100102)))),f249(x100101,x100102)))),x100105)),f331(f331(f9(x100101,f854(f853(x100101,x100102),a840),f854(x100102,a840)),f331(f331(f10(f854(x100102,f854(f854(f853(x100101,x100102),a840),a840)),f854(f854(f853(x100101,x100102),a840),f854(x100102,a840)),x100101),f9(x100102,f854(f853(x100101,x100102),a840),a840)),f331(f331(f10(f854(x100102,f853(x100101,x100102)),f854(x100102,f854(f854(f853(x100101,x100102),a840),a840)),x100101),f331(f10(f853(x100101,x100102),f854(f854(f853(x100101,x100102),a840),a840),x100102),f333(f853(x100101,x100102)))),f249(x100101,x100102)))),x100106)),x100103),x100104))
% 51.10/50.82 [10011]P1(f331(f331(f333(f853(x100111,x100112)),f331(f331(f249(x100111,x100112),x100113),x100114)),f331(f331(f109(f854(f853(x100111,x100112),a840)),x100115),x100116)))+~P1(f331(f331(f331(f331(f109(f854(x100111,f854(x100112,a840))),f331(f331(f9(x100111,f854(f853(x100111,x100112),a840),f854(x100112,a840)),f331(f331(f10(f854(x100112,f854(f854(f853(x100111,x100112),a840),a840)),f854(f854(f853(x100111,x100112),a840),f854(x100112,a840)),x100111),f9(x100112,f854(f853(x100111,x100112),a840),a840)),f331(f331(f10(f854(x100112,f853(x100111,x100112)),f854(x100112,f854(f854(f853(x100111,x100112),a840),a840)),x100111),f331(f10(f853(x100111,x100112),f854(f854(f853(x100111,x100112),a840),a840),x100112),f333(f853(x100111,x100112)))),f249(x100111,x100112)))),x100115)),f331(f331(f9(x100111,f854(f853(x100111,x100112),a840),f854(x100112,a840)),f331(f331(f10(f854(x100112,f854(f854(f853(x100111,x100112),a840),a840)),f854(f854(f853(x100111,x100112),a840),f854(x100112,a840)),x100111),f9(x100112,f854(f853(x100111,x100112),a840),a840)),f331(f331(f10(f854(x100112,f853(x100111,x100112)),f854(x100112,f854(f854(f853(x100111,x100112),a840),a840)),x100111),f331(f10(f853(x100111,x100112),f854(f854(f853(x100111,x100112),a840),a840),x100112),f333(f853(x100111,x100112)))),f249(x100111,x100112)))),x100116)),x100113),x100114))
% 51.10/50.82 [9999]~P1(f331(f331(f333(f853(x99992,x99993)),f331(f331(f249(x99992,x99993),x99995),x99996)),f331(f331(f51(x99991,f854(f853(x99992,x99993),a840)),f247(f854(x99991,a840))),x99994)))+P1(f331(f331(f331(f331(f51(x99991,f854(x99992,f854(x99993,a840))),f247(f854(x99991,a840))),f331(f331(f10(f854(f853(x99992,x99993),a840),f854(x99992,f854(x99993,a840)),x99991),f331(f9(x99992,f854(f853(x99992,x99993),a840),f854(x99993,a840)),f331(f331(f10(f854(x99993,f854(f854(f853(x99992,x99993),a840),a840)),f854(f854(f853(x99992,x99993),a840),f854(x99993,a840)),x99992),f9(x99993,f854(f853(x99992,x99993),a840),a840)),f331(f331(f10(f854(x99993,f853(x99992,x99993)),f854(x99993,f854(f854(f853(x99992,x99993),a840),a840)),x99992),f331(f10(f853(x99992,x99993),f854(f854(f853(x99992,x99993),a840),a840),x99993),f333(f853(x99992,x99993)))),f249(x99992,x99993))))),x99994)),x99995),x99996))
% 51.10/50.82 [10000]~P1(f331(f331(f333(f853(x100002,x100003)),f331(f331(f249(x100002,x100003),x100005),x100006)),f331(f331(f52(x100001,f854(f853(x100002,x100003),a840)),f247(f854(x100001,a840))),x100004)))+P1(f331(f331(f331(f331(f52(x100001,f854(x100002,f854(x100003,a840))),f247(f854(x100001,a840))),f331(f331(f10(f854(f853(x100002,x100003),a840),f854(x100002,f854(x100003,a840)),x100001),f331(f9(x100002,f854(f853(x100002,x100003),a840),f854(x100003,a840)),f331(f331(f10(f854(x100003,f854(f854(f853(x100002,x100003),a840),a840)),f854(f854(f853(x100002,x100003),a840),f854(x100003,a840)),x100002),f9(x100003,f854(f853(x100002,x100003),a840),a840)),f331(f331(f10(f854(x100003,f853(x100002,x100003)),f854(x100003,f854(f854(f853(x100002,x100003),a840),a840)),x100002),f331(f10(f853(x100002,x100003),f854(f854(f853(x100002,x100003),a840),a840),x100003),f333(f853(x100002,x100003)))),f249(x100002,x100003))))),x100004)),x100005),x100006))
% 51.10/50.82 [10008]P1(f331(f331(f333(f853(x100081,x100082)),f331(f331(f249(x100081,x100082),x100083),x100084)),f331(f331(f51(x100085,f854(f853(x100081,x100082),a840)),f247(f854(x100085,a840))),x100086)))+~P1(f331(f331(f331(f331(f51(x100085,f854(x100081,f854(x100082,a840))),f247(f854(x100085,a840))),f331(f331(f10(f854(f853(x100081,x100082),a840),f854(x100081,f854(x100082,a840)),x100085),f331(f9(x100081,f854(f853(x100081,x100082),a840),f854(x100082,a840)),f331(f331(f10(f854(x100082,f854(f854(f853(x100081,x100082),a840),a840)),f854(f854(f853(x100081,x100082),a840),f854(x100082,a840)),x100081),f9(x100082,f854(f853(x100081,x100082),a840),a840)),f331(f331(f10(f854(x100082,f853(x100081,x100082)),f854(x100082,f854(f854(f853(x100081,x100082),a840),a840)),x100081),f331(f10(f853(x100081,x100082),f854(f854(f853(x100081,x100082),a840),a840),x100082),f333(f853(x100081,x100082)))),f249(x100081,x100082))))),x100086)),x100083),x100084))
% 51.10/50.82 [10009]P1(f331(f331(f333(f853(x100091,x100092)),f331(f331(f249(x100091,x100092),x100093),x100094)),f331(f331(f52(x100095,f854(f853(x100091,x100092),a840)),f247(f854(x100095,a840))),x100096)))+~P1(f331(f331(f331(f331(f52(x100095,f854(x100091,f854(x100092,a840))),f247(f854(x100095,a840))),f331(f331(f10(f854(f853(x100091,x100092),a840),f854(x100091,f854(x100092,a840)),x100095),f331(f9(x100091,f854(f853(x100091,x100092),a840),f854(x100092,a840)),f331(f331(f10(f854(x100092,f854(f854(f853(x100091,x100092),a840),a840)),f854(f854(f853(x100091,x100092),a840),f854(x100092,a840)),x100091),f9(x100092,f854(f853(x100091,x100092),a840),a840)),f331(f331(f10(f854(x100092,f853(x100091,x100092)),f854(x100092,f854(f854(f853(x100091,x100092),a840),a840)),x100091),f331(f10(f853(x100091,x100092),f854(f854(f853(x100091,x100092),a840),a840),x100092),f333(f853(x100091,x100092)))),f249(x100091,x100092))))),x100096)),x100093),x100094))
% 51.10/50.82 [7334]E(f331(x73341,f331(x73342,x73343)),f331(x73344,x73343))+~E(f331(f80(x73345,x73346,x73347,x73341),x73342),x73344)
% 51.10/50.82 [9456]~P24(x94563,x94564,x94561,x94565,x94566,x94567)+E(f331(f331(x94561,x94562),x94562),x94562)
% 51.10/50.82 [9791]~P49(x97915,x97916,x97917,x97911,x97914,x97912,x97913)+P1(f331(f331(x97911,x97912),f572(x97913,x97912,x97914,x97911)))
% 51.10/50.82 [9820]~E(f331(f236(f851(x98207),x98201,f187(x98207),x98205),f331(x98204,x98203)),f331(f234(x98207),x98202))+E(f331(f234(x98201),f711(x98202,x98203,x98204,x98205,x98206,x98207,x98201)),f331(x98204,x98203))
% 51.10/50.82 [9821]~E(f331(f236(f851(x98216),x98217,f187(x98216),x98211),f331(x98214,x98213)),f331(f234(x98216),x98212))+E(f331(x98211,f711(x98212,x98213,x98214,x98211,x98215,x98216,x98217)),f331(f234(x98216),x98212))
% 51.10/50.82 [5846]~E(f331(f331(f147(x58461,x58465),x58466),x58462),f331(f331(f147(x58463,x58465),x58467),x58464))+E(f331(f185(f848(x58461)),x58462),f331(f185(f848(x58463)),x58464))
% 51.10/50.82 [7410]E(x74101,x74102)+~E(f331(f331(f331(f79(x74103,f851(x74104)),x74105),x74106),f331(f234(x74104),x74101)),f331(f331(f331(f79(x74103,f851(x74104)),x74107),x74106),f331(f234(x74104),x74102)))
% 51.10/50.82 [8372]E(f331(x83721,f331(x83722,x83723)),f331(x83724,x83723))+~E(f331(f80(x83725,x83726,x83727,x83721),x83722),f331(f80(x83726,x83726,x83727,f39(x83726)),x83724))
% 51.10/50.82 [9797]~P49(x97975,x97976,x97977,x97974,x97971,x97973,x97972)+P1(f331(f331(x97971,f572(x97972,x97973,x97971,x97974)),x97972))
% 51.10/50.82 [5893]E(x58931,x58932)+~E(f331(f331(f331(f98(x58933),x58934),x58935),x58931),f331(f331(f331(f98(x58933),x58936),x58937),x58932))
% 51.10/50.82 [5894]E(x58941,x58942)+~E(f331(f331(f331(f98(x58943),x58944),x58941),x58945),f331(f331(f331(f98(x58943),x58946),x58942),x58947))
% 51.10/50.82 [5895]E(x58951,x58952)+~E(f331(f331(f331(f98(x58953),x58951),x58954),x58955),f331(f331(f331(f98(x58953),x58952),x58956),x58957))
% 51.10/50.82 [8784]~P22(x87846,x87841,x87843,x87847)+E(f331(f80(x87841,x87841,x87842,f331(x87843,x87844)),f331(f80(x87841,x87841,x87842,f331(x87843,x87844)),x87845)),f331(f80(x87841,x87841,x87842,f331(x87843,x87844)),x87845))
% 51.10/50.82 [8783]~P1(f331(f331(f333(x87831),x87832),f331(f331(x87835,x87836),x87837)))+P1(f331(f331(f333(x87831),x87832),f331(f331(f259(x87833,x87834,f854(x87831,a840)),x87835),f331(f331(f249(x87833,x87834),x87836),x87837))))
% 51.10/50.82 [9046]P1(f331(f331(f331(x90461,x90462),x90463),x90464))+~P1(f331(f331(f331(f259(x90465,x90466,f854(x90467,a840)),x90461),f331(f331(f249(x90465,x90466),x90462),x90463)),x90464))
% 51.10/50.82 [9165]P1(f331(f331(f333(x91651),f331(f331(x91652,x91653),x91654)),f331(f311(f853(x91655,x91656),x91651,f331(f259(x91655,x91656,x91651),x91652)),x91657)))+~P1(f331(f331(f333(f853(x91655,x91656)),f331(f331(f249(x91655,x91656),x91653),x91654)),x91657))
% 51.10/50.82 [9496]P1(f331(f331(f333(f853(f848(x94961),f848(x94961))),f331(f331(f249(f848(x94961),f848(x94961)),f331(f331(f130(x94961),x94962),f331(f331(f145(x94961),x94963),x94964))),f331(f331(f130(x94961),x94962),f331(f331(f145(x94961),x94965),x94966)))),f142(x94961,x94967)))+~P1(f331(f331(f333(f853(x94961,x94961)),f331(f331(f249(x94961,x94961),x94963),x94965)),x94967))
% 51.10/50.82 [9925]P49(x99251,x99252,x99253,f331(f331(f9(x99251,f854(f853(x99251,x99252),a840),f854(x99252,a840)),f331(f331(f10(f854(x99252,f854(f854(f853(x99251,x99252),a840),a840)),f854(f854(f853(x99251,x99252),a840),f854(x99252,a840)),x99251),f9(x99252,f854(f853(x99251,x99252),a840),a840)),f331(f331(f10(f854(x99252,f853(x99251,x99252)),f854(x99252,f854(f854(f853(x99251,x99252),a840),a840)),x99251),f331(f10(f853(x99251,x99252),f854(f854(f853(x99251,x99252),a840),a840),x99252),f333(f853(x99251,x99252)))),f249(x99251,x99252)))),x99254),f331(f331(f9(x99252,f854(f853(x99252,x99253),a840),f854(x99253,a840)),f331(f331(f10(f854(x99253,f854(f854(f853(x99252,x99253),a840),a840)),f854(f854(f853(x99252,x99253),a840),f854(x99253,a840)),x99252),f9(x99253,f854(f853(x99252,x99253),a840),a840)),f331(f331(f10(f854(x99253,f853(x99252,x99253)),f854(x99253,f854(f854(f853(x99252,x99253),a840),a840)),x99252),f331(f10(f853(x99252,x99253),f854(f854(f853(x99252,x99253),a840),a840),x99253),f333(f853(x99252,x99253)))),f249(x99252,x99253)))),x99255),x99256,x99257)+~P1(f331(f331(f333(f853(x99251,x99253)),f331(f331(f249(x99251,x99253),x99256),x99257)),f331(f331(f289(x99251,x99252,x99253),x99254),x99255)))
% 51.10/50.82 [9956]~P49(x99561,x99565,x99562,f331(f331(f9(x99561,f854(f853(x99561,x99565),a840),f854(x99565,a840)),f331(f331(f10(f854(x99565,f854(f854(f853(x99561,x99565),a840),a840)),f854(f854(f853(x99561,x99565),a840),f854(x99565,a840)),x99561),f9(x99565,f854(f853(x99561,x99565),a840),a840)),f331(f331(f10(f854(x99565,f853(x99561,x99565)),f854(x99565,f854(f854(f853(x99561,x99565),a840),a840)),x99561),f331(f10(f853(x99561,x99565),f854(f854(f853(x99561,x99565),a840),a840),x99565),f333(f853(x99561,x99565)))),f249(x99561,x99565)))),x99566),f331(f331(f9(x99565,f854(f853(x99565,x99562),a840),f854(x99562,a840)),f331(f331(f10(f854(x99562,f854(f854(f853(x99565,x99562),a840),a840)),f854(f854(f853(x99565,x99562),a840),f854(x99562,a840)),x99565),f9(x99562,f854(f853(x99565,x99562),a840),a840)),f331(f331(f10(f854(x99562,f853(x99565,x99562)),f854(x99562,f854(f854(f853(x99565,x99562),a840),a840)),x99565),f331(f10(f853(x99565,x99562),f854(f854(f853(x99565,x99562),a840),a840),x99562),f333(f853(x99565,x99562)))),f249(x99565,x99562)))),x99567),x99563,x99564)+P1(f331(f331(f333(f853(x99561,x99562)),f331(f331(f249(x99561,x99562),x99563),x99564)),f331(f331(f289(x99561,x99565,x99562),x99566),x99567)))
% 51.10/50.82 [9564]P1(f331(f331(f333(x95641),x95644),f331(f163(x95641),x95646)))+E(f175(x95641,x95642,f331(f331(f331(f79(x95641,f851(x95642)),x95643),x95644),f331(f234(x95642),x95645)),f171(x95641,x95642,f331(f160(f853(x95641,x95642)),f331(f331(f172(x95641,x95642),x95646),x95647)))),f331(f331(f331(f79(x95641,f851(x95642)),f175(x95641,x95642,x95643,f171(x95641,x95642,f331(f160(f853(x95641,x95642)),f331(f331(f172(x95641,x95642),x95646),x95647))))),x95644),f331(f234(x95642),x95645)))
% 51.10/50.82 [9041]E(x90411,x90412)+E(f331(f331(f331(f79(x90413,x90414),f331(f331(f331(f79(x90413,x90414),x90415),x90411),x90416)),x90412),x90417),f331(f331(f331(f79(x90413,x90414),f331(f331(f331(f79(x90413,x90414),x90415),x90412),x90417)),x90411),x90416))
% 51.10/50.82 [9293]E(f175(x92931,x92932,f331(f331(f331(f79(x92931,f851(x92932)),x92933),x92934),f331(f234(x92932),x92935)),f171(x92931,x92932,f331(f160(f853(x92931,x92932)),f331(f331(f172(x92931,x92932),x92936),x92937)))),f175(x92931,x92932,x92933,f171(x92931,x92932,f331(f160(f853(x92931,x92932)),f331(f331(f172(x92931,x92932),x92936),x92937)))))+~P1(f331(f331(f333(x92931),x92934),f331(f163(x92931),f331(f331(f164(x92931),f331(f185(f848(x92932)),x92937)),x92936))))
% 51.10/50.82 [9585]E(f175(x95851,x95852,f331(f331(f331(f79(x95851,f851(x95852)),x95853),x95854),f331(f234(x95852),x95855)),f171(x95851,x95852,f331(f160(f853(x95851,x95852)),f331(f331(f172(x95851,x95852),x95856),x95857)))),f331(f331(f331(f79(x95851,f851(x95852)),f175(x95851,x95852,x95853,f171(x95851,x95852,f331(f160(f853(x95851,x95852)),f331(f331(f172(x95851,x95852),x95856),x95857))))),x95854),f331(f234(x95852),x95855)))+P1(f331(f331(f333(x95851),x95854),f331(f163(x95851),f331(f331(f164(x95851),f331(f185(f848(x95852)),x95857)),x95856))))
% 51.10/50.82 [9937]P1(f331(f331(f333(x99371),f644(x99372,x99373,x99374,x99375,x99376,x99377,x99371)),x99375))+P1(f331(f331(f331(f331(f52(x99371,f854(x99377,f854(x99376,a840))),x99375),x99374),x99373),x99372))
% 51.10/50.82 [9939]P1(f331(f331(f333(x99391),f422(x99392,x99393,x99394,x99395,x99396,x99397,x99391)),x99395))+~P1(f331(f331(f331(f331(f51(x99391,f854(x99397,f854(x99396,a840))),x99395),x99394),x99393),x99392))
% 51.10/50.82 [9966]P1(f331(f331(f331(x99661,f422(x99662,x99663,x99661,x99664,x99665,x99666,x99667)),x99663),x99662))+~P1(f331(f331(f331(f331(f51(x99667,f854(x99666,f854(x99665,a840))),x99664),x99661),x99663),x99662))
% 51.10/50.82 [9983]~P1(f331(f331(f331(x99835,f644(x99837,x99836,x99835,x99834,x99833,x99832,x99831)),x99836),x99837))+P1(f331(f331(f331(f331(f52(x99831,f854(x99832,f854(x99833,a840))),x99834),x99835),x99836),x99837))
% 51.10/50.82 [9948]~P136(x99482)+E(f331(f331(f8(x99481,x99482),f331(f331(f9(x99481,f854(x99483,a840),x99482),f331(f331(f10(f854(x99483,x99482),f854(f854(x99483,a840),x99482),x99481),f8(x99483,x99482)),f331(f331(f9(x99481,f854(x99483,x99482),f854(x99483,x99482)),f331(f331(f10(f854(x99482,x99482),f854(f854(x99483,x99482),f854(x99483,x99482)),x99481),f10(x99482,x99482,x99483)),f331(f331(f10(x99482,f854(x99482,x99482),x99481),f88(x99482)),x99484))),x99485))),x99486)),x99487),f331(f331(f88(x99482),f331(f331(f8(x99481,x99482),x99484),x99487)),f331(f331(f8(x99483,x99482),x99485),x99486)))
% 51.10/50.82 [9078]~P21(x90787,x90781,x90783,x90788)+E(f331(f80(x90781,x90781,x90782,f331(x90783,x90784)),f331(f80(x90781,x90781,x90782,f331(x90783,x90785)),x90786)),f331(f80(x90781,x90781,x90782,f331(x90783,x90785)),f331(f80(x90781,x90781,x90782,f331(x90783,x90784)),x90786)))
% 51.10/50.82 [9994]P26(x99941,x99942,f331(f331(f310(f846(x99941)),f331(f331(f331(f98(x99941),f331(f331(f10(f854(a845,a840),f854(a845,a840),x99941),f331(f20(a845,a840,a840),f331(f331(f10(a840,f854(a840,a840),a845),a329),f331(a328,x99943)))),f331(f331(f9(x99941,f854(a845,a845),f854(a845,a840)),f331(f331(f10(f854(a845,a840),f854(f854(a845,a845),f854(a845,a840)),x99941),f10(a845,a840,a845)),x99944)),f331(f331(f20(a845,a847,a845),f331(f331(f9(a845,a842,f854(a847,a845)),a193),f40(x99945))),x99946)))),f34(x99945,x99946,x99947)),x99948)),f184(f854(f846(x99941),a840))))+~P26(x99941,x99942,f331(f331(f310(f846(x99941)),f331(f331(f331(f98(x99941),x99944),x99947),f331(f331(f9(x99941,f854(a845,a845),f854(a845,a840)),f331(f331(f10(f854(a845,a840),f854(f854(a845,a845),f854(a845,a840)),x99941),f10(a845,a840,a845)),x99948)),f331(f331(f9(a845,a847,a845),f331(f331(f9(a845,a842,f854(a847,a845)),a193),f40(x99945))),f331(f331(a196,x99943),x99945))))),f184(f854(f846(x99941),a840))))
% 51.10/50.82 [10003]E(f331(f331(f249(x100031,x100032),f331(x100033,f555(x100034,x100035,x100033,x100036,x100037,x100038,x100032,x100031))),f331(x100035,f556(x100034,x100035,x100033,x100036,x100037,x100038,x100032,x100031))),x100038)+~P1(f331(f331(f333(f853(x100031,x100032)),x100038),f331(f311(f853(x100037,x100036),f853(x100031,x100032),f260(x100037,x100031,x100036,x100032,x100033,x100035)),x100034)))
% 51.10/50.82 [10015]P26(x100151,x100152,f331(f331(f310(f846(x100151)),f331(f331(f331(f98(x100151),f331(f331(f10(f854(a845,a840),f854(a845,a840),x100151),f331(f20(a845,a840,a840),f331(f331(f10(a840,f854(a840,a840),a845),a329),f331(a328,x100153)))),f331(f331(f9(x100151,f854(a845,a845),f854(a845,a840)),f331(f331(f10(f854(a845,a840),f854(f854(a845,a845),f854(a845,a840)),x100151),f10(a845,a840,a845)),x100154)),f331(f331(f20(a845,a847,a845),f331(f331(f9(a845,a842,f854(a847,a845)),f331(f331(f10(a845,f854(a842,f854(a847,a845)),a845),a193),f331(f331(f9(a845,f854(a844,a847),a845),a194),a195))),f40(a27))),x100155)))),f33(x100156,x100157,x100155)),x100158)),f184(f854(f846(x100151),a840))))+~P26(x100151,x100152,f331(f331(f310(f846(x100151)),f331(f331(f331(f98(x100151),x100154),f331(a29,x100157)),f331(f331(f9(x100151,f854(a845,a845),f854(a845,a840)),f331(f331(f10(f854(a845,a840),f854(f854(a845,a845),f854(a845,a840)),x100151),f10(a845,a840,a845)),x100158)),f331(f331(f20(a845,a847,a845),f331(f331(f9(a845,a842,f854(a847,a845)),f331(f331(f10(a845,f854(a842,f854(a847,a845)),a845),a193),f331(f331(f9(a845,f854(a844,a847),a845),a194),f331(a196,x100153)))),x100156)),f331(f331(f9(a845,a844,a847),a196),a28))))),f184(f854(f846(x100151),a840))))
% 51.10/50.82 [10016]~P1(f331(f331(f333(f853(x100168,x100167)),x100166),f331(f311(f853(x100161,x100162),f853(x100168,x100167),f260(x100161,x100168,x100162,x100167,x100165,x100164)),x100163)))+P1(f331(f331(f333(f853(x100161,x100162)),f331(f331(f249(x100161,x100162),f555(x100163,x100164,x100165,x100162,x100161,x100166,x100167,x100168)),f556(x100163,x100164,x100165,x100162,x100161,x100166,x100167,x100168))),x100163))
% 51.10/50.82 [9486]P1(f331(f331(f333(f853(f853(x94861,x94862),f853(x94861,x94862))),f331(f331(f249(f853(x94861,x94862),f853(x94861,x94862)),f331(f331(f249(x94861,x94862),x94863),x94864)),f331(f331(f249(x94861,x94862),x94865),x94866))),f324(x94861,x94862,x94867,x94868)))+~P1(f331(f331(f333(f853(x94861,x94861)),f331(f331(f249(x94861,x94861),x94863),x94865)),x94867))
% 51.10/50.82 [8377]E(f331(x83771,f331(x83772,x83773)),f331(x83774,f331(x83775,x83773)))+~E(f331(f80(x83776,x83777,x83778,x83771),x83772),f331(f80(x83779,x83777,x83778,x83774),x83775))
% 51.10/50.82 [8378]E(f331(x83781,f331(x83782,x83783)),f331(x83784,f331(x83785,x83783)))+~E(f331(f80(x83786,x83787,x83788,x83781),x83782),f331(f80(x83789,x83787,x83788,x83784),x83785))
% 51.10/50.82 [9871]P1(f331(f331(f333(f853(x98711,x98712)),f331(f331(f249(x98711,x98712),f331(x98713,x98714)),f331(x98715,x98716))),f331(f311(f853(x98717,x98718),f853(x98711,x98712),f260(x98717,x98711,x98718,x98712,x98713,x98715)),x98719)))+~P1(f331(f331(f333(f853(x98717,x98718)),f331(f331(f249(x98717,x98718),x98714),x98716)),x98719))
% 51.10/50.82 [8636]~E(f331(x86364,f331(x86365,x86366)),f331(x86369,f331(x863610,x863611)))+E(f331(f331(f80(x86361,x86362,x86363,x86364),x86365),x86366),f331(f331(f80(x86367,x86362,x86368,x86369),x863610),x863611))
% 51.10/50.82 [9138]~P21(x91388,x91389,x913810,x913811)+E(f331(f80(x91381,x91382,x91383,x91384),f331(f80(x91385,x91381,x91383,x91386),x91387)),f331(f80(x91385,x91382,x91383,f331(f80(x91381,x91382,x91385,x91384),x91386)),x91387))
% 51.10/50.82 [4461]~P102(x44611)+~P100(x44611)+E(f239(x44611),f108(x44611))
% 51.10/50.82 [4462]~P102(x44621)+~P101(x44621)+E(f244(x44621),f109(x44621))
% 51.10/50.82 [4699]~P86(x46991)+~P91(x46991)+E(f331(f82(x46991),f331(f111(x46991),a104)),f85(x46991))
% 51.10/50.82 [4972]E(x49721,f2(a1))+E(f89(a1,x49721),f331(f86(a1),f85(a1)))+P1(f331(f331(f241(a1),f2(a1)),x49721))
% 51.10/50.82 [5175]E(x51751,f2(a1))+E(f89(a1,x51751),f85(a1))+~P1(f331(f331(f241(a1),f2(a1)),x51751))
% 51.10/50.82 [6498]~P36(x64981)+~P1(f331(f68(a1),x64981))+P1(f331(f68(a847),f331(f311(a1,a847,a112),x64981)))
% 51.10/50.82 [6876]E(f59(f85(a1),f331(f111(a1),x68761)),f331(f331(f249(a1,a1),f2(a1)),f85(a1)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x68761)))+~P1(f331(f331(f241(a1),f85(a1)),f331(f111(a1),x68761)))
% 51.10/50.82 [7221]~P36(x72211)+P1(f331(f68(a1),x72211))+~P1(f331(f68(a847),f331(f311(a1,a847,a112),x72211)))
% 51.10/50.82 [8076]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f87(a1),f85(a1)),f331(f111(a1),x80761))),f62(f85(a1),f331(f111(a1),x80761)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x80761)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f85(a1)),f331(f111(a1),x80761))))
% 51.10/50.82 [8482]~P11(a500)+~P1(f331(f331(f333(f853(a843,a841)),x84821),f331(f163(f853(a843,a841)),a31)))+P1(f331(f331(f259(a843,a841,a840),f331(f18(f854(a841,a840),a843),a26)),x84821))
% 51.10/50.82 [9754]E(f331(f55(f331(f111(a1),x97541)),f59(f85(a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f111(a1),x97541)))),f59(f85(a1),f331(f111(a1),x97541)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x97541)))+P1(f331(f331(f241(a1),f85(a1)),f331(f111(a1),x97541)))
% 51.10/50.82 [9760]E(f331(f55(f331(f111(a1),x97601)),f62(f85(a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f111(a1),x97601)))),f62(f85(a1),f331(f111(a1),x97601)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x97601)))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f85(a1)),f331(f111(a1),x97601))))
% 51.10/50.82 [9455]E(x94551,f184(f854(f853(a847,a847),a840)))+~P1(f331(f68(f853(a847,a847)),x94551))+P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),f184(f854(f853(a847,a847),a840))),x94551)),a46))
% 51.10/50.82 [9610]E(x96101,f2(a847))+E(x96101,f331(a119,f2(a847)))+~P1(f331(f331(f241(a847),x96101),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9897]E(x98971,f2(a106))+E(f331(f331(f87(a1),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(a23,f331(f331(f48(a106),x98971),f331(f111(a106),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))),f85(a1)),f331(a23,x98971))+E(f57(a106,x98971,f331(f111(a106),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f2(a106))
% 51.10/50.82 [9740]E(x97401,f2(a106))+~E(f57(a106,x97401,f331(f111(a106),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f2(a106))+E(f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(a23,f331(f331(f48(a106),x97401),f331(f111(a106),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f331(a23,x97401))
% 51.10/50.82 [4535]~P54(x45351,x45352)+P40(x45351,x45352)+~P41(a840)
% 51.10/50.82 [4473]~P84(x44731)+P31(x44731,x44732)+~E(x44732,f2(x44731))
% 51.10/50.82 [4482]~P86(x44821)+~E(x44822,f2(x44821))+E(f89(x44821,x44822),f2(x44821))
% 51.10/50.82 [4483]~P81(x44831)+~E(x44832,f2(x44831))+E(f89(x44831,x44832),f2(x44831))
% 51.10/50.82 [4491]~P84(x44912)+~P31(x44912,x44911)+E(x44911,f2(x44912))
% 51.10/50.82 [4525]~P86(x45252)+~E(f89(x45252,x45251),f2(x45252))+E(x45251,f2(x45252))
% 51.10/50.82 [4542]~P8(x45422)+~P8(x45421)+P8(f192(x45421,x45422))
% 51.10/50.82 [4543]~P57(x45432)+~P57(x45431)+P57(f854(x45431,x45432))
% 51.10/50.82 [4544]~P57(x45442)+~P57(x45441)+P57(f853(x45441,x45442))
% 51.10/50.82 [4545]~P57(x45452)+~P57(x45451)+P57(f855(x45451,x45452))
% 51.10/50.82 [4546]~P139(x45462)+~P139(x45461)+P139(f853(x45461,x45462))
% 51.10/50.82 [4671]~P102(x46711)+~P16(x46711,x46712)+P16(x46711,f146(x46711,x46712))
% 51.10/50.82 [4904]~P8(x49042)+~P8(x49041)+P8(f57(a1,x49041,x49042))
% 51.10/50.82 [4492]~P67(x44921)+~E(x44922,f2(x44921))+E(f331(f86(x44921),x44922),x44922)
% 51.10/50.82 [4493]~P67(x44931)+~E(x44932,f2(x44931))+E(f331(f86(x44931),x44932),x44932)
% 51.10/50.82 [4496]~P90(x44961)+~E(x44962,f2(a1))+E(f331(f110(x44961),x44962),f2(x44961))
% 51.10/50.82 [4497]~P90(x44971)+~E(x44972,f2(a1))+E(f331(f110(x44971),x44972),f2(x44971))
% 51.10/50.82 [4498]~P133(x44981)+~E(x44982,f2(a1))+E(f331(f110(x44981),x44982),f2(x44981))
% 51.10/50.82 [4522]~P69(x45221)+~E(f2(x45221),x45222)+E(f331(f86(x45221),x45222),f2(x45221))
% 51.10/50.82 [4523]~P69(x45231)+~E(x45232,f2(x45231))+E(f331(f86(x45231),x45232),f2(x45231))
% 51.10/50.82 [4524]~P78(x45241)+~E(x45242,f2(x45241))+E(f331(f82(x45241),x45242),f2(x45241))
% 51.10/50.82 [4547]~P67(x45472)+E(x45471,f2(x45472))+~E(f331(f86(x45472),x45471),x45471)
% 51.10/50.82 [4548]~P67(x45482)+E(x45481,f2(x45482))+~E(f331(f86(x45482),x45481),x45481)
% 51.10/50.82 [4556]E(x45561,f331(a112,x45562))+~E(x45561,f2(a847))+~E(x45562,f331(f107(a1),x45561))
% 51.10/50.82 [4557]E(f331(a112,x45571),x45572)+~E(x45572,f2(a847))+~E(x45571,f331(f107(a1),x45572))
% 51.10/50.82 [4560]~P90(x45602)+E(x45601,f2(a1))+~E(f331(f110(x45602),x45601),f2(x45602))
% 51.10/50.82 [4561]~P90(x45612)+E(x45611,f2(a1))+~E(f331(f110(x45612),x45611),f2(x45612))
% 51.10/50.82 [4566]~P69(x45662)+E(x45661,f2(x45662))+~E(f331(f86(x45662),x45661),f2(x45662))
% 51.10/50.82 [4567]~P78(x45672)+E(x45671,f2(x45672))+~E(f331(f82(x45672),x45671),f2(x45672))
% 51.10/50.82 [4568]~P69(x45681)+E(f2(x45681),x45682)+~E(f331(f86(x45681),x45682),f2(x45681))
% 51.10/50.82 [4703]~P11(a500)+~E(f331(a32,x47032),f331(f234(a841),x47031))+P1(f331(a26,x47031))
% 51.10/50.82 [4744]~P102(x47441)+~P16(x47441,x47442)+P16(x47441,f331(f162(x47441),x47442))
% 51.10/50.82 [4770]~P1(x47702)+~P1(x47701)+P1(f331(f331(a329,x47701),x47702))
% 51.10/50.82 [4804]~E(f85(a847),f2(a847))+E(f331(f47(x48041),x48042),f2(a847))+~P1(f331(f68(x48041),x48042))
% 51.10/50.82 [4835]~P107(x48351)+~P136(x48351)+E(f331(f331(f250(x48351),f2(x48351)),f331(a119,x48352)),f2(x48351))
% 51.10/50.82 [4875]~P102(x48751)+P16(x48751,f135(x48751,x48752))+~P1(f331(f68(x48751),x48752))
% 51.10/50.82 [4895]~P102(x48951)+E(f331(f163(x48951),f135(x48951,x48952)),x48952)+~P1(f331(f68(x48951),x48952))
% 51.10/50.82 [4925]P1(x49251)+P1(x49252)+~P1(f331(f331(a330,x49252),x49251))
% 51.10/50.82 [4937]E(x49371,f184(f854(x49372,a840)))+~E(f331(f47(x49372),x49371),f2(a847))+~P1(f331(f68(x49372),x49371))
% 51.10/50.82 [4942]P1(x49421)+~P1(x49422)+~P1(f331(f331(a334,x49422),x49421))
% 51.10/50.82 [4990]~P65(x49901)+E(f331(f82(x49901),x49902),x49902)+P1(f331(f331(f241(x49901),x49902),f2(x49901)))
% 51.10/50.82 [5087]~P1(f331(a26,x50872))+~P1(f331(a26,x50871))+P1(f331(a26,f38(x50871,x50872)))
% 51.10/50.82 [5088]~P1(f331(a26,x50882))+~P1(f331(a26,x50881))+P1(f331(a26,f38(x50881,x50882)))
% 51.10/50.82 [5095]E(x50951,f120(x50952))+P1(f331(f132(x50952),f121(x50952,x50951)))+~P1(f331(f132(x50952),x50951))
% 51.10/50.82 [5100]~P102(x51001)+~P1(f331(f68(x51001),x51002))+P1(f331(f132(x51001),f135(x51001,x51002)))
% 51.10/50.82 [5106]~P133(x51061)+E(f331(f107(x51061),f331(a112,x51062)),f331(f110(x51061),x51062))+P1(f331(f331(f241(a1),x51062),f2(a1)))
% 51.10/50.82 [5132]P9(x51322,x51321)+E(f331(x51321,f480(x51321)),f331(x51321,f522(x51321)))+P1(f331(f331(x51321,f480(x51321)),f522(x51321)))
% 51.10/50.82 [5145]E(f331(f107(a1),f614(x51451,x51452)),x51451)+P1(f331(x51452,f331(a112,x51451)))+~P1(f331(x51452,f2(a847)))
% 51.10/50.82 [5185]~P86(x51851)+~E(f89(x51851,x51852),f331(f86(x51851),f85(x51851)))+P1(f331(f331(f241(x51851),x51852),f2(x51851)))
% 51.10/50.82 [5258]~E(x52582,f2(a1))+E(f217(x52581,x52582),f331(f331(f249(a1,a1),f2(a1)),f85(a1)))+P1(f331(f331(f241(a1),x52582),f2(a1)))
% 51.10/50.82 [5259]~E(x52591,f2(a1))+E(f217(x52591,x52592),f331(f331(f249(a1,a1),f2(a1)),f85(a1)))+P1(f331(f331(f241(a1),x52592),f2(a1)))
% 51.10/50.82 [5310]E(f331(f107(a1),f614(x53101,x53102)),x53101)+P1(f331(x53102,f331(a112,x53101)))+P1(f331(f331(f241(a1),x53101),f2(a1)))
% 51.10/50.82 [5375]~P86(x53751)+E(f89(x53751,x53752),f331(f86(x53751),f85(x53751)))+~P1(f331(f331(f241(x53751),x53752),f2(x53751)))
% 51.10/50.82 [5376]~P86(x53761)+E(f89(x53761,x53762),f331(f86(x53761),f85(x53761)))+~P1(f331(f331(f241(x53761),x53762),f2(x53761)))
% 51.10/50.82 [5377]~P78(x53771)+E(f331(f82(x53771),x53772),f331(f86(x53771),x53772))+~P1(f331(f331(f241(x53771),x53772),f2(x53771)))
% 51.10/50.82 [5378]~P78(x53781)+E(f331(f82(x53781),x53782),f331(f86(x53781),x53782))+~P1(f331(f331(f240(x53781),x53782),f2(x53781)))
% 51.10/50.82 [5379]~P65(x53791)+E(f331(f82(x53791),x53792),f331(f86(x53791),x53792))+~P1(f331(f331(f241(x53791),x53792),f2(x53791)))
% 51.10/50.82 [5473]~P1(f331(x54731,f614(x54732,x54731)))+P1(f331(x54731,f331(a112,x54732)))+~P1(f331(x54731,f2(a847)))
% 51.10/50.82 [5480]E(x54801,f2(a847))+E(f331(a119,f437(x54802,x54801)),x54801)+~P1(f331(f331(f241(a847),x54801),f331(a119,x54802)))
% 51.10/50.82 [5483]P9(x54831,x54832)+~E(f331(x54832,f480(x54832)),f331(x54832,f522(x54832)))+~P1(f331(f331(x54832,f480(x54832)),f522(x54832)))
% 51.10/50.82 [5503]~P102(x55031)+P16(x55031,x55032)+P1(f331(f331(f240(a847),f761(x55032,x55031)),f762(x55032,x55031)))
% 51.10/50.82 [5590]~P78(x55901)+~E(x55902,f2(x55901))+P1(f331(f331(f240(x55901),f331(f82(x55901),x55902)),f2(x55901)))
% 51.10/50.82 [5679]~P1(f331(x56791,f614(x56792,x56791)))+P1(f331(x56791,f331(a112,x56792)))+P1(f331(f331(f241(a1),x56792),f2(a1)))
% 51.10/50.82 [5705]~P1(f331(x57051,f331(a112,x57052)))+P1(f331(x57051,f2(a847)))+~P1(f331(f331(f241(a1),x57052),f2(a1)))
% 51.10/50.82 [6051]~P86(x60511)+~P1(f331(f331(f241(x60511),x60512),f2(x60511)))+P1(f331(f331(f241(x60511),f89(x60511,x60512)),f2(x60511)))
% 51.10/50.82 [6169]~P86(x61691)+P1(f331(f331(f241(x61691),f331(f110(x61691),x61692)),f2(x61691)))+~P1(f331(f331(f241(a1),x61692),f2(a1)))
% 51.10/50.82 [6170]~P86(x61701)+P1(f331(f331(f240(x61701),f331(f110(x61701),x61702)),f2(x61701)))+~P1(f331(f331(f240(a1),x61702),f2(a1)))
% 51.10/50.82 [6175]~P78(x61752)+E(x61751,f2(x61752))+~P1(f331(f331(f240(x61752),f331(f82(x61752),x61751)),f2(x61752)))
% 51.10/50.82 [6259]~P133(x62591)+~P1(f331(f331(f333(x62591),x62592),f117(x62591)))+P1(f331(f331(f333(x62591),f331(f86(x62591),x62592)),f117(x62591)))
% 51.10/50.82 [6291]~P86(x62911)+~P1(f331(f331(f241(x62911),f89(x62911,x62912)),f2(x62911)))+P1(f331(f331(f241(x62911),x62912),f2(x62911)))
% 51.10/50.82 [6372]~P88(x63721)+P48(a847,x63721,f287(a847),x63722)+P1(f331(f331(f287(a847),f338(x63722,x63721)),f341(x63722,x63721)))
% 51.10/50.82 [6469]~P86(x64692)+~P1(f331(f331(f241(x64692),f331(f110(x64692),x64691)),f2(x64692)))+P1(f331(f331(f241(a1),x64691),f2(a1)))
% 51.10/50.82 [6470]~P86(x64702)+~P1(f331(f331(f240(x64702),f331(f110(x64702),x64701)),f2(x64702)))+P1(f331(f331(f240(a1),x64701),f2(a1)))
% 51.10/50.82 [6992]~P67(x69921)+~P1(f331(f331(f241(x69921),x69922),f2(x69921)))+P1(f331(f331(f241(x69921),f331(f331(f87(x69921),x69922),x69922)),f2(x69921)))
% 51.10/50.82 [6993]~P86(x69931)+~P1(f331(f331(f241(x69931),x69932),f2(x69931)))+P1(f331(f331(f241(x69931),f331(f331(f87(x69931),x69932),x69932)),f2(x69931)))
% 51.10/50.82 [6994]~P67(x69941)+~P1(f331(f331(f240(x69941),x69942),f2(x69941)))+P1(f331(f331(f240(x69941),f331(f331(f87(x69941),x69942),x69942)),f2(x69941)))
% 51.10/50.82 [7589]~P67(x75891)+~P1(f331(f331(f241(x75891),f331(f331(f87(x75891),x75892),x75892)),f2(x75891)))+P1(f331(f331(f241(x75891),x75892),f2(x75891)))
% 51.10/50.82 [7590]~P86(x75901)+~P1(f331(f331(f241(x75901),f331(f331(f87(x75901),x75902),x75902)),f2(x75901)))+P1(f331(f331(f241(x75901),x75902),f2(x75901)))
% 51.10/50.82 [7591]~P67(x75911)+~P1(f331(f331(f240(x75911),f331(f331(f87(x75911),x75912),x75912)),f2(x75911)))+P1(f331(f331(f240(x75911),x75912),f2(x75911)))
% 51.10/50.82 [4603]~E(x46032,f85(a847))+~E(x46031,f85(a847))+E(f331(f331(f88(a847),x46031),x46032),f85(a847))
% 51.10/50.82 [4604]~E(x46042,f2(a847))+~E(x46041,f2(a847))+E(f331(f331(f87(a847),x46041),x46042),f2(a847))
% 51.10/50.82 [4605]~E(x46052,f85(a847))+~E(x46051,f85(a847))+E(f331(f331(f88(a847),x46051),x46052),f85(a847))
% 51.10/50.82 [4606]~E(x46062,f85(a1))+~E(x46061,f85(a1))+E(f331(f331(f88(a1),x46061),x46062),f85(a1))
% 51.10/50.82 [4657]~P5(x46572)+E(x46571,f2(x46572))+E(f331(f331(f48(x46572),x46571),x46571),f85(x46572))
% 51.10/50.82 [4658]~P114(x46582)+E(x46581,f2(x46582))+E(f331(f331(f291(x46582),x46581),x46581),f85(x46582))
% 51.10/50.82 [4659]~P115(x46592)+E(x46591,f2(x46592))+E(f331(f331(f291(x46592),x46591),x46591),f85(x46592))
% 51.10/50.82 [4674]~P67(x46741)+~E(x46742,f2(x46741))+E(f331(f331(f87(x46741),x46742),x46742),f2(x46741))
% 51.10/50.82 [4675]~P67(x46751)+~E(x46752,f2(x46751))+E(f331(f331(f87(x46751),x46752),x46752),f2(x46751))
% 51.10/50.82 [4678]~P120(x46781)+~E(x46782,f85(x46781))+E(f331(f331(f88(x46781),x46782),x46782),f85(x46781))
% 51.10/50.82 [4679]~P115(x46791)+~E(x46792,f2(x46791))+E(f331(f331(f291(x46791),x46792),x46792),f2(x46791))
% 51.10/50.82 [4723]~E(x47232,f2(a847))+~E(x47231,f2(a847))+E(f331(f86(a1),f331(f107(a1),x47231)),f331(f107(a1),x47232))
% 51.10/50.82 [4741]E(x47411,f85(a847))+E(x47412,f2(a847))+~E(f331(f331(f88(a847),x47412),x47411),x47412)
% 51.10/50.82 [4751]E(x47511,f2(a847))+E(x47512,f2(a847))+~E(f331(f331(f88(a847),x47512),x47511),f2(a847))
% 51.10/50.82 [4777]~E(x47772,f2(a847))+~E(x47771,f331(a119,f2(a847)))+E(f331(f331(f87(a847),x47771),x47772),f331(a119,f2(a847)))
% 51.10/50.82 [4778]~E(x47781,f2(a847))+~E(x47782,f331(a119,f2(a847)))+E(f331(f331(f87(a847),x47781),x47782),f331(a119,f2(a847)))
% 51.10/50.82 [4779]~E(x47792,f2(a847))+~E(x47791,f331(a119,f2(a847)))+E(f331(f331(f87(a847),x47791),x47792),f331(a119,f2(a847)))
% 51.10/50.82 [4780]~E(x47801,f2(a847))+~E(x47802,f331(a119,f2(a847)))+E(f331(f331(f87(a847),x47801),x47802),f331(a119,f2(a847)))
% 51.10/50.82 [4785]E(x47851,f85(a1))+E(x47852,f331(f111(a1),a104))+~E(f331(f331(f88(a1),x47851),x47852),f85(a1))
% 51.10/50.82 [4786]E(x47861,f85(a1))+E(x47862,f331(f111(a1),a104))+~E(f331(f331(f88(a1),x47862),x47861),f85(a1))
% 51.10/50.82 [4787]E(x47871,f85(a1))+E(x47871,f331(f111(a1),a104))+~E(f331(f331(f88(a1),x47872),x47871),f85(a1))
% 51.10/50.82 [4788]E(x47881,f85(a1))+E(x47881,f331(f111(a1),a104))+~E(f331(f331(f88(a1),x47881),x47882),f85(a1))
% 51.10/50.82 [4789]E(x47891,f85(a1))+E(x47891,f331(f111(a1),a104))+~E(f331(f331(f88(a1),x47891),x47892),f85(a1))
% 51.10/50.82 [4807]~P67(x48072)+E(x48071,f2(x48072))+~E(f331(f331(f87(x48072),x48071),x48071),f2(x48072))
% 51.10/50.82 [4808]~P67(x48082)+E(x48081,f2(x48082))+~E(f331(f331(f87(x48082),x48081),x48081),f2(x48082))
% 51.10/50.82 [4814]~E(x48141,f331(f111(a1),a104))+~E(x48142,f331(f111(a1),a104))+E(f331(f331(f88(a1),x48141),x48142),f85(a1))
% 51.10/50.82 [4825]E(x48251,f2(a847))+E(x48252,f2(a847))+~E(f331(f331(f87(a847),x48252),x48251),f331(a119,f2(a847)))
% 51.10/50.82 [4826]E(x48261,f2(a847))+E(x48262,f2(a847))+~E(f331(f331(f87(a847),x48262),x48261),f331(a119,f2(a847)))
% 51.10/50.82 [4834]~P91(x48341)+~P58(x48341)+E(f331(f331(f291(x48341),x48342),f331(f111(x48341),a90)),f2(x48341))
% 51.10/50.82 [4841]~P120(x48411)+~E(x48412,f331(f86(x48411),f85(x48411)))+E(f331(f331(f88(x48411),x48412),x48412),f85(x48411))
% 51.10/50.82 [4846]~P8(x48462)+~P8(x48461)+P8(f331(f331(f87(a1),x48461),x48462))
% 51.10/50.82 [4847]~P8(x48472)+~P8(x48471)+P8(f331(f331(f88(a1),x48471),x48472))
% 51.10/50.82 [4848]~P8(x48482)+~P8(x48481)+P8(f331(f331(f48(a1),x48481),x48482))
% 51.10/50.82 [4849]~E(x48492,f2(a1))+E(x48491,f2(a1))+E(f58(x48491,x48492),f331(f331(f249(a1,a1),f2(a1)),x48491))
% 51.10/50.82 [4850]~E(x48502,f2(a1))+E(x48501,f2(a1))+E(f58(x48501,x48502),f331(f331(f249(a1,a1),f2(a1)),x48501))
% 51.10/50.82 [4873]~E(x48732,f331(a119,f2(a847)))+~E(x48731,f331(a119,f2(a847)))+E(f331(f331(f88(a847),x48731),x48732),f331(a119,f2(a847)))
% 51.10/50.82 [4884]E(x48841,f2(a847))+E(x48841,f331(a119,f2(a847)))+~E(f331(f331(f87(a847),x48842),x48841),f331(a119,f2(a847)))
% 51.10/50.82 [4885]E(x48851,f2(a847))+E(x48851,f331(a119,f2(a847)))+~E(f331(f331(f87(a847),x48851),x48852),f331(a119,f2(a847)))
% 51.10/50.82 [4886]E(x48861,f2(a847))+E(x48862,f331(a119,f2(a847)))+~E(f331(f331(f250(a847),x48862),x48861),f331(a119,f2(a847)))
% 51.10/50.82 [4887]E(x48871,f2(a847))+E(x48871,f331(a119,f2(a847)))+~E(f331(f331(f87(a847),x48872),x48871),f331(a119,f2(a847)))
% 51.10/50.82 [4888]E(x48881,f2(a847))+E(x48881,f331(a119,f2(a847)))+~E(f331(f331(f87(a847),x48881),x48882),f331(a119,f2(a847)))
% 51.10/50.82 [4896]~P91(x48961)+~P58(x48961)+E(f331(f331(f291(x48961),x48962),f331(f111(x48961),a104)),f331(f86(x48961),x48962))
% 51.10/50.82 [4917]E(x49171,f331(a112,x49172))+~E(x49171,f2(a847))+P1(f331(f331(f240(a1),f2(a1)),x49172))
% 51.10/50.82 [4918]E(f331(a112,x49181),x49182)+~E(x49182,f2(a847))+P1(f331(f331(f240(a1),f2(a1)),x49181))
% 51.10/50.82 [4932]E(x49321,f331(a119,f2(a847)))+E(x49322,f331(a119,f2(a847)))+~E(f331(f331(f87(a847),x49321),x49322),f331(a119,f2(a847)))
% 51.10/50.82 [4933]E(x49331,f331(a119,f2(a847)))+E(x49332,f331(a119,f2(a847)))+~E(f331(f331(f87(a847),x49331),x49332),f331(a119,f2(a847)))
% 51.10/50.82 [4944]~E(x49441,f331(a112,x49442))+E(x49441,f2(a847))+P1(f331(f331(f240(a1),f2(a1)),x49442))
% 51.10/50.82 [4945]~E(f331(a112,x49452),x49451)+E(x49451,f2(a847))+P1(f331(f331(f240(a1),f2(a1)),x49452))
% 51.10/50.82 [4968]~P97(x49681)+E(f331(f70(x49681,f109(x49681)),x49682),f12(x49681,x49682))+~P1(f331(f68(x49681),x49682))
% 51.10/50.82 [4969]~P97(x49691)+E(f331(f70(x49691,f108(x49691)),x49692),f15(x49691,x49692))+~P1(f331(f68(x49691),x49692))
% 51.10/50.82 [4970]~P102(x49701)+E(f331(f70(x49701,f239(x49701)),x49702),f16(x49701,x49702))+~P1(f331(f68(x49701),x49702))
% 51.10/50.82 [4971]~P102(x49711)+E(f331(f70(x49711,f244(x49711)),x49712),f17(x49711,x49712))+~P1(f331(f68(x49711),x49712))
% 51.10/50.82 [5055]E(x50551,x50552)+~E(f331(f331(f3(a847),x50552),x50551),f2(a847))+~E(f331(f331(f3(a847),x50551),x50552),f2(a847))
% 51.10/50.82 [5066]P8(x50661)+~P36(x50662)+~P1(f331(f331(f333(a1),x50661),x50662))
% 51.10/50.82 [5096]~P86(x50961)+~E(f89(x50961,x50962),f85(x50961))+P1(f331(f331(f241(x50961),f2(x50961)),x50962))
% 51.10/50.82 [5107]~P91(x51071)+E(f331(f107(x51071),f331(f111(a847),x51072)),f331(f111(x51071),x51072))+P1(f331(a190,f331(f111(a1),x51072)))
% 51.10/50.82 [5112]~P40(x51121,x51122)+P41(a840)+P1(f331(f68(f853(x51121,x51121)),x51122))
% 51.10/50.82 [5177]~P102(x51771)+E(f331(f70(x51771,f239(x51771)),x51772),f13(x51771,f239(x51771),x51772))+~P1(f331(f68(x51771),x51772))
% 51.10/50.82 [5178]~P102(x51781)+E(f331(f70(x51781,f244(x51781)),x51782),f14(x51781,f244(x51781),x51782))+~P1(f331(f68(x51781),x51782))
% 51.10/50.82 [5191]E(x51911,x51912)+P1(f331(f331(f241(a847),x51912),x51911))+P1(f331(f331(f241(a847),x51911),x51912))
% 51.10/50.82 [5192]E(x51921,x51922)+P1(f331(f331(f241(a847),x51922),x51921))+P1(f331(f331(f241(a847),x51921),x51922))
% 51.10/50.82 [5193]E(x51931,x51932)+P1(f331(f331(f241(a1),x51932),x51931))+P1(f331(f331(f241(a1),x51931),x51932))
% 51.10/50.82 [5245]~P91(x52451)+E(f331(f107(x52451),f331(f111(a847),x52452)),f2(x52451))+~P1(f331(a190,f331(f111(a1),x52452)))
% 51.10/50.82 [5248]~E(x52482,f331(a112,x52481))+E(x52481,f331(f107(a1),x52482))+~P1(f331(f331(f240(a1),f2(a1)),x52481))
% 51.10/50.82 [5249]~E(f331(a112,x52491),x52492)+E(x52491,f331(f107(a1),x52492))+~P1(f331(f331(f240(a1),f2(a1)),x52491))
% 51.10/50.82 [5250]~E(x52501,f331(a112,x52502))+E(f331(f107(a1),x52501),x52502)+~P1(f331(f331(f240(a1),f2(a1)),x52502))
% 51.10/50.82 [5260]E(x52601,f331(a112,x52602))+~E(x52602,f331(f107(a1),x52601))+~P1(f331(f331(f240(a1),f2(a1)),x52602))
% 51.10/50.82 [5261]E(f331(a112,x52611),x52612)+~E(x52611,f331(f107(a1),x52612))+~P1(f331(f331(f240(a1),f2(a1)),x52611))
% 51.10/50.82 [5290]~P87(x52902)+E(x52901,f2(x52902))+~P1(f331(f331(f287(x52902),f2(x52902)),x52901))
% 51.10/50.82 [5299]~P78(x52992)+E(x52991,f2(x52992))+P1(f331(f331(f241(x52992),f2(x52992)),f331(f82(x52992),x52991)))
% 51.10/50.82 [5366]~P86(x53661)+E(f89(x53661,x53662),f85(x53661))+~P1(f331(f331(f241(x53661),f2(x53661)),x53662))
% 51.10/50.82 [5367]~P86(x53671)+E(f89(x53671,x53672),f85(x53671))+~P1(f331(f331(f241(x53671),f2(x53671)),x53672))
% 51.10/50.82 [5373]~P91(x53731)+E(f331(f107(x53731),f331(f111(a847),x53732)),f2(x53731))+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x53732)))
% 51.10/50.82 [5380]~P78(x53801)+E(f331(f82(x53801),x53802),x53802)+~P1(f331(f331(f241(x53801),f2(x53801)),x53802))
% 51.10/50.82 [5381]~P78(x53811)+E(f331(f82(x53811),x53812),x53812)+~P1(f331(f331(f240(x53811),f2(x53811)),x53812))
% 51.10/50.82 [5388]E(x53881,f2(a847))+~E(f135(a847,f331(f302(a847,x53882),x53881)),f120(a847))+P1(f331(f331(f240(a847),x53881),x53882))
% 51.10/50.82 [5398]~P68(x53981)+E(f331(f331(f8(x53981,x53981),f7(x53981)),f331(f163(x53981),x53982)),f331(f157(x53981),x53982))+~P1(f331(f132(x53981),x53982))
% 51.10/50.82 [5401]~P133(x54011)+E(f331(f107(x54011),f331(a112,x54012)),f331(f110(x54011),x54012))+~P1(f331(f331(f240(a1),f2(a1)),x54012))
% 51.10/50.82 [5403]~E(x54031,x54032)+P1(f331(f331(f241(a847),x54031),f331(a119,x54032)))+P1(f331(f331(f241(a847),x54031),x54032))
% 51.10/50.82 [5424]E(x54241,x54242)+P1(f331(f331(f241(a847),x54241),x54242))+~P1(f331(f331(f240(a847),x54241),x54242))
% 51.10/50.82 [5425]E(x54251,x54252)+P1(f331(f331(f241(a847),x54251),x54252))+~P1(f331(f331(f240(a847),x54251),x54252))
% 51.10/50.82 [5426]E(x54261,x54262)+P1(f331(f331(f241(a847),x54261),x54262))+~P1(f331(f331(f240(a847),x54261),x54262))
% 51.10/50.82 [5427]E(x54271,x54272)+P1(f331(f331(f241(a1),x54271),x54272))+~P1(f331(f331(f240(a1),x54271),x54272))
% 51.10/50.82 [5430]E(x54301,f85(a1))+~E(f331(f331(f88(a1),x54302),x54301),f85(a1))+~P1(f331(f331(f241(a1),f2(a1)),x54302))
% 51.10/50.82 [5431]E(x54311,f85(a1))+~E(f331(f331(f88(a1),x54311),x54312),f85(a1))+~P1(f331(f331(f241(a1),f2(a1)),x54311))
% 51.10/50.82 [5469]~P36(x54692)+P1(f331(f331(f240(a1),f2(a1)),x54691))+~P1(f331(f331(f333(a1),x54691),x54692))
% 51.10/50.82 [5470]~P36(x54702)+P1(f331(f331(f240(a1),f2(a1)),x54701))+~P1(f331(f331(f333(a1),x54701),x54702))
% 51.10/50.82 [5487]~P54(x54871,x54872)+P34(x54871,x54872)+~P1(f331(f68(f853(x54871,x54871)),x54872))
% 51.10/50.82 [5488]~P54(x54881,x54882)+P34(x54881,x54882)+~P1(f331(f68(f853(x54881,x54881)),x54882))
% 51.10/50.82 [5489]~P34(x54891,x54892)+P54(x54891,x54892)+~P1(f331(f68(f853(x54891,x54891)),x54892))
% 51.10/50.82 [5490]~P54(x54901,x54902)+P40(x54901,x54902)+~P1(f331(f68(f853(x54901,x54901)),x54902))
% 51.10/50.82 [5532]E(x55321,f184(f854(x55322,a840)))+~P1(f331(f68(x55322),x55321))+P1(f331(f331(f241(a847),f2(a847)),f331(f47(x55322),x55321)))
% 51.10/50.82 [5558]~P1(f331(x55581,x55582))+P1(f331(x55581,f2(a847)))+P1(f331(f331(f241(a847),f786(x55582,x55581)),x55582))
% 51.10/50.82 [5583]E(x55831,f2(a847))+~E(f331(f157(a847),x55832),f2(a847))+~P1(f331(f331(f333(a847),x55831),f331(f163(a847),x55832)))
% 51.10/50.82 [5616]~E(x56161,x56162)+P1(f331(f331(f241(a847),x56161),f331(a119,x56162)))+~P1(f331(f331(f240(a847),x56162),x56161))
% 51.10/50.82 [5645]~E(x56452,f2(a847))+P1(f331(f331(f240(a1),f2(a1)),x56451))+P1(f331(f331(f287(a847),f331(a112,x56451)),x56452))
% 51.10/50.82 [5648]E(x56481,x56482)+~P1(f331(f331(f240(a847),x56482),x56481))+~P1(f331(f331(f240(a847),x56481),x56482))
% 51.10/50.82 [5649]E(x56491,x56492)+~P1(f331(f331(f240(a1),x56492),x56491))+~P1(f331(f331(f240(a1),x56491),x56492))
% 51.10/50.82 [5650]E(x56501,x56502)+~P1(f331(f331(f287(a847),x56502),x56501))+~P1(f331(f331(f287(a847),x56501),x56502))
% 51.10/50.82 [5651]E(x56511,x56512)+~P1(f331(f331(f287(a847),x56512),x56511))+~P1(f331(f331(f287(a847),x56511),x56512))
% 51.10/50.82 [5652]E(x56521,x56522)+~P1(f331(f331(f287(a847),x56522),x56521))+~P1(f331(f331(f287(a847),x56521),x56522))
% 51.10/50.82 [5653]E(x56531,x56532)+~P1(f331(f331(f287(a847),x56532),x56531))+~P1(f331(f331(f287(a847),x56531),x56532))
% 51.10/50.82 [5654]E(x56541,x56542)+~P1(f331(f331(f287(a847),x56542),x56541))+~P1(f331(f331(f287(a847),x56541),x56542))
% 51.10/50.82 [5655]E(x56551,x56552)+~P1(f331(f331(f287(a847),x56552),x56551))+~P1(f331(f331(f287(a847),x56551),x56552))
% 51.10/50.82 [5656]E(x56561,x56562)+~P1(f331(f331(f287(a847),x56562),x56561))+~P1(f331(f331(f287(a847),x56561),x56562))
% 51.10/50.82 [5657]E(x56571,x56572)+~P1(f331(f331(f287(a847),x56572),x56571))+~P1(f331(f331(f287(a847),x56571),x56572))
% 51.10/50.82 [5658]E(x56581,x56582)+~P1(f331(f331(f287(a847),x56582),x56581))+~P1(f331(f331(f287(a847),x56581),x56582))
% 51.10/50.82 [5659]E(f331(f47(x56591),x56592),f2(a847))+~P1(f331(f68(x56591),x56592))+P1(f331(f331(f333(x56591),f617(x56592,x56591)),x56592))
% 51.10/50.82 [5665]E(f62(x56651,x56652),f58(x56651,x56652))+P1(f331(f331(f240(a1),f2(a1)),x56651))+~P1(f331(f331(f241(a1),f2(a1)),x56652))
% 51.10/50.82 [5694]~P1(f331(x56941,f767(x56941)))+P1(f331(x56941,f331(a112,x56942)))+~P1(f331(f331(f240(a1),f2(a1)),x56942))
% 51.10/50.82 [5696]P1(f331(f331(f241(a847),x56961),f369(x56962)))+~P1(f331(f68(a847),x56962))+~P1(f331(f331(f333(a847),x56961),x56962))
% 51.10/50.82 [5697]P1(f331(f331(f240(a847),x56971),f365(x56972)))+~P1(f331(f68(a847),x56972))+~P1(f331(f331(f333(a847),x56971),x56972))
% 51.10/50.82 [5723]E(x57231,x57232)+~P1(f331(f331(f241(a847),x57231),f331(a119,x57232)))+P1(f331(f331(f241(a847),x57231),x57232))
% 51.10/50.82 [5724]E(x57241,x57242)+~P1(f331(f331(f241(a847),x57241),f331(a119,x57242)))+P1(f331(f331(f241(a847),x57241),x57242))
% 51.10/50.82 [5725]E(x57251,x57252)+~P1(f331(f331(f241(a847),x57251),f331(a119,x57252)))+P1(f331(f331(f241(a847),x57251),x57252))
% 51.10/50.82 [5726]E(x57261,x57262)+~P1(f331(f331(f241(a847),x57261),f331(a119,x57262)))+P1(f331(f331(f241(a847),x57261),x57262))
% 51.10/50.82 [5764]E(x57641,f331(a119,x57642))+~P1(f331(f331(f240(a847),x57641),f331(a119,x57642)))+P1(f331(f331(f240(a847),x57641),x57642))
% 51.10/50.82 [5765]E(x57651,f331(a119,x57652))+~P1(f331(f331(f240(a847),x57651),f331(a119,x57652)))+P1(f331(f331(f240(a847),x57651),x57652))
% 51.10/50.82 [5775]P1(f331(x57751,f746(x57751)))+~P1(f331(x57751,f331(a112,x57752)))+~P1(f331(f331(f240(a1),f2(a1)),x57752))
% 51.10/50.82 [5777]E(f331(f82(a1),x57771),f331(f82(a1),x57772))+~P1(f331(f331(f287(a1),x57772),x57771))+~P1(f331(f331(f287(a1),x57771),x57772))
% 51.10/50.82 [5789]~P1(f331(x57891,x57892))+~P1(f331(f331(f240(a1),f2(a1)),x57892))+P1(f331(x57891,f331(f107(a1),f694(x57891))))
% 51.10/50.82 [5801]~P78(x58012)+~E(x58011,f2(x58012))+~P1(f331(f331(f241(x58012),f2(x58012)),f331(f82(x58012),x58011)))
% 51.10/50.82 [5826]~P54(x58261,x58262)+P34(x58261,f331(f286(x58261,x58261),x58262))+~P1(f331(f68(f853(x58261,x58261)),x58262))
% 51.10/50.82 [5834]~P91(x58341)+E(f331(f107(x58341),f331(f111(a847),x58342)),f331(f111(x58341),x58342))+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x58342)))
% 51.10/50.82 [5838]E(f331(a119,x58381),x58382)+~P1(f331(f331(f241(a847),x58381),x58382))+P1(f331(f331(f241(a847),f331(a119,x58381)),x58382))
% 51.10/50.82 [5850]E(f331(f331(f48(a1),x58501),x58502),f2(a1))+~P1(f331(f331(f240(a1),x58501),f2(a1)))+~P1(f331(f331(f241(a1),x58502),x58501))
% 51.10/50.82 [5851]E(f331(f331(f48(a1),x58511),x58512),f2(a1))+~P1(f331(f331(f240(a1),x58511),f2(a1)))+~P1(f331(f331(f241(a1),x58512),x58511))
% 51.10/50.82 [5864]E(f57(a1,x58641,x58642),x58641)+~P1(f331(f331(f240(a1),x58641),f2(a1)))+~P1(f331(f331(f241(a1),x58642),x58641))
% 51.10/50.82 [5877]E(f59(x58771,x58772),f58(x58771,x58772))+~P1(f331(f331(f240(a1),f2(a1)),x58771))+~P1(f331(f331(f240(a1),f2(a1)),x58772))
% 51.10/50.82 [5883]E(f331(f331(f48(a847),x58831),x58832),f2(a847))+~P1(f331(f331(f241(a847),f2(a847)),x58832))+~P1(f331(f331(f241(a847),x58831),x58832))
% 51.10/50.82 [5884]E(f331(f331(f48(a1),x58841),x58842),f2(a1))+~P1(f331(f331(f240(a1),f2(a1)),x58841))+~P1(f331(f331(f241(a1),x58841),x58842))
% 51.10/50.82 [5885]E(f331(f331(f48(a1),x58851),x58852),f2(a1))+~P1(f331(f331(f240(a1),f2(a1)),x58851))+~P1(f331(f331(f241(a1),x58851),x58852))
% 51.10/50.82 [5899]E(f57(a847,f331(f111(a847),x58991),f331(f111(a847),x58992)),f331(f111(a847),x58991))+P1(f331(a190,f331(f111(a1),x58991)))+~P1(f331(a190,f331(f111(a1),x58992)))
% 51.10/50.82 [5901]E(f57(a1,x59011,x59012),x59011)+~P1(f331(f331(f240(a1),f2(a1)),x59011))+~P1(f331(f331(f241(a1),x59011),x59012))
% 51.10/50.82 [5903]E(x59031,x59032)+~P1(f331(f331(f241(a847),x59031),f331(a119,x59032)))+~P1(f331(f331(f240(a847),x59032),x59031))
% 51.10/50.82 [5915]E(f331(f111(a1),x59151),f331(f107(a1),x59152))+~E(x59152,f331(a112,f331(f111(a1),x59151)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x59151)))
% 51.10/50.82 [5919]~P86(x59191)+~P1(f331(f331(f241(x59191),x59192),f2(x59191)))+P1(f331(f331(f241(x59191),x59192),f331(f86(x59191),x59192)))
% 51.10/50.82 [5920]~P67(x59201)+~P1(f331(f331(f240(x59201),x59202),f2(x59201)))+P1(f331(f331(f240(x59201),x59202),f331(f86(x59201),x59202)))
% 51.10/50.82 [5930]~P7(x59301)+E(f331(f331(f71(x59301,x59301,f109(x59301)),f247(x59301)),x59302),f50(x59301,x59302))+~P1(f331(f68(x59301),x59302))
% 51.10/50.82 [5931]~P7(x59311)+E(f331(f331(f71(x59311,x59311,f108(x59311)),f184(x59311)),x59312),f49(x59311,x59312))+~P1(f331(f68(x59311),x59312))
% 51.10/50.82 [5945]~P85(x59451)+~P1(f331(f331(f241(a847),f2(a847)),x59452))+P1(f331(f331(f241(x59451),f2(x59451)),f331(f107(x59451),x59452)))
% 51.10/50.82 [5946]~P86(x59461)+~P1(f331(f331(f241(a1),f2(a1)),x59462))+P1(f331(f331(f241(x59461),f2(x59461)),f331(f110(x59461),x59462)))
% 51.10/50.82 [5947]~P86(x59471)+~P1(f331(f331(f240(a1),f2(a1)),x59472))+P1(f331(f331(f240(x59471),f2(x59471)),f331(f110(x59471),x59472)))
% 51.10/50.82 [5950]~P8(x59502)+~P8(x59501)+E(f331(f311(a847,a1,f107(a1)),f303(a847,f331(a112,x59501),f331(a112,x59502))),f303(a1,x59501,x59502))
% 51.10/50.82 [5956]P1(f331(x59561,x59562))+~P1(f331(f331(f240(a1),f2(a1)),x59562))+~P1(f331(x59561,f331(f107(a1),f728(x59561))))
% 51.10/50.82 [5983]E(f331(f331(f87(a847),f331(f111(a847),x59831)),f331(f111(a847),x59832)),f331(f111(a847),x59831))+P1(f331(f331(f241(a1),x59831),a90))+~P1(f331(f331(f241(a1),x59832),a90))
% 51.10/50.82 [5987]~P86(x59871)+P1(f331(f331(f241(x59871),f2(x59871)),f89(x59871,x59872)))+~P1(f331(f331(f241(x59871),f2(x59871)),x59872))
% 51.10/50.82 [6001]~P76(x60011)+~P1(f331(f331(f241(x60011),x60012),f2(x60011)))+P1(f331(f331(f241(x60011),f2(x60011)),f331(f86(x60011),x60012)))
% 51.10/50.82 [6002]~P76(x60021)+~P1(f331(f331(f240(x60021),x60022),f2(x60021)))+P1(f331(f331(f240(x60021),f2(x60021)),f331(f86(x60021),x60022)))
% 51.10/50.82 [6005]E(x60051,f2(a847))+P1(f331(f331(f240(a1),f2(a1)),x60052))+~P1(f331(f331(f287(a847),f331(a112,x60052)),x60051))
% 51.10/50.82 [6006]E(x60061,f247(f854(x60062,a840)))+~E(f331(f47(x60062),x60061),f331(f47(x60062),f247(f854(x60062,a840))))+~P1(f331(f68(x60062),f247(f854(x60062,a840))))
% 51.10/50.82 [6037]~P1(f331(f331(f241(a847),f2(a847)),x60372))+~P1(f331(f331(f287(a847),x60371),x60372))+P1(f331(f331(f240(a847),x60371),x60372))
% 51.10/50.82 [6038]~P1(f331(f331(f241(a1),f2(a1)),x60382))+~P1(f331(f331(f287(a1),x60381),x60382))+P1(f331(f331(f240(a1),x60381),x60382))
% 51.10/50.82 [6044]~P86(x60441)+P1(f331(f331(f241(x60441),x60442),f2(x60441)))+~P1(f331(f331(f241(x60441),x60442),f331(f86(x60441),x60442)))
% 51.10/50.82 [6045]~P67(x60451)+P1(f331(f331(f240(x60451),x60452),f2(x60451)))+~P1(f331(f331(f240(x60451),x60452),f331(f86(x60451),x60452)))
% 51.10/50.82 [6050]E(f59(x60501,x60502),f331(f331(f249(a1,a1),f2(a1)),x60501))+~P1(f331(f331(f241(a1),f2(a1)),x60502))+~P1(f331(f331(f241(a1),x60501),x60502))
% 51.10/50.82 [6053]~P91(x60531)+P1(f331(f331(f333(x60531),f331(f111(x60531),x60532)),f181(x60531)))+~P1(f331(f331(f240(a1),a90),x60532))
% 51.10/50.82 [6084]E(x60841,f2(a847))+~P1(f331(f331(f241(a847),x60841),f331(a119,x60842)))+P1(f331(f331(f241(a847),f437(x60842,x60841)),x60842))
% 51.10/50.82 [6108]~P86(x61081)+~P1(f331(f331(f241(x61081),f2(x61081)),f89(x61081,x61082)))+P1(f331(f331(f241(x61081),f2(x61081)),x61082))
% 51.10/50.82 [6110]~E(f331(f111(a847),x61102),f331(f111(a847),x61101))+P1(f331(f331(f240(a1),f331(f111(a1),x61101)),f2(a1)))+~P1(f331(a190,f331(f111(a1),x61102)))
% 51.10/50.82 [6138]E(f331(f248(a1,a1),f62(x61381,x61382)),f331(f331(f48(a1),x61381),x61382))+~P1(f331(f331(f241(a1),x61381),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x61382))
% 51.10/50.82 [6172]E(f331(f258(a1,a1),f62(x61721,x61722)),f57(a1,x61721,x61722))+~P1(f331(f331(f241(a1),x61721),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x61722))
% 51.10/50.82 [6174]E(x61741,f2(a1))+~P1(f331(f331(f287(a1),x61742),x61741))+P1(f331(f331(f240(a1),f331(f82(a1),x61742)),f331(f82(a1),x61741)))
% 51.10/50.82 [6176]~P85(x61762)+~P1(f331(f331(f241(x61762),f2(x61762)),f331(f107(x61762),x61761)))+P1(f331(f331(f241(a847),f2(a847)),x61761))
% 51.10/50.82 [6177]~P86(x61772)+~P1(f331(f331(f241(x61772),f2(x61772)),f331(f110(x61772),x61771)))+P1(f331(f331(f241(a1),f2(a1)),x61771))
% 51.10/50.82 [6178]~P86(x61782)+~P1(f331(f331(f240(x61782),f2(x61782)),f331(f110(x61782),x61781)))+P1(f331(f331(f240(a1),f2(a1)),x61781))
% 51.10/50.82 [6182]~E(x61822,f2(a847))+P1(f331(f331(f287(a847),f331(a112,x61821)),x61822))+~P1(f331(f331(f287(a1),x61821),f331(f107(a1),x61822)))
% 51.10/50.82 [6183]E(f331(f248(a1,a1),f59(x61831,x61832)),f331(f331(f48(a1),x61831),x61832))+~P1(f331(f331(f241(a1),f2(a1)),x61831))+~P1(f331(f331(f240(a1),f2(a1)),x61832))
% 51.10/50.82 [6197]E(f331(f258(a1,a1),f59(x61971,x61972)),f57(a1,x61971,x61972))+~P1(f331(f331(f241(a1),f2(a1)),x61971))+~P1(f331(f331(f240(a1),f2(a1)),x61972))
% 51.10/50.82 [6215]~P76(x62151)+P1(f331(f331(f241(x62151),x62152),f2(x62151)))+~P1(f331(f331(f241(x62151),f2(x62151)),f331(f86(x62151),x62152)))
% 51.10/50.82 [6216]~P76(x62161)+P1(f331(f331(f240(x62161),x62162),f2(x62161)))+~P1(f331(f331(f240(x62161),f2(x62161)),f331(f86(x62161),x62162)))
% 51.10/50.82 [6242]P1(f331(f61(x62421,x62422),f62(x62421,x62422)))+~P1(f331(f331(f241(a1),x62421),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x62422))
% 51.10/50.82 [6257]~P1(f331(f331(f241(a847),f2(a847)),x62571))+~P1(f331(f331(f287(a847),x62572),x62571))+~P1(f331(f331(f241(a847),x62571),x62572))
% 51.10/50.82 [6258]~P1(f331(f331(f241(a1),f2(a1)),x62581))+~P1(f331(f331(f287(a1),x62582),x62581))+~P1(f331(f331(f241(a1),x62581),x62582))
% 51.10/50.82 [6270]P1(f331(f61(x62701,x62702),f59(x62701,x62702)))+~P1(f331(f331(f241(a1),f2(a1)),x62702))+~P1(f331(f331(f240(a1),f2(a1)),x62701))
% 51.10/50.82 [6312]~P76(x63121)+P1(f331(f331(f241(x63121),f331(f86(x63121),x63122)),f2(x63121)))+~P1(f331(f331(f241(x63121),f2(x63121)),x63122))
% 51.10/50.82 [6313]~P76(x63131)+P1(f331(f331(f240(x63131),f331(f86(x63131),x63132)),f2(x63131)))+~P1(f331(f331(f240(x63131),f2(x63131)),x63132))
% 51.10/50.82 [6335]E(f331(f331(f3(a847),f331(a112,x63351)),f331(a112,x63352)),f331(a112,f192(x63351,x63352)))+~P1(f331(f331(f240(a1),f2(a1)),x63352))+~P1(f331(f331(f240(a1),f2(a1)),x63351))
% 51.10/50.82 [6353]P1(f331(f331(f240(a1),f2(a1)),f192(x63531,x63532)))+~P1(f331(f331(f240(a1),f2(a1)),x63532))+~P1(f331(f331(f240(a1),f2(a1)),x63531))
% 51.10/50.82 [6392]~P1(f331(x63921,x63922))+P1(f331(x63921,f2(a847)))+P1(f331(x63921,f331(f331(f87(a847),f786(x63922,x63921)),f85(a847))))
% 51.10/50.82 [6398]E(f290(a847,f287(a847),x63981,x63982),f184(f854(a847,a840)))+P1(f331(f331(f287(a847),x63981),x63982))+~P1(f331(f331(f287(a847),x63982),x63981))
% 51.10/50.82 [6477]E(f331(f111(a847),x64771),f331(f111(a847),x64772))+~P1(f331(f331(f240(a1),f331(f111(a1),x64772)),f2(a1)))+~P1(f331(a190,f331(f111(a1),x64771)))
% 51.10/50.82 [6490]~E(x64901,f2(a847))+~E(f747(x64902,x64901),f2(a847))+E(f331(f137(a847,a847,f87(a847),x64901),x64902),f2(a847))
% 51.10/50.82 [6516]~P1(f331(f68(x65161),f659(x65162,x65161)))+~P1(f331(f68(f854(x65161,a840)),x65162))+P1(f331(f68(x65161),f49(f854(x65161,a840),x65162)))
% 51.10/50.82 [6522]E(x65221,x65222)+P1(f331(f331(f241(a1),x65221),x65222))+~P1(f331(f331(f241(a1),x65221),f331(f331(f87(a1),x65222),f85(a1))))
% 51.10/50.82 [6523]P1(f331(f331(f241(a847),f331(a112,x65231)),f331(a112,x65232)))+~P1(f331(f331(f241(a1),f2(a1)),x65232))+~P1(f331(f331(f241(a1),x65231),x65232))
% 51.10/50.82 [6524]P1(f331(f331(f241(a847),f331(a112,x65241)),f331(a112,x65242)))+~P1(f331(f331(f241(a1),f2(a1)),x65242))+~P1(f331(f331(f241(a1),x65241),x65242))
% 51.10/50.82 [6525]P1(f331(f331(f241(a847),f331(a112,x65251)),f331(a112,x65252)))+~P1(f331(f331(f240(a1),f2(a1)),x65251))+~P1(f331(f331(f241(a1),x65251),x65252))
% 51.10/50.82 [6526]P1(f331(f331(f240(a847),f331(a112,x65261)),f331(a112,x65262)))+~P1(f331(f331(f241(a1),f2(a1)),x65261))+~P1(f331(f331(f240(a1),x65261),x65262))
% 51.10/50.82 [6527]P1(f331(f331(f240(a847),f331(a112,x65271)),f331(a112,x65272)))+~P1(f331(f331(f240(a1),f2(a1)),x65272))+~P1(f331(f331(f240(a1),x65271),x65272))
% 51.10/50.82 [6537]E(f57(a847,f331(a112,x65371),f331(a112,x65372)),f331(a112,f57(a1,x65371,x65372)))+~P1(f331(f331(f240(a1),f2(a1)),x65372))+~P1(f331(f331(f240(a1),f2(a1)),x65371))
% 51.10/50.82 [6538]E(f57(a847,f331(a112,x65381),f331(a112,x65382)),f331(a112,f57(a1,x65381,x65382)))+~P1(f331(f331(f240(a1),f2(a1)),x65382))+~P1(f331(f331(f240(a1),f2(a1)),x65381))
% 51.10/50.82 [6558]~P76(x65581)+~P1(f331(f331(f241(x65581),f331(f86(x65581),x65582)),f2(x65581)))+P1(f331(f331(f241(x65581),f2(x65581)),x65582))
% 51.10/50.82 [6559]~P76(x65591)+~P1(f331(f331(f240(x65591),f331(f86(x65591),x65592)),f2(x65591)))+P1(f331(f331(f240(x65591),f2(x65591)),x65592))
% 51.10/50.82 [6576]~P1(f331(f331(f241(a1),a90),x65762))+~P1(f331(f331(f241(a1),x65761),x65762))+P1(f331(f331(f241(a847),f331(f111(a847),x65761)),f331(f111(a847),x65762)))
% 51.10/50.82 [6673]~P1(f331(f331(f240(a1),f2(a1)),x66731))+P1(f331(f331(f241(a847),f331(a112,x66731)),x66732))+~P1(f331(f331(f241(a1),x66731),f331(f107(a1),x66732)))
% 51.10/50.82 [6674]~P1(f331(f331(f240(a1),f2(a1)),x66741))+P1(f331(f331(f287(a847),f331(a112,x66741)),x66742))+~P1(f331(f331(f287(a1),x66741),f331(f107(a1),x66742)))
% 51.10/50.82 [6690]E(x66901,f2(a1))+E(f57(a1,x66902,x66901),f2(a1))+E(f331(f331(f3(a1),f331(f86(a1),f331(f331(f48(a1),x66902),x66901))),f85(a1)),f331(f331(f48(a1),x66902),f331(f86(a1),x66901)))
% 51.10/50.82 [6706]~P1(f331(f331(f240(a1),f2(a1)),x67061))+~P1(f331(f331(f241(a847),f331(a112,x67061)),x67062))+P1(f331(f331(f241(a1),x67061),f331(f107(a1),x67062)))
% 51.10/50.82 [6707]~P1(f331(f331(f240(a1),f2(a1)),x67071))+~P1(f331(f331(f287(a847),f331(a112,x67071)),x67072))+P1(f331(f331(f287(a1),x67071),f331(f107(a1),x67072)))
% 51.10/50.82 [6744]~P1(f331(f331(f241(a847),f331(a112,x67441)),f331(a112,x67442)))+~P1(f331(f331(f241(a1),f2(a1)),x67442))+P1(f331(f331(f241(a1),x67441),x67442))
% 51.10/50.82 [6745]~P1(f331(f331(f241(a847),f331(a112,x67451)),f331(a112,x67452)))+~P1(f331(f331(f240(a1),f2(a1)),x67451))+P1(f331(f331(f241(a1),x67451),x67452))
% 51.10/50.82 [6746]~P1(f331(f331(f240(a847),f331(a112,x67461)),f331(a112,x67462)))+~P1(f331(f331(f241(a1),f2(a1)),x67461))+P1(f331(f331(f240(a1),x67461),x67462))
% 51.10/50.82 [6747]~P1(f331(f331(f240(a847),f331(a112,x67471)),f331(a112,x67472)))+~P1(f331(f331(f240(a1),f2(a1)),x67472))+P1(f331(f331(f240(a1),x67471),x67472))
% 51.10/50.82 [6778]P1(f331(f331(f240(a1),x67781),x67782))+~P1(f331(f331(f240(a847),f331(f111(a847),x67781)),f331(f111(a847),x67782)))+P1(f331(f331(f240(a1),x67781),a90))
% 51.10/50.82 [6805]P1(f331(f331(f240(a1),f2(a1)),f57(a1,x68051,x68052)))+~P1(f331(f331(f240(a1),f2(a1)),x68052))+~P1(f331(f331(f240(a1),f2(a1)),x68051))
% 51.10/50.82 [6904]P1(f331(f331(f241(a1),a90),x69041))+~P1(f331(f331(f241(a1),x69042),x69041))+~P1(f331(f331(f241(a847),f331(f111(a847),x69042)),f331(f111(a847),x69041)))
% 51.10/50.82 [6952]E(f331(f331(f249(a1,a1),f331(f331(f48(a1),x69521),x69522)),f57(a1,x69521,x69522)),f62(x69521,x69522))+~P1(f331(f331(f241(a1),x69521),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x69522))
% 51.10/50.82 [6973]E(f331(f331(f249(a1,a1),f331(f331(f48(a1),x69731),x69732)),f57(a1,x69731,x69732)),f59(x69731,x69732))+~P1(f331(f331(f240(a1),f2(a1)),x69732))+~P1(f331(f331(f240(a1),f2(a1)),x69731))
% 51.10/50.82 [7028]~P94(x70282)+E(x70281,f120(x70282))+E(f331(f137(x70282,x70282,f88(x70282),f331(f136(x70282),x70281)),f331(f162(x70282),x70281)),f331(f70(x70282,f88(x70282)),f331(f163(x70282),x70281)))
% 51.10/50.82 [7142]~E(x71421,f2(a847))+E(f331(f137(a847,a847,f87(a847),x71421),x71422),f2(a847))+P1(f331(f331(f333(a847),f747(x71422,x71421)),f331(f163(a847),x71422)))
% 51.10/50.82 [7194]~P1(f331(f331(f241(a1),x71942),f2(a1)))+P1(f331(f331(f241(a1),f331(f331(f48(a1),x71941),x71942)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x71941))
% 51.10/50.82 [7195]~P1(f331(f331(f241(a1),x71951),f2(a1)))+P1(f331(f331(f241(a1),f331(f331(f48(a1),x71951),x71952)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x71952))
% 51.10/50.82 [7196]~P1(f331(f331(f241(a1),x71961),f2(a1)))+P1(f331(f331(f241(a1),f331(f331(f48(a1),x71961),x71962)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x71962))
% 51.10/50.82 [7197]~P1(f331(f331(f241(a1),x71972),f2(a1)))+P1(f331(f331(f240(a1),f331(f331(f48(a1),x71971),x71972)),f2(a1)))+~P1(f331(f331(f240(a1),f2(a1)),x71971))
% 51.10/50.82 [7198]~P1(f331(f331(f240(a1),x71981),f2(a1)))+P1(f331(f331(f240(a1),f331(f331(f48(a1),x71981),x71982)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x71982))
% 51.10/50.82 [7207]P1(f331(f331(f333(f854(x72071,a840)),f659(x72072,x72071)),x72072))+~P1(f331(f68(f854(x72071,a840)),x72072))+P1(f331(f68(x72071),f49(f854(x72071,a840),x72072)))
% 51.10/50.82 [7312]P27(x73121,x73121,x73122,f247(f854(x73121,a840)))+~E(f331(f311(x73121,x73121,x73122),f247(f854(x73121,a840))),f247(f854(x73121,a840)))+~P1(f331(f68(x73121),f247(f854(x73121,a840))))
% 51.10/50.82 [7442]~P27(x74421,x74421,x74422,f247(f854(x74421,a840)))+E(f331(f311(x74421,x74421,x74422),f247(f854(x74421,a840))),f247(f854(x74421,a840)))+~P1(f331(f68(x74421),f247(f854(x74421,a840))))
% 51.10/50.82 [7465]E(f59(f331(f111(a1),x74651),f331(f111(a1),x74652)),f331(f331(f249(a1,a1),f2(a1)),f331(f111(a1),x74651)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x74652)))+~P1(f331(f331(f241(a1),f331(f111(a1),x74651)),f331(f111(a1),x74652)))
% 51.10/50.82 [7583]E(f331(f331(f48(a1),x75831),x75832),f331(f111(a1),a104))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x75831),x75832)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x75831))
% 51.10/50.82 [7641]~P1(f331(f331(f241(a1),x76412),f2(a1)))+~P1(f331(f331(f241(a1),f331(f331(f48(a1),x76411),x76412)),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x76411))
% 51.10/50.82 [7646]E(f331(f331(f87(a1),x76461),x76462),f57(a1,x76461,x76462))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),x76461),x76462)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x76461))
% 51.10/50.82 [7648]P1(f331(f331(f241(a1),x76481),f2(a1)))+~P1(f331(f331(f241(a1),f331(f331(f48(a1),x76481),x76482)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x76482))
% 51.10/50.82 [7900]~P88(x79001)+P48(a847,x79001,f287(a847),x79002)+~P1(f331(f331(f240(x79001),f331(x79002,f338(x79002,x79001))),f331(x79002,f341(x79002,x79001))))
% 51.10/50.82 [8342]~P102(x83421)+P16(x83421,x83422)+~P1(f331(f331(f240(x83421),f331(f331(f155(x83421),x83422),f761(x83422,x83421))),f331(f331(f155(x83421),x83422),f762(x83422,x83421))))
% 51.10/50.82 [5526]E(x55261,f2(a1))+~E(f57(a1,x55262,x55261),f2(a1))+E(f331(f331(f48(a1),x55262),f331(f86(a1),x55261)),f331(f86(a1),f331(f331(f48(a1),x55262),x55261)))
% 51.10/50.82 [5543]~P36(x55432)+~P36(x55431)+P36(f331(f331(f108(f854(a1,a840)),x55431),x55432))
% 51.10/50.82 [5544]~P36(x55442)+~P36(x55441)+P36(f331(f331(f109(f854(a1,a840)),x55441),x55442))
% 51.10/50.82 [5561]~P91(x55611)+~P58(x55611)+E(f331(f86(x55611),f331(f331(f291(x55611),f85(x55611)),x55612)),f331(f331(f291(x55611),f331(f111(x55611),a104)),x55612))
% 51.10/50.82 [5686]E(x56861,f2(a1))+~E(f57(a1,x56862,x56861),f2(a1))+E(f331(f331(f48(a1),f331(f86(a1),x56862)),x56861),f331(f86(a1),f331(f331(f48(a1),x56862),x56861)))
% 51.10/50.82 [5821]~P102(x58211)+P16(x58211,x58212)+P1(f331(f331(f241(a847),f762(x58212,x58211)),f331(f185(f848(x58211)),x58212)))
% 51.10/50.82 [5979]~P91(x59791)+~E(f331(f111(x59791),x59792),f2(x59791))+P31(x59791,f331(f111(x59791),f331(f331(f87(a1),x59792),f331(f86(a1),a90))))
% 51.10/50.82 [5980]~P91(x59801)+~E(f331(f111(x59801),x59802),f2(x59801))+P31(x59801,f331(f111(x59801),f331(f331(f87(a1),a90),f331(f86(a1),x59802))))
% 51.10/50.82 [5982]E(f331(a63,f59(f331(f86(a1),x59821),f331(f86(a1),x59822))),f58(x59821,x59822))+P1(f331(f331(f241(a1),f2(a1)),x59822))+P1(f331(f331(f240(a1),f2(a1)),x59821))
% 51.10/50.82 [6116]~E(x61162,f2(a847))+~E(x61161,f2(a847))+P1(f331(f331(f240(a1),f331(f107(a1),x61161)),f331(f86(a1),f331(f107(a1),x61162))))
% 51.10/50.82 [6142]E(f331(f331(f87(a847),f331(f111(a847),x61421)),f331(f111(a847),x61422)),f331(f111(a847),f331(f331(f87(a1),x61421),x61422)))+P1(f331(f331(f241(a1),x61421),a90))+P1(f331(f331(f241(a1),x61422),a90))
% 51.10/50.82 [6279]~P67(x62791)+~P1(f331(f331(f241(x62791),f2(x62791)),x62792))+P1(f331(f331(f241(x62791),f331(f86(x62791),x62792)),x62792))
% 51.10/50.82 [6280]~P67(x62801)+~P1(f331(f331(f240(x62801),f2(x62801)),x62802))+P1(f331(f331(f240(x62801),f331(f86(x62801),x62802)),x62802))
% 51.10/50.82 [6462]E(f331(f331(f3(a847),f331(a112,x64621)),f331(a112,x64622)),f331(a112,f331(f331(f3(a1),x64621),x64622)))+~P1(f331(f331(f240(a1),f2(a1)),x64622))+~P1(f331(f331(f240(a1),x64622),x64621))
% 51.10/50.82 [6499]E(f331(a112,f57(a1,f331(f111(a1),x64991),f331(f111(a1),x64992))),f57(a847,f331(f111(a847),x64991),f331(f111(a847),x64992)))+P1(f331(a190,f331(f111(a1),x64991)))+P1(f331(a190,f331(f111(a1),x64992)))
% 51.10/50.82 [6517]~P67(x65171)+P1(f331(f331(f241(x65171),f2(x65171)),x65172))+~P1(f331(f331(f241(x65171),f331(f86(x65171),x65172)),x65172))
% 51.10/50.82 [6518]~P67(x65181)+P1(f331(f331(f240(x65181),f2(x65181)),x65182))+~P1(f331(f331(f240(x65181),f331(f86(x65181),x65182)),x65182))
% 51.10/50.82 [6529]~P67(x65291)+~P1(f331(f331(f241(x65291),f2(x65291)),x65292))+P1(f331(f331(f241(x65291),f2(x65291)),f331(f331(f87(x65291),x65292),x65292)))
% 51.10/50.82 [6531]~P67(x65311)+~P1(f331(f331(f240(x65311),f2(x65311)),x65312))+P1(f331(f331(f240(x65311),f2(x65311)),f331(f331(f87(x65311),x65312),x65312)))
% 51.10/50.82 [6541]E(f331(f331(f87(a847),f331(a112,x65411)),f331(a112,x65412)),f331(a112,f331(f331(f87(a1),x65411),x65412)))+~P1(f331(f331(f240(a1),f2(a1)),x65412))+~P1(f331(f331(f240(a1),f2(a1)),x65411))
% 51.10/50.82 [6542]E(f331(f331(f87(a847),f331(a112,x65421)),f331(a112,x65422)),f331(a112,f331(f331(f87(a1),x65421),x65422)))+~P1(f331(f331(f240(a1),f2(a1)),x65422))+~P1(f331(f331(f240(a1),f2(a1)),x65421))
% 51.10/50.82 [6543]E(f331(f331(f88(a847),f331(a112,x65431)),f331(a112,x65432)),f331(a112,f331(f331(f88(a1),x65431),x65432)))+~P1(f331(f331(f240(a1),f2(a1)),x65432))+~P1(f331(f331(f240(a1),f2(a1)),x65431))
% 51.10/50.82 [6544]E(f331(f331(f48(a847),f331(a112,x65441)),f331(a112,x65442)),f331(a112,f331(f331(f48(a1),x65441),x65442)))+~P1(f331(f331(f240(a1),f2(a1)),x65442))+~P1(f331(f331(f240(a1),f2(a1)),x65441))
% 51.10/50.82 [6554]E(x65541,f2(a847))+P1(f331(f331(f241(a847),f2(a847)),x65542))+~P1(f331(f331(f241(a847),f2(a847)),f331(f331(f250(a847),x65542),x65541)))
% 51.10/50.82 [6587]~P91(x65871)+E(f331(f111(x65871),x65872),f2(x65871))+~P31(x65871,f331(f111(x65871),f331(f331(f87(a1),a90),f331(f86(a1),x65872))))
% 51.10/50.82 [6588]~P91(x65881)+E(f331(f111(x65881),x65882),f2(x65881))+~P31(x65881,f331(f111(x65881),f331(f331(f87(a1),x65882),f331(f86(a1),a90))))
% 51.10/50.82 [6650]~P1(f331(f68(x66501),x66502))+~P1(f331(f68(x66501),f247(f854(x66501,a840))))+P1(f331(f68(x66501),f331(f86(f854(x66501,a840)),x66502)))
% 51.10/50.82 [6675]~P1(f331(f331(f241(a1),f2(a1)),x66752))+~P1(f331(f331(f240(a1),x66752),x66751))+P1(f331(f331(f241(a1),f2(a1)),f331(f331(f48(a1),x66751),x66752)))
% 51.10/50.82 [6676]~P1(f331(f331(f241(a1),x66762),f2(a1)))+~P1(f331(f331(f240(a1),x66761),f2(a1)))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f48(a1),x66761),x66762)))
% 51.10/50.82 [6717]~P1(f331(f331(f241(a847),f2(a847)),x67172))+~P1(f331(f331(f241(a847),f2(a847)),x67171))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f88(a847),x67171),x67172)))
% 51.10/50.82 [6718]~P1(f331(f331(f240(a1),f2(a1)),x67182))+~P1(f331(f331(f240(a1),f2(a1)),x67181))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),x67181),x67182)))
% 51.10/50.82 [6719]~P1(f331(f331(f240(a1),f2(a1)),x67192))+~P1(f331(f331(f240(a1),f2(a1)),x67191))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f88(a1),x67191),x67192)))
% 51.10/50.82 [6720]~P1(f331(f331(f241(a1),f2(a1)),x67202))+~P1(f331(f331(f240(a1),f2(a1)),x67201))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f48(a1),x67201),x67202)))
% 51.10/50.82 [6721]~P1(f331(f331(f240(a1),f2(a1)),x67212))+~P1(f331(f331(f240(a1),f2(a1)),x67211))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f48(a1),x67211),x67212)))
% 51.10/50.82 [6790]E(x67901,f2(a1))+E(f57(a1,x67902,x67901),f2(a1))+E(f331(f331(f3(a1),f331(f86(a1),f331(f331(f48(a1),x67902),x67901))),f85(a1)),f331(f331(f48(a1),f331(f86(a1),x67902)),x67901))
% 51.10/50.82 [6850]P1(f331(f331(f241(a847),f2(a847)),x68501))+P1(f331(f331(f241(a847),f2(a847)),x68502))+~P1(f331(f331(f241(a847),f2(a847)),f331(f331(f87(a847),x68502),x68501)))
% 51.10/50.82 [6851]~P67(x68511)+P1(f331(f331(f241(x68511),f2(x68511)),x68512))+~P1(f331(f331(f241(x68511),f2(x68511)),f331(f331(f87(x68511),x68512),x68512)))
% 51.10/50.82 [6852]~P67(x68521)+P1(f331(f331(f240(x68521),f2(x68521)),x68522))+~P1(f331(f331(f240(x68521),f2(x68521)),f331(f331(f87(x68521),x68522),x68522)))
% 51.10/50.82 [6905]~P1(f331(f68(x69051),x69052))+P1(f331(f68(x69051),f247(f854(x69051,a840))))+~P1(f331(f68(x69051),f331(f86(f854(x69051,a840)),x69052)))
% 51.10/50.82 [6965]P1(f331(f331(f240(a1),x69651),f2(a1)))+~P1(f331(f331(f241(a1),x69652),f2(a1)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f48(a1),x69651),x69652)))
% 51.10/50.82 [6971]~P1(f331(f331(f241(a1),f2(a1)),x69711))+P1(f331(f331(f240(a1),x69711),x69712))+~P1(f331(f331(f241(a1),f2(a1)),f331(f331(f48(a1),x69712),x69711)))
% 51.10/50.82 [6972]~P1(f331(f331(f240(a1),f2(a1)),x69722))+P1(f331(f331(f240(a1),x69721),x69722))+~P1(f331(f331(f241(a1),f2(a1)),f331(f331(f48(a1),x69722),x69721)))
% 51.10/50.82 [7004]P1(f331(f331(f241(a1),f2(a1)),x70041))+~P1(f331(f331(f240(a1),f2(a1)),x70042))+~P1(f331(f331(f241(a1),f2(a1)),f331(f331(f48(a1),x70042),x70041)))
% 51.10/50.82 [7005]P1(f331(f331(f240(a1),f2(a1)),x70051))+~P1(f331(f331(f241(a1),f2(a1)),x70052))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f48(a1),x70051),x70052)))
% 51.10/50.82 [7105]E(f218(x71051,x71052),x71051)+~E(x71052,f2(a847))+~P1(f331(f320(f853(a847,a847),a221),f331(f331(f249(a847,a847),x71051),x71052)))
% 51.10/50.82 [7332]E(f168(x73321,x73322),f120(a1))+P1(f331(f331(f240(a1),x73321),x73322))+~P1(f331(f320(f853(a1,a1),a173),f331(f331(f249(a1,a1),x73321),x73322)))
% 51.10/50.82 [7357]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f87(a1),x73571),x73572)),f62(x73571,x73572))+~P1(f331(f331(f241(a1),f2(a1)),x73572))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),x73571),x73572)))
% 51.10/50.82 [7384]E(x73841,f2(a847))+E(f218(x73841,f57(a847,x73842,x73841)),f218(x73842,x73841))+~P1(f331(f320(f853(a847,a847),a221),f331(f331(f249(a847,a847),x73842),x73841)))
% 51.10/50.82 [7473]~P1(f331(f68(x74732),f247(f854(x74732,a840))))+~P1(f331(f68(x74731),f247(f854(x74731,a840))))+P1(f331(f68(f853(x74731,x74732)),f247(f854(f853(x74731,x74732),a840))))
% 51.10/50.82 [7474]~P1(f331(f68(x74742),f247(f854(x74742,a840))))+~P1(f331(f68(x74741),f247(f854(x74741,a840))))+P1(f331(f68(f855(x74741,x74742)),f247(f854(f855(x74741,x74742),a840))))
% 51.10/50.82 [7546]~P1(f331(f331(f241(a847),f331(a119,f2(a847))),x75461))+~P1(f331(f331(f241(a847),f331(a119,f2(a847))),x75462))+P1(f331(f331(f241(a847),x75461),f331(f331(f88(a847),x75462),x75461)))
% 51.10/50.82 [7547]~P1(f331(f331(f241(a847),f331(a119,f2(a847))),x75471))+~P1(f331(f331(f241(a847),f331(a119,f2(a847))),x75472))+P1(f331(f331(f241(a847),x75471),f331(f331(f88(a847),x75471),x75472)))
% 51.10/50.82 [7582]E(f331(f47(x75821),f247(f854(x75821,a840))),f331(a119,f2(a847)))+P1(f331(f68(x75822),f247(f854(x75822,a840))))+~P1(f331(f68(f854(x75822,x75821)),f247(f854(f854(x75822,x75821),a840))))
% 51.10/50.82 [7634]E(f59(x76341,x76342),f331(f331(f249(a1,a1),f2(a1)),x76341))+~P1(f331(f331(f241(a1),x76341),x76342))+~P1(f331(f320(f853(a1,a1),a67),f331(f331(f249(a1,a1),x76341),x76342)))
% 51.10/50.82 [7638]E(f217(f331(f86(a1),x76381),f331(f86(a1),x76382)),f217(x76381,x76382))+~P1(f331(f331(f241(a1),x76382),f2(a1)))+~P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),x76381),x76382)))
% 51.10/50.82 [7655]E(f59(x76551,x76552),f331(f331(f249(a1,a1),f2(a1)),x76551))+~P1(f331(f331(f240(a1),x76552),f2(a1)))+~P1(f331(f320(f853(a1,a1),a67),f331(f331(f249(a1,a1),x76551),x76552)))
% 51.10/50.82 [7707]~P1(f331(f331(f241(a847),f331(a119,f2(a847))),x77072))+~P1(f331(f331(f241(a847),f331(a119,f2(a847))),x77071))+P1(f331(f331(f241(a847),f331(a119,f2(a847))),f331(f331(f88(a847),x77071),x77072)))
% 51.10/50.82 [7708]~P1(f331(f331(f240(a847),f331(a119,f2(a847))),x77081))+~P1(f331(f331(f240(a847),f331(a119,f2(a847))),x77082))+P1(f331(f331(f240(a847),f331(a119,f2(a847))),f331(f331(f88(a847),x77081),x77082)))
% 51.10/50.82 [7870]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f87(a1),x78701),x78702)),f62(x78701,x78702))+~P1(f331(f331(f240(a1),x78702),f2(a1)))+~P1(f331(f320(f853(a1,a1),a64),f331(f331(f249(a1,a1),x78701),x78702)))
% 51.10/50.82 [7911]E(f331(f331(f145(a1),x79111),f168(f331(f331(f87(a1),x79111),f85(a1)),x79112)),f168(x79111,x79112))+~P1(f331(f331(f240(a1),x79111),x79112))+~P1(f331(f320(f853(a1,a1),a173),f331(f331(f249(a1,a1),x79111),x79112)))
% 51.10/50.82 [8184]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f87(a1),x81841),x81842)),f62(x81841,x81842))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),x81841),x81842)))+~P1(f331(f320(f853(a1,a1),a64),f331(f331(f249(a1,a1),x81841),x81842)))
% 51.10/50.82 [8390]E(x83901,f120(x83902))+~P1(f331(f132(x83902),x83901))+E(f167(x83902,f331(f331(f10(a840,a840,x83902),a327),f331(f331(f9(x83902,x83902,a840),a328),f139(x83902,x83901))),x83901),f121(x83902,x83901))
% 51.10/50.82 [8464]E(f331(f331(f249(a1,a1),f331(f111(a1),a104)),f331(f331(f87(a1),f331(f111(a1),x84641)),f331(f111(a1),x84642))),f62(f331(f111(a1),x84641),f331(f111(a1),x84642)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x84642)))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f331(f111(a1),x84641)),f331(f111(a1),x84642))))
% 51.10/50.82 [8485]~P36(x84852)+~P36(x84851)+E(f331(f311(a847,a1,f107(a1)),f331(f331(f108(f854(a847,a840)),f331(f311(a1,a847,a112),x84851)),f331(f311(a1,a847,a112),x84852))),f331(f331(f108(f854(a1,a840)),x84851),x84852))
% 51.10/50.82 [8486]~P36(x84862)+~P36(x84861)+E(f331(f311(a847,a1,f107(a1)),f331(f331(f109(f854(a847,a840)),f331(f311(a1,a847,a112),x84861)),f331(f311(a1,a847,a112),x84862))),f331(f331(f109(f854(a1,a840)),x84861),x84862))
% 51.10/50.82 [9072]~P91(x90721)+~E(f331(f111(x90721),x90722),f85(x90721))+P31(x90721,f331(f111(x90721),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f86(a1),x90722))))
% 51.10/50.82 [9287]~P91(x92871)+E(f331(f111(x92871),x92872),f85(x92871))+~P31(x92871,f331(f111(x92871),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f86(a1),x92872))))
% 51.10/50.82 [9714]~P88(x97142)+P50(a847,x97142,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97141)+P1(f331(f331(f287(a847),f339(x97141,x97142)),f340(x97141,x97142)))
% 51.10/50.82 [9717]~P88(x97171)+P50(a847,x97171,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97172)+~P1(f331(f331(f287(a847),f340(x97172,x97171)),f339(x97172,x97171)))
% 51.10/50.82 [9718]~P88(x97181)+P50(a847,x97181,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x97182)+~P1(f331(f331(f241(x97181),f331(x97182,f339(x97182,x97181))),f331(x97182,f340(x97182,x97181))))
% 51.10/50.82 [9810]~P88(x98101)+P48(a847,x98101,f287(a847),x98102)+~P50(a847,x98101,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98102)
% 51.10/50.82 [10013]E(x100131,f2(a1))+E(x100132,f2(a1))+E(f331(f260(a1,a1,a1,a1,f39(a1),f331(f88(a1),f89(a1,x100132))),f331(f331(f331(f103(f853(a1,a1)),f331(f331(a328,f89(a1,x100131)),f89(a1,x100132))),f65(x100131,x100132)),f331(f331(f259(a1,a1,f853(a1,a1)),f331(f331(f20(a1,f854(a1,f853(a1,a1)),f854(a1,f853(a1,a1))),f331(f331(f10(f854(a1,f854(f853(a1,a1),f853(a1,a1))),f854(f854(a1,f853(a1,a1)),f854(a1,f853(a1,a1))),a1),f20(a1,f853(a1,a1),f853(a1,a1))),f331(f331(f10(f853(a1,a1),f854(a1,f854(f853(a1,a1),f853(a1,a1))),a1),f331(f9(a1,f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),f331(f331(f10(a840,f854(f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),a1),f103(f853(a1,a1))),f331(f331(f9(a1,a1,a840),a328),f2(a1))))),f331(f331(f9(a1,a1,f853(a1,a1)),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f86(a1))),f2(a1))))),f331(f331(f9(a1,f854(a1,a1),f854(a1,f853(a1,a1))),f331(f331(f10(f854(a1,f853(a1,a1)),f854(f854(a1,a1),f854(a1,f853(a1,a1))),a1),f10(a1,f853(a1,a1),a1)),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f331(f331(f9(a1,a1,a1),f331(f331(f10(a1,f854(a1,a1),a1),f3(a1)),f86(a1))),f85(a1))))),f331(f3(a1),f331(f82(a1),x100132))))),f65(x100131,x100132)))),f58(x100131,x100132))
% 51.10/50.82 [10014]E(x100141,f2(a1))+E(x100142,f2(a1))+E(f331(f260(a1,a1,a1,a1,f39(a1),f331(f88(a1),f89(a1,x100142))),f331(f331(f331(f103(f853(a1,a1)),f331(f331(a330,f331(f331(a329,f331(f331(f241(a1),f2(a1)),x100142)),f331(f331(f240(a1),f2(a1)),x100141))),f331(f331(a329,f331(f331(f241(a1),x100142),f2(a1))),f331(f331(f241(a1),x100141),f2(a1))))),f65(x100141,x100142)),f331(f331(f259(a1,a1,f853(a1,a1)),f331(f331(f20(a1,f854(a1,f853(a1,a1)),f854(a1,f853(a1,a1))),f331(f331(f10(f854(a1,f854(f853(a1,a1),f853(a1,a1))),f854(f854(a1,f853(a1,a1)),f854(a1,f853(a1,a1))),a1),f20(a1,f853(a1,a1),f853(a1,a1))),f331(f331(f10(f853(a1,a1),f854(a1,f854(f853(a1,a1),f853(a1,a1))),a1),f331(f9(a1,f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),f331(f331(f10(a840,f854(f853(a1,a1),f854(f853(a1,a1),f853(a1,a1))),a1),f103(f853(a1,a1))),f331(f331(f9(a1,a1,a840),a328),f2(a1))))),f331(f331(f9(a1,a1,f853(a1,a1)),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f86(a1))),f2(a1))))),f331(f331(f9(a1,f854(a1,a1),f854(a1,f853(a1,a1))),f331(f331(f10(f854(a1,f853(a1,a1)),f854(f854(a1,a1),f854(a1,f853(a1,a1))),a1),f10(a1,f853(a1,a1),a1)),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f331(f331(f9(a1,a1,a1),f331(f331(f10(a1,f854(a1,a1),a1),f3(a1)),f86(a1))),f85(a1))))),f331(f3(a1),f331(f82(a1),x100142))))),f65(x100141,x100142)))),f58(x100141,x100142))
% 51.10/50.82 [5551]~P86(x55511)+~P91(x55511)+E(f331(f82(x55511),f331(f331(f250(x55511),f331(f111(x55511),a104)),x55512)),f85(x55511))
% 51.10/50.82 [6054]~P133(x60541)+~P1(f331(f331(f241(a1),x60542),f2(a1)))+E(f331(f86(x60541),f331(f107(x60541),f331(a112,f331(f86(a1),x60542)))),f331(f110(x60541),x60542))
% 51.10/50.82 [6263]P1(f331(f331(f240(a106),x62631),f85(a106)))+E(f331(f331(f87(a106),f85(a106)),f275(x62631,f331(f331(f48(a106),x62632),x62631))),f275(x62631,x62632))+P1(f331(f331(f241(a106),x62632),x62631))
% 51.10/50.82 [6336]E(x63361,f2(a1))+~E(f331(f82(a1),x63362),f85(a1))+P1(f331(f331(f287(a1),f331(f331(f88(a1),x63361),x63362)),x63361))
% 51.10/50.82 [6759]~E(x67592,f85(a847))+~P1(f331(f331(f241(a847),f2(a847)),x67591))+P1(f331(f331(f287(a847),f331(f331(f88(a847),x67591),x67592)),x67591))
% 51.10/50.82 [6760]~E(x67601,f85(a847))+~P1(f331(f331(f241(a847),f2(a847)),x67602))+P1(f331(f331(f287(a847),f331(f331(f88(a847),x67601),x67602)),x67602))
% 51.10/50.82 [6893]~P90(x68931)+~P1(f331(f331(f333(x68931),x68932),f117(x68931)))+~E(f331(f331(f87(x68931),f331(f331(f87(x68931),f85(x68931)),x68932)),x68932),f2(x68931))
% 51.10/50.82 [7006]~P1(f331(f331(f241(a1),x70061),f2(a1)))+~P1(f331(f331(f240(a1),x70062),f2(a1)))+E(f331(f248(a1,a1),f331(a63,f59(f331(f86(a1),x70061),f331(f86(a1),x70062)))),f331(f331(f48(a1),x70061),x70062))
% 51.10/50.82 [7022]~P1(f331(f331(f241(a1),x70221),f2(a1)))+~P1(f331(f331(f240(a1),x70222),f2(a1)))+E(f331(f258(a1,a1),f331(a63,f59(f331(f86(a1),x70221),f331(f86(a1),x70222)))),f57(a1,x70221,x70222))
% 51.10/50.82 [7030]~P1(f331(f331(f241(a1),x70302),f2(a1)))+E(f331(f248(a1,a1),f331(a63,f62(f331(f86(a1),x70301),f331(f86(a1),x70302)))),f331(f331(f48(a1),x70301),x70302))+~P1(f331(f331(f241(a1),f2(a1)),x70301))
% 51.10/50.82 [7034]E(x70341,f2(a1))+E(f331(f82(a1),x70342),f85(a1))+~P1(f331(f331(f287(a1),f331(f331(f88(a1),x70341),x70342)),x70341))
% 51.10/50.82 [7049]~P1(f331(f331(f241(a1),x70492),f2(a1)))+E(f331(f258(a1,a1),f331(a63,f62(f331(f86(a1),x70491),f331(f86(a1),x70492)))),f57(a1,x70491,x70492))+~P1(f331(f331(f241(a1),f2(a1)),x70491))
% 51.10/50.82 [7100]E(f331(f331(f48(a1),f331(f331(f250(a1),x71001),x71002)),x71001),f331(f331(f250(a1),x71001),f331(f331(f3(a847),x71002),f331(a119,f2(a847)))))+~P1(f331(f331(f241(a847),f2(a847)),x71002))+~P1(f331(f331(f241(a1),f2(a1)),x71001))
% 51.10/50.82 [7203]~P1(f331(f331(f241(a847),f2(a847)),x72031))+~P1(f331(f331(f241(a847),f85(a847)),x72032))+P1(f331(f331(f241(a847),f331(f331(f48(a847),x72031),x72032)),x72031))
% 51.10/50.82 [7204]~P1(f331(f331(f241(a847),f2(a847)),x72041))+~P1(f331(f331(f241(a847),f2(a847)),x72042))+P1(f331(f331(f241(a847),f331(f331(f3(a847),x72041),x72042)),x72041))
% 51.10/50.82 [7205]~P1(f331(f331(f241(a1),f2(a1)),x72051))+~P1(f331(f331(f241(a1),f85(a1)),x72052))+P1(f331(f331(f241(a1),f331(f331(f48(a1),x72051),x72052)),x72051))
% 51.10/50.82 [7364]E(x73641,f2(a847))+~E(x73642,f2(a1))+~P1(f331(f331(f241(a1),f2(a1)),f331(f331(f250(a1),f331(f82(a1),x73642)),x73641)))
% 51.10/50.82 [7402]E(x74021,f85(a847))+~P1(f331(f331(f241(a847),f2(a847)),x74022))+~P1(f331(f331(f287(a847),f331(f331(f88(a847),x74022),x74021)),x74022))
% 51.10/50.82 [7403]E(x74031,f85(a847))+~P1(f331(f331(f241(a847),f2(a847)),x74032))+~P1(f331(f331(f287(a847),f331(f331(f88(a847),x74031),x74032)),x74032))
% 51.10/50.82 [7790]~E(x77902,f120(f848(x77901)))+E(f331(f185(f848(f848(x77901))),f169(x77901,x77902)),f2(a847))+~P16(a847,f331(f160(a847),f331(f331(f147(f848(x77901),a847),f185(f848(x77901))),x77902)))
% 51.10/50.82 [8040]P1(f331(x80401,x80402))+~P1(f331(x80401,f331(a115,f559(x80401,x80402))))+~P1(f331(f331(f333(f854(f853(a847,a847),a840)),x80402),a105))
% 51.10/50.82 [8054]E(x80541,f120(f848(x80542)))+E(f331(f185(f848(x80542)),f331(f331(f155(f848(x80542)),x80541),f2(a847))),f331(f185(f848(f848(x80542))),f169(x80542,x80541)))+~P16(a847,f331(f160(a847),f331(f331(f147(f848(x80542),a847),f185(f848(x80542))),x80541)))
% 51.10/50.82 [8725]~P1(f331(f68(x87251),f331(f264(x87251),x87252)))+~P1(f331(f68(x87251),f247(f854(x87251,a840))))+P1(f331(f68(x87251),f331(f264(x87251),f331(f331(f10(a840,a840,x87251),a327),x87252))))
% 51.10/50.82 [8778]E(f331(f331(f249(a847,a847),f331(a119,f331(f331(f48(a847),f331(f331(f3(a847),x87781),x87782)),x87782))),f57(a847,f331(f331(f3(a847),x87781),x87782),x87782)),f92(f853(a847,a847),f60(x87781,x87782)))+~P1(f331(f331(f241(a847),f2(a847)),x87782))+~P1(f331(f331(f240(a847),x87782),x87781))
% 51.10/50.82 [9039]~P1(f331(f68(x90391),f331(f264(x90391),x90392)))+P1(f331(f68(x90391),f247(f854(x90391,a840))))+~P1(f331(f68(x90391),f331(f264(x90391),f331(f331(f10(a840,a840,x90391),a327),x90392))))
% 51.10/50.82 [9711]P28(x97111,x97112)+~P34(x97111,f331(f248(f854(f853(x97111,x97111),a840),f854(f853(x97111,x97111),a840)),x97112))+~P1(f331(f331(f240(f854(f853(x97111,x97111),a840)),f331(f331(f289(x97111,x97111,x97111),f331(f248(f854(f853(x97111,x97111),a840),f854(f853(x97111,x97111),a840)),x97112)),f331(f258(f854(f853(x97111,x97111),a840),f854(f853(x97111,x97111),a840)),x97112))),f331(f248(f854(f853(x97111,x97111),a840),f854(f853(x97111,x97111),a840)),x97112)))
% 51.10/50.82 [9758]E(f331(f55(f331(f111(a1),x97581)),f59(f331(f111(a1),x97582),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f111(a1),x97581)))),f59(f331(f111(a1),x97582),f331(f111(a1),x97581)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x97581)))+P1(f331(f331(f241(a1),f331(f111(a1),x97582)),f331(f111(a1),x97581)))
% 51.10/50.82 [9764]E(f331(f55(f331(f111(a1),x97641)),f62(f331(f111(a1),x97642),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f111(a1),x97641)))),f62(f331(f111(a1),x97642),f331(f111(a1),x97641)))+~P1(f331(f331(f241(a1),f2(a1)),f331(f111(a1),x97641)))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f331(f111(a1),x97642)),f331(f111(a1),x97641))))
% 51.10/50.82 [9812]~E(f300(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98122,x98121),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x98122),x98121))+P1(f331(f331(f287(a847),x98121),x98122))
% 51.10/50.82 [9813]~E(f297(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98132,x98131),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x98132),x98131))+P1(f331(f331(f287(a847),x98131),x98132))
% 51.10/50.82 [9814]~E(f300(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98142,x98141),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x98142),x98141))+P1(f331(f331(f287(a847),x98141),x98142))
% 51.10/50.82 [9815]~E(f297(a847,f287(a847),f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98152,x98151),f184(f854(a847,a840)))+~P1(f331(f331(f287(a847),x98152),x98151))+P1(f331(f331(f287(a847),x98151),x98152))
% 51.10/50.82 [7123]~P1(f331(f331(f241(a847),f2(a847)),x71232))+P1(f331(f331(f241(a847),x71231),x71232))+E(f331(a119,f331(f331(f48(a847),f331(f331(f3(a847),x71231),x71232)),x71232)),f331(f331(f48(a847),x71231),x71232))
% 51.10/50.82 [7124]~P1(f331(f331(f241(a847),f2(a847)),x71242))+P1(f331(f331(f241(a847),x71241),x71242))+E(f331(a119,f331(f331(f48(a847),f331(f331(f3(a847),x71241),x71242)),x71242)),f331(f331(f48(a847),x71241),x71242))
% 51.10/50.82 [7279]~P1(f331(f331(f241(a847),f2(a847)),x72792))+~P1(f331(f331(f240(a847),x72792),x72791))+E(f331(a119,f331(f331(f48(a847),f331(f331(f3(a847),x72791),x72792)),x72792)),f331(f331(f48(a847),x72791),x72792))
% 51.10/50.82 [8255]~P91(x82551)+~P90(x82551)+~P31(x82551,f331(f111(x82551),f331(f331(f3(a1),f331(f331(f87(a1),x82552),x82552)),a104)))
% 51.10/50.82 [8951]E(x89511,f2(a847))+E(f331(f331(f259(a847,a847,f853(a847,a847)),f331(f331(f10(a847,f854(a847,f853(a847,a847)),a847),f249(a847,a847)),a119)),f92(f853(a847,a847),f60(f331(f331(f3(a847),x89512),x89511),x89511))),f92(f853(a847,a847),f60(x89512,x89511)))+P1(f331(f331(f241(a847),x89512),x89511))
% 51.10/50.82 [9346]P1(f331(x93462,f697(x93462,x93461)))+P1(f331(x93461,f697(x93462,x93461)))+E(f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x93461)),f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x93462)))
% 51.10/50.82 [9350]~P1(f331(x93502,f697(x93502,x93501)))+~P1(f331(x93501,f697(x93502,x93501)))+E(f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x93501)),f331(f264(a1),f331(f331(f20(a1,a840,a840),f331(f331(f10(a840,f854(a840,a840),a1),a329),f331(f240(a1),f2(a1)))),x93502)))
% 51.10/50.82 [9898]~P1(f331(f331(f287(a847),x98982),x98981))+P1(f331(f331(f287(a847),x98981),x98982))+P1(f331(f331(f333(a847),x98981),f295(a847,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98982)))
% 51.10/50.82 [9899]~P1(f331(f331(f287(a847),x98992),x98991))+P1(f331(f331(f287(a847),x98991),x98992))+P1(f331(f331(f333(a847),x98992),f298(a847,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98991)))
% 51.10/50.82 [7502]~P91(x75021)+~P59(x75021)+E(f331(f331(f291(x75021),x75022),f331(f111(x75021),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),x75022)
% 51.10/50.82 [7503]~P91(x75031)+~P59(x75031)+E(f331(f331(f291(x75031),x75032),f331(f111(x75031),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))),x75032)
% 51.10/50.82 [9071]~P91(x90711)+~E(f331(f111(x90711),x90712),f85(x90711))+P31(x90711,f331(f111(x90711),f331(f331(f87(a1),x90712),f331(f86(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9225]~P120(x92251)+~E(x92252,f2(x92251))+E(f331(f331(f250(x92251),x92252),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f2(x92251))
% 51.10/50.82 [9226]~P120(x92261)+~E(x92262,f85(x92261))+E(f331(f331(f250(x92261),x92262),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f85(x92261))
% 51.10/50.82 [9240]~P120(x92401)+~E(x92402,f331(f86(x92401),f85(x92401)))+E(f331(f331(f250(x92401),x92402),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f85(x92401))
% 51.10/50.82 [9260]~P74(x92601)+~P92(x92601)+E(f331(f331(f250(x92601),f331(f111(x92601),x92602)),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f88(x92601),f331(f111(x92601),x92602)),f331(f111(x92601),x92602)))
% 51.10/50.82 [9288]~P91(x92881)+E(f331(f111(x92881),x92882),f85(x92881))+~P31(x92881,f331(f111(x92881),f331(f331(f87(a1),x92882),f331(f86(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.82 [9400]~P120(x94002)+E(x94001,f2(x94002))+~E(f331(f331(f250(x94002),x94001),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f2(x94002))
% 51.10/50.82 [9651]~P86(x96512)+E(x96511,f2(x96512))+P1(f331(f331(f241(x96512),f2(x96512)),f331(f331(f250(x96512),x96511),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.82 [9710]~P86(x97102)+~E(x97101,f2(x97102))+~P1(f331(f331(f241(x97102),f2(x97102)),f331(f331(f250(x97102),x97101),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.82 [9749]P1(f331(f331(f240(a1),x97491),f2(a1)))+P1(f331(f331(f241(a1),x97492),x97491))+E(f331(f55(x97491),f59(x97492,f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97491))),f59(x97492,x97491))
% 51.10/50.82 [9750]~P1(f331(f331(f241(a1),f2(a1)),x97501))+P1(f331(f331(f241(a1),x97502),x97501))+E(f331(f55(x97501),f59(x97502,f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97501))),f59(x97502,x97501))
% 51.10/50.82 [9751]P1(f331(f331(f240(a1),x97511),f2(a1)))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),x97512),x97511)))+E(f331(f55(x97511),f62(x97512,f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97511))),f62(x97512,x97511))
% 51.10/50.82 [9752]~P1(f331(f331(f241(a1),f2(a1)),x97521))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),x97522),x97521)))+E(f331(f55(x97521),f62(x97522,f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97521))),f62(x97522,x97521))
% 51.10/50.82 [9753]~P84(x97531)+~P1(f331(f331(f240(a1),f2(a1)),x97532))+E(f331(f107(x97531),f331(a112,f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97532))),f331(f331(f87(x97531),f331(f107(x97531),f331(a112,x97532))),f331(f107(x97531),f331(a112,x97532))))
% 51.10/50.82 [4905]~P140(x49051,x49053,x49052)+~E(x49053,f2(a1))+P1(f331(x49051,x49052))
% 51.10/50.82 [5027]~P102(x50271)+~P16(x50271,x50273)+P16(x50271,f161(x50271,x50272,x50273))
% 51.10/50.82 [5028]~P102(x50281)+~P16(x50281,x50283)+P16(x50281,f167(x50281,x50282,x50283))
% 51.10/50.82 [5029]~P102(x50291)+~P16(x50291,x50293)+P16(x50291,f134(x50291,x50292,x50293))
% 51.10/50.82 [4613]~P69(x46132)+~E(x46133,f331(f86(x46132),x46131))+E(x46131,f331(f86(x46132),x46133))
% 51.10/50.82 [4614]~P69(x46142)+~E(x46143,f331(f86(x46142),x46141))+E(x46141,f331(f86(x46142),x46143))
% 51.10/50.82 [4615]~P69(x46151)+~E(f331(f86(x46151),x46153),x46152)+E(f331(f86(x46151),x46152),x46153)
% 51.10/50.82 [4616]~P69(x46161)+~E(f331(f86(x46161),x46163),x46162)+E(f331(f86(x46161),x46162),x46163)
% 51.10/50.82 [4689]~P89(x46893)+E(x46891,x46892)+~E(f331(f107(x46893),x46891),f331(f107(x46893),x46892))
% 51.10/50.82 [4690]~P90(x46903)+E(x46901,x46902)+~E(f331(f110(x46903),x46901),f331(f110(x46903),x46902))
% 51.10/50.82 [4691]~P69(x46913)+E(x46911,x46912)+~E(f331(f86(x46913),x46911),f331(f86(x46913),x46912))
% 51.10/50.82 [4692]~P93(x46923)+E(x46921,x46922)+~E(f331(f86(x46923),x46921),f331(f86(x46923),x46922))
% 51.10/50.82 [4693]~P102(x46933)+E(x46931,x46932)+~E(f331(f301(x46933),x46931),f331(f301(x46933),x46932))
% 51.10/50.82 [4694]~P102(x46943)+E(x46941,x46942)+~E(f331(f265(x46943),x46941),f331(f265(x46943),x46942))
% 51.10/50.82 [4695]~P102(x46953)+E(x46951,x46952)+~E(f331(f266(x46953),x46951),f331(f266(x46953),x46952))
% 51.10/50.82 [4696]~P102(x46963)+E(x46961,x46962)+~E(f331(f304(x46963),x46961),f331(f304(x46963),x46962))
% 51.10/50.82 [4924]~P141(x49241,x49242,x49243)+~E(x49242,f2(a1))+P1(f331(x49241,f2(a1)))
% 51.10/50.82 [4963]~E(x49631,f2(a847))+E(f363(x49631,x49632,x49633),f184(f854(x49633,a840)))+~E(f331(f47(x49633),x49632),f331(a119,x49631))
% 51.10/50.82 [5111]~E(x51112,f2(a847))+E(f331(f248(a847,a847),x51111),f2(a847))+~P1(f331(f60(x51113,x51112),x51111))
% 51.10/50.82 [5155]P1(f331(x51551,x51552))+~E(x51553,f331(f107(a1),x51552))+~P1(f331(x51551,f331(a112,x51553)))
% 51.10/50.82 [5613]~E(x56133,f2(a847))+~P1(f331(x56131,x56132))+P1(f331(x56131,f57(a847,x56132,x56133)))
% 51.10/50.82 [5760]~P1(f331(a26,x57603))+~P1(f331(a26,x57602))+P1(f331(a26,f35(x57601,x57602,x57603)))
% 51.10/50.82 [5761]~P1(f331(a26,x57613))+~P1(f331(a26,x57612))+P1(f331(a26,f35(x57611,x57612,x57613)))
% 51.10/50.82 [6036]~E(x60363,f2(a847))+P1(f331(x60361,x60362))+~P1(f331(x60361,f57(a847,x60362,x60363)))
% 51.10/50.82 [6743]E(x67431,f2(a847))+~P1(f331(x67432,f795(x67431,x67433,x67432)))+P1(f331(x67432,f57(a847,x67433,x67431)))
% 51.10/50.82 [6856]~P7(x68561)+~P1(f331(f331(f240(x68561),x68562),f661(x68563,x68562,x68561)))+P1(f331(f331(f240(x68561),x68562),f50(x68561,x68563)))
% 51.10/50.82 [6858]~P1(f331(x68581,x68582))+~P1(f331(x68581,f795(x68583,x68582,x68581)))+P1(f331(x68581,f57(a847,x68582,x68583)))
% 51.10/50.82 [6958]E(x69581,f120(x69582))+E(f331(f331(f145(x69582),f748(x69583,x69581,x69582)),f756(x69583,x69581,x69582)),x69581)+~P1(f331(f331(f333(f848(x69582)),x69581),f153(x69582,x69583)))
% 51.10/50.82 [6995]~P133(x69951)+~P1(f331(f331(f333(x69951),x69952),f117(x69951)))+P1(f331(f331(f333(x69951),f331(f331(f250(x69951),x69952),x69953)),f117(x69951)))
% 51.10/50.82 [7331]P34(x73311,x73312)+~P1(f331(f331(f333(x73311),x73313),f692(x73312,x73311)))+P1(f331(f331(f333(x73311),f696(x73312,x73311,x73313)),f692(x73312,x73311)))
% 51.10/50.82 [7608]E(x76081,f120(x76082))+~P1(f331(f331(f333(f848(x76082)),x76081),f153(x76082,x76083)))+P1(f331(f331(f333(f848(x76082)),f756(x76083,x76081,x76082)),f153(x76082,x76083)))
% 51.10/50.82 [7658]E(x76581,f2(a847))+E(f331(f331(f87(a847),f331(f331(f88(a847),x76581),f798(x76581,x76582,x76583))),f795(x76581,x76582,x76583)),x76582)+P1(f331(x76583,f57(a847,x76582,x76581)))
% 51.10/50.82 [7701]~P1(f331(x77013,x77012))+E(f331(f331(f87(a847),f331(f331(f88(a847),x77011),f798(x77011,x77012,x77013))),f795(x77011,x77012,x77013)),x77012)+P1(f331(x77013,f57(a847,x77012,x77011)))
% 51.10/50.82 [7845]P1(f331(f331(f241(a1),x78451),f788(x78452,x78453,x78451)))+P1(f331(f331(x78453,f331(f331(f48(a1),x78452),x78451)),f57(a1,x78452,x78451)))+~P1(f331(f331(f241(a1),x78451),f2(a1)))
% 51.10/50.82 [8111]P1(f331(f331(x81112,f331(f331(f48(a1),x81111),x81113)),f57(a1,x81111,x81113)))+~P1(f331(f331(f241(a1),x81113),f2(a1)))+P1(f331(f331(f240(a1),f788(x81111,x81112,x81113)),f2(a1)))
% 51.10/50.82 [8292]E(f331(f331(f87(a1),f331(f331(f88(a1),x82921),f791(x82922,x82923,x82921))),f788(x82922,x82923,x82921)),x82922)+P1(f331(f331(x82923,f331(f331(f48(a1),x82922),x82921)),f57(a1,x82922,x82921)))+~P1(f331(f331(f241(a1),x82921),f2(a1)))
% 51.10/50.82 [8523]~P1(f331(f331(x85231,f791(x85232,x85231,x85233)),f788(x85232,x85231,x85233)))+P1(f331(f331(x85231,f331(f331(f48(a1),x85232),x85233)),f57(a1,x85232,x85233)))+~P1(f331(f331(f241(a1),x85233),f2(a1)))
% 51.10/50.82 [8735]~P102(x87351)+~P16(x87351,x87353)+P16(x87351,f144(x87351,x87351,f7(x87351),x87352,x87353))
% 51.10/50.82 [9175]~P118(x91752)+E(x91751,f2(x91752))+~P1(f331(f331(f240(x91752),f331(f331(f87(x91752),f331(f331(f88(x91752),x91753),x91753)),f331(f331(f88(x91752),x91751),x91751))),f2(x91752)))
% 51.10/50.82 [9176]~P118(x91762)+E(x91761,f2(x91762))+~P1(f331(f331(f240(x91762),f331(f331(f87(x91762),f331(f331(f88(x91762),x91761),x91761)),f331(f331(f88(x91762),x91763),x91763))),f2(x91762)))
% 51.10/50.82 [9954]~P86(x99541)+~P1(f331(f331(f241(x99541),x99542),f2(x99541)))+P1(f331(f331(f241(x99541),f331(f331(f250(x99541),x99542),f331(a119,f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x99543)))),f2(x99541)))
% 51.10/50.82 [9964]~P86(x99642)+E(x99641,f2(x99642))+~P1(f331(f331(f240(x99642),f331(f331(f87(x99642),f331(f331(f250(x99642),x99643),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x99642),x99641),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f2(x99642)))
% 51.10/50.82 [9965]~P86(x99652)+E(x99651,f2(x99652))+~P1(f331(f331(f240(x99652),f331(f331(f87(x99652),f331(f331(f250(x99652),x99651),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x99652),x99653),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f2(x99652)))
% 51.10/50.82 [4646]~E(x46462,x46463)+~P69(x46461)+E(f331(f331(f3(x46461),x46462),x46463),f2(x46461))
% 51.10/50.82 [4647]~E(x46472,x46473)+~P4(x46471)+E(f331(f331(f3(x46471),x46472),x46473),f2(x46471))
% 51.10/50.82 [4660]~P137(x46601)+~E(x46603,f2(x46601))+E(f331(f331(f87(x46601),x46602),x46603),x46602)
% 51.10/50.82 [4676]~P134(x46761)+~E(x46763,f2(x46761))+E(f331(f331(f88(x46761),x46762),x46763),f2(x46761))
% 51.10/50.82 [4677]~P134(x46771)+~E(x46772,f2(x46771))+E(f331(f331(f88(x46771),x46772),x46773),f2(x46771))
% 51.10/50.82 [4697]~E(x46973,f120(x46971))+~E(x46972,f120(x46971))+E(f331(f331(f130(x46971),x46972),x46973),f120(x46971))
% 51.10/50.82 [4698]~E(x46983,f120(x46981))+~E(x46982,f120(x46981))+E(f331(f331(f130(x46981),x46982),x46983),f120(x46981))
% 51.10/50.82 [4783]~P137(x47832)+E(x47831,f2(x47832))+~E(f331(f331(f87(x47832),x47833),x47831),x47833)
% 51.10/50.83 [4784]~P69(x47841)+~E(x47842,f331(f86(x47841),x47843))+E(f331(f331(f87(x47841),x47842),x47843),f2(x47841))
% 51.10/50.83 [4791]E(x47911,f120(x47912))+E(x47913,f2(a847))+~E(f331(f331(f164(x47912),x47913),x47911),f120(x47912))
% 51.10/50.83 [4799]~P69(x47993)+E(x47991,x47992)+~E(f331(f331(f3(x47993),x47991),x47992),f2(x47993))
% 51.10/50.83 [4800]~P4(x48003)+E(x48001,x48002)+~E(f331(f331(f3(x48003),x48001),x48002),f2(x48003))
% 51.10/50.83 [4809]~P120(x48092)+E(x48091,f2(x48092))+~E(f331(f331(f250(x48092),x48091),x48093),f2(x48092))
% 51.10/50.83 [4810]~P95(x48102)+E(x48101,f184(x48102))+~E(f331(f331(f108(x48102),x48103),x48101),f184(x48102))
% 51.10/50.83 [4811]~P95(x48112)+E(x48111,f184(x48112))+~E(f331(f331(f108(x48112),x48111),x48113),f184(x48112))
% 51.10/50.83 [4812]~P99(x48122)+E(x48121,f247(x48122))+~E(f331(f331(f109(x48122),x48123),x48121),f247(x48122))
% 51.10/50.83 [4813]~P99(x48132)+E(x48131,f247(x48132))+~E(f331(f331(f109(x48132),x48131),x48133),f247(x48132))
% 51.10/50.83 [4878]~P69(x48782)+E(x48781,f331(f86(x48782),x48783))+~E(f331(f331(f87(x48782),x48781),x48783),f2(x48782))
% 51.10/50.83 [4879]~P69(x48791)+E(f331(f86(x48791),x48792),x48793)+~E(f331(f331(f87(x48791),x48792),x48793),f2(x48791))
% 51.10/50.83 [4880]~E(x48802,x48803)+~P88(x48801)+P1(f331(f331(f240(x48801),x48802),x48803))
% 51.10/50.83 [4881]~E(x48812,x48813)+~P88(x48811)+P1(f331(f331(f240(x48811),x48812),x48813))
% 51.10/50.83 [4882]~E(x48822,x48823)+~P88(x48821)+P1(f331(f331(f240(x48821),x48822),x48823))
% 51.10/50.83 [4883]~E(x48832,x48833)+~P105(x48831)+P1(f331(f331(f240(x48831),x48832),x48833))
% 51.10/50.83 [4977]~P112(x49771)+~E(x49772,f331(f86(x49771),x49773))+E(f331(f331(f88(x49771),x49772),x49772),f331(f331(f88(x49771),x49773),x49773))
% 51.10/50.83 [4985]~P102(x49851)+~P16(x49851,x49853)+P16(x49851,f331(f331(f164(x49851),x49852),x49853))
% 51.10/50.83 [4986]~P102(x49861)+~P16(x49861,x49863)+P16(x49861,f331(f331(f133(x49861),x49862),x49863))
% 51.10/50.83 [5024]E(x50241,x50242)+E(x50243,f2(a847))+~E(f331(f331(f88(a847),x50243),x50241),f331(f331(f88(a847),x50243),x50242))
% 51.10/50.83 [5025]E(x50251,x50252)+E(x50253,f2(a847))+~E(f331(f331(f88(a847),x50253),x50251),f331(f331(f88(a847),x50253),x50252))
% 51.10/50.83 [5026]E(x50261,x50262)+E(x50263,f2(a847))+~E(f331(f331(f88(a847),x50261),x50263),f331(f331(f88(a847),x50262),x50263))
% 51.10/50.83 [5103]~E(x51032,x51033)+~P88(x51031)+E(f303(x51031,x51032,x51033),f331(f331(f310(x51031),x51032),f184(f854(x51031,a840))))
% 51.10/50.83 [5143]~P86(x51431)+~E(f331(f82(x51431),x51432),f331(f82(x51431),x51433))+P1(f331(f331(f287(x51431),x51432),x51433))
% 51.10/50.83 [5147]~E(x51471,x51472)+~P88(x51473)+~P1(f331(f331(f241(x51473),x51471),x51472))
% 51.10/50.83 [5148]~E(x51481,x51482)+~P88(x51483)+~P1(f331(f331(f241(x51483),x51481),x51482))
% 51.10/50.83 [5149]~E(x51491,x51492)+~P88(x51493)+~P1(f331(f331(f241(x51493),x51491),x51492))
% 51.10/50.83 [5150]~E(x51501,x51502)+~P102(x51503)+~P1(f331(f331(f241(x51503),x51501),x51502))
% 51.10/50.83 [5151]~E(x51511,x51512)+~P102(x51513)+~P1(f331(f331(f241(x51513),x51511),x51512))
% 51.10/50.83 [5152]~E(x51521,x51522)+~P88(x51523)+~P1(f331(f331(f241(x51523),x51521),x51522))
% 51.10/50.83 [5153]~E(x51531,x51532)+~P102(x51533)+~P1(f331(f331(f241(x51533),x51531),x51532))
% 51.10/50.83 [5159]~P88(x51591)+E(f331(f302(x51591,x51592),x51593),f184(f854(x51591,a840)))+P1(f331(f331(f241(x51591),x51592),x51593))
% 51.10/50.83 [5160]~P88(x51601)+E(f331(f302(x51601,x51602),x51603),f184(f854(x51601,a840)))+P1(f331(f331(f241(x51601),x51602),x51603))
% 51.10/50.83 [5206]~P88(x52061)+E(f305(x52061,x52062,x52063),f184(f854(x52061,a840)))+P1(f331(f331(f241(x52061),x52062),x52063))
% 51.10/50.83 [5207]~P88(x52071)+E(f303(x52071,x52072,x52073),f184(f854(x52071,a840)))+P1(f331(f331(f240(x52071),x52072),x52073))
% 51.10/50.83 [5208]~P88(x52081)+E(f184(f854(x52081,a840)),f305(x52081,x52082,x52083))+P1(f331(f331(f241(x52081),x52082),x52083))
% 51.10/50.83 [5209]~P88(x52091)+E(f184(f854(x52091,a840)),f303(x52091,x52092,x52093))+P1(f331(f331(f240(x52091),x52092),x52093))
% 51.10/50.83 [5217]~P102(x52171)+~E(f331(f331(f244(x52171),x52172),x52173),x52172)+P1(f331(f331(f240(x52171),x52172),x52173))
% 51.10/50.83 [5218]~P102(x52181)+~E(f331(f331(f239(x52181),x52182),x52183),x52183)+P1(f331(f331(f240(x52181),x52182),x52183))
% 51.10/50.83 [5219]~P100(x52191)+~E(f331(f331(f108(x52191),x52192),x52193),x52193)+P1(f331(f331(f240(x52191),x52192),x52193))
% 51.10/50.83 [5220]~P101(x52201)+~E(f331(f331(f109(x52201),x52202),x52203),x52202)+P1(f331(f331(f240(x52201),x52202),x52203))
% 51.10/50.83 [5235]~P102(x52351)+P16(x52351,x52352)+~P16(x52351,f331(f331(f145(x52351),x52353),x52352))
% 51.10/50.83 [5236]~P102(x52361)+P16(x52361,x52362)+~P16(x52361,f331(f331(f145(x52361),x52363),x52362))
% 51.10/50.83 [5237]~P102(x52371)+P16(x52371,x52372)+~P16(x52371,f331(f331(f130(x52371),x52373),x52372))
% 51.10/50.83 [5238]~P102(x52381)+P16(x52381,x52382)+~P16(x52381,f331(f331(f130(x52381),x52382),x52383))
% 51.10/50.83 [5243]~P5(x52431)+~E(f57(x52431,x52433,x52432),f2(x52431))+P1(f331(f331(f287(x52431),x52432),x52433))
% 51.10/50.83 [5302]~P102(x53021)+P1(f331(f331(f240(x53021),x53023),x53022))+P1(f331(f331(f241(x53021),x53022),x53023))
% 51.10/50.83 [5303]~P102(x53031)+P1(f331(f331(f240(x53031),x53033),x53032))+P1(f331(f331(f241(x53031),x53032),x53033))
% 51.10/50.83 [5304]~P102(x53041)+P1(f331(f331(f240(x53041),x53043),x53042))+P1(f331(f331(f241(x53041),x53042),x53043))
% 51.10/50.83 [5305]~P102(x53051)+P1(f331(f331(f240(x53051),x53053),x53052))+P1(f331(f331(f241(x53051),x53052),x53053))
% 51.10/50.83 [5306]~P102(x53061)+P1(f331(f331(f240(x53061),x53063),x53062))+P1(f331(f331(f241(x53061),x53062),x53063))
% 51.10/50.83 [5307]~P102(x53071)+P1(f331(f331(f240(x53071),x53073),x53072))+P1(f331(f331(f240(x53071),x53072),x53073))
% 51.10/50.83 [5308]~P102(x53081)+P1(f331(f331(f240(x53081),x53083),x53082))+P1(f331(f331(f240(x53081),x53082),x53083))
% 51.10/50.83 [5347]~P102(x53471)+E(f331(f331(f244(x53471),x53472),x53473),x53473)+~P1(f331(f331(f240(x53471),x53473),x53472))
% 51.10/50.83 [5348]~P102(x53481)+E(f331(f331(f244(x53481),x53482),x53483),x53482)+~P1(f331(f331(f240(x53481),x53482),x53483))
% 51.10/50.83 [5349]~P102(x53491)+E(f331(f331(f244(x53491),x53492),x53493),x53492)+~P1(f331(f331(f240(x53491),x53492),x53493))
% 51.10/50.83 [5350]~P102(x53501)+E(f331(f331(f239(x53501),x53502),x53503),x53502)+~P1(f331(f331(f240(x53501),x53503),x53502))
% 51.10/50.83 [5351]~P102(x53511)+E(f331(f331(f239(x53511),x53512),x53513),x53513)+~P1(f331(f331(f240(x53511),x53512),x53513))
% 51.10/50.83 [5352]~P102(x53521)+E(f331(f331(f239(x53521),x53522),x53523),x53523)+~P1(f331(f331(f240(x53521),x53522),x53523))
% 51.10/50.83 [5353]~P100(x53531)+E(f331(f331(f108(x53531),x53532),x53533),x53532)+~P1(f331(f331(f240(x53531),x53533),x53532))
% 51.10/50.83 [5354]~P100(x53541)+E(f331(f331(f108(x53541),x53542),x53543),x53543)+~P1(f331(f331(f240(x53541),x53542),x53543))
% 51.10/50.83 [5355]~P100(x53551)+E(f331(f331(f108(x53551),x53552),x53553),x53553)+~P1(f331(f331(f240(x53551),x53552),x53553))
% 51.10/50.83 [5356]~P101(x53561)+E(f331(f331(f109(x53561),x53562),x53563),x53563)+~P1(f331(f331(f240(x53561),x53563),x53562))
% 51.10/50.83 [5357]~P101(x53571)+E(f331(f331(f109(x53571),x53572),x53573),x53572)+~P1(f331(f331(f240(x53571),x53572),x53573))
% 51.10/50.83 [5358]~P101(x53581)+E(f331(f331(f109(x53581),x53582),x53583),x53582)+~P1(f331(f331(f240(x53581),x53582),x53583))
% 51.10/50.83 [5365]~P114(x53652)+E(x53651,f2(x53652))+E(f331(f331(f291(x53652),f331(f86(x53652),x53653)),f331(f86(x53652),x53651)),f331(f331(f291(x53652),x53653),x53651))
% 51.10/50.83 [5371]~P5(x53711)+E(f57(x53711,x53712,x53713),f2(x53711))+~P1(f331(f331(f287(x53711),x53713),x53712))
% 51.10/50.83 [5372]~P5(x53721)+E(f57(x53721,x53722,x53723),f2(x53721))+~P1(f331(f331(f287(x53721),x53723),x53722))
% 51.10/50.83 [5413]~P88(x54131)+E(f331(f302(x54131,x54132),x54133),f184(f854(x54131,a840)))+~P1(f331(f331(f240(x54131),x54133),x54132))
% 51.10/50.83 [5442]~P88(x54421)+E(f306(x54421,x54422,x54423),f184(f854(x54421,a840)))+~P1(f331(f331(f240(x54421),x54423),x54422))
% 51.10/50.83 [5443]~P88(x54431)+E(f305(x54431,x54432,x54433),f184(f854(x54431,a840)))+~P1(f331(f331(f240(x54431),x54433),x54432))
% 51.10/50.83 [5444]~P88(x54441)+E(f303(x54441,x54442,x54443),f184(f854(x54441,a840)))+~P1(f331(f331(f241(x54441),x54443),x54442))
% 51.10/50.83 [5495]~E(f331(f331(f3(a847),x54951),x54953),x54952)+E(x54951,f331(f331(f87(a847),x54952),x54953))+~P1(f331(f331(f240(a847),x54953),x54951))
% 51.10/50.83 [5496]~E(x54961,f331(f331(f87(a847),x54963),x54962))+E(f331(f331(f3(a847),x54961),x54962),x54963)+~P1(f331(f331(f240(a847),x54962),x54961))
% 51.10/50.83 [5540]~P1(f331(x55401,x55403))+P1(f331(x55401,f438(x55401,x55402)))+~P1(f331(f331(f240(a847),x55403),x55402))
% 51.10/50.83 [5541]~P1(f331(x55411,x55413))+P1(f331(x55411,f481(x55411,x55412)))+~P1(f331(f331(f241(a847),x55413),x55412))
% 51.10/50.83 [5548]~P88(x55481)+~E(f331(f302(x55481,x55482),x55483),f184(f854(x55481,a840)))+~P1(f331(f331(f241(x55481),x55482),x55483))
% 51.10/50.83 [5549]~P88(x55491)+~E(f331(f302(x55491,x55492),x55493),f184(f854(x55491,a840)))+~P1(f331(f331(f241(x55491),x55492),x55493))
% 51.10/50.83 [5552]~P88(x55521)+~P1(f331(f331(f241(x55521),x55522),x55523))+P1(f331(f331(f240(x55521),x55522),x55523))
% 51.10/50.83 [5553]~P88(x55531)+~P1(f331(f331(f241(x55531),x55532),x55533))+P1(f331(f331(f240(x55531),x55532),x55533))
% 51.10/50.83 [5554]~P105(x55541)+~P1(f331(f331(f241(x55541),x55542),x55543))+P1(f331(f331(f240(x55541),x55542),x55543))
% 51.10/50.83 [5555]~P105(x55551)+~P1(f331(f331(f241(x55551),x55552),x55553))+P1(f331(f331(f240(x55551),x55552),x55553))
% 51.10/50.83 [5668]~P88(x56681)+~E(f305(x56681,x56682,x56683),f184(f854(x56681,a840)))+~P1(f331(f331(f241(x56681),x56682),x56683))
% 51.10/50.83 [5669]~P88(x56691)+~E(f303(x56691,x56692,x56693),f184(f854(x56691,a840)))+~P1(f331(f331(f240(x56691),x56692),x56693))
% 51.10/50.83 [5670]~P88(x56701)+~E(f184(f854(x56701,a840)),f305(x56701,x56702,x56703))+~P1(f331(f331(f241(x56701),x56702),x56703))
% 51.10/50.83 [5671]~P88(x56711)+~E(f184(f854(x56711,a840)),f303(x56711,x56712,x56713))+~P1(f331(f331(f240(x56711),x56712),x56713))
% 51.10/50.83 [5684]P1(f331(x56841,x56842))+~P1(f331(x56841,f439(x56841,x56843)))+~P1(f331(f331(f240(a847),x56842),x56843))
% 51.10/50.83 [5685]P1(f331(x56851,x56852))+~P1(f331(x56851,f482(x56851,x56853)))+~P1(f331(f331(f241(a847),x56852),x56853))
% 51.10/50.83 [5693]~E(x56931,f331(a119,x56933))+P1(f331(f331(f241(a847),x56931),f331(a119,x56932)))+~P1(f331(f331(f241(a847),x56933),x56932))
% 51.10/50.83 [5709]E(x57091,x57092)+~E(f331(f331(f88(a847),x57093),x57091),f331(f331(f88(a847),x57093),x57092))+~P1(f331(f331(f241(a847),f2(a847)),x57093))
% 51.10/50.83 [5771]E(f331(x57711,f485(x57711,x57712,x57713)),f85(a847))+~E(f331(f331(f8(x57713,a847),x57711),x57712),f85(a847))+~P1(f331(f68(x57713),x57712))
% 51.10/50.83 [5781]~P7(x57811)+P1(f331(f331(f240(x57811),x57812),f49(x57811,x57813)))+~P1(f331(f331(f333(x57811),x57812),x57813))
% 51.10/50.83 [5805]~P88(x58051)+~P1(f331(f331(f241(x58051),x58053),x58052))+~P1(f331(f331(f241(x58051),x58052),x58053))
% 51.10/50.83 [5806]~P105(x58061)+~P1(f331(f331(f241(x58061),x58063),x58062))+~P1(f331(f331(f241(x58061),x58062),x58063))
% 51.10/50.83 [5807]~P105(x58071)+~P1(f331(f331(f241(x58071),x58073),x58072))+~P1(f331(f331(f241(x58071),x58072),x58073))
% 51.10/50.83 [5808]~P105(x58081)+~P1(f331(f331(f241(x58081),x58083),x58082))+~P1(f331(f331(f241(x58081),x58082),x58083))
% 51.10/50.83 [5809]~P105(x58091)+~P1(f331(f331(f241(x58091),x58093),x58092))+~P1(f331(f331(f241(x58091),x58092),x58093))
% 51.10/50.83 [5810]~P105(x58101)+~P1(f331(f331(f240(x58101),x58103),x58102))+~P1(f331(f331(f241(x58101),x58102),x58103))
% 51.10/50.83 [5811]~P102(x58111)+~P1(f331(f331(f241(x58111),x58113),x58112))+~P1(f331(f331(f241(x58111),x58112),x58113))
% 51.10/50.83 [5812]~P102(x58121)+~P1(f331(f331(f240(x58121),x58123),x58122))+~P1(f331(f331(f241(x58121),x58122),x58123))
% 51.10/50.83 [5813]~P102(x58131)+~P1(f331(f331(f240(x58131),x58133),x58132))+~P1(f331(f331(f241(x58131),x58132),x58133))
% 51.10/50.83 [5814]~P102(x58141)+~P1(f331(f331(f240(x58141),x58143),x58142))+~P1(f331(f331(f241(x58141),x58142),x58143))
% 51.10/50.83 [5833]~E(x58332,x58333)+~E(x58331,x58332)+E(f290(a847,f287(a847),x58331,x58332),f331(f331(f310(a847),x58333),f184(f854(a847,a840))))
% 51.10/50.83 [5841]~E(f331(x58412,f392(x58412,x58413,x58411)),f85(a847))+E(f331(f331(f11(x58411,a847),x58412),x58413),f85(a847))+~P1(f331(f68(x58411),x58413))
% 51.10/50.83 [5842]~E(f331(x58422,f486(x58422,x58423,x58421)),f2(a847))+E(f331(f331(f8(x58421,a847),x58422),x58423),f2(a847))+~P1(f331(f68(x58421),x58423))
% 51.10/50.83 [5856]~P106(x58561)+~P1(f331(f331(f287(x58561),x58562),x58563))+P1(f331(f331(f287(x58561),x58562),f331(f86(x58561),x58563)))
% 51.10/50.83 [5857]~P86(x58571)+~P1(f331(f331(f287(x58571),x58572),x58573))+P1(f331(f331(f287(x58571),x58572),f331(f82(x58571),x58573)))
% 51.10/50.83 [5858]~P104(x58581)+~P1(f331(f331(f240(x58581),x58583),x58582))+P1(f331(f331(f333(x58581),x58582),f331(f266(x58581),x58583)))
% 51.10/50.83 [5859]~P104(x58591)+~P1(f331(f331(f241(x58591),x58593),x58592))+P1(f331(f331(f333(x58591),x58592),f331(f304(x58591),x58593)))
% 51.10/50.83 [5860]~P104(x58601)+~P1(f331(f331(f240(x58601),x58602),x58603))+P1(f331(f331(f333(x58601),x58602),f331(f301(x58601),x58603)))
% 51.10/50.83 [5861]~P104(x58611)+~P1(f331(f331(f241(x58611),x58612),x58613))+P1(f331(f331(f333(x58611),x58612),f331(f265(x58611),x58613)))
% 51.10/50.83 [5872]E(f331(x58721,f498(x58721,x58722,x58723)),f331(a119,f2(a847)))+~E(f331(f331(f8(x58723,a847),x58721),x58722),f331(a119,f2(a847)))+~P1(f331(f68(x58723),x58722))
% 51.10/50.83 [5957]~P7(x59571)+~P1(f331(f331(f333(x59571),x59573),x59572))+P1(f331(f331(f240(x59571),f50(x59571,x59572)),x59573))
% 51.10/50.83 [5975]~P1(f331(f331(f240(a847),x59751),x59753))+P1(f331(f331(f240(a847),x59751),x59752))+~P1(f331(f331(f240(a847),x59753),x59752))
% 51.10/50.83 [5976]~P1(f331(f331(f240(a1),x59761),x59763))+P1(f331(f331(f240(a1),x59761),x59762))+~P1(f331(f331(f240(a1),x59763),x59762))
% 51.10/50.83 [5977]~P1(f331(f331(f287(a847),x59771),x59773))+P1(f331(f331(f287(a847),x59771),x59772))+~P1(f331(f331(f287(a847),x59773),x59772))
% 51.10/50.83 [5995]~P104(x59951)+~P1(f331(f331(f333(x59951),x59953),f331(f304(x59951),x59952)))+P1(f331(f331(f241(x59951),x59952),x59953))
% 51.10/50.83 [5996]~P104(x59961)+~P1(f331(f331(f333(x59961),x59962),f331(f265(x59961),x59963)))+P1(f331(f331(f241(x59961),x59962),x59963))
% 51.10/50.83 [5997]~P104(x59971)+~P1(f331(f331(f333(x59971),x59973),f331(f266(x59971),x59972)))+P1(f331(f331(f240(x59971),x59972),x59973))
% 51.10/50.83 [5998]~P104(x59981)+~P1(f331(f331(f333(x59981),x59982),f331(f301(x59981),x59983)))+P1(f331(f331(f240(x59981),x59982),x59983))
% 51.10/50.83 [5999]~P86(x59991)+~P1(f331(f331(f287(x59991),x59992),f331(f82(x59991),x59993)))+P1(f331(f331(f287(x59991),x59992),x59993))
% 51.10/50.83 [6000]~P106(x60001)+~P1(f331(f331(f287(x60001),x60002),f331(f86(x60001),x60003)))+P1(f331(f331(f287(x60001),x60002),x60003))
% 51.10/50.83 [6225]~P60(x62251)+P1(f331(f331(f241(x62251),f2(x62251)),f793(x62253,x62252,x62251)))+P1(f331(f331(f240(x62251),x62252),x62253))
% 51.10/50.83 [6226]~P61(x62261)+P1(f331(f331(f241(x62261),f2(x62261)),f801(x62263,x62262,x62261)))+P1(f331(f331(f240(x62261),x62262),x62263))
% 51.10/50.83 [6295]~P76(x62951)+~P1(f331(f331(f241(x62951),x62953),f331(f86(x62951),x62952)))+P1(f331(f331(f241(x62951),x62952),f331(f86(x62951),x62953)))
% 51.10/50.83 [6296]~P76(x62961)+~P1(f331(f331(f241(x62961),x62963),f331(f86(x62961),x62962)))+P1(f331(f331(f241(x62961),x62962),f331(f86(x62961),x62963)))
% 51.10/50.83 [6297]~P76(x62971)+~P1(f331(f331(f240(x62971),x62973),f331(f86(x62971),x62972)))+P1(f331(f331(f240(x62971),x62972),f331(f86(x62971),x62973)))
% 51.10/50.83 [6298]~P76(x62981)+~P1(f331(f331(f240(x62981),x62983),f331(f86(x62981),x62982)))+P1(f331(f331(f240(x62981),x62982),f331(f86(x62981),x62983)))
% 51.10/50.83 [6309]~P1(f331(f331(f241(a847),x63091),x63093))+~P1(f331(f331(f241(a847),x63093),x63092))+P1(f331(f331(f241(a847),f331(a119,x63091)),x63092))
% 51.10/50.83 [6341]~P85(x63411)+P1(f331(f331(f241(x63411),f331(f107(x63411),x63412)),f331(f107(x63411),x63413)))+~P1(f331(f331(f241(a847),x63412),x63413))
% 51.10/50.83 [6342]~P86(x63421)+P1(f331(f331(f241(x63421),f331(f110(x63421),x63422)),f331(f110(x63421),x63423)))+~P1(f331(f331(f241(a1),x63422),x63423))
% 51.10/50.83 [6343]~P85(x63431)+P1(f331(f331(f241(x63431),f331(f107(x63431),x63432)),f331(f107(x63431),x63433)))+~P1(f331(f331(f241(a847),x63432),x63433))
% 51.10/50.83 [6344]~P85(x63441)+P1(f331(f331(f240(x63441),f331(f107(x63441),x63442)),f331(f107(x63441),x63443)))+~P1(f331(f331(f240(a847),x63442),x63443))
% 51.10/50.83 [6345]~P86(x63451)+P1(f331(f331(f240(x63451),f331(f110(x63451),x63452)),f331(f110(x63451),x63453)))+~P1(f331(f331(f240(a1),x63452),x63453))
% 51.10/50.83 [6351]~P102(x63511)+E(f331(f331(f108(f854(x63511,a840)),f331(f265(x63511),x63512)),f331(f302(x63511,x63512),x63513)),f331(f265(x63511),x63513))+~P1(f331(f331(f240(x63511),x63512),x63513))
% 51.10/50.83 [6382]~P76(x63821)+~P1(f331(f331(f241(x63821),x63823),x63822))+P1(f331(f331(f241(x63821),f331(f86(x63821),x63822)),f331(f86(x63821),x63823)))
% 51.10/50.83 [6383]~P76(x63831)+~P1(f331(f331(f240(x63831),x63833),x63832))+P1(f331(f331(f240(x63831),f331(f86(x63831),x63832)),f331(f86(x63831),x63833)))
% 51.10/50.83 [6384]~P76(x63841)+~P1(f331(f331(f240(x63841),x63843),x63842))+P1(f331(f331(f240(x63841),f331(f86(x63841),x63842)),f331(f86(x63841),x63843)))
% 51.10/50.83 [6385]~P93(x63851)+~P1(f331(f331(f240(x63851),x63853),x63852))+P1(f331(f331(f240(x63851),f331(f86(x63851),x63852)),f331(f86(x63851),x63853)))
% 51.10/50.83 [6386]~P93(x63861)+~P1(f331(f331(f240(x63861),x63863),x63862))+P1(f331(f331(f240(x63861),f331(f86(x63861),x63862)),f331(f86(x63861),x63863)))
% 51.10/50.83 [6421]~P102(x64211)+E(f331(f331(f108(f854(x64211,a840)),f331(f301(x64211),x64212)),f306(x64211,x64212,x64213)),f331(f265(x64211),x64213))+~P1(f331(f331(f241(x64211),x64212),x64213))
% 51.10/50.83 [6422]~P102(x64221)+E(f331(f331(f108(f854(x64221,a840)),f331(f301(x64221),x64222)),f305(x64221,x64222,x64223)),f331(f301(x64221),x64223))+~P1(f331(f331(f240(x64221),x64222),x64223))
% 51.10/50.83 [6423]~P102(x64231)+E(f331(f331(f108(f854(x64231,a840)),f331(f265(x64231),x64232)),f303(x64231,x64232,x64233)),f331(f301(x64231),x64233))+~P1(f331(f331(f240(x64231),x64232),x64233))
% 51.10/50.83 [6460]~P102(x64601)+E(f331(f331(f108(f854(x64601,a840)),f331(f302(x64601,x64602),x64603)),f331(f266(x64601),x64603)),f331(f266(x64601),x64602))+~P1(f331(f331(f240(x64601),x64602),x64603))
% 51.10/50.83 [6622]~P102(x66221)+E(f331(f331(f108(f854(x66221,a840)),f306(x66221,x66222,x66223)),f331(f266(x66221),x66223)),f331(f304(x66221),x66222))+~P1(f331(f331(f241(x66221),x66222),x66223))
% 51.10/50.83 [6623]~P102(x66231)+E(f331(f331(f108(f854(x66231,a840)),f305(x66231,x66232,x66233)),f331(f304(x66231),x66233)),f331(f304(x66231),x66232))+~P1(f331(f331(f240(x66231),x66232),x66233))
% 51.10/50.83 [6624]~P102(x66241)+E(f331(f331(f108(f854(x66241,a840)),f303(x66241,x66242,x66243)),f331(f304(x66241),x66243)),f331(f266(x66241),x66242))+~P1(f331(f331(f240(x66241),x66242),x66243))
% 51.10/50.83 [6641]P1(f331(x66411,x66412))+~P1(f331(f331(f240(a847),x66412),x66413))+P1(f331(f331(f333(a847),f439(x66411,x66413)),f303(a847,f2(a847),x66413)))
% 51.10/50.83 [6651]P1(f331(f331(f287(a1),x66511),f57(a1,x66512,x66513)))+~P1(f331(f331(f287(a1),x66511),x66512))+~P1(f331(f331(f287(a1),x66511),x66513))
% 51.10/50.83 [6677]E(x66771,x66772)+~E(f331(f331(f155(x66773),x66771),f724(x66773,x66772,x66771)),f331(f331(f155(x66773),x66772),f724(x66773,x66772,x66771)))+~E(f331(f185(f848(x66773)),x66771),f331(f185(f848(x66773)),x66772))
% 51.10/50.83 [6683]~E(x66833,f331(f331(f48(a847),x66831),x66832))+~P1(f331(f331(f241(a847),f2(a847)),x66832))+P1(f331(f331(f241(a847),x66831),f331(f331(f88(a847),x66832),f331(a119,x66833))))
% 51.10/50.83 [6698]~P1(f331(x66981,x66983))+~P1(f331(f331(f240(a847),x66983),x66982))+P1(f331(f331(f333(a847),f438(x66981,x66982)),f303(a847,f2(a847),x66982)))
% 51.10/50.83 [6740]~P1(f331(x67401,x67403))+P1(f331(x67401,f449(x67401,x67402)))+~P1(f331(f331(f333(a847),x67403),f303(a847,f2(a847),x67402)))
% 51.10/50.83 [6762]~P85(x67623)+~P1(f331(f331(f241(x67623),f331(f107(x67623),x67621)),f331(f107(x67623),x67622)))+P1(f331(f331(f241(a847),x67621),x67622))
% 51.10/50.83 [6763]~P85(x67633)+~P1(f331(f331(f241(x67633),f331(f107(x67633),x67631)),f331(f107(x67633),x67632)))+P1(f331(f331(f241(a847),x67631),x67632))
% 51.10/50.83 [6764]~P86(x67643)+~P1(f331(f331(f241(x67643),f331(f110(x67643),x67641)),f331(f110(x67643),x67642)))+P1(f331(f331(f241(a1),x67641),x67642))
% 51.10/50.83 [6765]~P85(x67653)+~P1(f331(f331(f240(x67653),f331(f107(x67653),x67651)),f331(f107(x67653),x67652)))+P1(f331(f331(f240(a847),x67651),x67652))
% 51.10/50.83 [6766]~P86(x67663)+~P1(f331(f331(f240(x67663),f331(f110(x67663),x67661)),f331(f110(x67663),x67662)))+P1(f331(f331(f240(a1),x67661),x67662))
% 51.10/50.83 [6782]~P85(x67821)+~P1(f331(f331(f241(x67821),f85(x67821)),x67822))+P1(f331(f331(f241(x67821),f85(x67821)),f331(f331(f250(x67821),x67822),f331(a119,x67823))))
% 51.10/50.83 [6786]~P76(x67861)+~P1(f331(f331(f241(x67861),f331(f86(x67861),x67863)),f331(f86(x67861),x67862)))+P1(f331(f331(f241(x67861),x67862),x67863))
% 51.10/50.83 [6787]~P76(x67871)+~P1(f331(f331(f240(x67871),f331(f86(x67871),x67873)),f331(f86(x67871),x67872)))+P1(f331(f331(f240(x67871),x67872),x67873))
% 51.10/50.83 [6788]~P93(x67881)+~P1(f331(f331(f240(x67881),f331(f86(x67881),x67883)),f331(f86(x67881),x67882)))+P1(f331(f331(f240(x67881),x67882),x67883))
% 51.10/50.83 [6814]P1(f331(x68141,x68142))+~P1(f331(x68141,f442(x68141,x68143)))+~P1(f331(f331(f333(a847),x68142),f303(a847,f2(a847),x68143)))
% 51.10/50.83 [6835]~P60(x68351)+P1(f331(f331(f241(x68351),f793(x68353,x68352,x68351)),f85(x68351)))+P1(f331(f331(f240(x68351),x68352),x68353))
% 51.10/50.83 [6854]~E(f57(a847,x68543,x68542),f57(a847,x68541,x68542))+E(f331(f331(f87(a847),x68541),f331(f331(f88(a847),x68542),f803(x68541,x68542,x68543))),x68543)+~P1(f331(f331(f240(a847),x68541),x68543))
% 51.10/50.83 [6872]E(f331(x68721,f598(x68721,x68722,x68723)),f187(x68722))+~P1(f331(f68(x68723),f174(x68723,x68722,x68721)))+P1(f331(f68(x68723),f247(f854(x68723,a840))))
% 51.10/50.83 [6913]E(f331(f331(f11(x69131,a847),x69132),x69133),f85(a847))+~P1(f331(f68(x69131),x69133))+P1(f331(f331(f333(x69131),f392(x69132,x69133,x69131)),x69133))
% 51.10/50.83 [6914]E(f331(f331(f8(x69141,a847),x69142),x69143),f2(a847))+~P1(f331(f68(x69141),x69143))+P1(f331(f331(f333(x69141),f486(x69142,x69143,x69141)),x69143))
% 51.10/50.83 [6936]~P102(x69361)+~P1(f331(f331(f241(x69361),x69362),x69363))+P1(f331(f331(f241(f854(x69361,a840)),f331(f265(x69361),x69362)),f331(f265(x69361),x69363)))
% 51.10/50.83 [6937]~P88(x69371)+~P1(f331(f331(f240(x69371),x69372),x69373))+P1(f331(f331(f240(f854(x69371,a840)),f331(f301(x69371),x69372)),f331(f301(x69371),x69373)))
% 51.10/50.83 [6938]~P102(x69381)+~P1(f331(f331(f240(x69381),x69382),x69383))+P1(f331(f331(f240(f854(x69381,a840)),f331(f265(x69381),x69382)),f331(f265(x69381),x69383)))
% 51.10/50.83 [6939]~P88(x69391)+~P1(f331(f331(f240(x69391),x69393),x69392))+P1(f331(f331(f240(f854(x69391,a840)),f331(f266(x69391),x69392)),f331(f266(x69391),x69393)))
% 51.10/50.83 [6940]~P102(x69401)+~P1(f331(f331(f240(x69401),x69403),x69402))+P1(f331(f331(f240(f854(x69401,a840)),f331(f304(x69401),x69402)),f331(f304(x69401),x69403)))
% 51.10/50.83 [6945]~P7(x69451)+P1(f331(f331(f240(x69451),x69452),f50(x69451,x69453)))+P1(f331(f331(f333(x69451),f661(x69453,x69452,x69451)),x69453))
% 51.10/50.83 [6950]~P76(x69501)+P1(f331(f331(f241(x69501),f331(f331(f3(x69501),x69502),x69503)),f2(x69501)))+~P1(f331(f331(f241(x69501),x69502),x69503))
% 51.10/50.83 [6951]~P76(x69511)+P1(f331(f331(f240(x69511),f331(f331(f3(x69511),x69512),x69513)),f2(x69511)))+~P1(f331(f331(f240(x69511),x69512),x69513))
% 51.10/50.83 [6989]~P1(f331(f331(f287(a1),x69891),f57(a1,x69892,x69893)))+~P1(f331(f331(f287(a1),x69891),x69893))+P1(f331(f331(f287(a1),x69891),x69892))
% 51.10/50.83 [6996]P1(f331(x69961,x69962))+P1(f331(f331(f240(a847),f442(x69961,x69963)),x69963))+~P1(f331(f331(f333(a847),x69962),f303(a847,f2(a847),x69963)))
% 51.10/50.83 [7038]~E(f331(f331(f8(x70381,a847),x70382),x70383),f85(a847))+~P1(f331(f68(x70381),x70383))+P1(f331(f331(f333(x70381),f485(x70382,x70383,x70381)),x70383))
% 51.10/50.83 [7039]~P1(f331(x70391,x70393))+P1(f331(f331(f240(a847),f449(x70391,x70392)),x70392))+~P1(f331(f331(f333(a847),x70393),f303(a847,f2(a847),x70392)))
% 51.10/50.83 [7077]~P7(x70771)+P1(f331(f331(f333(x70771),f662(x70773,x70772,x70771)),x70772))+P1(f331(f331(f240(x70771),f49(x70771,x70772)),x70773))
% 51.10/50.83 [7107]~E(f331(f331(f8(x71071,a847),x71072),x71073),f331(a119,f2(a847)))+~P1(f331(f68(x71071),x71073))+P1(f331(f331(f333(x71071),f498(x71072,x71073,x71071)),x71073))
% 51.10/50.83 [7118]E(x71181,f2(a847))+P1(f331(x71182,f57(a847,x71183,x71181)))+P1(f331(f331(f241(a847),f795(x71181,x71183,x71182)),x71181))
% 51.10/50.83 [7240]~P1(f331(x72401,x72402))+P1(f331(x72401,f57(a847,x72402,x72403)))+P1(f331(f331(f241(a847),f795(x72403,x72402,x72401)),x72403))
% 51.10/50.83 [7367]E(x73671,f120(x73672))+~P1(f331(f331(f333(f848(x73672)),x73671),f153(x73672,x73673)))+P1(f331(f331(f333(x73672),f748(x73673,x73671,x73672)),x73673))
% 51.10/50.83 [7387]~P102(x73871)+E(f331(f331(f108(f854(x73871,a840)),f331(f331(f310(x73871),x73872),f184(f854(x73871,a840)))),f306(x73871,x73872,x73873)),f331(f302(x73871,x73872),x73873))+~P1(f331(f331(f241(x73871),x73872),x73873))
% 51.10/50.83 [7412]~P102(x74121)+E(f331(f331(f108(f854(x74121,a840)),f331(f331(f310(x74121),x74122),f184(f854(x74121,a840)))),f305(x74121,x74122,x74123)),f303(x74121,x74122,x74123))+~P1(f331(f331(f240(x74121),x74122),x74123))
% 51.10/50.83 [7525]~P102(x75251)+P1(f331(f331(f241(x75251),x75252),x75253))+~P1(f331(f331(f241(f854(x75251,a840)),f331(f265(x75251),x75252)),f331(f265(x75251),x75253)))
% 51.10/50.83 [7526]~P88(x75261)+P1(f331(f331(f240(x75261),x75262),x75263))+~P1(f331(f331(f240(f854(x75261,a840)),f331(f266(x75261),x75263)),f331(f266(x75261),x75262)))
% 51.10/50.83 [7527]~P102(x75271)+P1(f331(f331(f240(x75271),x75272),x75273))+~P1(f331(f331(f240(f854(x75271,a840)),f331(f304(x75271),x75273)),f331(f304(x75271),x75272)))
% 51.10/50.83 [7528]~P88(x75281)+P1(f331(f331(f240(x75281),x75282),x75283))+~P1(f331(f331(f240(f854(x75281,a840)),f331(f301(x75281),x75282)),f331(f301(x75281),x75283)))
% 51.10/50.83 [7529]~P102(x75291)+P1(f331(f331(f240(x75291),x75292),x75293))+~P1(f331(f331(f240(f854(x75291,a840)),f331(f265(x75291),x75292)),f331(f265(x75291),x75293)))
% 51.10/50.83 [7553]~P76(x75531)+~P1(f331(f331(f241(x75531),f331(f331(f3(x75531),x75532),x75533)),f2(x75531)))+P1(f331(f331(f241(x75531),x75532),x75533))
% 51.10/50.83 [7554]~P76(x75541)+~P1(f331(f331(f240(x75541),f331(f331(f3(x75541),x75542),x75543)),f2(x75541)))+P1(f331(f331(f240(x75541),x75542),x75543))
% 51.10/50.83 [7714]E(x77141,f2(a847))+~E(f331(f137(a847,a847,f87(a847),x77142),x77143),f2(a847))+~P1(f331(f331(f333(a847),x77141),f331(f163(a847),x77143)))
% 51.10/50.83 [7718]~P7(x77181)+~P1(f331(f331(f240(x77181),f662(x77183,x77182,x77181)),x77183))+P1(f331(f331(f240(x77181),f49(x77181,x77182)),x77183))
% 51.10/50.83 [7869]P1(f331(f331(f240(a1),f2(a1)),f789(x78691,x78692,x78693)))+P1(f331(f331(x78692,f331(f331(f48(a1),x78691),x78693)),f57(a1,x78691,x78693)))+~P1(f331(f331(f241(a1),f2(a1)),x78693))
% 51.10/50.83 [7962]E(x79621,x79622)+~E(f331(f185(f848(x79623)),x79621),f331(f185(f848(x79623)),x79622))+~P1(f331(f331(f259(x79623,x79623,a840),a328),f712(x79623,x79621,x79622)))
% 51.10/50.83 [8028]~P34(x80282,x80283)+E(x80281,f184(f854(x80282,a840)))+~P1(f331(f331(f240(f854(x80282,a840)),x80281),f331(f285(x80282,x80282,x80283),x80281)))
% 51.10/50.83 [8056]~P61(x80561)+~P1(f331(f331(f240(x80561),x80562),f331(f331(f87(x80561),x80563),f801(x80563,x80562,x80561))))+P1(f331(f331(f240(x80561),x80562),x80563))
% 51.10/50.83 [8092]P45(x80921,x80922,x80923)+P1(f331(f331(f333(x80921),f585(x80923,x80922,x80921)),x80922))+P1(f331(f331(f333(f853(x80921,x80921)),f586(x80923,x80922,x80921)),x80923))
% 51.10/50.83 [8115]P1(f331(f331(x81152,f331(f331(f48(a1),x81151),x81153)),f57(a1,x81151,x81153)))+~P1(f331(f331(f241(a1),f2(a1)),x81153))+P1(f331(f331(f241(a1),f789(x81151,x81152,x81153)),x81153))
% 51.10/50.83 [8139]E(f331(f311(a847,a847,f331(f331(f9(a847,a847,a847),f3(a847)),x81391)),f331(f302(a847,x81392),x81393)),f184(f854(a847,a840)))+P1(f331(f331(f241(a847),x81391),x81393))+P1(f331(f331(f241(a847),x81392),x81393))
% 51.10/50.83 [8243]E(f331(f311(a847,a847,f331(f331(f9(a847,a847,a847),f3(a847)),x82431)),f331(f302(a847,x82432),x82433)),f331(f331(f310(a847),f2(a847)),f184(f854(a847,a840))))+P1(f331(f331(f241(a847),x82431),x82433))+~P1(f331(f331(f241(a847),x82432),x82433))
% 51.10/50.83 [8258]~P102(x82581)+E(f144(x82581,x82581,f7(x82581),x82582,x82583),x82583)+~P1(f331(f331(f333(x82581),x82582),f331(f163(x82581),x82583)))
% 51.10/50.83 [8273]P27(x82731,x82731,x82732,x82733)+~P1(f331(f68(x82731),x82733))+~P1(f331(f331(f240(f854(x82731,a840)),x82733),f331(f311(x82731,x82731,x82732),x82733)))
% 51.10/50.83 [8300]E(f331(f331(f87(a1),f331(f331(f88(a1),x83001),f790(x83002,x83003,x83001))),f789(x83002,x83003,x83001)),x83002)+P1(f331(f331(x83003,f331(f331(f48(a1),x83002),x83001)),f57(a1,x83002,x83001)))+~P1(f331(f331(f241(a1),f2(a1)),x83001))
% 51.10/50.83 [8387]~P142(x83871,x83873)+~P37(f331(a29,a861),x83873,f331(a119,a862),x83872)+P143(x83871,f331(f331(f331(a193,f331(f331(a194,x83872),f331(a196,a859))),a857),f331(f331(a196,x83872),a28)))
% 51.10/50.83 [8528]~P1(f331(f331(x85281,f790(x85282,x85281,x85283)),f789(x85282,x85281,x85283)))+P1(f331(f331(x85281,f331(f331(f48(a1),x85282),x85283)),f57(a1,x85282,x85283)))+~P1(f331(f331(f241(a1),f2(a1)),x85283))
% 51.10/50.83 [9315]~P1(f331(f68(x93151),x93152))+~P1(f331(f331(f333(x93151),x93153),x93152))+P1(f331(f331(f241(a847),f331(f47(x93151),f331(f331(f3(f854(x93151,a840)),x93152),f331(f331(f310(x93151),x93153),f184(f854(x93151,a840)))))),f331(f47(x93151),x93152)))
% 51.10/50.83 [9908]P45(x99081,x99082,x99083)+~P1(f331(f331(f259(x99081,x99081,a840),f331(f331(f9(x99081,f854(x99081,a840),f854(x99081,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x99081,a840),f854(x99081,a840)),x99081),f10(a840,a840,x99081)),f331(f331(f10(a840,f854(a840,a840),x99081),a329),f331(f331(f9(x99081,f854(x99081,a840),a840),f333(x99081)),x99082)))),f331(f331(f9(x99081,f854(x99081,a840),a840),f333(x99081)),x99082))),f586(x99083,x99082,x99081)))+P1(f331(f331(f333(x99081),f585(x99083,x99082,x99081)),x99082))
% 51.10/50.83 [5326]~P114(x53262)+E(x53261,f2(x53262))+E(f331(f331(f291(x53262),x53263),f331(f86(x53262),x53261)),f331(f86(x53262),f331(f331(f291(x53262),x53263),x53261)))
% 51.10/50.83 [5459]~E(x54593,f184(f854(x54591,a840)))+~E(x54592,f184(f854(x54591,a840)))+E(f331(f331(f108(f854(x54591,a840)),x54592),x54593),f184(f854(x54591,a840)))
% 51.10/50.83 [5513]~E(x55133,f2(a847))+~P1(f331(x55131,f2(a847)))+P1(f331(x55131,f331(f331(f48(a847),x55132),x55133)))
% 51.10/50.83 [5514]~E(x55143,f2(a847))+~P1(f331(x55141,f2(a847)))+P1(f331(x55141,f331(f331(f48(a847),x55142),x55143)))
% 51.10/50.83 [5663]~P61(x56632)+E(x56631,f2(x56632))+E(f331(f331(f291(x56632),f331(f82(x56632),x56633)),f331(f82(x56632),x56631)),f331(f82(x56632),f331(f331(f291(x56632),x56633),x56631)))
% 51.10/50.83 [5759]~P87(x57591)+~E(x57592,f85(x57591))+P1(f331(f331(f287(x57591),x57592),f331(f331(f250(x57591),x57592),x57593)))
% 51.10/50.83 [5776]~P5(x57761)+E(f331(f331(f88(x57761),x57762),f331(f331(f48(x57761),x57763),x57762)),x57763)+~P1(f331(f331(f287(x57761),x57762),x57763))
% 51.10/50.83 [5829]~P1(f331(f68(x58291),x58293))+E(f331(f47(x58291),f331(f331(f310(x58291),x58292),x58293)),f331(a119,f331(f47(x58291),x58293)))+P1(f331(f331(f333(x58291),x58292),x58293))
% 51.10/50.83 [5830]~P1(f331(f68(x58301),x58303))+E(f331(f47(x58301),f331(f331(f310(x58301),x58302),x58303)),f331(a119,f331(f47(x58301),x58303)))+P1(f331(f331(f333(x58301),x58302),x58303))
% 51.10/50.83 [5906]~E(x59062,f2(a847))+P1(f331(x59061,f2(a847)))+~P1(f331(x59061,f331(f331(f48(a847),x59063),x59062)))
% 51.10/50.83 [5925]~P1(f331(f68(x59251),x59253))+E(f331(f47(x59251),f331(f331(f310(x59251),x59252),x59253)),f331(f47(x59251),x59253))+~P1(f331(f331(f333(x59251),x59252),x59253))
% 51.10/50.83 [5959]~P1(f331(f68(x59591),x59593))+E(f331(f47(x59591),f331(f331(f310(x59591),x59592),x59593)),f331(f331(f87(a847),f85(a847)),f331(f47(x59591),x59593)))+P1(f331(f331(f333(x59591),x59592),x59593))
% 51.10/50.83 [5966]~P6(x59661)+E(f331(f331(f48(x59661),x59662),f331(f86(x59661),x59663)),f331(f86(x59661),f331(f331(f48(x59661),x59662),x59663)))+~P1(f331(f331(f287(x59661),x59663),x59662))
% 51.10/50.83 [6082]E(f331(f331(f87(a847),x60821),f792(x60821,x60822,x60823)),x60822)+~P1(f331(x60823,f2(a847)))+P1(f331(x60823,f331(f331(f3(a847),x60822),x60821)))
% 51.10/50.83 [6083]E(f331(f331(f87(a847),x60831),f800(x60831,x60832,x60833)),x60832)+~P1(f331(x60833,f2(a847)))+P1(f331(x60833,f331(f331(f3(a847),x60832),x60831)))
% 51.10/50.83 [6107]~P6(x61071)+E(f331(f331(f48(x61071),f331(f86(x61071),x61072)),x61073),f331(f86(x61071),f331(f331(f48(x61071),x61072),x61073)))+~P1(f331(f331(f287(x61071),x61073),x61072))
% 51.10/50.83 [6130]~P7(x61301)+~P1(f331(f68(x61301),x61303))+E(f331(f331(f71(x61301,x61301,f108(x61301)),x61302),x61303),f331(f331(f108(x61301),x61302),f49(x61301,x61303)))
% 51.10/50.83 [6131]~P7(x61311)+~P1(f331(f68(x61311),x61313))+E(f331(f331(f71(x61311,x61311,f109(x61311)),x61312),x61313),f331(f331(f109(x61311),x61312),f50(x61311,x61313)))
% 51.10/50.83 [6137]~P91(x61371)+~E(f331(f111(x61371),x61372),f331(f111(x61371),x61373))+P31(x61371,f331(f111(x61371),f331(f331(f87(a1),x61372),f331(f86(a1),x61373))))
% 51.10/50.83 [6144]~P133(x61441)+E(f331(f331(f3(x61441),f331(f107(x61441),x61442)),f331(f107(x61441),x61443)),f331(f107(x61441),f331(f331(f3(a847),x61442),x61443)))+~P1(f331(f331(f240(a847),x61443),x61442))
% 51.10/50.83 [6150]~P106(x61501)+~P1(f331(f331(f287(x61501),x61502),x61503))+P1(f331(f331(f287(x61501),f331(f86(x61501),x61502)),x61503))
% 51.10/50.83 [6151]~P86(x61511)+~P1(f331(f331(f287(x61511),x61512),x61513))+P1(f331(f331(f287(x61511),f331(f82(x61511),x61512)),x61513))
% 51.10/50.83 [6236]E(f331(f331(f87(a847),x62361),f792(x62361,x62362,x62363)),x62362)+P1(f331(f331(f241(a847),x62362),x62361))+P1(f331(x62363,f331(f331(f3(a847),x62362),x62361)))
% 51.10/50.83 [6237]E(f331(f331(f87(a847),x62371),f800(x62371,x62372,x62373)),x62372)+P1(f331(f331(f241(a847),x62372),x62371))+P1(f331(x62373,f331(f331(f3(a847),x62372),x62371)))
% 51.10/50.83 [6254]~P86(x62541)+E(f331(f331(f88(x62541),f331(f82(x62541),x62542)),x62543),f331(f82(x62541),f331(f331(f88(x62541),x62542),x62543)))+~P1(f331(f331(f240(x62541),f2(x62541)),x62543))
% 51.10/50.83 [6255]~P60(x62551)+E(f331(f331(f291(x62551),f331(f82(x62551),x62552)),x62553),f331(f82(x62551),f331(f331(f291(x62551),x62552),x62553)))+~P1(f331(f331(f241(x62551),f2(x62551)),x62553))
% 51.10/50.83 [6264]~P97(x62641)+~P1(f331(f68(x62641),x62643))+E(f331(f331(f71(x62641,x62641,f109(x62641)),x62642),x62643),f12(x62641,f331(f331(f310(x62641),x62642),x62643)))
% 51.10/50.83 [6265]~P97(x62651)+~P1(f331(f68(x62651),x62653))+E(f331(f331(f71(x62651,x62651,f108(x62651)),x62652),x62653),f15(x62651,f331(f331(f310(x62651),x62652),x62653)))
% 51.10/50.83 [6266]~P102(x62661)+~P1(f331(f68(x62661),x62663))+E(f331(f331(f71(x62661,x62661,f239(x62661)),x62662),x62663),f16(x62661,f331(f331(f310(x62661),x62662),x62663)))
% 51.10/50.83 [6267]~P102(x62671)+~P1(f331(f68(x62671),x62673))+E(f331(f331(f71(x62671,x62671,f244(x62671)),x62672),x62673),f17(x62671,f331(f331(f310(x62671),x62672),x62673)))
% 51.10/50.83 [6311]E(x63111,f120(x63112))+~E(f169(x63112,x63113),f120(f848(x63112)))+~P1(f331(f331(f333(f848(x63112)),x63111),f331(f163(f848(x63112)),x63113)))
% 51.10/50.83 [6330]~P87(x63301)+~P1(f331(f331(f241(a847),f2(a847)),x63303))+P1(f331(f331(f287(x63301),x63302),f331(f331(f250(x63301),x63302),x63303)))
% 51.10/50.83 [6361]~P1(f331(f132(x63611),x63613))+P1(f331(f331(f333(x63611),x63612),f331(f163(x63611),x63613)))+P1(f331(f132(x63611),f331(f331(f145(x63611),x63612),x63613)))
% 51.10/50.83 [6373]~P94(x63731)+~P1(f331(f68(x63731),x63733))+E(f331(f70(x63731,f88(x63731)),f331(f331(f310(x63731),x63732),x63733)),f331(f331(f71(x63731,x63731,f88(x63731)),x63732),x63733))
% 51.10/50.83 [6394]~P102(x63941)+~P1(f331(f68(x63941),x63943))+E(f13(x63941,f239(x63941),f331(f331(f310(x63941),x63942),x63943)),f331(f331(f71(x63941,x63941,f239(x63941)),x63942),x63943))
% 51.10/50.83 [6395]~P102(x63951)+~P1(f331(f68(x63951),x63953))+E(f14(x63951,f244(x63951),f331(f331(f310(x63951),x63952),x63953)),f331(f331(f71(x63951,x63951,f244(x63951)),x63952),x63953))
% 51.10/50.83 [6396]P1(f331(x63961,f2(a847)))+~P1(f331(f331(f241(a847),x63962),x63963))+~P1(f331(x63961,f331(f331(f3(a847),x63962),x63963)))
% 51.10/50.83 [6397]P1(f331(x63971,f2(a847)))+~P1(f331(f331(f241(a847),x63972),x63973))+~P1(f331(x63971,f331(f331(f3(a847),x63972),x63973)))
% 51.10/50.83 [6416]~P86(x64161)+P1(f331(f331(f241(x64161),x64162),x64163))+~P1(f331(f331(f241(x64161),f331(f82(x64161),x64162)),x64163))
% 51.10/50.83 [6417]~P78(x64171)+P1(f331(f331(f240(x64171),x64172),x64173))+~P1(f331(f331(f240(x64171),f331(f82(x64171),x64172)),x64173))
% 51.10/50.83 [6418]~P78(x64181)+P1(f331(f331(f240(x64181),x64182),x64183))+~P1(f331(f331(f240(x64181),f331(f82(x64181),x64182)),x64183))
% 51.10/50.83 [6419]~P86(x64191)+P1(f331(f331(f287(x64191),x64192),x64193))+~P1(f331(f331(f287(x64191),f331(f82(x64191),x64192)),x64193))
% 51.10/50.83 [6420]~P106(x64201)+P1(f331(f331(f287(x64201),x64202),x64203))+~P1(f331(f331(f287(x64201),f331(f86(x64201),x64202)),x64203))
% 51.10/50.83 [6439]E(x64391,f120(x64392))+E(f331(f136(x64392),f331(f331(f133(x64392),x64393),x64391)),f331(f331(f155(x64392),x64391),x64393))+~P1(f331(f331(f241(a847),x64393),f331(f185(f848(x64392)),x64391)))
% 51.10/50.83 [6492]~P1(f331(x64921,x64923))+P1(f331(x64921,f487(x64921,x64922)))+~P1(f331(f331(f333(a847),x64923),f331(f302(a847,f2(a847)),x64922)))
% 51.10/50.83 [6515]P1(f331(x65151,x65152))+~P1(f331(f331(f241(a847),x65152),x65153))+P1(f331(f331(f333(a847),f482(x65151,x65153)),f331(f302(a847,f2(a847)),x65153)))
% 51.10/50.83 [6530]~P85(x65301)+~P1(f331(f331(f241(x65301),f2(x65301)),x65302))+P1(f331(f331(f241(x65301),f2(x65301)),f331(f331(f250(x65301),x65302),x65303)))
% 51.10/50.83 [6532]~P85(x65321)+~P1(f331(f331(f240(x65321),f2(x65321)),x65322))+P1(f331(f331(f240(x65321),f2(x65321)),f331(f331(f250(x65321),x65322),x65323)))
% 51.10/50.83 [6533]~P85(x65331)+~P1(f331(f331(f240(x65331),f85(x65331)),x65332))+P1(f331(f331(f240(x65331),f85(x65331)),f331(f331(f250(x65331),x65332),x65333)))
% 51.10/50.83 [6557]~P1(f331(x65571,x65573))+~P1(f331(f331(f241(a847),x65573),x65572))+P1(f331(f331(f333(a847),f481(x65571,x65572)),f331(f302(a847,f2(a847)),x65572)))
% 51.10/50.83 [6561]P1(f331(f68(x65611),x65612))+~P1(f331(f68(x65611),x65613))+~P1(f331(f331(f240(f854(x65611,a840)),x65612),x65613))
% 51.10/50.83 [6562]P1(f331(f68(x65621),x65622))+~P1(f331(f68(x65621),x65623))+~P1(f331(f331(f240(f854(x65621,a840)),x65622),x65623))
% 51.10/50.83 [6571]~P1(f331(f331(f287(a847),x65711),x65712))+~P1(f331(f331(f287(a847),x65711),x65713))+P1(f331(f331(f287(a847),x65711),f331(f331(f3(a847),x65712),x65713)))
% 51.10/50.83 [6572]P1(f331(x65721,x65722))+~P1(f331(x65721,f483(x65721,x65723)))+~P1(f331(f331(f333(a847),x65722),f331(f302(a847,f2(a847)),x65723)))
% 51.10/50.83 [6585]E(x65851,f2(a847))+P1(f331(x65852,f787(x65851,x65853,x65852)))+~P1(f331(x65852,f331(f331(f48(a847),x65853),x65851)))
% 51.10/50.83 [6594]~P118(x65942)+E(x65941,f2(x65942))+~E(f331(f331(f87(x65942),f331(f331(f88(x65942),x65943),x65943)),f331(f331(f88(x65942),x65941),x65941)),f2(x65942))
% 51.10/50.83 [6595]~P118(x65952)+E(x65951,f2(x65952))+~E(f331(f331(f87(x65952),f331(f331(f88(x65952),x65951),x65951)),f331(f331(f88(x65952),x65953),x65953)),f2(x65952))
% 51.10/50.83 [6642]E(x66421,f2(a847))+~P1(f331(x66422,f794(x66421,x66423,x66422)))+P1(f331(x66422,f331(f331(f48(a847),x66423),x66421)))
% 51.10/50.83 [6647]~P102(x66471)+~P16(x66471,x66473)+P16(x66471,f331(f331(f143(x66471,x66471,f7(x66471)),x66472),x66473))
% 51.10/50.83 [6691]P1(f331(x66911,f787(x66912,x66913,x66911)))+P1(f331(x66911,f2(a847)))+~P1(f331(x66911,f331(f331(f48(a847),x66913),x66912)))
% 51.10/50.83 [6697]~P91(x66971)+E(f331(f111(x66971),x66972),f331(f111(x66971),x66973))+~P31(x66971,f331(f111(x66971),f331(f331(f87(a1),x66972),f331(f86(a1),x66973))))
% 51.10/50.83 [6769]E(x67691,f2(a1))+E(x67692,f2(a1))+~P1(f331(f61(x67692,x67692),f331(f331(f249(a1,a1),x67693),x67691)))
% 51.10/50.83 [6770]E(x67701,f85(a1))+E(x67702,f2(a1))+~P1(f331(f61(x67702,x67702),f331(f331(f249(a1,a1),x67701),x67703)))
% 51.10/50.83 [6784]P1(f331(x67841,x67842))+P1(f331(f331(f241(a847),f483(x67841,x67843)),x67843))+~P1(f331(f331(f333(a847),x67842),f331(f302(a847,f2(a847)),x67843)))
% 51.10/50.83 [6809]~P1(f331(x68091,f794(x68093,x68092,x68091)))+~P1(f331(x68091,f2(a847)))+P1(f331(x68091,f331(f331(f48(a847),x68092),x68093)))
% 51.10/50.83 [6810]~P1(f331(x68101,f792(x68103,x68102,x68101)))+~P1(f331(x68101,f2(a847)))+P1(f331(x68101,f331(f331(f3(a847),x68102),x68103)))
% 51.10/50.83 [6811]~P1(f331(x68111,f800(x68113,x68112,x68111)))+~P1(f331(x68111,f2(a847)))+P1(f331(x68111,f331(f331(f3(a847),x68112),x68113)))
% 51.10/50.83 [6831]~P1(f331(x68311,x68313))+P1(f331(f331(f241(a847),f487(x68311,x68312)),x68312))+~P1(f331(f331(f333(a847),x68313),f331(f302(a847,f2(a847)),x68312)))
% 51.10/50.83 [6832]E(f331(f331(f3(a847),f331(f331(f3(a847),x68321),x68322)),f331(f331(f3(a847),x68323),x68322)),f331(f331(f3(a847),x68321),x68323))+~P1(f331(f331(f240(a847),x68322),x68321))+~P1(f331(f331(f240(a847),x68322),x68323))
% 51.10/50.83 [6865]~P76(x68651)+~P1(f331(f331(f241(x68651),f331(f86(x68651),x68653)),x68652))+P1(f331(f331(f241(x68651),f331(f86(x68651),x68652)),x68653))
% 51.10/50.83 [6866]~P76(x68661)+~P1(f331(f331(f241(x68661),f331(f86(x68661),x68663)),x68662))+P1(f331(f331(f241(x68661),f331(f86(x68661),x68662)),x68663))
% 51.10/50.83 [6867]~P86(x68671)+~P1(f331(f331(f241(x68671),f331(f82(x68671),x68672)),x68673))+P1(f331(f331(f241(x68671),f331(f86(x68671),x68672)),x68673))
% 51.10/50.83 [6868]~P76(x68681)+~P1(f331(f331(f240(x68681),f331(f86(x68681),x68683)),x68682))+P1(f331(f331(f240(x68681),f331(f86(x68681),x68682)),x68683))
% 51.10/50.83 [6869]~P76(x68691)+~P1(f331(f331(f240(x68691),f331(f86(x68691),x68693)),x68692))+P1(f331(f331(f240(x68691),f331(f86(x68691),x68692)),x68693))
% 51.10/50.83 [6870]~P78(x68701)+~P1(f331(f331(f240(x68701),f331(f82(x68701),x68702)),x68703))+P1(f331(f331(f240(x68701),f331(f86(x68701),x68702)),x68703))
% 51.10/50.83 [6871]~P78(x68711)+~P1(f331(f331(f240(x68711),f331(f82(x68711),x68712)),x68713))+P1(f331(f331(f240(x68711),f331(f86(x68711),x68712)),x68713))
% 51.10/50.83 [6874]~P1(f331(f331(f287(a1),x68741),x68743))+P1(f331(f331(f287(a1),x68741),x68742))+~P1(f331(f331(f287(a1),x68741),f331(f331(f3(a1),x68742),x68743)))
% 51.10/50.83 [6907]~P1(f331(x69073,f792(x69072,x69071,x69073)))+P1(f331(f331(f241(a847),x69071),x69072))+P1(f331(x69073,f331(f331(f3(a847),x69071),x69072)))
% 51.10/50.83 [6908]~P1(f331(x69083,f800(x69082,x69081,x69083)))+P1(f331(f331(f241(a847),x69081),x69082))+P1(f331(x69083,f331(f331(f3(a847),x69081),x69082)))
% 51.10/50.83 [6954]~E(f666(x69543,x69542,x69541),f667(x69543,x69542,x69541))+E(f331(f331(f109(f854(x69541,a840)),x69542),f49(f854(x69541,a840),x69543)),f184(f854(x69541,a840)))+P1(f331(f331(f333(f854(x69541,a840)),x69542),x69543))
% 51.10/50.83 [6963]~P1(f331(f68(x69631),x69633))+P1(f331(f68(x69631),f50(f854(x69631,a840),x69632)))+~P1(f331(f331(f333(f854(x69631,a840)),x69633),x69632))
% 51.10/50.83 [7024]~P102(x70241)+E(f331(f331(f108(f854(x70241,a840)),f331(f302(x70241,x70242),x70243)),f331(f331(f310(x70241),x70243),f184(f854(x70241,a840)))),f303(x70241,x70242,x70243))+~P1(f331(f331(f240(x70241),x70242),x70243))
% 51.10/50.83 [7027]E(x70271,f2(a847))+P1(f331(f331(f241(a847),f796(x70271,x70273,x70272)),x70271))+P1(f331(x70272,f331(f331(f48(a847),x70273),x70271)))
% 51.10/50.83 [7061]E(x70611,x70612)+~P1(f331(f331(f240(f854(x70613,a840)),x70611),x70612))+P1(f331(f331(f241(f854(x70613,a840)),x70611),x70612))
% 51.10/50.83 [7062]E(x70621,x70622)+~P1(f331(f331(f240(f854(x70623,a840)),x70621),x70622))+P1(f331(f331(f241(f854(x70623,a840)),x70621),x70622))
% 51.10/50.83 [7074]E(x70741,x70742)+~E(f331(f185(f848(x70743)),x70741),f331(f185(f848(x70743)),x70742))+P1(f331(f331(f241(a847),f724(x70743,x70741,x70742)),f331(f185(f848(x70743)),x70742)))
% 51.10/50.83 [7119]P10(x71191,x71192,x71193)+~E(f331(f269(x71191,x71191),x71193),x71192)+~E(f331(f331(f289(x71191,x71191,x71191),f331(f286(x71191,x71191),x71193)),x71193),x71193)
% 51.10/50.83 [7199]E(x71991,f2(a1))+~P1(f331(f331(f287(a1),x71992),x71993))+P1(f331(f331(f287(a1),f331(f331(f88(a1),x71991),x71992)),f331(f331(f88(a1),x71991),x71993)))
% 51.10/50.83 [7202]~P1(f331(x72021,f2(a847)))+P1(f331(f331(f241(a847),f796(x72023,x72022,x72021)),x72023))+P1(f331(x72021,f331(f331(f48(a847),x72022),x72023)))
% 51.10/50.83 [7215]~P102(x72151)+E(f331(f331(f108(f854(x72151,a840)),f306(x72151,x72152,x72153)),f331(f331(f310(x72151),x72153),f184(f854(x72151,a840)))),f305(x72151,x72152,x72153))+~P1(f331(f331(f241(x72151),x72152),x72153))
% 51.10/50.83 [7320]~P1(f331(f68(x73201),x73203))+P1(f331(f331(f241(a847),f331(f47(x73201),x73202)),f331(f47(x73201),x73203)))+~P1(f331(f331(f241(f854(x73201,a840)),x73202),x73203))
% 51.10/50.83 [7321]~P1(f331(f68(x73211),x73213))+P1(f331(f331(f240(a847),f331(f47(x73211),x73212)),f331(f47(x73211),x73213)))+~P1(f331(f331(f240(f854(x73211,a840)),x73212),x73213))
% 51.10/50.83 [7362]~P1(f331(x73623,x73622))+P1(f331(f331(f191(x73621),x73622),f541(x73622,x73621,x73623)))+~P1(f331(f331(f191(f37(x73623,x73621)),x73622),x73622))
% 51.10/50.83 [7460]E(x74601,x74602)+~P1(f331(f331(f240(f854(x74603,a840)),x74602),x74601))+~P1(f331(f331(f240(f854(x74603,a840)),x74601),x74602))
% 51.10/50.83 [7461]E(x74611,x74612)+~P1(f331(f331(f240(f854(x74613,a840)),x74612),x74611))+~P1(f331(f331(f240(f854(x74613,a840)),x74611),x74612))
% 51.10/50.83 [7464]~P102(x74641)+P16(x74641,x74642)+~P16(x74641,f331(f331(f143(x74641,x74641,f7(x74641)),x74643),x74642))
% 51.10/50.83 [7533]~P1(f331(f331(f241(a847),x75333),x75332))+~P1(f331(f331(f241(a847),x75333),x75331))+P1(f331(f331(f241(a847),f331(f331(f3(a847),x75331),x75332)),f331(f331(f3(a847),x75331),x75333)))
% 51.10/50.83 [7534]~P1(f331(f331(f241(a847),x75341),x75343))+~P1(f331(f331(f240(a847),x75342),x75341))+P1(f331(f331(f241(a847),f331(f331(f3(a847),x75341),x75342)),f331(f331(f3(a847),x75343),x75342)))
% 51.10/50.83 [7551]~P1(f331(f331(f241(a1),x75512),f2(a1)))+~P1(f331(f331(f240(a1),x75513),x75511))+P1(f331(f331(f240(a1),f331(f331(f48(a1),x75511),x75512)),f331(f331(f48(a1),x75513),x75512)))
% 51.10/50.83 [7568]~P1(f331(f331(f241(a847),f2(a847)),x75681))+~P1(f331(f331(f241(a847),x75682),x75683))+P1(f331(f331(f241(a847),f331(f331(f88(a847),x75681),x75682)),f331(f331(f88(a847),x75681),x75683)))
% 51.10/50.83 [7569]~P1(f331(f331(f241(a847),f2(a847)),x75691))+~P1(f331(f331(f241(a847),x75692),x75693))+P1(f331(f331(f241(a847),f331(f331(f88(a847),x75691),x75692)),f331(f331(f88(a847),x75691),x75693)))
% 51.10/50.83 [7570]~P1(f331(f331(f241(a847),f2(a847)),x75702))+~P1(f331(f331(f241(a847),x75701),x75703))+P1(f331(f331(f241(a847),f331(f331(f88(a847),x75701),x75702)),f331(f331(f88(a847),x75703),x75702)))
% 51.10/50.83 [7571]~P1(f331(f331(f241(a847),f2(a847)),x75712))+~P1(f331(f331(f241(a847),x75711),x75713))+P1(f331(f331(f241(a847),f331(f331(f88(a847),x75711),x75712)),f331(f331(f88(a847),x75713),x75712)))
% 51.10/50.83 [7572]~P1(f331(f331(f241(a847),f2(a847)),x75721))+~P1(f331(f331(f241(a847),x75722),x75723))+P1(f331(f331(f241(a847),f331(f331(f88(a847),x75721),x75722)),f331(f331(f88(a847),x75721),x75723)))
% 51.10/50.83 [7573]~P1(f331(f331(f241(a1),f2(a1)),x75731))+~P1(f331(f331(f241(a1),x75732),x75733))+P1(f331(f331(f241(a1),f331(f331(f88(a1),x75731),x75732)),f331(f331(f88(a1),x75731),x75733)))
% 51.10/50.83 [7574]~P1(f331(f331(f241(a847),f2(a847)),x75741))+~P1(f331(f331(f240(a847),x75742),x75743))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x75741),x75742)),f331(f331(f88(a847),x75741),x75743)))
% 51.10/50.83 [7575]~P1(f331(f331(f241(a847),f2(a847)),x75753))+~P1(f331(f331(f240(a847),x75753),x75752))+P1(f331(f331(f240(a847),f331(f331(f48(a847),x75751),x75752)),f331(f331(f48(a847),x75751),x75753)))
% 51.10/50.83 [7576]~P1(f331(f331(f241(a1),f2(a1)),x75762))+~P1(f331(f331(f240(a1),x75761),x75763))+P1(f331(f331(f240(a1),f331(f331(f48(a1),x75761),x75762)),f331(f331(f48(a1),x75763),x75762)))
% 51.10/50.83 [7577]~P1(f331(f331(f241(a847),f2(a847)),x75771))+~P1(f331(f331(f287(a847),x75772),x75773))+P1(f331(f331(f287(a847),f331(f331(f88(a847),x75771),x75772)),f331(f331(f88(a847),x75771),x75773)))
% 51.10/50.83 [7625]E(x76251,f2(a847))+E(f331(f331(f87(a847),f331(f331(f88(a847),x76251),f794(x76251,x76252,x76253))),f796(x76251,x76252,x76253)),x76252)+P1(f331(x76253,f331(f331(f48(a847),x76252),x76251)))
% 51.10/50.83 [7683]E(f331(f331(f87(a847),f331(f331(f88(a847),x76831),f794(x76831,x76832,x76833))),f796(x76831,x76832,x76833)),x76832)+~P1(f331(x76833,f2(a847)))+P1(f331(x76833,f331(f331(f48(a847),x76832),x76831)))
% 51.10/50.83 [7699]~P1(f331(f68(x76991),x76993))+P1(f331(f331(f333(x76991),f396(x76992,x76993,x76991)),x76993))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f11(x76991,a847),x76992),x76993)))
% 51.10/50.83 [7700]~P1(f331(f68(x77001),x77003))+P1(f331(f331(f333(x77001),f548(x77002,x77003,x77001)),x77003))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f11(x77001,a847),x77002),x77003)))
% 51.10/50.83 [7805]E(x78051,f2(a847))+P1(f331(f331(f287(a847),x78052),x78053))+~P1(f331(f331(f287(a847),f331(f331(f88(a847),x78051),x78052)),f331(f331(f88(a847),x78051),x78053)))
% 51.10/50.83 [7806]E(x78061,f2(a1))+P1(f331(f331(f287(a1),x78062),x78063))+~P1(f331(f331(f287(a1),f331(f331(f88(a1),x78061),x78062)),f331(f331(f88(a1),x78061),x78063)))
% 51.10/50.83 [7807]E(x78071,f2(a1))+P1(f331(f331(f287(a1),x78072),x78073))+~P1(f331(f331(f287(a1),f331(f331(f88(a1),x78071),x78072)),f331(f331(f88(a1),x78071),x78073)))
% 51.10/50.83 [7993]E(x79931,f184(f854(x79932,a840)))+E(x79931,f331(f331(f310(x79932),x79933),f184(f854(x79932,a840))))+~P1(f331(f331(f240(f854(x79932,a840)),x79931),f331(f331(f310(x79932),x79933),f184(f854(x79932,a840)))))
% 51.10/50.83 [8029]~P1(f331(f331(f241(a847),f2(a847)),x80293))+P1(f331(f331(f241(a847),x80291),x80292))+~P1(f331(f331(f241(a847),f331(f331(f88(a847),x80293),x80291)),f331(f331(f88(a847),x80293),x80292)))
% 51.10/50.83 [8030]~P1(f331(f331(f241(a847),f2(a847)),x80303))+P1(f331(f331(f241(a847),x80301),x80302))+~P1(f331(f331(f241(a847),f331(f331(f250(a847),x80303),x80301)),f331(f331(f250(a847),x80303),x80302)))
% 51.10/50.83 [8031]~P1(f331(f331(f241(a847),f2(a847)),x80313))+P1(f331(f331(f240(a847),x80311),x80312))+~P1(f331(f331(f240(a847),f331(f331(f88(a847),x80313),x80311)),f331(f331(f88(a847),x80313),x80312)))
% 51.10/50.83 [8032]~P1(f331(f331(f241(a847),f2(a847)),x80323))+P1(f331(f331(f240(a847),x80321),x80322))+~P1(f331(f331(f240(a847),f331(f331(f88(a847),x80323),x80321)),f331(f331(f88(a847),x80323),x80322)))
% 51.10/50.83 [8033]~P1(f331(f331(f241(a847),f85(a847)),x80333))+P1(f331(f331(f240(a847),x80331),x80332))+~P1(f331(f331(f287(a847),f331(f331(f250(a847),x80333),x80331)),f331(f331(f250(a847),x80333),x80332)))
% 51.10/50.83 [8034]~P1(f331(f331(f241(a847),f2(a847)),x80343))+P1(f331(f331(f240(a847),x80341),x80342))+~P1(f331(f331(f240(a847),f331(f331(f88(a847),x80341),x80343)),f331(f331(f88(a847),x80342),x80343)))
% 51.10/50.83 [8035]~P1(f331(f331(f241(a847),f2(a847)),x80353))+P1(f331(f331(f287(a847),x80351),x80352))+~P1(f331(f331(f287(a847),f331(f331(f88(a847),x80353),x80351)),f331(f331(f88(a847),x80353),x80352)))
% 51.10/50.83 [8036]~P1(f331(f331(f241(a847),f2(a847)),x80363))+P1(f331(f331(f287(a847),x80361),x80362))+~P1(f331(f331(f287(a847),f331(f331(f88(a847),x80363),x80361)),f331(f331(f88(a847),x80363),x80362)))
% 51.10/50.83 [8064]~P1(f331(x80641,x80643))+P1(f331(f331(f191(f37(x80641,x80642)),f541(x80643,x80642,x80641)),x80643))+~P1(f331(f331(f191(f37(x80641,x80642)),x80643),x80643))
% 51.10/50.83 [8072]~E(f331(f331(f109(f854(x80721,a840)),f667(x80723,x80722,x80721)),f666(x80723,x80722,x80721)),f184(f854(x80721,a840)))+E(f331(f331(f109(f854(x80721,a840)),x80722),f49(f854(x80721,a840),x80723)),f184(f854(x80721,a840)))+P1(f331(f331(f333(f854(x80721,a840)),x80722),x80723))
% 51.10/50.83 [8086]E(x80861,f120(x80862))+~E(f331(f137(f848(x80862),f848(x80862),f130(x80862),f120(x80862)),x80863),f120(x80862))+~P1(f331(f331(f333(f848(x80862)),x80861),f331(f163(f848(x80862)),x80863)))
% 51.10/50.83 [8087]E(x80871,f120(x80872))+~E(f331(f137(f848(x80872),f848(x80872),f130(x80872),f120(x80872)),x80873),f120(x80872))+~P1(f331(f331(f333(f848(x80872)),x80871),f331(f163(f848(x80872)),x80873)))
% 51.10/50.83 [8144]E(x81441,f184(f854(f854(x81442,a840),a840)))+P1(f331(f331(f333(f854(x81442,a840)),f664(x81443,x81441,x81442)),x81441))+P1(f331(f331(f240(f854(x81442,a840)),f50(f854(x81442,a840),x81441)),x81443))
% 51.10/50.83 [8150]~P68(x81501)+~P70(x81501)+E(f331(f331(f11(a1,x81501),f331(f331(f10(a847,x81501,a1),x81502),a112)),f331(f311(a847,a1,f107(a1)),x81503)),f331(f331(f11(a847,x81501),x81502),x81503))
% 51.10/50.83 [8151]~P68(x81511)+~P70(x81511)+E(f331(f331(f8(a1,x81511),f331(f331(f10(a847,x81511,a1),x81512),a112)),f331(f311(a847,a1,f107(a1)),x81513)),f331(f331(f8(a847,x81511),x81512),x81513))
% 51.10/50.83 [8189]~P1(f331(f68(x81891),x81893))+~P1(f331(f331(f241(a847),f2(a847)),f331(x81892,f396(x81892,x81893,x81891))))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f11(x81891,a847),x81892),x81893)))
% 51.10/50.83 [8190]~P1(f331(f68(x81901),x81903))+~P1(f331(f331(f241(a847),f2(a847)),f331(x81902,f548(x81902,x81903,x81901))))+P1(f331(f331(f241(a847),f2(a847)),f331(f331(f11(x81901,a847),x81902),x81903)))
% 51.10/50.83 [8226]~P59(x82262)+E(x82261,f85(x82262))+E(f331(f331(f291(x82262),f331(f331(f3(x82262),f331(f331(f250(x82262),x82261),x82263)),f85(x82262))),f331(f331(f3(x82262),x82261),f85(x82262))),f331(f331(f8(a847,x82262),f331(f250(x82262),x82261)),f331(f302(a847,f2(a847)),x82263)))
% 51.10/50.83 [8285]E(x82851,f2(a847))+~P1(f331(x82853,f331(f331(f48(a847),x82852),x82851)))+P1(f331(f331(f241(a847),x82852),f331(f331(f88(a847),x82851),f331(a119,f787(x82851,x82852,x82853)))))
% 51.10/50.83 [8306]P1(f331(x83061,f2(a847)))+~P1(f331(x83061,f331(f331(f48(a847),x83062),x83063)))+P1(f331(f331(f241(a847),x83062),f331(f331(f88(a847),x83063),f331(a119,f787(x83063,x83062,x83061)))))
% 51.10/50.83 [8343]E(x83431,f2(a847))+~P1(f331(x83433,f331(f331(f48(a847),x83432),x83431)))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x83431),f787(x83431,x83432,x83433))),x83432))
% 51.10/50.83 [8380]P1(f331(x83801,f2(a847)))+~P1(f331(x83801,f331(f331(f48(a847),x83803),x83802)))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x83802),f787(x83802,x83803,x83801))),x83803))
% 51.10/50.83 [8383]~P102(x83831)+E(f331(f331(f143(x83831,x83831,f7(x83831)),x83832),x83833),f144(x83831,x83831,f7(x83831),x83832,x83833))+P1(f331(f331(f333(x83831),x83832),f331(f163(x83831),x83833)))
% 51.10/50.83 [8424]~E(f331(x84243,f601(x84242,x84243,x84241)),f331(x84243,f603(x84242,x84243,x84241)))+~P56(x84241,f331(x84243,f602(x84242,x84243,x84241)))+P56(x84241,f331(f331(f51(x84242,f854(x84241,f854(x84241,a840))),f247(f854(x84242,a840))),x84243))
% 51.10/50.83 [8432]E(x84321,f184(f854(f854(x84322,a840),a840)))+~P1(f331(f331(f240(f854(x84322,a840)),f664(x84323,x84321,x84322)),x84323))+P1(f331(f331(f240(f854(x84322,a840)),f50(f854(x84322,a840),x84321)),x84323))
% 51.10/50.83 [8488]~P61(x84881)+~P1(f331(f331(f241(x84881),x84882),x84883))+P1(f331(f331(f241(x84881),x84882),f331(f331(f291(x84881),f331(f331(f87(x84881),x84882),x84883)),f331(f331(f87(x84881),f85(x84881)),f85(x84881)))))
% 51.10/50.83 [8531]~P1(f331(f331(x85311,f816(x85311,x85313,x85312)),f817(x85311,x85313,x85312)))+P1(f331(f331(x85311,x85312),x85313))+~P1(f331(f320(f853(a1,a1),a64),f331(f331(f249(a1,a1),x85312),x85313)))
% 51.10/50.83 [8532]~P1(f331(f331(x85321,f819(x85321,x85323,x85322)),f820(x85321,x85323,x85322)))+P1(f331(f331(x85321,x85322),x85323))+~P1(f331(f320(f853(a1,a1),a67),f331(f331(f249(a1,a1),x85322),x85323)))
% 51.10/50.83 [8533]~P1(f331(f331(x85331,f821(x85331,x85333,x85332)),f824(x85331,x85333,x85332)))+P1(f331(f331(x85331,x85332),x85333))+~P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),x85332),x85333)))
% 51.10/50.83 [8534]~P1(f331(f331(x85341,f825(x85341,x85343,x85342)),f826(x85341,x85343,x85342)))+P1(f331(f331(x85341,x85342),x85343))+~P1(f331(f320(f853(a847,a847),a221),f331(f331(f249(a847,a847),x85342),x85343)))
% 51.10/50.83 [8535]~P1(f331(f331(x85351,f730(x85351,x85353,x85352)),f733(x85351,x85353,x85352)))+P1(f331(f331(x85351,x85352),x85353))+~P1(f331(f320(f853(a1,a1),a173),f331(f331(f249(a1,a1),x85352),x85353)))
% 51.10/50.83 [8770]P1(f331(f331(x87701,x87702),x87703))+P1(f331(f320(f853(a847,a847),a221),f331(f331(f249(a847,a847),f825(x87701,x87703,x87702)),f826(x87701,x87703,x87702))))+~P1(f331(f320(f853(a847,a847),a221),f331(f331(f249(a847,a847),x87702),x87703)))
% 51.10/50.83 [8771]P1(f331(f331(x87711,x87712),x87713))+P1(f331(f320(f853(a1,a1),a64),f331(f331(f249(a1,a1),f816(x87711,x87713,x87712)),f817(x87711,x87713,x87712))))+~P1(f331(f320(f853(a1,a1),a64),f331(f331(f249(a1,a1),x87712),x87713)))
% 51.10/50.83 [8772]P1(f331(f331(x87721,x87722),x87723))+P1(f331(f320(f853(a1,a1),a67),f331(f331(f249(a1,a1),f819(x87721,x87723,x87722)),f820(x87721,x87723,x87722))))+~P1(f331(f320(f853(a1,a1),a67),f331(f331(f249(a1,a1),x87722),x87723)))
% 51.10/50.83 [8773]P1(f331(f331(x87731,x87732),x87733))+P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),f821(x87731,x87733,x87732)),f824(x87731,x87733,x87732))))+~P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),x87732),x87733)))
% 51.10/50.83 [8774]P1(f331(f331(x87741,x87742),x87743))+P1(f331(f320(f853(a1,a1),a173),f331(f331(f249(a1,a1),f730(x87741,x87743,x87742)),f733(x87741,x87743,x87742))))+~P1(f331(f320(f853(a1,a1),a173),f331(f331(f249(a1,a1),x87742),x87743)))
% 51.10/50.83 [9082]~P1(f331(f68(x90821),x90823))+P1(f331(f331(f333(f853(f854(x90821,a840),f854(x90821,a840))),f331(f331(f249(f854(x90821,a840),f854(x90821,a840)),x90822),x90823)),f307(x90821)))+~P1(f331(f331(f241(f854(x90821,a840)),x90822),x90823))
% 51.10/50.83 [9134]~P56(x91341,f331(x91343,f602(x91342,x91343,x91341)))+P56(x91341,f331(f331(f51(x91342,f854(x91341,f854(x91341,a840))),f247(f854(x91342,a840))),x91343))+~E(f331(f331(f109(f854(x91341,a840)),f254(x91341,x91341,f331(x91343,f601(x91342,x91343,x91341)))),f255(x91341,x91341,f331(x91343,f603(x91342,x91343,x91341)))),f184(f854(x91341,a840)))
% 51.10/50.83 [9328]P45(x93281,x93282,x93283)+P1(f331(f331(f333(f853(x93281,x93281)),f586(x93283,x93282,x93281)),x93283))+~P1(f331(f331(f333(f853(x93281,x93281)),f331(f331(f249(x93281,x93281),f585(x93283,x93282,x93281)),f585(x93283,x93282,x93281))),x93283))
% 51.10/50.83 [9910]P45(x99101,x99102,x99103)+~P1(f331(f331(f259(x99101,x99101,a840),f331(f331(f9(x99101,f854(x99101,a840),f854(x99101,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x99101,a840),f854(x99101,a840)),x99101),f10(a840,a840,x99101)),f331(f331(f10(a840,f854(a840,a840),x99101),a329),f331(f331(f9(x99101,f854(x99101,a840),a840),f333(x99101)),x99102)))),f331(f331(f9(x99101,f854(x99101,a840),a840),f333(x99101)),x99102))),f586(x99103,x99102,x99101)))+~P1(f331(f331(f333(f853(x99101,x99101)),f331(f331(f249(x99101,x99101),f585(x99103,x99102,x99101)),f585(x99103,x99102,x99101))),x99103))
% 51.10/50.83 [5497]~P5(x54972)+E(x54971,f2(x54972))+E(f331(f331(f48(x54972),f331(f331(f88(x54972),x54973),x54971)),x54971),x54973)
% 51.10/50.83 [5498]~P5(x54982)+E(x54981,f2(x54982))+E(f331(f331(f48(x54982),f331(f331(f88(x54982),x54981),x54983)),x54981),x54983)
% 51.10/50.83 [6145]~P5(x61451)+E(f331(f331(f88(x61451),f331(f331(f48(x61451),x61452),x61453)),x61453),x61452)+~P1(f331(f331(f287(x61451),x61453),x61452))
% 51.10/50.83 [6310]~P68(x63101)+~E(f331(x63102,f2(a847)),f2(x63101))+E(f331(f331(f8(a847,x63101),x63102),f331(f302(a847,f331(a119,f2(a847))),x63103)),f331(f331(f8(a847,x63101),x63102),f331(f302(a847,f2(a847)),x63103)))
% 51.10/50.83 [6452]~P5(x64522)+E(x64521,f2(x64522))+E(f331(f331(f48(x64522),f331(f331(f87(x64522),x64523),x64521)),x64521),f331(f331(f87(x64522),f331(f331(f48(x64522),x64523),x64521)),f85(x64522)))
% 51.10/50.83 [6453]~P5(x64532)+E(x64531,f2(x64532))+E(f331(f331(f48(x64532),f331(f331(f87(x64532),x64531),x64533)),x64531),f331(f331(f87(x64532),f331(f331(f48(x64532),x64533),x64531)),f85(x64532)))
% 51.10/50.83 [6681]~P1(f331(x66813,f2(a1)))+P1(f331(f331(f240(a847),x66811),x66812))+P1(f331(x66813,f331(f107(a1),f331(f331(f3(a847),x66812),x66811))))
% 51.10/50.83 [6791]P1(f331(f331(f240(a847),x67912),x67911))+P1(f331(f331(f241(a847),x67911),x67912))+P1(f331(x67913,f331(f107(a1),f331(f331(f3(a847),x67911),x67912))))
% 51.10/50.83 [6864]E(f331(f331(f87(a847),f331(f111(a847),x68641)),f331(f331(f87(a847),f331(f111(a847),x68642)),x68643)),f331(f331(f87(a847),f331(f111(a847),x68641)),x68643))+P1(f331(a190,f331(f111(a1),x68641)))+~P1(f331(a190,f331(f111(a1),x68642)))
% 51.10/50.83 [6942]~E(x69422,f331(f331(f48(a847),x69423),x69421))+~P1(f331(f331(f241(a847),f2(a847)),x69421))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x69421),x69422)),x69423))
% 51.10/50.83 [7058]~P1(f331(f68(x70581),x70583))+~P1(f331(f68(x70581),x70582))+P1(f331(f68(x70581),f331(f331(f3(f854(x70581,a840)),x70582),x70583)))
% 51.10/50.83 [7059]~P1(f331(f68(x70591),x70593))+~P1(f331(f68(x70591),x70592))+P1(f331(f68(x70591),f331(f331(f108(f854(x70591,a840)),x70592),x70593)))
% 51.10/50.83 [7060]~P1(f331(f68(x70601),x70603))+~P1(f331(f68(x70601),x70602))+P1(f331(f68(x70601),f331(f331(f108(f854(x70601,a840)),x70602),x70603)))
% 51.10/50.83 [7373]~P102(x73731)+~P1(f331(f68(x73731),x73732))+E(f135(x73731,f331(f331(f3(f854(x73731,a840)),x73732),f331(f331(f310(x73731),x73733),f184(f854(x73731,a840))))),f161(x73731,x73733,f135(x73731,x73732)))
% 51.10/50.83 [7440]P1(f331(x74401,f2(a1)))+~P1(f331(f331(f241(a847),x74402),x74403))+~P1(f331(x74401,f331(f107(a1),f331(f331(f3(a847),x74402),x74403))))
% 51.10/50.83 [7458]~P1(f331(f68(x74581),x74582))+E(f331(f47(x74581),f331(f331(f3(f854(x74581,a840)),x74582),f331(f331(f310(x74581),x74583),f184(f854(x74581,a840))))),f331(f47(x74581),x74582))+P1(f331(f331(f333(x74581),x74583),x74582))
% 51.10/50.83 [7592]~P85(x75921)+~P1(f331(f331(f241(x75921),f85(x75921)),x75922))+P1(f331(f331(f241(x75921),f85(x75921)),f331(f331(f88(x75921),x75922),f331(f331(f250(x75921),x75922),x75923))))
% 51.10/50.83 [7636]~P1(f331(f68(x76361),x76363))+E(f331(f331(f3(a847),f331(f47(x76361),x76362)),f331(f47(x76361),x76363)),f331(f47(x76361),f331(f331(f3(f854(x76361,a840)),x76362),x76363)))+~P1(f331(f331(f240(f854(x76361,a840)),x76363),x76362))
% 51.10/50.83 [7691]~P1(f331(f331(f240(a847),x76912),x76913))+~P1(f331(f331(f240(a847),x76911),f331(f331(f3(a847),x76913),x76912)))+P1(f331(f331(f240(a847),f331(f331(f87(a847),x76911),x76912)),x76913))
% 51.10/50.83 [7748]P1(f331(f68(x77481),x77482))+~P1(f331(f68(x77481),x77483))+~P1(f331(f68(x77481),f331(f331(f3(f854(x77481,a840)),x77482),x77483)))
% 51.10/50.83 [7754]~P1(f331(f68(x77541),x77542))+E(f331(f47(x77541),f331(f331(f3(f854(x77541,a840)),x77542),f331(f331(f310(x77541),x77543),f184(f854(x77541,a840))))),f331(f331(f3(a847),f331(f47(x77541),x77542)),f85(a847)))+~P1(f331(f331(f333(x77541),x77543),x77542))
% 51.10/50.83 [7755]~P1(f331(f68(x77551),x77552))+E(f331(f47(x77551),f331(f331(f3(f854(x77551,a840)),x77552),f331(f331(f310(x77551),x77553),f184(f854(x77551,a840))))),f331(f331(f3(a847),f331(f47(x77551),x77552)),f85(a847)))+~P1(f331(f331(f333(x77551),x77553),x77552))
% 51.10/50.83 [7830]P56(x78301,x78302)+~P56(x78301,x78303)+~P1(f331(f331(f240(f854(x78301,f854(x78301,a840))),x78302),x78303))
% 51.10/50.83 [7868]~P1(f331(f331(f240(a847),x78683),x78682))+P1(f331(f331(f240(a847),x78681),f331(f331(f3(a847),x78682),x78683)))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),x78681),x78683)),x78682))
% 51.10/50.83 [7888]P34(x78881,x78882)+~P34(x78881,x78883)+~P1(f331(f331(f240(f854(f853(x78881,x78881),a840)),x78882),x78883))
% 51.10/50.83 [7889]P54(x78891,x78892)+~P54(x78891,x78893)+~P1(f331(f331(f240(f854(f853(x78891,x78891),a840)),x78892),x78893))
% 51.10/50.83 [8122]~P85(x81221)+~P1(f331(f331(f241(x81221),f85(x81221)),x81222))+P1(f331(f331(f241(x81221),f331(f331(f250(x81221),x81222),x81223)),f331(f331(f88(x81221),x81222),f331(f331(f250(x81221),x81222),x81223))))
% 51.10/50.83 [8209]~P1(f331(x82091,f2(a1)))+~P1(f331(x82091,f331(f331(f3(a1),f331(f107(a1),x82092)),f331(f107(a1),x82093))))+P1(f331(x82091,f331(f107(a1),f331(f331(f3(a847),x82092),x82093))))
% 51.10/50.83 [8222]~P1(f331(f331(f240(a847),x82223),x82222))+P1(f331(x82221,f331(f331(f3(a1),f331(f107(a1),x82222)),f331(f107(a1),x82223))))+~P1(f331(x82221,f331(f107(a1),f331(f331(f3(a847),x82222),x82223))))
% 51.10/50.83 [8240]P1(f331(f331(f241(a847),x82401),x82402))+~P1(f331(x82403,f331(f331(f3(a1),f331(f107(a1),x82401)),f331(f107(a1),x82402))))+P1(f331(x82403,f331(f107(a1),f331(f331(f3(a847),x82401),x82402))))
% 51.10/50.83 [8297]~P118(x82972)+E(x82971,f2(x82972))+P1(f331(f331(f241(x82972),f2(x82972)),f331(f331(f87(x82972),f331(f331(f88(x82972),x82973),x82973)),f331(f331(f88(x82972),x82971),x82971))))
% 51.10/50.83 [8298]~P118(x82982)+E(x82981,f2(x82982))+P1(f331(f331(f241(x82982),f2(x82982)),f331(f331(f87(x82982),f331(f331(f88(x82982),x82981),x82981)),f331(f331(f88(x82982),x82983),x82983))))
% 51.10/50.83 [8403]~P1(f331(f331(f241(a847),f2(a847)),x84031))+~P1(f331(f331(f241(a1),x84032),x84033))+P1(f331(f331(f241(a1),f331(f331(f88(a1),f331(f107(a1),x84031)),x84032)),f331(f331(f88(a1),f331(f107(a1),x84031)),x84033)))
% 51.10/50.83 [8460]E(f331(f331(f109(f854(x84601,a840)),x84602),f49(f854(x84601,a840),x84603)),f184(f854(x84601,a840)))+P1(f331(f331(f333(f854(x84601,a840)),x84602),x84603))+P1(f331(f331(f333(f854(x84601,a840)),f667(x84603,x84602,x84601)),f331(f331(f310(f854(x84601,a840)),x84602),x84603)))
% 51.10/50.83 [8461]E(f331(f331(f109(f854(x84611,a840)),x84612),f49(f854(x84611,a840),x84613)),f184(f854(x84611,a840)))+P1(f331(f331(f333(f854(x84611,a840)),x84612),x84613))+P1(f331(f331(f333(f854(x84611,a840)),f666(x84613,x84612,x84611)),f331(f331(f310(f854(x84611,a840)),x84612),x84613)))
% 51.10/50.83 [8487]E(x84871,x84872)+~E(f331(f185(f848(x84873)),x84871),f331(f185(f848(x84873)),x84872))+P1(f331(f331(f333(f853(x84873,x84873)),f712(x84873,x84871,x84872)),f331(f163(f853(x84873,x84873)),f331(f331(f172(x84873,x84873),x84872),x84871))))
% 51.10/50.83 [8698]E(f308(x86981,x86982),f308(x86981,x86983))+~P1(f331(f331(f240(f854(f853(x86981,x86981),a840)),x86983),f308(x86981,x86982)))+~P1(f331(f331(f240(f854(f853(x86981,x86981),a840)),x86982),x86983))
% 51.10/50.83 [8751]~P45(x87511,f247(f854(x87511,a840)),x87513)+P1(f331(f331(f240(f854(f853(f848(x87511),f848(x87511)),a840)),f150(x87511,x87512)),f151(x87511,x87513)))+~P1(f331(f331(f240(f854(f853(x87511,x87511),a840)),x87512),x87513))
% 51.10/50.83 [8928]P34(x89281,x89282)+~P1(f331(f331(f333(x89281),x89283),f692(x89282,x89281)))+P1(f331(f331(f333(f853(x89281,x89281)),f331(f331(f249(x89281,x89281),f696(x89282,x89281,x89283)),x89283)),x89282))
% 51.10/50.83 [8964]~P1(f331(f68(x89641),x89642))+P1(f331(f68(f854(x89641,a840)),f331(f331(f66(x89641),x89642),x89643)))+~P1(f331(f331(f240(f854(f853(x89641,x89641),a840)),x89643),f331(f331(f256(x89641,x89641),x89642),f331(f18(f854(x89641,a840),x89641),x89642))))
% 51.10/50.83 [8995]P45(x89951,x89952,x89953)+P1(f331(f331(f333(x89951),f552(x89953,x89952,x89951)),x89952))+~P1(f331(f331(f240(f854(f853(x89951,x89951),a840)),x89953),f331(f331(f256(x89951,x89951),x89952),f331(f18(f854(x89951,a840),x89951),x89952))))
% 51.10/50.83 [8996]P45(x89961,x89962,x89963)+P1(f331(f331(f333(x89961),f557(x89962,x89963,x89961)),x89962))+~P1(f331(f331(f240(f854(f853(x89961,x89961),a840)),x89963),f331(f331(f256(x89961,x89961),x89962),f331(f18(f854(x89961,a840),x89961),x89962))))
% 51.10/50.83 [9030]~P61(x90301)+~P1(f331(f331(f241(x90301),x90302),x90303))+P1(f331(f331(f241(x90301),f331(f331(f291(x90301),f331(f331(f87(x90301),x90302),x90303)),f331(f331(f87(x90301),f85(x90301)),f85(x90301)))),x90303))
% 51.10/50.83 [9057]~P60(x90571)+P1(f331(f331(f240(x90571),x90572),x90573))+~P1(f331(f331(f240(x90571),f331(f331(f88(x90571),f793(x90573,x90572,x90571)),x90572)),x90573))
% 51.10/50.83 [9163]E(f314(x91631,x91632,x91633),f187(f848(a838)))+~P1(f331(f331(f241(a1),x91632),x91633))+~P1(f331(f320(f853(f854(a1,f851(f848(a838))),f853(a1,a1)),a318),f331(f331(f249(f854(a1,f851(f848(a838))),f853(a1,a1)),x91631),f331(f331(f249(a1,a1),x91632),x91633))))
% 51.10/50.83 [9166]E(f331(f185(f848(f848(x91661))),f331(f131(f848(x91661),f331(f331(f10(a847,a840,f848(x91661)),f331(f241(a847),x91662)),f185(f848(x91661)))),f169(x91661,x91663))),f331(f185(f848(x91661)),f331(f331(f155(f848(x91661)),x91663),x91662)))+~P16(a847,f331(f160(a847),f331(f331(f147(f848(x91661),a847),f185(f848(x91661))),x91663)))+~P1(f331(f331(f241(a847),x91662),f331(f185(f848(f848(x91661))),x91663)))
% 51.10/50.83 [9278]~P34(x92781,x92782)+P28(x92781,f331(f331(f249(f854(f853(x92781,x92781),a840),f854(f853(x92781,x92781),a840)),x92782),x92783))+~P1(f331(f331(f240(f854(f853(x92781,x92781),a840)),f331(f331(f289(x92781,x92781,x92781),x92782),x92783)),x92782))
% 51.10/50.83 [9280]E(f331(f236(f851(f848(a838)),f848(a838),f314(x92801,x92802,f331(f331(f87(a1),x92803),f85(a1))),f234(f848(a838))),f331(x92801,x92803)),f314(x92801,x92802,x92803))+P1(f331(f331(f241(a1),x92802),x92803))+~P1(f331(f320(f853(f854(a1,f851(f848(a838))),f853(a1,a1)),a318),f331(f331(f249(f854(a1,f851(f848(a838))),f853(a1,a1)),x92801),f331(f331(f249(a1,a1),x92802),x92803))))
% 51.10/50.83 [9285]E(f331(f331(f147(f848(x92851),x92851),f331(f331(f9(f848(x92851),a847,x92851),f155(x92851)),x92852)),f331(f131(f848(x92851),f331(f331(f10(a847,a840,f848(x92851)),f331(f241(a847),x92852)),f185(f848(x92851)))),f169(x92851,x92853))),f331(f331(f155(f848(x92851)),x92853),x92852))+~P16(a847,f331(f160(a847),f331(f331(f147(f848(x92851),a847),f185(f848(x92851))),x92853)))+~P1(f331(f331(f241(a847),x92852),f331(f185(f848(f848(x92851))),x92853)))
% 51.10/50.83 [9414]P45(x94141,x94142,x94143)+~P1(f331(f331(f333(f853(x94141,x94141)),f331(f331(f249(x94141,x94141),f552(x94143,x94142,x94141)),f552(x94143,x94142,x94141))),x94143))+~P1(f331(f331(f240(f854(f853(x94141,x94141),a840)),x94143),f331(f331(f256(x94141,x94141),x94142),f331(f18(f854(x94141,a840),x94141),x94142))))
% 51.10/50.83 [9415]P45(x94151,x94152,x94153)+~P1(f331(f331(f333(f853(x94151,x94151)),f331(f331(f249(x94151,x94151),f557(x94152,x94153,x94151)),f557(x94152,x94153,x94151))),x94153))+~P1(f331(f331(f240(f854(f853(x94151,x94151),a840)),x94153),f331(f331(f256(x94151,x94151),x94152),f331(f18(f854(x94151,a840),x94151),x94152))))
% 51.10/50.83 [9584]~P133(x95841)+~P117(x95841)+E(f331(f331(f291(x95841),f331(f110(x95841),f331(f331(f80(f853(a1,a1),a1,x95842,f248(a1,a1)),f214(x95842)),x95843))),f331(f110(x95841),f331(f331(f80(f853(a1,a1),a1,x95842,f258(a1,a1)),f214(x95842)),x95843))),f224(x95842,x95841,x95843))
% 51.10/50.83 [9781]~E(x97813,f2(a847))+~E(f331(f185(f848(x97811)),f331(f331(f155(f848(x97811)),x97812),f770(x97813,x97811,x97812))),x97813)+E(f331(f331(f147(a847,f848(x97811)),f331(f331(f9(a847,f848(a847),f848(x97811)),f331(f331(f10(f854(a847,x97811),f854(f848(a847),f848(x97811)),a847),f147(a847,x97811)),f331(f9(a847,a847,x97811),f331(f331(f10(f848(x97811),f854(a847,x97811),a847),f155(x97811)),f331(f155(f848(x97811)),x97812))))),f135(a847,f331(f302(a847,f2(a847)),f331(f185(f848(f848(x97811))),x97812))))),f135(a847,f331(f302(a847,f2(a847)),x97813))),f169(x97811,x97812))
% 51.10/50.83 [9782]E(x97821,f120(f848(x97822)))+~E(f331(f185(f848(x97822)),f331(f331(f155(f848(x97822)),x97821),f770(x97823,x97822,x97821))),x97823)+E(f331(f331(f147(a847,f848(x97822)),f331(f331(f9(a847,f848(a847),f848(x97822)),f331(f331(f10(f854(a847,x97822),f854(f848(a847),f848(x97822)),a847),f147(a847,x97822)),f331(f9(a847,a847,x97822),f331(f331(f10(f848(x97822),f854(a847,x97822),a847),f155(x97822)),f331(f155(f848(x97822)),x97821))))),f135(a847,f331(f302(a847,f2(a847)),f331(f185(f848(f848(x97822))),x97821))))),f135(a847,f331(f302(a847,f2(a847)),x97823))),f169(x97822,x97821))
% 51.10/50.83 [9783]~E(x97833,f2(a847))+E(f331(f331(f147(a847,f848(x97831)),f331(f331(f9(a847,f848(a847),f848(x97831)),f331(f331(f10(f854(a847,x97831),f854(f848(a847),f848(x97831)),a847),f147(a847,x97831)),f331(f9(a847,a847,x97831),f331(f331(f10(f848(x97831),f854(a847,x97831),a847),f155(x97831)),f331(f155(f848(x97831)),x97832))))),f135(a847,f331(f302(a847,f2(a847)),f331(f185(f848(f848(x97831))),x97832))))),f135(a847,f331(f302(a847,f2(a847)),x97833))),f169(x97831,x97832))+P1(f331(f331(f241(a847),f770(x97833,x97831,x97832)),f331(f185(f848(f848(x97831))),x97832)))
% 51.10/50.83 [9784]E(x97841,f120(f848(x97842)))+E(f331(f331(f147(a847,f848(x97842)),f331(f331(f9(a847,f848(a847),f848(x97842)),f331(f331(f10(f854(a847,x97842),f854(f848(a847),f848(x97842)),a847),f147(a847,x97842)),f331(f9(a847,a847,x97842),f331(f331(f10(f848(x97842),f854(a847,x97842),a847),f155(x97842)),f331(f155(f848(x97842)),x97841))))),f135(a847,f331(f302(a847,f2(a847)),f331(f185(f848(f848(x97842))),x97841))))),f135(a847,f331(f302(a847,f2(a847)),x97843))),f169(x97842,x97841))+P1(f331(f331(f241(a847),f770(x97843,x97842,x97841)),f331(f185(f848(f848(x97842))),x97841)))
% 51.10/50.83 [7633]E(f331(f331(f87(a847),f331(f111(a847),x76331)),f331(f331(f87(a847),f331(f111(a847),x76332)),x76333)),f331(f331(f87(a847),f331(f111(a847),f331(f331(f87(a1),x76331),x76332))),x76333))+P1(f331(a190,f331(f111(a1),x76331)))+P1(f331(a190,f331(f111(a1),x76332)))
% 51.10/50.83 [8394]~P1(f331(f68(x83941),x83942))+~P1(f331(f331(f333(x83941),x83943),x83942))+E(f331(a119,f331(f47(x83941),f331(f331(f3(f854(x83941,a840)),x83942),f331(f331(f310(x83941),x83943),f184(f854(x83941,a840)))))),f331(f47(x83941),x83942))
% 51.10/50.83 [8414]~P1(f331(f68(x84141),x84142))+~P1(f331(f331(f333(x84141),x84143),x84142))+E(f331(f331(f87(a847),f85(a847)),f331(f47(x84141),f331(f331(f3(f854(x84141,a840)),x84142),f331(f331(f310(x84141),x84143),f184(f854(x84141,a840)))))),f331(f47(x84141),x84142))
% 51.10/50.83 [8495]~P102(x84951)+~P1(f331(f68(x84951),x84953))+E(f331(f331(f143(x84951,x84951,f7(x84951)),x84952),f135(x84951,f331(f331(f3(f854(x84951,a840)),x84953),f331(f331(f310(x84951),x84952),f184(f854(x84951,a840)))))),f135(x84951,f331(f331(f310(x84951),x84952),x84953)))
% 51.10/50.83 [8633]~P1(f331(f68(x86331),x86333))+~P1(f331(f68(x86331),x86332))+E(f331(f331(f87(a847),f331(f47(x86331),f331(f331(f108(f854(x86331,a840)),x86332),x86333))),f331(f47(x86331),f331(f331(f109(f854(x86331,a840)),x86332),x86333))),f331(f331(f87(a847),f331(f47(x86331),x86332)),f331(f47(x86331),x86333)))
% 51.10/50.83 [8634]~P1(f331(f68(x86341),x86343))+~P1(f331(f68(x86341),x86342))+E(f331(f331(f87(a847),f331(f47(x86341),f331(f331(f108(f854(x86341,a840)),x86342),x86343))),f331(f47(x86341),f331(f331(f109(f854(x86341,a840)),x86342),x86343))),f331(f331(f87(a847),f331(f47(x86341),x86342)),f331(f47(x86341),x86343)))
% 51.10/50.83 [9730]~P27(x97301,f854(f854(x97301,a840),a840),f331(f331(f9(x97301,f854(f853(x97301,x97301),a840),f854(f854(x97301,a840),a840)),f331(f331(f10(f854(x97301,a840),f854(f854(f853(x97301,x97301),a840),f854(f854(x97301,a840),a840)),x97301),f66(x97301)),f331(f331(f9(x97301,f854(x97301,a840),f854(x97301,a840)),f310(x97301)),f184(f854(x97301,a840))))),x97303),x97302)+~P1(f331(f68(x97301),x97302))+E(f331(f47(f854(x97301,a840)),f331(f331(f66(x97301),x97302),x97303)),f331(f47(x97301),x97302))
% 51.10/50.83 [7905]~P91(x79051)+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x79053)))+E(f331(f331(f250(x79051),x79052),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x79053),x79053)),a104))),f85(x79051))
% 51.10/50.83 [7994]~P91(x79941)+P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x79943)))+E(f331(f331(f250(x79941),f331(f111(x79941),x79942)),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x79943),x79943)),a104))),f85(x79941))
% 51.10/50.83 [9261]~P91(x92611)+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x92613)))+E(f331(f331(f250(x92611),x92612),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x92613),x92613)),a104))),f331(f331(f93(x92611,x92611),f331(f331(f250(x92611),x92612),f331(f111(a847),x92613))),f331(f331(f20(x92611,x92611,x92611),f331(f331(f10(x92611,f854(x92611,x92611),x92611),f88(x92611)),f331(f88(x92611),x92612))),f7(x92611))))
% 51.10/50.83 [9327]~P91(x93271)+~P1(f331(f331(f240(a1),f2(a1)),f331(f111(a1),x93273)))+E(f331(f331(f250(x93271),f331(f111(x93271),x93272)),f331(f111(a847),f331(f331(f3(a1),f331(f331(f87(a1),x93273),x93273)),a104))),f331(f331(f93(x93271,x93271),f331(f331(f250(x93271),f331(f111(x93271),x93272)),f331(f111(a847),x93273))),f331(f331(f20(x93271,x93271,x93271),f331(f331(f10(x93271,f854(x93271,x93271),x93271),f88(x93271)),f331(f88(x93271),f331(f111(x93271),x93272)))),f7(x93271))))
% 51.10/50.83 [9395]~P1(f331(f132(x93951),x93953))+~P1(f331(f331(f333(x93951),x93952),f331(f163(x93951),x93953)))+E(f331(f160(x93951),f331(f162(x93951),f134(x93951,f331(f331(f10(a840,a840,x93951),a327),f331(f331(f9(x93951,x93951,a840),a328),x93952)),x93953))),f167(x93951,f331(f331(f10(a840,a840,x93951),a327),f331(f331(f9(x93951,x93951,a840),a328),x93952)),f331(f160(x93951),x93953)))
% 51.10/50.83 [9396]~P1(f331(f132(x93961),x93963))+~P1(f331(f331(f333(x93961),x93962),f331(f163(x93961),x93963)))+E(f331(f331(f145(x93961),x93962),f331(f160(x93961),f167(x93961,f331(f331(f10(a840,a840,x93961),a327),f331(f331(f9(x93961,x93961,a840),a328),x93962)),x93963))),f134(x93961,f331(f331(f10(a840,a840,x93961),a327),f331(f331(f9(x93961,x93961,a840),a328),x93962)),f331(f160(x93961),x93963)))
% 51.10/50.83 [9695]P1(f331(f331(f240(f854(f853(x96951,x96951),a840)),f308(x96951,x96952)),x96953))+~P1(f331(f331(f240(f854(f853(x96951,x96951),a840)),f308(x96951,f184(f854(f853(x96951,x96951),a840)))),x96953))+~P1(f331(f331(f240(f854(f853(x96951,x96951),a840)),f331(f331(f289(x96951,x96951,x96951),f331(f331(f109(f854(f853(x96951,x96951),a840)),f308(x96951,x96952)),x96953)),x96952)),x96953))
% 51.10/50.83 [9556]~P1(f331(f68(x95561),f331(f264(x95561),x95563)))+~P1(f331(f68(x95561),f331(f264(x95561),x95562)))+P1(f331(f68(x95561),f331(f264(x95561),f331(f331(f20(x95561,a840,a840),f331(f331(f10(a840,f854(a840,a840),x95561),a330),x95562)),x95563))))
% 51.10/50.83 [9853]P1(f331(f331(f240(f854(f853(x98531,x98531),a840)),f331(f331(f289(x98531,x98531,x98531),x98532),f308(x98531,x98532))),x98533))+~P1(f331(f331(f240(f854(f853(x98531,x98531),a840)),x98532),x98533))+~P1(f331(f331(f240(f854(f853(x98531,x98531),a840)),f331(f331(f289(x98531,x98531,x98531),f331(f331(f109(f854(f853(x98531,x98531),a840)),f331(f331(f289(x98531,x98531,x98531),x98532),f308(x98531,x98532))),x98533)),x98532)),x98533))
% 51.10/50.83 [9798]~P86(x97982)+E(x97981,f2(x97982))+~E(f331(f331(f87(x97982),f331(f331(f250(x97982),x97983),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x97982),x97981),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f2(x97982))
% 51.10/50.83 [9799]~P86(x97992)+E(x97991,f2(x97992))+~E(f331(f331(f87(x97992),f331(f331(f250(x97992),x97991),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x97992),x97993),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f2(x97992))
% 51.10/50.83 [9895]~P86(x98952)+E(x98951,f2(x98952))+P1(f331(f331(f241(x98952),f2(x98952)),f331(f331(f87(x98952),f331(f331(f250(x98952),x98953),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x98952),x98951),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))))
% 51.10/50.83 [9896]~P86(x98962)+E(x98961,f2(x98962))+P1(f331(f331(f241(x98962),f2(x98962)),f331(f331(f87(x98962),f331(f331(f250(x98962),x98961),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x98962),x98963),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))))
% 51.10/50.83 [9946]~P86(x99461)+P1(f331(f331(f240(x99461),f2(x99461)),x99462))+~P1(f331(f331(f240(x99461),f2(x99461)),f331(f331(f250(x99461),x99462),f331(a119,f331(f331(f88(a847),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x99463)))))
% 51.10/50.83 [5339]~P26(x53391,x53394,x53393)+P26(x53391,x53392,x53393)+~P26(x53391,x53392,x53394)
% 51.10/50.83 [4819]~E(x48192,f97(x48193,x48191))+P1(f331(x48191,x48192))+~P1(f331(x48191,x48194))
% 51.10/50.83 [6586]~P34(x65862,x65864)+~P34(x65861,x65863)+P34(f853(x65861,x65862),f324(x65861,x65862,x65863,x65864))
% 51.10/50.83 [7976]~P37(f37(x79764,x79761),x79762,x79763,x79762)+P37(x79761,x79762,x79763,f501(x79763,x79762,x79761,x79764))+~P1(f331(x79764,x79762))
% 51.10/50.83 [8003]~P37(f37(x80031,x80032),x80034,x80033,x80034)+P37(f37(x80031,x80032),f501(x80033,x80034,x80032,x80031),x80033,x80034)+~P1(f331(x80031,x80034))
% 51.10/50.83 [4996]~P9(x49964,x49961)+~E(f331(x49961,x49962),f331(x49961,x49963))+P1(f331(f331(x49961,x49962),x49963))
% 51.10/50.83 [5158]~P9(x51584,x51581)+E(f331(x51581,x51582),f331(x51581,x51583))+~P1(f331(f331(x51581,x51582),x51583))
% 51.10/50.83 [5246]~P20(x52463,x52464,x52461)+E(f331(x52461,x52462),f331(f70(x52463,x52464),x52462))+~P1(f331(f68(x52463),x52462))
% 51.10/50.83 [5247]~P12(x52473,x52474,x52471)+E(f331(x52471,x52472),f331(f70(x52473,x52474),x52472))+~P1(f331(f68(x52473),x52472))
% 51.10/50.83 [5374]~P9(x53744,x53741)+~P1(f331(f331(x53741,x53743),x53742))+P1(f331(f331(x53741,x53742),x53743))
% 51.10/50.83 [5438]E(x54381,x54382)+~E(f331(f248(x54383,x54384),x54381),f331(f248(x54383,x54384),x54382))+~E(f331(f258(x54383,x54384),x54381),f331(f258(x54383,x54384),x54382))
% 51.10/50.83 [5439]E(x54391,x54392)+~E(f331(f248(x54393,x54394),x54391),f331(f248(x54393,x54394),x54392))+~E(f331(f258(x54393,x54394),x54391),f331(f258(x54393,x54394),x54392))
% 51.10/50.83 [5466]E(x54661,x54662)+~P1(f331(f60(x54663,x54664),x54662))+~P1(f331(f60(x54663,x54664),x54661))
% 51.10/50.83 [5662]~P68(x56622)+E(f232(x56621,x56622,x56623,x56624),f2(x56622))+P1(f331(f68(x56621),x56624))
% 51.10/50.83 [5798]~P1(f331(f320(x57981,x57982),x57984))+P1(f331(f320(x57981,x57982),x57983))+~P1(f331(f331(x57982,x57983),x57984))
% 51.10/50.83 [5799]~P1(f331(f320(x57991,x57992),x57994))+P1(f331(f320(x57991,x57992),x57993))+~P1(f331(f331(x57992,x57993),x57994))
% 51.10/50.83 [5800]~P1(f331(f320(x58001,x58002),x58004))+P1(f331(f320(x58001,x58002),x58003))+~P1(f331(f331(x58002,x58003),x58004))
% 51.10/50.83 [8046]~P1(f331(f68(x80462),x80464))+~P1(f331(f68(x80461),x80463))+P1(f331(f68(f855(x80461,x80462)),f319(x80461,x80462,x80463,x80464)))
% 51.10/50.83 [8047]~P1(f331(f68(x80472),x80474))+~P1(f331(f68(x80471),x80473))+P1(f331(f68(f855(x80471,x80472)),f319(x80471,x80472,x80473,x80474)))
% 51.10/50.83 [8050]P1(f331(f331(f333(f848(x80501)),f331(f331(f130(x80501),x80502),x80503)),f153(x80501,x80504)))+~P1(f331(f331(f333(f848(x80501)),x80503),f153(x80501,x80504)))+~P1(f331(f331(f333(f848(x80501)),x80502),f153(x80501,x80504)))
% 51.10/50.83 [8623]~P1(f331(f331(f333(f853(x86231,x86231)),f331(f331(f249(x86231,x86231),x86232),x86234)),f308(x86231,x86233)))+P1(f331(f331(f333(x86231),x86232),f321(x86231,x86233)))+~P1(f331(f331(f333(x86231),x86234),f321(x86231,x86233)))
% 51.10/50.83 [8624]~P1(f331(f331(f333(f853(x86241,x86241)),f331(f331(f249(x86241,x86241),x86242),x86244)),f308(x86241,x86243)))+P1(f331(f331(f333(x86241),x86242),f321(x86241,x86243)))+~P1(f331(f331(f333(x86241),x86244),f321(x86241,x86243)))
% 51.10/50.83 [4978]~P70(x49782)+E(f331(f331(f11(x49781,x49782),x49783),x49784),f85(x49782))+P1(f331(f68(x49781),x49784))
% 51.10/50.83 [4979]~P70(x49792)+E(f331(f331(f11(x49791,x49792),x49793),x49794),f85(x49792))+P1(f331(f68(x49791),x49794))
% 51.10/50.83 [4980]~P70(x49802)+E(f331(f331(f11(x49801,x49802),x49803),x49804),f85(x49802))+P1(f331(f68(x49801),x49804))
% 51.10/50.83 [4981]~P68(x49812)+E(f331(f331(f8(x49811,x49812),x49813),x49814),f2(x49812))+P1(f331(f68(x49811),x49814))
% 51.10/50.83 [4982]~P68(x49822)+E(f331(f331(f8(x49821,x49822),x49823),x49824),f2(x49822))+P1(f331(f68(x49821),x49824))
% 51.10/50.83 [4983]~P68(x49832)+E(f331(f331(f8(x49831,x49832),x49833),x49834),f2(x49832))+P1(f331(f68(x49831),x49834))
% 51.10/50.83 [5126]~P62(x51263)+E(x51261,x51262)+~E(f331(f331(f87(x51263),x51264),x51261),f331(f331(f87(x51263),x51264),x51262))
% 51.10/50.83 [5127]~P62(x51273)+E(x51271,x51272)+~E(f331(f331(f87(x51273),x51274),x51271),f331(f331(f87(x51273),x51274),x51272))
% 51.10/50.83 [5128]~P63(x51283)+E(x51281,x51282)+~E(f331(f331(f87(x51283),x51284),x51281),f331(f331(f87(x51283),x51284),x51282))
% 51.10/50.83 [5129]~P62(x51293)+E(x51291,x51292)+~E(f331(f331(f87(x51293),x51291),x51294),f331(f331(f87(x51293),x51292),x51294))
% 51.10/50.83 [5130]~P62(x51303)+E(x51301,x51302)+~E(f331(f331(f87(x51303),x51301),x51304),f331(f331(f87(x51303),x51302),x51304))
% 51.10/50.83 [5216]~P113(x52161)+~E(x52163,f331(f331(f88(x52161),x52162),x52164))+P1(f331(f331(f287(x52161),x52162),x52163))
% 51.10/50.83 [5241]~P7(x52413)+E(x52411,f184(f854(x52412,a840)))+E(f331(f331(f51(x52412,x52413),x52411),f331(f18(x52413,x52412),x52414)),x52414)
% 51.10/50.83 [5242]~P7(x52423)+E(x52421,f184(f854(x52422,a840)))+E(f331(f331(f52(x52422,x52423),x52421),f331(f18(x52423,x52422),x52424)),x52424)
% 51.10/50.83 [5453]~P88(x54533)+E(x54531,x54532)+~E(f303(x54533,x54534,x54531),f331(f331(f310(x54533),x54532),f184(f854(x54533,a840))))
% 51.10/50.83 [5454]~P88(x54543)+E(x54541,x54542)+~E(f303(x54543,x54541,x54542),f331(f331(f310(x54543),x54544),f184(f854(x54543,a840))))
% 51.10/50.83 [5762]P1(f331(x57621,x57622))+~P1(f331(f253(x57623,x57621),x57624))+~P1(f331(f331(f333(x57623),x57622),x57624))
% 51.10/50.83 [5791]E(x57911,x57912)+~P1(f331(f331(f191(x57913),x57914),x57912))+~P1(f331(f331(f191(x57913),x57914),x57911))
% 51.10/50.83 [5873]~P68(x58731)+E(f331(f331(f8(a847,x58731),x58732),f331(f302(a847,x58733),f331(a119,x58734))),f2(x58731))+~P1(f331(f331(f241(a847),x58734),x58733))
% 51.10/50.83 [5878]~P6(x58781)+~E(f57(x58781,x58782,x58783),f57(x58781,x58784,x58783))+E(f57(x58781,f331(f86(x58781),x58782),x58783),f57(x58781,f331(f86(x58781),x58784),x58783))
% 51.10/50.83 [5948]P1(f331(x59481,x59482))+~E(f331(f131(x59483,x59481),x59484),x59484)+~P1(f331(f331(f333(x59483),x59482),f331(f163(x59483),x59484)))
% 51.10/50.83 [5967]~E(f331(f331(f87(a847),x59673),x59672),f331(f331(f87(a847),x59671),x59674))+~P1(f331(f331(f241(a847),x59673),x59674))+P1(f331(f331(f241(a847),x59671),x59672))
% 51.10/50.83 [5974]~P5(x59741)+E(f57(x59741,f57(x59741,x59742,x59743),x59744),f57(x59741,x59742,x59744))+~P1(f331(f331(f287(x59741),x59744),x59743))
% 51.10/50.83 [6012]~E(f331(f131(x60121,x60122),x60123),f120(x60121))+~P1(f331(x60122,x60124))+~P1(f331(f331(f333(x60121),x60124),f331(f163(x60121),x60123)))
% 51.10/50.83 [6013]~E(f167(x60133,x60131,x60134),x60134)+P1(f331(x60131,x60132))+~P1(f331(f331(f333(x60133),x60132),f331(f163(x60133),x60134)))
% 51.10/50.83 [6048]~E(x60484,f184(f854(x60482,a840)))+~E(x60483,f184(f854(x60481,a840)))+E(f319(x60481,x60482,x60483,x60484),f184(f854(f855(x60481,x60482),a840)))
% 51.10/50.83 [6481]~P68(x64811)+E(f331(f331(f8(a847,x64811),x64812),f303(a847,x64813,f331(a119,x64814))),f2(x64811))+~P1(f331(f331(f241(a847),f331(a119,x64814)),x64813))
% 51.10/50.83 [6629]~P102(x66291)+E(f331(f331(f3(f854(x66291,a840)),f331(f302(x66291,x66292),x66293)),f331(f302(x66291,x66292),x66294)),f331(f302(x66291,x66294),x66293))+~P1(f331(f331(f240(x66291),x66292),x66294))
% 51.10/50.83 [6990]~P1(f331(f331(f333(f848(x69901)),x69904),f153(x69901,x69903)))+P1(f331(f331(f333(x69901),x69902),x69903))+~P1(f331(f331(f333(x69901),x69902),f331(f163(x69901),x69904)))
% 51.10/50.83 [6997]~P34(x69971,x69972)+P1(f331(f331(f333(x69971),f693(x69972,x69971,x69973)),x69973))+~P1(f331(f331(f333(x69971),x69974),x69973))
% 51.10/50.83 [7029]~P27(x70292,x70291,x70293,x70294)+E(f331(f47(x70291),f331(f311(x70292,x70291,x70293),x70294)),f331(f47(x70292),x70294))+~P1(f331(f68(x70292),x70294))
% 51.10/50.83 [7053]~P70(x70531)+E(f331(f331(f331(f72(x70531,x70532,f88(x70531)),x70533),f85(x70531)),x70534),f331(f331(f11(x70532,x70531),x70533),x70534))+~P1(f331(f68(x70532),x70534))
% 51.10/50.83 [7054]~P70(x70541)+E(f331(f331(f331(f72(x70541,x70542,f88(x70541)),x70543),f85(x70541)),x70544),f331(f331(f11(x70542,x70541),x70543),x70544))+~P1(f331(f68(x70542),x70544))
% 51.10/50.83 [7055]~P68(x70551)+E(f331(f331(f331(f72(x70551,x70552,f87(x70551)),x70553),f2(x70551)),x70554),f331(f331(f8(x70552,x70551),x70553),x70554))+~P1(f331(f68(x70552),x70554))
% 51.10/50.83 [7056]~P68(x70561)+E(f331(f331(f331(f72(x70561,x70562,f87(x70561)),x70563),f2(x70561)),x70564),f331(f331(f8(x70562,x70561),x70563),x70564))+~P1(f331(f68(x70562),x70564))
% 51.10/50.83 [7082]P27(x70821,x70822,x70823,x70824)+~E(f331(f47(x70822),f331(f311(x70821,x70822,x70823),x70824)),f331(f47(x70821),x70824))+~P1(f331(f68(x70821),x70824))
% 51.10/50.83 [7083]P27(x70831,x70832,x70833,x70834)+~E(f331(f47(x70832),f331(f311(x70831,x70832,x70833),x70834)),f331(f47(x70831),x70834))+~P1(f331(f68(x70831),x70834))
% 51.10/50.83 [7285]~P68(x72851)+E(f331(f331(f87(x72851),f331(x72852,x72853)),f331(f331(f8(a847,x72851),x72852),f305(a847,x72853,x72854))),f331(f331(f8(a847,x72851),x72852),f303(a847,x72853,x72854)))+~P1(f331(f331(f240(a847),x72853),x72854))
% 51.10/50.83 [7295]~P70(x72951)+~P27(x72952,x72951,x72953,x72954)+E(f331(f331(f11(x72951,x72951),f39(x72951)),f331(f311(x72952,x72951,x72953),x72954)),f331(f331(f11(x72952,x72951),x72953),x72954))
% 51.10/50.83 [7296]~P68(x72961)+~P27(x72962,x72961,x72963,x72964)+E(f331(f331(f8(x72961,x72961),f39(x72961)),f331(f311(x72962,x72961,x72963),x72964)),f331(f331(f8(x72962,x72961),x72963),x72964))
% 51.10/50.83 [7354]E(f331(f47(f855(x73541,x73542)),f319(x73541,x73542,x73543,x73544)),f331(f331(f87(a847),f331(f47(x73541),x73543)),f331(f47(x73542),x73544)))+~P1(f331(f68(x73542),x73544))+~P1(f331(f68(x73541),x73543))
% 51.10/50.83 [7355]E(f331(f47(f855(x73551,x73552)),f319(x73551,x73552,x73553,x73554)),f331(f331(f87(a847),f331(f47(x73551),x73553)),f331(f47(x73552),x73554)))+~P1(f331(f68(x73552),x73554))+~P1(f331(f68(x73551),x73553))
% 51.10/50.83 [7441]E(x74411,x74412)+P1(f331(f331(f333(x74413),x74411),f331(f163(x74413),f161(x74413,x74412,x74414))))+~P1(f331(f331(f333(x74413),x74411),f331(f163(x74413),x74414)))
% 51.10/50.83 [7667]~P68(x76671)+E(f331(f331(f87(x76671),f331(f331(f8(a847,x76671),x76672),f331(f302(a847,x76673),x76674))),f331(x76672,x76674)),f331(f331(f8(a847,x76671),x76672),f331(f302(a847,x76673),f331(a119,x76674))))+P1(f331(f331(f241(a847),x76674),x76673))
% 51.10/50.83 [7724]~P27(x77241,x77242,x77243,f247(f854(x77241,a840)))+~P1(f331(f68(x77242),x77244))+P1(f331(f68(x77241),f331(f312(x77241,x77242,x77243),x77244)))
% 51.10/50.83 [7838]P1(f331(f331(f333(f848(x78381)),f331(f331(f145(x78381),x78382),x78383)),f153(x78381,x78384)))+~P1(f331(f331(f333(f848(x78381)),x78383),f153(x78381,x78384)))+~P1(f331(f331(f333(x78381),x78382),x78384))
% 51.10/50.83 [7887]E(x78871,x78872)+~P1(f331(f331(f333(x78873),x78871),f331(f163(x78873),f161(x78873,x78872,x78874))))+P1(f331(f331(f333(x78873),x78871),f331(f163(x78873),x78874)))
% 51.10/50.83 [7929]~E(f331(f311(x79293,x79291,x79294),f247(f854(x79293,a840))),f247(f854(x79291,a840)))+P1(f331(f68(x79291),x79292))+~P1(f331(f68(x79293),f331(f312(x79293,x79291,x79294),x79292)))
% 51.10/50.83 [8019]~P27(x80191,x80193,x80194,x80192)+P1(f331(f68(x80191),x80192))+~P1(f331(f68(x80193),f331(f311(x80191,x80193,x80194),x80192)))
% 51.10/50.83 [8041]~E(x80412,x80413)+P1(f331(f331(f333(f853(x80411,x80411)),f331(f331(f249(x80411,x80411),x80412),x80413)),f268(x80411,x80414)))+~P1(f331(f331(f333(x80411),x80412),x80414))
% 51.10/50.83 [8042]~E(x80422,x80423)+P1(f331(f331(f333(f853(x80421,x80421)),f331(f331(f249(x80421,x80421),x80422),x80423)),f268(x80421,x80424)))+~P1(f331(f331(f333(x80421),x80422),x80424))
% 51.10/50.83 [8073]~P68(x80731)+E(f331(f331(f87(x80731),f331(f331(f8(a847,x80731),x80732),f303(a847,x80733,x80734))),f331(x80732,f331(a119,x80734))),f331(f331(f8(a847,x80731),x80732),f303(a847,x80733,f331(a119,x80734))))+P1(f331(f331(f241(a847),f331(a119,x80734)),x80733))
% 51.10/50.83 [8134]~E(x81342,x81344)+P1(f331(f331(f333(f853(x81341,x81341)),f331(f331(f249(x81341,x81341),x81342),x81344)),f308(x81341,x81343)))+P1(f331(f331(f333(x81341),x81342),f331(f269(x81341,x81341),x81343)))
% 51.10/50.83 [8136]P1(f331(x81361,x81362))+~P1(f331(x81361,f331(f331(f155(x81363),x81364),f725(x81361,x81364,x81363))))+~P1(f331(f331(f333(x81363),x81362),f331(f163(x81363),x81364)))
% 51.10/50.83 [8272]~P1(f331(f331(f333(x82721),x82722),f321(x82721,x82724)))+P1(f331(f331(f333(f848(x82721)),f331(f331(f145(x82721),x82722),x82723)),f321(f848(x82721),f150(x82721,x82724))))+~P1(f331(f331(f333(f848(x82721)),x82723),f321(f848(x82721),f150(x82721,x82724))))
% 51.10/50.83 [8288]~P27(x82882,x82883,x82884,f665(x82884,x82883,x82882,x82881))+P27(x82882,x82883,x82884,f50(f854(x82882,a840),x82881))+E(x82881,f184(f854(f854(x82882,a840),a840)))
% 51.10/50.83 [8545]E(x85451,x85452)+~P1(f331(f331(f333(f853(x85453,x85453)),f331(f331(f249(x85453,x85453),x85451),x85452)),f308(x85453,x85454)))+P1(f331(f331(f333(x85453),x85451),f331(f269(x85453,x85453),x85454)))
% 51.10/50.83 [8793]P27(x87932,x87933,x87934,f50(f854(x87932,a840),x87931))+E(x87931,f184(f854(f854(x87932,a840),a840)))+P1(f331(f331(f333(f854(x87932,a840)),f665(x87934,x87933,x87932,x87931)),x87931))
% 51.10/50.83 [8919]P1(f331(f68(x89191),x89192))+~P1(f331(f68(x89194),f331(f311(x89191,x89194,x89193),x89192)))+P1(f331(f331(f333(x89191),f587(x89193,x89194,x89192,x89191)),x89192))
% 51.10/50.83 [9009]~P7(x90092)+E(f331(f331(f71(x90091,x90092,f331(f331(f10(x90092,f854(x90092,x90092),x90091),f108(x90092)),x90093)),f184(x90092)),x90094),f331(f331(f51(x90091,x90092),x90094),x90093))+~P1(f331(f68(x90091),x90094))
% 51.10/50.83 [9010]~P7(x90102)+E(f331(f331(f71(x90101,x90102,f331(f331(f10(x90102,f854(x90102,x90102),x90101),f109(x90102)),x90103)),f247(x90102)),x90104),f331(f331(f52(x90101,x90102),x90104),x90103))+~P1(f331(f68(x90101),x90104))
% 51.10/50.83 [9036]~P1(f331(f331(f287(a847),x90363),x90364))+P1(f331(f331(f287(a847),x90361),x90362))+P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x90361,x90362)),f290(a847,f287(a847),x90363,x90364)))
% 51.10/50.83 [9047]~P1(f331(f331(f287(a847),x90472),x90474))+~P1(f331(f331(f287(a847),x90473),x90471))+P1(f331(f331(f240(f854(a847,a840)),f290(a847,f287(a847),x90471,x90472)),f290(a847,f287(a847),x90473,x90474)))
% 51.10/50.83 [9102]E(x91021,x91022)+~P1(f331(f331(f333(f853(x91023,x91023)),f331(f331(f249(x91023,x91023),x91021),x91022)),f308(x91023,x91024)))+P1(f331(f331(f333(f853(x91023,x91023)),f331(f331(f249(x91023,x91023),x91021),x91022)),f331(f331(f289(x91023,x91023,x91023),x91024),f308(x91023,x91024))))
% 51.10/50.83 [9103]E(x91031,x91032)+~P1(f331(f331(f333(f853(x91033,x91033)),f331(f331(f249(x91033,x91033),x91031),x91032)),f308(x91033,x91034)))+P1(f331(f331(f333(f853(x91033,x91033)),f331(f331(f249(x91033,x91033),x91031),x91032)),f331(f331(f289(x91033,x91033,x91033),x91034),f308(x91033,x91034))))
% 51.10/50.83 [9135]~E(f331(f185(f848(x91351)),x91352),f331(f185(f848(x91351)),x91353))+~P1(f331(f331(f333(f853(f848(x91351),f848(x91351))),f331(f331(f249(f848(x91351),f848(x91351)),x91352),x91353)),f142(x91351,x91354)))+P1(f331(f331(f333(f853(f848(x91351),f848(x91351))),f331(f331(f249(f848(x91351),f848(x91351)),x91352),x91353)),f140(x91351,x91354)))
% 51.10/50.83 [9155]E(x91551,x91552)+P1(f331(f331(f333(f853(x91553,x91553)),f331(f331(f249(x91553,x91553),x91551),x91552)),f308(x91553,x91554)))+~P1(f331(f331(f333(f853(x91553,x91553)),f331(f331(f249(x91553,x91553),x91551),x91552)),f331(f331(f289(x91553,x91553,x91553),x91554),f308(x91553,x91554))))
% 51.10/50.83 [9248]P1(f331(f331(f287(a847),x92481),x92482))+~P1(f331(f331(f287(a847),x92483),x92481))+~P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x92483,x92481)),f290(a847,f287(a847),x92484,x92482)))
% 51.10/50.83 [9249]P1(f331(f331(f287(a847),x92491),x92492))+~P1(f331(f331(f287(a847),x92493),x92491))+~P1(f331(f331(f240(f854(a847,a840)),f290(a847,f287(a847),x92493,x92491)),f290(a847,f287(a847),x92494,x92492)))
% 51.10/50.83 [9250]P1(f331(f331(f287(a847),x92501),x92502))+~P1(f331(f331(f287(a847),x92502),x92503))+~P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x92502,x92503)),f290(a847,f287(a847),x92501,x92504)))
% 51.10/50.83 [9251]P1(f331(f331(f287(a847),x92511),x92512))+~P1(f331(f331(f287(a847),x92512),x92513))+~P1(f331(f331(f240(f854(a847,a840)),f290(a847,f287(a847),x92512,x92513)),f290(a847,f287(a847),x92511,x92514)))
% 51.10/50.83 [9559]~P4(x95591)+E(f331(f331(f8(a847,x95591),f331(f331(f20(a847,x95591,x95591),f331(f331(f10(x95591,f854(x95591,x95591),a847),f3(x95591)),x95592)),f331(f331(f10(a847,x95591,a847),x95592),f331(f331(f9(a847,a847,a847),f87(a847)),f85(a847))))),f303(a847,x95593,x95594)),f2(x95591))+P1(f331(f331(f240(a847),x95593),x95594))
% 51.10/50.83 [9796]~P34(x97962,x97964)+~P27(x97962,x97961,x97963,f247(f854(x97962,a840)))+P34(x97961,f331(f311(f853(x97962,x97962),f853(x97961,x97961),f260(x97962,x97961,x97962,x97961,x97963,x97963)),x97964))
% 51.10/50.83 [9974]~E(f331(f185(f848(x99741)),x99743),f331(f185(f848(x99741)),x99742))+P1(f331(f331(f333(f853(f848(x99741),f848(x99741))),f331(f331(f249(f848(x99741),f848(x99741)),x99742),x99743)),f151(x99741,x99744)))+~P1(f331(f331(f259(x99741,x99741,a840),f331(f331(f9(x99741,f854(f853(x99741,x99741),a840),f854(x99741,a840)),f331(f331(f10(f854(x99741,f854(f854(f853(x99741,x99741),a840),a840)),f854(f854(f853(x99741,x99741),a840),f854(x99741,a840)),x99741),f9(x99741,f854(f853(x99741,x99741),a840),a840)),f331(f331(f10(f854(x99741,f853(x99741,x99741)),f854(x99741,f854(f854(f853(x99741,x99741),a840),a840)),x99741),f331(f10(f853(x99741,x99741),f854(f854(f853(x99741,x99741),a840),a840),x99741),f333(f853(x99741,x99741)))),f249(x99741,x99741)))),x99744)),f715(x99744,x99743,x99742,x99741)))
% 51.10/50.83 [5837]~E(x58374,x58372)+P1(f331(x58371,x58372))+P1(f331(f331(f191(f37(x58371,x58373)),x58372),x58374))
% 51.10/50.83 [5932]~P5(x59321)+~E(x59322,f2(x59321))+E(f331(f331(f48(x59321),f331(f331(f88(x59321),x59322),x59323)),f331(f331(f88(x59321),x59322),x59324)),f2(x59321))
% 51.10/50.83 [5971]E(x59711,f120(x59712))+E(x59713,f331(f331(f3(a847),f331(f185(f848(x59712)),x59711)),f85(a847)))+E(f139(x59712,f331(f331(f152(x59712,x59711),x59713),x59714)),f139(x59712,x59711))
% 51.10/50.83 [6003]E(x60031,x60032)+P1(f331(x60033,x60032))+~P1(f331(f331(f331(f310(x60034),x60031),x60033),x60032))
% 51.10/50.83 [6017]~P68(x60171)+~P1(f331(f132(x60172),x60174))+E(f331(f157(x60171),f331(f331(f147(x60172,x60171),x60173),x60174)),f331(f331(f8(x60172,x60171),x60173),f331(f163(x60172),x60174)))
% 51.10/50.83 [6041]~P70(x60412)+~P1(f331(f68(x60411),x60414))+E(f331(f331(f11(x60411,x60412),f331(f18(x60412,x60411),x60413)),x60414),f331(f331(f250(x60412),x60413),f331(f47(x60411),x60414)))
% 51.10/50.83 [6096]~P5(x60962)+E(x60961,f2(x60962))+E(f331(f331(f48(x60962),f331(f331(f88(x60962),x60963),x60961)),f331(f331(f88(x60962),x60964),x60961)),f331(f331(f48(x60962),x60963),x60964))
% 51.10/50.83 [6097]~P5(x60972)+E(x60971,f2(x60972))+E(f331(f331(f48(x60972),f331(f331(f88(x60972),x60971),x60973)),f331(f331(f88(x60972),x60971),x60974)),f331(f331(f48(x60972),x60973),x60974))
% 51.10/50.83 [6098]~P58(x60982)+E(x60981,f2(x60982))+E(f331(f331(f291(x60982),f331(f331(f88(x60982),x60983),x60981)),f331(f331(f88(x60982),x60984),x60981)),f331(f331(f291(x60982),x60983),x60984))
% 51.10/50.83 [6099]~P58(x60992)+E(x60991,f2(x60992))+E(f331(f331(f291(x60992),f331(f331(f88(x60992),x60991),x60993)),f331(f331(f88(x60992),x60991),x60994)),f331(f331(f291(x60992),x60993),x60994))
% 51.10/50.83 [6100]~P5(x61002)+E(x61001,f2(x61002))+E(f331(f331(f48(x61002),f331(f331(f88(x61002),x61001),x61003)),f331(f331(f88(x61002),x61001),x61004)),f331(f331(f48(x61002),x61003),x61004))
% 51.10/50.83 [6165]P1(f331(x61651,x61652))+~E(x61653,f331(f331(f87(a847),x61654),x61652))+~P1(f331(x61651,f331(f331(f3(a847),x61653),x61654)))
% 51.10/50.83 [6166]P1(f331(x61661,x61662))+~E(x61663,f331(f331(f87(a847),x61664),x61662))+~P1(f331(x61661,f331(f331(f3(a847),x61663),x61664)))
% 51.10/50.83 [6249]P30(x62491,x62492,x62493)+P29(x62491,f594(x62493,x62492,x62491),x62494)+~P1(f331(f331(f333(f846(x62491)),x62494),x62492))
% 51.10/50.83 [6294]E(x62941,f120(x62942))+~E(x62943,f331(f331(f3(a847),f331(f185(f848(x62942)),x62941)),f85(a847)))+E(f139(x62942,f331(f331(f152(x62942,x62941),x62943),x62944)),x62944)
% 51.10/50.83 [6316]~P102(x63161)+~P1(f331(f331(f241(x63161),x63162),x63164))+P1(f331(f331(f241(x63161),x63162),f331(f331(f239(x63161),x63163),x63164)))
% 51.10/50.83 [6317]~P102(x63171)+~P1(f331(f331(f241(x63171),x63172),x63174))+P1(f331(f331(f241(x63171),x63172),f331(f331(f239(x63171),x63173),x63174)))
% 51.10/50.83 [6318]~P102(x63181)+~P1(f331(f331(f241(x63181),x63182),x63183))+P1(f331(f331(f241(x63181),x63182),f331(f331(f239(x63181),x63183),x63184)))
% 51.10/50.83 [6319]~P102(x63191)+~P1(f331(f331(f241(x63191),x63192),x63193))+P1(f331(f331(f241(x63191),x63192),f331(f331(f239(x63191),x63193),x63194)))
% 51.10/50.83 [6320]~P100(x63201)+~P1(f331(f331(f241(x63201),x63202),x63204))+P1(f331(f331(f241(x63201),x63202),f331(f331(f108(x63201),x63203),x63204)))
% 51.10/50.83 [6321]~P100(x63211)+~P1(f331(f331(f241(x63211),x63212),x63213))+P1(f331(f331(f241(x63211),x63212),f331(f331(f108(x63211),x63213),x63214)))
% 51.10/50.83 [6322]~P102(x63221)+~P1(f331(f331(f240(x63221),x63222),x63224))+P1(f331(f331(f240(x63221),x63222),f331(f331(f239(x63221),x63223),x63224)))
% 51.10/50.83 [6323]~P102(x63231)+~P1(f331(f331(f240(x63231),x63232),x63234))+P1(f331(f331(f240(x63231),x63232),f331(f331(f239(x63231),x63233),x63234)))
% 51.10/50.83 [6324]~P102(x63241)+~P1(f331(f331(f240(x63241),x63242),x63243))+P1(f331(f331(f240(x63241),x63242),f331(f331(f239(x63241),x63243),x63244)))
% 51.10/50.83 [6325]~P102(x63251)+~P1(f331(f331(f240(x63251),x63252),x63253))+P1(f331(f331(f240(x63251),x63252),f331(f331(f239(x63251),x63253),x63254)))
% 51.10/50.83 [6326]~P100(x63261)+~P1(f331(f331(f240(x63261),x63262),x63264))+P1(f331(f331(f240(x63261),x63262),f331(f331(f108(x63261),x63263),x63264)))
% 51.10/50.83 [6327]~P100(x63271)+~P1(f331(f331(f240(x63271),x63272),x63273))+P1(f331(f331(f240(x63271),x63272),f331(f331(f108(x63271),x63273),x63274)))
% 51.10/50.83 [6328]~P87(x63281)+~P1(f331(f331(f287(x63281),x63282),x63284))+P1(f331(f331(f287(x63281),x63282),f331(f331(f88(x63281),x63283),x63284)))
% 51.10/50.83 [6329]~P87(x63291)+~P1(f331(f331(f287(x63291),x63292),x63293))+P1(f331(f331(f287(x63291),x63292),f331(f331(f88(x63291),x63293),x63294)))
% 51.10/50.83 [6424]~E(f331(f331(f155(x64241),x64242),x64243),x64244)+E(f331(f331(f152(x64241,x64242),x64243),x64244),x64242)+~P1(f331(f331(f241(a847),x64243),f331(f185(f848(x64241)),x64242)))
% 51.10/50.83 [6443]E(x64431,x64432)+P1(f331(x64433,x64431))+~P1(f331(f331(f191(f37(x64433,x64434)),x64431),x64432))
% 51.10/50.83 [6463]P1(f331(x64631,x64632))+~P1(f331(x64633,x64632))+~P1(f331(f331(f240(f854(x64634,a840)),x64633),x64631))
% 51.10/50.83 [6464]P1(f331(x64641,x64642))+~P1(f331(x64643,x64642))+~P1(f331(f331(f240(f854(x64644,a840)),x64643),x64641))
% 51.10/50.83 [6500]~E(f331(f331(f152(x65001,x65002),x65003),x65004),x65002)+E(f331(f331(f155(x65001),x65002),x65003),x65004)+~P1(f331(f331(f241(a847),x65003),f331(f185(f848(x65001)),x65002)))
% 51.10/50.83 [6617]P29(x66171,x66172,x66173)+~P29(x66171,f331(a119,x66172),f595(x66172,x66174,x66171))+~P1(f331(f331(f333(f846(x66171)),x66173),x66174))
% 51.10/50.83 [6626]E(x66261,f184(f854(x66262,a840)))+E(x66263,f184(f854(x66264,a840)))+~E(f331(f331(f256(x66264,x66262),x66263),f331(f18(f854(x66262,a840),x66264),x66261)),f184(f854(f853(x66264,x66262),a840)))
% 51.10/50.83 [6643]E(x66431,x66432)+P1(f331(f331(f333(x66433),x66431),x66434))+~P1(f331(f331(f333(x66433),x66431),f331(f331(f310(x66433),x66432),x66434)))
% 51.10/50.83 [6644]E(x66441,x66442)+P1(f331(f331(f333(x66443),x66441),x66444))+~P1(f331(f331(f333(x66443),x66441),f331(f331(f310(x66443),x66442),x66444)))
% 51.10/50.83 [6661]~P102(x66611)+P1(f331(f331(f241(x66611),x66612),x66613))+~P1(f331(f331(f241(x66611),x66612),f331(f331(f244(x66611),x66614),x66613)))
% 51.10/50.83 [6662]~P102(x66621)+P1(f331(f331(f241(x66621),x66622),x66623))+~P1(f331(f331(f241(x66621),x66622),f331(f331(f244(x66621),x66623),x66624)))
% 51.10/50.83 [6663]~P102(x66631)+P1(f331(f331(f240(x66631),x66632),x66633))+~P1(f331(f331(f240(x66631),x66632),f331(f331(f244(x66631),x66634),x66633)))
% 51.10/50.83 [6664]~P102(x66641)+P1(f331(f331(f240(x66641),x66642),x66643))+~P1(f331(f331(f240(x66641),x66642),f331(f331(f244(x66641),x66644),x66643)))
% 51.10/50.83 [6665]~P102(x66651)+P1(f331(f331(f240(x66651),x66652),x66653))+~P1(f331(f331(f240(x66651),x66652),f331(f331(f244(x66651),x66653),x66654)))
% 51.10/50.83 [6666]~P102(x66661)+P1(f331(f331(f240(x66661),x66662),x66663))+~P1(f331(f331(f240(x66661),x66662),f331(f331(f244(x66661),x66663),x66664)))
% 51.10/50.83 [6667]~P101(x66671)+P1(f331(f331(f240(x66671),x66672),x66673))+~P1(f331(f331(f240(x66671),x66672),f331(f331(f109(x66671),x66674),x66673)))
% 51.10/50.83 [6668]~P101(x66681)+P1(f331(f331(f240(x66681),x66682),x66683))+~P1(f331(f331(f240(x66681),x66682),f331(f331(f109(x66681),x66684),x66683)))
% 51.10/50.83 [6669]~P101(x66691)+P1(f331(f331(f240(x66691),x66692),x66693))+~P1(f331(f331(f240(x66691),x66692),f331(f331(f109(x66691),x66693),x66694)))
% 51.10/50.83 [6670]~P101(x66701)+P1(f331(f331(f240(x66701),x66702),x66703))+~P1(f331(f331(f240(x66701),x66702),f331(f331(f109(x66701),x66703),x66704)))
% 51.10/50.83 [6692]~E(f331(f331(f155(x66921),x66923),x66924),x66922)+P1(f331(f331(f333(x66921),x66922),f331(f163(x66921),x66923)))+~P1(f331(f331(f241(a847),x66924),f331(f185(f848(x66921)),x66923)))
% 51.10/50.83 [6704]~P102(x67041)+~P16(x67041,f331(f331(f145(x67041),x67042),f331(f331(f145(x67041),x67043),x67044)))+P1(f331(f331(f240(x67041),x67042),x67043))
% 51.10/50.83 [6761]~P102(x67611)+P16(x67611,f331(f331(f145(x67611),x67612),x67613))+~P16(x67611,f331(f331(f145(x67611),x67614),f331(f331(f145(x67611),x67612),x67613)))
% 51.10/50.83 [6873]E(x68731,f2(a1))+E(f331(f331(f48(a1),x68732),x68731),x68733)+~P1(f331(f61(x68732,x68731),f331(f331(f249(a1,a1),x68733),x68734)))
% 51.10/50.83 [6896]E(f57(a1,x68962,x68961),x68963)+E(x68961,f2(a1))+~P1(f331(f61(x68962,x68961),f331(f331(f249(a1,a1),x68964),x68963)))
% 51.10/50.83 [7011]P1(f331(f331(f333(x70111),x70112),x70113))+~P1(f331(f331(f333(x70111),x70112),x70114))+~P1(f331(f331(f241(f854(x70111,a840)),x70114),x70113))
% 51.10/50.83 [7012]P1(f331(f331(f333(x70121),x70122),x70123))+~P1(f331(f331(f333(x70121),x70122),x70124))+~P1(f331(f331(f240(f854(x70121,a840)),x70124),x70123))
% 51.10/50.83 [7013]P1(f331(f331(f333(x70131),x70132),x70133))+~P1(f331(f331(f333(x70131),x70132),x70134))+~P1(f331(f331(f240(f854(x70131,a840)),x70134),x70133))
% 51.10/50.83 [7014]P1(f331(f331(f333(x70141),x70142),x70143))+~P1(f331(f331(f333(x70141),x70142),x70144))+~P1(f331(f331(f240(f854(x70141,a840)),x70144),x70143))
% 51.10/50.83 [7015]P1(f331(f331(f333(x70151),x70152),x70153))+~P1(f331(f331(f333(x70151),x70152),x70154))+~P1(f331(f331(f240(f854(x70151,a840)),x70154),x70153))
% 51.10/50.83 [7025]~P112(x70251)+~E(x70253,f2(x70251))+P1(f331(f331(f287(x70251),f331(f331(f88(x70251),x70252),x70253)),f331(f331(f88(x70251),x70254),x70253)))
% 51.10/50.83 [7026]~P112(x70261)+~E(x70262,f2(x70261))+P1(f331(f331(f287(x70261),f331(f331(f88(x70261),x70262),x70263)),f331(f331(f88(x70261),x70262),x70264)))
% 51.10/50.83 [7249]~P104(x72492)+~P1(f331(f331(f241(f854(x72491,x72492)),x72493),x72494))+P1(f331(f331(f240(f854(x72491,x72492)),x72493),x72494))
% 51.10/50.83 [7344]~P26(x73441,x73442,x73444)+P26(x73441,x73442,f331(f331(f310(f846(x73441)),x73443),x73444))+~P26(x73441,x73442,f331(f331(f310(f846(x73441)),x73443),f184(f854(f846(x73441),a840))))
% 51.10/50.83 [7383]~P1(f331(f331(f333(x73831),x73832),x73834))+P1(f331(f331(f333(x73831),x73832),f49(f854(x73831,a840),x73833)))+~P1(f331(f331(f333(f854(x73831,a840)),x73834),x73833))
% 51.10/50.83 [7385]~P87(x73851)+~P1(f331(f331(f240(a847),x73853),x73854))+P1(f331(f331(f287(x73851),f331(f331(f250(x73851),x73852),x73853)),f331(f331(f250(x73851),x73852),x73854)))
% 51.10/50.83 [7396]P29(x73961,x73962,x73963)+P1(f331(f331(f333(f846(x73961)),f595(x73962,x73964,x73961)),x73964))+~P1(f331(f331(f333(f846(x73961)),x73963),x73964))
% 51.10/50.83 [7415]~P66(x74151)+~P1(f331(f331(f241(x74151),x74153),x74154))+P1(f331(f331(f241(x74151),f331(f331(f87(x74151),x74152),x74153)),f331(f331(f87(x74151),x74152),x74154)))
% 51.10/50.83 [7416]~P79(x74161)+~P1(f331(f331(f241(x74161),x74163),x74164))+P1(f331(f331(f241(x74161),f331(f331(f87(x74161),x74162),x74163)),f331(f331(f87(x74161),x74162),x74164)))
% 51.10/50.83 [7417]~P66(x74171)+~P1(f331(f331(f241(x74171),x74172),x74174))+P1(f331(f331(f241(x74171),f331(f331(f87(x74171),x74172),x74173)),f331(f331(f87(x74171),x74174),x74173)))
% 51.10/50.83 [7418]~P79(x74181)+~P1(f331(f331(f241(x74181),x74182),x74184))+P1(f331(f331(f241(x74181),f331(f331(f87(x74181),x74182),x74183)),f331(f331(f87(x74181),x74184),x74183)))
% 51.10/50.83 [7419]~P66(x74191)+~P1(f331(f331(f240(x74191),x74193),x74194))+P1(f331(f331(f240(x74191),f331(f331(f87(x74191),x74192),x74193)),f331(f331(f87(x74191),x74192),x74194)))
% 51.10/50.83 [7420]~P77(x74201)+~P1(f331(f331(f240(x74201),x74203),x74204))+P1(f331(f331(f240(x74201),f331(f331(f87(x74201),x74202),x74203)),f331(f331(f87(x74201),x74202),x74204)))
% 51.10/50.83 [7421]~P66(x74211)+~P1(f331(f331(f240(x74211),x74212),x74214))+P1(f331(f331(f240(x74211),f331(f331(f87(x74211),x74212),x74213)),f331(f331(f87(x74211),x74214),x74213)))
% 51.10/50.83 [7422]~P77(x74221)+~P1(f331(f331(f240(x74221),x74222),x74224))+P1(f331(f331(f240(x74221),f331(f331(f87(x74221),x74222),x74223)),f331(f331(f87(x74221),x74224),x74223)))
% 51.10/50.83 [7423]~P112(x74231)+~P1(f331(f331(f287(x74231),x74233),x74234))+P1(f331(f331(f287(x74231),f331(f331(f88(x74231),x74232),x74233)),f331(f331(f88(x74231),x74232),x74234)))
% 51.10/50.83 [7424]~P112(x74241)+~P1(f331(f331(f287(x74241),x74242),x74244))+P1(f331(f331(f287(x74241),f331(f331(f88(x74241),x74242),x74243)),f331(f331(f88(x74241),x74244),x74243)))
% 51.10/50.83 [7425]~P87(x74251)+~P1(f331(f331(f287(x74251),x74252),x74254))+P1(f331(f331(f287(x74251),f331(f331(f250(x74251),x74252),x74253)),f331(f331(f250(x74251),x74254),x74253)))
% 51.10/50.83 [7434]~P135(x74341)+~P92(x74341)+E(f331(f331(f87(x74341),f331(f331(f88(x74341),x74342),f331(f111(x74341),x74343))),f331(f331(f88(x74341),x74344),f331(f111(x74341),x74343))),f331(f331(f88(x74341),f331(f331(f87(x74341),x74342),x74344)),f331(f111(x74341),x74343)))
% 51.10/50.83 [7435]~P121(x74351)+~P92(x74351)+E(f331(f331(f3(x74351),f331(f331(f88(x74351),x74352),f331(f111(x74351),x74353))),f331(f331(f88(x74351),x74354),f331(f111(x74351),x74353))),f331(f331(f88(x74351),f331(f331(f3(x74351),x74352),x74354)),f331(f111(x74351),x74353)))
% 51.10/50.83 [7472]~P68(x74721)+E(f331(f331(f87(x74721),f331(x74722,x74723)),f331(f331(f8(a847,x74721),x74722),f303(a847,f331(a119,x74723),x74724))),f331(f331(f8(a847,x74721),x74722),f303(a847,x74723,x74724)))+~P1(f331(f331(f240(a847),x74723),x74724))
% 51.10/50.83 [7483]~P27(x74832,x74831,x74833,f331(f163(x74832),x74834))+~P1(f331(f132(x74832),x74834))+P1(f331(f132(x74831),f331(f331(f147(x74832,x74831),x74833),x74834)))
% 51.10/50.83 [7532]~P1(f331(f331(f241(a847),x75322),x75324))+~P1(f331(f331(f241(a847),x75321),x75323))+P1(f331(f331(f241(a847),f331(f331(f87(a847),x75321),x75322)),f331(f331(f87(a847),x75323),x75324)))
% 51.10/50.83 [7535]~P1(f331(f331(f241(a1),x75351),x75353))+~P1(f331(f331(f240(a1),x75352),x75354))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x75351),x75352)),f331(f331(f87(a1),x75353),x75354)))
% 51.10/50.83 [7536]~P1(f331(f331(f240(a847),x75362),x75364))+~P1(f331(f331(f240(a847),x75361),x75363))+P1(f331(f331(f240(a847),f331(f331(f87(a847),x75361),x75362)),f331(f331(f87(a847),x75363),x75364)))
% 51.10/50.83 [7537]~P1(f331(f331(f240(a847),x75372),x75374))+~P1(f331(f331(f240(a847),x75371),x75373))+P1(f331(f331(f240(a847),f331(f331(f88(a847),x75371),x75372)),f331(f331(f88(a847),x75373),x75374)))
% 51.10/50.83 [7586]P1(f331(f331(f333(x75861),x75862),x75863))+~P1(f331(f331(f333(x75861),x75862),f50(f854(x75861,a840),x75864)))+~P1(f331(f331(f333(f854(x75861,a840)),x75863),x75864))
% 51.10/50.83 [7587]P1(f331(f331(f333(x75871),x75872),x75873))+~P1(f331(f331(f333(x75871),x75872),f50(f854(x75871,a840),x75874)))+~P1(f331(f331(f333(f854(x75871,a840)),x75873),x75874))
% 51.10/50.83 [7603]~P1(f331(x76031,f723(x76031,x76033,x76032)))+P1(f331(x76031,f331(f331(f155(x76032),x76033),x76034)))+~P1(f331(f331(f241(a847),x76034),f331(f185(f848(x76032)),x76033)))
% 51.10/50.83 [7607]P1(f331(x76071,x76072))+~P1(f331(f331(f333(x76074),x76072),f331(f163(x76074),x76073)))+P1(f331(f331(f241(a847),f725(x76071,x76073,x76074)),f331(f185(f848(x76074)),x76073)))
% 51.10/50.83 [7626]~P1(f331(f331(f191(x76262),x76263),x76264))+~P1(f331(f331(f191(f37(x76261,x76262)),x76264),x76263))+P1(f331(f331(f191(f37(x76261,x76262)),x76263),x76263))
% 51.10/50.83 [7654]~P104(x76541)+~P1(f331(f331(f240(f854(x76542,x76541)),x76544),x76543))+~P1(f331(f331(f241(f854(x76542,x76541)),x76543),x76544))
% 51.10/50.83 [7697]~P1(f331(x76974,x76972))+~P1(f331(f331(f333(x76971),x76972),x76973))+P1(f331(f331(f333(x76971),x76972),f331(f331(f109(f854(x76971,a840)),x76973),f331(f264(x76971),x76974))))
% 51.10/50.83 [7716]P1(f331(f331(f333(x77161),x77162),x77163))+~P1(f331(f331(f240(f854(x77161,a840)),x77163),x77164))+P1(f331(f331(f240(f854(x77161,a840)),x77163),f331(f331(f310(x77161),x77162),x77164)))
% 51.10/50.83 [7717]P1(f331(f331(f333(x77171),x77172),x77173))+~P1(f331(f331(f240(f854(x77171,a840)),x77173),x77174))+P1(f331(f331(f240(f854(x77171,a840)),x77173),f331(f331(f310(x77171),x77172),x77174)))
% 51.10/50.83 [7846]~P1(f331(f331(f333(x78461),x78463),x78464))+~P1(f331(f331(f241(f854(x78461,a840)),x78462),x78464))+P1(f331(f331(f241(f854(x78461,a840)),x78462),f331(f331(f310(x78461),x78463),x78464)))
% 51.10/50.83 [7848]E(f331(f331(f109(f854(x78481,a840)),x78482),x78483),f184(f854(x78481,a840)))+~E(f331(f331(f109(f854(x78481,a840)),f49(f854(x78481,a840),x78484)),x78483),f184(f854(x78481,a840)))+~P1(f331(f331(f333(f854(x78481,a840)),x78482),x78484))
% 51.10/50.83 [7924]P1(f331(f331(f333(x79241),x79242),x79243))+~P1(f331(f331(f240(f854(x79241,a840)),x79243),f331(f331(f310(x79241),x79242),x79244)))+P1(f331(f331(f240(f854(x79241,a840)),x79243),x79244))
% 51.10/50.83 [7925]P1(f331(f331(f333(x79251),x79252),x79253))+~P1(f331(f331(f240(f854(x79251,a840)),x79253),f331(f331(f310(x79251),x79252),x79254)))+P1(f331(f331(f240(f854(x79251,a840)),x79253),x79254))
% 51.10/50.83 [7945]P1(f331(f331(f333(x79452),f723(x79451,x79453,x79452)),f331(f163(x79452),x79453)))+P1(f331(x79451,f331(f331(f155(x79452),x79453),x79454)))+~P1(f331(f331(f241(a847),x79454),f331(f185(f848(x79452)),x79453)))
% 51.10/50.83 [7953]~P1(f331(f331(f241(f854(x79531,a840)),x79532),x79534))+P1(f331(f331(f241(f854(x79531,a840)),x79532),x79533))+~P1(f331(f331(f241(f854(x79531,a840)),x79534),x79533))
% 51.10/50.83 [7954]~P1(f331(f331(f240(f854(x79541,a840)),x79542),x79544))+P1(f331(f331(f241(f854(x79541,a840)),x79542),x79543))+~P1(f331(f331(f241(f854(x79541,a840)),x79544),x79543))
% 51.10/50.83 [7955]~P1(f331(f331(f240(f854(x79551,a840)),x79554),x79553))+~P1(f331(f331(f241(f854(x79551,a840)),x79552),x79554))+P1(f331(f331(f241(f854(x79551,a840)),x79552),x79553))
% 51.10/50.83 [7956]~P1(f331(f331(f240(f854(x79561,a840)),x79562),x79564))+P1(f331(f331(f240(f854(x79561,a840)),x79562),x79563))+~P1(f331(f331(f240(f854(x79561,a840)),x79564),x79563))
% 51.10/50.83 [7992]~P1(f331(f331(f333(x79921),x79924),x79923))+~P1(f331(f331(f241(f854(x79921,a840)),x79922),f331(f331(f310(x79921),x79924),x79923)))+P1(f331(f331(f241(f854(x79921,a840)),x79922),x79923))
% 51.10/50.83 [8004]~P66(x80041)+P1(f331(f331(f241(x80041),x80042),x80043))+~P1(f331(f331(f241(x80041),f331(f331(f87(x80041),x80044),x80042)),f331(f331(f87(x80041),x80044),x80043)))
% 51.10/50.83 [8005]~P66(x80051)+P1(f331(f331(f241(x80051),x80052),x80053))+~P1(f331(f331(f241(x80051),f331(f331(f87(x80051),x80054),x80052)),f331(f331(f87(x80051),x80054),x80053)))
% 51.10/50.83 [8006]~P66(x80061)+P1(f331(f331(f241(x80061),x80062),x80063))+~P1(f331(f331(f241(x80061),f331(f331(f87(x80061),x80062),x80064)),f331(f331(f87(x80061),x80063),x80064)))
% 51.10/50.83 [8007]~P66(x80071)+P1(f331(f331(f241(x80071),x80072),x80073))+~P1(f331(f331(f241(x80071),f331(f331(f87(x80071),x80072),x80074)),f331(f331(f87(x80071),x80073),x80074)))
% 51.10/50.83 [8008]~P66(x80081)+P1(f331(f331(f240(x80081),x80082),x80083))+~P1(f331(f331(f240(x80081),f331(f331(f87(x80081),x80084),x80082)),f331(f331(f87(x80081),x80084),x80083)))
% 51.10/50.83 [8009]~P66(x80091)+P1(f331(f331(f240(x80091),x80092),x80093))+~P1(f331(f331(f240(x80091),f331(f331(f87(x80091),x80094),x80092)),f331(f331(f87(x80091),x80094),x80093)))
% 51.10/50.83 [8010]~P66(x80101)+P1(f331(f331(f240(x80101),x80102),x80103))+~P1(f331(f331(f240(x80101),f331(f331(f87(x80101),x80102),x80104)),f331(f331(f87(x80101),x80103),x80104)))
% 51.10/50.83 [8011]~P66(x80111)+P1(f331(f331(f240(x80111),x80112),x80113))+~P1(f331(f331(f240(x80111),f331(f331(f87(x80111),x80112),x80114)),f331(f331(f87(x80111),x80113),x80114)))
% 51.10/50.83 [8176]P1(f331(x81761,x81762))+~P1(f331(f331(f333(x81763),x81762),f331(f163(x81763),x81764)))+P1(f331(f331(f241(a847),f331(f185(f848(x81763)),f331(f131(x81763,x81761),x81764))),f331(f185(f848(x81763)),x81764)))
% 51.10/50.83 [8307]E(x83071,x83072)+P1(f331(f331(f191(x83073),x83071),f536(x83072,x83071,x83073,x83074)))+~P1(f331(f331(f191(f37(x83074,x83073)),x83071),x83072))
% 51.10/50.83 [8334]~P1(f331(x83344,x83342))+P1(f331(f331(f191(x83341),x83342),f536(x83343,x83342,x83341,x83344)))+~P1(f331(f331(f191(f37(x83344,x83341)),x83342),x83343))
% 51.10/50.83 [8657]~P27(x86574,x86573,x86571,f247(f854(x86574,a840)))+E(f331(x86571,f516(x86572,x86571,x86573,x86574)),x86572)+~P1(f331(f331(f333(x86573),x86572),f331(f311(x86574,x86573,x86571),f247(f854(x86574,a840)))))
% 51.10/50.83 [8795]~P1(f331(f68(x87951),x87954))+P1(f331(f331(f333(x87951),f549(x87952,x87953,x87954,x87951)),x87954))+P1(f331(f68(f853(x87951,x87953)),f331(f331(f256(x87951,x87953),x87954),x87952)))
% 51.10/50.83 [8839]E(x88391,x88392)+P1(f331(f331(f191(f37(x88393,x88394)),f536(x88391,x88392,x88394,x88393)),x88391))+~P1(f331(f331(f191(f37(x88393,x88394)),x88392),x88391))
% 51.10/50.83 [8859]~P1(f331(x88591,x88594))+P1(f331(f331(f191(f37(x88591,x88592)),f536(x88593,x88594,x88592,x88591)),x88593))+~P1(f331(f331(f191(f37(x88591,x88592)),x88594),x88593))
% 51.10/50.83 [9094]~P1(f331(f68(x90941),x90943))+~P1(f331(f68(x90942),f331(x90944,f549(x90944,x90942,x90943,x90941))))+P1(f331(f68(f853(x90941,x90942)),f331(f331(f256(x90941,x90942),x90943),x90944)))
% 51.10/50.83 [9109]~E(f331(f185(f848(x91094)),x91092),f331(f185(f848(x91094)),x91093))+P1(f331(f331(f333(f853(f848(x91094),f848(x91094))),f331(f331(f249(f848(x91094),f848(x91094)),x91093),x91092)),f151(x91094,x91091)))+P1(f331(f331(f241(a847),f731(x91091,x91092,x91093,x91094)),f331(f185(f848(x91094)),x91093)))
% 51.10/50.83 [9222]E(f331(f331(f164(x92221),f732(x92222,x92223,x92224,x92221)),x92223),f331(f331(f164(x92221),f732(x92222,x92223,x92224,x92221)),x92224))+~P1(f331(f331(f333(f853(f848(x92221),f848(x92221))),f331(f331(f249(f848(x92221),f848(x92221)),x92224),x92223)),f142(x92221,x92222)))+P1(f331(f331(f241(a847),f331(f185(f848(x92221)),x92224)),f331(f185(f848(x92221)),x92223)))
% 51.10/50.83 [9281]~P1(f331(f331(f241(a847),f2(a847)),x92813))+~P1(f331(f331(f241(a847),x92814),x92811))+P1(f331(f331(f241(a847),f331(f331(f87(a847),f331(f331(f88(a847),x92811),f57(a847,x92812,x92813))),x92814)),f331(f331(f88(a847),x92811),x92813)))
% 51.10/50.83 [9468]~P104(x94682)+~P1(f331(f331(f240(x94682),f331(x94683,f680(x94684,x94683,x94681,x94682))),f331(x94684,f680(x94684,x94683,x94681,x94682))))+P1(f331(f331(f240(f854(x94681,x94682)),x94683),x94684))
% 51.10/50.83 [9563]~P4(x95631)+E(f331(f331(f8(a847,x95631),f331(f331(f20(a847,x95631,x95631),f331(f331(f10(x95631,f854(x95631,x95631),a847),f3(x95631)),x95632)),f331(f331(f10(a847,x95631,a847),x95632),f331(f331(f9(a847,a847,a847),f87(a847)),f85(a847))))),f303(a847,x95633,x95634)),f331(f331(f3(x95631),f331(x95632,x95633)),f331(x95632,f331(f331(f87(a847),x95634),f85(a847)))))+~P1(f331(f331(f240(a847),x95633),x95634))
% 51.10/50.83 [6606]~P5(x66061)+E(f331(f331(f48(x66061),f331(f331(f88(x66061),x66062),x66063)),x66064),f331(f331(f88(x66061),x66062),f331(f331(f48(x66061),x66063),x66064)))+~P1(f331(f331(f287(x66061),x66064),x66063))
% 51.10/50.83 [6696]E(f331(f331(f130(x66961),x66962),x66963),x66964)+~E(x66963,f331(f331(f133(x66961),f331(f185(f848(x66961)),x66962)),x66964))+~E(f331(f331(f164(x66961),f331(f185(f848(x66961)),x66962)),x66964),x66962)
% 51.10/50.83 [6756]~P59(x67562)+E(x67561,f2(x67562))+E(f331(f331(f291(x67562),f331(f331(f250(x67562),x67563),x67564)),f331(f331(f250(x67562),x67561),x67564)),f331(f331(f250(x67562),f331(f331(f291(x67562),x67563),x67561)),x67564))
% 51.10/50.83 [6906]~P5(x69061)+E(f331(f331(f48(x69061),f331(f331(f88(x69061),x69062),x69063)),x69064),f331(f331(f88(x69061),f331(f331(f48(x69061),x69062),x69064)),x69063))+~P1(f331(f331(f287(x69061),x69064),x69062))
% 51.10/50.83 [6915]~P102(x69151)+~P1(f331(f331(f241(x69151),x69153),x69154))+P1(f331(f331(f241(x69151),f331(f331(f244(x69151),x69152),x69153)),x69154))
% 51.10/50.83 [6916]~P102(x69161)+~P1(f331(f331(f241(x69161),x69163),x69164))+P1(f331(f331(f241(x69161),f331(f331(f244(x69161),x69162),x69163)),x69164))
% 51.10/50.83 [6917]~P102(x69171)+~P1(f331(f331(f241(x69171),x69172),x69174))+P1(f331(f331(f241(x69171),f331(f331(f244(x69171),x69172),x69173)),x69174))
% 51.10/50.83 [6918]~P102(x69181)+~P1(f331(f331(f241(x69181),x69182),x69184))+P1(f331(f331(f241(x69181),f331(f331(f244(x69181),x69182),x69183)),x69184))
% 51.10/50.83 [6919]~P101(x69191)+~P1(f331(f331(f241(x69191),x69193),x69194))+P1(f331(f331(f241(x69191),f331(f331(f109(x69191),x69192),x69193)),x69194))
% 51.10/50.83 [6920]~P101(x69201)+~P1(f331(f331(f241(x69201),x69202),x69204))+P1(f331(f331(f241(x69201),f331(f331(f109(x69201),x69202),x69203)),x69204))
% 51.10/50.83 [6921]~P102(x69211)+~P1(f331(f331(f240(x69211),x69213),x69214))+P1(f331(f331(f240(x69211),f331(f331(f244(x69211),x69212),x69213)),x69214))
% 51.10/50.83 [6922]~P102(x69221)+~P1(f331(f331(f240(x69221),x69223),x69224))+P1(f331(f331(f240(x69221),f331(f331(f244(x69221),x69222),x69223)),x69224))
% 51.10/50.83 [6923]~P102(x69231)+~P1(f331(f331(f240(x69231),x69232),x69234))+P1(f331(f331(f240(x69231),f331(f331(f244(x69231),x69232),x69233)),x69234))
% 51.10/50.83 [6924]~P102(x69241)+~P1(f331(f331(f240(x69241),x69242),x69244))+P1(f331(f331(f240(x69241),f331(f331(f244(x69241),x69242),x69243)),x69244))
% 51.10/50.83 [6925]~P101(x69251)+~P1(f331(f331(f240(x69251),x69253),x69254))+P1(f331(f331(f240(x69251),f331(f331(f109(x69251),x69252),x69253)),x69254))
% 51.10/50.83 [6926]~P101(x69261)+~P1(f331(f331(f240(x69261),x69262),x69264))+P1(f331(f331(f240(x69261),f331(f331(f109(x69261),x69262),x69263)),x69264))
% 51.10/50.83 [6943]~P1(f331(x69433,x69434))+~P1(f331(x69432,x69434))+P1(f331(f331(f331(f109(f854(x69431,a840)),x69432),x69433),x69434))
% 51.10/50.83 [6975]~E(f331(f185(f848(x69751)),x69753),f331(f185(f848(x69752)),x69754))+~P1(f331(f132(x69751),x69753))+E(f174(x69751,x69752,f171(x69751,x69752,f331(f331(f172(x69751,x69752),x69753),x69754))),f331(f163(x69751),x69753))
% 51.10/50.83 [7069]P26(x70691,x70692,x70693)+~P26(x70691,x70694,x70693)+~P1(f331(f331(f240(f854(f846(x70691),a840)),x70694),x70692))
% 51.10/50.83 [7070]P26(x70701,x70702,x70703)+~P26(x70701,x70702,x70704)+~P1(f331(f331(f240(f854(f846(x70701),a840)),x70703),x70704))
% 51.10/50.83 [7206]~P5(x72061)+E(f331(f331(f48(x72061),f331(f331(f250(x72061),x72062),x72063)),f331(f331(f250(x72061),x72064),x72063)),f331(f331(f250(x72061),f331(f331(f48(x72061),x72062),x72064)),x72063))+~P1(f331(f331(f287(x72061),x72064),x72062))
% 51.10/50.83 [7462]~P68(x74621)+E(f331(f331(f87(x74621),f331(x74622,x74623)),f331(f331(f8(a847,x74621),x74622),f331(f302(a847,f331(a119,x74623)),x74624))),f331(f331(f8(a847,x74621),x74622),f331(f302(a847,x74623),x74624)))+~P1(f331(f331(f241(a847),x74623),x74624))
% 51.10/50.83 [7490]~P102(x74901)+P1(f331(f331(f241(x74901),x74902),x74903))+~P1(f331(f331(f241(x74901),f331(f331(f239(x74901),x74904),x74902)),x74903))
% 51.10/50.83 [7491]~P102(x74911)+P1(f331(f331(f241(x74911),x74912),x74913))+~P1(f331(f331(f241(x74911),f331(f331(f239(x74911),x74912),x74914)),x74913))
% 51.10/50.83 [7492]~P102(x74921)+P1(f331(f331(f240(x74921),x74922),x74923))+~P1(f331(f331(f240(x74921),f331(f331(f239(x74921),x74924),x74922)),x74923))
% 51.10/50.83 [7493]~P102(x74931)+P1(f331(f331(f240(x74931),x74932),x74933))+~P1(f331(f331(f240(x74931),f331(f331(f239(x74931),x74934),x74932)),x74933))
% 51.10/50.83 [7494]~P102(x74941)+P1(f331(f331(f240(x74941),x74942),x74943))+~P1(f331(f331(f240(x74941),f331(f331(f239(x74941),x74942),x74944)),x74943))
% 51.10/50.83 [7495]~P102(x74951)+P1(f331(f331(f240(x74951),x74952),x74953))+~P1(f331(f331(f240(x74951),f331(f331(f239(x74951),x74952),x74954)),x74953))
% 51.10/50.83 [7496]~P100(x74961)+P1(f331(f331(f240(x74961),x74962),x74963))+~P1(f331(f331(f240(x74961),f331(f331(f108(x74961),x74964),x74962)),x74963))
% 51.10/50.83 [7497]~P100(x74971)+P1(f331(f331(f240(x74971),x74972),x74973))+~P1(f331(f331(f240(x74971),f331(f331(f108(x74971),x74974),x74972)),x74973))
% 51.10/50.83 [7498]~P100(x74981)+P1(f331(f331(f240(x74981),x74982),x74983))+~P1(f331(f331(f240(x74981),f331(f331(f108(x74981),x74982),x74984)),x74983))
% 51.10/50.83 [7499]~P100(x74991)+P1(f331(f331(f240(x74991),x74992),x74993))+~P1(f331(f331(f240(x74991),f331(f331(f108(x74991),x74992),x74994)),x74993))
% 51.10/50.83 [7500]~P87(x75001)+P1(f331(f331(f287(x75001),x75002),x75003))+~P1(f331(f331(f287(x75001),f331(f331(f88(x75001),x75004),x75002)),x75003))
% 51.10/50.83 [7501]~P87(x75011)+P1(f331(f331(f287(x75011),x75012),x75013))+~P1(f331(f331(f287(x75011),f331(f331(f88(x75011),x75012),x75014)),x75013))
% 51.10/50.83 [7578]~P1(f331(f331(f333(x75781),x75782),x75784))+P1(f331(f331(f333(x75781),x75782),x75783))+P1(f331(f331(f333(x75781),x75782),f331(f331(f3(f854(x75781,a840)),x75784),x75783)))
% 51.10/50.83 [7579]~P1(f331(f331(f333(x75791),x75792),x75794))+P1(f331(f331(f333(x75791),x75792),x75793))+P1(f331(f331(f333(x75791),x75792),f331(f331(f3(f854(x75791,a840)),x75794),x75793)))
% 51.10/50.83 [7659]P1(f331(x76591,x76592))+P1(f331(x76593,x76592))+~P1(f331(f331(f331(f108(f854(x76594,a840)),x76593),x76591),x76592))
% 51.10/50.83 [7668]~P1(f331(f331(f333(x76681),x76682),x76684))+~P1(f331(f331(f333(x76681),x76682),x76683))+P1(f331(f331(f333(x76681),x76682),f331(f331(f109(f854(x76681,a840)),x76683),x76684)))
% 51.10/50.83 [7669]~P1(f331(f331(f333(x76691),x76692),x76694))+~P1(f331(f331(f333(x76691),x76692),x76693))+P1(f331(f331(f333(x76691),x76692),f331(f331(f109(f854(x76691,a840)),x76693),x76694)))
% 51.10/50.83 [7725]~P102(x77251)+~P1(f331(f68(x77251),x77254))+E(f331(f331(f71(x77251,x77251,f244(x77251)),x77252),f331(f331(f310(x77251),x77253),x77254)),f331(f331(f244(x77251),x77253),f331(f331(f71(x77251,x77251,f244(x77251)),x77252),x77254)))
% 51.10/50.83 [7726]~P102(x77261)+~P1(f331(f68(x77261),x77264))+E(f331(f331(f71(x77261,x77261,f239(x77261)),x77262),f331(f331(f310(x77261),x77263),x77264)),f331(f331(f239(x77261),x77263),f331(f331(f71(x77261,x77261,f239(x77261)),x77262),x77264)))
% 51.10/50.83 [7727]~P100(x77271)+~P1(f331(f68(x77271),x77274))+E(f331(f331(f71(x77271,x77271,f108(x77271)),x77272),f331(f331(f310(x77271),x77273),x77274)),f331(f331(f108(x77271),x77273),f331(f331(f71(x77271,x77271,f108(x77271)),x77272),x77274)))
% 51.10/50.83 [7728]~P101(x77281)+~P1(f331(f68(x77281),x77284))+E(f331(f331(f71(x77281,x77281,f109(x77281)),x77282),f331(f331(f310(x77281),x77283),x77284)),f331(f331(f109(x77281),x77283),f331(f331(f71(x77281,x77281,f109(x77281)),x77282),x77284)))
% 51.10/50.83 [7730]~P135(x77301)+~P92(x77301)+E(f331(f331(f87(x77301),f331(f331(f88(x77301),f331(f111(x77301),x77302)),x77303)),f331(f331(f88(x77301),f331(f111(x77301),x77302)),x77304)),f331(f331(f88(x77301),f331(f111(x77301),x77302)),f331(f331(f87(x77301),x77303),x77304)))
% 51.10/50.83 [7731]~P121(x77311)+~P92(x77311)+E(f331(f331(f3(x77311),f331(f331(f88(x77311),f331(f111(x77311),x77312)),x77313)),f331(f331(f88(x77311),f331(f111(x77311),x77312)),x77314)),f331(f331(f88(x77311),f331(f111(x77311),x77312)),f331(f331(f3(x77311),x77313),x77314)))
% 51.10/50.83 [7844]E(x78441,x78442)+P1(f331(f331(f333(x78443),x78441),f331(f163(x78443),x78444)))+~P1(f331(f331(f333(x78443),x78441),f331(f163(x78443),f331(f331(f145(x78443),x78442),x78444))))
% 51.10/50.83 [8015]P51(x80151,x80152,x80153)+~P51(x80151,x80152,x80154)+~P1(f331(f331(f240(f854(f853(x80151,x80152),a840)),x80153),x80154))
% 51.10/50.83 [8057]P1(f331(f331(f333(x80571),x80572),x80573))+P1(f331(f331(f333(x80571),x80572),x80574))+~P1(f331(f331(f333(x80571),x80572),f331(f331(f108(f854(x80571,a840)),x80574),x80573)))
% 51.10/50.83 [8058]P1(f331(f331(f333(x80581),x80582),x80583))+P1(f331(f331(f333(x80581),x80582),x80584))+~P1(f331(f331(f333(x80581),x80582),f331(f331(f108(f854(x80581,a840)),x80584),x80583)))
% 51.10/50.83 [8067]~P45(x80671,x80674,x80673)+~P1(f331(f331(f333(x80671),x80672),x80674))+P1(f331(f331(f333(f853(x80671,x80671)),f331(f331(f249(x80671,x80671),x80672),x80672)),x80673))
% 51.10/50.83 [8068]~P45(x80681,x80684,x80683)+~P1(f331(f331(f333(x80681),x80682),x80684))+P1(f331(f331(f333(f853(x80681,x80681)),f331(f331(f249(x80681,x80681),x80682),x80682)),x80683))
% 51.10/50.83 [8069]~P45(x80691,x80694,x80693)+~P1(f331(f331(f333(x80691),x80692),x80694))+P1(f331(f331(f333(f853(x80691,x80691)),f331(f331(f249(x80691,x80691),x80692),x80692)),x80693))
% 51.10/50.83 [8081]~P1(f331(f68(x80812),x80814))+~P1(f331(f68(x80811),x80813))+P1(f331(f68(f853(x80811,x80812)),f331(f331(f256(x80811,x80812),x80813),f331(f18(f854(x80812,a840),x80811),x80814))))
% 51.10/50.83 [8082]~P1(f331(f331(f333(x80821),x80822),x80824))+~P1(f331(f331(f240(f854(x80821,a840)),x80823),x80824))+P1(f331(f331(f240(f854(x80821,a840)),f331(f331(f310(x80821),x80822),x80823)),x80824))
% 51.10/50.83 [8090]~P84(x80902)+~P70(x80902)+E(f331(f331(f11(x80901,x80902),f331(f331(f10(a847,x80902,x80901),f107(x80902)),x80903)),x80904),f331(f107(x80902),f331(f331(f11(x80901,a847),x80903),x80904)))
% 51.10/50.83 [8091]~P133(x80912)+~P70(x80912)+E(f331(f331(f11(x80911,x80912),f331(f331(f10(a1,x80912,x80911),f110(x80912)),x80913)),x80914),f331(f110(x80912),f331(f331(f11(x80911,a1),x80913),x80914)))
% 51.10/50.83 [8117]E(f331(f331(f3(f854(x81171,a840)),x81172),f331(f331(f3(f854(x81171,a840)),x81173),x81174)),x81174)+~P1(f331(f331(f240(f854(x81171,a840)),x81172),x81173))+~P1(f331(f331(f240(f854(x81171,a840)),x81174),x81172))
% 51.10/50.83 [8210]~P1(f331(f68(x82101),x82104))+E(f331(f331(f3(a847),f331(f331(f8(x82101,a847),x82102),x82103)),f331(f331(f8(x82101,a847),x82102),x82104)),f331(f331(f8(x82101,a847),x82102),f331(f331(f3(f854(x82101,a840)),x82103),x82104)))+~P1(f331(f331(f240(f854(x82101,a840)),x82104),x82103))
% 51.10/50.83 [8366]~P10(x83661,x83664,x83663)+~P1(f331(f331(f333(x83661),x83662),x83664))+P1(f331(f331(f333(x83661),x83662),f331(f285(x83661,x83661,x83663),f331(f331(f310(x83661),x83662),f184(f854(x83661,a840))))))
% 51.10/50.83 [8430]~P1(f331(f331(f240(f854(x84301,a840)),x84302),x84303))+~P1(f331(f331(f240(f854(x84301,a840)),x84302),x84304))+P1(f331(f331(f240(f854(x84301,a840)),x84302),f331(f331(f109(f854(x84301,a840)),x84303),x84304)))
% 51.10/50.83 [8519]E(x85191,f184(f854(x85192,a840)))+P1(f331(f68(x85193),x85194))+~P1(f331(f68(f853(x85193,x85192)),f331(f331(f256(x85193,x85192),x85194),f331(f18(f854(x85192,a840),x85193),x85191))))
% 51.10/50.83 [8520]E(x85201,f184(f854(x85202,a840)))+P1(f331(f68(x85203),x85204))+~P1(f331(f68(f853(x85202,x85203)),f331(f331(f256(x85202,x85203),x85201),f331(f18(f854(x85203,a840),x85202),x85204))))
% 51.10/50.83 [8578]P1(f331(f331(f333(x85781),x85782),f321(x85781,x85783)))+~P1(f331(f331(f333(x85781),x85784),f321(x85781,x85783)))+~P1(f331(f331(f333(f853(x85781,x85781)),f331(f331(f249(x85781,x85781),x85782),x85784)),x85783))
% 51.10/50.83 [8579]P1(f331(f331(f333(x85791),x85792),f321(x85791,x85793)))+~P1(f331(f331(f333(x85791),x85794),f321(x85791,x85793)))+~P1(f331(f331(f333(f853(x85791,x85791)),f331(f331(f249(x85791,x85791),x85792),x85794)),x85793))
% 51.10/50.83 [8631]~P34(x86311,x86314)+P1(f331(f331(f333(f853(x86311,x86311)),f331(f331(f249(x86311,x86311),x86313),x86312)),f308(x86311,x86314)))+P34(x86311,f331(f331(f310(f853(x86311,x86311)),f331(f331(f249(x86311,x86311),x86312),x86313)),x86314))
% 51.10/50.83 [8632]~P54(x86321,x86324)+P1(f331(f331(f333(f853(x86321,x86321)),f331(f331(f249(x86321,x86321),x86323),x86322)),f308(x86321,x86324)))+P54(x86321,f331(f331(f310(f853(x86321,x86321)),f331(f331(f249(x86321,x86321),x86322),x86323)),x86324))
% 51.10/50.83 [8703]~E(x87032,x87033)+~P1(f331(f331(f333(x87031),x87032),f331(f163(x87031),x87034)))+P1(f331(f331(f333(f853(x87031,x87031)),f331(f331(f249(x87031,x87031),x87032),x87033)),f331(f163(f853(x87031,x87031)),f331(f331(f172(x87031,x87031),x87034),x87034))))
% 51.10/50.83 [8775]~E(x87753,x87754)+P1(f331(f331(f259(x87751,x87751,a840),a328),x87752))+~P1(f331(f331(f333(f853(x87751,x87751)),x87752),f331(f163(f853(x87751,x87751)),f331(f331(f172(x87751,x87751),x87753),x87754))))
% 51.10/50.83 [8811]P1(f331(f331(f333(f853(f848(x88111),f848(x88111))),f331(f331(f249(f848(x88111),f848(x88111)),x88112),x88113)),f142(x88111,x88114)))+~E(f331(f331(f164(x88111),f331(f185(f848(x88111)),x88112)),x88113),x88112)+~P1(f331(f331(f241(a847),f331(f185(f848(x88111)),x88112)),f331(f185(f848(x88111)),x88113)))
% 51.10/50.83 [8903]~P1(f331(f68(x89031),x89034))+P1(f331(f331(f333(x89031),f401(x89032,x89033,x89034,x89031)),x89034))+P1(f331(f68(x89033),f331(f331(f51(x89031,f854(x89033,a840)),x89034),x89032)))
% 51.10/50.83 [8904]~P1(f331(f68(x89041),x89044))+P1(f331(f331(f333(x89041),f600(x89042,x89043,x89044,x89041)),x89044))+P1(f331(f68(x89043),f331(f331(f51(x89041,f854(x89043,a840)),x89044),x89042)))
% 51.10/50.83 [8981]P1(f331(f331(f333(f853(x89811,x89811)),x89812),f331(f331(f289(x89811,x89811,x89811),x89813),f308(x89811,x89813))))+~P1(f331(f331(f241(a847),f2(a847)),x89814))+~P1(f331(f331(f333(f853(x89811,x89811)),x89812),f331(f331(f178(f853(x89811,x89811),a840),x89814),x89813)))
% 51.10/50.83 [8988]~P34(x89881,x89882)+~P1(f331(f331(f333(f853(x89881,x89881)),f331(f331(f249(x89881,x89881),x89884),x89883)),x89882))+~P1(f331(f331(f333(f853(x89881,x89881)),f331(f331(f249(x89881,x89881),x89883),x89884)),x89882))
% 51.10/50.83 [8989]~P34(x89891,x89892)+~P1(f331(f331(f333(f853(x89891,x89891)),f331(f331(f249(x89891,x89891),x89894),x89893)),x89892))+~P1(f331(f331(f333(f853(x89891,x89891)),f331(f331(f249(x89891,x89891),x89893),x89894)),x89892))
% 51.10/50.83 [9105]~P1(f331(f68(x91051),x91054))+E(f331(f331(f8(x91051,a847),f331(f331(f10(f854(x91052,a840),a847,x91051),f47(x91052)),x91053)),x91054),f331(f47(f853(x91051,x91052)),f331(f331(f256(x91051,x91052),x91054),x91053)))+P1(f331(f331(f333(x91051),f542(x91053,x91052,x91054,x91051)),x91054))
% 51.10/50.83 [9107]~P1(f331(f132(x91071),x91072))+P1(f331(f132(x91071),f331(f331(f152(x91071,x91072),x91073),x91074)))+P1(f331(f331(f333(x91071),x91074),f331(f331(f3(f854(x91071,a840)),f331(f163(x91071),x91072)),f331(f331(f310(x91071),f331(f331(f155(x91071),x91072),x91073)),f184(f854(x91071,a840))))))
% 51.10/50.83 [9116]~P1(f331(f68(x91162),x91163))+~P1(f331(f68(x91161),f331(x91164,f401(x91164,x91161,x91163,x91162))))+P1(f331(f68(x91161),f331(f331(f51(x91162,f854(x91161,a840)),x91163),x91164)))
% 51.10/50.83 [9117]~P1(f331(f68(x91172),x91173))+~P1(f331(f68(x91171),f331(x91174,f600(x91174,x91171,x91173,x91172))))+P1(f331(f68(x91171),f331(f331(f51(x91172,f854(x91171,a840)),x91173),x91174)))
% 51.10/50.83 [9182]~P1(f331(f331(f333(f853(x91821,x91821)),x91822),f331(f331(f289(x91821,x91821,x91821),x91824),f308(x91821,x91824))))+P1(f331(f331(f333(f853(x91821,x91821)),x91822),f331(f331(f289(x91821,x91821,x91821),x91823),f308(x91821,x91823))))+~P1(f331(f331(f240(f854(f853(x91821,x91821),a840)),x91824),x91823))
% 51.10/50.83 [9190]E(f331(f331(f164(x91901),f732(x91904,x91903,x91902,x91901)),x91903),f331(f331(f164(x91901),f732(x91904,x91903,x91902,x91901)),x91902))+~P1(f331(f331(f333(f853(f848(x91901),f848(x91901))),f331(f331(f249(f848(x91901),f848(x91901)),x91902),x91903)),f142(x91901,x91904)))+E(f331(f331(f164(x91901),f331(f185(f848(x91901)),x91902)),x91903),x91902)
% 51.10/50.83 [9206]~P1(f331(f68(x92061),x92064))+E(f331(f331(f8(x92061,a847),f331(f331(f10(f854(x92062,a840),a847,x92061),f47(x92062)),x92063)),x92064),f331(f47(f853(x92061,x92062)),f331(f331(f256(x92061,x92062),x92064),x92063)))+~P1(f331(f68(x92062),f331(x92063,f542(x92063,x92062,x92064,x92061))))
% 51.10/50.83 [9211]~E(f331(f185(f848(x92111)),x92113),f331(f185(f848(x92111)),x92112))+P1(f331(f331(f333(f853(f848(x92111),f848(x92111))),f331(f331(f249(f848(x92111),f848(x92111)),x92112),x92113)),f151(x92111,x92114)))+P1(f331(f331(f333(f853(x92111,x92111)),f715(x92114,x92113,x92112,x92111)),f331(f163(f853(x92111,x92111)),f331(f331(f172(x92111,x92111),x92112),x92113))))
% 51.10/50.83 [9294]~P1(f331(f331(f333(f853(f848(x92941),f848(x92941))),f331(f331(f249(f848(x92941),f848(x92941)),x92942),x92943)),f142(x92941,x92944)))+E(f331(f331(f164(x92941),f331(f185(f848(x92941)),x92942)),x92943),x92942)+P1(f331(f331(f241(a847),f732(x92944,x92943,x92942,x92941)),f331(f331(f244(a847),f331(f185(f848(x92941)),x92942)),f331(f185(f848(x92941)),x92943))))
% 51.10/50.83 [9313]~P1(f331(f331(f333(f853(f848(x93131),f848(x93131))),f331(f331(f249(f848(x93131),f848(x93131)),x93132),x93133)),f142(x93131,x93134)))+P1(f331(f331(f241(a847),f331(f185(f848(x93131)),x93132)),f331(f185(f848(x93131)),x93133)))+P1(f331(f331(f241(a847),f732(x93134,x93133,x93132,x93131)),f331(f331(f244(a847),f331(f185(f848(x93131)),x93132)),f331(f185(f848(x93131)),x93133))))
% 51.10/50.83 [9601]~P1(f331(f331(f331(x96011,f708(x96011,x96014,x96013,x96012)),f709(x96011,x96014,x96013,x96012)),f710(x96011,x96014,x96013,x96012)))+P1(f331(f331(f331(x96011,x96012),x96013),x96014))+~P1(f331(f320(f853(f854(a1,f851(f848(a838))),f853(a1,a1)),a318),f331(f331(f249(f854(a1,f851(f848(a838))),f853(a1,a1)),x96012),f331(f331(f249(a1,a1),x96013),x96014))))
% 51.10/50.83 [9662]P1(f331(f331(f331(x96621,x96622),x96623),x96624))+P1(f331(f320(f853(f854(a1,f851(f848(a838))),f853(a1,a1)),a318),f331(f331(f249(f854(a1,f851(f848(a838))),f853(a1,a1)),f708(x96621,x96624,x96623,x96622)),f331(f331(f249(a1,a1),f709(x96621,x96624,x96623,x96622)),f710(x96621,x96624,x96623,x96622)))))+~P1(f331(f320(f853(f854(a1,f851(f848(a838))),f853(a1,a1)),a318),f331(f331(f249(f854(a1,f851(f848(a838))),f853(a1,a1)),x96622),f331(f331(f249(a1,a1),x96623),x96624))))
% 51.10/50.83 [9701]~P1(f331(f331(f333(f853(f848(x97011),f848(x97011))),f331(f331(f249(f848(x97011),f848(x97011)),x97012),x97013)),f142(x97011,x97014)))+E(f331(f331(f164(x97011),f331(f185(f848(x97011)),x97012)),x97013),x97012)+P1(f331(f331(f333(f853(x97011,x97011)),f331(f331(f249(x97011,x97011),f331(f331(f155(x97011),x97012),f732(x97014,x97013,x97012,x97011))),f331(f331(f155(x97011),x97013),f732(x97014,x97013,x97012,x97011)))),x97014))
% 51.10/50.83 [9704]~P1(f331(f331(f333(f853(f848(x97041),f848(x97041))),f331(f331(f249(f848(x97041),f848(x97041)),x97042),x97043)),f142(x97041,x97044)))+P1(f331(f331(f241(a847),f331(f185(f848(x97041)),x97042)),f331(f185(f848(x97041)),x97043)))+P1(f331(f331(f333(f853(x97041,x97041)),f331(f331(f249(x97041,x97041),f331(f331(f155(x97041),x97042),f732(x97044,x97043,x97042,x97041))),f331(f331(f155(x97041),x97043),f732(x97044,x97043,x97042,x97041)))),x97044))
% 51.10/50.83 [9774]~E(f331(f185(f848(x97741)),x97742),f331(f185(f848(x97741)),x97743))+P1(f331(f331(f333(f853(f848(x97741),f848(x97741))),f331(f331(f249(f848(x97741),f848(x97741)),x97742),x97743)),f151(x97741,x97744)))+~P1(f331(f331(f333(f853(x97741,x97741)),f331(f331(f249(x97741,x97741),f331(f331(f155(x97741),x97742),f731(x97744,x97743,x97742,x97741))),f331(f331(f155(x97741),x97743),f731(x97744,x97743,x97742,x97741)))),x97744))
% 51.10/50.83 [9918]~P68(x99181)+~P1(f331(f68(x99182),x99184))+E(f331(f157(x99181),f331(f331(f147(x99182,x99181),x99183),f97(f848(x99182),f331(f331(f20(f848(x99182),a840,a840),f331(f331(f10(a840,f854(a840,a840),f848(x99182)),a329),f331(f331(f9(f848(x99182),f854(x99182,a840),a840),f331(f331(f10(f854(x99182,a840),f854(f854(x99182,a840),a840),f848(x99182)),a328),f163(x99182))),x99184))),f132(x99182))))),f232(x99182,x99181,x99183,x99184))
% 51.10/50.83 [7297]~P58(x72972)+E(x72971,f2(x72972))+E(f331(f331(f291(x72972),f331(f331(f87(x72972),x72973),f331(f331(f88(x72972),x72974),x72971))),x72971),f331(f331(f87(x72972),x72974),f331(f331(f291(x72972),x72973),x72971)))
% 51.10/50.83 [7298]~P5(x72982)+E(x72981,f2(x72982))+E(f331(f331(f48(x72982),f331(f331(f87(x72982),x72983),f331(f331(f88(x72982),x72984),x72981))),x72981),f331(f331(f87(x72982),x72984),f331(f331(f48(x72982),x72983),x72981)))
% 51.10/50.83 [7299]~P5(x72992)+E(x72991,f2(x72992))+E(f331(f331(f48(x72992),f331(f331(f87(x72992),x72993),f331(f331(f88(x72992),x72991),x72994))),x72991),f331(f331(f87(x72992),x72994),f331(f331(f48(x72992),x72993),x72991)))
% 51.10/50.83 [7541]~P58(x75412)+E(x75411,f2(x75412))+E(f331(f331(f291(x75412),f331(f331(f87(x75412),x75413),f331(f331(f88(x75412),x75414),x75411))),x75411),f331(f331(f87(x75412),f331(f331(f291(x75412),x75413),x75411)),x75414))
% 51.10/50.83 [7542]~P59(x75422)+E(x75421,f2(x75422))+E(f331(f331(f291(x75422),f331(f331(f87(x75422),x75423),f331(f331(f88(x75422),x75421),x75424))),x75421),f331(f331(f87(x75422),f331(f331(f291(x75422),x75423),x75421)),x75424))
% 51.10/50.83 [7543]~P59(x75432)+E(x75431,f2(x75432))+E(f331(f331(f291(x75432),f331(f331(f3(x75432),x75433),f331(f331(f88(x75432),x75431),x75434))),x75431),f331(f331(f3(x75432),f331(f331(f291(x75432),x75433),x75431)),x75434))
% 51.10/50.83 [8593]~E(f331(f331(f289(x85931,x85931,x85931),x85932),x85934),f184(f854(f853(x85931,x85931),a840)))+~E(f331(f331(f289(x85931,x85931,x85931),x85932),x85933),f184(f854(f853(x85931,x85931),a840)))+E(f331(f331(f289(x85931,x85931,x85931),x85932),f331(f331(f108(f854(f853(x85931,x85931),a840)),x85933),x85934)),f184(f854(f853(x85931,x85931),a840)))
% 51.10/50.83 [8704]~P1(f331(f331(f240(f854(x87041,a840)),x87043),x87044))+~P1(f331(f331(f240(f854(x87041,a840)),x87042),x87044))+P1(f331(f331(f240(f854(x87041,a840)),f331(f331(f108(f854(x87041,a840)),x87042),x87043)),x87044))
% 51.10/50.83 [9040]~P1(f331(f68(x90401),x90404))+~P1(f331(f68(x90401),x90403))+E(f331(f331(f3(a847),f331(f331(f87(a847),f331(f331(f8(x90401,a847),x90402),x90403)),f331(f331(f8(x90401,a847),x90402),x90404))),f331(f331(f8(x90401,a847),x90402),f331(f331(f109(f854(x90401,a840)),x90403),x90404))),f331(f331(f8(x90401,a847),x90402),f331(f331(f108(f854(x90401,a840)),x90403),x90404)))
% 51.10/50.83 [9114]~P1(f331(f331(f333(x91141),x91143),x91142))+~P1(f331(f331(f240(f854(x91141,a840)),x91142),f331(f331(f310(x91141),x91143),x91144)))+P1(f331(f331(f240(f854(x91141,a840)),f331(f331(f3(f854(x91141,a840)),x91142),f331(f331(f310(x91141),x91143),f184(f854(x91141,a840))))),x91144))
% 51.10/50.83 [9265]~P1(f331(f331(f333(x92651),x92653),x92652))+P1(f331(f331(f240(f854(x92651,a840)),x92652),f331(f331(f310(x92651),x92653),x92654)))+~P1(f331(f331(f240(f854(x92651,a840)),f331(f331(f3(f854(x92651,a840)),x92652),f331(f331(f310(x92651),x92653),f184(f854(x92651,a840))))),x92654))
% 51.10/50.83 [9266]~P1(f331(f331(f333(x92661),x92663),x92662))+P1(f331(f331(f240(f854(x92661,a840)),x92662),f331(f331(f310(x92661),x92663),x92664)))+~P1(f331(f331(f240(f854(x92661,a840)),f331(f331(f3(f854(x92661,a840)),x92662),f331(f331(f310(x92661),x92663),f184(f854(x92661,a840))))),x92664))
% 51.10/50.83 [9292]~P1(f331(f331(f240(f854(x92921,a840)),x92922),x92924))+P1(f331(f331(f240(f854(x92921,a840)),x92922),f331(f331(f310(x92921),x92923),x92924)))+~P1(f331(f331(f240(f854(x92921,a840)),f331(f331(f3(f854(x92921,a840)),x92922),f331(f331(f310(x92921),x92923),f184(f854(x92921,a840))))),x92924))
% 51.10/50.83 [9351]~P1(f331(f331(f241(a847),x93512),x93514))+~P1(f331(f331(f240(a847),x93511),x93513))+P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),f331(f331(f249(a847,a847),x93511),x93512)),f331(f331(f249(a847,a847),x93513),x93514))),a45))
% 51.10/50.83 [9352]~P1(f331(f331(f240(a847),x93522),x93524))+~P1(f331(f331(f240(a847),x93521),x93523))+P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),f331(f331(f249(a847,a847),x93521),x93522)),f331(f331(f249(a847,a847),x93523),x93524))),a77))
% 51.10/50.83 [9739]~P27(x97391,f854(f854(x97391,a840),a840),f331(f331(f9(x97391,f854(f853(x97391,x97391),a840),f854(f854(x97391,a840),a840)),f331(f331(f10(f854(x97391,a840),f854(f854(f853(x97391,x97391),a840),f854(f854(x97391,a840),a840)),x97391),f66(x97391)),f331(f331(f9(x97391,f854(x97391,a840),f854(x97391,a840)),f310(x97391)),f184(f854(x97391,a840))))),x97393),x97392)+~P1(f331(f331(f333(x97391),x97394),x97392))+E(f331(f331(f3(f854(f854(x97391,a840),a840)),f331(f331(f66(x97391),x97392),x97393)),f331(f331(f66(x97391),f331(f331(f310(x97391),x97394),f184(f854(x97391,a840)))),x97393)),f331(f331(f66(x97391),f331(f331(f3(f854(x97391,a840)),x97392),f331(f331(f310(x97391),x97394),f184(f854(x97391,a840))))),x97393))
% 51.10/50.83 [9882]~P45(x98821,x98822,x98824)+~P1(f331(f331(f333(f853(x98821,x98821)),x98823),x98824))+P1(f331(f331(f259(x98821,x98821,a840),f331(f331(f9(x98821,f854(x98821,a840),f854(x98821,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x98821,a840),f854(x98821,a840)),x98821),f10(a840,a840,x98821)),f331(f331(f10(a840,f854(a840,a840),x98821),a329),f331(f331(f9(x98821,f854(x98821,a840),a840),f333(x98821)),x98822)))),f331(f331(f9(x98821,f854(x98821,a840),a840),f333(x98821)),x98822))),x98823))
% 51.10/50.83 [9892]P1(f331(f68(x98921),x98922))+~P1(f331(f68(x98923),f331(f311(x98921,x98923,x98924),x98922)))+~P1(f331(f68(x98921),f331(f264(x98921),f331(f331(f20(x98921,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98921),a329),f331(f331(f9(x98921,f854(x98921,a840),a840),f333(x98921)),x98922))),f331(f331(f9(x98921,x98923,a840),f331(f331(f10(x98923,f854(x98923,a840),x98921),a328),x98924)),f331(x98924,f587(x98924,x98923,x98922,x98921)))))))
% 51.10/50.83 [7998]~P59(x79982)+E(x79981,f2(x79982))+E(f331(f331(f291(x79982),f331(f331(f87(x79982),f331(f331(f88(x79982),x79981),x79983)),x79984)),x79981),f331(f331(f87(x79982),x79983),f331(f331(f291(x79982),x79984),x79981)))
% 51.10/50.83 [7999]~P59(x79992)+E(x79991,f2(x79992))+E(f331(f331(f291(x79992),f331(f331(f3(x79992),f331(f331(f88(x79992),x79991),x79993)),x79994)),x79991),f331(f331(f3(x79992),x79993),f331(f331(f291(x79992),x79994),x79991)))
% 51.10/50.83 [8838]~E(f331(f331(f289(x88381,x88381,x88381),x88383),x88384),f184(f854(f853(x88381,x88381),a840)))+~E(f331(f331(f289(x88381,x88381,x88381),x88382),x88384),f184(f854(f853(x88381,x88381),a840)))+E(f331(f331(f289(x88381,x88381,x88381),f331(f331(f108(f854(f853(x88381,x88381),a840)),x88382),x88383)),x88384),f184(f854(f853(x88381,x88381),a840)))
% 51.10/50.83 [9826]~P139(x98261)+~P139(x98262)+E(f331(f331(f317(x98261),f331(f331(f9(x98261,a106,f851(f848(a838))),f331(f331(f10(f854(x98262,f851(f848(a838))),f854(a106,f851(f848(a838))),x98261),f317(x98262)),f331(f331(f10(f854(x98262,f853(x98261,x98262)),f854(x98262,f851(f848(a838))),x98261),f331(f10(f853(x98261,x98262),f851(f848(a838)),x98262),x98263)),f249(x98261,x98262)))),x98264)),x98264),f331(f331(f317(f853(x98261,x98262)),x98263),x98264))
% 51.10/50.83 [9818]P1(f331(x98181,f566(x98182,x98183,x98181,x98184)))+~P1(f331(f68(x98184),f331(f264(x98184),x98181)))+P1(f331(f68(x98183),f331(f264(x98183),f331(f331(f10(f854(x98184,a840),a840,x98183),f94(x98184)),f331(f331(f10(f854(x98184,a840),f854(x98184,a840),x98183),f331(f20(x98184,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98184),a329),x98181))),x98182)))))
% 51.10/50.83 [9839]~P1(f331(f68(x98392),f331(f264(x98392),x98393)))+~P1(f331(f68(x98391),f331(f264(x98391),f331(f331(f9(x98391,x98392,a840),x98394),f566(x98394,x98391,x98393,x98392)))))+P1(f331(f68(x98391),f331(f264(x98391),f331(f331(f10(f854(x98392,a840),a840,x98391),f94(x98392)),f331(f331(f10(f854(x98392,a840),f854(x98392,a840),x98391),f331(f20(x98392,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98392),a329),x98393))),x98394)))))
% 51.10/50.83 [5683]~E(x56835,x56832)+P37(f37(x56831,x56833),x56832,x56834,x56835)+P1(f331(x56831,x56832))
% 51.10/50.83 [6253]E(x62531,x62532)+~P37(f37(x62533,x62534),x62531,x62535,x62532)+P1(f331(x62533,x62531))
% 51.10/50.83 [7804]~P37(x78042,x78043,x78044,x78045)+~P37(f37(x78041,x78042),x78045,x78044,x78043)+P37(f37(x78041,x78042),x78043,x78044,x78043)
% 51.10/50.83 [8958]E(x89581,x89582)+~P37(f37(x89585,x89583),x89581,x89584,x89582)+P37(x89583,x89581,x89584,f527(x89582,x89584,x89581,x89583,x89585))
% 51.10/50.83 [8960]E(x89601,x89602)+P37(f37(x89603,x89604),f527(x89601,x89605,x89602,x89604,x89603),x89605,x89601)+~P37(f37(x89603,x89604),x89602,x89605,x89601)
% 51.10/50.83 [8962]~P37(f37(x89625,x89621),x89622,x89623,x89624)+P37(x89621,x89622,x89623,f527(x89624,x89623,x89622,x89621,x89625))+~P1(f331(x89625,x89622))
% 51.10/50.83 [8966]~P37(f37(x89661,x89662),x89665,x89664,x89663)+P37(f37(x89661,x89662),f527(x89663,x89664,x89665,x89662,x89661),x89664,x89663)+~P1(f331(x89661,x89665))
% 51.10/50.83 [6402]E(x64021,x64022)+~E(f331(x64023,x64021),f331(x64023,x64022))+~P27(x64024,x64025,x64023,f247(f854(x64024,a840)))
% 51.10/50.83 [6403]E(x64031,x64032)+~E(f331(x64033,x64031),f331(x64033,x64032))+~P27(x64034,x64035,x64033,f247(f854(x64034,a840)))
% 51.10/50.83 [6566]~E(f331(x65663,x65665),f187(x65662))+~E(f331(x65664,x65665),f187(x65662))+E(f331(f175(x65661,x65662,x65663,x65664),x65665),f187(x65662))
% 51.10/50.83 [7338]E(x73381,x73382)+~P27(x73383,x73384,x73385,f247(f854(x73383,a840)))+~E(f331(f311(x73383,x73384,x73385),x73381),f331(f311(x73383,x73384,x73385),x73382))
% 51.10/50.83 [7597]P27(x75972,x75973,f443(x75974,x75973,x75972,x75971),x75971)+~E(f331(f311(x75973,x75972,x75975),x75974),x75971)+E(x75971,f184(f854(x75972,a840)))
% 51.10/50.83 [8128]~P1(f331(f331(x81283,x81282),x81285))+~P1(f331(f331(x81283,x81284),x81282))+P1(f331(f331(f333(x81281),x81282),f299(x81281,x81283,x81284,x81285)))
% 51.10/50.83 [8129]~P1(f331(f331(x81293,x81292),x81295))+~P1(f331(f331(x81293,x81294),x81292))+P1(f331(f331(f333(x81291),x81292),f290(x81291,x81293,x81294,x81295)))
% 51.10/50.83 [8666]~P27(x86661,x86663,x86665,f247(f854(x86661,a840)))+~P27(x86663,x86662,x86664,f247(f854(x86663,a840)))+P27(x86661,x86662,f331(f80(x86663,x86662,x86661,x86664),x86665),f247(f854(x86661,a840)))
% 51.10/50.83 [9160]P1(f331(f331(f333(f853(x91601,x91601)),f331(f331(f249(x91601,x91601),x91602),x91603)),f308(x91601,x91604)))+~P1(f331(f331(f333(f853(x91601,x91601)),f331(f331(f249(x91601,x91601),x91602),x91605)),f308(x91601,x91604)))+~P1(f331(f331(f333(f853(x91601,x91601)),f331(f331(f249(x91601,x91601),x91605),x91603)),f308(x91601,x91604)))
% 51.10/50.83 [9197]~P102(x91972)+~P1(f331(f132(x91971),x91975))+P1(f331(f132(x91971),f144(x91971,x91972,x91973,x91974,x91975)))
% 51.10/50.83 [5211]~E(x52112,f120(x52111))+E(f331(f331(f130(x52111),x52112),x52113),f331(f331(f145(x52111),x52114),x52115))+~E(x52113,f331(f331(f145(x52111),x52114),x52115))
% 51.10/50.83 [5212]~E(x52122,f120(x52121))+E(f331(f331(f130(x52121),x52122),x52123),f331(f331(f145(x52121),x52124),x52125))+~E(f331(f331(f145(x52121),x52124),x52125),x52123)
% 51.10/50.83 [6359]~E(f331(f185(f848(x63591)),x63595),f331(f185(f848(x63592)),x63594))+E(f331(f331(f147(f853(x63591,x63592),x63592),f258(x63591,x63592)),x63593),x63594)+~E(f331(f331(f172(x63591,x63592),x63595),x63594),x63593)
% 51.10/50.83 [6360]~E(f331(f185(f848(x63601)),x63604),f331(f185(f848(x63602)),x63605))+E(f331(f331(f147(f853(x63601,x63602),x63601),f248(x63601,x63602)),x63603),x63604)+~E(f331(f331(f172(x63601,x63602),x63604),x63605),x63603)
% 51.10/50.83 [6855]~P102(x68551)+~P16(x68551,f331(f331(f147(x68552,x68551),x68553),x68555))+P16(x68551,f331(f331(f147(x68552,x68551),x68553),f331(f131(x68552,x68554),x68555)))
% 51.10/50.83 [6901]~P1(f331(x69013,x69015))+~P1(f331(f331(x69012,x69014),x69015))+P1(f331(f331(f99(x69011,x69012,x69013),x69014),x69015))
% 51.10/50.83 [6998]~P102(x69981)+P16(x69981,f331(f331(f147(x69982,x69981),x69983),f161(x69982,x69984,x69985)))+~P16(x69981,f331(f331(f147(x69982,x69981),x69983),x69985))
% 51.10/50.83 [7021]~P51(x70213,x70212,x70215)+~P51(x70211,x70213,x70214)+P51(x70211,x70212,f331(f331(f289(x70211,x70213,x70212),x70214),x70215))
% 51.10/50.83 [7111]E(x71111,x71112)+~P27(x71113,x71114,x71115,f247(f854(x71113,a840)))+~E(f331(f331(f147(x71113,x71114),x71115),x71111),f331(f331(f147(x71113,x71114),x71115),x71112))
% 51.10/50.83 [7112]E(x71121,x71122)+~P27(x71123,x71124,x71125,f247(f854(x71123,a840)))+~E(f331(f331(f147(x71123,x71124),x71125),x71121),f331(f331(f147(x71123,x71124),x71125),x71122))
% 51.10/50.83 [7193]P37(x71931,x71932,x71933,x71934)+~P37(x71931,x71932,x71935,x71934)+~P1(f331(f331(f240(a847),x71935),x71933))
% 51.10/50.83 [7283]~P1(f331(f331(f241(a847),x72831),f331(x72833,x72835)))+P1(f331(f331(f241(a847),x72831),f148(x72832,x72833,x72834)))+~P1(f331(f331(f333(x72832),x72835),f331(f163(x72832),x72834)))
% 51.10/50.83 [7284]~P1(f331(f331(f240(a847),x72841),f331(x72843,x72845)))+P1(f331(f331(f240(a847),x72841),f148(x72842,x72843,x72844)))+~P1(f331(f331(f333(x72842),x72845),f331(f163(x72842),x72844)))
% 51.10/50.83 [7696]~P88(x76961)+P1(f331(f331(f240(f854(x76961,a840)),f303(x76961,x76962,x76963)),f303(x76961,x76964,x76965)))+P1(f331(f331(f240(x76961),x76962),x76963))
% 51.10/50.83 [7723]~P7(x77231)+P1(f331(f331(f240(x77231),f331(f331(f52(x77232,x77231),x77233),x77234)),f331(x77234,x77235)))+~P1(f331(f331(f333(x77232),x77235),x77233))
% 51.10/50.83 [7791]~P27(x77911,x77912,x77914,x77913)+E(f331(f84(x77911,x77912,x77913,x77914),f331(x77914,x77915)),x77915)+~P1(f331(f331(f333(x77911),x77915),x77913))
% 51.10/50.83 [7987]~P1(f331(x79871,x79875))+P1(f331(x79871,f343(x79871,x79872,x79873,x79874)))+~P1(f331(f331(f333(x79874),x79875),x79873))
% 51.10/50.83 [7988]~P1(f331(x79881,x79885))+P1(f331(x79881,f343(x79881,x79882,x79883,x79884)))+~P1(f331(f331(f333(x79884),x79885),x79882))
% 51.10/50.83 [8079]P1(f331(f68(x80791),x80792))+~P1(f331(f68(x80793),x80794))+~P1(f331(f331(f240(f854(x80791,a840)),x80792),f331(f311(x80793,x80791,x80795),x80794)))
% 51.10/50.83 [8089]~P27(x80894,x80891,x80892,f247(f854(x80894,a840)))+~P1(f331(f331(f333(x80894),x80893),x80895))+P1(f331(f331(f333(x80891),f331(x80892,x80893)),f331(f311(x80894,x80891,x80892),x80895)))
% 51.10/50.83 [8241]E(x82411,x82412)+~P27(x82413,x82414,x82415,f331(f331(f108(f854(x82413,a840)),f331(f163(x82413),x82411)),f331(f163(x82413),x82412)))+~E(f331(f331(f147(x82413,x82414),x82415),x82411),f331(f331(f147(x82413,x82414),x82415),x82412))
% 51.10/50.83 [8242]E(x82421,x82422)+~P27(x82423,x82424,x82425,f331(f331(f108(f854(x82423,a840)),f331(f163(x82423),x82421)),f331(f163(x82423),x82422)))+~E(f331(f331(f147(x82423,x82424),x82425),x82421),f331(f331(f147(x82423,x82424),x82425),x82422))
% 51.10/50.83 [8299]~P88(x82991)+~P1(f331(f331(f241(f854(x82991,a840)),f303(x82991,x82994,x82995)),f303(x82991,x82992,x82993)))+P1(f331(f331(f240(x82991),x82992),x82993))
% 51.10/50.83 [8365]~P27(x83651,x83654,x83655,f247(f854(x83651,a840)))+~P1(f331(f331(f333(x83654),f331(x83655,x83652)),f331(f311(x83651,x83654,x83655),x83653)))+P1(f331(f331(f333(x83651),x83652),x83653))
% 51.10/50.83 [8443]P1(f331(x84431,x84432))+~P1(f331(x84431,f351(x84431,x84433,x84434,x84435)))+~P1(f331(f331(f333(x84435),x84432),x84434))
% 51.10/50.83 [8444]P1(f331(x84441,x84442))+~P1(f331(x84441,f351(x84441,x84443,x84444,x84445)))+~P1(f331(f331(f333(x84445),x84442),x84443))
% 51.10/50.83 [8701]~P27(x87012,x87013,x87011,x87014)+E(f331(x87011,f331(f84(x87012,x87013,x87014,x87011),x87015)),x87015)+~P1(f331(f331(f333(x87013),x87015),f331(f311(x87012,x87013,x87011),x87014)))
% 51.10/50.83 [8785]E(x87851,f120(x87852))+E(f331(f331(f145(x87852),x87853),f735(x87854,x87853,x87855,x87851,x87852)),x87851)+~E(f331(f331(f130(x87852),x87851),x87855),f331(f331(f145(x87852),x87853),x87854))
% 51.10/50.83 [8786]E(x87861,f120(x87862))+E(f331(f331(f145(x87862),x87863),f734(x87864,x87861,x87865,x87863,x87862)),x87861)+~E(f331(f331(f130(x87862),x87861),x87864),f331(f331(f145(x87862),x87863),x87865))
% 51.10/50.83 [8801]E(f331(f331(f145(x88012),x88013),f735(x88014,x88013,x88011,x88015,x88012)),x88015)+~E(f331(f331(f130(x88012),x88015),x88011),f331(f331(f145(x88012),x88013),x88014))+E(x88011,f331(f331(f145(x88012),x88013),x88014))
% 51.10/50.83 [8802]E(f331(f331(f145(x88021),x88022),f734(x88024,x88025,x88023,x88022,x88021)),x88025)+~E(f331(f331(f130(x88021),x88025),x88024),f331(f331(f145(x88021),x88022),x88023))+E(f331(f331(f145(x88021),x88022),x88023),x88024)
% 51.10/50.83 [8876]~E(f331(f311(x88763,x88762,x88764),f247(f854(x88763,a840))),f247(f854(x88762,a840)))+~E(f331(f311(x88761,x88763,x88765),f247(f854(x88761,a840))),f247(f854(x88763,a840)))+E(f331(f311(x88761,x88762,f331(f80(x88763,x88762,x88761,x88764),x88765)),f247(f854(x88761,a840))),f247(f854(x88762,a840)))
% 51.10/50.83 [9203]E(x92031,f120(x92032))+~E(f331(f331(f130(x92032),x92031),x92033),f331(f331(f145(x92032),x92035),x92034))+E(f331(f331(f130(x92032),f734(x92033,x92031,x92034,x92035,x92032)),x92033),x92034)
% 51.10/50.83 [9204]E(x92041,f120(x92042))+~E(f331(f331(f130(x92042),x92041),x92045),f331(f331(f145(x92042),x92044),x92043))+E(f331(f331(f130(x92042),f735(x92043,x92044,x92045,x92041,x92042)),x92045),x92043)
% 51.10/50.83 [9212]E(f331(f331(f130(x92122),f735(x92124,x92123,x92121,x92125,x92122)),x92121),x92124)+~E(f331(f331(f130(x92122),x92125),x92121),f331(f331(f145(x92122),x92123),x92124))+E(x92121,f331(f331(f145(x92122),x92123),x92124))
% 51.10/50.83 [9213]~E(f331(f331(f130(x92131),x92135),x92134),f331(f331(f145(x92131),x92132),x92133))+E(f331(f331(f130(x92131),f734(x92134,x92135,x92133,x92132,x92131)),x92134),x92133)+E(f331(f331(f145(x92131),x92132),x92133),x92134)
% 51.10/50.83 [9214]E(f331(f331(f130(x92141),x92145),f739(x92143,x92142,x92144,x92145,x92141)),x92142)+E(f331(f331(f130(x92141),x92142),f738(x92143,x92142,x92144,x92145,x92141)),x92145)+~E(f331(f331(f130(x92141),x92145),x92144),f331(f331(f130(x92141),x92142),x92143))
% 51.10/50.83 [9246]~P102(x92461)+P16(x92461,f331(f331(f147(x92462,x92461),x92463),f144(x92462,x92461,x92463,x92464,x92465)))+~P16(x92461,f331(f331(f147(x92462,x92461),x92463),x92465))
% 51.10/50.83 [9262]~P55(x92625,x92621,x92624,x92623)+P1(f331(f331(x92621,x92622),f529(x92623,x92624,x92621,x92625,x92622)))+~P1(f331(f331(f333(x92625),x92622),x92624))
% 51.10/50.83 [9360]~P1(f331(f331(f333(f853(x93601,x93601)),f331(f331(f249(x93601,x93601),x93605),x93603)),f308(x93601,x93604)))+P1(f331(f331(f333(f853(x93601,x93601)),f331(f331(f249(x93601,x93601),x93602),x93603)),f331(f331(f289(x93601,x93601,x93601),x93604),f308(x93601,x93604))))+~P1(f331(f331(f333(f853(x93601,x93601)),f331(f331(f249(x93601,x93601),x93602),x93605)),f331(f331(f289(x93601,x93601,x93601),x93604),f308(x93601,x93604))))
% 51.10/50.83 [9361]~P1(f331(f331(f333(f853(x93611,x93611)),f331(f331(f249(x93611,x93611),x93612),x93615)),f308(x93611,x93614)))+P1(f331(f331(f333(f853(x93611,x93611)),f331(f331(f249(x93611,x93611),x93612),x93613)),f331(f331(f289(x93611,x93611,x93611),x93614),f308(x93611,x93614))))+~P1(f331(f331(f333(f853(x93611,x93611)),f331(f331(f249(x93611,x93611),x93615),x93613)),f331(f331(f289(x93611,x93611,x93611),x93614),f308(x93611,x93614))))
% 51.10/50.83 [9363]P1(f331(f331(f333(f853(f848(x93631),f848(x93631))),f331(f331(f249(f848(x93631),f848(x93631)),x93632),x93633)),f151(x93631,f308(x93631,x93634))))+~P1(f331(f331(f333(f853(f848(x93631),f848(x93631))),f331(f331(f249(f848(x93631),f848(x93631)),x93632),x93635)),f151(x93631,f308(x93631,x93634))))+~P1(f331(f331(f333(f853(f848(x93631),f848(x93631))),f331(f331(f249(f848(x93631),f848(x93631)),x93635),x93633)),f151(x93631,f308(x93631,x93634))))
% 51.10/50.83 [9368]E(f331(f331(f130(x93681),x93682),f738(x93683,x93682,x93684,x93685,x93681)),x93685)+E(f331(f331(f130(x93681),f739(x93683,x93682,x93684,x93685,x93681)),x93683),x93684)+~E(f331(f331(f130(x93681),x93682),x93683),f331(f331(f130(x93681),x93685),x93684))
% 51.10/50.83 [9369]E(f331(f331(f130(x93691),x93692),f739(x93693,x93694,x93695,x93692,x93691)),x93694)+E(f331(f331(f130(x93691),f738(x93693,x93694,x93695,x93692,x93691)),x93695),x93693)+~E(f331(f331(f130(x93691),x93692),x93695),f331(f331(f130(x93691),x93694),x93693))
% 51.10/50.83 [9429]P1(f331(f331(f333(f853(x94291,x94291)),f331(f331(f249(x94291,x94291),x94292),x94293)),f331(f331(f289(x94291,x94291,x94291),x94294),f308(x94291,x94294))))+~P1(f331(f331(f333(f853(x94291,x94291)),f331(f331(f249(x94291,x94291),x94292),x94295)),f331(f331(f289(x94291,x94291,x94291),x94294),f308(x94291,x94294))))+~P1(f331(f331(f333(f853(x94291,x94291)),f331(f331(f249(x94291,x94291),x94295),x94293)),f331(f331(f289(x94291,x94291,x94291),x94294),f308(x94291,x94294))))
% 51.10/50.83 [9463]E(f331(f331(f130(x94631),f738(x94632,x94633,x94634,x94635,x94631)),x94634),x94632)+~E(f331(f331(f130(x94631),x94633),x94632),f331(f331(f130(x94631),x94635),x94634))+E(f331(f331(f130(x94631),f739(x94632,x94633,x94634,x94635,x94631)),x94632),x94634)
% 51.10/50.83 [9478]~P55(x94781,x94784,x94783,x94782)+~P1(f331(f331(f333(x94781),x94785),x94783))+P1(f331(f331(f333(x94781),f529(x94782,x94783,x94784,x94781,x94785)),x94782))
% 51.10/50.83 [9593]~P1(f331(f331(f333(f853(f854(x95931,a840),f854(x95931,a840))),f331(f331(f249(f854(x95931,a840),f854(x95931,a840)),x95934),x95933)),f323(x95931,x95932)))+~P1(f331(f331(f333(x95931),x95935),x95934))+P1(f331(f331(f333(x95931),f627(x95932,x95933,x95934,x95931,x95935)),x95933))
% 51.10/50.83 [6435]~P19(x64352,x64355,x64351)+~P1(f331(f68(x64352),x64354))+E(f331(x64351,f331(f331(f310(x64352),x64353),x64354)),f331(f331(f71(x64352,x64352,x64355),x64353),x64354))
% 51.10/50.83 [6436]~E(x64363,x64364)+~E(x64362,x64365)+E(f331(f331(f310(x64361),x64362),f331(f331(f310(x64361),x64363),f184(f854(x64361,a840)))),f331(f331(f310(x64361),x64364),f331(f331(f310(x64361),x64365),f184(f854(x64361,a840)))))
% 51.10/50.83 [6447]P1(f331(x64472,x64475))+E(f167(x64471,x64472,f331(f331(f130(x64471),x64473),x64474)),f167(x64471,x64472,x64473))+~P1(f331(f331(f333(x64471),x64475),f331(f163(x64471),x64473)))
% 51.10/50.83 [6482]E(f331(x64821,x64822),f184(f854(x64823,a840)))+~E(f331(f331(f51(x64824,f854(x64823,a840)),x64825),x64821),f184(f854(x64823,a840)))+~P1(f331(f331(f333(x64824),x64822),x64825))
% 51.10/50.83 [6483]E(f331(x64831,x64832),f247(f854(x64833,a840)))+~E(f331(f331(f52(x64834,f854(x64833,a840)),x64835),x64831),f247(f854(x64833,a840)))+~P1(f331(f331(f333(x64834),x64832),x64835))
% 51.10/50.83 [6484]E(f331(x64841,x64842),f184(f854(x64843,a840)))+~E(f331(f331(f51(x64844,f854(x64843,a840)),x64845),x64841),f184(f854(x64843,a840)))+~P1(f331(f331(f333(x64844),x64842),x64845))
% 51.10/50.83 [6485]E(f331(x64851,x64852),f247(f854(x64853,a840)))+~E(f331(f331(f52(x64854,f854(x64853,a840)),x64855),x64851),f247(f854(x64853,a840)))+~P1(f331(f331(f333(x64854),x64852),x64855))
% 51.10/50.83 [6803]~P1(f331(f331(f191(x68031),x68033),x68035))+~P1(f331(f331(f191(x68032),x68035),x68034))+P1(f331(f331(f191(f38(x68031,x68032)),x68033),x68034))
% 51.10/50.83 [6804]~P1(f331(f331(f191(x68041),x68043),x68045))+~P1(f331(f331(f191(x68042),x68045),x68044))+P1(f331(f331(f191(f38(x68041,x68042)),x68043),x68044))
% 51.10/50.83 [7007]~E(x70072,x70074)+~P137(x70071)+E(f331(f331(f87(x70071),f331(f331(f88(x70071),x70072),x70073)),f331(f331(f88(x70071),x70074),x70075)),f331(f331(f87(x70071),f331(f331(f88(x70071),x70072),x70075)),f331(f331(f88(x70071),x70074),x70073)))
% 51.10/50.83 [7008]~E(x70082,x70084)+~P137(x70081)+E(f331(f331(f87(x70081),f331(f331(f88(x70081),x70082),x70083)),f331(f331(f88(x70081),x70084),x70085)),f331(f331(f87(x70081),f331(f331(f88(x70081),x70082),x70085)),f331(f331(f88(x70081),x70084),x70083)))
% 51.10/50.83 [7068]~P7(x70681)+~P1(f331(f331(f333(x70684),x70683),x70685))+P1(f331(f331(f240(x70681),f331(x70682,x70683)),f331(f331(f51(x70684,x70681),x70685),x70682)))
% 51.10/50.83 [7115]~P104(x71151)+P1(f331(f331(f240(x71151),f331(x71152,x71153)),f331(x71154,x71153)))+~P1(f331(f331(f240(f854(x71155,x71151)),x71152),x71154))
% 51.10/50.83 [7116]~P104(x71161)+P1(f331(f331(f240(x71161),f331(x71162,x71163)),f331(x71164,x71163)))+~P1(f331(f331(f240(f854(x71165,x71161)),x71162),x71164))
% 51.10/50.83 [7117]~P104(x71171)+P1(f331(f331(f240(x71171),f331(x71172,x71173)),f331(x71174,x71173)))+~P1(f331(f331(f240(f854(x71175,x71171)),x71172),x71174))
% 51.10/50.83 [7251]E(x72511,x72512)+E(x72513,x72511)+~E(f331(f331(f310(x72514),x72511),f331(f331(f310(x72514),x72515),f184(f854(x72514,a840)))),f331(f331(f310(x72514),x72512),f331(f331(f310(x72514),x72513),f184(f854(x72514,a840)))))
% 51.10/50.83 [7252]E(x72521,x72522)+E(x72523,x72521)+~E(f331(f331(f310(x72524),x72523),f331(f331(f310(x72524),x72522),f184(f854(x72524,a840)))),f331(f331(f310(x72524),x72525),f331(f331(f310(x72524),x72521),f184(f854(x72524,a840)))))
% 51.10/50.83 [7253]E(x72531,x72532)+E(x72531,x72533)+~E(f331(f331(f310(x72534),x72533),f331(f331(f310(x72534),x72532),f184(f854(x72534,a840)))),f331(f331(f310(x72534),x72535),f331(f331(f310(x72534),x72531),f184(f854(x72534,a840)))))
% 51.10/50.83 [7254]E(x72541,x72542)+E(x72541,x72543)+~E(f331(f331(f310(x72544),x72541),f331(f331(f310(x72544),x72545),f184(f854(x72544,a840)))),f331(f331(f310(x72544),x72542),f331(f331(f310(x72544),x72543),f184(f854(x72544,a840)))))
% 51.10/50.83 [7801]P27(x78011,x78012,x78013,x78014)+~P27(x78011,x78012,x78013,x78015)+~P1(f331(f331(f240(f854(x78011,a840)),x78014),x78015))
% 51.10/50.83 [7902]P1(f331(x79021,x79022))+~P1(f331(f331(f191(x79024),x79022),x79025))+P1(f331(f331(f191(f35(x79021,x79023,x79024)),x79022),x79025))
% 51.10/50.83 [7903]P1(f331(x79031,x79032))+~P1(f331(f331(f191(x79034),x79032),x79035))+P1(f331(f331(f191(f35(x79031,x79033,x79034)),x79032),x79035))
% 51.10/50.83 [7904]P1(f331(x79041,x79042))+~P1(f331(f331(f191(x79044),x79042),x79045))+P1(f331(f331(f191(f35(x79041,x79043,x79044)),x79042),x79045))
% 51.10/50.83 [7930]~P1(f331(x79301,x79304))+~P1(f331(f331(f191(x79302),x79304),x79305))+P1(f331(f331(f191(f35(x79301,x79302,x79303)),x79304),x79305))
% 51.10/50.83 [7931]~P1(f331(x79311,x79314))+~P1(f331(f331(f191(x79312),x79314),x79315))+P1(f331(f331(f191(f35(x79311,x79312,x79313)),x79314),x79315))
% 51.10/50.83 [7932]~P1(f331(x79321,x79324))+~P1(f331(f331(f191(x79322),x79324),x79325))+P1(f331(f331(f191(f35(x79321,x79322,x79323)),x79324),x79325))
% 51.10/50.83 [7977]E(x79771,x79772)+~E(f331(f311(x79773,x79774,x79775),x79771),f331(f311(x79773,x79774,x79775),x79772))+~P27(x79773,x79774,x79775,f331(f331(f108(f854(x79773,a840)),x79771),x79772))
% 51.10/50.83 [8077]~P27(x80771,x80772,x80773,x80775)+~P27(x80771,x80772,x80773,x80774)+P27(x80771,x80772,x80773,f331(f331(f109(f854(x80771,a840)),x80774),x80775))
% 51.10/50.83 [8183]~P68(x81831)+E(f331(f331(f87(x81831),f331(x81832,x81833)),f331(f157(x81831),f331(f331(f147(x81834,x81831),x81832),f161(x81834,x81833,x81835)))),f331(f157(x81831),f331(f331(f147(x81834,x81831),x81832),x81835)))+~P1(f331(f331(f333(x81834),x81833),f331(f163(x81834),x81835)))
% 51.10/50.83 [8271]~P102(x82711)+~P16(x82711,f331(f331(f147(x82712,x82711),x82713),x82715))+P16(x82711,f331(f331(f147(x82712,x82711),x82713),f331(f331(f143(x82712,x82711,x82713),x82714),x82715)))
% 51.10/50.83 [8348]P1(f331(x83481,x83482))+P1(f331(f331(f191(x83483),x83482),x83484))+~P1(f331(f331(f191(f35(x83481,x83485,x83483)),x83482),x83484))
% 51.10/50.83 [8349]P1(f331(x83491,x83492))+P1(f331(f331(f191(x83493),x83492),x83494))+~P1(f331(f331(f191(f35(x83491,x83495,x83493)),x83492),x83494))
% 51.10/50.83 [8350]P1(f331(x83501,x83502))+P1(f331(f331(f191(x83503),x83502),x83504))+~P1(f331(f331(f191(f35(x83501,x83505,x83503)),x83502),x83504))
% 51.10/50.83 [8361]~P7(x83611)+P1(f331(f331(f240(x83611),f331(f331(f51(x83612,x83611),x83613),x83614)),f331(f331(f51(x83612,x83611),x83615),x83614)))+~P1(f331(f331(f240(f854(x83612,a840)),x83613),x83615))
% 51.10/50.83 [8362]~P7(x83621)+P1(f331(f331(f240(x83621),f331(f331(f52(x83622,x83621),x83623),x83624)),f331(f331(f52(x83622,x83621),x83625),x83624)))+~P1(f331(f331(f240(f854(x83622,a840)),x83625),x83623))
% 51.10/50.83 [8369]~P1(f331(x83694,x83692))+P1(f331(f331(f191(x83691),x83692),x83693))+~P1(f331(f331(f191(f35(x83694,x83691,x83695)),x83692),x83693))
% 51.10/50.83 [8370]~P1(f331(x83704,x83702))+P1(f331(f331(f191(x83701),x83702),x83703))+~P1(f331(f331(f191(f35(x83704,x83701,x83705)),x83702),x83703))
% 51.10/50.83 [8371]~P1(f331(x83714,x83712))+P1(f331(f331(f191(x83711),x83712),x83713))+~P1(f331(f331(f191(f35(x83714,x83711,x83715)),x83712),x83713))
% 51.10/50.83 [8396]~P102(x83963)+P1(f331(f132(x83961),x83962))+~P1(f331(f132(x83961),f331(f331(f143(x83961,x83963,x83964),x83965),x83962)))
% 51.10/50.83 [8404]P1(f331(f331(f191(x84041),x84042),x84043))+P1(f331(f331(f191(x84044),x84042),x84043))+~P1(f331(f331(f191(f35(x84045,x84041,x84044)),x84042),x84043))
% 51.10/50.83 [8405]P1(f331(f331(f191(x84051),x84052),x84053))+P1(f331(f331(f191(x84054),x84052),x84053))+~P1(f331(f331(f191(f35(x84055,x84051,x84054)),x84052),x84053))
% 51.10/50.83 [8406]P1(f331(f331(f191(x84061),x84062),x84063))+P1(f331(f331(f191(x84064),x84062),x84063))+~P1(f331(f331(f191(f35(x84065,x84061,x84064)),x84062),x84063))
% 51.10/50.83 [8527]~P102(x85271)+~P1(f331(f331(f333(x85272),x85273),f331(f163(x85272),x85274)))+~P1(f331(f132(x85272),f331(f331(f143(x85272,x85271,x85275),x85273),x85274)))
% 51.10/50.83 [8603]~P102(x86031)+P16(x86031,f331(f331(f147(x86032,x86031),x86033),x86034))+~P16(x86031,f331(f331(f147(x86032,x86031),x86033),f331(f331(f143(x86032,x86031,x86033),x86035),x86034)))
% 51.10/50.83 [8688]~P102(x86882)+E(f331(f331(f143(x86881,x86882,x86883),x86884),x86885),f144(x86881,x86882,x86883,x86884,x86885))+P1(f331(f331(f333(x86882),f331(x86883,x86884)),f331(f311(x86881,x86882,x86883),f331(f163(x86881),x86885))))
% 51.10/50.83 [8755]~P102(x87552)+E(f144(x87551,x87552,x87553,x87554,x87555),x87555)+~P1(f331(f331(f333(x87552),f331(x87553,x87554)),f331(f311(x87551,x87552,x87553),f331(f163(x87551),x87555))))
% 51.10/50.83 [8769]~P27(x87692,x87691,x87693,x87695)+P1(f331(f331(f241(f854(x87691,a840)),f331(f311(x87692,x87691,x87693),x87694)),f331(f311(x87692,x87691,x87693),x87695)))+~P1(f331(f331(f241(f854(x87692,a840)),x87694),x87695))
% 51.10/50.83 [8792]~P27(x87922,x87921,x87923,f247(f854(x87922,a840)))+P1(f331(f331(f240(f854(x87921,a840)),f331(f311(x87922,x87921,x87923),x87924)),f331(f311(x87922,x87921,x87923),x87925)))+~P1(f331(f331(f240(f854(x87922,a840)),x87924),x87925))
% 51.10/50.83 [8914]~P27(x89141,x89142,x89143,f247(f854(x89141,a840)))+~P1(f331(f331(f240(f854(x89142,a840)),x89144),f331(f311(x89141,x89142,x89143),x89145)))+P1(f331(f331(f240(f854(x89141,a840)),f331(f312(x89141,x89142,x89143),x89144)),x89145))
% 51.10/50.83 [8933]~E(f331(f311(x89333,x89331,x89334),f247(f854(x89333,a840))),f247(f854(x89331,a840)))+P1(f331(f331(f240(f854(x89331,a840)),x89332),f331(f311(x89333,x89331,x89334),x89335)))+~P1(f331(f331(f240(f854(x89333,a840)),f331(f312(x89333,x89331,x89334),x89332)),x89335))
% 51.10/50.83 [8967]~E(f331(f234(x89672),x89674),f331(f171(x89671,x89672,x89675),x89673))+~P1(f331(f132(x89671),f331(f331(f147(f853(x89671,x89672),x89671),f248(x89671,x89672)),x89675)))+P1(f331(f331(f333(f853(x89671,x89672)),f331(f331(f249(x89671,x89672),x89673),x89674)),f331(f163(f853(x89671,x89672)),x89675)))
% 51.10/50.83 [8968]~E(f331(f171(x89681,x89682,x89685),x89683),f331(f234(x89682),x89684))+~P1(f331(f132(x89681),f331(f331(f147(f853(x89681,x89682),x89681),f248(x89681,x89682)),x89685)))+P1(f331(f331(f333(f853(x89681,x89682)),f331(f331(f249(x89681,x89682),x89683),x89684)),f331(f163(f853(x89681,x89682)),x89685)))
% 51.10/50.83 [9033]~P27(x90331,x90334,x90335,f247(f854(x90331,a840)))+~P1(f331(f331(f240(f854(x90334,a840)),f331(f311(x90331,x90334,x90335),x90332)),f331(f311(x90331,x90334,x90335),x90333)))+P1(f331(f331(f240(f854(x90331,a840)),x90332),x90333))
% 51.10/50.83 [9097]E(f331(f234(x90971),x90972),f331(f171(x90973,x90971,x90974),x90975))+~P1(f331(f132(x90973),f331(f331(f147(f853(x90973,x90971),x90973),f248(x90973,x90971)),x90974)))+~P1(f331(f331(f333(f853(x90973,x90971)),f331(f331(f249(x90973,x90971),x90975),x90972)),f331(f163(f853(x90973,x90971)),x90974)))
% 51.10/50.83 [9098]E(f331(f171(x90981,x90982,x90983),x90984),f331(f234(x90982),x90985))+~P1(f331(f132(x90981),f331(f331(f147(f853(x90981,x90982),x90981),f248(x90981,x90982)),x90983)))+~P1(f331(f331(f333(f853(x90981,x90982)),f331(f331(f249(x90981,x90982),x90984),x90985)),f331(f163(f853(x90981,x90982)),x90983)))
% 51.10/50.83 [9099]E(f331(f171(x90991,x90992,x90993),x90994),f331(f234(x90992),x90995))+~P1(f331(f132(x90991),f331(f331(f147(f853(x90991,x90992),x90991),f248(x90991,x90992)),x90993)))+~P1(f331(f331(f333(f853(x90991,x90992)),f331(f331(f249(x90991,x90992),x90994),x90995)),f331(f163(f853(x90991,x90992)),x90993)))
% 51.10/50.83 [9308]~P18(x93081,x93082,x93083)+~P1(f331(f68(x93081),x93085))+P1(f331(f73(x93081,x93082,x93083,x93084,x93085),f331(f331(f71(x93081,x93082,x93083),x93084),x93085)))
% 51.10/50.83 [9383]P1(f331(x93831,f698(x93832,x93831,x93833,x93834,x93835)))+~P1(f331(f331(f240(f854(x93835,a840)),x93834),x93833))+P1(f331(f331(f240(f854(x93835,a840)),f331(f331(f109(f854(x93835,a840)),x93834),f331(f264(x93835),x93831))),f331(f331(f109(f854(x93835,a840)),x93833),f331(f264(x93835),x93832))))
% 51.10/50.83 [9476]~P7(x94765)+P1(f331(f331(f333(x94761),f634(x94762,x94763,x94761,x94764,x94765)),x94763))+P1(f331(f331(f240(x94765),x94764),f331(f331(f52(x94761,x94765),x94763),x94762)))
% 51.10/50.83 [9488]~P1(f331(x94885,f698(x94885,x94883,x94884,x94882,x94881)))+~P1(f331(f331(f240(f854(x94881,a840)),x94882),x94884))+P1(f331(f331(f240(f854(x94881,a840)),f331(f331(f109(f854(x94881,a840)),x94882),f331(f264(x94881),x94883))),f331(f331(f109(f854(x94881,a840)),x94884),f331(f264(x94881),x94885))))
% 51.10/50.83 [9554]P1(f331(f331(f333(x95541),f698(x95542,x95543,x95544,x95545,x95541)),x95545))+~P1(f331(f331(f240(f854(x95541,a840)),x95545),x95544))+P1(f331(f331(f240(f854(x95541,a840)),f331(f331(f109(f854(x95541,a840)),x95545),f331(f264(x95541),x95543))),f331(f331(f109(f854(x95541,a840)),x95544),f331(f264(x95541),x95542))))
% 51.10/50.83 [9604]~P7(x96041)+~P1(f331(f331(f240(x96041),x96042),f331(x96045,f634(x96045,x96044,x96043,x96042,x96041))))+P1(f331(f331(f240(x96041),x96042),f331(f331(f52(x96043,x96041),x96044),x96045)))
% 51.10/50.83 [9634]~P70(x96341)+~P1(f331(f68(x96342),x96345))+E(f331(f331(f331(f72(x96341,x96342,f88(x96341)),f331(f331(f20(x96342,x96341,x96341),f331(f331(f10(x96341,f854(x96341,x96341),x96342),f88(x96341)),x96343)),x96344)),f85(x96341)),x96345),f331(f331(f88(x96341),f331(f331(f331(f72(x96341,x96342,f88(x96341)),x96343),f85(x96341)),x96345)),f331(f331(f331(f72(x96341,x96342,f88(x96341)),x96344),f85(x96341)),x96345)))
% 51.10/50.83 [9683]~P1(f331(f331(f333(f853(f854(x96831,a840),f854(x96831,a840))),f331(f331(f249(f854(x96831,a840),f854(x96831,a840)),x96835),x96834)),f323(x96831,x96833)))+~P1(f331(f331(f333(x96831),x96832),x96835))+P1(f331(f331(f333(f853(x96831,x96831)),f331(f331(f249(x96831,x96831),x96832),f627(x96833,x96834,x96835,x96831,x96832))),x96833))
% 51.10/50.83 [9836]~P1(f331(f331(f333(f853(f848(x98361),f848(x98361))),f331(f331(f249(f848(x98361),f848(x98361)),f331(f331(f130(x98361),x98365),x98362)),f331(f331(f130(x98361),x98365),x98363))),f142(x98361,x98364)))+P1(f331(f331(f333(f853(f848(x98361),f848(x98361))),f331(f331(f249(f848(x98361),f848(x98361)),x98362),x98363)),f142(x98361,x98364)))+P1(f331(f331(f333(f853(x98361,x98361)),f331(f331(f249(x98361,x98361),f740(x98364,x98363,x98362,x98365,x98361)),f740(x98364,x98363,x98362,x98365,x98361))),x98364))
% 51.10/50.83 [7120]~E(x71203,x71205)+E(f331(f331(f155(x71201),f331(f331(f152(x71201,x71202),x71203),x71204)),x71205),x71204)+~P1(f331(f331(f241(a847),x71203),f331(f185(f848(x71201)),x71202)))
% 51.10/50.83 [7129]~E(f331(f185(f848(x71291)),x71293),f331(f185(f848(x71292)),x71294))+E(f331(f171(x71291,x71292,f331(f331(f172(x71291,x71292),x71293),x71294)),x71295),f187(x71292))+P1(f331(f331(f333(x71291),x71295),f331(f163(x71291),x71293)))
% 51.10/50.83 [7247]~E(f331(f331(f130(x72471),x72472),x72474),f331(f331(f130(x72471),x72473),x72475))+E(f331(f331(f164(x72471),f331(f185(f848(x72471)),x72472)),x72473),x72472)+P1(f331(f331(f240(a847),f331(f185(f848(x72471)),x72473)),f331(f185(f848(x72471)),x72472)))
% 51.10/50.83 [7248]E(x72481,x72482)+E(f331(f331(f155(x72483),f331(f331(f152(x72483,x72484),x72481),x72485)),x72482),f331(f331(f155(x72483),x72484),x72482))+~P1(f331(f331(f241(a847),x72481),f331(f185(f848(x72483)),x72484)))
% 51.10/50.83 [7762]~E(f331(f331(f130(x77621),x77622),x77624),f331(f331(f130(x77621),x77623),x77625))+E(f331(f331(f164(x77621),f331(f185(f848(x77621)),x77622)),x77623),x77622)+~P1(f331(f331(f240(a847),f331(f185(f848(x77621)),x77622)),f331(f185(f848(x77621)),x77623)))
% 51.10/50.83 [7786]~P1(f331(f68(x77861),f331(x77864,x77865)))+~P1(f331(f331(f333(x77862),x77865),x77863))+P1(f331(f68(x77861),f331(f331(f52(x77862,f854(x77861,a840)),x77863),x77864)))
% 51.10/50.83 [7898]~E(f331(f185(f848(x78981)),x78982),f331(f185(f848(x78983)),x78984))+~E(f331(f171(x78981,x78983,f331(f331(f172(x78981,x78983),x78982),x78984)),x78985),f187(x78983))+~P1(f331(f331(f333(x78981),x78985),f331(f163(x78981),x78982)))
% 51.10/50.83 [7964]~P45(x79641,x79643,x79645)+~P45(x79641,x79642,x79644)+P45(x79641,f331(f331(f108(f854(x79641,a840)),x79642),x79643),f331(f331(f108(f854(f853(x79641,x79641),a840)),x79644),x79645))
% 51.10/50.83 [7965]~P45(x79651,x79653,x79655)+~P45(x79651,x79652,x79654)+P45(x79651,f331(f331(f109(f854(x79651,a840)),x79652),x79653),f331(f331(f109(f854(f853(x79651,x79651),a840)),x79654),x79655))
% 51.10/50.83 [8314]E(f331(f331(f249(x83141,x83142),f331(f331(f155(x83141),x83143),x83144)),f331(f331(f155(x83142),x83145),x83144)),f331(f331(f155(f853(x83141,x83142)),f331(f331(f172(x83141,x83142),x83143),x83145)),x83144))+~P1(f331(f331(f241(a847),x83144),f331(f185(f848(x83141)),x83143)))+~P1(f331(f331(f241(a847),x83144),f331(f185(f848(x83142)),x83145)))
% 51.10/50.83 [8471]~P45(x84711,x84713,x84714)+P1(f331(f331(f333(x84711),x84712),x84713))+~P1(f331(f331(f333(f853(x84711,x84711)),f331(f331(f249(x84711,x84711),x84715),x84712)),x84714))
% 51.10/50.83 [8472]~P45(x84721,x84723,x84724)+P1(f331(f331(f333(x84721),x84722),x84723))+~P1(f331(f331(f333(f853(x84721,x84721)),f331(f331(f249(x84721,x84721),x84722),x84725)),x84724))
% 51.10/50.83 [8473]~P10(x84731,x84733,x84734)+P1(f331(f331(f333(x84731),x84732),x84733))+~P1(f331(f331(f333(f853(x84731,x84731)),f331(f331(f249(x84731,x84731),x84735),x84732)),x84734))
% 51.10/50.83 [8474]~P10(x84741,x84743,x84744)+P1(f331(f331(f333(x84741),x84742),x84743))+~P1(f331(f331(f333(f853(x84741,x84741)),f331(f331(f249(x84741,x84741),x84742),x84745)),x84744))
% 51.10/50.83 [8710]~P10(x87101,x87105,x87102)+E(f331(f285(x87101,x87101,x87102),f331(f331(f310(x87101),x87103),f184(f854(x87101,a840)))),f331(f285(x87101,x87101,x87102),f331(f331(f310(x87101),x87104),f184(f854(x87101,a840)))))+~P1(f331(f331(f333(f853(x87101,x87101)),f331(f331(f249(x87101,x87101),x87103),x87104)),x87102))
% 51.10/50.83 [8711]~P10(x87111,x87115,x87112)+E(f331(f285(x87111,x87111,x87112),f331(f331(f310(x87111),x87113),f184(f854(x87111,a840)))),f331(f285(x87111,x87111,x87112),f331(f331(f310(x87111),x87114),f184(f854(x87111,a840)))))+~P1(f331(f331(f333(f853(x87111,x87111)),f331(f331(f249(x87111,x87111),x87113),x87114)),x87112))
% 51.10/50.83 [8873]P1(f331(x88731,x88732))+~P1(f331(f331(f333(x88733),x88732),x88735))+P1(f331(f331(f333(x88733),f351(x88731,x88734,x88735,x88733)),f331(f331(f108(f854(x88733,a840)),x88735),x88734)))
% 51.10/50.83 [8874]P1(f331(x88741,x88742))+~P1(f331(f331(f333(x88743),x88742),x88744))+P1(f331(f331(f333(x88743),f351(x88741,x88744,x88745,x88743)),f331(f331(f108(f854(x88743,a840)),x88745),x88744)))
% 51.10/50.83 [8882]~P1(f331(x88822,x88825))+~P1(f331(f331(f333(x88821),x88825),x88824))+P1(f331(f331(f333(x88821),f343(x88822,x88823,x88824,x88821)),f331(f331(f108(f854(x88821,a840)),x88824),x88823)))
% 51.10/50.83 [8883]~P1(f331(x88832,x88835))+~P1(f331(f331(f333(x88831),x88835),x88833))+P1(f331(f331(f333(x88831),f343(x88832,x88833,x88834,x88831)),f331(f331(f108(f854(x88831,a840)),x88834),x88833)))
% 51.10/50.83 [8896]~P1(f331(f331(f240(f854(x88961,a840)),x88965),x88963))+~P1(f331(f331(f240(f854(x88961,a840)),x88962),x88964))+P1(f331(f331(f240(f854(x88961,a840)),f331(f331(f3(f854(x88961,a840)),x88962),x88963)),f331(f331(f3(f854(x88961,a840)),x88964),x88965)))
% 51.10/50.83 [8897]~P1(f331(f331(f240(f854(x88971,a840)),x88973),x88975))+~P1(f331(f331(f240(f854(x88971,a840)),x88972),x88974))+P1(f331(f331(f240(f854(x88971,a840)),f331(f331(f108(f854(x88971,a840)),x88972),x88973)),f331(f331(f108(f854(x88971,a840)),x88974),x88975)))
% 51.10/50.83 [8898]~P1(f331(f331(f240(f854(x88981,a840)),x88983),x88985))+~P1(f331(f331(f240(f854(x88981,a840)),x88982),x88984))+P1(f331(f331(f240(f854(x88981,a840)),f331(f331(f109(f854(x88981,a840)),x88982),x88983)),f331(f331(f109(f854(x88981,a840)),x88984),x88985)))
% 51.10/50.83 [8984]P1(f331(f331(f333(f853(x89841,x89841)),f331(f331(f249(x89841,x89841),x89842),x89843)),f326(x89841,x89844,x89845)))+~P1(f331(f331(f240(a847),f331(x89844,x89842)),f331(x89844,x89843)))+~P1(f331(f331(f333(f853(x89841,x89841)),f331(f331(f249(x89841,x89841),x89842),x89843)),x89845))
% 51.10/50.83 [8991]~E(f331(f185(f848(x89911)),x89913),f331(f185(f848(x89912)),x89914))+E(f331(f171(x89911,x89912,f331(f331(f172(x89911,x89912),x89913),x89914)),x89915),f331(f234(x89912),f714(x89915,x89914,x89912,x89913,x89911)))+~P1(f331(f331(f333(x89911),x89915),f331(f163(x89911),x89913)))
% 51.10/50.83 [9140]P1(f331(f331(f333(f853(x91401,x91401)),f331(f331(f249(x91401,x91401),x91402),x91403)),f308(x91401,x91404)))+~P1(f331(f331(f333(f853(x91401,x91401)),f331(f331(f249(x91401,x91401),x91402),x91405)),f308(x91401,x91404)))+~P1(f331(f331(f333(f853(x91401,x91401)),f331(f331(f249(x91401,x91401),x91405),x91403)),x91404))
% 51.10/50.83 [9141]P1(f331(f331(f333(f853(x91411,x91411)),f331(f331(f249(x91411,x91411),x91412),x91413)),f308(x91411,x91414)))+~P1(f331(f331(f333(f853(x91411,x91411)),f331(f331(f249(x91411,x91411),x91415),x91413)),f308(x91411,x91414)))+~P1(f331(f331(f333(f853(x91411,x91411)),f331(f331(f249(x91411,x91411),x91412),x91415)),x91414))
% 51.10/50.83 [9236]E(x92361,x92362)+E(f331(a119,f652(x92363,x92364,x92361,x92362,x92365)),x92364)+~P1(f331(f331(f333(f853(x92365,x92365)),f331(f331(f249(x92365,x92365),x92362),x92361)),f331(f331(f178(f853(x92365,x92365),a840),x92364),x92363)))
% 51.10/50.83 [9237]E(x92371,x92372)+E(f331(a119,f654(x92373,x92374,x92371,x92372,x92375)),x92374)+~P1(f331(f331(f333(f853(x92375,x92375)),f331(f331(f249(x92375,x92375),x92372),x92371)),f331(f331(f178(f853(x92375,x92375),a840),x92374),x92373)))
% 51.10/50.83 [9238]E(x92381,f2(a847))+E(f331(a119,f652(x92382,x92381,x92383,x92384,x92385)),x92381)+~P1(f331(f331(f333(f853(x92385,x92385)),f331(f331(f249(x92385,x92385),x92384),x92383)),f331(f331(f178(f853(x92385,x92385),a840),x92381),x92382)))
% 51.10/50.83 [9239]E(x92391,f2(a847))+E(f331(a119,f654(x92392,x92391,x92393,x92394,x92395)),x92391)+~P1(f331(f331(f333(f853(x92395,x92395)),f331(f331(f249(x92395,x92395),x92394),x92393)),f331(f331(f178(f853(x92395,x92395),a840),x92391),x92392)))
% 51.10/50.83 [9258]P1(f331(f331(f333(f853(x92581,x92581)),f331(f331(f249(x92581,x92581),x92582),x92583)),f331(f331(f289(x92581,x92581,x92581),x92584),f308(x92581,x92584))))+~P1(f331(f331(f333(f853(x92581,x92581)),f331(f331(f249(x92581,x92581),x92582),x92585)),x92584))+~P1(f331(f331(f333(f853(x92581,x92581)),f331(f331(f249(x92581,x92581),x92585),x92583)),x92584))
% 51.10/50.83 [9267]~P1(f331(f331(f333(f853(x92671,x92671)),f331(f331(f249(x92671,x92671),x92672),x92675)),f308(x92671,x92674)))+P1(f331(f331(f333(f853(x92671,x92671)),f331(f331(f249(x92671,x92671),x92672),x92673)),f331(f331(f289(x92671,x92671,x92671),x92674),f308(x92671,x92674))))+~P1(f331(f331(f333(f853(x92671,x92671)),f331(f331(f249(x92671,x92671),x92675),x92673)),x92674))
% 51.10/50.83 [9268]~P1(f331(f331(f333(f853(x92681,x92681)),f331(f331(f249(x92681,x92681),x92685),x92683)),f308(x92681,x92684)))+P1(f331(f331(f333(f853(x92681,x92681)),f331(f331(f249(x92681,x92681),x92682),x92683)),f331(f331(f289(x92681,x92681,x92681),x92684),f308(x92681,x92684))))+~P1(f331(f331(f333(f853(x92681,x92681)),f331(f331(f249(x92681,x92681),x92682),x92685)),x92684))
% 51.10/50.83 [9304]~P10(x93041,x93045,x93042)+~P1(f331(f331(f333(f853(x93041,x93041)),f331(f331(f249(x93041,x93041),x93043),x93044)),x93042))+P1(f331(f331(f240(f854(x93041,a840)),f331(f285(x93041,x93041,x93042),f331(f331(f310(x93041),x93043),f184(f854(x93041,a840))))),f331(f285(x93041,x93041,x93042),f331(f331(f310(x93041),x93044),f184(f854(x93041,a840))))))
% 51.10/50.83 [9356]P1(f331(f331(f333(f853(x93561,x93561)),f331(f331(f249(x93561,x93561),x93562),x93563)),f331(f331(f289(x93561,x93561,x93561),x93564),f308(x93561,x93564))))+~P1(f331(f331(f333(f853(x93561,x93561)),f331(f331(f249(x93561,x93561),x93562),x93565)),f331(f331(f289(x93561,x93561,x93561),x93564),f308(x93561,x93564))))+~P1(f331(f331(f333(f853(x93561,x93561)),f331(f331(f249(x93561,x93561),x93565),x93563)),x93564))
% 51.10/50.83 [9357]P1(f331(f331(f333(f853(x93571,x93571)),f331(f331(f249(x93571,x93571),x93572),x93573)),f331(f331(f289(x93571,x93571,x93571),x93574),f308(x93571,x93574))))+~P1(f331(f331(f333(f853(x93571,x93571)),f331(f331(f249(x93571,x93571),x93575),x93573)),f331(f331(f289(x93571,x93571,x93571),x93574),f308(x93571,x93574))))+~P1(f331(f331(f333(f853(x93571,x93571)),f331(f331(f249(x93571,x93571),x93572),x93575)),x93574))
% 51.10/50.83 [9406]~P1(f331(f73(x94061,x94061,x94064,x94062,x94063),x94065))+P1(f331(f331(f333(x94061),x94062),x94063))+P1(f331(f69(x94061,x94064,f331(f331(f310(x94061),x94062),x94063)),x94065))
% 51.10/50.83 [9451]~E(f331(f311(x94513,x94512,x94515),x94514),x94511)+E(x94511,f184(f854(x94512,a840)))+P1(f331(f331(f240(f854(x94513,a840)),f331(f311(x94512,x94513,f443(x94514,x94513,x94512,x94511)),x94511)),x94514))
% 51.10/50.83 [9491]~P7(x94915)+P1(f331(f331(f333(x94911),f411(x94912,x94913,x94914,x94911,x94915)),x94914))+P1(f331(f331(f240(x94915),f331(f331(f51(x94911,x94915),x94914),x94913)),x94912))
% 51.10/50.83 [9660]E(x96601,x96602)+P1(f331(f331(f333(f853(x96603,x96603)),f331(f331(f249(x96603,x96603),x96601),f653(x96604,x96605,x96602,x96601,x96603))),x96604))+~P1(f331(f331(f333(f853(x96603,x96603)),f331(f331(f249(x96603,x96603),x96601),x96602)),f331(f331(f178(f853(x96603,x96603),a840),x96605),x96604)))
% 51.10/50.83 [9661]E(x96611,f2(a847))+P1(f331(f331(f333(f853(x96612,x96612)),f331(f331(f249(x96612,x96612),x96613),f653(x96614,x96611,x96615,x96613,x96612))),x96614))+~P1(f331(f331(f333(f853(x96612,x96612)),f331(f331(f249(x96612,x96612),x96613),x96615)),f331(f331(f178(f853(x96612,x96612),a840),x96611),x96614)))
% 51.10/50.83 [9706]~P7(x97061)+~P1(f331(f331(f240(x97061),f331(x97064,f411(x97065,x97064,x97063,x97062,x97061))),x97065))+P1(f331(f331(f240(x97061),f331(f331(f51(x97062,x97061),x97063),x97064)),x97065))
% 51.10/50.83 [9761]E(x97611,x97612)+P1(f331(f331(f333(f853(x97613,x97613)),f331(f331(f249(x97613,x97613),f655(x97614,x97615,x97611,x97612,x97613)),x97611)),x97614))+~P1(f331(f331(f333(f853(x97613,x97613)),f331(f331(f249(x97613,x97613),x97612),x97611)),f331(f331(f178(f853(x97613,x97613),a840),x97615),x97614)))
% 51.10/50.83 [9762]E(x97621,f2(a847))+P1(f331(f331(f333(f853(x97622,x97622)),f331(f331(f249(x97622,x97622),f655(x97623,x97621,x97624,x97625,x97622)),x97624)),x97623))+~P1(f331(f331(f333(f853(x97622,x97622)),f331(f331(f249(x97622,x97622),x97625),x97624)),f331(f331(f178(f853(x97622,x97622),a840),x97621),x97623)))
% 51.10/50.83 [9766]E(x97661,x97662)+P1(f331(f331(f333(f853(x97663,x97663)),f331(f331(f249(x97663,x97663),x97661),f655(x97664,x97665,x97662,x97661,x97663))),f331(f331(f178(f853(x97663,x97663),a840),f654(x97664,x97665,x97662,x97661,x97663)),x97664)))+~P1(f331(f331(f333(f853(x97663,x97663)),f331(f331(f249(x97663,x97663),x97661),x97662)),f331(f331(f178(f853(x97663,x97663),a840),x97665),x97664)))
% 51.10/50.83 [9767]E(x97671,f2(a847))+P1(f331(f331(f333(f853(x97672,x97672)),f331(f331(f249(x97672,x97672),x97673),f655(x97674,x97671,x97675,x97673,x97672))),f331(f331(f178(f853(x97672,x97672),a840),f654(x97674,x97671,x97675,x97673,x97672)),x97674)))+~P1(f331(f331(f333(f853(x97672,x97672)),f331(f331(f249(x97672,x97672),x97673),x97675)),f331(f331(f178(f853(x97672,x97672),a840),x97671),x97674)))
% 51.10/50.83 [9827]E(x98271,x98272)+P1(f331(f331(f333(f853(x98273,x98273)),f331(f331(f249(x98273,x98273),f653(x98274,x98275,x98271,x98272,x98273)),x98271)),f331(f331(f178(f853(x98273,x98273),a840),f652(x98274,x98275,x98271,x98272,x98273)),x98274)))+~P1(f331(f331(f333(f853(x98273,x98273)),f331(f331(f249(x98273,x98273),x98272),x98271)),f331(f331(f178(f853(x98273,x98273),a840),x98275),x98274)))
% 51.10/50.83 [9828]E(x98281,f2(a847))+P1(f331(f331(f333(f853(x98282,x98282)),f331(f331(f249(x98282,x98282),f653(x98283,x98281,x98284,x98285,x98282)),x98284)),f331(f331(f178(f853(x98282,x98282),a840),f652(x98283,x98281,x98284,x98285,x98282)),x98283)))+~P1(f331(f331(f333(f853(x98282,x98282)),f331(f331(f249(x98282,x98282),x98285),x98284)),f331(f331(f178(f853(x98282,x98282),a840),x98281),x98283)))
% 51.10/50.83 [9861]~P68(x98612)+~P1(f331(f68(x98611),x98615))+E(f331(f331(f8(x98611,x98612),f331(f331(f9(x98611,x98612,x98612),f331(f331(f20(x98611,x98612,f854(x98612,x98612)),f331(f331(f10(a840,f854(x98612,f854(x98612,x98612)),x98611),f103(x98612)),f331(f331(f9(x98611,f854(x98611,a840),a840),f333(x98611)),x98613))),x98614)),f2(x98612))),x98615),f331(f331(f8(x98611,x98612),x98614),f331(f331(f109(f854(x98611,a840)),x98615),x98613)))
% 51.10/50.83 [8525]~P70(x85251)+~P1(f331(f68(x85254),x85255))+E(f331(f331(f88(x85251),f331(x85252,x85253)),f331(f331(f11(x85254,x85251),x85252),f331(f331(f3(f854(x85254,a840)),x85255),f331(f331(f310(x85254),x85253),f184(f854(x85254,a840)))))),f331(f331(f11(x85254,x85251),x85252),f331(f331(f310(x85254),x85253),x85255)))
% 51.10/50.83 [8526]~P68(x85261)+~P1(f331(f68(x85264),x85265))+E(f331(f331(f87(x85261),f331(x85262,x85263)),f331(f331(f8(x85264,x85261),x85262),f331(f331(f3(f854(x85264,a840)),x85265),f331(f331(f310(x85264),x85263),f184(f854(x85264,a840)))))),f331(f331(f8(x85264,x85261),x85262),f331(f331(f310(x85264),x85263),x85265)))
% 51.10/50.83 [8807]~P102(x88072)+~P16(x88072,f331(f160(x88072),f331(f331(f147(x88071,x88072),x88074),x88075)))+E(f331(f131(x88071,f331(f331(f10(x88072,a840,x88071),f331(f241(x88072),x88073)),x88074)),x88075),f167(x88071,f331(f331(f10(x88072,a840,x88071),f331(f241(x88072),x88073)),x88074),x88075))
% 51.10/50.83 [8828]~P68(x88281)+E(f331(f331(f87(x88281),f331(f331(f8(a847,x88281),x88282),f303(a847,x88283,x88284))),f331(f331(f8(a847,x88281),x88282),f303(a847,f331(f331(f87(a847),x88284),f85(a847)),f331(f331(f87(a847),x88284),x88285)))),f331(f331(f8(a847,x88281),x88282),f303(a847,x88283,f331(f331(f87(a847),x88284),x88285))))+~P1(f331(f331(f240(a847),x88283),f331(f331(f87(a847),x88284),f85(a847))))
% 51.10/50.83 [8829]~P1(f331(f331(f333(x88291),x88294),x88295))+~P1(f331(f331(f240(f854(x88291,a840)),f331(f163(x88291),x88292)),x88295))+P1(f331(f331(f240(f854(x88291,a840)),f331(f163(x88291),f331(f331(f152(x88291,x88292),x88293),x88294))),x88295))
% 51.10/50.83 [9042]~P7(x90422)+~P1(f331(f68(x90421),x90425))+E(f331(f331(f71(x90421,x90422,f331(f331(f10(x90422,f854(x90422,x90422),x90421),f108(x90422)),x90423)),x90424),x90425),f331(f331(f108(x90422),x90424),f331(f331(f51(x90421,x90422),x90425),x90423)))
% 51.10/50.83 [9043]~P7(x90432)+~P1(f331(f68(x90431),x90435))+E(f331(f331(f71(x90431,x90432,f331(f331(f10(x90432,f854(x90432,x90432),x90431),f109(x90432)),x90433)),x90434),x90435),f331(f331(f109(x90432),x90434),f331(f331(f52(x90431,x90432),x90435),x90433)))
% 51.10/50.83 [9127]~P27(x91271,x91272,x91273,x91275)+P27(x91271,x91272,x91273,f331(f331(f310(x91271),x91274),x91275))+P1(f331(f331(f333(x91272),f331(x91273,x91274)),f331(f311(x91271,x91272,x91273),f331(f331(f3(f854(x91271,a840)),x91275),f331(f331(f310(x91271),x91274),f184(f854(x91271,a840)))))))
% 51.10/50.83 [9330]~P1(f331(f331(f333(f853(f848(x93301),f848(x93301))),f331(f331(f249(f848(x93301),f848(x93301)),x93302),x93304)),f151(x93301,x93305)))+~P1(f331(f331(f241(a847),x93303),f331(f185(f848(x93301)),x93302)))+P1(f331(f331(f333(f853(x93301,x93301)),f331(f331(f249(x93301,x93301),f331(f331(f155(x93301),x93302),x93303)),f331(f331(f155(x93301),x93304),x93303))),x93305))
% 51.10/50.83 [9565]E(x95651,f2(a1))+~P1(f331(f61(x95653,x95651),f331(f331(f249(a1,a1),x95654),x95655)))+P1(f331(f61(f331(f331(f88(a1),x95652),x95653),x95651),f331(f331(f249(a1,a1),f331(f331(f87(a1),f331(f331(f88(a1),x95652),x95654)),f331(f331(f48(a1),f331(f331(f88(a1),x95652),x95655)),x95651))),f57(a1,f331(f331(f88(a1),x95652),x95655),x95651))))
% 51.10/50.83 [9570]~P1(f331(f331(f241(a847),f2(a847)),x95703))+~P1(f331(f60(x95702,x95703),f331(f331(f249(a847,a847),x95704),x95705)))+P1(f331(f60(f331(f331(f88(a847),x95701),x95702),x95703),f331(f331(f249(a847,a847),f331(f331(f87(a847),f331(f331(f88(a847),x95701),x95704)),f331(f331(f48(a847),f331(f331(f88(a847),x95701),x95705)),x95703))),f57(a847,f331(f331(f88(a847),x95701),x95705),x95703))))
% 51.10/50.83 [9883]~P68(x98832)+~P1(f331(f68(x98831),x98834))+E(f331(f331(f8(x98831,x98832),x98833),f331(f264(x98831),f331(f331(f20(x98831,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98831),a329),f331(f331(f9(x98831,f854(x98831,a840),a840),f333(x98831)),x98834))),f331(f331(f9(x98831,f854(x98831,a840),a840),f333(x98831)),x98835)))),f331(f331(f8(x98831,x98832),f331(f331(f9(x98831,x98832,x98832),f331(f331(f20(x98831,x98832,f854(x98832,x98832)),f331(f331(f10(a840,f854(x98832,f854(x98832,x98832)),x98831),f103(x98832)),f331(f331(f9(x98831,f854(x98831,a840),a840),f333(x98831)),x98835))),x98833)),f2(x98832))),x98834))
% 51.10/50.83 [8166]~E(f331(f331(f130(x81661),x81662),x81665),f331(f331(f130(x81661),x81663),x81664))+E(f331(f331(f130(x81661),f331(f331(f133(x81661),f331(f185(f848(x81661)),x81662)),x81663)),x81664),x81665)+P1(f331(f331(f240(a847),f331(f185(f848(x81661)),x81663)),f331(f185(f848(x81661)),x81662)))
% 51.10/50.83 [8364]~E(f331(f331(f130(x83642),x83643),x83641),f331(f331(f130(x83642),x83644),x83645))+E(x83641,f331(f331(f130(x83642),f331(f331(f133(x83642),f331(f185(f848(x83642)),x83643)),x83644)),x83645))+~P1(f331(f331(f240(a847),f331(f185(f848(x83642)),x83643)),f331(f185(f848(x83642)),x83644)))
% 51.10/50.83 [8454]~E(f331(f331(f87(a847),f331(f331(f88(a847),x84543),x84544)),x84541),f331(f331(f87(a847),f331(f331(f88(a847),x84542),x84544)),x84545))+~P1(f331(f331(f240(a847),x84543),x84542))+E(x84541,f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x84542),x84543)),x84544)),x84545))
% 51.10/50.83 [8455]~E(f331(f331(f87(a847),f331(f331(f88(a847),x84551),x84553)),x84554),f331(f331(f87(a847),f331(f331(f88(a847),x84552),x84553)),x84555))+~P1(f331(f331(f240(a847),x84552),x84551))+E(f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x84551),x84552)),x84553)),x84554),x84555)
% 51.10/50.83 [8596]E(f331(f331(f87(a847),f331(f331(f88(a847),x85961),x85962)),x85963),f331(f331(f87(a847),f331(f331(f88(a847),x85964),x85962)),x85965))+~P1(f331(f331(f240(a847),x85964),x85961))+~E(x85965,f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x85961),x85964)),x85962)),x85963))
% 51.10/50.83 [8597]E(f331(f331(f87(a847),f331(f331(f88(a847),x85971),x85972)),x85973),f331(f331(f87(a847),f331(f331(f88(a847),x85974),x85972)),x85975))+~P1(f331(f331(f240(a847),x85974),x85971))+~E(f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x85971),x85974)),x85972)),x85973),x85975)
% 51.10/50.83 [8929]~P1(f331(f331(f287(a1),x89291),x89294))+~P1(f331(f331(f287(a1),x89291),f331(f331(f87(a1),x89292),x89295)))+P1(f331(f331(f287(a1),x89291),f331(f331(f87(a1),f331(f331(f87(a1),x89292),f331(f331(f88(a1),x89293),x89294))),x89295)))
% 51.10/50.83 [9128]~P1(f331(f331(f287(a1),x91281),x91284))+P1(f331(f331(f287(a1),x91281),f331(f331(f87(a1),x91282),x91283)))+~P1(f331(f331(f287(a1),x91281),f331(f331(f87(a1),f331(f331(f87(a1),x91282),f331(f331(f88(a1),x91285),x91284))),x91283)))
% 51.10/50.83 [9379]~P70(x93792)+~P1(f331(f68(x93791),x93795))+E(f331(f331(f11(x93791,x93792),f331(f331(f20(x93791,x93792,x93792),f331(f331(f10(x93792,f854(x93792,x93792),x93791),f88(x93792)),x93793)),x93794)),x93795),f331(f331(f88(x93792),f331(f331(f11(x93791,x93792),x93793),x93795)),f331(f331(f11(x93791,x93792),x93794),x93795)))
% 51.10/50.83 [9380]~P58(x93802)+~P1(f331(f68(x93801),x93805))+E(f331(f331(f11(x93801,x93802),f331(f331(f20(x93801,x93802,x93802),f331(f331(f10(x93802,f854(x93802,x93802),x93801),f291(x93802)),x93803)),x93804)),x93805),f331(f331(f291(x93802),f331(f331(f11(x93801,x93802),x93803),x93805)),f331(f331(f11(x93801,x93802),x93804),x93805)))
% 51.10/50.83 [9381]~P68(x93812)+~P1(f331(f68(x93811),x93815))+E(f331(f331(f8(x93811,x93812),f331(f331(f20(x93811,x93812,x93812),f331(f331(f10(x93812,f854(x93812,x93812),x93811),f87(x93812)),x93813)),x93814)),x93815),f331(f331(f87(x93812),f331(f331(f8(x93811,x93812),x93813),x93815)),f331(f331(f8(x93811,x93812),x93814),x93815)))
% 51.10/50.83 [9506]~E(f681(x95065,x95064,x95063,x95062,x95061),f682(x95065,x95064,x95063,x95062,x95061))+P1(f331(f331(f333(f853(x95061,x95061)),f331(f331(f249(x95061,x95061),x95062),x95063)),f308(x95061,x95064)))+~P1(f331(f331(f333(f853(x95061,x95061)),f331(f331(f249(x95061,x95061),x95062),x95063)),f308(x95061,f331(f331(f108(f854(f853(x95061,x95061),a840)),x95064),x95065))))
% 51.10/50.83 [9507]~E(f683(x95075,x95074,x95073,x95072,x95071),f684(x95075,x95074,x95073,x95072,x95071))+P1(f331(f331(f333(f853(x95071,x95071)),f331(f331(f249(x95071,x95071),x95072),x95073)),f308(x95071,x95074)))+~P1(f331(f331(f333(f853(x95071,x95071)),f331(f331(f249(x95071,x95071),x95072),x95073)),f308(x95071,f331(f331(f108(f854(f853(x95071,x95071),a840)),x95074),x95075))))
% 51.10/50.83 [9694]P1(f331(f331(f333(f853(x96941,x96941)),f331(f331(f249(x96941,x96941),x96942),f682(x96945,x96944,x96943,x96942,x96941))),f308(x96941,x96944)))+P1(f331(f331(f333(f853(x96941,x96941)),f331(f331(f249(x96941,x96941),x96942),x96943)),f308(x96941,x96944)))+~P1(f331(f331(f333(f853(x96941,x96941)),f331(f331(f249(x96941,x96941),x96942),x96943)),f308(x96941,f331(f331(f108(f854(f853(x96941,x96941),a840)),x96944),x96945))))
% 51.10/50.83 [9788]P1(f331(f331(f333(f853(x97881,x97881)),f331(f331(f249(x97881,x97881),f684(x97885,x97884,x97883,x97882,x97881)),x97883)),f308(x97881,x97884)))+P1(f331(f331(f333(f853(x97881,x97881)),f331(f331(f249(x97881,x97881),x97882),x97883)),f308(x97881,x97884)))+~P1(f331(f331(f333(f853(x97881,x97881)),f331(f331(f249(x97881,x97881),x97882),x97883)),f308(x97881,f331(f331(f108(f854(f853(x97881,x97881),a840)),x97884),x97885))))
% 51.10/50.83 [9834]P1(f331(f331(f333(f853(x98341,x98341)),f331(f331(f249(x98341,x98341),x98342),x98343)),f308(x98341,x98344)))+P1(f331(f331(f333(f853(x98341,x98341)),f331(f331(f249(x98341,x98341),f682(x98345,x98344,x98343,x98342,x98341)),f681(x98345,x98344,x98343,x98342,x98341))),x98345))+~P1(f331(f331(f333(f853(x98341,x98341)),f331(f331(f249(x98341,x98341),x98342),x98343)),f308(x98341,f331(f331(f108(f854(f853(x98341,x98341),a840)),x98344),x98345))))
% 51.10/50.83 [9835]P1(f331(f331(f333(f853(x98351,x98351)),f331(f331(f249(x98351,x98351),x98352),x98353)),f308(x98351,x98354)))+P1(f331(f331(f333(f853(x98351,x98351)),f331(f331(f249(x98351,x98351),f683(x98355,x98354,x98353,x98352,x98351)),f684(x98355,x98354,x98353,x98352,x98351))),x98355))+~P1(f331(f331(f333(f853(x98351,x98351)),f331(f331(f249(x98351,x98351),x98352),x98353)),f308(x98351,f331(f331(f108(f854(f853(x98351,x98351),a840)),x98354),x98355))))
% 51.10/50.83 [9962]~P1(f331(f331(f333(f853(f848(x99621),f848(x99621))),f331(f331(f249(f848(x99621),f848(x99621)),x99624),x99625)),f151(x99621,x99622)))+~P1(f331(f331(f333(f853(x99621,x99621)),x99623),f331(f163(f853(x99621,x99621)),f331(f331(f172(x99621,x99621),x99624),x99625))))+P1(f331(f331(f259(x99621,x99621,a840),f331(f331(f9(x99621,f854(f853(x99621,x99621),a840),f854(x99621,a840)),f331(f331(f10(f854(x99621,f854(f854(f853(x99621,x99621),a840),a840)),f854(f854(f853(x99621,x99621),a840),f854(x99621,a840)),x99621),f9(x99621,f854(f853(x99621,x99621),a840),a840)),f331(f331(f10(f854(x99621,f853(x99621,x99621)),f854(x99621,f854(f854(f853(x99621,x99621),a840),a840)),x99621),f331(f10(f853(x99621,x99621),f854(f854(f853(x99621,x99621),a840),a840),x99621),f333(f853(x99621,x99621)))),f249(x99621,x99621)))),x99622)),x99623))
% 51.10/50.83 [9410]~P1(f331(f331(f240(a847),x94103),x94102))+~P1(f331(f331(f241(a847),f331(f331(f87(a847),f331(f331(f88(a847),x94103),x94104)),x94101)),f331(f331(f87(a847),f331(f331(f88(a847),x94102),x94104)),x94105)))+P1(f331(f331(f241(a847),x94101),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x94102),x94103)),x94104)),x94105)))
% 51.10/50.83 [9411]~P1(f331(f331(f240(a847),x94113),x94112))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),f331(f331(f88(a847),x94113),x94114)),x94111)),f331(f331(f87(a847),f331(f331(f88(a847),x94112),x94114)),x94115)))+P1(f331(f331(f240(a847),x94111),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x94112),x94113)),x94114)),x94115)))
% 51.10/50.83 [9433]~P1(f331(f331(f240(a847),x94331),x94334))+P1(f331(f331(f241(a847),f331(f331(f87(a847),f331(f331(f88(a847),x94331),x94332)),x94333)),f331(f331(f87(a847),f331(f331(f88(a847),x94334),x94332)),x94335)))+~P1(f331(f331(f241(a847),x94333),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x94334),x94331)),x94332)),x94335)))
% 51.10/50.83 [9434]~P1(f331(f331(f240(a847),x94341),x94344))+P1(f331(f331(f240(a847),f331(f331(f87(a847),f331(f331(f88(a847),x94341),x94342)),x94343)),f331(f331(f87(a847),f331(f331(f88(a847),x94344),x94342)),x94345)))+~P1(f331(f331(f240(a847),x94343),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x94344),x94341)),x94342)),x94345)))
% 51.10/50.83 [9543]~P1(f331(f331(f240(a847),x95432),x95431))+~P1(f331(f331(f241(a847),f331(f331(f87(a847),f331(f331(f88(a847),x95431),x95433)),x95434)),f331(f331(f87(a847),f331(f331(f88(a847),x95432),x95433)),x95435)))+P1(f331(f331(f241(a847),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x95431),x95432)),x95433)),x95434)),x95435))
% 51.10/50.83 [9544]~P1(f331(f331(f240(a847),x95442),x95441))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),f331(f331(f88(a847),x95441),x95443)),x95444)),f331(f331(f87(a847),f331(f331(f88(a847),x95442),x95443)),x95445)))+P1(f331(f331(f240(a847),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x95441),x95442)),x95443)),x95444)),x95445))
% 51.10/50.83 [9590]~P1(f331(f331(f240(a847),x95904),x95901))+P1(f331(f331(f241(a847),f331(f331(f87(a847),f331(f331(f88(a847),x95901),x95902)),x95903)),f331(f331(f87(a847),f331(f331(f88(a847),x95904),x95902)),x95905)))+~P1(f331(f331(f241(a847),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x95901),x95904)),x95902)),x95903)),x95905))
% 51.10/50.83 [9591]~P1(f331(f331(f240(a847),x95914),x95911))+P1(f331(f331(f240(a847),f331(f331(f87(a847),f331(f331(f88(a847),x95911),x95912)),x95913)),f331(f331(f87(a847),f331(f331(f88(a847),x95914),x95912)),x95915)))+~P1(f331(f331(f240(a847),f331(f331(f87(a847),f331(f331(f88(a847),f331(f331(f3(a847),x95911),x95914)),x95912)),x95913)),x95915))
% 51.10/50.83 [9819]~P14(x98191,x98192,x98195,x98193)+~P1(f331(f331(f333(f853(x98191,x98191)),x98194),x98195))+P1(f331(f331(f259(x98191,x98191,a840),f331(f331(f9(x98191,f854(x98191,x98192),f854(x98191,a840)),f331(f331(f10(f854(x98192,a840),f854(f854(x98191,x98192),f854(x98191,a840)),x98191),f10(x98192,a840,x98191)),f331(f331(f10(x98192,f854(x98192,a840),x98191),a328),x98193))),x98193)),x98194))
% 51.10/50.83 [7133]~P37(x71334,x71332,x71335,x71336)+P37(f35(x71331,x71333,x71334),x71332,x71335,x71336)+P1(f331(x71331,x71332))
% 51.10/50.83 [7134]~P37(x71344,x71342,x71345,x71346)+P37(f35(x71341,x71343,x71344),x71342,x71345,x71346)+P1(f331(x71341,x71342))
% 51.10/50.83 [7135]~P37(x71354,x71352,x71355,x71356)+P37(f35(x71351,x71353,x71354),x71352,x71355,x71356)+P1(f331(x71351,x71352))
% 51.10/50.83 [7211]~P37(x72112,x72114,x72115,x72116)+P37(f35(x72111,x72112,x72113),x72114,x72115,x72116)+~P1(f331(x72111,x72114))
% 51.10/50.83 [7212]~P37(x72122,x72124,x72125,x72126)+P37(f35(x72121,x72122,x72123),x72124,x72125,x72126)+~P1(f331(x72121,x72124))
% 51.10/50.83 [7213]~P37(x72132,x72134,x72135,x72136)+P37(f35(x72131,x72132,x72133),x72134,x72135,x72136)+~P1(f331(x72131,x72134))
% 51.10/50.83 [7302]P37(x73023,x73022,x73024,x73025)+~P37(f35(x73021,x73026,x73023),x73022,x73024,x73025)+P1(f331(x73021,x73022))
% 51.10/50.83 [7303]P37(x73033,x73032,x73034,x73035)+~P37(f35(x73031,x73036,x73033),x73032,x73034,x73035)+P1(f331(x73031,x73032))
% 51.10/50.83 [7304]P37(x73043,x73042,x73044,x73045)+~P37(f35(x73041,x73046,x73043),x73042,x73044,x73045)+P1(f331(x73041,x73042))
% 51.10/50.83 [7335]P37(x73351,x73352,x73353,x73354)+~P37(f35(x73355,x73351,x73356),x73352,x73353,x73354)+~P1(f331(x73355,x73352))
% 51.10/50.83 [7336]P37(x73361,x73362,x73363,x73364)+~P37(f35(x73365,x73361,x73366),x73362,x73363,x73364)+~P1(f331(x73365,x73362))
% 51.10/50.83 [7337]P37(x73371,x73372,x73373,x73374)+~P37(f35(x73375,x73371,x73376),x73372,x73373,x73374)+~P1(f331(x73375,x73372))
% 51.10/50.83 [7709]~P37(x77091,x77093,x77094,x77096)+~P37(x77092,x77096,x77094,x77095)+P37(f38(x77091,x77092),x77093,x77094,x77095)
% 51.10/50.83 [7710]~P37(x77101,x77103,x77104,x77106)+~P37(x77102,x77106,x77104,x77105)+P37(f38(x77101,x77102),x77103,x77104,x77105)
% 51.10/50.83 [7711]P37(x77111,x77112,x77113,x77114)+P37(x77115,x77112,x77113,x77114)+~P37(f35(x77116,x77111,x77115),x77112,x77113,x77114)
% 51.10/50.83 [7712]P37(x77121,x77122,x77123,x77124)+P37(x77125,x77122,x77123,x77124)+~P37(f35(x77126,x77121,x77125),x77122,x77123,x77124)
% 51.10/50.83 [7713]P37(x77131,x77132,x77133,x77134)+P37(x77135,x77132,x77133,x77134)+~P37(f35(x77136,x77131,x77135),x77132,x77133,x77134)
% 51.10/50.83 [6686]~E(f331(x66864,x66865),f187(x66862))+E(f331(f175(x66861,x66862,x66863,x66864),x66865),f331(f234(x66862),x66866))+~E(f331(x66863,x66865),f331(f234(x66862),x66866))
% 51.10/50.83 [6792]~E(f331(x67923,x67926),f187(x67921))+E(f331(f236(f851(x67921),x67922,f187(x67921),x67923),f331(x67924,x67925)),f187(x67921))+~E(f331(x67924,x67925),f331(f234(x67922),x67926))
% 51.10/50.83 [7394]E(f331(x73941,x73942),f187(x73943))+~E(f331(f175(x73945,x73943,x73946,x73941),x73942),f331(f234(x73943),x73944))+E(f331(x73941,x73942),f331(f234(x73943),x73944))
% 51.10/50.83 [7395]E(f331(x73951,x73952),f187(x73953))+~E(f331(f175(x73955,x73953,x73956,x73951),x73952),f331(f234(x73953),x73954))+E(f331(x73951,x73952),f331(f234(x73953),x73954))
% 51.10/50.83 [7432]~E(f331(f175(x74326,x74323,x74325,x74321),x74322),f331(f234(x74323),x74324))+E(f331(x74321,x74322),f331(f234(x74323),x74324))+E(f331(x74325,x74322),f331(f234(x74323),x74324))
% 51.10/50.83 [7433]~E(f331(f175(x74336,x74333,x74335,x74331),x74332),f331(f234(x74333),x74334))+E(f331(x74331,x74332),f331(f234(x74333),x74334))+E(f331(x74335,x74332),f331(f234(x74333),x74334))
% 51.10/50.83 [8326]~P21(x83266,x83261,x83262,x83264)+E(f331(f80(x83261,x83261,x83261,f331(x83262,x83263)),f331(x83264,x83265)),f331(f80(x83261,x83261,x83261,f331(x83264,x83265)),f331(x83262,x83263)))+~P1(f331(f68(x83266),x83265))
% 51.10/50.83 [8720]~P27(x87201,x87203,x87205,x87206)+~P27(x87203,x87202,x87204,f331(f311(x87201,x87203,x87205),x87206))+P27(x87201,x87202,f331(f80(x87203,x87202,x87201,x87204),x87205),x87206)
% 51.10/50.83 [8721]~P27(x87211,x87213,x87215,x87216)+~P27(x87213,x87212,x87214,f331(f311(x87211,x87213,x87215),x87216))+P27(x87211,x87212,f331(f80(x87213,x87212,x87211,x87214),x87215),x87216)
% 51.10/50.83 [8878]~P27(x88784,x88781,x88785,x88786)+~P27(x88784,x88782,f331(f80(x88781,x88782,x88784,x88783),x88785),x88786)+P27(x88781,x88782,x88783,f331(f311(x88784,x88781,x88785),x88786))
% 51.10/50.83 [9220]~P1(f331(f331(x92203,x92202),x92206))+~P1(f331(f331(x92204,x92205),x92202))+P1(f331(f331(f333(x92201),x92202),f300(x92201,x92203,x92204,x92205,x92206)))
% 51.10/50.83 [9221]~P1(f331(f331(x92214,x92212),x92216))+~P1(f331(f331(x92213,x92215),x92212))+P1(f331(f331(f333(x92211),x92212),f297(x92211,x92213,x92214,x92215,x92216)))
% 51.10/50.83 [9331]E(x93311,x93312)+E(x93313,x93314)+~P1(f331(f331(f333(f853(f848(x93315),f848(x93315))),f331(f331(f249(f848(x93315),f848(x93315)),f331(f331(f145(x93315),x93313),x93311)),f331(f331(f145(x93315),x93314),x93312))),f150(x93315,x93316)))
% 51.10/50.83 [9340]~E(x93402,x93404)+P1(f331(f331(f333(f853(f848(x93401),f848(x93401))),f331(f331(f249(f848(x93401),f848(x93401)),f331(f331(f145(x93401),x93402),x93403)),f331(f331(f145(x93401),x93404),x93405))),f140(x93401,x93406)))+~P1(f331(f331(f333(f853(f848(x93401),f848(x93401))),f331(f331(f249(f848(x93401),f848(x93401)),x93403),x93405)),f140(x93401,x93406)))
% 51.10/50.83 [9341]~E(x93412,x93414)+P1(f331(f331(f333(f853(f848(x93411),f848(x93411))),f331(f331(f249(f848(x93411),f848(x93411)),f331(f331(f145(x93411),x93412),x93413)),f331(f331(f145(x93411),x93414),x93415))),f142(x93411,x93416)))+~P1(f331(f331(f333(f853(f848(x93411),f848(x93411))),f331(f331(f249(f848(x93411),f848(x93411)),x93413),x93415)),f142(x93411,x93416)))
% 51.10/50.83 [9342]~E(x93422,x93424)+P1(f331(f331(f333(f853(f848(x93421),f848(x93421))),f331(f331(f249(f848(x93421),f848(x93421)),f331(f331(f145(x93421),x93422),x93423)),f331(f331(f145(x93421),x93424),x93425))),f150(x93421,x93426)))+~P1(f331(f331(f333(f853(f848(x93421),f848(x93421))),f331(f331(f249(f848(x93421),f848(x93421)),x93423),x93425)),f150(x93421,x93426)))
% 51.10/50.83 [9343]~E(x93432,x93434)+P1(f331(f331(f333(f853(f848(x93431),f848(x93431))),f331(f331(f249(f848(x93431),f848(x93431)),f331(f331(f130(x93431),x93432),x93433)),f331(f331(f130(x93431),x93434),x93435))),f150(x93431,x93436)))+~P1(f331(f331(f333(f853(f848(x93431),f848(x93431))),f331(f331(f249(f848(x93431),f848(x93431)),x93433),x93435)),f150(x93431,x93436)))
% 51.10/50.83 [9344]~E(x93443,x93445)+P1(f331(f331(f333(f853(f848(x93441),f848(x93441))),f331(f331(f249(f848(x93441),f848(x93441)),f331(f331(f130(x93441),x93442),x93443)),f331(f331(f130(x93441),x93444),x93445))),f150(x93441,x93446)))+~P1(f331(f331(f333(f853(f848(x93441),f848(x93441))),f331(f331(f249(f848(x93441),f848(x93441)),x93442),x93444)),f150(x93441,x93446)))
% 51.10/50.83 [9399]E(x93991,x93992)+P1(f331(f331(f333(f853(f848(x93993),f848(x93993))),f331(f331(f249(f848(x93993),f848(x93993)),x93991),x93992)),f150(x93993,x93994)))+~P1(f331(f331(f333(f853(f848(x93993),f848(x93993))),f331(f331(f249(f848(x93993),f848(x93993)),f331(f331(f145(x93993),x93995),x93991)),f331(f331(f145(x93993),x93996),x93992))),f150(x93993,x93994)))
% 51.10/50.83 [9545]~E(x95453,x95455)+P1(f331(f331(f333(f853(f848(x95451),f848(x95451))),f331(f331(f249(f848(x95451),f848(x95451)),f331(f331(f130(x95451),x95452),f331(f331(f145(x95451),x95453),f120(x95451)))),f331(f331(f130(x95451),x95454),f331(f331(f145(x95451),x95455),f120(x95451))))),f150(x95451,x95456)))+~P1(f331(f331(f333(f853(f848(x95451),f848(x95451))),f331(f331(f249(f848(x95451),f848(x95451)),x95452),x95454)),f150(x95451,x95456)))
% 51.10/50.83 [9557]E(f331(x95571,x95572),f187(x95573))+~E(f331(f236(f851(x95576),x95573,f187(x95576),x95574),f331(x95571,x95572)),f187(x95576))+E(f331(x95574,f707(x95572,x95571,x95574,x95575,x95576,x95573)),f187(x95576))
% 51.10/50.83 [9558]E(f331(x95581,x95582),f187(x95583))+~E(f331(f236(f851(x95586),x95583,f187(x95586),x95584),f331(x95581,x95582)),f187(x95586))+E(f331(f234(x95583),f707(x95582,x95581,x95584,x95585,x95586,x95583)),f331(x95581,x95582))
% 51.10/50.83 [9594]E(x95941,x95942)+E(x95943,x95944)+~P1(f331(f331(f333(f853(f848(x95945),f848(x95945))),f331(f331(f249(f848(x95945),f848(x95945)),f331(f331(f130(x95945),x95943),f331(f331(f145(x95945),x95941),f120(x95945)))),f331(f331(f130(x95945),x95944),f331(f331(f145(x95945),x95942),f120(x95945))))),f150(x95945,x95946)))
% 51.10/50.83 [9616]E(x96161,x96162)+~P1(f331(f331(f333(f853(f848(x96163),f848(x96163))),f331(f331(f249(f848(x96163),f848(x96163)),f331(f331(f130(x96163),x96161),f331(f331(f145(x96163),x96165),f120(x96163)))),f331(f331(f130(x96163),x96162),f331(f331(f145(x96163),x96166),f120(x96163))))),f150(x96163,x96164)))+P1(f331(f331(f333(f853(f848(x96163),f848(x96163))),f331(f331(f249(f848(x96163),f848(x96163)),x96161),x96162)),f150(x96163,x96164)))
% 51.10/50.83 [9645]~P1(f331(f331(f333(f853(f854(x96451,a840),f854(x96451,a840))),f331(f331(f249(f854(x96451,a840),f854(x96451,a840)),x96452),x96454)),f323(x96451,x96456)))+~P1(f331(f331(f333(f853(f854(x96451,a840),f854(x96451,a840))),f331(f331(f249(f854(x96451,a840),f854(x96451,a840)),x96453),x96455)),f323(x96451,x96456)))+P1(f331(f331(f333(f853(f854(x96451,a840),f854(x96451,a840))),f331(f331(f249(f854(x96451,a840),f854(x96451,a840)),f331(f331(f108(f854(x96451,a840)),x96452),x96453)),f331(f331(f108(f854(x96451,a840)),x96454),x96455))),f323(x96451,x96456)))
% 51.10/50.83 [5104]~E(f331(x51043,x51046),x51045)+~E(x51044,f331(f234(x51041),x51046))+E(f331(f331(f203(x51041,x51042),x51043),x51044),f331(f234(x51042),x51045))
% 51.10/50.83 [5505]~E(f331(f331(f130(x55051),x55056),x55053),x55055)+E(f331(f331(f130(x55051),x55052),x55053),f331(f331(f145(x55051),x55054),x55055))+~E(x55052,f331(f331(f145(x55051),x55054),x55056))
% 51.10/50.83 [5506]~E(f331(f331(f130(x55061),x55066),x55063),x55065)+E(f331(f331(f130(x55061),x55062),x55063),f331(f331(f130(x55061),x55064),x55065))+~E(x55062,f331(f331(f130(x55061),x55064),x55066))
% 51.10/50.83 [5507]E(f331(f331(f130(x55071),x55072),x55073),f331(f331(f145(x55071),x55074),x55075))+~E(f331(f331(f145(x55071),x55074),x55076),x55072)+~E(x55075,f331(f331(f130(x55071),x55076),x55073))
% 51.10/50.83 [5508]E(f331(f331(f130(x55081),x55082),x55083),f331(f331(f145(x55081),x55084),x55085))+~E(f331(f331(f145(x55081),x55084),x55086),x55082)+~E(x55085,f331(f331(f130(x55081),x55086),x55083))
% 51.10/50.83 [5509]~E(f331(f331(f130(x55091),x55092),x55096),x55094)+E(f331(f331(f130(x55091),x55092),x55093),f331(f331(f130(x55091),x55094),x55095))+~E(x55093,f331(f331(f130(x55091),x55096),x55095))
% 51.10/50.83 [5510]~E(f331(f331(f130(x55101),x55102),x55106),x55104)+E(f331(f331(f130(x55101),x55102),x55103),f331(f331(f130(x55101),x55104),x55105))+~E(x55103,f331(f331(f130(x55101),x55106),x55105))
% 51.10/50.83 [6679]E(f331(x66791,x66792),f331(x66793,x66792))+~E(f331(f331(f147(x66794,x66795),x66791),x66796),f331(f331(f147(x66794,x66795),x66793),x66796))+~P1(f331(f331(f333(x66794),x66792),f331(f163(x66794),x66796)))
% 51.10/50.83 [7071]~P21(x70714,x70715,x70716,x70711)+E(f331(f331(x70711,x70712),x70713),f331(f331(f71(x70714,x70715,x70716),x70713),x70712))+~P1(f331(f68(x70714),x70712))
% 51.10/50.83 [7138]~E(x71382,f331(x71384,x71386))+~P1(f331(f331(f333(x71383),x71386),x71385))+P1(f331(f331(f333(x71381),x71382),f331(f311(x71383,x71381,x71384),x71385)))
% 51.10/50.83 [7139]~E(x71392,f331(x71394,x71396))+~P1(f331(f331(f333(x71393),x71396),x71395))+P1(f331(f331(f333(x71391),x71392),f331(f311(x71393,x71391,x71394),x71395)))
% 51.10/50.83 [7140]~E(x71402,f331(x71404,x71406))+~P1(f331(f331(f333(x71403),x71406),x71405))+P1(f331(f331(f333(x71401),x71402),f331(f311(x71403,x71401,x71404),x71405)))
% 51.10/50.83 [7141]~E(f331(x71414,x71412),x71416)+~P1(f331(f331(f333(x71413),x71416),x71415))+P1(f331(f331(f333(x71411),x71412),f331(f312(x71411,x71413,x71414),x71415)))
% 51.10/50.83 [7615]~P32(x76151,x76152,x76154,x76156)+P32(x76151,x76152,f331(f331(f145(x76151),x76153),x76154),f331(f331(f145(x76151),x76155),x76156))+~P1(f331(f331(x76152,x76153),x76155))
% 51.10/50.83 [7616]~P32(x76161,x76162,x76164,x76166)+P32(x76161,x76162,f331(f331(f145(x76161),x76163),x76164),f331(f331(f145(x76161),x76165),x76166))+~P1(f331(f331(x76162,x76163),x76165))
% 51.10/50.83 [8604]~P53(x86044,x86045,x86041,x86042,x86046)+E(f331(x86041,f331(x86042,x86043)),x86043)+~P1(f331(f331(f333(x86045),x86043),x86046))
% 51.10/50.83 [9333]E(x93331,x93332)+E(f331(f185(f848(x93333)),x93334),f331(f185(f848(x93333)),x93335))+~P1(f331(f331(f333(f853(f848(x93333),f848(x93333))),f331(f331(f249(f848(x93333),f848(x93333)),f331(f331(f145(x93333),x93331),x93334)),f331(f331(f145(x93333),x93332),x93335))),f140(x93333,x93336)))
% 51.10/50.83 [9394]~P18(x93941,x93942,x93943)+E(f331(f331(f71(x93941,x93942,x93943),x93944),x93945),x93946)+~P1(f331(f73(x93941,x93942,x93943,x93944,x93945),x93946))
% 51.10/50.83 [9402]E(f331(f185(f848(x94021)),x94022),f331(f185(f848(x94021)),x94023))+P1(f331(f331(f333(f853(f848(x94021),f848(x94021))),f331(f331(f249(f848(x94021),f848(x94021)),x94022),x94023)),f140(x94021,x94024)))+~P1(f331(f331(f333(f853(f848(x94021),f848(x94021))),f331(f331(f249(f848(x94021),f848(x94021)),f331(f331(f145(x94021),x94025),x94022)),f331(f331(f145(x94021),x94026),x94023))),f140(x94021,x94024)))
% 51.10/50.83 [9424]~P1(f331(f331(f333(f853(x94241,x94241)),f331(f331(f249(x94241,x94241),x94242),x94244)),f308(x94241,x94246)))+P1(f331(f331(f333(f853(f848(x94241),f848(x94241))),f331(f331(f249(f848(x94241),f848(x94241)),f331(f331(f145(x94241),x94242),x94243)),f331(f331(f145(x94241),x94244),x94245))),f308(f848(x94241),f150(x94241,x94246))))+~P1(f331(f331(f333(f853(f848(x94241),f848(x94241))),f331(f331(f249(f848(x94241),f848(x94241)),x94243),x94245)),f308(f848(x94241),f150(x94241,x94246))))
% 51.10/50.83 [9911]~P68(x99112)+E(f331(f331(f8(x99111,x99112),f331(f331(f10(f854(x99113,a840),x99112,x99111),f331(f8(x99113,x99112),x99114)),f331(f331(f10(f854(x99113,a840),f854(x99113,a840),x99111),f264(x99113)),f331(f331(f10(f854(x99113,a840),f854(x99113,a840),x99111),f331(f20(x99113,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99113),a329),f331(f331(f9(x99113,f854(x99113,a840),a840),f333(x99113)),x99115)))),f331(f9(x99113,x99111,a840),f331(f331(f10(x99111,f854(x99111,a840),x99113),a328),x99116)))))),f331(f311(x99113,x99111,x99116),x99115)),f331(f331(f8(x99113,x99112),x99114),x99115))+~P1(f331(f68(x99113),x99115))
% 51.10/50.83 [6739]~P102(x67393)+P1(f331(x67392,x67395))+E(f331(f131(x67391,x67392),f331(f331(f143(x67391,x67393,x67394),x67395),x67396)),f331(f131(x67391,x67392),x67396))
% 51.10/50.83 [6741]P1(f331(x67411,x67412))+~E(f158(x67413,x67411,x67414),f331(f331(f249(f848(x67413),f848(x67413)),x67415),x67416))+~P1(f331(f331(f333(x67413),x67412),f331(f163(x67413),x67415)))
% 51.10/50.83 [6789]~P1(f331(x67892,x67896))+~E(f158(x67891,x67892,x67893),f331(f331(f249(f848(x67891),f848(x67891)),x67894),x67895))+~P1(f331(f331(f333(x67891),x67896),f331(f163(x67891),x67895)))
% 51.10/50.83 [7479]~P17(x74791,x74792,x74793)+~P1(f331(f68(x74791),x74796))+E(f331(f331(f71(x74791,x74792,x74793),x74794),f331(f331(f310(x74791),x74795),x74796)),f331(f331(f71(x74791,x74792,x74793),f331(f331(x74793,x74795),x74794)),x74796))
% 51.10/50.83 [7531]~P102(x75312)+~P1(f331(f331(f240(x75312),f331(x75313,x75314)),f331(x75313,x75315)))+E(f331(f331(f143(x75311,x75312,x75313),x75314),f331(f331(f145(x75311),x75315),x75316)),f331(f331(f145(x75311),x75314),f331(f331(f145(x75311),x75315),x75316)))
% 51.10/50.83 [7647]E(x76471,x76472)+~E(f331(f331(f256(x76473,x76474),x76471),f331(f18(f854(x76474,a840),x76473),x76475)),f331(f331(f256(x76473,x76474),x76472),f331(f18(f854(x76474,a840),x76473),x76475)))+~P1(f331(f331(f333(x76474),x76476),x76475))
% 51.10/50.83 [7715]~P17(x77151,x77152,x77153)+~P1(f331(f68(x77151),x77156))+E(f331(f331(f71(x77151,x77152,x77153),x77154),f331(f331(f310(x77151),x77155),x77156)),f331(f331(x77153,x77155),f331(f331(f71(x77151,x77152,x77153),x77154),x77156)))
% 51.10/50.83 [7831]~P18(x78311,x78312,x78313)+~P1(f331(f68(x78311),x78316))+E(f331(f331(f71(x78311,x78312,x78313),f331(f331(x78313,x78314),x78315)),x78316),f331(f331(x78313,x78314),f331(f331(f71(x78311,x78312,x78313),x78315),x78316)))
% 51.10/50.83 [7899]~P22(x78992,x78995,x78996,x78991)+~P1(f331(f68(x78992),x78994))+E(f331(x78991,f331(f331(f310(x78992),x78993),x78994)),f331(f80(x78995,x78995,x78995,f331(x78991,x78994)),f331(x78996,x78993)))
% 51.10/50.83 [7937]~P102(x79372)+P1(f331(f331(f240(x79372),f331(x79373,x79374)),f331(x79373,x79375)))+E(f331(f331(f143(x79371,x79372,x79373),x79374),f331(f331(f145(x79371),x79375),x79376)),f331(f331(f145(x79371),x79375),f331(f331(f143(x79371,x79372,x79373),x79374),x79376)))
% 51.10/50.83 [8070]~E(f331(f185(f848(x80701)),x80705),f331(f185(f848(x80702)),x80706))+~E(f331(f185(f848(x80701)),x80703),f331(f185(f848(x80702)),x80704))+E(f331(f331(f130(f853(x80701,x80702)),f331(f331(f172(x80701,x80702),x80703),x80704)),f331(f331(f172(x80701,x80702),x80705),x80706)),f331(f331(f172(x80701,x80702),f331(f331(f130(x80701),x80703),x80705)),f331(f331(f130(x80702),x80704),x80706)))
% 51.10/50.83 [8180]~E(x81802,f331(f311(x81803,x81801,x81804),x81806))+P1(f331(f331(f240(f854(x81801,a840)),x81802),f331(f311(x81803,x81801,x81804),x81805)))+~P1(f331(f331(f240(f854(x81803,a840)),x81806),x81805))
% 51.10/50.83 [8283]~P102(x82835)+E(f331(x82831,x82832),f331(x82831,x82833))+E(f331(f331(f143(x82834,x82835,x82831),x82832),f331(f331(f143(x82834,x82835,x82831),x82833),x82836)),f331(f331(f143(x82834,x82835,x82831),x82833),f331(f331(f143(x82834,x82835,x82831),x82832),x82836)))
% 51.10/50.83 [8319]~P27(x83193,x83191,x83194,x83195)+P27(x83193,x83191,f331(f331(f331(f79(x83193,x83191),x83194),x83196),x83192),x83195)+P1(f331(f331(f333(x83191),x83192),f331(f311(x83193,x83191,x83194),x83195)))
% 51.10/50.83 [8462]~P1(f331(f331(f333(x84622),x84624),f331(x84626,x84623)))+~P1(f331(f331(f333(x84621),x84623),x84625))+P1(f331(f331(f333(f853(x84621,x84622)),f331(f331(f249(x84621,x84622),x84623),x84624)),f331(f331(f256(x84621,x84622),x84625),x84626)))
% 51.10/50.83 [8463]~P1(f331(f331(f333(x84632),x84634),f331(x84636,x84633)))+~P1(f331(f331(f333(x84631),x84633),x84635))+P1(f331(f331(f333(f853(x84631,x84632)),f331(f331(f249(x84631,x84632),x84633),x84634)),f331(f331(f256(x84631,x84632),x84635),x84636)))
% 51.10/50.83 [8871]~P70(x88712)+~P27(x88714,x88711,x88715,x88716)+E(f331(f331(f11(x88711,x88712),x88713),f331(f311(x88714,x88711,x88715),x88716)),f331(f331(f11(x88714,x88712),f331(f80(x88711,x88712,x88714,x88713),x88715)),x88716))
% 51.10/50.83 [8872]~P68(x88722)+~P27(x88724,x88721,x88725,x88726)+E(f331(f331(f8(x88721,x88722),x88723),f331(f311(x88724,x88721,x88725),x88726)),f331(f331(f8(x88724,x88722),f331(f80(x88721,x88722,x88724,x88723),x88725)),x88726))
% 51.10/50.83 [9104]~E(f331(f331(f331(a193,x91045),f40(x91041)),f331(f331(a196,x91044),x91041)),f331(f331(f331(a193,x91046),f40(x91041)),f331(f331(a196,x91044),x91041)))+~P1(f331(f331(f191(x91043),f331(f331(f331(a193,x91044),f40(x91041)),f331(x91042,x91044))),x91046))+P1(f331(f331(f191(f34(x91041,x91042,x91043)),x91044),f331(f331(f331(a193,x91045),f40(x91041)),f331(f331(a196,x91044),x91041))))
% 51.10/50.83 [9108]~P21(x91083,x91081,x91086,x91082)+~P1(f331(f68(x91083),x91084))+E(f331(f80(x91081,x91081,x91081,f331(x91082,f331(f331(f3(f854(x91083,a840)),x91084),f331(f331(f310(x91083),x91085),f184(f854(x91083,a840)))))),f331(x91086,x91085)),f331(x91082,f331(f331(f310(x91083),x91085),x91084)))
% 51.10/50.83 [9500]~E(f331(f331(f331(a193,f331(f331(a194,x95005),f331(a196,x95004))),x95001),f331(f331(a196,x95005),a28)),f331(f331(f331(a193,f331(f331(a194,x95006),f331(a196,x95004))),x95001),f331(f331(a196,x95006),a28)))+~P1(f331(f331(f191(f331(a29,x95002)),f331(f331(f331(a193,f331(f331(a194,x95004),a195)),f40(a27)),f331(x95003,x95004))),x95006))+P1(f331(f331(f191(f33(x95001,x95002,x95003)),x95004),f331(f331(f331(a193,f331(f331(a194,x95005),f331(a196,x95004))),x95001),f331(f331(a196,x95005),a28))))
% 51.10/50.83 [9674]~E(f331(f311(x96742,x96744,x96746),f247(f854(x96742,a840))),f247(f854(x96744,a840)))+~E(f331(f311(x96741,x96743,x96745),f247(f854(x96741,a840))),f247(f854(x96743,a840)))+E(f331(f311(f853(x96741,x96742),f853(x96743,x96744),f260(x96741,x96743,x96742,x96744,x96745,x96746)),f247(f854(f853(x96741,x96742),a840))),f247(f854(f853(x96743,x96744),a840)))
% 51.10/50.83 [9737]~P27(x97373,x97374,x97375,f331(x97376,f674(x97376,x97375,x97374,x97373,x97372,x97371)))+P27(x97373,x97374,x97375,f331(f331(f52(x97372,f854(x97373,a840)),x97371),x97376))+E(x97371,f184(f854(x97372,a840)))
% 51.10/50.83 [9795]P27(x97956,x97955,x97954,f331(f331(f52(x97952,f854(x97956,a840)),x97951),x97953))+E(x97951,f184(f854(x97952,a840)))+P1(f331(f331(f333(x97952),f674(x97953,x97954,x97955,x97956,x97952,x97951)),x97951))
% 51.10/50.83 [9803]P1(f331(f331(f333(x98031),f619(x98032,x98033,x98034,x98035,x98036,x98031)),x98036))+P1(f331(f331(f240(f854(f853(x98031,x98034),a840)),f331(f331(f256(x98031,x98034),x98036),x98033)),f331(f331(f256(x98031,x98034),x98035),x98032)))+~P1(f331(f331(f240(f854(x98031,a840)),x98036),x98035))
% 51.10/50.83 [9848]P26(x98486,x98485,f331(f331(f310(f846(x98486)),f331(f331(f331(f98(x98486),x98481),x98483),x98482)),f184(f854(f846(x98486),a840))))+~P26(x98486,x98485,f331(f331(f310(f846(x98486)),f331(f331(f331(f98(x98486),x98484),x98483),x98482)),f184(f854(f846(x98486),a840))))+P1(f331(f331(x98481,f834(x98481,x98482,x98483,x98484,x98485,x98486)),f835(x98481,x98482,x98483,x98484,x98485,x98486)))
% 51.10/50.83 [9849]P26(x98496,x98495,f331(f331(f310(f846(x98496)),f331(f331(f331(f98(x98496),x98494),x98493),x98492)),f184(f854(f846(x98496),a840))))+~P26(x98496,x98495,f331(f331(f310(f846(x98496)),f331(f331(f331(f98(x98496),x98494),x98493),x98491)),f184(f854(f846(x98496),a840))))+P1(f331(f331(x98491,f836(x98492,x98491,x98493,x98494,x98495,x98496)),f837(x98492,x98491,x98493,x98494,x98495,x98496)))
% 51.10/50.83 [9886]~P26(x98861,x98862,f331(f331(f310(f846(x98861)),f331(f331(f331(f98(x98861),x98863),x98864),x98866)),f184(f854(f846(x98861),a840))))+P26(x98861,x98862,f331(f331(f310(f846(x98861)),f331(f331(f331(f98(x98861),x98863),x98864),x98865)),f184(f854(f846(x98861),a840))))+~P1(f331(f331(x98865,f836(x98865,x98866,x98864,x98863,x98862,x98861)),f837(x98865,x98866,x98864,x98863,x98862,x98861)))
% 51.10/50.83 [9887]~P26(x98871,x98872,f331(f331(f310(f846(x98871)),f331(f331(f331(f98(x98871),x98876),x98874),x98875)),f184(f854(f846(x98871),a840))))+P26(x98871,x98872,f331(f331(f310(f846(x98871)),f331(f331(f331(f98(x98871),x98873),x98874),x98875)),f184(f854(f846(x98871),a840))))+~P1(f331(f331(x98876,f834(x98873,x98875,x98874,x98876,x98872,x98871)),f835(x98873,x98875,x98874,x98876,x98872,x98871)))
% 51.10/50.83 [9928]~P1(f331(f331(f240(f854(x99282,a840)),f331(x99284,f619(x99286,x99284,x99282,x99285,x99283,x99281))),f331(x99286,f619(x99286,x99284,x99282,x99285,x99283,x99281))))+~P1(f331(f331(f240(f854(x99281,a840)),x99283),x99285))+P1(f331(f331(f240(f854(f853(x99281,x99282),a840)),f331(f331(f256(x99281,x99282),x99283),x99284)),f331(f331(f256(x99281,x99282),x99285),x99286)))
% 51.10/50.83 [7664]~P1(f331(x76641,x76645))+~P1(f331(x76646,x76644))+P1(f331(x76641,f331(f258(x76642,x76643),f331(f331(f249(x76642,x76643),x76644),x76645))))
% 51.10/50.83 [7665]~P1(f331(x76651,x76654))+~P1(f331(x76656,x76655))+P1(f331(x76651,f331(f248(x76652,x76653),f331(f331(f249(x76652,x76653),x76654),x76655))))
% 51.10/50.83 [7719]~P1(f331(f331(x77194,x77196),x77195))+~P1(f331(f331(f333(x77191),x77196),x77193))+P1(f331(f331(f331(f51(x77191,f854(x77192,a840)),x77193),x77194),x77195))
% 51.10/50.83 [7720]~P1(f331(f331(x77204,x77206),x77205))+~P1(f331(f331(f333(x77201),x77206),x77203))+P1(f331(f331(f331(f51(x77201,f854(x77202,a840)),x77203),x77204),x77205))
% 51.10/50.83 [7753]~E(f331(f185(f848(x77531)),x77533),f331(f185(f848(x77534)),x77535))+~E(f331(f171(x77531,x77534,f331(f331(f172(x77531,x77534),x77533),x77535)),x77532),f331(f234(x77534),x77536))+P1(f331(f331(f333(x77531),x77532),f331(f163(x77531),x77533)))
% 51.10/50.83 [8022]~P1(f331(f331(f333(x80221),x80222),f331(x80225,x80226)))+~P1(f331(f331(f333(x80223),x80226),x80224))+P1(f331(f331(f333(x80221),x80222),f331(f331(f51(x80223,f854(x80221,a840)),x80224),x80225)))
% 51.10/50.83 [8023]~P1(f331(f331(f333(x80231),x80232),f331(x80235,x80236)))+~P1(f331(f331(f333(x80233),x80236),x80234))+P1(f331(f331(f333(x80231),x80232),f331(f331(f51(x80233,f854(x80231,a840)),x80234),x80235)))
% 51.10/50.83 [8062]P1(f331(f331(x80621,x80622),x80623))+~P1(f331(f331(x80624,x80622),x80623))+~P1(f331(f331(f240(f854(x80625,f854(x80626,a840))),x80624),x80621))
% 51.10/50.83 [8063]P1(f331(f331(x80631,x80632),x80633))+~P1(f331(f331(x80634,x80632),x80633))+~P1(f331(f331(f240(f854(x80635,f854(x80636,a840))),x80634),x80631))
% 51.10/50.83 [8202]P1(f331(f331(x82021,x82022),x82023))+~P1(f331(f331(f333(x82024),x82022),x82025))+~P1(f331(f331(f331(f52(x82024,f854(x82026,a840)),x82025),x82021),x82023))
% 51.10/50.83 [8203]P1(f331(f331(x82031,x82032),x82033))+~P1(f331(f331(f333(x82034),x82032),x82035))+~P1(f331(f331(f331(f52(x82034,f854(x82036,a840)),x82035),x82031),x82033))
% 51.10/50.83 [8204]P1(f331(f331(x82041,x82042),x82043))+~P1(f331(f331(f333(x82044),x82042),x82045))+~P1(f331(f331(f331(f52(x82044,f854(x82046,a840)),x82045),x82041),x82043))
% 51.10/50.83 [8339]P1(f331(f331(f333(x83391),x83392),f331(x83393,x83394)))+~P1(f331(f331(f333(x83395),x83394),x83396))+~P1(f331(f331(f333(x83391),x83392),f331(f331(f52(x83395,f854(x83391,a840)),x83396),x83393)))
% 51.10/50.83 [8340]P1(f331(f331(f333(x83401),x83402),f331(x83403,x83404)))+~P1(f331(f331(f333(x83405),x83404),x83406))+~P1(f331(f331(f333(x83401),x83402),f331(f331(f52(x83405,f854(x83401,a840)),x83406),x83403)))
% 51.10/50.83 [8341]P1(f331(f331(f333(x83411),x83412),f331(x83413,x83414)))+~P1(f331(f331(f333(x83415),x83414),x83416))+~P1(f331(f331(f333(x83411),x83412),f331(f331(f52(x83415,f854(x83411,a840)),x83416),x83413)))
% 51.10/50.83 [8586]~P14(x85864,x85865,x85866,x85861)+E(f331(x85861,x85862),f331(x85861,x85863))+~P1(f331(f331(f333(f853(x85864,x85864)),f331(f331(f249(x85864,x85864),x85862),x85863)),x85866))
% 51.10/50.83 [8617]P1(f331(f331(f240(f854(x86171,a840)),x86172),f331(x86173,x86174)))+~P1(f331(f331(f333(x86175),x86174),x86176))+~P1(f331(f331(f240(f854(x86171,a840)),x86172),f331(f331(f52(x86175,f854(x86171,a840)),x86176),x86173)))
% 51.10/50.83 [8642]~P51(x86423,x86424,f331(f286(x86424,x86423),x86425))+E(x86421,f184(f854(x86422,a840)))+E(f331(f331(f52(x86422,f854(x86423,a840)),x86421),f331(f331(f10(f854(x86424,a840),f854(x86423,a840),x86422),f285(x86424,x86423,x86425)),x86426)),f331(f285(x86424,x86423,x86425),f331(f331(f52(x86422,f854(x86424,a840)),x86421),x86426)))
% 51.10/50.83 [8713]P1(f331(f331(f333(x87131),x87132),f331(f285(x87133,x87131,x87134),x87135)))+~P1(f331(f331(f333(x87133),x87136),x87135))+~P1(f331(f331(f333(f853(x87133,x87131)),f331(f331(f249(x87133,x87131),x87136),x87132)),x87134))
% 51.10/50.83 [8714]P1(f331(f331(f333(x87141),x87142),f331(f285(x87143,x87141,x87144),x87145)))+~P1(f331(f331(f333(x87143),x87146),x87145))+~P1(f331(f331(f333(f853(x87143,x87141)),f331(f331(f249(x87143,x87141),x87146),x87142)),x87144))
% 51.10/50.83 [8986]P1(f331(f331(f240(f854(x89861,a840)),f331(f285(x89862,x89861,x89863),x89864)),f331(f285(x89862,x89861,x89865),x89866)))+~P1(f331(f331(f240(f854(x89862,a840)),x89864),x89866))+~P1(f331(f331(f240(f854(f853(x89862,x89861),a840)),x89863),x89865))
% 51.10/50.83 [9142]~P1(f331(f331(f333(x91422),x91426),x91424))+~P1(f331(f331(f240(f854(x91421,a840)),x91423),x91425))+P1(f331(f331(f240(f854(f853(x91421,x91422),a840)),f331(f331(f256(x91421,x91422),x91423),f331(f18(f854(x91422,a840),x91421),x91424))),f331(f331(f256(x91421,x91422),x91425),f331(f18(f854(x91422,a840),x91421),x91424))))
% 51.10/50.83 [9291]~E(x92913,x92915)+P1(f331(f331(f333(f853(f848(x92911),f848(x92911))),f331(f331(f249(f848(x92911),f848(x92911)),f331(f331(f145(x92911),x92912),x92913)),f331(f331(f145(x92911),x92914),x92915))),f150(x92911,x92916)))+~P1(f331(f331(f333(f853(x92911,x92911)),f331(f331(f249(x92911,x92911),x92912),x92914)),x92916))
% 51.10/50.83 [9297]~E(f331(f185(f848(x92971)),x92973),f331(f185(f848(x92971)),x92975))+P1(f331(f331(f333(f853(f848(x92971),f848(x92971))),f331(f331(f249(f848(x92971),f848(x92971)),f331(f331(f145(x92971),x92972),x92973)),f331(f331(f145(x92971),x92974),x92975))),f140(x92971,x92976)))+~P1(f331(f331(f333(f853(x92971,x92971)),f331(f331(f249(x92971,x92971),x92972),x92974)),x92976))
% 51.10/50.83 [9325]P1(f331(f331(f333(f853(x93251,x93251)),f331(f331(f249(x93251,x93251),x93252),x93253)),f331(f331(f178(f853(x93251,x93251),a840),f331(a119,x93254)),x93255)))+~P1(f331(f331(f333(f853(x93251,x93251)),f331(f331(f249(x93251,x93251),x93256),x93253)),x93255))+~P1(f331(f331(f333(f853(x93251,x93251)),f331(f331(f249(x93251,x93251),x93252),x93256)),f331(f331(f178(f853(x93251,x93251),a840),x93254),x93255)))
% 51.10/50.83 [9326]P1(f331(f331(f333(f853(x93261,x93261)),f331(f331(f249(x93261,x93261),x93262),x93263)),f331(f331(f178(f853(x93261,x93261),a840),f331(a119,x93264)),x93265)))+~P1(f331(f331(f333(f853(x93261,x93261)),f331(f331(f249(x93261,x93261),x93262),x93266)),x93265))+~P1(f331(f331(f333(f853(x93261,x93261)),f331(f331(f249(x93261,x93261),x93266),x93263)),f331(f331(f178(f853(x93261,x93261),a840),x93264),x93265)))
% 51.10/50.83 [9329]~P1(f331(f331(f333(x93294),x93295),x93296))+P1(f331(f331(f240(f854(x93291,a840)),x93292),x93293))+~P1(f331(f331(f240(f854(f853(x93291,x93294),a840)),f331(f331(f256(x93291,x93294),x93292),f331(f18(f854(x93294,a840),x93291),x93296))),f331(f331(f256(x93291,x93294),x93293),f331(f18(f854(x93294,a840),x93291),x93296))))
% 51.10/50.83 [9370]E(x93701,x93702)+~P1(f331(f331(f333(f853(f848(x93703),f848(x93703))),f331(f331(f249(f848(x93703),f848(x93703)),f331(f331(f145(x93703),x93701),x93705)),f331(f331(f145(x93703),x93702),x93706))),f140(x93703,x93704)))+P1(f331(f331(f333(f853(x93703,x93703)),f331(f331(f249(x93703,x93703),x93701),x93702)),x93704))
% 51.10/50.83 [9371]E(x93711,x93712)+~P1(f331(f331(f333(f853(f848(x93713),f848(x93713))),f331(f331(f249(f848(x93713),f848(x93713)),f331(f331(f145(x93713),x93711),x93715)),f331(f331(f145(x93713),x93712),x93716))),f142(x93713,x93714)))+P1(f331(f331(f333(f853(x93713,x93713)),f331(f331(f249(x93713,x93713),x93711),x93712)),x93714))
% 51.10/50.83 [9372]E(x93721,x93722)+~P1(f331(f331(f333(f853(f848(x93723),f848(x93723))),f331(f331(f249(f848(x93723),f848(x93723)),f331(f331(f145(x93723),x93721),x93725)),f331(f331(f145(x93723),x93722),x93726))),f150(x93723,x93724)))+P1(f331(f331(f333(f853(x93723,x93723)),f331(f331(f249(x93723,x93723),x93721),x93722)),x93724))
% 51.10/50.83 [9409]P1(f331(f331(f333(f853(f848(x94091),f848(x94091))),f331(f331(f249(f848(x94091),f848(x94091)),f331(f331(f145(x94091),x94092),x94093)),f331(f331(f145(x94091),x94094),x94095))),f151(x94091,x94096)))+~P1(f331(f331(f333(f853(f848(x94091),f848(x94091))),f331(f331(f249(f848(x94091),f848(x94091)),x94093),x94095)),f151(x94091,x94096)))+~P1(f331(f331(f333(f853(x94091,x94091)),f331(f331(f249(x94091,x94091),x94092),x94094)),x94096))
% 51.10/50.83 [9431]P1(f331(x94311,x94312))+~P1(f331(x94311,f408(x94311,x94313,x94314,x94315,x94316)))+~P1(f331(f331(f333(x94316),x94312),f331(f331(f51(x94315,f854(x94316,a840)),x94314),x94313)))
% 51.10/50.83 [9436]~P1(f331(f331(f333(f853(f848(x94361),f848(x94361))),f331(f331(f249(f848(x94361),f848(x94361)),f331(f331(f145(x94361),x94362),x94365)),f331(f331(f145(x94361),x94363),x94366))),f140(x94361,x94364)))+P1(f331(f331(f333(f853(f848(x94361),f848(x94361))),f331(f331(f249(f848(x94361),f848(x94361)),x94365),x94366)),f140(x94361,x94364)))+P1(f331(f331(f333(f853(x94361,x94361)),f331(f331(f249(x94361,x94361),x94362),x94363)),x94364))
% 51.10/50.83 [9437]~P1(f331(f331(f333(f853(f848(x94371),f848(x94371))),f331(f331(f249(f848(x94371),f848(x94371)),f331(f331(f145(x94371),x94372),x94375)),f331(f331(f145(x94371),x94373),x94376))),f142(x94371,x94374)))+P1(f331(f331(f333(f853(f848(x94371),f848(x94371))),f331(f331(f249(f848(x94371),f848(x94371)),x94375),x94376)),f142(x94371,x94374)))+P1(f331(f331(f333(f853(x94371,x94371)),f331(f331(f249(x94371,x94371),x94372),x94373)),x94374))
% 51.10/50.83 [9438]~P1(f331(f331(f333(f853(f848(x94381),f848(x94381))),f331(f331(f249(f848(x94381),f848(x94381)),f331(f331(f145(x94381),x94382),x94385)),f331(f331(f145(x94381),x94383),x94386))),f150(x94381,x94384)))+P1(f331(f331(f333(f853(f848(x94381),f848(x94381))),f331(f331(f249(f848(x94381),f848(x94381)),x94385),x94386)),f150(x94381,x94384)))+P1(f331(f331(f333(f853(x94381,x94381)),f331(f331(f249(x94381,x94381),x94382),x94383)),x94384))
% 51.10/50.83 [9516]P1(f331(x95161,x95162))+P1(f331(f331(f333(x95163),f409(x95161,x95164,x95165,x95163,x95166)),x95165))+~P1(f331(f331(f333(x95166),x95162),f331(f331(f51(x95163,f854(x95166,a840)),x95165),x95164)))
% 51.10/50.83 [9522]~E(x95222,x95224)+P1(f331(f331(f333(f853(f848(x95221),f848(x95221))),f331(f331(f249(f848(x95221),f848(x95221)),f331(f331(f130(x95221),x95222),f331(f331(f145(x95221),x95223),f120(x95221)))),f331(f331(f130(x95221),x95224),f331(f331(f145(x95221),x95225),f120(x95221))))),f150(x95221,x95226)))+~P1(f331(f331(f333(f853(x95221,x95221)),f331(f331(f249(x95221,x95221),x95223),x95225)),x95226))
% 51.10/50.83 [9608]E(x96081,x96082)+~P1(f331(f331(f333(f853(f848(x96083),f848(x96083))),f331(f331(f249(f848(x96083),f848(x96083)),f331(f331(f130(x96083),x96085),f331(f331(f145(x96083),x96081),f120(x96083)))),f331(f331(f130(x96083),x96086),f331(f331(f145(x96083),x96082),f120(x96083))))),f150(x96083,x96084)))+P1(f331(f331(f333(f853(x96083,x96083)),f331(f331(f249(x96083,x96083),x96081),x96082)),x96084))
% 51.10/50.83 [9633]~P1(f331(f331(f333(f853(f848(x96331),f848(x96331))),f331(f331(f249(f848(x96331),f848(x96331)),f331(f331(f130(x96331),x96335),f331(f331(f145(x96331),x96332),f120(x96331)))),f331(f331(f130(x96331),x96336),f331(f331(f145(x96331),x96333),f120(x96331))))),f150(x96331,x96334)))+P1(f331(f331(f333(f853(f848(x96331),f848(x96331))),f331(f331(f249(f848(x96331),f848(x96331)),x96335),x96336)),f150(x96331,x96334)))+P1(f331(f331(f333(f853(x96331,x96331)),f331(f331(f249(x96331,x96331),x96332),x96333)),x96334))
% 51.10/50.83 [9646]P1(f331(x96461,x96462))+P1(f331(f331(f333(x96463),f408(x96461,x96464,x96465,x96466,x96463)),f331(x96464,f409(x96461,x96464,x96465,x96466,x96463))))+~P1(f331(f331(f333(x96463),x96462),f331(f331(f51(x96466,f854(x96463,a840)),x96465),x96464)))
% 51.10/50.83 [8727]~P18(x87273,x87274,x87271)+~P1(f331(f68(x87273),x87276))+E(f331(f331(x87271,x87272),f331(f331(f71(x87273,x87274,x87271),x87275),f331(f331(f3(f854(x87273,a840)),x87276),f331(f331(f310(x87273),x87272),f184(f854(x87273,a840)))))),f331(f331(f71(x87273,x87274,x87271),x87275),f331(f331(f310(x87273),x87272),x87276)))
% 51.10/50.83 [8824]~E(f331(f171(x88241,x88242,x88244),x88245),f331(f234(x88242),x88246))+~P1(f331(f331(x88243,x88245),x88246))+E(f331(f171(x88241,x88242,f331(f131(f853(x88241,x88242),f331(f259(x88241,x88242,a840),x88243)),x88244)),x88245),f331(f234(x88242),x88246))
% 51.10/50.83 [8992]~P1(f331(f331(f333(x89925),x89923),x89926))+P1(f331(f331(f240(f854(x89921,a840)),f331(x89922,x89923)),x89924))+~P1(f331(f331(f240(f854(x89921,a840)),f331(f331(f51(x89925,f854(x89921,a840)),x89926),x89922)),x89924))
% 51.10/50.83 [9583]~P10(x95831,x95835,x95834)+P1(f331(f331(f333(f853(x95831,x95831)),f331(f331(f249(x95831,x95831),x95832),x95833)),x95834))+~P1(f331(f331(f333(x95831),x95836),f331(f331(f109(f854(x95831,a840)),f331(f285(x95831,x95831,x95834),f331(f331(f310(x95831),x95832),f184(f854(x95831,a840))))),f331(f285(x95831,x95831,x95834),f331(f331(f310(x95831),x95833),f184(f854(x95831,a840)))))))
% 51.10/50.83 [8496]~P121(x84962)+~E(f331(f331(f87(x84962),f331(f331(f88(x84962),x84964),x84965)),x84961),f331(f331(f87(x84962),f331(f331(f88(x84962),x84963),x84965)),x84966))+E(x84961,f331(f331(f87(x84962),f331(f331(f88(x84962),f331(f331(f3(x84962),x84963),x84964)),x84965)),x84966))
% 51.10/50.83 [8497]~P121(x84971)+~E(f331(f331(f87(x84971),f331(f331(f88(x84971),x84972),x84974)),x84975),f331(f331(f87(x84971),f331(f331(f88(x84971),x84973),x84974)),x84976))+E(f331(f331(f87(x84971),f331(f331(f88(x84971),f331(f331(f3(x84971),x84972),x84973)),x84974)),x84975),x84976)
% 51.10/50.83 [8645]~P121(x86451)+E(f331(f331(f87(x86451),f331(f331(f88(x86451),x86452),x86453)),x86454),f331(f331(f87(x86451),f331(f331(f88(x86451),x86455),x86453)),x86456))+~E(x86456,f331(f331(f87(x86451),f331(f331(f88(x86451),f331(f331(f3(x86451),x86452),x86455)),x86453)),x86454))
% 51.10/50.83 [8646]~P121(x86461)+E(f331(f331(f87(x86461),f331(f331(f88(x86461),x86462),x86463)),x86464),f331(f331(f87(x86461),f331(f331(f88(x86461),x86465),x86463)),x86466))+~E(f331(f331(f87(x86461),f331(f331(f88(x86461),f331(f331(f3(x86461),x86462),x86465)),x86463)),x86464),x86466)
% 51.10/50.83 [8935]~P1(f331(f331(x89354,x89355),x89356))+~P1(f331(f331(x89353,x89355),x89356))+P1(f331(f331(f331(f331(f109(f854(x89351,f854(x89352,a840))),x89353),x89354),x89355),x89356))
% 51.10/50.83 [9161]P1(f331(f331(x91611,x91612),x91613))+P1(f331(f331(x91614,x91612),x91613))+~P1(f331(f331(f331(f331(f108(f854(x91615,f854(x91616,a840))),x91614),x91611),x91612),x91613))
% 51.10/50.83 [9321]~E(f331(f185(f848(x93211)),x93215),f331(f185(f848(x93212)),x93216))+E(f175(x93211,x93212,f177(x93211,x93212,x93213,f331(f331(f3(f854(x93211,a840)),x93214),f331(f163(x93211),x93215))),f171(x93211,x93212,f331(f160(f853(x93211,x93212)),f331(f331(f172(x93211,x93212),x93215),x93216)))),f177(x93211,x93212,f175(x93211,x93212,x93213,f171(x93211,x93212,f331(f160(f853(x93211,x93212)),f331(f331(f172(x93211,x93212),x93215),x93216)))),x93214))+~P1(f331(f331(f240(f854(x93211,a840)),f331(f163(x93211),x93215)),x93214))
% 51.10/50.83 [9453]~P129(x94531)+~P1(f331(f331(f241(x94531),f331(f331(f87(x94531),f331(f331(f88(x94531),x94534),x94535)),x94532)),f331(f331(f87(x94531),f331(f331(f88(x94531),x94533),x94535)),x94536)))+P1(f331(f331(f241(x94531),x94532),f331(f331(f87(x94531),f331(f331(f88(x94531),f331(f331(f3(x94531),x94533),x94534)),x94535)),x94536)))
% 51.10/50.83 [9454]~P129(x94541)+~P1(f331(f331(f240(x94541),f331(f331(f87(x94541),f331(f331(f88(x94541),x94544),x94545)),x94542)),f331(f331(f87(x94541),f331(f331(f88(x94541),x94543),x94545)),x94546)))+P1(f331(f331(f240(x94541),x94542),f331(f331(f87(x94541),f331(f331(f88(x94541),f331(f331(f3(x94541),x94543),x94544)),x94545)),x94546)))
% 51.10/50.83 [9472]~P129(x94721)+P1(f331(f331(f241(x94721),f331(f331(f87(x94721),f331(f331(f88(x94721),x94722),x94723)),x94724)),f331(f331(f87(x94721),f331(f331(f88(x94721),x94725),x94723)),x94726)))+~P1(f331(f331(f241(x94721),x94724),f331(f331(f87(x94721),f331(f331(f88(x94721),f331(f331(f3(x94721),x94725),x94722)),x94723)),x94726)))
% 51.10/50.83 [9473]~P129(x94731)+P1(f331(f331(f240(x94731),f331(f331(f87(x94731),f331(f331(f88(x94731),x94732),x94733)),x94734)),f331(f331(f87(x94731),f331(f331(f88(x94731),x94735),x94733)),x94736)))+~P1(f331(f331(f240(x94731),x94734),f331(f331(f87(x94731),f331(f331(f88(x94731),f331(f331(f3(x94731),x94735),x94732)),x94733)),x94736)))
% 51.10/50.83 [9576]~P129(x95761)+~P1(f331(f331(f241(x95761),f331(f331(f87(x95761),f331(f331(f88(x95761),x95762),x95764)),x95765)),f331(f331(f87(x95761),f331(f331(f88(x95761),x95763),x95764)),x95766)))+P1(f331(f331(f241(x95761),f331(f331(f87(x95761),f331(f331(f88(x95761),f331(f331(f3(x95761),x95762),x95763)),x95764)),x95765)),x95766))
% 51.10/50.83 [9577]~P129(x95771)+~P1(f331(f331(f240(x95771),f331(f331(f87(x95771),f331(f331(f88(x95771),x95772),x95774)),x95775)),f331(f331(f87(x95771),f331(f331(f88(x95771),x95773),x95774)),x95776)))+P1(f331(f331(f240(x95771),f331(f331(f87(x95771),f331(f331(f88(x95771),f331(f331(f3(x95771),x95772),x95773)),x95774)),x95775)),x95776))
% 51.10/50.83 [9618]~P129(x96181)+P1(f331(f331(f241(x96181),f331(f331(f87(x96181),f331(f331(f88(x96181),x96182),x96183)),x96184)),f331(f331(f87(x96181),f331(f331(f88(x96181),x96185),x96183)),x96186)))+~P1(f331(f331(f241(x96181),f331(f331(f87(x96181),f331(f331(f88(x96181),f331(f331(f3(x96181),x96182),x96185)),x96183)),x96184)),x96186))
% 51.10/50.83 [9619]~P129(x96191)+P1(f331(f331(f240(x96191),f331(f331(f87(x96191),f331(f331(f88(x96191),x96192),x96193)),x96194)),f331(f331(f87(x96191),f331(f331(f88(x96191),x96195),x96193)),x96196)))+~P1(f331(f331(f240(x96191),f331(f331(f87(x96191),f331(f331(f88(x96191),f331(f331(f3(x96191),x96192),x96195)),x96193)),x96194)),x96196))
% 51.10/50.83 [9789]~P68(x97892)+~P1(f331(f68(x97891),x97896))+E(f331(f331(f8(x97891,x97892),f331(f331(f20(x97891,x97892,x97892),f331(f331(f20(x97891,x97892,f854(x97892,x97892)),f331(f331(f10(a840,f854(x97892,f854(x97892,x97892)),x97891),f103(x97892)),x97893)),x97894)),x97895)),x97896),f331(f331(f87(x97892),f331(f331(f8(x97891,x97892),x97894),f331(f331(f109(f854(x97891,a840)),x97896),f331(f264(x97891),x97893)))),f331(f331(f8(x97891,x97892),x97895),f331(f331(f109(f854(x97891,a840)),x97896),f331(f86(f854(x97891,a840)),f331(f264(x97891),x97893))))))
% 51.10/50.83 [9857]P1(f331(f331(f333(x98572),x98574),x98576))+P1(f331(f331(f333(x98572),x98575),x98576))+E(f331(f312(x98571,x98572,f331(f331(f9(x98571,x98572,x98572),f331(f331(f9(x98571,x98572,f854(x98572,x98572)),f331(f331(f10(a840,f854(x98572,f854(x98572,x98572)),x98571),f103(x98572)),f331(f331(f9(x98571,f854(x98571,a840),a840),f333(x98571)),x98573))),x98574)),x98575)),x98576),f184(f854(x98571,a840)))
% 51.10/50.83 [9858]P1(f331(f331(f333(x98582),x98585),x98586))+~P1(f331(f331(f333(x98582),x98584),x98586))+E(f331(f312(x98581,x98582,f331(f331(f9(x98581,x98582,x98582),f331(f331(f9(x98581,x98582,f854(x98582,x98582)),f331(f331(f10(a840,f854(x98582,f854(x98582,x98582)),x98581),f103(x98582)),f331(f331(f9(x98581,f854(x98581,a840),a840),f333(x98581)),x98583))),x98584)),x98585)),x98586),x98583)
% 51.10/50.83 [9859]P1(f331(f331(f333(x98592),x98594),x98596))+~P1(f331(f331(f333(x98592),x98595),x98596))+E(f331(f312(x98591,x98592,f331(f331(f9(x98591,x98592,x98592),f331(f331(f9(x98591,x98592,f854(x98592,x98592)),f331(f331(f10(a840,f854(x98592,f854(x98592,x98592)),x98591),f103(x98592)),f331(f331(f9(x98591,f854(x98591,a840),a840),f333(x98591)),x98593))),x98594)),x98595)),x98596),f331(f86(f854(x98591,a840)),x98593))
% 51.10/50.83 [9860]~P1(f331(f331(f333(x98602),x98604),x98606))+~P1(f331(f331(f333(x98602),x98605),x98606))+E(f331(f312(x98601,x98602,f331(f331(f9(x98601,x98602,x98602),f331(f331(f9(x98601,x98602,f854(x98602,x98602)),f331(f331(f10(a840,f854(x98602,f854(x98602,x98602)),x98601),f103(x98602)),f331(f331(f9(x98601,f854(x98601,a840),a840),f333(x98601)),x98603))),x98604)),x98605)),x98606),f247(f854(x98601,a840)))
% 51.10/50.83 [9995]P26(x99951,x99952,f331(f331(f310(f846(x99951)),f331(f331(f331(f98(x99951),f331(x99953,x99954)),f331(a29,x99954)),f331(x99955,x99954))),f184(f854(f846(x99951),a840))))+~P1(f331(f331(f333(a843),x99954),x99956))+~P26(x99951,f331(f331(f108(f854(f846(x99951),a840)),x99952),f331(f311(a843,f846(x99951),f331(f331(f20(a843,f854(x99951,f854(a845,a840)),f846(x99951)),f331(f331(f20(a843,a841,f854(f854(x99951,f854(a845,a840)),f846(x99951))),f331(f331(f10(f854(x99951,f854(a845,a840)),f854(a841,f854(f854(x99951,f854(a845,a840)),f846(x99951))),a843),f98(x99951)),x99953)),a29)),x99955)),x99956)),f331(f311(a843,f846(x99951),f331(f331(f20(a843,f854(x99951,f854(a845,a840)),f846(x99951)),f331(f331(f20(a843,a841,f854(f854(x99951,f854(a845,a840)),f846(x99951))),f331(f331(f10(f854(x99951,f854(a845,a840)),f854(a841,f854(f854(x99951,f854(a845,a840)),f846(x99951))),a843),f98(x99951)),x99953)),f331(f331(f10(f851(a841),a841,a843),f238(a841)),a32))),x99955)),x99956))
% 51.10/50.83 [8521]E(x85211,x85212)+~P53(x85214,x85215,x85213,x85216,x85217)+~E(f331(x85213,x85211),f331(x85213,x85212))
% 51.10/50.83 [6899]E(f331(f236(f851(x68991),x68992,f187(x68991),x68993),f331(x68994,x68995)),f331(f234(x68991),x68996))+~E(f331(x68994,x68995),f331(f234(x68992),x68997))+~E(f331(x68993,x68997),f331(f234(x68991),x68996))
% 51.10/50.83 [8542]~P13(x85426,x85425,x85427,x85424,x85421)+E(f331(f331(x85421,x85422),x85423),x85424)+P1(f331(f68(x85425),x85423))
% 51.10/50.83 [8543]~P13(x85436,x85435,x85437,x85434,x85431)+E(f331(f331(x85431,x85432),x85433),x85434)+P1(f331(f68(x85435),x85433))
% 51.10/50.83 [9316]P39(x93161,x93162,x93163,x93164,x93165,f331(f331(x93163,x93166),x93167))+~E(f331(f331(x93163,x93166),x93167),x93164)+~E(x93165,f184(f854(x93161,a840)))
% 51.10/50.83 [9492]~P1(f331(x94926,x94923))+~P1(f331(f331(f333(f853(x94922,x94922)),f331(f331(f249(x94922,x94922),x94924),x94925)),f331(x94927,x94923)))+P1(f331(f331(f333(f853(f853(x94921,x94922),f853(x94921,x94922))),f331(f331(f249(f853(x94921,x94922),f853(x94921,x94922)),f331(f331(f249(x94921,x94922),x94923),x94924)),f331(f331(f249(x94921,x94922),x94923),x94925))),f283(x94921,x94922,x94926,x94927)))
% 51.10/50.83 [9672]~P27(x96723,x96721,x96724,f247(f854(x96723,a840)))+E(f331(f171(x96721,x96722,f331(f331(f147(f853(x96723,x96722),f853(x96721,x96722)),f331(f259(x96723,x96722,f853(x96721,x96722)),f331(f331(f10(x96721,f854(x96722,f853(x96721,x96722)),x96723),f249(x96721,x96722)),x96724))),x96725)),f331(x96724,x96726)),f331(f234(x96722),x96727))+~E(f331(f171(x96723,x96722,x96725),x96726),f331(f234(x96722),x96727))
% 51.10/50.83 [9913]~P39(x99132,x99137,x99133,x99136,x99131,f331(f331(x99133,x99135),x99134))+E(f331(f331(x99133,f347(x99134,x99135,x99131,x99136,x99133,x99137,x99132)),f348(x99134,x99135,x99131,x99136,x99133,x99137,x99132)),f331(f331(x99133,x99135),x99134))+E(x99131,f184(f854(x99132,a840)))
% 51.10/50.83 [9914]~P39(x99147,x99146,x99141,x99144,x99145,f331(f331(x99141,x99142),x99143))+E(f331(f331(x99141,f347(x99143,x99142,x99145,x99144,x99141,x99146,x99147)),f348(x99143,x99142,x99145,x99144,x99141,x99146,x99147)),f331(f331(x99141,x99142),x99143))+E(f331(f331(x99141,x99142),x99143),x99144)
% 51.10/50.83 [8549]~P37(x85493,f331(f331(f331(a193,x85494),f40(x85491)),f331(x85492,x85494)),x85495,x85497)+P37(f34(x85491,x85492,x85493),x85494,x85495,f331(f331(f331(a193,x85496),f40(x85491)),f331(f331(a196,x85494),x85491)))+~E(f331(f331(f331(a193,x85496),f40(x85491)),f331(f331(a196,x85494),x85491)),f331(f331(f331(a193,x85497),f40(x85491)),f331(f331(a196,x85494),x85491)))
% 51.10/50.83 [9232]~P37(f331(a29,x92322),f331(f331(f331(a193,f331(f331(a194,x92324),a195)),f40(a27)),f331(x92323,x92324)),x92325,x92327)+P37(f33(x92321,x92322,x92323),x92324,x92325,f331(f331(f331(a193,f331(f331(a194,x92326),f331(a196,x92324))),x92321),f331(f331(a196,x92326),a28)))+~E(f331(f331(f331(a193,f331(f331(a194,x92326),f331(a196,x92324))),x92321),f331(f331(a196,x92326),a28)),f331(f331(f331(a193,f331(f331(a194,x92327),f331(a196,x92324))),x92321),f331(f331(a196,x92327),a28)))
% 51.10/50.83 [9561]~P1(f331(f73(x95611,x95614,x95615,x95616,x95613),x95617))+P1(f331(f73(x95611,x95614,x95615,x95616,f331(f331(f310(x95611),x95612),x95613)),f331(f331(x95615,x95612),x95617)))+P1(f331(f331(f333(x95611),x95612),x95613))
% 51.10/50.83 [9940]~P39(x99402,x99407,x99406,x99405,x99401,f331(f331(x99406,x99404),x99403))+E(x99401,f184(f854(x99402,a840)))+P1(f331(f331(f333(x99402),f347(x99403,x99404,x99401,x99405,x99406,x99407,x99402)),x99401))
% 51.10/50.83 [9941]~P39(x99415,x99417,x99411,x99414,x99416,f331(f331(x99411,x99412),x99413))+E(f331(f331(x99411,x99412),x99413),x99414)+P1(f331(f331(f333(x99415),f347(x99413,x99412,x99416,x99414,x99411,x99417,x99415)),x99416))
% 51.10/50.83 [6678]~E(x66785,x66787)+~E(x66786,x66784)+E(f331(f331(f331(f331(f79(x66781,f851(x66782)),x66783),x66784),f331(f234(x66782),x66785)),x66786),f331(f234(x66782),x66787))
% 51.10/50.83 [6813]E(x68131,x68132)+~E(f331(x68135,x68131),f331(f234(x68134),x68137))+E(f331(f331(f331(f331(f79(x68133,f851(x68134)),x68135),x68132),f331(f234(x68134),x68136)),x68131),f331(f234(x68134),x68137))
% 51.10/50.83 [7557]E(x75571,x75572)+~E(x75573,x75574)+~E(f331(f331(f331(f331(f79(x75575,f851(x75576)),x75577),x75574),f331(f234(x75576),x75571)),x75573),f331(f234(x75576),x75572))
% 51.10/50.83 [7622]E(x76221,x76222)+E(f331(x76223,x76224),f331(f234(x76225),x76221))+~E(f331(f331(f331(f331(f79(x76226,f851(x76225)),x76223),x76227),f331(f234(x76225),x76222)),x76224),f331(f234(x76225),x76221))
% 51.10/50.83 [7623]E(x76231,x76232)+E(f331(x76233,x76231),f331(f234(x76234),x76235))+~E(f331(f331(f331(f331(f79(x76236,f851(x76234)),x76233),x76232),f331(f234(x76234),x76237)),x76231),f331(f234(x76234),x76235))
% 51.10/50.83 [8748]~P23(x87484,x87485,x87486,x87487,x87481)+~P1(f331(f68(x87485),x87483))+E(f331(f331(x87481,x87482),x87483),f331(f331(f331(f72(x87484,x87485,x87486),x87482),x87487),x87483))
% 51.10/50.83 [8749]~P13(x87494,x87495,x87496,x87497,x87491)+~P1(f331(f68(x87495),x87493))+E(f331(f331(x87491,x87492),x87493),f331(f331(f331(f72(x87494,x87495,x87496),x87492),x87497),x87493))
% 51.10/50.83 [9284]~P26(x92841,x92842,f331(f331(f310(f846(x92841)),f331(f331(f331(f98(x92841),x92843),x92844),x92847)),f184(f854(f846(x92841),a840))))+P26(x92841,x92842,f331(f331(f310(f846(x92841)),f331(f331(f331(f98(x92841),x92843),f38(x92844,x92845)),x92846)),f184(f854(f846(x92841),a840))))+~P26(x92841,x92842,f331(f331(f310(f846(x92841)),f331(f331(f331(f98(x92841),x92847),x92845),x92846)),f184(f854(f846(x92841),a840))))
% 51.10/50.83 [9467]~P25(x94673,x94674,x94675,x94677,x94676,x94671)+~P1(f331(f68(x94674),x94672))+E(f331(x94671,x94672),f331(f331(f331(f72(x94673,x94674,x94675),x94676),x94677),x94672))
% 51.10/50.83 [9613]P39(x96131,x96132,x96133,x96134,x96135,f331(f331(x96133,x96136),x96137))+~P39(x96131,x96132,x96133,x96134,f331(f331(f3(f854(x96131,a840)),x96135),f331(f331(f310(x96131),x96136),f184(f854(x96131,a840)))),x96137)+~P1(f331(f331(f333(x96131),x96136),x96135))
% 51.10/50.83 [9888]~P26(x98881,x98882,f331(f331(f310(f846(x98881)),f331(f331(f331(f98(x98881),f99(x98881,x98883,x98884)),x98885),x98887)),f184(f854(f846(x98881),a840))))+P26(x98881,x98882,f331(f331(f310(f846(x98881)),f331(f331(f331(f98(x98881),x98883),f35(x98884,x98885,x98886)),x98887)),f184(f854(f846(x98881),a840))))+~P26(x98881,x98882,f331(f331(f310(f846(x98881)),f331(f331(f331(f98(x98881),f99(x98881,x98883,f331(f80(a840,a840,a845,a327),x98884))),x98886),x98887)),f184(f854(f846(x98881),a840))))
% 51.10/50.83 [9958]P1(f331(f331(x99587,f828(x99584,x99585,x99581,x99586,x99583,x99582,x99587)),f829(x99584,x99585,x99581,x99586,x99583,x99582,x99587)))+~P1(f331(f331(x99587,f331(f258(x99582,x99583),x99586)),f331(f248(x99582,x99583),x99586)))+P1(f331(x99581,f331(f331(f259(x99582,x99583,x99584),x99585),x99586)))
% 51.10/50.83 [9967]~P39(x99672,x99673,x99674,x99675,x99671,f331(f331(x99674,x99677),x99676))+P39(x99672,x99673,x99674,x99675,f331(f331(f3(f854(x99672,a840)),x99671),f331(f331(f310(x99672),f347(x99676,x99677,x99671,x99675,x99674,x99673,x99672)),f184(f854(x99672,a840)))),f348(x99676,x99677,x99671,x99675,x99674,x99673,x99672))+E(x99671,f184(f854(x99672,a840)))
% 51.10/50.83 [9968]~P39(x99685,x99686,x99681,x99684,x99687,f331(f331(x99681,x99682),x99683))+P39(x99685,x99686,x99681,x99684,f331(f331(f3(f854(x99685,a840)),x99687),f331(f331(f310(x99685),f347(x99683,x99682,x99687,x99684,x99681,x99686,x99685)),f184(f854(x99685,a840)))),f348(x99683,x99682,x99687,x99684,x99681,x99686,x99685))+E(f331(f331(x99681,x99682),x99683),x99684)
% 51.10/50.83 [9988]~P1(f331(x99881,f331(f331(x99885,f829(x99884,x99885,x99881,x99886,x99883,x99882,x99887)),f828(x99884,x99885,x99881,x99886,x99883,x99882,x99887))))+~P1(f331(f331(x99887,f331(f258(x99882,x99883),x99886)),f331(f248(x99882,x99883),x99886)))+P1(f331(x99881,f331(f331(f259(x99882,x99883,x99884),x99885),x99886)))
% 51.10/50.83 [9305]P1(f331(f331(f240(f854(f853(x93051,x93052),a840)),f331(f331(f289(x93051,x93053,x93052),x93054),x93055)),f331(f331(f289(x93051,x93053,x93052),x93056),x93057)))+~P1(f331(f331(f240(f854(f853(x93053,x93052),a840)),x93055),x93057))+~P1(f331(f331(f240(f854(f853(x93051,x93053),a840)),x93054),x93056))
% 51.10/50.83 [9624]~P1(f331(f331(f333(x96241),x96246),x96245))+P1(f331(f73(x96241,x96242,x96243,x96244,x96245),f331(f331(x96243,x96246),x96247)))+~P1(f331(f73(x96241,x96242,x96243,x96244,f331(f331(f3(f854(x96241,a840)),x96245),f331(f331(f310(x96241),x96246),f184(f854(x96241,a840))))),x96247))
% 51.10/50.83 [9210]E(f175(x92101,x92102,x92103,f171(x92101,x92102,f331(f160(f853(x92101,x92102)),f331(f331(f172(x92101,x92102),x92104),f331(f331(f152(x92102,x92105),x92106),x92107))))),f175(x92101,x92102,x92103,f171(x92101,x92102,f331(f160(f853(x92101,x92102)),f331(f331(f172(x92101,x92102),x92104),x92105)))))+~P1(f331(f331(f241(a847),x92106),f331(f185(f848(x92102)),x92105)))+~P1(f331(f331(f240(a847),f331(f185(f848(x92101)),x92104)),x92106))
% 51.10/50.83 [10021]~P136(x100211)+~P27(f853(x100212,x100213),x100211,f331(f259(x100212,x100213,x100211),f331(f331(f9(x100212,f854(x100213,x100211),f854(x100213,x100211)),f331(f331(f10(f854(x100211,x100211),f854(f854(x100213,x100211),f854(x100213,x100211)),x100212),f10(x100211,x100211,x100213)),f331(f331(f10(x100211,f854(x100211,x100211),x100212),f88(x100211)),x100214))),x100215)),f331(f331(f256(x100212,x100213),x100216),f331(f18(f854(x100213,a840),x100212),x100217)))+E(f331(f331(f8(x100211,x100211),f39(x100211)),f331(f264(x100211),f331(f331(f10(f854(x100212,a840),a840,x100211),f94(x100212)),f331(f331(f10(f854(x100212,f854(x100213,a840)),f854(x100212,a840),x100211),f331(f10(f854(x100213,a840),a840,x100212),f94(x100213))),f331(f331(f9(x100211,f854(x100212,f854(x100213,a840)),f854(x100212,f854(x100213,a840))),f331(f331(f10(f854(x100212,f854(f854(x100213,a840),f854(x100213,a840))),f854(f854(x100212,f854(x100213,a840)),f854(x100212,f854(x100213,a840))),x100211),f20(x100212,f854(x100213,a840),f854(x100213,a840))),f331(f331(f10(f854(x100212,f854(x100213,f854(a840,a840))),f854(x100212,f854(f854(x100213,a840),f854(x100213,a840))),x100211),f331(f10(f854(x100213,f854(a840,a840)),f854(f854(x100213,a840),f854(x100213,a840)),x100212),f20(x100213,a840,a840))),f331(f331(f10(f854(x100212,f854(x100213,a840)),f854(x100212,f854(x100213,f854(a840,a840))),x100211),f331(f10(f854(x100213,a840),f854(x100213,f854(a840,a840)),x100212),f331(f10(a840,f854(a840,a840),x100213),a329))),f331(f331(f9(x100211,f854(x100212,f854(x100213,x100211)),f854(x100212,f854(x100213,a840))),f331(f331(f10(f854(f854(x100213,x100211),f854(x100213,a840)),f854(f854(x100212,f854(x100213,x100211)),f854(x100212,f854(x100213,a840))),x100211),f10(f854(x100213,x100211),f854(x100213,a840),x100212)),f331(f331(f10(f854(x100211,a840),f854(f854(x100213,x100211),f854(x100213,a840)),x100211),f10(x100211,a840,x100213)),a328))),f331(f331(f9(x100212,f854(x100213,x100211),f854(x100213,x100211)),f331(f331(f10(f854(x100211,x100211),f854(f854(x100213,x100211),f854(x100213,x100211)),x100212),f10(x100211,x100211,x100213)),f331(f331(f10(x100211,f854(x100211,x100211),x100212),f88(x100211)),x100214))),x100215)))))),f331(f331(f9(x100212,f854(x100213,a840),f854(x100213,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x100213,a840),f854(x100213,a840)),x100212),f10(a840,a840,x100213)),f331(f331(f10(a840,f854(a840,a840),x100212),a329),f331(f331(f9(x100212,f854(x100212,a840),a840),f333(x100212)),x100216)))),f331(f331(f9(x100213,f854(x100213,a840),a840),f333(x100213)),x100217))))))),f331(f331(f88(x100211),f331(f331(f8(x100212,x100211),x100214),x100216)),f331(f331(f8(x100213,x100211),x100215),x100217)))
% 51.10/50.83 [9702]P49(x97021,x97022,x97023,x97024,x97025,x97026,x97027)+~P1(f331(f331(x97024,x97026),x97028))+~P1(f331(f331(x97025,x97028),x97027))
% 51.10/50.83 [9703]P49(x97031,x97032,x97033,x97034,x97035,x97036,x97037)+~P1(f331(f331(x97034,x97036),x97038))+~P1(f331(f331(x97035,x97038),x97037))
% 51.10/50.83 [9089]~P21(x90898,x90891,x90893,x90895)+~P1(f331(f68(x90898),x90896))+E(f331(f80(x90891,x90891,x90892,f331(x90893,x90894)),f331(f80(x90891,x90891,x90892,f331(x90895,x90896)),x90897)),f331(f80(x90891,x90891,x90892,f331(x90895,x90896)),f331(f80(x90891,x90891,x90892,f331(x90893,x90894)),x90897)))
% 51.10/50.83 [9458]~P24(x94587,x94582,x94585,x94588,x94586,x94581)+~P1(f331(f68(x94582),x94584))+E(f331(x94581,f331(f331(f310(x94582),x94583),x94584)),f331(f331(x94585,f331(x94586,x94583)),f331(x94581,x94584)))
% 51.10/50.83 [9572]~P27(x95722,x95724,x95726,x95728)+~P27(x95721,x95723,x95725,x95727)+P27(f853(x95721,x95722),f853(x95723,x95724),f260(x95721,x95723,x95722,x95724,x95725,x95726),f331(f331(f256(x95721,x95722),x95727),f331(f18(f854(x95722,a840),x95721),x95728)))
% 51.10/50.83 [9247]P1(f331(f331(f333(f853(x92471,x92472)),f331(f331(f249(x92471,x92472),x92473),x92474)),f331(f331(f289(x92471,x92475,x92472),x92476),x92477)))+~P1(f331(f331(f333(f853(x92471,x92475)),f331(f331(f249(x92471,x92475),x92473),x92478)),x92476))+~P1(f331(f331(f333(f853(x92475,x92472)),f331(f331(f249(x92475,x92472),x92478),x92474)),x92477))
% 51.10/50.83 [9441]~P1(f331(f331(f240(f854(f853(x94413,x94412),a840)),x94415),f331(f331(f256(x94413,x94412),x94418),f331(f18(f854(x94412,a840),x94413),x94417))))+~P1(f331(f331(f240(f854(f853(x94411,x94413),a840)),x94414),f331(f331(f256(x94411,x94413),x94416),f331(f18(f854(x94413,a840),x94411),x94418))))+P1(f331(f331(f240(f854(f853(x94411,x94412),a840)),f331(f331(f289(x94411,x94413,x94412),x94414),x94415)),f331(f331(f256(x94411,x94412),x94416),f331(f18(f854(x94412,a840),x94411),x94417))))
% 51.10/50.83 [9487]~E(x94873,x94875)+P1(f331(f331(f333(f853(f853(x94871,x94872),f853(x94871,x94872))),f331(f331(f249(f853(x94871,x94872),f853(x94871,x94872)),f331(f331(f249(x94871,x94872),x94873),x94874)),f331(f331(f249(x94871,x94872),x94875),x94876))),f324(x94871,x94872,x94877,x94878)))+~P1(f331(f331(f333(f853(x94872,x94872)),f331(f331(f249(x94872,x94872),x94874),x94876)),x94878))
% 51.10/50.83 [9592]E(x95921,x95922)+~P1(f331(f331(f333(f853(f853(x95923,x95925),f853(x95923,x95925))),f331(f331(f249(f853(x95923,x95925),f853(x95923,x95925)),f331(f331(f249(x95923,x95925),x95921),x95926)),f331(f331(f249(x95923,x95925),x95922),x95927))),f324(x95923,x95925,x95924,x95928)))+P1(f331(f331(f333(f853(x95923,x95923)),f331(f331(f249(x95923,x95923),x95921),x95922)),x95924))
% 51.10/50.83 [9607]~P1(f331(f331(f333(f853(f853(x96071,x96075),f853(x96071,x96075))),f331(f331(f249(f853(x96071,x96075),f853(x96071,x96075)),f331(f331(f249(x96071,x96075),x96072),x96076)),f331(f331(f249(x96071,x96075),x96073),x96077))),f324(x96071,x96075,x96074,x96078)))+P1(f331(f331(f333(f853(x96071,x96071)),f331(f331(f249(x96071,x96071),x96072),x96073)),x96074))+P1(f331(f331(f333(f853(x96075,x96075)),f331(f331(f249(x96075,x96075),x96076),x96077)),x96078))
% 51.10/50.83 [9517]~P25(x95177,x95175,x95171,x95178,x95172,x95174)+~P1(f331(f68(x95175),x95176))+E(f331(f331(x95171,f331(x95172,x95173)),f331(x95174,f331(f331(f3(f854(x95175,a840)),x95176),f331(f331(f310(x95175),x95173),f184(f854(x95175,a840)))))),f331(x95174,f331(f331(f310(x95175),x95173),x95176)))
% 51.10/50.83 [9049]~P1(f331(f331(f331(x90495,x90498),x90496),x90497))+~P1(f331(f331(f333(x90491),x90498),x90494))+P1(f331(f331(f331(f331(f51(x90491,f854(x90492,f854(x90493,a840))),x90494),x90495),x90496),x90497))
% 51.10/50.83 [9050]~P1(f331(f331(f331(x90505,x90508),x90506),x90507))+~P1(f331(f331(f333(x90501),x90508),x90504))+P1(f331(f331(f331(f331(f51(x90501,f854(x90502,f854(x90503,a840))),x90504),x90505),x90506),x90507))
% 51.10/50.83 [9233]P1(f331(f331(f331(x92331,x92332),x92333),x92334))+~P1(f331(f331(f333(x92335),x92332),x92336))+~P1(f331(f331(f331(f331(f52(x92335,f854(x92337,f854(x92338,a840))),x92336),x92331),x92333),x92334))
% 51.10/50.83 [9234]P1(f331(f331(f331(x92341,x92342),x92343),x92344))+~P1(f331(f331(f333(x92345),x92342),x92346))+~P1(f331(f331(f331(f331(f52(x92345,f854(x92347,f854(x92348,a840))),x92346),x92341),x92343),x92344))
% 51.10/50.83 [9235]P1(f331(f331(f331(x92351,x92352),x92353),x92354))+~P1(f331(f331(f333(x92355),x92352),x92356))+~P1(f331(f331(f331(f331(f52(x92355,f854(x92357,f854(x92358,a840))),x92356),x92351),x92353),x92354))
% 51.10/50.83 [9432]~P23(x94323,x94322,x94324,x94328,x94321)+~P1(f331(f68(x94322),x94327))+E(f331(f331(x94321,f331(f331(f20(x94322,x94323,x94323),f331(f331(f10(x94323,f854(x94323,x94323),x94322),x94324),x94325)),x94326)),x94327),f331(f331(x94324,f331(f331(x94321,x94325),x94327)),f331(f331(x94321,x94326),x94327)))
% 51.10/50.83 [9680]~E(f331(f311(x96802,x96804,x96806),x96808),x968010)+~E(f331(f311(x96801,x96803,x96805),x96807),x96809)+E(f331(f311(f853(x96801,x96802),f853(x96803,x96804),f260(x96801,x96803,x96802,x96804,x96805,x96806)),f331(f331(f256(x96801,x96802),x96807),f331(f18(f854(x96802,a840),x96801),x96808))),f331(f331(f256(x96803,x96804),x96809),f331(f18(f854(x96804,a840),x96803),x968010)))
% 51.10/50.83 [4704]~P102(x47042)+~P16(x47042,x47041)+P16(x47042,f121(x47042,x47041))+E(x47041,f120(x47042))
% 51.10/50.83 [4935]~P7(x49352)+E(f12(x49352,x49351),f50(x49352,x49351))+E(x49351,f184(f854(x49352,a840)))+~P1(f331(f68(x49352),x49351))
% 51.10/50.83 [4936]~P7(x49362)+E(f15(x49362,x49361),f49(x49362,x49361))+E(x49361,f184(f854(x49362,a840)))+~P1(f331(f68(x49362),x49361))
% 51.10/50.83 [5882]~P97(x58822)+E(x58821,f184(f854(x58822,a840)))+P1(f331(f331(f240(x58822),f12(x58822,x58821)),f15(x58822,x58821)))+~P1(f331(f68(x58822),x58821))
% 51.10/50.83 [5896]~P36(x58962)+~P36(x58961)+E(x58961,x58962)+~E(f331(f311(a1,a847,a112),x58961),f331(f311(a1,a847,a112),x58962))
% 51.10/50.83 [8915]~P86(x89151)+~P1(f331(f331(f333(x89151),x89152),f117(x89151)))+P1(f331(f331(f241(x89151),f331(f331(f87(x89151),f331(f331(f87(x89151),f85(x89151)),x89152)),x89152)),f2(x89151)))+~P1(f331(f331(f241(x89151),x89152),f2(x89151)))
% 51.10/50.83 [9131]~P86(x91311)+~P1(f331(f331(f333(x91311),x91312),f117(x91311)))+~P1(f331(f331(f241(x91311),f331(f331(f87(x91311),f331(f331(f87(x91311),f85(x91311)),x91312)),x91312)),f2(x91311)))+P1(f331(f331(f241(x91311),x91312),f2(x91311)))
% 51.10/50.83 [4759]~P107(x47592)+~P136(x47592)+E(x47591,f2(a847))+E(f331(f331(f250(x47592),f2(x47592)),x47591),f2(x47592))
% 51.10/50.83 [4763]~P107(x47631)+~P136(x47631)+~E(x47632,f2(a847))+E(f331(f331(f250(x47631),f2(x47631)),x47632),f85(x47631))
% 51.10/50.83 [4922]~P120(x49222)+E(x49221,f85(x49222))+E(x49221,f331(f86(x49222),f85(x49222)))+~E(f331(f331(f88(x49222),x49221),x49221),f85(x49222))
% 51.10/50.83 [5167]~P81(x51672)+E(x51671,f2(x51672))+E(f89(x51672,x51671),f331(f86(x51672),f85(x51672)))+P1(f331(f331(f241(x51672),f2(x51672)),x51671))
% 51.10/50.83 [5359]~E(x53592,f85(a1))+~E(x53591,f85(a1))+E(f331(f331(f88(a1),x53591),x53592),f85(a1))+~P1(f331(f331(f241(a1),f2(a1)),x53591))
% 51.10/50.83 [5399]~P81(x53992)+E(f89(x53992,x53991),f85(x53992))+E(x53991,f2(x53992))+~P1(f331(f331(f241(x53992),f2(x53992)),x53991))
% 51.10/50.83 [5408]E(x54081,x54082)+~E(f331(f111(a847),x54081),f331(f111(a847),x54082))+P1(f331(a190,f331(f111(a1),x54082)))+P1(f331(a190,f331(f111(a1),x54081)))
% 51.10/50.83 [5456]~P90(x54561)+~E(x54562,f2(x54561))+E(f331(f331(f87(x54561),x54562),x54562),f2(x54561))+~P1(f331(f331(f333(x54561),x54562),f117(x54561)))
% 51.10/50.83 [5494]E(x54941,f2(a1))+~E(f331(f331(f48(a1),x54942),x54941),f2(a1))+P1(f331(f331(f241(a1),x54941),x54942))+P1(f331(f331(f241(a1),x54942),x54941))
% 51.10/50.83 [5524]E(x55241,f2(a1))+~E(f331(f331(f48(a1),x55242),x55241),f2(a1))+P1(f331(f331(f240(a1),x55242),f2(a1)))+P1(f331(f331(f241(a1),x55242),x55241))
% 51.10/50.83 [5556]E(x55561,f2(a1))+~E(f331(f331(f48(a1),x55562),x55561),f2(a1))+P1(f331(f331(f240(a1),f2(a1)),x55562))+P1(f331(f331(f241(a1),x55561),x55562))
% 51.10/50.83 [5592]E(x55921,f2(a1))+~E(f331(f331(f48(a1),x55922),x55921),f2(a1))+P1(f331(f331(f240(a1),x55922),f2(a1)))+P1(f331(f331(f240(a1),f2(a1)),x55922))
% 51.10/50.83 [5593]~P90(x55932)+E(x55931,f2(x55932))+~E(f331(f331(f87(x55932),x55931),x55931),f2(x55932))+~P1(f331(f331(f333(x55932),x55931),f117(x55932)))
% 51.10/50.83 [5660]E(f331(f111(a847),x56601),f331(f111(a847),x56602))+~E(f331(f111(a1),x56602),f2(a1))+P1(f331(a190,f331(f111(a1),x56602)))+~P1(f331(a190,f331(f111(a1),x56601)))
% 51.10/50.83 [5689]~E(f331(f111(a847),x56892),f331(f111(a847),x56891))+E(f331(f111(a1),x56891),f2(a1))+P1(f331(a190,f331(f111(a1),x56891)))+~P1(f331(a190,f331(f111(a1),x56892)))
% 51.10/50.83 [5698]~P102(x56982)+E(x56981,f184(f854(x56982,a840)))+~P1(f331(f68(x56982),x56981))+P1(f331(f331(f333(x56982),f16(x56982,x56981)),x56981))
% 51.10/50.83 [5699]~P102(x56992)+E(x56991,f184(f854(x56992,a840)))+~P1(f331(f68(x56992),x56991))+P1(f331(f331(f333(x56992),f17(x56992,x56991)),x56991))
% 51.10/50.83 [5862]~P86(x58621)+~P91(x58621)+P1(f331(f331(f241(x58621),f2(x58621)),f331(f111(x58621),x58622)))+~P1(f331(f331(f241(a1),a90),x58622))
% 51.10/50.83 [5863]~P86(x58631)+~P91(x58631)+P1(f331(f331(f240(x58631),f2(x58631)),f331(f111(x58631),x58632)))+~P1(f331(f331(f240(a1),a90),x58632))
% 51.10/50.83 [5881]~P86(x58811)+~P91(x58811)+E(f331(f82(x58811),f331(f111(x58811),x58812)),f331(f111(x58811),x58812))+P1(f331(f331(f241(x58811),f331(f111(x58811),x58812)),f2(x58811)))
% 51.10/50.83 [5922]E(x59221,x59222)+~E(f331(a112,x59221),f331(a112,x59222))+~P1(f331(f331(f240(a1),f2(a1)),x59222))+~P1(f331(f331(f240(a1),f2(a1)),x59221))
% 51.10/50.83 [5923]E(x59231,x59232)+~E(f331(a112,x59231),f331(a112,x59232))+~P1(f331(f331(f240(a1),f2(a1)),x59232))+~P1(f331(f331(f240(a1),f2(a1)),x59231))
% 51.10/50.83 [5951]~E(x59511,f2(a1))+E(f58(x59511,x59512),f331(f331(f249(a1,a1),f2(a1)),f2(a1)))+P1(f331(f331(f240(a1),f2(a1)),x59512))+~P1(f331(f331(f240(a1),f2(a1)),x59511))
% 51.10/50.83 [6122]~P91(x61222)+~P86(x61222)+~P1(f331(f331(f241(x61222),f2(x61222)),f331(f111(x61222),x61221)))+P1(f331(f331(f241(a1),a90),x61221))
% 51.10/50.83 [6123]~P91(x61232)+~P86(x61232)+~P1(f331(f331(f240(x61232),f2(x61232)),f331(f111(x61232),x61231)))+P1(f331(f331(f240(a1),a90),x61231))
% 51.10/50.83 [6128]~P86(x61281)+~P91(x61281)+P1(f331(f331(f241(x61281),f331(f111(x61281),x61282)),f2(x61281)))+~P1(f331(f331(f241(a1),x61282),a90))
% 51.10/50.83 [6129]~P86(x61291)+~P91(x61291)+P1(f331(f331(f240(x61291),f331(f111(x61291),x61292)),f2(x61291)))+~P1(f331(f331(f240(a1),x61292),a90))
% 51.10/50.83 [6458]~P91(x64582)+~P86(x64582)+~P1(f331(f331(f241(x64582),f331(f111(x64582),x64581)),f2(x64582)))+P1(f331(f331(f241(a1),x64581),a90))
% 51.10/50.83 [6459]~P91(x64592)+~P86(x64592)+~P1(f331(f331(f240(x64592),f331(f111(x64592),x64591)),f2(x64592)))+P1(f331(f331(f240(a1),x64591),a90))
% 51.10/50.83 [6550]~P86(x65501)+~P91(x65501)+E(f331(f82(x65501),f331(f111(x65501),x65502)),f331(f86(x65501),f331(f111(x65501),x65502)))+~P1(f331(f331(f241(x65501),f331(f111(x65501),x65502)),f2(x65501)))
% 51.10/50.83 [6567]E(f331(f111(a847),x65671),f331(f111(a847),x65672))+~E(f331(f111(a1),x65672),f2(a1))+~P1(f331(f331(f240(a1),f331(f111(a1),x65671)),f2(a1)))+~P1(f331(a190,f331(f111(a1),x65671)))
% 51.10/50.83 [6748]E(x67481,x67482)+~E(f331(a5,x67481),f331(a5,x67482))+~P1(f331(f331(f333(a847),x67482),f247(f854(a847,a840))))+~P1(f331(f331(f333(a847),x67481),f247(f854(a847,a840))))
% 51.10/50.83 [6977]P1(f331(f331(f241(a847),f331(a112,x69771)),f331(a112,x69772)))+~P1(f331(f331(f240(a1),f2(a1)),x69772))+~P1(f331(f331(f240(a1),f2(a1)),x69771))+~P1(f331(f331(f241(a1),x69771),x69772))
% 51.10/50.83 [6978]P1(f331(f331(f240(a847),f331(a112,x69781)),f331(a112,x69782)))+~P1(f331(f331(f240(a1),f2(a1)),x69782))+~P1(f331(f331(f240(a1),f2(a1)),x69781))+~P1(f331(f331(f240(a1),x69781),x69782))
% 51.10/50.83 [6979]P1(f331(f331(f287(a847),f331(a112,x69791)),f331(a112,x69792)))+~P1(f331(f331(f240(a1),f2(a1)),x69792))+~P1(f331(f331(f240(a1),f2(a1)),x69791))+~P1(f331(f331(f287(a1),x69791),x69792))
% 51.10/50.83 [7210]~P8(x72101)+~P36(x72102)+~P1(f331(f331(f333(a1),x72101),x72102))+P1(f331(f331(f333(a847),f331(a112,x72101)),f331(f311(a1,a847,a112),x72102)))
% 51.10/50.83 [7218]~P1(f331(f331(f241(a847),f331(a112,x72181)),f331(a112,x72182)))+~P1(f331(f331(f240(a1),f2(a1)),x72182))+~P1(f331(f331(f240(a1),f2(a1)),x72181))+P1(f331(f331(f241(a1),x72181),x72182))
% 51.10/50.83 [7219]~P1(f331(f331(f240(a847),f331(a112,x72191)),f331(a112,x72192)))+~P1(f331(f331(f240(a1),f2(a1)),x72192))+~P1(f331(f331(f240(a1),f2(a1)),x72191))+P1(f331(f331(f240(a1),x72191),x72192))
% 51.10/50.83 [7220]~P1(f331(f331(f287(a847),f331(a112,x72201)),f331(a112,x72202)))+~P1(f331(f331(f240(a1),f2(a1)),x72202))+~P1(f331(f331(f240(a1),f2(a1)),x72201))+P1(f331(f331(f287(a1),x72201),x72202))
% 51.10/50.83 [7485]~P102(x74852)+E(x74851,f184(f854(x74852,a840)))+~P1(f331(f68(x74852),x74851))+P1(f331(f331(f240(x74852),f14(x74852,f244(x74852),x74851)),f13(x74852,f239(x74852),x74851)))
% 51.10/50.83 [7810]~P8(x78101)+~P36(x78102)+P1(f331(f331(f333(a1),x78101),x78102))+~P1(f331(f331(f333(a847),f331(a112,x78101)),f331(f311(a1,a847,a112),x78102)))
% 51.10/50.83 [5695]~P133(x56952)+E(x56951,f2(a1))+E(f331(f86(x56952),f331(f110(x56952),f331(f86(a1),x56951))),f331(f110(x56952),x56951))+~P1(f331(f331(f241(a1),x56951),f2(a1)))
% 51.10/50.83 [5772]~P90(x57721)+~P91(x57721)+~P31(x57721,f331(f111(x57721),x57722))+P31(x57721,f331(f111(x57721),f331(f331(f87(a1),x57722),x57722)))
% 51.10/50.83 [6112]~P67(x61122)+E(x61121,f184(f854(x61122,a840)))+E(f17(x61122,f331(f311(x61122,x61122,f86(x61122)),x61121)),f331(f86(x61122),f16(x61122,x61121)))+~P1(f331(f68(x61122),x61121))
% 51.10/50.83 [6113]~P67(x61132)+E(x61131,f184(f854(x61132,a840)))+E(f16(x61132,f331(f311(x61132,x61132,f86(x61132)),x61131)),f331(f86(x61132),f17(x61132,x61131)))+~P1(f331(f68(x61132),x61131))
% 51.10/50.83 [6143]~P90(x61431)+~P91(x61431)+P31(x61431,f331(f111(x61431),x61432))+~P31(x61431,f331(f111(x61431),f331(f331(f87(a1),x61432),x61432)))
% 51.10/50.83 [6238]E(x62381,f2(a1))+E(f331(a63,f62(f331(f86(a1),x62381),f331(f86(a1),x62382))),f58(x62381,x62382))+P1(f331(f331(f240(a1),f2(a1)),x62382))+~P1(f331(f331(f240(a1),f2(a1)),x62381))
% 51.10/50.83 [7122]~P1(f331(f331(f241(a1),f2(a1)),x71222))+~P1(f331(f331(f240(a1),f2(a1)),x71221))+~P1(f331(f331(f240(a1),x71222),x71221))+P1(f331(f331(f241(a1),f2(a1)),f331(f331(f48(a1),x71221),x71222)))
% 51.10/50.83 [7562]~E(x75622,f2(a1))+E(f217(x75621,x75622),f331(f331(f249(a1,a1),f2(a1)),f85(a1)))+P1(f331(f331(f241(a1),x75622),f2(a1)))+~P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),x75621),x75622)))
% 51.10/50.83 [7563]~E(x75631,f2(a1))+E(f217(x75631,x75632),f331(f331(f249(a1,a1),f2(a1)),f85(a1)))+P1(f331(f331(f241(a1),x75632),f2(a1)))+~P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),x75631),x75632)))
% 51.10/50.83 [8566]~P36(x85662)+~P36(x85661)+P1(f331(f331(f241(f854(a847,a840)),f331(f311(a1,a847,a112),x85661)),f331(f311(a1,a847,a112),x85662)))+~P1(f331(f331(f241(f854(a1,a840)),x85661),x85662))
% 51.10/50.83 [8567]~P36(x85672)+~P36(x85671)+P1(f331(f331(f240(f854(a847,a840)),f331(f311(a1,a847,a112),x85671)),f331(f311(a1,a847,a112),x85672)))+~P1(f331(f331(f240(f854(a1,a840)),x85671),x85672))
% 51.10/50.83 [8840]~P36(x88402)+~P36(x88401)+~P1(f331(f331(f241(f854(a847,a840)),f331(f311(a1,a847,a112),x88401)),f331(f311(a1,a847,a112),x88402)))+P1(f331(f331(f241(f854(a1,a840)),x88401),x88402))
% 51.10/50.83 [8841]~P36(x88412)+~P36(x88411)+~P1(f331(f331(f240(f854(a847,a840)),f331(f311(a1,a847,a112),x88411)),f331(f311(a1,a847,a112),x88412)))+P1(f331(f331(f240(f854(a1,a840)),x88411),x88412))
% 51.10/50.83 [9276]E(x92761,f2(a1))+E(x92762,f2(a1))+E(f331(f331(f93(a1,f853(a1,a1)),f331(f331(a219,x92762),x92761)),f331(f331(f20(a1,a1,f853(a1,a1)),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f331(f48(a1),x92762))),f331(f48(a1),x92761))),f217(x92762,x92761))+P1(f331(f331(f241(a1),x92761),f2(a1)))
% 51.10/50.83 [8132]~P91(x81322)+~P86(x81322)+~P1(f331(f331(f241(x81322),f331(f111(x81322),x81321)),f85(x81322)))+P1(f331(f331(f241(a1),x81321),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))
% 51.10/50.83 [8133]~P91(x81332)+~P86(x81332)+~P1(f331(f331(f240(x81332),f331(f111(x81332),x81331)),f85(x81332)))+P1(f331(f331(f240(a1),x81331),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))
% 51.10/50.83 [8408]~P86(x84081)+~P91(x84081)+P1(f331(f331(f241(x84081),f331(f111(x84081),x84082)),f85(x84081)))+~P1(f331(f331(f241(a1),x84082),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))
% 51.10/50.83 [8409]~P86(x84091)+~P91(x84091)+P1(f331(f331(f240(x84091),f331(f111(x84091),x84092)),f85(x84091)))+~P1(f331(f331(f240(a1),x84092),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))
% 51.10/50.83 [8591]~P91(x85912)+~P86(x85912)+~P1(f331(f331(f241(x85912),f85(x85912)),f331(f111(x85912),x85911)))+P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),x85911))
% 51.10/50.83 [8592]~P91(x85922)+~P86(x85922)+~P1(f331(f331(f240(x85922),f85(x85922)),f331(f111(x85922),x85921)))+P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),x85921))
% 51.10/50.83 [8922]~P86(x89221)+~P91(x89221)+P1(f331(f331(f241(x89221),f85(x89221)),f331(f111(x89221),x89222)))+~P1(f331(f331(f241(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),x89222))
% 51.10/50.83 [8923]~P86(x89231)+~P91(x89231)+P1(f331(f331(f240(x89231),f85(x89231)),f331(f111(x89231),x89232)))+~P1(f331(f331(f240(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),x89232))
% 51.10/50.83 [9401]~P120(x94012)+E(x94011,f85(x94012))+E(x94011,f331(f86(x94012),f85(x94012)))+~E(f331(f331(f250(x94012),x94011),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f85(x94012))
% 51.10/50.83 [9655]~P60(x96551)+~P91(x96551)+~P1(f331(f331(f241(x96551),f2(x96551)),x96552))+P1(f331(f331(f241(x96551),f2(x96551)),f331(f331(f291(x96551),x96552),f331(f111(x96551),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.83 [9656]~P60(x96561)+~P91(x96561)+~P1(f331(f331(f241(x96561),f2(x96561)),x96562))+P1(f331(f331(f241(x96561),f2(x96561)),f331(f331(f291(x96561),x96562),f331(f111(x96561),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.83 [9712]~P60(x97121)+~P91(x97121)+P1(f331(f331(f241(x97121),f2(x97121)),x97122))+~P1(f331(f331(f241(x97121),f2(x97121)),f331(f331(f291(x97121),x97122),f331(f111(x97121),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.83 [9993]~P133(x99932)+E(x99931,f2(a1))+P1(f331(f331(f241(a1),x99931),f2(a1)))+E(f331(f331(f259(a1,a1,x99932),f331(f331(f9(a1,f854(a1,f854(x99932,x99932)),f854(a1,x99932)),f331(f331(f10(f854(f854(x99932,x99932),x99932),f854(f854(a1,f854(x99932,x99932)),f854(a1,x99932)),a1),f10(f854(x99932,x99932),x99932,a1)),f331(f331(f10(x99932,f854(f854(x99932,x99932),x99932),a1),f93(x99932,x99932)),f110(x99932)))),f331(f331(f9(a1,f854(x99932,x99932),f854(x99932,x99932)),f331(f331(f10(f854(x99932,f854(x99932,x99932)),f854(f854(x99932,x99932),f854(x99932,x99932)),a1),f20(x99932,x99932,x99932)),f331(f331(f9(a1,f854(x99932,x99932),f854(x99932,f854(x99932,x99932))),f331(f331(f10(f854(x99932,f854(x99932,x99932)),f854(f854(x99932,x99932),f854(x99932,f854(x99932,x99932))),a1),f10(x99932,f854(x99932,x99932),x99932)),f331(f331(f10(a840,f854(x99932,f854(x99932,x99932)),a1),f103(x99932)),f331(f331(f9(a1,a1,a840),a328),f2(a1))))),f331(f331(f20(x99932,x99932,x99932),f87(x99932)),f7(x99932))))),f331(f331(f9(x99932,x99932,x99932),f331(f331(f10(x99932,f854(x99932,x99932),x99932),f87(x99932)),f331(f331(f20(x99932,x99932,x99932),f87(x99932)),f7(x99932)))),f85(x99932))))),f58(x99931,f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f110(x99932),x99931))
% 51.10/50.83 [9759]P1(f331(f331(f240(a1),x97591),f2(a1)))+P1(f331(f331(f241(a1),x97592),x97591))+~P1(f331(f320(f853(a1,a1),a67),f331(f331(f249(a1,a1),x97592),x97591)))+E(f331(f55(x97591),f59(x97592,f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97591))),f59(x97592,x97591))
% 51.10/50.83 [9763]P1(f331(f331(f240(a1),x97631),f2(a1)))+~P1(f331(f320(f853(a1,a1),a64),f331(f331(f249(a1,a1),x97632),x97631)))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),x97632),x97631)))+E(f331(f55(x97631),f62(x97632,f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),x97631))),f62(x97632,x97631))
% 51.10/50.83 [4730]~P90(x47303)+~P91(x47303)+E(x47301,x47302)+~E(f331(f111(x47303),x47301),f331(f111(x47303),x47302))
% 51.10/50.83 [5871]~P1(f331(x58711,x58712))+~P1(f331(x58711,x58713))+~P1(f331(f331(f240(a847),x58713),f786(x58712,x58711)))+P1(f331(x58711,f2(a847)))
% 51.10/50.83 [6304]P140(x63042,x63041,x63043)+E(x63041,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f774(x63043,x63041,x63042)))+P1(f331(f331(f241(a1),x63041),f2(a1)))
% 51.10/50.83 [6305]P141(x63052,x63051,x63053)+E(x63051,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f783(x63053,x63051,x63052)))+P1(f331(f331(f241(a1),x63051),f2(a1)))
% 51.10/50.83 [6437]P140(x64371,x64372,x64373)+~P1(f331(x64371,x64373))+P1(f331(f331(f240(a1),f2(a1)),f774(x64373,x64372,x64371)))+P1(f331(f331(f241(a1),x64372),f2(a1)))
% 51.10/50.83 [6461]P141(x64611,x64612,x64613)+P1(f331(f331(f240(a1),f2(a1)),f783(x64613,x64612,x64611)))+~P1(f331(x64611,f2(a1)))+P1(f331(f331(f241(a1),x64612),f2(a1)))
% 51.10/50.83 [6493]P140(x64932,x64931,x64933)+E(x64931,f2(a1))+~P1(f331(x64932,f774(x64933,x64931,x64932)))+P1(f331(f331(f241(a1),x64931),f2(a1)))
% 51.10/50.83 [6494]P141(x64942,x64941,x64943)+E(x64941,f2(a1))+~P1(f331(x64942,f784(x64943,x64941,x64942)))+P1(f331(f331(f241(a1),x64941),f2(a1)))
% 51.10/50.83 [6597]~P102(x65971)+~P7(x65971)+~P1(f331(f331(f241(x65971),x65972),f49(x65971,x65973)))+P1(f331(f331(f241(x65971),x65972),f660(x65973,x65972,x65971)))
% 51.10/50.83 [6607]P140(x66071,x66072,x66073)+~P1(f331(x66071,x66073))+~P1(f331(x66071,f774(x66073,x66072,x66071)))+P1(f331(f331(f241(a1),x66072),f2(a1)))
% 51.10/50.83 [6640]P141(x66401,x66402,x66403)+~P1(f331(x66401,f784(x66403,x66402,x66401)))+~P1(f331(x66401,f2(a1)))+P1(f331(f331(f241(a1),x66402),f2(a1)))
% 51.10/50.83 [6902]P140(x69022,x69021,x69023)+E(x69021,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f774(x69023,x69021,x69022)))+P1(f331(f331(f241(a1),x69021),f780(x69023,x69021,x69022)))
% 51.10/50.83 [6903]P141(x69032,x69031,x69033)+E(x69031,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f783(x69033,x69031,x69032)))+P1(f331(f331(f241(a1),x69031),f782(x69033,x69031,x69032)))
% 51.10/50.83 [7020]P140(x70201,x70202,x70203)+~P1(f331(x70201,x70203))+P1(f331(f331(f240(a1),f2(a1)),f774(x70203,x70202,x70201)))+P1(f331(f331(f241(a1),x70202),f780(x70203,x70202,x70201)))
% 51.10/50.83 [7041]P141(x70411,x70412,x70413)+P1(f331(f331(f240(a1),f2(a1)),f783(x70413,x70412,x70411)))+P1(f331(f331(f241(a1),x70412),f782(x70413,x70412,x70411)))+~P1(f331(x70411,f2(a1)))
% 51.10/50.83 [7072]P140(x70722,x70721,x70723)+E(x70721,f2(a1))+~P1(f331(x70722,f774(x70723,x70721,x70722)))+P1(f331(f331(f241(a1),x70721),f780(x70723,x70721,x70722)))
% 51.10/50.83 [7073]P141(x70732,x70731,x70733)+E(x70731,f2(a1))+~P1(f331(x70732,f784(x70733,x70731,x70732)))+P1(f331(f331(f241(a1),x70731),f782(x70733,x70731,x70732)))
% 51.10/50.83 [7113]P140(x71132,x71131,x71133)+E(x71131,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f774(x71133,x71131,x71132)))+~P1(f331(x71132,f780(x71133,x71131,x71132)))
% 51.10/50.83 [7114]P141(x71142,x71141,x71143)+E(x71141,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f783(x71143,x71141,x71142)))+~P1(f331(x71142,f785(x71143,x71141,x71142)))
% 51.10/50.83 [7217]P140(x72171,x72172,x72173)+~P1(f331(x72171,x72173))+~P1(f331(x72171,f774(x72173,x72172,x72171)))+P1(f331(f331(f241(a1),x72172),f780(x72173,x72172,x72171)))
% 51.10/50.83 [7233]P141(x72331,x72332,x72333)+~P1(f331(x72331,f784(x72333,x72332,x72331)))+P1(f331(f331(f241(a1),x72332),f782(x72333,x72332,x72331)))+~P1(f331(x72331,f2(a1)))
% 51.10/50.83 [7239]P140(x72391,x72392,x72393)+~P1(f331(x72391,x72393))+P1(f331(f331(f240(a1),f2(a1)),f774(x72393,x72392,x72391)))+~P1(f331(x72391,f780(x72393,x72392,x72391)))
% 51.10/50.83 [7257]P141(x72571,x72572,x72573)+P1(f331(f331(f240(a1),f2(a1)),f783(x72573,x72572,x72571)))+~P1(f331(x72571,f785(x72573,x72572,x72571)))+~P1(f331(x72571,f2(a1)))
% 51.10/50.83 [7281]P140(x72812,x72811,x72813)+E(x72811,f2(a1))+~P1(f331(x72812,f774(x72813,x72811,x72812)))+~P1(f331(x72812,f780(x72813,x72811,x72812)))
% 51.10/50.83 [7282]P141(x72822,x72821,x72823)+E(x72821,f2(a1))+~P1(f331(x72822,f784(x72823,x72821,x72822)))+~P1(f331(x72822,f785(x72823,x72821,x72822)))
% 51.10/50.83 [7378]P140(x73781,x73782,x73783)+~P1(f331(x73781,x73783))+~P1(f331(x73781,f774(x73783,x73782,x73781)))+~P1(f331(x73781,f780(x73783,x73782,x73781)))
% 51.10/50.83 [7393]P141(x73931,x73932,x73933)+~P1(f331(x73931,f784(x73933,x73932,x73931)))+~P1(f331(x73931,f785(x73933,x73932,x73931)))+~P1(f331(x73931,f2(a1)))
% 51.10/50.83 [7445]P140(x74452,x74451,x74453)+E(x74451,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f774(x74453,x74451,x74452)))+P1(f331(f331(f240(a1),f780(x74453,x74451,x74452)),f2(a1)))
% 51.10/50.83 [7446]P141(x74462,x74461,x74463)+E(x74461,f2(a1))+P1(f331(f331(f240(a1),f2(a1)),f783(x74463,x74461,x74462)))+P1(f331(f331(f240(a1),f782(x74463,x74461,x74462)),f2(a1)))
% 51.10/50.83 [7447]~P80(x74471)+~P1(f331(f331(f241(x74471),x74473),f2(x74471)))+~P1(f331(f331(f241(x74471),x74472),f2(x74471)))+P1(f331(f331(f241(x74471),f331(f331(f87(x74471),x74472),x74473)),f2(x74471)))
% 51.10/50.83 [7448]~P80(x74481)+~P1(f331(f331(f240(x74481),x74482),f2(x74481)))+~P1(f331(f331(f241(x74481),x74483),f2(x74481)))+P1(f331(f331(f241(x74481),f331(f331(f87(x74481),x74482),x74483)),f2(x74481)))
% 51.10/50.83 [7449]~P80(x74491)+~P1(f331(f331(f240(x74491),x74493),f2(x74491)))+~P1(f331(f331(f241(x74491),x74492),f2(x74491)))+P1(f331(f331(f241(x74491),f331(f331(f87(x74491),x74492),x74493)),f2(x74491)))
% 51.10/50.83 [7450]~P80(x74501)+~P1(f331(f331(f240(x74501),x74503),f2(x74501)))+~P1(f331(f331(f240(x74501),x74502),f2(x74501)))+P1(f331(f331(f240(x74501),f331(f331(f87(x74501),x74502),x74503)),f2(x74501)))
% 51.10/50.83 [7451]~P84(x74511)+~P1(f331(f331(f333(x74511),x74513),f181(x74511)))+~P1(f331(f331(f333(x74511),x74512),f181(x74511)))+P1(f331(f331(f333(x74511),f331(f331(f87(x74511),x74512),x74513)),f181(x74511)))
% 51.10/50.83 [7452]~P133(x74521)+~P1(f331(f331(f333(x74521),x74523),f117(x74521)))+~P1(f331(f331(f333(x74521),x74522),f117(x74521)))+P1(f331(f331(f333(x74521),f331(f331(f87(x74521),x74522),x74523)),f117(x74521)))
% 51.10/50.83 [7453]~P84(x74531)+~P1(f331(f331(f333(x74531),x74533),f181(x74531)))+~P1(f331(f331(f333(x74531),x74532),f181(x74531)))+P1(f331(f331(f333(x74531),f331(f331(f88(x74531),x74532),x74533)),f181(x74531)))
% 51.10/50.83 [7454]~P133(x74541)+~P1(f331(f331(f333(x74541),x74543),f117(x74541)))+~P1(f331(f331(f333(x74541),x74542),f117(x74541)))+P1(f331(f331(f333(x74541),f331(f331(f88(x74541),x74542),x74543)),f117(x74541)))
% 51.10/50.83 [7455]~P133(x74551)+~P1(f331(f331(f333(x74551),x74553),f117(x74551)))+~P1(f331(f331(f333(x74551),x74552),f117(x74551)))+P1(f331(f331(f333(x74551),f331(f331(f3(x74551),x74552),x74553)),f117(x74551)))
% 51.10/50.83 [7481]P140(x74813,x74811,x74812)+E(x74811,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x74811),f775(x74812,x74811,x74813))),f774(x74812,x74811,x74813)),x74812)+P1(f331(f331(f241(a1),x74811),f2(a1)))
% 51.10/50.83 [7482]P141(x74823,x74821,x74822)+E(x74821,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x74821),f784(x74822,x74821,x74823))),f783(x74822,x74821,x74823)),x74822)+P1(f331(f331(f241(a1),x74821),f2(a1)))
% 51.10/50.83 [7567]P140(x75671,x75672,x75673)+~P1(f331(x75671,x75673))+P1(f331(f331(f240(a1),f2(a1)),f774(x75673,x75672,x75671)))+P1(f331(f331(f240(a1),f780(x75673,x75672,x75671)),f2(a1)))
% 51.10/50.83 [7598]P141(x75981,x75982,x75983)+P1(f331(f331(f240(a1),f2(a1)),f783(x75983,x75982,x75981)))+~P1(f331(x75981,f2(a1)))+P1(f331(f331(f240(a1),f782(x75983,x75982,x75981)),f2(a1)))
% 51.10/50.83 [7606]P140(x76063,x76061,x76062)+~P1(f331(x76063,x76062))+E(f331(f331(f87(a1),f331(f331(f88(a1),x76061),f775(x76062,x76061,x76063))),f774(x76062,x76061,x76063)),x76062)+P1(f331(f331(f241(a1),x76061),f2(a1)))
% 51.10/50.83 [7611]P140(x76112,x76111,x76113)+E(x76111,f2(a1))+~P1(f331(x76112,f774(x76113,x76111,x76112)))+P1(f331(f331(f240(a1),f780(x76113,x76111,x76112)),f2(a1)))
% 51.10/50.83 [7612]P141(x76122,x76121,x76123)+E(x76121,f2(a1))+~P1(f331(x76122,f784(x76123,x76121,x76122)))+P1(f331(f331(f240(a1),f782(x76123,x76121,x76122)),f2(a1)))
% 51.10/50.83 [7617]P141(x76173,x76171,x76172)+E(f331(f331(f87(a1),f331(f331(f88(a1),x76171),f784(x76172,x76171,x76173))),f783(x76172,x76171,x76173)),x76172)+~P1(f331(x76173,f2(a1)))+P1(f331(f331(f241(a1),x76171),f2(a1)))
% 51.10/50.83 [7670]P140(x76701,x76702,x76703)+~P1(f331(x76701,x76703))+~P1(f331(x76701,f774(x76703,x76702,x76701)))+P1(f331(f331(f240(a1),f780(x76703,x76702,x76701)),f2(a1)))
% 51.10/50.83 [7675]P141(x76751,x76752,x76753)+~P1(f331(x76751,f784(x76753,x76752,x76751)))+~P1(f331(x76751,f2(a1)))+P1(f331(f331(f240(a1),f782(x76753,x76752,x76751)),f2(a1)))
% 51.10/50.83 [7749]~P60(x77491)+~P1(f331(f331(f241(x77491),f331(f331(f291(x77491),x77493),x77492)),f2(x77491)))+P1(f331(f331(f241(x77491),x77492),f2(x77491)))+P1(f331(f331(f241(x77491),x77493),f2(x77491)))
% 51.10/50.83 [7750]~P118(x77501)+~P1(f331(f331(f240(x77501),f331(f331(f88(x77501),x77503),x77502)),f2(x77501)))+P1(f331(f331(f240(x77501),x77502),f2(x77501)))+P1(f331(f331(f240(x77501),x77503),f2(x77501)))
% 51.10/50.83 [7751]~P60(x77511)+~P1(f331(f331(f240(x77511),f331(f331(f291(x77511),x77513),x77512)),f2(x77511)))+P1(f331(f331(f240(x77511),x77512),f2(x77511)))+P1(f331(f331(f240(x77511),x77513),f2(x77511)))
% 51.10/50.83 [7863]P140(x78633,x78631,x78632)+E(x78631,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x78631),f775(x78632,x78631,x78633))),f774(x78632,x78631,x78633)),x78632)+P1(f331(f331(f241(a1),x78631),f780(x78632,x78631,x78633)))
% 51.10/50.83 [7864]P141(x78643,x78641,x78642)+E(x78641,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x78641),f784(x78642,x78641,x78643))),f783(x78642,x78641,x78643)),x78642)+P1(f331(f331(f241(a1),x78641),f782(x78642,x78641,x78643)))
% 51.10/50.83 [7875]P140(x78753,x78751,x78752)+E(x78751,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x78751),f776(x78752,x78751,x78753))),f780(x78752,x78751,x78753)),x78752)+P1(f331(f331(f240(a1),f2(a1)),f774(x78752,x78751,x78753)))
% 51.10/50.83 [7876]P141(x78763,x78761,x78762)+E(x78761,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x78761),f785(x78762,x78761,x78763))),f782(x78762,x78761,x78763)),x78762)+P1(f331(f331(f240(a1),f2(a1)),f783(x78762,x78761,x78763)))
% 51.10/50.83 [7923]P140(x79233,x79231,x79232)+~P1(f331(x79233,x79232))+E(f331(f331(f87(a1),f331(f331(f88(a1),x79231),f775(x79232,x79231,x79233))),f774(x79232,x79231,x79233)),x79232)+P1(f331(f331(f241(a1),x79231),f780(x79232,x79231,x79233)))
% 51.10/50.83 [7934]P141(x79343,x79341,x79342)+E(f331(f331(f87(a1),f331(f331(f88(a1),x79341),f784(x79342,x79341,x79343))),f783(x79342,x79341,x79343)),x79342)+P1(f331(f331(f241(a1),x79341),f782(x79342,x79341,x79343)))+~P1(f331(x79343,f2(a1)))
% 51.10/50.83 [7940]P140(x79403,x79401,x79402)+~P1(f331(x79403,x79402))+E(f331(f331(f87(a1),f331(f331(f88(a1),x79401),f776(x79402,x79401,x79403))),f780(x79402,x79401,x79403)),x79402)+P1(f331(f331(f240(a1),f2(a1)),f774(x79402,x79401,x79403)))
% 51.10/50.83 [7947]P141(x79473,x79471,x79472)+E(f331(f331(f87(a1),f331(f331(f88(a1),x79471),f785(x79472,x79471,x79473))),f782(x79472,x79471,x79473)),x79472)+P1(f331(f331(f240(a1),f2(a1)),f783(x79472,x79471,x79473)))+~P1(f331(x79473,f2(a1)))
% 51.10/50.83 [7957]P140(x79573,x79571,x79572)+E(x79571,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x79571),f775(x79572,x79571,x79573))),f774(x79572,x79571,x79573)),x79572)+~P1(f331(x79573,f780(x79572,x79571,x79573)))
% 51.10/50.83 [7958]P141(x79583,x79581,x79582)+E(x79581,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x79581),f784(x79582,x79581,x79583))),f783(x79582,x79581,x79583)),x79582)+~P1(f331(x79583,f785(x79582,x79581,x79583)))
% 51.10/50.83 [7959]P140(x79593,x79591,x79592)+E(x79591,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x79591),f776(x79592,x79591,x79593))),f780(x79592,x79591,x79593)),x79592)+~P1(f331(x79593,f774(x79592,x79591,x79593)))
% 51.10/50.83 [7960]P141(x79603,x79601,x79602)+E(x79601,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x79601),f785(x79602,x79601,x79603))),f782(x79602,x79601,x79603)),x79602)+~P1(f331(x79603,f784(x79602,x79601,x79603)))
% 51.10/50.83 [8013]P140(x80133,x80131,x80132)+~P1(f331(x80133,x80132))+E(f331(f331(f87(a1),f331(f331(f88(a1),x80131),f775(x80132,x80131,x80133))),f774(x80132,x80131,x80133)),x80132)+~P1(f331(x80133,f780(x80132,x80131,x80133)))
% 51.10/50.83 [8014]P140(x80143,x80141,x80142)+~P1(f331(x80143,x80142))+E(f331(f331(f87(a1),f331(f331(f88(a1),x80141),f776(x80142,x80141,x80143))),f780(x80142,x80141,x80143)),x80142)+~P1(f331(x80143,f774(x80142,x80141,x80143)))
% 51.10/50.83 [8026]P141(x80263,x80261,x80262)+E(f331(f331(f87(a1),f331(f331(f88(a1),x80261),f784(x80262,x80261,x80263))),f783(x80262,x80261,x80263)),x80262)+~P1(f331(x80263,f785(x80262,x80261,x80263)))+~P1(f331(x80263,f2(a1)))
% 51.10/50.83 [8027]P141(x80273,x80271,x80272)+E(f331(f331(f87(a1),f331(f331(f88(a1),x80271),f785(x80272,x80271,x80273))),f782(x80272,x80271,x80273)),x80272)+~P1(f331(x80273,f784(x80272,x80271,x80273)))+~P1(f331(x80273,f2(a1)))
% 51.10/50.83 [8125]P140(x81253,x81251,x81252)+E(x81251,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x81251),f775(x81252,x81251,x81253))),f774(x81252,x81251,x81253)),x81252)+P1(f331(f331(f240(a1),f780(x81252,x81251,x81253)),f2(a1)))
% 51.10/50.83 [8126]P141(x81263,x81261,x81262)+E(x81261,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x81261),f784(x81262,x81261,x81263))),f783(x81262,x81261,x81263)),x81262)+P1(f331(f331(f240(a1),f782(x81262,x81261,x81263)),f2(a1)))
% 51.10/50.83 [8165]P140(x81653,x81651,x81652)+~P1(f331(x81653,x81652))+E(f331(f331(f87(a1),f331(f331(f88(a1),x81651),f775(x81652,x81651,x81653))),f774(x81652,x81651,x81653)),x81652)+P1(f331(f331(f240(a1),f780(x81652,x81651,x81653)),f2(a1)))
% 51.10/50.83 [8170]P141(x81703,x81701,x81702)+E(f331(f331(f87(a1),f331(f331(f88(a1),x81701),f784(x81702,x81701,x81703))),f783(x81702,x81701,x81703)),x81702)+~P1(f331(x81703,f2(a1)))+P1(f331(f331(f240(a1),f782(x81702,x81701,x81703)),f2(a1)))
% 51.10/50.83 [8302]P140(x83023,x83021,x83022)+E(x83021,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x83021),f776(x83022,x83021,x83023))),f780(x83022,x83021,x83023)),x83022)+E(f331(f331(f87(a1),f331(f331(f88(a1),x83021),f775(x83022,x83021,x83023))),f774(x83022,x83021,x83023)),x83022)
% 51.10/50.83 [8303]P141(x83033,x83031,x83032)+E(x83031,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x83031),f785(x83032,x83031,x83033))),f782(x83032,x83031,x83033)),x83032)+E(f331(f331(f87(a1),f331(f331(f88(a1),x83031),f784(x83032,x83031,x83033))),f783(x83032,x83031,x83033)),x83032)
% 51.10/50.83 [8325]P140(x83253,x83251,x83252)+~P1(f331(x83253,x83252))+E(f331(f331(f87(a1),f331(f331(f88(a1),x83251),f776(x83252,x83251,x83253))),f780(x83252,x83251,x83253)),x83252)+E(f331(f331(f87(a1),f331(f331(f88(a1),x83251),f775(x83252,x83251,x83253))),f774(x83252,x83251,x83253)),x83252)
% 51.10/50.83 [8336]P141(x83363,x83361,x83362)+E(f331(f331(f87(a1),f331(f331(f88(a1),x83361),f785(x83362,x83361,x83363))),f782(x83362,x83361,x83363)),x83362)+E(f331(f331(f87(a1),f331(f331(f88(a1),x83361),f784(x83362,x83361,x83363))),f783(x83362,x83361,x83363)),x83362)+~P1(f331(x83363,f2(a1)))
% 51.10/50.83 [8927]~P118(x89271)+~E(x89273,f2(x89271))+~E(x89272,f2(x89271))+P1(f331(f331(f240(x89271),f331(f331(f87(x89271),f331(f331(f88(x89271),x89272),x89272)),f331(f331(f88(x89271),x89273),x89273))),f2(x89271)))
% 51.10/50.83 [9943]~P86(x99431)+~E(x99433,f2(x99431))+~E(x99432,f2(x99431))+P1(f331(f331(f240(x99431),f331(f331(f87(x99431),f331(f331(f250(x99431),x99432),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x99431),x99433),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))),f2(x99431)))
% 51.10/50.83 [4680]~E(x46803,x46801)+~P114(x46802)+E(x46801,f2(x46802))+E(f331(f331(f291(x46802),x46803),x46801),f85(x46802))
% 51.10/50.83 [4731]~P95(x47311)+~E(x47313,f184(x47311))+~E(x47312,f184(x47311))+E(f331(f331(f108(x47311),x47312),x47313),f184(x47311))
% 51.10/50.83 [4732]~P99(x47321)+~E(x47323,f247(x47321))+~E(x47322,f247(x47321))+E(f331(f331(f109(x47321),x47322),x47323),f247(x47321))
% 51.10/50.83 [4820]~P114(x48203)+E(x48201,x48202)+E(x48202,f2(x48203))+~E(f331(f331(f291(x48203),x48201),x48202),f85(x48203))
% 51.10/50.83 [4836]~P134(x48362)+E(x48361,f2(x48362))+E(x48363,f2(x48362))+~E(f331(f331(f88(x48362),x48363),x48361),f2(x48362))
% 51.10/50.83 [4837]~P127(x48372)+E(x48371,f2(x48372))+E(x48373,f2(x48372))+~E(f331(f331(f88(x48372),x48373),x48371),f2(x48372))
% 51.10/50.83 [4838]~P127(x48382)+E(x48381,f2(x48382))+E(x48383,f2(x48382))+~E(f331(f331(f88(x48382),x48383),x48381),f2(x48382))
% 51.10/50.83 [5204]~P112(x52043)+E(x52041,x52042)+E(x52041,f331(f86(x52043),x52042))+~E(f331(f331(f88(x52043),x52041),x52041),f331(f331(f88(x52043),x52042),x52042))
% 51.10/50.83 [5240]~P93(x52401)+E(f331(f86(x52401),x52402),x52403)+~E(f331(f331(f108(x52401),x52402),x52403),f247(x52401))+~E(f331(f331(f109(x52401),x52402),x52403),f184(x52401))
% 51.10/50.83 [5315]~P86(x53153)+E(x53151,x53152)+P1(f331(f331(f241(x53153),x53152),x53151))+P1(f331(f331(f241(x53153),x53151),x53152))
% 51.10/50.83 [5316]~P102(x53163)+E(x53161,x53162)+P1(f331(f331(f241(x53163),x53162),x53161))+P1(f331(f331(f241(x53163),x53161),x53162))
% 51.10/50.83 [5317]~P102(x53173)+E(x53171,x53172)+P1(f331(f331(f241(x53173),x53172),x53171))+P1(f331(f331(f241(x53173),x53171),x53172))
% 51.10/50.83 [5318]~P102(x53183)+E(x53181,x53182)+P1(f331(f331(f241(x53183),x53182),x53181))+P1(f331(f331(f241(x53183),x53181),x53182))
% 51.10/50.83 [5319]~P102(x53193)+E(x53191,x53192)+P1(f331(f331(f241(x53193),x53192),x53191))+P1(f331(f331(f241(x53193),x53191),x53192))
% 51.10/50.83 [5320]~P102(x53203)+E(x53201,x53202)+P1(f331(f331(f241(x53203),x53202),x53201))+P1(f331(f331(f241(x53203),x53201),x53202))
% 51.10/50.83 [5321]~P102(x53213)+E(x53211,x53212)+P1(f331(f331(f241(x53213),x53212),x53211))+P1(f331(f331(f241(x53213),x53211),x53212))
% 51.10/50.83 [5322]~E(x53222,x53223)+~P102(x53221)+P1(f331(f331(f240(x53221),x53222),x53223))+P1(f331(f331(f241(x53221),x53222),x53223))
% 51.10/50.83 [5485]P140(x54852,x54851,x54853)+E(x54851,f2(a1))+P1(f331(f331(f241(a1),x54851),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x54851))
% 51.10/50.83 [5486]P141(x54862,x54861,x54863)+E(x54861,f2(a1))+P1(f331(f331(f241(a1),x54861),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x54861))
% 51.10/50.83 [5512]E(x55121,x55122)+P1(f331(f331(x55123,x55121),x55122))+P1(f331(f331(f241(a847),x55122),x55121))+P1(f331(f331(f241(a847),x55121),x55122))
% 51.10/50.83 [5572]~P88(x55723)+E(x55721,x55722)+~P1(f331(f331(f240(x55723),x55722),x55721))+P1(f331(f331(f241(x55723),x55722),x55721))
% 51.10/50.83 [5573]~P88(x55733)+E(x55731,x55732)+~P1(f331(f331(f240(x55733),x55731),x55732))+P1(f331(f331(f241(x55733),x55731),x55732))
% 51.10/50.83 [5574]~P88(x55743)+E(x55741,x55742)+~P1(f331(f331(f240(x55743),x55741),x55742))+P1(f331(f331(f241(x55743),x55741),x55742))
% 51.10/50.83 [5575]~P88(x55753)+E(x55751,x55752)+~P1(f331(f331(f240(x55753),x55751),x55752))+P1(f331(f331(f241(x55753),x55751),x55752))
% 51.10/50.83 [5576]~P88(x55763)+E(x55761,x55762)+~P1(f331(f331(f240(x55763),x55761),x55762))+P1(f331(f331(f241(x55763),x55761),x55762))
% 51.10/50.83 [5577]~P88(x55773)+E(x55771,x55772)+~P1(f331(f331(f240(x55773),x55771),x55772))+P1(f331(f331(f241(x55773),x55771),x55772))
% 51.10/50.83 [5578]~P88(x55783)+E(x55781,x55782)+~P1(f331(f331(f240(x55783),x55781),x55782))+P1(f331(f331(f241(x55783),x55781),x55782))
% 51.10/50.83 [5579]~P102(x55793)+E(x55791,x55792)+~P1(f331(f331(f240(x55793),x55791),x55792))+P1(f331(f331(f241(x55793),x55791),x55792))
% 51.10/50.83 [5580]~P102(x55803)+E(x55801,x55802)+~P1(f331(f331(f240(x55803),x55801),x55802))+P1(f331(f331(f241(x55803),x55801),x55802))
% 51.10/50.83 [5692]P140(x56921,x56922,x56923)+~P1(f331(x56921,x56923))+P1(f331(f331(f241(a1),x56922),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x56922))
% 51.10/50.83 [5743]P141(x57431,x57432,x57433)+~P1(f331(x57431,f2(a1)))+P1(f331(f331(f241(a1),x57432),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x57432))
% 51.10/50.83 [5747]~P97(x57471)+E(f331(f331(f108(x57471),x57472),f12(x57471,x57473)),x57472)+~P1(f331(f68(x57471),x57473))+~P1(f331(f331(f333(x57471),x57472),x57473))
% 51.10/50.83 [5748]~P97(x57481)+E(f331(f331(f109(x57481),x57482),f15(x57481,x57483)),x57482)+~P1(f331(f68(x57481),x57483))+~P1(f331(f331(f333(x57481),x57482),x57483))
% 51.10/50.83 [5782]~P102(x57821)+E(f331(f331(f244(x57821),x57822),f17(x57821,x57823)),f17(x57821,x57823))+~P1(f331(f68(x57821),x57823))+~P1(f331(f331(f333(x57821),x57822),x57823))
% 51.10/50.83 [5783]~P102(x57831)+E(f331(f331(f239(x57831),x57832),f16(x57831,x57833)),f16(x57831,x57833))+~P1(f331(f68(x57831),x57833))+~P1(f331(f331(f333(x57831),x57832),x57833))
% 51.10/50.83 [5784]~P97(x57841)+E(f331(f331(f108(x57841),x57842),f15(x57841,x57843)),f15(x57841,x57843))+~P1(f331(f68(x57841),x57843))+~P1(f331(f331(f333(x57841),x57842),x57843))
% 51.10/50.83 [5785]~P97(x57851)+E(f331(f331(f109(x57851),x57852),f12(x57851,x57853)),f12(x57851,x57853))+~P1(f331(f68(x57851),x57853))+~P1(f331(f331(f333(x57851),x57852),x57853))
% 51.10/50.83 [5822]E(x58221,x58222)+~P88(x58223)+~P1(f331(f331(f240(x58223),x58222),x58221))+~P1(f331(f331(f240(x58223),x58221),x58222))
% 51.10/50.83 [5823]E(x58231,x58232)+~P88(x58233)+~P1(f331(f331(f240(x58233),x58232),x58231))+~P1(f331(f331(f240(x58233),x58231),x58232))
% 51.10/50.83 [5824]E(x58241,x58242)+~P88(x58243)+~P1(f331(f331(f240(x58243),x58242),x58241))+~P1(f331(f331(f240(x58243),x58241),x58242))
% 51.10/50.83 [5825]E(x58251,x58252)+~P88(x58253)+~P1(f331(f331(f240(x58253),x58252),x58251))+~P1(f331(f331(f240(x58253),x58251),x58252))
% 51.10/50.83 [5827]~E(x58271,x58272)+~P102(x58273)+~P1(f331(f331(f241(x58273),x58271),x58272))+~P1(f331(f331(f240(x58273),x58271),x58272))
% 51.10/50.83 [5968]~P105(x59681)+P1(f331(f331(f240(x59681),x59683),x59682))+~P1(f331(f331(f240(x59681),x59682),x59683))+P1(f331(f331(f241(x59681),x59682),x59683))
% 51.10/50.83 [5992]~P102(x59921)+~P1(f331(f68(x59921),x59923))+P1(f331(f331(f240(x59921),x59922),f16(x59921,x59923)))+~P1(f331(f331(f333(x59921),x59922),x59923))
% 51.10/50.83 [6046]~P102(x60461)+E(f331(f331(f244(x60461),x60462),f13(x60461,f239(x60461),x60463)),x60462)+~P1(f331(f68(x60461),x60463))+~P1(f331(f331(f333(x60461),x60462),x60463))
% 51.10/50.83 [6047]~P102(x60471)+E(f331(f331(f239(x60471),x60472),f14(x60471,f244(x60471),x60473)),x60472)+~P1(f331(f68(x60471),x60473))+~P1(f331(f331(f333(x60471),x60472),x60473))
% 51.10/50.83 [6189]E(x61891,x61892)+~E(f331(f331(f3(a847),x61891),x61893),f331(f331(f3(a847),x61892),x61893))+~P1(f331(f331(f240(a847),x61893),x61891))+~P1(f331(f331(f240(a847),x61893),x61892))
% 51.10/50.83 [6217]~P102(x62171)+~P1(f331(f68(x62171),x62172))+~P1(f331(f331(f333(x62171),x62173),x62172))+P1(f331(f331(f240(x62171),f17(x62171,x62172)),x62173))
% 51.10/50.83 [6260]E(x62601,f2(a847))+~P1(f331(f60(x62603,x62601),x62602))+P1(f331(f331(f241(a847),f2(a847)),x62601))+P1(f331(f331(f241(a847),x62601),f331(f258(a847,a847),x62602)))
% 51.10/50.83 [6283]P140(x62832,x62831,x62833)+E(x62831,f2(a1))+P1(f331(f331(f241(a1),x62831),f780(x62833,x62831,x62832)))+P1(f331(f331(f241(a1),f2(a1)),x62831))
% 51.10/50.83 [6284]P141(x62842,x62841,x62843)+E(x62841,f2(a1))+P1(f331(f331(f241(a1),x62841),f782(x62843,x62841,x62842)))+P1(f331(f331(f241(a1),f2(a1)),x62841))
% 51.10/50.83 [6285]~P102(x62851)+E(f331(f331(f244(x62851),x62852),f14(x62851,f244(x62851),x62853)),f14(x62851,f244(x62851),x62853))+~P1(f331(f68(x62851),x62853))+~P1(f331(f331(f333(x62851),x62852),x62853))
% 51.10/50.83 [6286]~P102(x62861)+E(f331(f331(f239(x62861),x62862),f13(x62861,f239(x62861),x62863)),f13(x62861,f239(x62861),x62863))+~P1(f331(f68(x62861),x62863))+~P1(f331(f331(f333(x62861),x62862),x62863))
% 51.10/50.83 [6293]~P1(f331(x62931,x62932))+P1(f331(x62931,f802(x62932,x62931,x62933)))+P1(f331(x62931,f2(a847)))+~P1(f331(f331(f241(a847),x62932),x62933))
% 51.10/50.83 [6331]~P1(f331(f331(f287(a847),x63312),x63311))+~P1(f331(f331(f287(a847),x63311),x63313))+P1(f331(f331(f287(a847),x63311),x63312))+P1(f331(f331(f287(a847),x63312),x63313))
% 51.10/50.83 [6332]~P1(f331(f331(f287(a847),x63323),x63322))+~P1(f331(f331(f287(a847),x63322),x63321))+P1(f331(f331(f287(a847),x63321),x63322))+P1(f331(f331(f287(a847),x63323),x63321))
% 51.10/50.83 [6352]~P1(f331(x63521,x63522))+~P1(f331(f68(x63523),x63522))+P1(f331(x63521,f440(x63521,x63522,x63523)))+P1(f331(x63521,f184(f854(x63523,a840))))
% 51.10/50.83 [6367]~P86(x63671)+~P91(x63671)+P1(f331(f331(f241(x63671),f331(f111(x63671),x63672)),f331(f111(x63671),x63673)))+~P1(f331(f331(f241(a1),x63672),x63673))
% 51.10/50.83 [6368]~P86(x63681)+~P91(x63681)+P1(f331(f331(f240(x63681),f331(f111(x63681),x63682)),f331(f111(x63681),x63683)))+~P1(f331(f331(f240(a1),x63682),x63683))
% 51.10/50.83 [6371]~P1(f331(x63711,x63713))+~P1(f331(f68(x63712),x63713))+P1(f331(f68(x63712),f440(x63711,x63713,x63712)))+P1(f331(x63711,f184(f854(x63712,a840))))
% 51.10/50.83 [6405]P140(x64051,x64052,x64053)+~P1(f331(x64051,x64053))+P1(f331(f331(f241(a1),x64052),f780(x64053,x64052,x64051)))+P1(f331(f331(f241(a1),f2(a1)),x64052))
% 51.10/50.83 [6444]P141(x64441,x64442,x64443)+P1(f331(f331(f241(a1),x64442),f782(x64443,x64442,x64441)))+~P1(f331(x64441,f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x64442))
% 51.10/50.83 [6472]~P104(x64721)+~P92(x64721)+E(f331(f331(f244(x64721),f331(f111(x64721),x64722)),f331(f111(x64721),x64723)),f331(f111(x64721),x64723))+P1(f331(f331(f240(x64721),f331(f111(x64721),x64722)),f331(f111(x64721),x64723)))
% 51.10/50.83 [6473]~P104(x64731)+~P92(x64731)+E(f331(f331(f239(x64731),f331(f111(x64731),x64732)),f331(f111(x64731),x64733)),f331(f111(x64731),x64732))+P1(f331(f331(f240(x64731),f331(f111(x64731),x64732)),f331(f111(x64731),x64733)))
% 51.10/50.83 [6480]E(x64801,f2(a847))+~P1(f331(f60(x64803,x64801),x64802))+~P1(f331(f331(f241(a847),f2(a847)),x64801))+P1(f331(f331(f240(a847),f2(a847)),f331(f258(a847,a847),x64802)))
% 51.10/50.83 [6486]~P1(f331(f331(f287(a847),x64861),x64863))+~P1(f331(f331(f287(a847),x64862),x64861))+~P1(f331(f331(f287(a847),x64863),x64862))+P1(f331(f331(f287(a847),x64861),x64862))
% 51.10/50.83 [6487]~P1(f331(f331(f287(a847),x64871),x64873))+~P1(f331(f331(f287(a847),x64872),x64871))+P1(f331(f331(f287(a847),x64871),x64872))+~P1(f331(f331(f287(a847),x64873),x64872))
% 51.10/50.83 [6535]P140(x65352,x65351,x65353)+E(x65351,f2(a1))+~P1(f331(x65352,f780(x65353,x65351,x65352)))+P1(f331(f331(f241(a1),f2(a1)),x65351))
% 51.10/50.83 [6536]P141(x65362,x65361,x65363)+E(x65361,f2(a1))+~P1(f331(x65362,f785(x65363,x65361,x65362)))+P1(f331(f331(f241(a1),f2(a1)),x65361))
% 51.10/50.83 [6556]~P5(x65561)+~P92(x65561)+~E(f57(x65561,f331(f111(x65561),x65563),f331(f111(x65561),x65562)),f2(x65561))+P1(f331(f331(f287(x65561),f331(f111(x65561),x65562)),f331(f111(x65561),x65563)))
% 51.10/50.83 [6630]P140(x66301,x66302,x66303)+~P1(f331(x66301,x66303))+~P1(f331(x66301,f780(x66303,x66302,x66301)))+P1(f331(f331(f241(a1),f2(a1)),x66302))
% 51.10/50.83 [6660]P141(x66601,x66602,x66603)+~P1(f331(x66601,f785(x66603,x66602,x66601)))+~P1(f331(x66601,f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x66602))
% 51.10/50.83 [6671]E(x66711,f2(a847))+~P1(f331(f60(x66713,x66711),x66712))+P1(f331(f331(f240(a847),f331(f258(a847,a847),x66712)),f2(a847)))+P1(f331(f331(f241(a847),f2(a847)),x66711))
% 51.10/50.83 [6776]~P91(x67763)+~P86(x67763)+~P1(f331(f331(f241(x67763),f331(f111(x67763),x67761)),f331(f111(x67763),x67762)))+P1(f331(f331(f241(a1),x67761),x67762))
% 51.10/50.83 [6777]~P91(x67773)+~P86(x67773)+~P1(f331(f331(f240(x67773),f331(f111(x67773),x67771)),f331(f111(x67773),x67772)))+P1(f331(f331(f240(a1),x67771),x67772))
% 51.10/50.83 [6806]~P102(x68061)+~P16(x68061,x68063)+P16(x68061,f331(f331(f145(x68061),x68062),x68063))+~P1(f331(f331(f240(x68061),x68062),f763(x68063,x68062,x68061)))
% 51.10/50.83 [6807]~P102(x68071)+~P16(x68071,x68073)+P16(x68071,f331(f331(f145(x68071),x68072),x68073))+~P1(f331(f331(f240(x68071),x68072),f766(x68073,x68072,x68071)))
% 51.10/50.83 [6880]~P5(x68801)+~P92(x68801)+E(f57(x68801,f331(f111(x68801),x68802),f331(f111(x68801),x68803)),f2(x68801))+~P1(f331(f331(f287(x68801),f331(f111(x68801),x68803)),f331(f111(x68801),x68802)))
% 51.10/50.83 [6894]P140(x68942,x68941,x68943)+E(x68941,f2(a1))+P1(f331(f331(f241(a1),x68941),f2(a1)))+P1(f331(f331(f241(a1),f774(x68943,x68941,x68942)),x68941))
% 51.10/50.83 [6895]P141(x68952,x68951,x68953)+E(x68951,f2(a1))+P1(f331(f331(f241(a1),x68951),f2(a1)))+P1(f331(f331(f241(a1),f783(x68953,x68951,x68952)),x68951))
% 51.10/50.83 [6900]~P102(x69001)+~P92(x69001)+P1(f331(f331(f241(x69001),f331(f111(x69001),x69002)),f331(f111(x69001),x69003)))+P1(f331(f331(f240(x69001),f331(f111(x69001),x69003)),f331(f111(x69001),x69002)))
% 51.10/50.83 [6934]P140(x69342,x69341,x69343)+E(x69341,f2(a1))+P1(f331(f331(f240(a1),f780(x69343,x69341,x69342)),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x69341))
% 51.10/50.83 [6935]P141(x69352,x69351,x69353)+E(x69351,f2(a1))+P1(f331(f331(f240(a1),f782(x69353,x69351,x69352)),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x69351))
% 51.10/50.83 [6953]~P102(x69531)+~P16(x69531,x69533)+E(f331(f331(f143(x69531,x69531,f7(x69531)),x69532),f161(x69531,x69532,x69533)),x69533)+~P1(f331(f331(f333(x69531),x69532),f331(f163(x69531),x69533)))
% 51.10/50.83 [7003]P140(x70031,x70032,x70033)+~P1(f331(x70031,x70033))+P1(f331(f331(f241(a1),x70032),f2(a1)))+P1(f331(f331(f241(a1),f774(x70033,x70032,x70031)),x70032))
% 51.10/50.83 [7009]~P104(x70091)+~P92(x70091)+E(f331(f331(f244(x70091),f331(f111(x70091),x70092)),f331(f111(x70091),x70093)),f331(f111(x70091),x70092))+~P1(f331(f331(f240(x70091),f331(f111(x70091),x70092)),f331(f111(x70091),x70093)))
% 51.10/50.83 [7010]~P104(x70101)+~P92(x70101)+E(f331(f331(f239(x70101),f331(f111(x70101),x70102)),f331(f111(x70101),x70103)),f331(f111(x70101),x70103))+~P1(f331(f331(f240(x70101),f331(f111(x70101),x70102)),f331(f111(x70101),x70103)))
% 51.10/50.83 [7023]P141(x70231,x70232,x70233)+~P1(f331(x70231,f2(a1)))+P1(f331(f331(f241(a1),x70232),f2(a1)))+P1(f331(f331(f241(a1),f783(x70233,x70232,x70231)),x70232))
% 51.10/50.83 [7033]P140(x70331,x70332,x70333)+~P1(f331(x70331,x70333))+P1(f331(f331(f240(a1),f780(x70333,x70332,x70331)),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x70332))
% 51.10/50.83 [7057]P141(x70571,x70572,x70573)+~P1(f331(x70571,f2(a1)))+P1(f331(f331(f240(a1),f782(x70573,x70572,x70571)),f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x70572))
% 51.10/50.83 [7084]~P1(f331(x70841,x70842))+P1(f331(x70841,f2(a847)))+~P1(f331(f331(f241(a847),x70842),x70843))+P1(f331(f331(f241(a847),f802(x70842,x70841,x70843)),x70843))
% 51.10/50.83 [7101]~P102(x71011)+~P16(x71011,x71013)+P16(x71011,f331(f331(f145(x71011),x71012),x71013))+P1(f331(f331(f333(x71011),f763(x71013,x71012,x71011)),f331(f163(x71011),x71013)))
% 51.10/50.83 [7102]~P102(x71021)+~P16(x71021,x71023)+P16(x71021,f331(f331(f145(x71021),x71022),x71023))+P1(f331(f331(f333(x71021),f766(x71023,x71022,x71021)),f331(f163(x71021),x71023)))
% 51.10/50.83 [7222]~P102(x72221)+~P7(x72221)+~P1(f331(f331(f241(x72221),x72223),f49(x72221,x72222)))+P1(f331(f331(f333(x72221),f660(x72222,x72223,x72221)),x72222))
% 51.10/50.83 [7391]~P102(x73911)+~P7(x73911)+~P1(f331(f331(f241(x73911),f50(x73911,x73913)),x73912))+P1(f331(f331(f241(x73911),f651(x73912,x73913,x73911)),x73912))
% 51.10/50.83 [7392]~P102(x73921)+~P7(x73921)+~P1(f331(f331(f241(x73921),f50(x73921,x73923)),x73922))+P1(f331(f331(f333(x73921),f651(x73922,x73923,x73921)),x73923))
% 51.10/50.83 [7406]P140(x74062,x74061,x74063)+E(x74061,f2(a1))+P1(f331(f331(f241(a1),x74061),f780(x74063,x74061,x74062)))+P1(f331(f331(f241(a1),f774(x74063,x74061,x74062)),x74061))
% 51.10/50.83 [7407]P141(x74072,x74071,x74073)+E(x74071,f2(a1))+P1(f331(f331(f241(a1),x74071),f782(x74073,x74071,x74072)))+P1(f331(f331(f241(a1),f783(x74073,x74071,x74072)),x74071))
% 51.10/50.83 [7504]P140(x75043,x75041,x75042)+E(x75041,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x75041),f776(x75042,x75041,x75043))),f780(x75042,x75041,x75043)),x75042)+P1(f331(f331(f241(a1),f2(a1)),x75041))
% 51.10/50.83 [7505]P141(x75053,x75051,x75052)+E(x75051,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x75051),f785(x75052,x75051,x75053))),f782(x75052,x75051,x75053)),x75052)+P1(f331(f331(f241(a1),f2(a1)),x75051))
% 51.10/50.83 [7506]~P123(x75061)+~P1(f331(f331(f241(x75061),x75062),f2(x75061)))+P1(f331(f331(f241(x75061),f331(f331(f88(x75061),x75062),x75063)),f2(x75061)))+~P1(f331(f331(f241(x75061),f2(x75061)),x75063))
% 51.10/50.83 [7507]~P123(x75071)+~P1(f331(f331(f241(x75071),x75073),f2(x75071)))+P1(f331(f331(f241(x75071),f331(f331(f88(x75071),x75072),x75073)),f2(x75071)))+~P1(f331(f331(f241(x75071),f2(x75071)),x75072))
% 51.10/50.83 [7508]~P123(x75081)+~P1(f331(f331(f241(x75081),x75082),f2(x75081)))+P1(f331(f331(f241(x75081),f331(f331(f88(x75081),x75082),x75083)),f2(x75081)))+~P1(f331(f331(f241(x75081),f2(x75081)),x75083))
% 51.10/50.83 [7509]~P60(x75091)+~P1(f331(f331(f241(x75091),x75093),f2(x75091)))+P1(f331(f331(f241(x75091),f331(f331(f291(x75091),x75092),x75093)),f2(x75091)))+~P1(f331(f331(f241(x75091),f2(x75091)),x75092))
% 51.10/50.83 [7510]~P60(x75101)+~P1(f331(f331(f241(x75101),x75102),f2(x75101)))+P1(f331(f331(f241(x75101),f331(f331(f291(x75101),x75102),x75103)),f2(x75101)))+~P1(f331(f331(f241(x75101),f2(x75101)),x75103))
% 51.10/50.83 [7511]~P61(x75111)+~P1(f331(f331(f241(x75111),x75113),f2(x75111)))+P1(f331(f331(f241(x75111),f331(f331(f291(x75111),x75112),x75113)),f2(x75111)))+~P1(f331(f331(f241(x75111),f2(x75111)),x75112))
% 51.10/50.83 [7512]~P61(x75121)+~P1(f331(f331(f241(x75121),x75122),f2(x75121)))+P1(f331(f331(f241(x75121),f331(f331(f291(x75121),x75122),x75123)),f2(x75121)))+~P1(f331(f331(f241(x75121),f2(x75121)),x75123))
% 51.10/50.83 [7513]~P128(x75131)+~P1(f331(f331(f240(x75131),x75132),f2(x75131)))+P1(f331(f331(f240(x75131),f331(f331(f88(x75131),x75132),x75133)),f2(x75131)))+~P1(f331(f331(f240(x75131),f2(x75131)),x75133))
% 51.10/50.83 [7514]~P118(x75141)+~P1(f331(f331(f240(x75141),x75143),f2(x75141)))+P1(f331(f331(f240(x75141),f331(f331(f88(x75141),x75142),x75143)),f2(x75141)))+~P1(f331(f331(f240(x75141),f2(x75141)),x75142))
% 51.10/50.83 [7515]~P118(x75151)+~P1(f331(f331(f240(x75151),x75152),f2(x75151)))+P1(f331(f331(f240(x75151),f331(f331(f88(x75151),x75152),x75153)),f2(x75151)))+~P1(f331(f331(f240(x75151),f2(x75151)),x75153))
% 51.10/50.83 [7516]~P128(x75161)+~P1(f331(f331(f240(x75161),x75163),f2(x75161)))+P1(f331(f331(f240(x75161),f331(f331(f88(x75161),x75162),x75163)),f2(x75161)))+~P1(f331(f331(f240(x75161),f2(x75161)),x75162))
% 51.10/50.83 [7517]~P128(x75171)+~P1(f331(f331(f240(x75171),x75173),f2(x75171)))+P1(f331(f331(f240(x75171),f331(f331(f88(x75171),x75172),x75173)),f2(x75171)))+~P1(f331(f331(f240(x75171),f2(x75171)),x75172))
% 51.10/50.83 [7518]~P128(x75181)+~P1(f331(f331(f240(x75181),x75182),f2(x75181)))+P1(f331(f331(f240(x75181),f331(f331(f88(x75181),x75182),x75183)),f2(x75181)))+~P1(f331(f331(f240(x75181),f2(x75181)),x75183))
% 51.10/50.83 [7519]~P128(x75191)+~P1(f331(f331(f240(x75191),x75192),f2(x75191)))+P1(f331(f331(f240(x75191),f331(f331(f88(x75191),x75192),x75193)),f2(x75191)))+~P1(f331(f331(f240(x75191),f2(x75191)),x75193))
% 51.10/50.83 [7520]~P60(x75201)+~P1(f331(f331(f240(x75201),x75203),f2(x75201)))+P1(f331(f331(f240(x75201),f331(f331(f291(x75201),x75202),x75203)),f2(x75201)))+~P1(f331(f331(f240(x75201),f2(x75201)),x75202))
% 51.10/50.83 [7521]~P60(x75211)+~P1(f331(f331(f240(x75211),x75212),f2(x75211)))+P1(f331(f331(f240(x75211),f331(f331(f291(x75211),x75212),x75213)),f2(x75211)))+~P1(f331(f331(f240(x75211),f2(x75211)),x75213))
% 51.10/50.83 [7522]~P61(x75221)+~P1(f331(f331(f241(x75221),x75223),f2(x75221)))+P1(f331(f331(f240(x75221),f331(f331(f291(x75221),x75222),x75223)),f2(x75221)))+~P1(f331(f331(f240(x75221),f2(x75221)),x75222))
% 51.10/50.83 [7523]~P61(x75231)+~P1(f331(f331(f240(x75231),x75232),f2(x75231)))+P1(f331(f331(f240(x75231),f331(f331(f291(x75231),x75232),x75233)),f2(x75231)))+~P1(f331(f331(f241(x75231),f2(x75231)),x75233))
% 51.10/50.83 [7539]P140(x75391,x75392,x75393)+~P1(f331(x75391,x75393))+P1(f331(f331(f241(a1),x75392),f780(x75393,x75392,x75391)))+P1(f331(f331(f241(a1),f774(x75393,x75392,x75391)),x75392))
% 51.10/50.83 [7552]P141(x75521,x75522,x75523)+P1(f331(f331(f241(a1),x75522),f782(x75523,x75522,x75521)))+~P1(f331(x75521,f2(a1)))+P1(f331(f331(f241(a1),f783(x75523,x75522,x75521)),x75522))
% 51.10/50.83 [7604]P140(x76042,x76041,x76043)+E(x76041,f2(a1))+~P1(f331(x76042,f780(x76043,x76041,x76042)))+P1(f331(f331(f241(a1),f774(x76043,x76041,x76042)),x76041))
% 51.10/50.83 [7605]P141(x76052,x76051,x76053)+E(x76051,f2(a1))+~P1(f331(x76052,f785(x76053,x76051,x76052)))+P1(f331(f331(f241(a1),f783(x76053,x76051,x76052)),x76051))
% 51.10/50.83 [7614]P140(x76143,x76141,x76142)+~P1(f331(x76143,x76142))+E(f331(f331(f87(a1),f331(f331(f88(a1),x76141),f776(x76142,x76141,x76143))),f780(x76142,x76141,x76143)),x76142)+P1(f331(f331(f241(a1),f2(a1)),x76141))
% 51.10/50.83 [7632]P141(x76323,x76321,x76322)+E(f331(f331(f87(a1),f331(f331(f88(a1),x76321),f785(x76322,x76321,x76323))),f782(x76322,x76321,x76323)),x76322)+~P1(f331(x76323,f2(a1)))+P1(f331(f331(f241(a1),f2(a1)),x76321))
% 51.10/50.83 [7656]~P1(f331(x76561,x76563))+~P1(f331(f68(x76562),x76563))+P1(f331(f331(f333(x76562),f441(x76561,x76563,x76562)),f440(x76561,x76563,x76562)))+P1(f331(x76561,f184(f854(x76562,a840))))
% 51.10/50.83 [7666]P140(x76661,x76662,x76663)+~P1(f331(x76661,x76663))+~P1(f331(x76661,f780(x76663,x76662,x76661)))+P1(f331(f331(f241(a1),f774(x76663,x76662,x76661)),x76662))
% 51.10/50.83 [7672]P141(x76721,x76722,x76723)+~P1(f331(x76721,f785(x76723,x76722,x76721)))+~P1(f331(x76721,f2(a1)))+P1(f331(f331(f241(a1),f783(x76723,x76722,x76721)),x76722))
% 51.10/50.83 [7744]~P92(x77441)+~P102(x77441)+~P1(f331(f331(f241(x77441),f331(f111(x77441),x77442)),f331(f111(x77441),x77443)))+~P1(f331(f331(f240(x77441),f331(f111(x77441),x77443)),f331(f111(x77441),x77442)))
% 51.10/50.83 [7780]~P60(x77801)+~P1(f331(f331(f241(x77801),f331(f331(f291(x77801),x77803),x77802)),f2(x77801)))+P1(f331(f331(f241(x77801),x77802),f2(x77801)))+P1(f331(f331(f241(x77801),f2(x77801)),x77802))
% 51.10/50.83 [7781]~P60(x77811)+~P1(f331(f331(f241(x77811),f331(f331(f291(x77811),x77812),x77813)),f2(x77811)))+P1(f331(f331(f241(x77811),x77812),f2(x77811)))+P1(f331(f331(f241(x77811),f2(x77811)),x77812))
% 51.10/50.83 [7782]~P118(x77821)+~P1(f331(f331(f240(x77821),f331(f331(f88(x77821),x77823),x77822)),f2(x77821)))+P1(f331(f331(f240(x77821),x77822),f2(x77821)))+P1(f331(f331(f240(x77821),f2(x77821)),x77822))
% 51.10/50.83 [7783]~P118(x77831)+~P1(f331(f331(f240(x77831),f331(f331(f88(x77831),x77832),x77833)),f2(x77831)))+P1(f331(f331(f240(x77831),x77832),f2(x77831)))+P1(f331(f331(f240(x77831),f2(x77831)),x77832))
% 51.10/50.83 [7784]~P60(x77841)+~P1(f331(f331(f240(x77841),f331(f331(f291(x77841),x77843),x77842)),f2(x77841)))+P1(f331(f331(f240(x77841),x77842),f2(x77841)))+P1(f331(f331(f240(x77841),f2(x77841)),x77842))
% 51.10/50.83 [7785]~P60(x77851)+~P1(f331(f331(f240(x77851),f331(f331(f291(x77851),x77852),x77853)),f2(x77851)))+P1(f331(f331(f240(x77851),x77852),f2(x77851)))+P1(f331(f331(f240(x77851),f2(x77851)),x77852))
% 51.10/50.83 [7811]~P60(x78111)+~P1(f331(f331(f241(x78111),f331(f331(f291(x78111),x78112),x78113)),f2(x78111)))+P1(f331(f331(f241(x78111),f2(x78111)),x78112))+P1(f331(f331(f241(x78111),f2(x78111)),x78113))
% 51.10/50.83 [7812]~P118(x78121)+~P1(f331(f331(f240(x78121),f331(f331(f88(x78121),x78122),x78123)),f2(x78121)))+P1(f331(f331(f240(x78121),f2(x78121)),x78122))+P1(f331(f331(f240(x78121),f2(x78121)),x78123))
% 51.10/50.83 [7813]~P60(x78131)+~P1(f331(f331(f240(x78131),f331(f331(f291(x78131),x78132),x78133)),f2(x78131)))+P1(f331(f331(f240(x78131),f2(x78131)),x78132))+P1(f331(f331(f240(x78131),f2(x78131)),x78133))
% 51.10/50.83 [7832]P140(x78322,x78321,x78323)+E(x78321,f2(a1))+P1(f331(f331(f240(a1),f780(x78323,x78321,x78322)),f2(a1)))+P1(f331(f331(f241(a1),f774(x78323,x78321,x78322)),x78321))
% 51.10/50.83 [7833]P141(x78332,x78331,x78333)+E(x78331,f2(a1))+P1(f331(f331(f240(a1),f782(x78333,x78331,x78332)),f2(a1)))+P1(f331(f331(f241(a1),f783(x78333,x78331,x78332)),x78331))
% 51.10/50.83 [7839]~P85(x78391)+~P1(f331(f331(f241(x78391),x78392),f85(x78391)))+P1(f331(f331(f241(x78391),f331(f331(f250(x78391),x78392),f331(a119,x78393))),f85(x78391)))+~P1(f331(f331(f241(x78391),f2(x78391)),x78392))
% 51.10/50.83 [7893]~P102(x78931)+~E(x78933,f120(x78931))+~P16(x78931,f331(f160(x78931),x78933))+E(f331(f137(x78931,x78931,f331(f9(x78931,x78931,x78931),f239(x78931)),x78932),f331(f160(x78931),x78933)),x78932)
% 51.10/50.83 [7895]P140(x78951,x78952,x78953)+~P1(f331(x78951,x78953))+P1(f331(f331(f240(a1),f780(x78953,x78952,x78951)),f2(a1)))+P1(f331(f331(f241(a1),f774(x78953,x78952,x78951)),x78952))
% 51.10/50.83 [7907]P141(x79071,x79072,x79073)+~P1(f331(x79071,f2(a1)))+P1(f331(f331(f240(a1),f782(x79073,x79072,x79071)),f2(a1)))+P1(f331(f331(f241(a1),f783(x79073,x79072,x79071)),x79072))
% 51.10/50.83 [8120]P140(x81203,x81201,x81202)+E(x81201,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x81201),f776(x81202,x81201,x81203))),f780(x81202,x81201,x81203)),x81202)+P1(f331(f331(f241(a1),f774(x81202,x81201,x81203)),x81201))
% 51.10/50.83 [8121]P141(x81213,x81211,x81212)+E(x81211,f2(a1))+E(f331(f331(f87(a1),f331(f331(f88(a1),x81211),f785(x81212,x81211,x81213))),f782(x81212,x81211,x81213)),x81212)+P1(f331(f331(f241(a1),f783(x81212,x81211,x81213)),x81211))
% 51.10/50.83 [8156]P140(x81563,x81561,x81562)+~P1(f331(x81563,x81562))+E(f331(f331(f87(a1),f331(f331(f88(a1),x81561),f776(x81562,x81561,x81563))),f780(x81562,x81561,x81563)),x81562)+P1(f331(f331(f241(a1),f774(x81562,x81561,x81563)),x81561))
% 51.10/50.83 [8157]~P68(x81571)+~P70(x81571)+~P36(x81573)+E(f331(f331(f11(a847,x81571),f331(f331(f10(a1,x81571,a847),x81572),f107(a1))),f331(f311(a1,a847,a112),x81573)),f331(f331(f11(a1,x81571),x81572),x81573))
% 51.10/50.83 [8158]~P68(x81581)+~P70(x81581)+~P36(x81583)+E(f331(f331(f8(a847,x81581),f331(f331(f10(a1,x81581,a847),x81582),f107(a1))),f331(f311(a1,a847,a112),x81583)),f331(f331(f8(a1,x81581),x81582),x81583))
% 51.10/50.83 [8167]P141(x81673,x81671,x81672)+E(f331(f331(f87(a1),f331(f331(f88(a1),x81671),f785(x81672,x81671,x81673))),f782(x81672,x81671,x81673)),x81672)+~P1(f331(x81673,f2(a1)))+P1(f331(f331(f241(a1),f783(x81672,x81671,x81673)),x81671))
% 51.10/50.83 [8185]~E(x81852,f2(a847))+~E(f331(f248(a847,a847),x81853),f2(a847))+~E(x81851,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x81853)),x81852)),f331(f258(a847,a847),x81853)))+P1(f331(f60(x81851,x81852),x81853))
% 51.10/50.83 [9027]P1(f331(f331(f240(a1),x90271),f2(a1)))+~P1(f331(f331(f241(a1),f331(f331(f87(a1),f331(f331(f88(a1),x90272),x90271)),x90273)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x90272))+~P1(f331(f331(f240(a1),f2(a1)),x90273))
% 51.10/50.83 [5641]~P97(x56412)+E(x56411,f184(f854(x56412,a840)))+~P1(f331(f68(x56412),x56411))+E(f12(x56412,f331(f331(f310(x56412),x56413),x56411)),f331(f331(f109(x56412),x56413),f12(x56412,x56411)))
% 51.10/50.83 [5642]~P97(x56422)+E(x56421,f184(f854(x56422,a840)))+~P1(f331(f68(x56422),x56421))+E(f15(x56422,f331(f331(f310(x56422),x56423),x56421)),f331(f331(f108(x56422),x56423),f15(x56422,x56421)))
% 51.10/50.83 [5643]~P102(x56432)+E(x56431,f184(f854(x56432,a840)))+~P1(f331(f68(x56432),x56431))+E(f16(x56432,f331(f331(f310(x56432),x56433),x56431)),f331(f331(f239(x56432),x56433),f16(x56432,x56431)))
% 51.10/50.83 [5644]~P102(x56442)+E(x56441,f184(f854(x56442,a840)))+~P1(f331(f68(x56442),x56441))+E(f17(x56442,f331(f331(f310(x56442),x56443),x56441)),f331(f331(f244(x56442),x56443),f17(x56442,x56441)))
% 51.10/50.83 [5965]~P118(x59651)+~E(x59653,f2(x59651))+~E(x59652,f2(x59651))+E(f331(f331(f87(x59651),f331(f331(f88(x59651),x59652),x59652)),f331(f331(f88(x59651),x59653),x59653)),f2(x59651))
% 51.10/50.83 [6040]~P94(x60402)+E(x60401,f184(f854(x60402,a840)))+~P1(f331(f68(x60402),x60401))+E(f331(f70(x60402,f88(x60402)),f331(f331(f310(x60402),x60403),x60401)),f331(f331(f88(x60402),x60403),f331(f70(x60402,f88(x60402)),x60401)))
% 51.10/50.83 [6167]~P102(x61672)+E(x61671,f184(f854(x61672,a840)))+~P1(f331(f68(x61672),x61671))+E(f13(x61672,f239(x61672),f331(f331(f310(x61672),x61673),x61671)),f331(f331(f239(x61672),x61673),f13(x61672,f239(x61672),x61671)))
% 51.10/50.83 [6168]~P102(x61682)+E(x61681,f184(f854(x61682,a840)))+~P1(f331(f68(x61682),x61681))+E(f14(x61682,f244(x61682),f331(f331(f310(x61682),x61683),x61681)),f331(f331(f244(x61682),x61683),f14(x61682,f244(x61682),x61681)))
% 51.10/50.83 [6577]~P97(x65771)+~P1(f331(f68(x65771),x65773))+E(f331(f331(f71(x65771,x65771,f109(x65771)),x65772),x65773),f12(x65771,f331(f331(f310(x65771),x65772),x65773)))+P1(f331(f331(f333(x65771),x65772),x65773))
% 51.10/50.83 [6578]~P97(x65781)+~P1(f331(f68(x65781),x65783))+E(f331(f331(f71(x65781,x65781,f108(x65781)),x65782),x65783),f15(x65781,f331(f331(f310(x65781),x65782),x65783)))+P1(f331(f331(f333(x65781),x65782),x65783))
% 51.10/50.83 [6579]~P102(x65791)+~P1(f331(f68(x65791),x65793))+E(f331(f331(f71(x65791,x65791,f239(x65791)),x65792),x65793),f16(x65791,f331(f331(f310(x65791),x65792),x65793)))+P1(f331(f331(f333(x65791),x65792),x65793))
% 51.10/50.83 [6580]~P102(x65801)+~P1(f331(f68(x65801),x65803))+E(f331(f331(f71(x65801,x65801,f244(x65801)),x65802),x65803),f17(x65801,f331(f331(f310(x65801),x65802),x65803)))+P1(f331(f331(f333(x65801),x65802),x65803))
% 51.10/50.83 [6695]~P64(x66951)+~P1(f331(f68(x66951),x66953))+E(f331(f70(x66951,f88(x66951)),f331(f331(f310(x66951),x66952),x66953)),f331(f331(f71(x66951,x66951,f88(x66951)),x66952),x66953))+P1(f331(f331(f333(x66951),x66952),x66953))
% 51.10/50.83 [6713]~P102(x67131)+~P1(f331(f68(x67131),x67133))+E(f13(x67131,f239(x67131),f331(f331(f310(x67131),x67132),x67133)),f331(f331(f71(x67131,x67131,f239(x67131)),x67132),x67133))+P1(f331(f331(f333(x67131),x67132),x67133))
% 51.10/50.83 [6714]~P102(x67141)+~P1(f331(f68(x67141),x67143))+E(f14(x67141,f244(x67141),f331(f331(f310(x67141),x67142),x67143)),f331(f331(f71(x67141,x67141,f244(x67141)),x67142),x67143))+P1(f331(f331(f333(x67141),x67142),x67143))
% 51.10/50.83 [6781]~E(f331(f331(f87(a1),x67812),f331(f331(f88(a1),x67813),x67811)),x67813)+~P1(f331(f331(f241(a1),f2(a1)),x67813))+P1(f331(f331(f240(a1),f85(a1)),x67811))+~P1(f331(f331(f241(a1),x67812),x67813))
% 51.10/50.83 [6812]~E(f331(f331(f87(a1),x68122),f331(f331(f88(a1),x68123),x68121)),x68123)+P1(f331(f331(f240(a1),x68121),f85(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x68123))+~P1(f331(f331(f240(a1),f2(a1)),x68122))
% 51.10/50.83 [6830]E(x68301,f2(a847))+~P1(f331(f60(x68303,x68301),x68302))+~P1(f331(f331(f241(a847),f2(a847)),x68301))+P1(f331(f331(f241(a847),f331(f258(a847,a847),x68302)),x68301))
% 51.10/50.83 [6859]~P132(x68591)+~P1(f331(f331(f240(x68591),x68592),f2(x68591)))+~P1(f331(f331(f240(x68591),x68593),f2(x68591)))+E(f331(f331(f88(x68591),f331(f82(x68591),x68592)),f331(f82(x68591),x68593)),f331(f82(x68591),f331(f331(f88(x68591),x68592),x68593)))
% 51.10/50.83 [6911]~P132(x69111)+~P1(f331(f331(f240(x69111),x69112),f2(x69111)))+E(f331(f331(f88(x69111),f331(f82(x69111),x69112)),f331(f82(x69111),x69113)),f331(f82(x69111),f331(f331(f88(x69111),x69112),x69113)))+~P1(f331(f331(f240(x69111),f2(x69111)),x69113))
% 51.10/50.83 [6912]~P132(x69121)+~P1(f331(f331(f240(x69121),x69123),f2(x69121)))+E(f331(f331(f88(x69121),f331(f82(x69121),x69122)),f331(f82(x69121),x69123)),f331(f82(x69121),f331(f331(f88(x69121),x69122),x69123)))+~P1(f331(f331(f240(x69121),f2(x69121)),x69122))
% 51.10/50.83 [6962]~P132(x69621)+E(f331(f331(f88(x69621),f331(f82(x69621),x69622)),f331(f82(x69621),x69623)),f331(f82(x69621),f331(f331(f88(x69621),x69622),x69623)))+~P1(f331(f331(f240(x69621),f2(x69621)),x69622))+~P1(f331(f331(f240(x69621),f2(x69621)),x69623))
% 51.10/50.83 [6980]~P118(x69801)+~P1(f331(f331(f241(x69801),x69803),f2(x69801)))+~P1(f331(f331(f241(x69801),x69802),f2(x69801)))+P1(f331(f331(f241(x69801),f2(x69801)),f331(f331(f88(x69801),x69802),x69803)))
% 51.10/50.83 [6981]~P60(x69811)+~P1(f331(f331(f241(x69811),x69813),f2(x69811)))+~P1(f331(f331(f241(x69811),x69812),f2(x69811)))+P1(f331(f331(f241(x69811),f2(x69811)),f331(f331(f291(x69811),x69812),x69813)))
% 51.10/50.83 [6982]~P61(x69821)+~P1(f331(f331(f241(x69821),x69823),f2(x69821)))+~P1(f331(f331(f241(x69821),x69822),f2(x69821)))+P1(f331(f331(f241(x69821),f2(x69821)),f331(f331(f291(x69821),x69822),x69823)))
% 51.10/50.83 [6983]~P118(x69831)+~P1(f331(f331(f240(x69831),x69833),f2(x69831)))+~P1(f331(f331(f240(x69831),x69832),f2(x69831)))+P1(f331(f331(f240(x69831),f2(x69831)),f331(f331(f88(x69831),x69832),x69833)))
% 51.10/50.83 [6984]~P129(x69841)+~P1(f331(f331(f240(x69841),x69843),f2(x69841)))+~P1(f331(f331(f240(x69841),x69842),f2(x69841)))+P1(f331(f331(f240(x69841),f2(x69841)),f331(f331(f88(x69841),x69842),x69843)))
% 51.10/50.83 [6985]~P129(x69851)+~P1(f331(f331(f240(x69851),x69853),f2(x69851)))+~P1(f331(f331(f240(x69851),x69852),f2(x69851)))+P1(f331(f331(f240(x69851),f2(x69851)),f331(f331(f88(x69851),x69852),x69853)))
% 51.10/50.83 [6986]~P60(x69861)+~P1(f331(f331(f240(x69861),x69863),f2(x69861)))+~P1(f331(f331(f240(x69861),x69862),f2(x69861)))+P1(f331(f331(f240(x69861),f2(x69861)),f331(f331(f291(x69861),x69862),x69863)))
% 51.10/50.83 [6987]~P61(x69871)+~P1(f331(f331(f241(x69871),x69873),f2(x69871)))+~P1(f331(f331(f240(x69871),x69872),f2(x69871)))+P1(f331(f331(f240(x69871),f2(x69871)),f331(f331(f291(x69871),x69872),x69873)))
% 51.10/50.83 [6988]~P85(x69881)+~P1(f331(f331(f241(a847),f2(a847)),x69883))+~P1(f331(f331(f241(x69881),f85(x69881)),x69882))+P1(f331(f331(f241(x69881),f85(x69881)),f331(f331(f250(x69881),x69882),x69883)))
% 51.10/50.83 [7085]~P80(x70851)+~P1(f331(f331(f241(x70851),f2(x70851)),x70853))+~P1(f331(f331(f241(x70851),f2(x70851)),x70852))+P1(f331(f331(f241(x70851),f2(x70851)),f331(f331(f87(x70851),x70852),x70853)))
% 51.10/50.83 [7086]~P80(x70861)+~P1(f331(f331(f240(x70861),f2(x70861)),x70862))+~P1(f331(f331(f241(x70861),f2(x70861)),x70863))+P1(f331(f331(f241(x70861),f2(x70861)),f331(f331(f87(x70861),x70862),x70863)))
% 51.10/50.83 [7087]~P80(x70871)+~P1(f331(f331(f240(x70871),f2(x70871)),x70873))+~P1(f331(f331(f241(x70871),f2(x70871)),x70872))+P1(f331(f331(f241(x70871),f2(x70871)),f331(f331(f87(x70871),x70872),x70873)))
% 51.10/50.83 [7088]~P123(x70881)+~P1(f331(f331(f241(x70881),f2(x70881)),x70883))+~P1(f331(f331(f241(x70881),f2(x70881)),x70882))+P1(f331(f331(f241(x70881),f2(x70881)),f331(f331(f88(x70881),x70882),x70883)))
% 51.10/50.83 [7089]~P60(x70891)+~P1(f331(f331(f241(x70891),f2(x70891)),x70893))+~P1(f331(f331(f241(x70891),f2(x70891)),x70892))+P1(f331(f331(f241(x70891),f2(x70891)),f331(f331(f291(x70891),x70892),x70893)))
% 51.10/50.83 [7090]~P61(x70901)+~P1(f331(f331(f241(x70901),f2(x70901)),x70903))+~P1(f331(f331(f241(x70901),f2(x70901)),x70902))+P1(f331(f331(f241(x70901),f2(x70901)),f331(f331(f291(x70901),x70902),x70903)))
% 51.10/50.83 [7091]~P85(x70911)+~P1(f331(f331(f241(x70911),f85(x70911)),x70913))+~P1(f331(f331(f241(x70911),f85(x70911)),x70912))+P1(f331(f331(f241(x70911),f85(x70911)),f331(f331(f88(x70911),x70912),x70913)))
% 51.10/50.83 [7092]~P80(x70921)+~P1(f331(f331(f240(x70921),f2(x70921)),x70923))+~P1(f331(f331(f240(x70921),f2(x70921)),x70922))+P1(f331(f331(f240(x70921),f2(x70921)),f331(f331(f87(x70921),x70922),x70923)))
% 51.10/50.83 [7093]~P118(x70931)+~P1(f331(f331(f240(x70931),f2(x70931)),x70933))+~P1(f331(f331(f240(x70931),f2(x70931)),x70932))+P1(f331(f331(f240(x70931),f2(x70931)),f331(f331(f88(x70931),x70932),x70933)))
% 51.10/50.83 [7094]~P128(x70941)+~P1(f331(f331(f240(x70941),f2(x70941)),x70943))+~P1(f331(f331(f240(x70941),f2(x70941)),x70942))+P1(f331(f331(f240(x70941),f2(x70941)),f331(f331(f88(x70941),x70942),x70943)))
% 51.10/50.83 [7095]~P129(x70951)+~P1(f331(f331(f240(x70951),f2(x70951)),x70953))+~P1(f331(f331(f240(x70951),f2(x70951)),x70952))+P1(f331(f331(f240(x70951),f2(x70951)),f331(f331(f88(x70951),x70952),x70953)))
% 51.10/50.83 [7096]~P60(x70961)+~P1(f331(f331(f240(x70961),f2(x70961)),x70963))+~P1(f331(f331(f240(x70961),f2(x70961)),x70962))+P1(f331(f331(f240(x70961),f2(x70961)),f331(f331(f291(x70961),x70962),x70963)))
% 51.10/50.83 [7097]~P61(x70971)+~P1(f331(f331(f241(x70971),f2(x70971)),x70973))+~P1(f331(f331(f240(x70971),f2(x70971)),x70972))+P1(f331(f331(f240(x70971),f2(x70971)),f331(f331(f291(x70971),x70972),x70973)))
% 51.10/50.83 [7173]~P97(x71731)+~P1(f331(f68(x71731),x71733))+E(f12(x71731,f331(f331(f310(x71731),x71732),x71733)),x71732)+~E(f331(f331(f3(f854(x71731,a840)),x71733),f331(f331(f310(x71731),x71732),f184(f854(x71731,a840)))),f184(f854(x71731,a840)))
% 51.10/50.83 [7174]~P97(x71741)+~P1(f331(f68(x71741),x71743))+E(f15(x71741,f331(f331(f310(x71741),x71742),x71743)),x71742)+~E(f331(f331(f3(f854(x71741,a840)),x71743),f331(f331(f310(x71741),x71742),f184(f854(x71741,a840)))),f184(f854(x71741,a840)))
% 51.10/50.83 [7175]~P102(x71751)+~P1(f331(f68(x71751),x71753))+E(f16(x71751,f331(f331(f310(x71751),x71752),x71753)),x71752)+~E(f331(f331(f3(f854(x71751,a840)),x71753),f331(f331(f310(x71751),x71752),f184(f854(x71751,a840)))),f184(f854(x71751,a840)))
% 51.10/50.83 [7176]~P102(x71761)+~P1(f331(f68(x71761),x71763))+E(f17(x71761,f331(f331(f310(x71761),x71762),x71763)),x71762)+~E(f331(f331(f3(f854(x71761,a840)),x71763),f331(f331(f310(x71761),x71762),f184(f854(x71761,a840)))),f184(f854(x71761,a840)))
% 51.10/50.83 [7177]~P60(x71771)+P1(f331(f331(f241(x71771),x71772),f2(x71771)))+P1(f331(f331(f241(x71771),f2(x71771)),x71773))+~P1(f331(f331(f241(x71771),f2(x71771)),f331(f331(f291(x71771),x71773),x71772)))
% 51.10/50.83 [7178]~P60(x71781)+P1(f331(f331(f241(x71781),x71782),f2(x71781)))+P1(f331(f331(f241(x71781),f2(x71781)),x71783))+~P1(f331(f331(f241(x71781),f2(x71781)),f331(f331(f291(x71781),x71782),x71783)))
% 51.10/50.83 [7179]~P60(x71791)+P1(f331(f331(f241(x71791),x71792),f2(x71791)))+P1(f331(f331(f241(x71791),f2(x71791)),x71792))+~P1(f331(f331(f241(x71791),f2(x71791)),f331(f331(f291(x71791),x71793),x71792)))
% 51.10/50.83 [7180]~P60(x71801)+P1(f331(f331(f241(x71801),x71802),f2(x71801)))+P1(f331(f331(f241(x71801),f2(x71801)),x71802))+~P1(f331(f331(f241(x71801),f2(x71801)),f331(f331(f291(x71801),x71802),x71803)))
% 51.10/50.83 [7181]~P118(x71811)+P1(f331(f331(f240(x71811),x71812),f2(x71811)))+P1(f331(f331(f240(x71811),f2(x71811)),x71813))+~P1(f331(f331(f240(x71811),f2(x71811)),f331(f331(f88(x71811),x71813),x71812)))
% 51.10/50.83 [7182]~P118(x71821)+P1(f331(f331(f240(x71821),x71822),f2(x71821)))+P1(f331(f331(f240(x71821),f2(x71821)),x71823))+~P1(f331(f331(f240(x71821),f2(x71821)),f331(f331(f88(x71821),x71822),x71823)))
% 51.10/50.83 [7183]~P60(x71831)+P1(f331(f331(f240(x71831),x71832),f2(x71831)))+P1(f331(f331(f240(x71831),f2(x71831)),x71833))+~P1(f331(f331(f240(x71831),f2(x71831)),f331(f331(f291(x71831),x71833),x71832)))
% 51.10/50.83 [7184]~P60(x71841)+P1(f331(f331(f240(x71841),x71842),f2(x71841)))+P1(f331(f331(f240(x71841),f2(x71841)),x71843))+~P1(f331(f331(f240(x71841),f2(x71841)),f331(f331(f291(x71841),x71842),x71843)))
% 51.10/50.83 [7185]~P118(x71851)+P1(f331(f331(f240(x71851),x71852),f2(x71851)))+P1(f331(f331(f240(x71851),f2(x71851)),x71852))+~P1(f331(f331(f240(x71851),f2(x71851)),f331(f331(f88(x71851),x71853),x71852)))
% 51.10/50.83 [7186]~P118(x71861)+P1(f331(f331(f240(x71861),x71862),f2(x71861)))+P1(f331(f331(f240(x71861),f2(x71861)),x71862))+~P1(f331(f331(f240(x71861),f2(x71861)),f331(f331(f88(x71861),x71862),x71863)))
% 51.10/50.83 [7187]~P60(x71871)+P1(f331(f331(f240(x71871),x71872),f2(x71871)))+P1(f331(f331(f240(x71871),f2(x71871)),x71872))+~P1(f331(f331(f240(x71871),f2(x71871)),f331(f331(f291(x71871),x71873),x71872)))
% 51.10/50.83 [7188]~P60(x71881)+P1(f331(f331(f240(x71881),x71882),f2(x71881)))+P1(f331(f331(f240(x71881),f2(x71881)),x71882))+~P1(f331(f331(f240(x71881),f2(x71881)),f331(f331(f291(x71881),x71882),x71883)))
% 51.10/50.83 [7273]~P1(f331(f331(f287(a847),x72731),x72733))+P1(f331(f331(f287(a847),x72731),x72732))+~P1(f331(f331(f240(a847),x72732),x72733))+~P1(f331(f331(f287(a847),x72731),f331(f331(f3(a847),x72733),x72732)))
% 51.10/50.83 [7274]~P1(f331(f331(f287(a847),x72741),x72743))+P1(f331(f331(f287(a847),x72741),x72742))+~P1(f331(f331(f240(a847),x72743),x72742))+~P1(f331(f331(f287(a847),x72741),f331(f331(f3(a847),x72742),x72743)))
% 51.10/50.83 [7289]~E(f331(f331(f109(f854(x72891,a840)),f331(f163(x72891),x72892)),f331(f163(x72891),x72893)),f184(f854(x72891,a840)))+~P1(f331(f132(x72891),x72893))+~P1(f331(f132(x72891),x72892))+P1(f331(f132(x72891),f331(f331(f130(x72891),x72892),x72893)))
% 51.10/50.83 [7290]~P102(x72901)+~P1(f331(f68(x72901),x72903))+E(f13(x72901,f239(x72901),f331(f331(f310(x72901),x72902),x72903)),x72902)+~E(f331(f331(f3(f854(x72901,a840)),x72903),f331(f331(f310(x72901),x72902),f184(f854(x72901,a840)))),f184(f854(x72901,a840)))
% 51.10/50.83 [7291]~P102(x72911)+~P1(f331(f68(x72911),x72913))+E(f14(x72911,f244(x72911),f331(f331(f310(x72911),x72912),x72913)),x72912)+~E(f331(f331(f3(f854(x72911,a840)),x72913),f331(f331(f310(x72911),x72912),f184(f854(x72911,a840)))),f184(f854(x72911,a840)))
% 51.10/50.83 [7309]~P86(x73091)+~P1(f331(f331(f241(x73091),x73092),x73093))+~P1(f331(f331(f241(x73091),f331(f86(x73091),x73092)),x73093))+P1(f331(f331(f241(x73091),f331(f82(x73091),x73092)),x73093))
% 51.10/50.83 [7310]~P78(x73101)+~P1(f331(f331(f240(x73101),x73102),x73103))+~P1(f331(f331(f240(x73101),f331(f86(x73101),x73102)),x73103))+P1(f331(f331(f240(x73101),f331(f82(x73101),x73102)),x73103))
% 51.10/50.83 [7311]~P78(x73111)+~P1(f331(f331(f240(x73111),x73112),x73113))+~P1(f331(f331(f240(x73111),f331(f86(x73111),x73112)),x73113))+P1(f331(f331(f240(x73111),f331(f82(x73111),x73112)),x73113))
% 51.10/50.83 [7380]~P123(x73801)+P1(f331(f331(f241(x73801),f2(x73801)),x73802))+~P1(f331(f331(f241(x73801),f2(x73801)),x73803))+~P1(f331(f331(f241(x73801),f2(x73801)),f331(f331(f88(x73801),x73803),x73802)))
% 51.10/50.83 [7381]~P123(x73811)+P1(f331(f331(f241(x73811),f2(x73811)),x73812))+~P1(f331(f331(f241(x73811),f2(x73811)),x73813))+~P1(f331(f331(f241(x73811),f2(x73811)),f331(f331(f88(x73811),x73812),x73813)))
% 51.10/50.83 [7689]E(x76891,x76892)+~P1(f331(f68(x76893),x76891))+~P1(f331(f331(f240(a847),f331(f47(x76893),x76891)),f331(f47(x76893),x76892)))+~P1(f331(f331(f240(f854(x76893,a840)),x76892),x76891))
% 51.10/50.83 [7760]~P1(f331(f331(f240(a847),x77602),x77601))+~P1(f331(f331(f241(a847),x77601),x77603))+~P1(f331(f331(f240(a847),x77602),x77603))+P1(f331(f331(f241(a847),f331(f331(f3(a847),x77601),x77602)),f331(f331(f3(a847),x77603),x77602)))
% 51.10/50.83 [7761]~P1(f331(f331(f240(a847),x77612),x77611))+~P1(f331(f331(f240(a847),x77612),x77613))+~P1(f331(f331(f240(a847),x77611),x77613))+P1(f331(f331(f240(a847),f331(f331(f3(a847),x77611),x77612)),f331(f331(f3(a847),x77613),x77612)))
% 51.10/50.83 [7836]~P1(f331(f331(f241(a1),x78361),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x78362))+~P1(f331(f331(f240(a1),x78362),x78363))+P1(f331(f331(f240(a1),f331(f331(f48(a1),x78361),x78362)),f331(f331(f48(a1),x78361),x78363)))
% 51.10/50.83 [7847]~P1(f331(f331(f241(a1),f2(a1)),x78473))+~P1(f331(f331(f240(a1),f2(a1)),x78471))+~P1(f331(f331(f240(a1),x78473),x78472))+P1(f331(f331(f240(a1),f331(f331(f48(a1),x78471),x78472)),f331(f331(f48(a1),x78471),x78473)))
% 51.10/50.83 [7982]E(f331(x79821,f807(x79822,x79821,x79823)),x79822)+~P1(f331(f331(f240(a1),x79822),f331(x79821,x79823)))+P1(f331(f331(f241(a847),f808(x79822,x79821,x79823)),x79823))+~P1(f331(f331(f240(a1),f331(x79821,f2(a847))),x79822))
% 51.10/50.83 [7983]E(f331(x79831,f809(x79832,x79831,x79833)),x79832)+~P1(f331(f331(f240(a1),x79832),f331(x79831,x79833)))+P1(f331(f331(f241(a847),f810(x79832,x79831,x79833)),x79833))+~P1(f331(f331(f240(a1),f331(x79831,f2(a847))),x79832))
% 51.10/50.83 [8080]~P1(f331(f68(x80801),x80803))+~P1(f331(f331(f241(a847),f331(f47(x80801),x80802)),f331(f47(x80801),x80803)))+~P1(f331(f331(f240(f854(x80801,a840)),x80802),x80803))+P1(f331(f331(f241(f854(x80801,a840)),x80802),x80803))
% 51.10/50.83 [8109]E(f331(f331(f3(a1),f459(x81093,x81091,x81092)),f460(x81093,x81091,x81092)),x81091)+E(f331(f331(f87(a1),x81091),x81092),x81091)+~P1(f331(f331(f241(a1),f2(a1)),x81092))+~P1(f331(f331(f333(a1),f331(f331(f87(a1),x81091),f85(a1))),x81093))
% 51.10/50.83 [8110]E(f331(f331(f87(a1),f450(x81103,x81101,x81102)),f451(x81103,x81101,x81102)),x81101)+E(f331(f331(f3(a1),x81101),x81102),x81101)+~P1(f331(f331(f241(a1),f2(a1)),x81102))+~P1(f331(f331(f333(a1),f331(f331(f3(a1),x81101),f85(a1))),x81103))
% 51.10/50.83 [8162]~P1(f331(f331(f240(a847),x81623),x81621))+P1(f331(f331(f241(a847),x81621),x81622))+~P1(f331(f331(f240(a847),x81623),x81622))+~P1(f331(f331(f241(a847),f331(f331(f3(a847),x81621),x81623)),f331(f331(f3(a847),x81622),x81623)))
% 51.10/50.83 [8163]~P1(f331(f331(f240(a847),x81633),x81631))+P1(f331(f331(f240(a847),x81631),x81632))+~P1(f331(f331(f240(a847),x81633),x81632))+~P1(f331(f331(f240(a847),f331(f331(f3(a847),x81631),x81633)),f331(f331(f3(a847),x81632),x81633)))
% 51.10/50.83 [8178]~P102(x81782)+E(x81781,f120(x81782))+~P16(x81782,f331(f160(x81782),x81781))+E(f331(f137(x81782,x81782,f331(f9(x81782,x81782,x81782),f239(x81782)),x81783),f331(f160(x81782),x81781)),f331(f331(f239(x81782),f331(f331(f155(x81782),x81781),f2(a847))),x81783))
% 51.10/50.83 [8244]E(f331(f331(f87(a1),x82441),x82442),x82441)+~P1(f331(f331(f241(a1),f2(a1)),x82442))+P1(f331(f331(f333(a1),f459(x82443,x82441,x82442)),x82443))+~P1(f331(f331(f333(a1),f331(f331(f87(a1),x82441),f85(a1))),x82443))
% 51.10/50.83 [8245]E(f331(f331(f3(a1),x82451),x82452),x82451)+~P1(f331(f331(f241(a1),f2(a1)),x82452))+P1(f331(f331(f333(a1),f450(x82453,x82451,x82452)),x82453))+~P1(f331(f331(f333(a1),f331(f331(f3(a1),x82451),f85(a1))),x82453))
% 51.10/50.83 [8323]~P1(f331(f331(f240(a1),x83231),f331(x83232,x83233)))+P1(f331(f331(f240(a847),f807(x83231,x83232,x83233)),x83233))+P1(f331(f331(f241(a847),f808(x83231,x83232,x83233)),x83233))+~P1(f331(f331(f240(a1),f331(x83232,f2(a847))),x83231))
% 51.10/50.83 [8324]~P1(f331(f331(f240(a1),x83241),f331(x83242,x83243)))+P1(f331(f331(f240(a847),f809(x83241,x83242,x83243)),x83243))+P1(f331(f331(f241(a847),f810(x83241,x83242,x83243)),x83243))+~P1(f331(f331(f240(a1),f331(x83242,f2(a847))),x83241))
% 51.10/50.83 [8399]E(f331(f331(f87(a1),x83991),x83992),x83991)+~P1(f331(f331(f241(a1),f2(a1)),x83992))+P1(f331(f331(f333(a1),f460(x83993,x83991,x83992)),f303(a1,f85(a1),x83992)))+~P1(f331(f331(f333(a1),f331(f331(f87(a1),x83991),f85(a1))),x83993))
% 51.10/50.83 [8400]E(f331(f331(f3(a1),x84001),x84002),x84001)+~P1(f331(f331(f241(a1),f2(a1)),x84002))+P1(f331(f331(f333(a1),f451(x84003,x84001,x84002)),f303(a1,f85(a1),x84002)))+~P1(f331(f331(f333(a1),f331(f331(f3(a1),x84001),f85(a1))),x84003))
% 51.10/50.83 [8522]~P85(x85221)+~P1(f331(f331(f241(x85221),x85222),f85(x85221)))+~P1(f331(f331(f241(x85221),f2(x85221)),x85222))+P1(f331(f331(f241(x85221),f331(f331(f88(x85221),x85222),f331(f331(f250(x85221),x85222),x85223))),f331(f331(f250(x85221),x85222),x85223)))
% 51.10/50.83 [8598]~P1(f331(x85981,x85982))+P1(f331(x85981,f2(a847)))+~P1(f331(f331(f241(a847),x85982),x85983))+~P1(f331(x85981,f57(a847,f331(a119,f802(x85982,x85981,x85983)),x85983)))
% 51.10/50.83 [8728]E(f826(x87281,x87282,x87283),f2(a847))+P1(f331(f331(x87281,x87283),x87282))+P1(f331(f331(x87281,f826(x87281,x87282,x87283)),f57(a847,f825(x87281,x87282,x87283),f826(x87281,x87282,x87283))))+~P1(f331(f320(f853(a847,a847),a221),f331(f331(f249(a847,a847),x87283),x87282)))
% 51.10/50.83 [8760]~P27(x87601,x87601,x87602,x87603)+E(f331(f311(x87601,x87601,x87602),x87603),x87603)+~P1(f331(f68(x87601),x87603))+~P1(f331(f331(f240(f854(x87601,a840)),f331(f311(x87601,x87601,x87602),x87603)),x87603))
% 51.10/50.83 [8974]P1(f331(f331(x89741,x89742),x89743))+~P1(f331(f331(f241(a1),f824(x89741,x89743,x89742)),f2(a1)))+P1(f331(f331(x89741,f331(f86(a1),f821(x89741,x89743,x89742))),f331(f86(a1),f824(x89741,x89743,x89742))))+~P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),x89742),x89743)))
% 51.10/50.83 [9133]P1(f331(f331(x91331,x91332),x91333))+P1(f331(f331(x91331,f331(f331(f87(a1),f730(x91331,x91333,x91332)),f85(a1))),f733(x91331,x91333,x91332)))+~P1(f331(f331(f240(a1),f730(x91331,x91333,x91332)),f733(x91331,x91333,x91332)))+~P1(f331(f320(f853(a1,a1),a173),f331(f331(f249(a1,a1),x91332),x91333)))
% 51.10/50.83 [9824]E(f331(x98241,f807(x98242,x98241,x98243)),x98242)+~P1(f331(f331(f240(a1),x98242),f331(x98241,x98243)))+~P1(f331(f331(f240(a1),f331(f82(a1),f331(f331(f3(a1),f331(x98241,f331(f331(f87(a847),f808(x98242,x98241,x98243)),f85(a847)))),f331(x98241,f808(x98242,x98241,x98243))))),f85(a1)))+~P1(f331(f331(f240(a1),f331(x98241,f2(a847))),x98242))
% 51.10/50.83 [9825]E(f331(x98251,f809(x98252,x98251,x98253)),x98252)+~P1(f331(f331(f240(a1),x98252),f331(x98251,x98253)))+~P1(f331(f331(f240(a1),f331(f82(a1),f331(f331(f3(a1),f331(x98251,f331(f331(f87(a847),f810(x98252,x98251,x98253)),f85(a847)))),f331(x98251,f810(x98252,x98251,x98253))))),f85(a1)))+~P1(f331(f331(f240(a1),f331(x98251,f2(a847))),x98252))
% 51.10/50.83 [9829]~P1(f331(f331(f240(a1),x98291),f331(x98292,x98293)))+~P1(f331(f331(f240(a1),f331(f82(a1),f331(f331(f3(a1),f331(x98292,f331(f331(f87(a847),f808(x98291,x98292,x98293)),f85(a847)))),f331(x98292,f808(x98291,x98292,x98293))))),f85(a1)))+P1(f331(f331(f240(a847),f807(x98291,x98292,x98293)),x98293))+~P1(f331(f331(f240(a1),f331(x98292,f2(a847))),x98291))
% 51.10/50.83 [9830]~P1(f331(f331(f240(a1),x98301),f331(x98302,x98303)))+~P1(f331(f331(f240(a1),f331(f82(a1),f331(f331(f3(a1),f331(x98302,f331(f331(f87(a847),f810(x98301,x98302,x98303)),f85(a847)))),f331(x98302,f810(x98301,x98302,x98303))))),f85(a1)))+P1(f331(f331(f240(a847),f809(x98301,x98302,x98303)),x98303))+~P1(f331(f331(f240(a1),f331(x98302,f2(a847))),x98301))
% 51.10/50.83 [9884]E(x98841,x98842)+~E(f331(f137(f848(x98843),f848(x98843),f130(x98843),f120(x98843)),x98841),f331(f137(f848(x98843),f848(x98843),f130(x98843),f120(x98843)),x98842))+~E(f331(f185(f848(f848(x98843))),x98841),f331(f185(f848(f848(x98843))),x98842))+~P1(f331(f331(f259(f848(x98843),f848(x98843),a840),f331(f331(f9(f848(x98843),f854(f848(x98843),a847),f854(f848(x98843),a840)),f331(f331(f10(f854(a847,a840),f854(f854(f848(x98843),a847),f854(f848(x98843),a840)),f848(x98843)),f10(a847,a840,f848(x98843))),f331(f331(f10(a847,f854(a847,a840),f848(x98843)),a328),f185(f848(x98843))))),f185(f848(x98843)))),f772(x98841,x98842,x98843)))
% 51.10/50.83 [9885]E(x98851,x98852)+~E(f331(f137(f848(x98853),f848(x98853),f130(x98853),f120(x98853)),x98851),f331(f137(f848(x98853),f848(x98853),f130(x98853),f120(x98853)),x98852))+~E(f331(f185(f848(f848(x98853))),x98851),f331(f185(f848(f848(x98853))),x98852))+~P1(f331(f331(f259(f848(x98853),f848(x98853),a840),f331(f331(f9(f848(x98853),f854(f848(x98853),a847),f854(f848(x98853),a840)),f331(f331(f10(f854(a847,a840),f854(f854(f848(x98853),a847),f854(f848(x98853),a840)),f848(x98853)),f10(a847,a840,f848(x98853))),f331(f331(f10(a847,f854(a847,a840),f848(x98853)),a328),f185(f848(x98853))))),f185(f848(x98853)))),f773(x98852,x98851,x98853)))
% 51.10/50.83 [6684]~E(f85(a847),f2(a847))+~P1(f331(f68(x66841),x66843))+~P1(f331(f68(x66841),x66842))+E(f331(f331(f87(a847),f331(f47(x66841),x66842)),f331(f47(x66841),x66843)),f331(f47(x66841),f331(f331(f108(f854(x66841,a840)),x66842),x66843)))
% 51.10/50.83 [7103]~P102(x71031)+~P1(f331(f68(x71031),x71032))+~P1(f331(f331(f333(x71031),x71033),x71032))+P1(f331(f331(f240(x71031),f331(f70(x71031,f244(x71031)),x71032)),x71033))
% 51.10/50.83 [7104]~P101(x71041)+~P1(f331(f68(x71041),x71042))+~P1(f331(f331(f333(x71041),x71043),x71042))+P1(f331(f331(f240(x71041),f331(f70(x71041,f109(x71041)),x71042)),x71043))
% 51.10/50.83 [7377]~P1(f331(f68(x73771),x73773))+~P1(f331(f68(x73771),x73772))+~E(f331(f331(f109(f854(x73771,a840)),x73772),x73773),f184(f854(x73771,a840)))+E(f331(f331(f87(a847),f331(f47(x73771),x73772)),f331(f47(x73771),x73773)),f331(f47(x73771),f331(f331(f108(f854(x73771,a840)),x73772),x73773)))
% 51.10/50.83 [8168]~P34(x81681,x81683)+~P34(x81681,x81682)+~E(f331(f331(f109(f854(x81681,a840)),f331(f269(x81681,x81681),x81682)),f331(f267(x81681,x81681),x81683)),f184(f854(x81681,a840)))+P34(x81681,f331(f331(f108(f854(f853(x81681,x81681),a840)),x81682),x81683))
% 51.10/50.83 [8257]E(x82571,f331(f331(f48(a847),x82572),x82573))+~P1(f331(f331(f241(a847),f2(a847)),x82573))+~P1(f331(f331(f241(a847),x82572),f331(f331(f88(a847),x82573),f331(a119,x82571))))+~P1(f331(f331(f240(a847),f331(f331(f88(a847),x82573),x82571)),x82572))
% 51.10/50.83 [8397]~P1(f331(f68(x83971),x83972))+~P1(f331(f68(x83971),x83973))+E(f331(f331(f87(a847),f331(f47(x83971),x83972)),f331(f47(x83971),x83973)),f331(f47(x83971),f331(f331(f108(f854(x83971,a840)),x83972),x83973)))+P1(f331(f331(f333(x83971),f374(x83973,x83972,x83971)),f331(f331(f109(f854(x83971,a840)),x83972),x83973)))
% 51.10/50.83 [8739]~P118(x87392)+~E(x87391,f2(x87392))+~E(x87393,f2(x87392))+~P1(f331(f331(f241(x87392),f2(x87392)),f331(f331(f87(x87392),f331(f331(f88(x87392),x87393),x87393)),f331(f331(f88(x87392),x87391),x87391))))
% 51.10/50.83 [9205]~P34(x92051,x92053)+~P34(x92051,x92052)+P34(x92051,f331(f331(f108(f854(f853(x92051,x92051),a840)),x92052),x92053))+~P1(f331(f331(f240(f854(f853(x92051,x92051),a840)),f331(f331(f289(x92051,x92051,x92051),x92052),x92053)),x92052))
% 51.10/50.83 [9332]~P1(f331(x93321,x93323))+~P1(f331(f68(x93322),x93323))+P1(f331(x93321,f184(f854(x93322,a840))))+~P1(f331(x93321,f331(f331(f3(f854(x93322,a840)),f440(x93321,x93323,x93322)),f331(f331(f310(x93322),f441(x93321,x93323,x93322)),f184(f854(x93322,a840))))))
% 51.10/50.83 [8552]~P1(f331(f331(f241(a1),f2(a1)),x85523))+P1(f331(f331(f240(a1),f2(a1)),x85521))+~P1(f331(f331(f241(a1),x85522),x85523))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f331(f331(f88(a1),x85523),x85521)),x85522)))
% 51.10/50.83 [8572]~P97(x85721)+~P1(f331(f68(x85721),x85722))+E(f331(f331(f3(f854(x85721,a840)),x85722),f331(f331(f310(x85721),x85723),f184(f854(x85721,a840)))),f184(f854(x85721,a840)))+E(f331(f331(f109(x85721),x85723),f12(x85721,f331(f331(f3(f854(x85721,a840)),x85722),f331(f331(f310(x85721),x85723),f184(f854(x85721,a840)))))),f12(x85721,f331(f331(f310(x85721),x85723),x85722)))
% 51.10/50.83 [8573]~P97(x85731)+~P1(f331(f68(x85731),x85732))+E(f331(f331(f3(f854(x85731,a840)),x85732),f331(f331(f310(x85731),x85733),f184(f854(x85731,a840)))),f184(f854(x85731,a840)))+E(f331(f331(f108(x85731),x85733),f15(x85731,f331(f331(f3(f854(x85731,a840)),x85732),f331(f331(f310(x85731),x85733),f184(f854(x85731,a840)))))),f15(x85731,f331(f331(f310(x85731),x85733),x85732)))
% 51.10/50.83 [8574]~P102(x85741)+~P1(f331(f68(x85741),x85742))+E(f331(f331(f3(f854(x85741,a840)),x85742),f331(f331(f310(x85741),x85743),f184(f854(x85741,a840)))),f184(f854(x85741,a840)))+E(f331(f331(f239(x85741),x85743),f16(x85741,f331(f331(f3(f854(x85741,a840)),x85742),f331(f331(f310(x85741),x85743),f184(f854(x85741,a840)))))),f16(x85741,f331(f331(f310(x85741),x85743),x85742)))
% 51.10/50.83 [8575]~P102(x85751)+~P1(f331(f68(x85751),x85752))+E(f331(f331(f3(f854(x85751,a840)),x85752),f331(f331(f310(x85751),x85753),f184(f854(x85751,a840)))),f184(f854(x85751,a840)))+E(f331(f331(f244(x85751),x85753),f17(x85751,f331(f331(f3(f854(x85751,a840)),x85752),f331(f331(f310(x85751),x85753),f184(f854(x85751,a840)))))),f17(x85751,f331(f331(f310(x85751),x85753),x85752)))
% 51.10/50.83 [8637]~P102(x86371)+~P1(f331(f68(x86371),x86372))+E(f331(f331(f3(f854(x86371,a840)),x86372),f331(f331(f310(x86371),x86373),f184(f854(x86371,a840)))),f184(f854(x86371,a840)))+E(f331(f331(f239(x86371),x86373),f13(x86371,f239(x86371),f331(f331(f3(f854(x86371,a840)),x86372),f331(f331(f310(x86371),x86373),f184(f854(x86371,a840)))))),f13(x86371,f239(x86371),f331(f331(f310(x86371),x86373),x86372)))
% 51.10/50.83 [8638]~P102(x86381)+~P1(f331(f68(x86381),x86382))+E(f331(f331(f3(f854(x86381,a840)),x86382),f331(f331(f310(x86381),x86383),f184(f854(x86381,a840)))),f184(f854(x86381,a840)))+E(f331(f331(f244(x86381),x86383),f14(x86381,f244(x86381),f331(f331(f3(f854(x86381,a840)),x86382),f331(f331(f310(x86381),x86383),f184(f854(x86381,a840)))))),f14(x86381,f244(x86381),f331(f331(f310(x86381),x86383),x86382)))
% 51.10/50.83 [9147]E(x91471,x91472)+~E(f331(f137(f848(x91473),f848(x91473),f130(x91473),f120(x91473)),x91471),f331(f137(f848(x91473),f848(x91473),f130(x91473),f120(x91473)),x91472))+~E(f331(f185(f848(f848(x91473))),x91471),f331(f185(f848(f848(x91473))),x91472))+P1(f331(f331(f333(f853(f848(x91473),f848(x91473))),f772(x91471,x91472,x91473)),f331(f163(f853(f848(x91473),f848(x91473))),f331(f331(f172(f848(x91473),f848(x91473)),x91472),x91471))))
% 51.10/50.83 [9148]E(x91481,x91482)+~E(f331(f137(f848(x91483),f848(x91483),f130(x91483),f120(x91483)),x91481),f331(f137(f848(x91483),f848(x91483),f130(x91483),f120(x91483)),x91482))+~E(f331(f185(f848(f848(x91483))),x91481),f331(f185(f848(f848(x91483))),x91482))+P1(f331(f331(f333(f853(f848(x91483),f848(x91483))),f773(x91482,x91481,x91483)),f331(f163(f853(f848(x91483),f848(x91483))),f331(f331(f172(f848(x91483),f848(x91483)),x91481),x91482))))
% 51.10/50.83 [9977]~P73(x99772)+E(x99771,f184(f854(x99772,a840)))+~P1(f331(f68(x99772),x99771))+E(f16(x99772,f331(f264(x99772),f331(f331(f10(f854(x99772,a840),a840,x99772),f94(x99772)),f331(f331(f9(x99772,f854(x99772,a840),f854(x99772,a840)),f331(f331(f10(f854(x99772,f854(a840,a840)),f854(f854(x99772,a840),f854(x99772,a840)),x99772),f20(x99772,a840,a840)),f331(f331(f10(f854(x99772,a840),f854(x99772,f854(a840,a840)),x99772),f331(f10(a840,f854(a840,a840),x99772),a329)),f331(f331(f9(x99772,f854(x99772,x99772),f854(x99772,a840)),f331(f331(f10(f854(x99772,a840),f854(f854(x99772,x99772),f854(x99772,a840)),x99772),f10(x99772,a840,x99772)),a328)),f331(f87(x99772),x99773))))),f331(f331(f9(x99772,f854(x99772,a840),a840),f333(x99772)),x99771))))),f331(f331(f87(x99772),x99773),f16(x99772,x99771)))
% 51.10/50.83 [9978]~P73(x99782)+E(x99781,f184(f854(x99782,a840)))+~P1(f331(f68(x99782),x99781))+E(f17(x99782,f331(f264(x99782),f331(f331(f10(f854(x99782,a840),a840,x99782),f94(x99782)),f331(f331(f9(x99782,f854(x99782,a840),f854(x99782,a840)),f331(f331(f10(f854(x99782,f854(a840,a840)),f854(f854(x99782,a840),f854(x99782,a840)),x99782),f20(x99782,a840,a840)),f331(f331(f10(f854(x99782,a840),f854(x99782,f854(a840,a840)),x99782),f331(f10(a840,f854(a840,a840),x99782),a329)),f331(f331(f9(x99782,f854(x99782,x99782),f854(x99782,a840)),f331(f331(f10(f854(x99782,a840),f854(f854(x99782,x99782),f854(x99782,a840)),x99782),f10(x99782,a840,x99782)),a328)),f331(f87(x99782),x99783))))),f331(f331(f9(x99782,f854(x99782,a840),a840),f333(x99782)),x99781))))),f331(f331(f87(x99782),x99783),f17(x99782,x99781)))
% 51.10/50.83 [9979]~P98(x99792)+E(x99791,f184(f854(x99792,a840)))+~P1(f331(f68(x99792),x99791))+E(f12(x99792,f331(f264(x99792),f331(f331(f10(f854(x99792,a840),a840,x99792),f94(x99792)),f331(f331(f9(x99792,f854(x99792,a840),f854(x99792,a840)),f331(f331(f10(f854(x99792,f854(a840,a840)),f854(f854(x99792,a840),f854(x99792,a840)),x99792),f20(x99792,a840,a840)),f331(f331(f10(f854(x99792,a840),f854(x99792,f854(a840,a840)),x99792),f331(f10(a840,f854(a840,a840),x99792),a329)),f331(f331(f9(x99792,f854(x99792,x99792),f854(x99792,a840)),f331(f331(f10(f854(x99792,a840),f854(f854(x99792,x99792),f854(x99792,a840)),x99792),f10(x99792,a840,x99792)),a328)),f331(f108(x99792),x99793))))),f331(f331(f9(x99792,f854(x99792,a840),a840),f333(x99792)),x99791))))),f331(f331(f108(x99792),x99793),f12(x99792,x99791)))
% 51.10/50.83 [9980]~P98(x99802)+E(x99801,f184(f854(x99802,a840)))+~P1(f331(f68(x99802),x99801))+E(f15(x99802,f331(f264(x99802),f331(f331(f10(f854(x99802,a840),a840,x99802),f94(x99802)),f331(f331(f9(x99802,f854(x99802,a840),f854(x99802,a840)),f331(f331(f10(f854(x99802,f854(a840,a840)),f854(f854(x99802,a840),f854(x99802,a840)),x99802),f20(x99802,a840,a840)),f331(f331(f10(f854(x99802,a840),f854(x99802,f854(a840,a840)),x99802),f331(f10(a840,f854(a840,a840),x99802),a329)),f331(f331(f9(x99802,f854(x99802,x99802),f854(x99802,a840)),f331(f331(f10(f854(x99802,a840),f854(f854(x99802,x99802),f854(x99802,a840)),x99802),f10(x99802,a840,x99802)),a328)),f331(f109(x99802),x99803))))),f331(f331(f9(x99802,f854(x99802,a840),a840),f333(x99802)),x99801))))),f331(f331(f109(x99802),x99803),f15(x99802,x99801)))
% 51.10/50.83 [9981]~P102(x99812)+E(x99811,f184(f854(x99812,a840)))+~P1(f331(f68(x99812),x99811))+E(f13(x99812,f239(x99812),f331(f264(x99812),f331(f331(f10(f854(x99812,a840),a840,x99812),f94(x99812)),f331(f331(f9(x99812,f854(x99812,a840),f854(x99812,a840)),f331(f331(f10(f854(x99812,f854(a840,a840)),f854(f854(x99812,a840),f854(x99812,a840)),x99812),f20(x99812,a840,a840)),f331(f331(f10(f854(x99812,a840),f854(x99812,f854(a840,a840)),x99812),f331(f10(a840,f854(a840,a840),x99812),a329)),f331(f331(f9(x99812,f854(x99812,x99812),f854(x99812,a840)),f331(f331(f10(f854(x99812,a840),f854(f854(x99812,x99812),f854(x99812,a840)),x99812),f10(x99812,a840,x99812)),a328)),f331(f244(x99812),x99813))))),f331(f331(f9(x99812,f854(x99812,a840),a840),f333(x99812)),x99811))))),f331(f331(f244(x99812),x99813),f13(x99812,f239(x99812),x99811)))
% 51.10/50.83 [9982]~P102(x99822)+E(x99821,f184(f854(x99822,a840)))+~P1(f331(f68(x99822),x99821))+E(f14(x99822,f244(x99822),f331(f264(x99822),f331(f331(f10(f854(x99822,a840),a840,x99822),f94(x99822)),f331(f331(f9(x99822,f854(x99822,a840),f854(x99822,a840)),f331(f331(f10(f854(x99822,f854(a840,a840)),f854(f854(x99822,a840),f854(x99822,a840)),x99822),f20(x99822,a840,a840)),f331(f331(f10(f854(x99822,a840),f854(x99822,f854(a840,a840)),x99822),f331(f10(a840,f854(a840,a840),x99822),a329)),f331(f331(f9(x99822,f854(x99822,x99822),f854(x99822,a840)),f331(f331(f10(f854(x99822,a840),f854(f854(x99822,x99822),f854(x99822,a840)),x99822),f10(x99822,a840,x99822)),a328)),f331(f239(x99822),x99823))))),f331(f331(f9(x99822,f854(x99822,a840),a840),f333(x99822)),x99821))))),f331(f331(f239(x99822),x99823),f14(x99822,f244(x99822),x99821)))
% 51.10/50.83 [9705]~P86(x97051)+~E(x97053,f2(x97051))+~E(x97052,f2(x97051))+E(f331(f331(f87(x97051),f331(f331(f250(x97051),x97052),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x97051),x97053),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f2(x97051))
% 51.10/50.83 [9868]~P85(x98681)+~P1(f331(f331(f240(x98681),f2(x98681)),x98683))+P1(f331(f331(f241(x98681),x98682),x98683))+~P1(f331(f331(f241(x98681),f331(f331(f250(x98681),x98682),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x98681),x98683),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.83 [9869]~P85(x98691)+~P1(f331(f331(f240(x98691),f2(x98691)),x98693))+P1(f331(f331(f240(x98691),x98692),x98693))+~P1(f331(f331(f240(x98691),f331(f331(f250(x98691),x98692),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x98691),x98693),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))))
% 51.10/50.83 [9915]~P86(x99152)+~E(x99151,f2(x99152))+~E(x99153,f2(x99152))+~P1(f331(f331(f241(x99152),f2(x99152)),f331(f331(f87(x99152),f331(f331(f250(x99152),x99153),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104))))),f331(f331(f250(x99152),x99151),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))))
% 51.10/50.83 [9121]E(x91211,x91212)+~E(f752(x91211,x91212,x91214,x91213),f754(x91211,x91212,x91214,x91213))+P1(f331(f331(f333(f853(f848(x91213),f848(x91213))),f331(f331(f249(f848(x91213),f848(x91213)),x91212),x91211)),f142(x91213,x91214)))+P1(f331(f331(f333(f853(f848(x91213),f848(x91213))),f331(f331(f249(f848(x91213),f848(x91213)),x91211),x91212)),f142(x91213,x91214)))
% 51.10/50.83 [4717]~P58(x47172)+~E(x47174,f2(x47172))+~E(x47171,f2(x47172))+E(x47171,f331(f331(f291(x47172),x47173),x47174))
% 51.10/50.83 [4718]~P58(x47181)+~E(x47183,f2(x47181))+~E(x47184,f2(x47181))+E(f331(f331(f291(x47181),x47182),x47183),x47184)
% 51.10/50.83 [4827]~P58(x48272)+E(x48271,f2(x48272))+~E(x48273,f2(x48272))+~E(x48271,f331(f331(f291(x48272),x48274),x48273))
% 51.10/50.83 [4828]~P58(x48282)+E(x48281,f2(x48282))+~E(x48283,f2(x48282))+~E(f331(f331(f291(x48282),x48284),x48283),x48281)
% 51.10/50.83 [5003]~P114(x50032)+E(x50031,f2(x50032))+~E(f331(f331(f291(x50032),x50033),x50031),x50034)+E(x50033,f331(f331(f88(x50032),x50034),x50031))
% 51.10/50.83 [5004]~P114(x50042)+E(x50041,f2(x50042))+~E(f331(f331(f88(x50042),x50043),x50041),x50044)+E(x50043,f331(f331(f291(x50042),x50044),x50041))
% 51.10/50.83 [5005]~P114(x50052)+E(x50051,f2(x50052))+~E(f331(f331(f88(x50052),x50053),x50051),x50054)+E(x50053,f331(f331(f291(x50052),x50054),x50051))
% 51.10/50.83 [5006]~P58(x50062)+E(x50061,f2(x50062))+~E(f331(f331(f291(x50062),x50063),x50061),x50064)+E(x50063,f331(f331(f88(x50062),x50064),x50061))
% 51.10/50.83 [5007]~P58(x50072)+E(x50071,f2(x50072))+~E(f331(f331(f88(x50072),x50073),x50071),x50074)+E(x50073,f331(f331(f291(x50072),x50074),x50071))
% 51.10/50.83 [5008]~P114(x50082)+E(x50081,f2(x50082))+~E(x50083,f331(f331(f291(x50082),x50084),x50081))+E(f331(f331(f88(x50082),x50083),x50081),x50084)
% 51.10/50.83 [5009]~P114(x50092)+E(x50091,f2(x50092))+~E(x50093,f331(f331(f88(x50092),x50094),x50091))+E(f331(f331(f291(x50092),x50093),x50091),x50094)
% 51.10/50.83 [5010]~P114(x50102)+E(x50101,f2(x50102))+~E(x50103,f331(f331(f88(x50102),x50104),x50101))+E(f331(f331(f291(x50102),x50103),x50101),x50104)
% 51.10/50.83 [5011]~P58(x50112)+E(x50111,f2(x50112))+~E(x50113,f331(f331(f291(x50112),x50114),x50111))+E(f331(f331(f88(x50112),x50113),x50111),x50114)
% 51.10/50.83 [5012]~P58(x50122)+E(x50121,f2(x50122))+~E(x50123,f331(f331(f88(x50122),x50124),x50121))+E(f331(f331(f291(x50122),x50123),x50121),x50124)
% 51.10/50.83 [5046]~P58(x50462)+~E(x50461,f2(x50462))+~E(f331(f331(f88(x50462),x50461),x50464),x50463)+E(x50461,f331(f331(f291(x50462),x50463),x50464))
% 51.10/50.83 [5047]~P58(x50471)+~E(x50474,f2(x50471))+~E(x50472,f331(f331(f88(x50471),x50474),x50473))+E(f331(f331(f291(x50471),x50472),x50473),x50474)
% 51.10/50.83 [5114]~E(x51143,x51144)+~E(x51142,x51143)+~P88(x51141)+E(f303(x51141,x51142,x51143),f331(f331(f310(x51141),x51144),f184(f854(x51141,a840))))
% 51.10/50.83 [5309]~E(f139(x53092,x53091),x53094)+~E(f121(x53092,x53091),x53093)+E(x53091,f120(x53092))+E(f331(f331(f130(x53092),x53093),f331(f331(f145(x53092),x53094),f120(x53092))),x53091)
% 51.10/50.83 [5933]~P85(x59333)+E(x59331,x59332)+~E(f331(f331(f250(x59333),x59334),x59331),f331(f331(f250(x59333),x59334),x59332))+~P1(f331(f331(f241(x59333),f85(x59333)),x59334))
% 51.10/50.83 [5934]E(x59341,x59342)+~E(f331(f331(f310(x59343),x59344),x59341),f331(f331(f310(x59343),x59344),x59342))+P1(f331(f331(f333(x59343),x59344),x59342))+P1(f331(f331(f333(x59343),x59344),x59341))
% 51.10/50.83 [5972]E(f331(x59721,x59722),f2(a847))+~E(f331(f331(f8(x59723,a847),x59721),x59724),f2(a847))+~P1(f331(f68(x59723),x59724))+~P1(f331(f331(f333(x59723),x59722),x59724))
% 51.10/50.83 [5973]E(f331(x59731,x59732),f85(a847))+~E(f331(f331(f11(x59733,a847),x59731),x59734),f85(a847))+~P1(f331(f68(x59733),x59734))+~P1(f331(f331(f333(x59733),x59732),x59734))
% 51.10/50.83 [6199]~P88(x61991)+~P1(f331(f331(f241(x61991),x61994),x61993))+P1(f331(f331(f241(x61991),x61992),x61993))+~P1(f331(f331(f241(x61991),x61992),x61994))
% 51.10/50.83 [6200]~P88(x62001)+~P1(f331(f331(f240(x62001),x62004),x62003))+P1(f331(f331(f241(x62001),x62002),x62003))+~P1(f331(f331(f241(x62001),x62002),x62004))
% 51.10/50.83 [6201]~P88(x62011)+~P1(f331(f331(f240(x62011),x62012),x62014))+P1(f331(f331(f241(x62011),x62012),x62013))+~P1(f331(f331(f241(x62011),x62014),x62013))
% 51.10/50.83 [6202]~P105(x62021)+~P1(f331(f331(f241(x62021),x62022),x62024))+P1(f331(f331(f241(x62021),x62022),x62023))+~P1(f331(f331(f241(x62021),x62024),x62023))
% 51.10/50.83 [6203]~P105(x62031)+~P1(f331(f331(f240(x62031),x62032),x62034))+P1(f331(f331(f241(x62031),x62032),x62033))+~P1(f331(f331(f241(x62031),x62034),x62033))
% 51.10/50.83 [6204]~P105(x62041)+~P1(f331(f331(f240(x62041),x62044),x62043))+P1(f331(f331(f241(x62041),x62042),x62043))+~P1(f331(f331(f241(x62041),x62042),x62044))
% 51.10/50.83 [6205]~P88(x62051)+~P1(f331(f331(f240(x62051),x62054),x62053))+P1(f331(f331(f240(x62051),x62052),x62053))+~P1(f331(f331(f240(x62051),x62052),x62054))
% 51.10/50.83 [6206]~P105(x62061)+~P1(f331(f331(f240(x62061),x62062),x62064))+P1(f331(f331(f240(x62061),x62062),x62063))+~P1(f331(f331(f240(x62061),x62064),x62063))
% 51.10/50.83 [6207]~P87(x62071)+~P1(f331(f331(f287(x62071),x62072),x62074))+P1(f331(f331(f287(x62071),x62072),x62073))+~P1(f331(f331(f287(x62071),x62074),x62073))
% 51.10/50.83 [6450]~P7(x64501)+~P1(f331(f331(f240(x64501),x64502),f50(x64501,x64504)))+P1(f331(f331(f240(x64501),x64502),x64503))+~P1(f331(f331(f333(x64501),x64503),x64504))
% 51.10/50.83 [6599]~P102(x65991)+~P16(x65991,f331(f331(f145(x65991),x65992),x65994))+~P1(f331(f331(f333(x65991),x65993),f331(f163(x65991),x65994)))+P1(f331(f331(f240(x65991),x65992),x65993))
% 51.10/50.83 [6600]~P102(x66001)+~P16(x66001,f331(f331(f145(x66001),x66002),x66004))+~P1(f331(f331(f333(x66001),x66003),f331(f163(x66001),x66004)))+P1(f331(f331(f240(x66001),x66002),x66003))
% 51.10/50.83 [6693]~P7(x66931)+~P1(f331(f331(f240(x66931),f49(x66931,x66934)),x66933))+P1(f331(f331(f240(x66931),x66932),x66933))+~P1(f331(f331(f333(x66931),x66932),x66934))
% 51.10/50.83 [6844]~P5(x68441)+P1(f331(f331(f287(x68441),x68442),f57(x68441,x68443,x68444)))+~P1(f331(f331(f287(x68441),x68442),x68444))+~P1(f331(f331(f287(x68441),x68442),x68443))
% 51.10/50.83 [6845]~P5(x68451)+P1(f331(f331(f287(x68451),x68452),f57(x68451,x68453,x68454)))+~P1(f331(f331(f287(x68451),x68452),x68454))+~P1(f331(f331(f287(x68451),x68452),x68453))
% 51.10/50.83 [7106]~P102(x71061)+E(f331(f331(f108(f854(x71061,a840)),f331(f302(x71061,x71062),x71063)),f331(f302(x71061,x71063),x71064)),f331(f302(x71061,x71062),x71064))+~P1(f331(f331(f240(x71061),x71063),x71064))+~P1(f331(f331(f240(x71061),x71062),x71063))
% 51.10/50.83 [7190]~P5(x71901)+~P1(f331(f331(f287(x71901),x71902),f57(x71901,x71903,x71904)))+P1(f331(f331(f287(x71901),x71902),x71903))+~P1(f331(f331(f287(x71901),x71902),x71904))
% 51.10/50.83 [7191]~P5(x71911)+~P1(f331(f331(f287(x71911),x71912),f57(x71911,x71913,x71914)))+P1(f331(f331(f287(x71911),x71912),x71913))+~P1(f331(f331(f287(x71911),x71912),x71914))
% 51.10/50.83 [7232]~P102(x72321)+E(f331(f331(f108(f854(x72321,a840)),f331(f302(x72321,x72322),x72323)),f303(x72321,x72323,x72324)),f303(x72321,x72322,x72324))+~P1(f331(f331(f240(x72321),x72323),x72324))+~P1(f331(f331(f240(x72321),x72322),x72323))
% 51.10/50.83 [7246]~P88(x72461)+~P48(a847,x72461,f287(a847),x72462)+P1(f331(f331(f240(x72461),f331(x72462,x72463)),f331(x72462,x72464)))+~P1(f331(f331(f287(a847),x72463),x72464))
% 51.10/50.83 [7300]~P102(x73001)+E(f331(f331(f108(f854(x73001,a840)),f306(x73001,x73002,x73003)),f331(f302(x73001,x73003),x73004)),f306(x73001,x73002,x73004))+~P1(f331(f331(f241(x73001),x73002),x73003))+~P1(f331(f331(f240(x73001),x73003),x73004))
% 51.10/50.83 [7323]~P102(x73231)+E(f331(f331(f108(f854(x73231,a840)),f303(x73231,x73232,x73233)),f306(x73231,x73233,x73234)),f331(f302(x73231,x73232),x73234))+~P1(f331(f331(f241(x73231),x73233),x73234))+~P1(f331(f331(f240(x73231),x73232),x73233))
% 51.10/50.83 [7358]~P102(x73581)+E(f331(f331(f108(f854(x73581,a840)),f306(x73581,x73582,x73583)),f303(x73581,x73583,x73584)),f305(x73581,x73582,x73584))+~P1(f331(f331(f241(x73581),x73582),x73583))+~P1(f331(f331(f240(x73581),x73583),x73584))
% 51.10/50.83 [7359]~P102(x73591)+E(f331(f331(f108(f854(x73591,a840)),f305(x73591,x73592,x73593)),f306(x73591,x73593,x73594)),f306(x73591,x73592,x73594))+~P1(f331(f331(f241(x73591),x73593),x73594))+~P1(f331(f331(f240(x73591),x73592),x73593))
% 51.10/50.83 [7360]~P102(x73601)+E(f331(f331(f108(f854(x73601,a840)),f305(x73601,x73602,x73603)),f305(x73601,x73603,x73604)),f305(x73601,x73602,x73604))+~P1(f331(f331(f240(x73601),x73603),x73604))+~P1(f331(f331(f240(x73601),x73602),x73603))
% 51.10/50.83 [7361]~P102(x73611)+E(f331(f331(f108(f854(x73611,a840)),f303(x73611,x73612,x73613)),f305(x73611,x73613,x73614)),f303(x73611,x73612,x73614))+~P1(f331(f331(f240(x73611),x73613),x73614))+~P1(f331(f331(f240(x73611),x73612),x73613))
% 51.10/50.83 [8152]P27(x81521,x81522,f445(x81523,x81522,x81524,x81521),x81524)+~P1(f331(f68(x81522),x81523))+~P1(f331(f68(x81521),x81524))+~P1(f331(f331(f240(a847),f331(f47(x81521),x81524)),f331(f47(x81522),x81523)))
% 51.10/50.83 [8223]~P70(x82231)+~E(f331(x82233,f621(x82233,x82234,x82232,x82231)),f85(x82231))+E(f331(f331(f331(f72(x82231,x82232,f88(x82231)),x82233),f85(x82231)),x82234),f85(x82231))+~P1(f331(f68(x82232),x82234))
% 51.10/50.83 [8494]~P85(x84941)+~P1(f331(f331(f240(x84941),f2(x84941)),x84943))+P1(f331(f331(f240(x84941),x84942),x84943))+~P1(f331(f331(f240(x84941),f331(f331(f250(x84941),x84942),f331(a119,x84944))),f331(f331(f250(x84941),x84943),f331(a119,x84944))))
% 51.10/50.83 [8825]~P70(x88251)+E(f331(f331(f331(f72(x88251,x88252,f88(x88251)),x88253),f85(x88251)),x88254),f85(x88251))+~P1(f331(f68(x88252),x88254))+P1(f331(f331(f333(x88252),f621(x88253,x88254,x88252,x88251)),x88254))
% 51.10/50.83 [9073]~P10(x90732,x90733,x90734)+~P1(f331(f68(x90732),x90733))+~P1(f331(f331(f287(a847),x90731),f331(f47(x90732),f394(x90731,x90734,x90733,x90732))))+P1(f331(f331(f287(a847),x90731),f331(f47(x90732),x90733)))
% 51.10/50.83 [9259]~P1(f331(f331(f287(a847),x92592),x92593))+P1(f331(f331(f287(a847),x92591),x92592))+P1(f331(f331(f287(a847),x92593),x92594))+~P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x92592,x92593)),f290(a847,f287(a847),x92591,x92594)))
% 51.10/50.83 [9263]P1(f331(f331(f287(a847),x92631),x92632))+~P1(f331(f331(f287(a847),x92632),x92633))+~P1(f331(f331(f287(a847),x92634),x92633))+~P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x92632,x92633)),f290(a847,f287(a847),x92631,x92634)))
% 51.10/50.83 [9264]~P1(f331(f331(f287(a847),x92643),x92641))+P1(f331(f331(f287(a847),x92641),x92642))+~P1(f331(f331(f287(a847),x92643),x92644))+~P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x92643,x92641)),f290(a847,f287(a847),x92644,x92642)))
% 51.10/50.83 [9271]~P1(f331(f331(f287(a847),x92711),x92713))+~P1(f331(f331(f287(a847),x92711),x92712))+~P1(f331(f331(f287(a847),x92714),x92713))+~P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x92711,x92713)),f290(a847,f287(a847),x92712,x92714)))
% 51.10/50.83 [9277]~P1(f331(f331(f240(a1),x92774),f2(a1)))+P1(f331(f331(f240(a1),f331(f331(f87(a1),f331(f331(f88(a1),x92771),f57(a1,x92772,x92773))),x92774)),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x92773))+~P1(f331(f331(f241(a1),x92771),x92774))
% 51.10/50.83 [9696]~P1(f331(f68(x96961),x96962))+~P1(f331(f331(f333(x96961),x96964),x96962))+~P1(f331(f331(f333(x96961),x96963),x96962))+P1(f331(f331(f241(a847),f331(f47(x96961),f331(f331(f3(f854(x96961,a840)),f331(f331(f3(f854(x96961,a840)),x96962),f331(f331(f310(x96961),x96963),f184(f854(x96961,a840))))),f331(f331(f310(x96961),x96964),f184(f854(x96961,a840)))))),f331(f47(x96961),x96962)))
% 51.10/50.83 [6755]~P136(x67553)+~P113(x67553)+P1(f331(x67551,f814(x67552,x67551,x67553)))+~P1(f331(x67551,f331(f331(f88(x67553),x67552),x67554)))
% 51.10/50.83 [6815]~P102(x68151)+~P1(f331(f331(f241(x68151),x68152),x68154))+~P1(f331(f331(f241(x68151),x68152),x68153))+P1(f331(f331(f241(x68151),x68152),f331(f331(f244(x68151),x68153),x68154)))
% 51.10/50.83 [6816]~P102(x68161)+~P1(f331(f331(f240(x68161),x68162),x68164))+~P1(f331(f331(f240(x68161),x68162),x68163))+P1(f331(f331(f240(x68161),x68162),f331(f331(f244(x68161),x68163),x68164)))
% 51.10/50.83 [6817]~P102(x68171)+~P1(f331(f331(f240(x68171),x68172),x68174))+~P1(f331(f331(f240(x68171),x68172),x68173))+P1(f331(f331(f240(x68171),x68172),f331(f331(f244(x68171),x68173),x68174)))
% 51.10/50.83 [6818]~P102(x68181)+~P1(f331(f331(f240(x68181),x68182),x68184))+~P1(f331(f331(f240(x68181),x68182),x68183))+P1(f331(f331(f240(x68181),x68182),f331(f331(f244(x68181),x68183),x68184)))
% 51.10/50.83 [6819]~P101(x68191)+~P1(f331(f331(f240(x68191),x68192),x68194))+~P1(f331(f331(f240(x68191),x68192),x68193))+P1(f331(f331(f240(x68191),x68192),f331(f331(f109(x68191),x68193),x68194)))
% 51.10/50.83 [6820]~P101(x68201)+~P1(f331(f331(f240(x68201),x68202),x68204))+~P1(f331(f331(f240(x68201),x68202),x68203))+P1(f331(f331(f240(x68201),x68202),f331(f331(f109(x68201),x68203),x68204)))
% 51.10/50.83 [6821]~P101(x68211)+~P1(f331(f331(f240(x68211),x68212),x68214))+~P1(f331(f331(f240(x68211),x68212),x68213))+P1(f331(f331(f240(x68211),x68212),f331(f331(f109(x68211),x68213),x68214)))
% 51.10/50.83 [6822]~P87(x68221)+~P1(f331(f331(f287(x68221),x68222),x68224))+~P1(f331(f331(f287(x68221),x68222),x68223))+P1(f331(f331(f287(x68221),x68222),f331(f331(f87(x68221),x68223),x68224)))
% 51.10/50.83 [6823]~P106(x68231)+~P1(f331(f331(f287(x68231),x68232),x68234))+~P1(f331(f331(f287(x68231),x68232),x68233))+P1(f331(f331(f287(x68231),x68232),f331(f331(f3(x68231),x68233),x68234)))
% 51.10/50.83 [6843]~P59(x68432)+E(x68431,f2(x68432))+E(f331(f331(f291(x68432),f331(f331(f250(x68432),x68431),x68433)),f331(f331(f250(x68432),x68431),x68434)),f331(f331(f250(x68432),x68431),f331(f331(f3(a847),x68433),x68434)))+~P1(f331(f331(f240(a847),x68434),x68433))
% 51.10/50.83 [6887]~P102(x68871)+~P16(x68871,f331(f331(f145(x68871),x68873),x68874))+P16(x68871,f331(f331(f145(x68871),x68872),f331(f331(f145(x68871),x68873),x68874)))+~P1(f331(f331(f240(x68871),x68872),x68873))
% 51.10/50.83 [6888]~P102(x68881)+~P16(x68881,f331(f331(f145(x68881),x68883),x68884))+P16(x68881,f331(f331(f145(x68881),x68882),f331(f331(f145(x68881),x68883),x68884)))+~P1(f331(f331(f240(x68881),x68882),x68883))
% 51.10/50.83 [6928]~P80(x69281)+~P1(f331(f331(f240(x69281),f2(x69281)),x69283))+~P1(f331(f331(f241(x69281),x69282),x69284))+P1(f331(f331(f241(x69281),x69282),f331(f331(f87(x69281),x69283),x69284)))
% 51.10/50.83 [6929]~P80(x69291)+~P1(f331(f331(f240(x69291),x69292),x69294))+~P1(f331(f331(f241(x69291),f2(x69291)),x69293))+P1(f331(f331(f241(x69291),x69292),f331(f331(f87(x69291),x69293),x69294)))
% 51.10/50.83 [6930]~P85(x69301)+~P1(f331(f331(f241(x69301),f2(x69301)),x69303))+~P1(f331(f331(f241(x69301),x69302),x69304))+P1(f331(f331(f241(x69301),x69302),f331(f331(f87(x69301),x69303),x69304)))
% 51.10/50.83 [6931]~P80(x69311)+~P1(f331(f331(f240(x69311),f2(x69311)),x69314))+~P1(f331(f331(f240(x69311),x69312),x69313))+P1(f331(f331(f240(x69311),x69312),f331(f331(f87(x69311),x69313),x69314)))
% 51.10/50.83 [6932]~P80(x69321)+~P1(f331(f331(f240(x69321),f2(x69321)),x69323))+~P1(f331(f331(f240(x69321),x69322),x69324))+P1(f331(f331(f240(x69321),x69322),f331(f331(f87(x69321),x69323),x69324)))
% 51.10/50.83 [6966]~P102(x69661)+P1(f331(f331(f241(x69661),x69662),x69663))+P1(f331(f331(f241(x69661),x69662),x69664))+~P1(f331(f331(f241(x69661),x69662),f331(f331(f239(x69661),x69664),x69663)))
% 51.10/50.83 [6967]~P102(x69671)+P1(f331(f331(f240(x69671),x69672),x69673))+P1(f331(f331(f240(x69671),x69672),x69674))+~P1(f331(f331(f240(x69671),x69672),f331(f331(f239(x69671),x69674),x69673)))
% 51.10/50.83 [7650]~P61(x76501)+~P1(f331(f331(f241(x76501),x76504),f2(x76501)))+~P1(f331(f331(f241(x76501),x76503),f331(f331(f291(x76501),x76502),x76504)))+P1(f331(f331(f241(x76501),x76502),f331(f331(f88(x76501),x76503),x76504)))
% 51.10/50.83 [7651]~P61(x76511)+~P1(f331(f331(f241(x76511),x76514),f2(x76511)))+~P1(f331(f331(f241(x76511),x76513),f331(f331(f88(x76511),x76512),x76514)))+P1(f331(f331(f241(x76511),x76512),f331(f331(f291(x76511),x76513),x76514)))
% 51.10/50.83 [7652]~P61(x76521)+~P1(f331(f331(f241(x76521),x76524),f2(x76521)))+~P1(f331(f331(f240(x76521),x76523),f331(f331(f291(x76521),x76522),x76524)))+P1(f331(f331(f240(x76521),x76522),f331(f331(f88(x76521),x76523),x76524)))
% 51.10/50.83 [7653]~P61(x76531)+~P1(f331(f331(f241(x76531),x76534),f2(x76531)))+~P1(f331(f331(f240(x76531),x76533),f331(f331(f88(x76531),x76532),x76534)))+P1(f331(f331(f240(x76531),x76532),f331(f331(f291(x76531),x76533),x76534)))
% 51.10/50.83 [7763]~P118(x77631)+~P1(f331(f331(f241(x77631),x77632),f2(x77631)))+~P1(f331(f331(f241(x77631),x77634),x77633))+P1(f331(f331(f241(x77631),f331(f331(f88(x77631),x77632),x77633)),f331(f331(f88(x77631),x77632),x77634)))
% 51.10/50.83 [7764]~P118(x77641)+~P1(f331(f331(f241(x77641),x77642),f2(x77641)))+~P1(f331(f331(f241(x77641),x77644),x77643))+P1(f331(f331(f241(x77641),f331(f331(f88(x77641),x77642),x77643)),f331(f331(f88(x77641),x77642),x77644)))
% 51.10/50.83 [7765]~P118(x77651)+~P1(f331(f331(f241(x77651),x77653),f2(x77651)))+~P1(f331(f331(f241(x77651),x77654),x77652))+P1(f331(f331(f241(x77651),f331(f331(f88(x77651),x77652),x77653)),f331(f331(f88(x77651),x77654),x77653)))
% 51.10/50.83 [7766]~P118(x77661)+~P1(f331(f331(f241(x77661),x77663),f2(x77661)))+~P1(f331(f331(f241(x77661),x77664),x77662))+P1(f331(f331(f241(x77661),f331(f331(f88(x77661),x77662),x77663)),f331(f331(f88(x77661),x77664),x77663)))
% 51.10/50.83 [7767]~P118(x77671)+~P1(f331(f331(f241(x77671),x77672),f2(x77671)))+~P1(f331(f331(f241(x77671),x77674),x77673))+P1(f331(f331(f241(x77671),f331(f331(f88(x77671),x77672),x77673)),f331(f331(f88(x77671),x77672),x77674)))
% 51.10/50.83 [7768]~P61(x77681)+~P1(f331(f331(f241(x77681),x77683),f2(x77681)))+~P1(f331(f331(f241(x77681),x77684),x77682))+P1(f331(f331(f241(x77681),f331(f331(f291(x77681),x77682),x77683)),f331(f331(f291(x77681),x77684),x77683)))
% 51.10/50.83 [7769]~P118(x77691)+~P1(f331(f331(f241(x77691),x77692),f2(x77691)))+~P1(f331(f331(f240(x77691),x77694),x77693))+P1(f331(f331(f240(x77691),f331(f331(f88(x77691),x77692),x77693)),f331(f331(f88(x77691),x77692),x77694)))
% 51.10/50.83 [7770]~P129(x77701)+~P1(f331(f331(f240(x77701),x77702),f2(x77701)))+~P1(f331(f331(f240(x77701),x77704),x77703))+P1(f331(f331(f240(x77701),f331(f331(f88(x77701),x77702),x77703)),f331(f331(f88(x77701),x77702),x77704)))
% 51.10/50.83 [7771]~P129(x77711)+~P1(f331(f331(f240(x77711),x77713),f2(x77711)))+~P1(f331(f331(f240(x77711),x77714),x77712))+P1(f331(f331(f240(x77711),f331(f331(f88(x77711),x77712),x77713)),f331(f331(f88(x77711),x77714),x77713)))
% 51.10/50.83 [7772]~P60(x77721)+~P1(f331(f331(f240(x77721),x77723),f2(x77721)))+~P1(f331(f331(f240(x77721),x77724),x77722))+P1(f331(f331(f240(x77721),f331(f331(f291(x77721),x77722),x77723)),f331(f331(f291(x77721),x77724),x77723)))
% 51.10/50.83 [7773]~P85(x77731)+~P1(f331(f331(f241(x77731),f85(x77731)),x77732))+~P1(f331(f331(f241(a847),x77733),x77734))+P1(f331(f331(f241(x77731),f331(f331(f250(x77731),x77732),x77733)),f331(f331(f250(x77731),x77732),x77734)))
% 51.10/50.83 [7774]~P85(x77741)+~P1(f331(f331(f241(x77741),f85(x77741)),x77742))+~P1(f331(f331(f241(a847),x77743),x77744))+P1(f331(f331(f241(x77741),f331(f331(f250(x77741),x77742),x77743)),f331(f331(f250(x77741),x77742),x77744)))
% 51.10/50.83 [7775]~P85(x77751)+~P1(f331(f331(f241(x77751),f85(x77751)),x77752))+~P1(f331(f331(f240(a847),x77753),x77754))+P1(f331(f331(f240(x77751),f331(f331(f250(x77751),x77752),x77753)),f331(f331(f250(x77751),x77752),x77754)))
% 51.10/50.83 [7776]~P85(x77761)+~P1(f331(f331(f240(x77761),f85(x77761)),x77762))+~P1(f331(f331(f240(a847),x77763),x77764))+P1(f331(f331(f240(x77761),f331(f331(f250(x77761),x77762),x77763)),f331(f331(f250(x77761),x77762),x77764)))
% 51.10/50.83 [7803]P1(f331(f331(f241(a847),f2(a847)),f331(x78031,x78032)))+~P1(f331(f68(x78033),x78034))+~P1(f331(f331(f333(x78033),x78032),x78034))+~P1(f331(f331(f241(a847),f2(a847)),f331(f331(f11(x78033,a847),x78031),x78034)))
% 51.10/50.83 [7814]~P118(x78141)+~P1(f331(f331(f241(x78141),x78143),x78144))+~P1(f331(f331(f241(x78141),f2(x78141)),x78142))+P1(f331(f331(f241(x78141),f331(f331(f88(x78141),x78142),x78143)),f331(f331(f88(x78141),x78142),x78144)))
% 51.10/50.83 [7815]~P116(x78151)+~P1(f331(f331(f241(x78151),x78153),x78154))+~P1(f331(f331(f241(x78151),f2(x78151)),x78152))+P1(f331(f331(f241(x78151),f331(f331(f88(x78151),x78152),x78153)),f331(f331(f88(x78151),x78152),x78154)))
% 51.10/50.83 [7816]~P123(x78161)+~P1(f331(f331(f241(x78161),x78163),x78164))+~P1(f331(f331(f241(x78161),f2(x78161)),x78162))+P1(f331(f331(f241(x78161),f331(f331(f88(x78161),x78162),x78163)),f331(f331(f88(x78161),x78162),x78164)))
% 51.10/50.83 [7817]~P118(x78171)+~P1(f331(f331(f241(x78171),x78172),x78174))+~P1(f331(f331(f241(x78171),f2(x78171)),x78173))+P1(f331(f331(f241(x78171),f331(f331(f88(x78171),x78172),x78173)),f331(f331(f88(x78171),x78174),x78173)))
% 51.10/50.83 [7818]~P123(x78181)+~P1(f331(f331(f241(x78181),x78182),x78184))+~P1(f331(f331(f241(x78181),f2(x78181)),x78183))+P1(f331(f331(f241(x78181),f331(f331(f88(x78181),x78182),x78183)),f331(f331(f88(x78181),x78184),x78183)))
% 51.10/50.83 [7819]~P118(x78191)+~P1(f331(f331(f241(x78191),x78193),x78194))+~P1(f331(f331(f241(x78191),f2(x78191)),x78192))+P1(f331(f331(f241(x78191),f331(f331(f88(x78191),x78192),x78193)),f331(f331(f88(x78191),x78192),x78194)))
% 51.10/50.83 [7820]~P61(x78201)+~P1(f331(f331(f241(x78201),x78202),x78204))+~P1(f331(f331(f241(x78201),f2(x78201)),x78203))+P1(f331(f331(f241(x78201),f331(f331(f291(x78201),x78202),x78203)),f331(f331(f291(x78201),x78204),x78203)))
% 51.10/50.83 [7821]~P118(x78211)+~P1(f331(f331(f241(x78211),f2(x78211)),x78212))+~P1(f331(f331(f240(x78211),x78213),x78214))+P1(f331(f331(f240(x78211),f331(f331(f88(x78211),x78212),x78213)),f331(f331(f88(x78211),x78212),x78214)))
% 51.10/50.83 [7822]~P131(x78221)+~P1(f331(f331(f240(x78221),x78223),x78224))+~P1(f331(f331(f240(x78221),f2(x78221)),x78222))+P1(f331(f331(f240(x78221),f331(f331(f88(x78221),x78222),x78223)),f331(f331(f88(x78221),x78222),x78224)))
% 51.10/50.83 [7823]~P130(x78231)+~P1(f331(f331(f240(x78231),x78233),x78234))+~P1(f331(f331(f240(x78231),f2(x78231)),x78232))+P1(f331(f331(f240(x78231),f331(f331(f88(x78231),x78232),x78233)),f331(f331(f88(x78231),x78232),x78234)))
% 51.10/50.83 [7824]~P131(x78241)+~P1(f331(f331(f240(x78241),x78242),x78244))+~P1(f331(f331(f240(x78241),f2(x78241)),x78243))+P1(f331(f331(f240(x78241),f331(f331(f88(x78241),x78242),x78243)),f331(f331(f88(x78241),x78244),x78243)))
% 51.10/50.83 [7825]~P85(x78251)+~P1(f331(f331(f240(x78251),x78252),x78254))+~P1(f331(f331(f240(x78251),f2(x78251)),x78252))+P1(f331(f331(f240(x78251),f331(f331(f250(x78251),x78252),x78253)),f331(f331(f250(x78251),x78254),x78253)))
% 51.10/50.83 [7826]~P60(x78261)+~P1(f331(f331(f240(x78261),x78262),x78264))+~P1(f331(f331(f240(x78261),f2(x78261)),x78263))+P1(f331(f331(f240(x78261),f331(f331(f291(x78261),x78262),x78263)),f331(f331(f291(x78261),x78264),x78263)))
% 51.10/50.83 [7865]~P104(x78652)+P1(f331(f331(f240(f854(x78651,x78652)),x78654),x78653))+~P1(f331(f331(f240(f854(x78651,x78652)),x78653),x78654))+P1(f331(f331(f241(f854(x78651,x78652)),x78653),x78654))
% 51.10/50.83 [7909]P1(f331(f331(f333(x79091),x79092),x79093))+P1(f331(f331(f333(x79091),x79092),x79094))+~P1(f331(f331(f240(f854(x79091,a840)),x79094),x79093))+P1(f331(f331(f241(f854(x79091,a840)),x79094),f331(f331(f310(x79091),x79092),x79093)))
% 51.10/50.83 [8016]~P112(x80162)+E(x80161,f2(x80162))+P1(f331(f331(f287(x80162),x80163),x80164))+~P1(f331(f331(f287(x80162),f331(f331(f88(x80162),x80163),x80161)),f331(f331(f88(x80162),x80164),x80161)))
% 51.10/50.83 [8017]~P112(x80172)+E(x80171,f2(x80172))+P1(f331(f331(f287(x80172),x80173),x80174))+~P1(f331(f331(f287(x80172),f331(f331(f88(x80172),x80171),x80173)),f331(f331(f88(x80172),x80171),x80174)))
% 51.10/50.83 [8061]P1(f331(f331(f333(x80611),x80612),x80613))+P1(f331(f331(f333(x80611),x80612),x80614))+~P1(f331(f331(f241(f854(x80611,a840)),x80614),f331(f331(f310(x80611),x80612),x80613)))+P1(f331(f331(f240(f854(x80611,a840)),x80614),x80613))
% 51.10/50.83 [8130]~P118(x81301)+P1(f331(f331(f241(x81301),x81303),x81302))+P1(f331(f331(f241(x81301),x81302),x81303))+~P1(f331(f331(f241(x81301),f331(f331(f88(x81301),x81304),x81302)),f331(f331(f88(x81301),x81304),x81303)))
% 51.10/50.83 [8131]~P118(x81311)+P1(f331(f331(f241(x81311),x81313),x81312))+P1(f331(f331(f241(x81311),x81312),x81313))+~P1(f331(f331(f241(x81311),f331(f331(f88(x81311),x81312),x81314)),f331(f331(f88(x81311),x81313),x81314)))
% 51.10/50.83 [8142]~P118(x81421)+P1(f331(f331(f241(x81421),x81424),f2(x81421)))+P1(f331(f331(f241(x81421),x81422),x81423))+~P1(f331(f331(f241(x81421),f331(f331(f88(x81421),x81422),x81424)),f331(f331(f88(x81421),x81423),x81424)))
% 51.10/50.83 [8143]~P118(x81431)+P1(f331(f331(f241(x81431),x81434),f2(x81431)))+P1(f331(f331(f241(x81431),x81432),x81433))+~P1(f331(f331(f241(x81431),f331(f331(f88(x81431),x81434),x81432)),f331(f331(f88(x81431),x81434),x81433)))
% 51.10/50.83 [8146]~P118(x81461)+P1(f331(f331(f241(x81461),x81462),x81463))+P1(f331(f331(f241(x81461),f2(x81461)),x81464))+~P1(f331(f331(f241(x81461),f331(f331(f88(x81461),x81464),x81463)),f331(f331(f88(x81461),x81464),x81462)))
% 51.10/50.83 [8147]~P118(x81471)+P1(f331(f331(f241(x81471),x81472),x81473))+P1(f331(f331(f241(x81471),f2(x81471)),x81474))+~P1(f331(f331(f241(x81471),f331(f331(f88(x81471),x81473),x81474)),f331(f331(f88(x81471),x81472),x81474)))
% 51.10/50.83 [8160]~P118(x81601)+P1(f331(f331(f241(x81601),x81602),f2(x81601)))+P1(f331(f331(f241(x81601),f2(x81601)),x81602))+~P1(f331(f331(f241(x81601),f331(f331(f88(x81601),x81603),x81602)),f331(f331(f88(x81601),x81604),x81602)))
% 51.10/50.83 [8161]~P118(x81611)+P1(f331(f331(f241(x81611),x81612),f2(x81611)))+P1(f331(f331(f241(x81611),f2(x81611)),x81612))+~P1(f331(f331(f241(x81611),f331(f331(f88(x81611),x81612),x81613)),f331(f331(f88(x81611),x81612),x81614)))
% 51.10/50.83 [8186]~P118(x81861)+~P1(f331(f331(f241(x81861),x81864),f2(x81861)))+P1(f331(f331(f241(x81861),x81862),x81863))+~P1(f331(f331(f241(x81861),f331(f331(f88(x81861),x81864),x81863)),f331(f331(f88(x81861),x81864),x81862)))
% 51.10/50.83 [8187]~P118(x81871)+~P1(f331(f331(f241(x81871),x81874),f2(x81871)))+P1(f331(f331(f240(x81871),x81872),x81873))+~P1(f331(f331(f240(x81871),f331(f331(f88(x81871),x81874),x81873)),f331(f331(f88(x81871),x81874),x81872)))
% 51.10/50.83 [8198]~P85(x81983)+~P1(f331(f331(f241(x81983),f85(x81983)),x81984))+P1(f331(f331(f241(a847),x81981),x81982))+~P1(f331(f331(f241(x81983),f331(f331(f250(x81983),x81984),x81981)),f331(f331(f250(x81983),x81984),x81982)))
% 51.10/50.83 [8199]~P85(x81993)+~P1(f331(f331(f241(x81993),f85(x81993)),x81994))+P1(f331(f331(f241(a847),x81991),x81992))+~P1(f331(f331(f241(x81993),f331(f331(f250(x81993),x81994),x81991)),f331(f331(f250(x81993),x81994),x81992)))
% 51.10/50.83 [8200]~P85(x82003)+~P1(f331(f331(f241(x82003),f85(x82003)),x82004))+P1(f331(f331(f240(a847),x82001),x82002))+~P1(f331(f331(f240(x82003),f331(f331(f250(x82003),x82004),x82001)),f331(f331(f250(x82003),x82004),x82002)))
% 51.10/50.83 [8201]~P85(x82013)+~P1(f331(f331(f241(x82013),f85(x82013)),x82014))+P1(f331(f331(f240(a847),x82011),x82012))+~P1(f331(f331(f240(x82013),f331(f331(f250(x82013),x82014),x82011)),f331(f331(f250(x82013),x82014),x82012)))
% 51.10/50.83 [8211]~P118(x82111)+P1(f331(f331(f241(x82111),x82112),x82113))+~P1(f331(f331(f241(x82111),f2(x82111)),x82114))+~P1(f331(f331(f241(x82111),f331(f331(f88(x82111),x82114),x82112)),f331(f331(f88(x82111),x82114),x82113)))
% 51.10/50.83 [8212]~P123(x82121)+P1(f331(f331(f241(x82121),x82122),x82123))+~P1(f331(f331(f240(x82121),f2(x82121)),x82124))+~P1(f331(f331(f241(x82121),f331(f331(f88(x82121),x82124),x82122)),f331(f331(f88(x82121),x82124),x82123)))
% 51.10/50.83 [8213]~P125(x82131)+P1(f331(f331(f241(x82131),x82132),x82133))+~P1(f331(f331(f240(x82131),f2(x82131)),x82134))+~P1(f331(f331(f241(x82131),f331(f331(f88(x82131),x82134),x82132)),f331(f331(f88(x82131),x82134),x82133)))
% 51.10/50.83 [8214]~P85(x82141)+~P1(f331(f331(f240(x82141),f2(x82141)),x82143))+P1(f331(f331(f241(x82141),x82142),x82143))+~P1(f331(f331(f241(x82141),f331(f331(f250(x82141),x82142),x82144)),f331(f331(f250(x82141),x82143),x82144)))
% 51.10/50.83 [8215]~P123(x82151)+P1(f331(f331(f241(x82151),x82152),x82153))+~P1(f331(f331(f240(x82151),f2(x82151)),x82154))+~P1(f331(f331(f241(x82151),f331(f331(f88(x82151),x82152),x82154)),f331(f331(f88(x82151),x82153),x82154)))
% 51.10/50.83 [8216]~P125(x82161)+P1(f331(f331(f241(x82161),x82162),x82163))+~P1(f331(f331(f240(x82161),f2(x82161)),x82164))+~P1(f331(f331(f241(x82161),f331(f331(f88(x82161),x82162),x82164)),f331(f331(f88(x82161),x82163),x82164)))
% 51.10/50.83 [8217]~P118(x82171)+P1(f331(f331(f240(x82171),x82172),x82173))+~P1(f331(f331(f241(x82171),f2(x82171)),x82174))+~P1(f331(f331(f240(x82171),f331(f331(f88(x82171),x82174),x82172)),f331(f331(f88(x82171),x82174),x82173)))
% 51.10/50.83 [8218]~P123(x82181)+P1(f331(f331(f240(x82181),x82182),x82183))+~P1(f331(f331(f241(x82181),f2(x82181)),x82184))+~P1(f331(f331(f240(x82181),f331(f331(f88(x82181),x82184),x82182)),f331(f331(f88(x82181),x82184),x82183)))
% 51.10/50.83 [8219]~P123(x82191)+P1(f331(f331(f240(x82191),x82192),x82193))+~P1(f331(f331(f241(x82191),f2(x82191)),x82194))+~P1(f331(f331(f240(x82191),f331(f331(f88(x82191),x82192),x82194)),f331(f331(f88(x82191),x82193),x82194)))
% 51.10/50.83 [8260]P1(f331(f331(f333(x82601),x82602),x82603))+~P1(f331(f331(f240(f854(x82601,a840)),x82603),x82604))+~P1(f331(f331(f241(f854(x82601,a840)),x82603),x82604))+P1(f331(f331(f241(f854(x82601,a840)),x82603),f331(f331(f310(x82601),x82602),x82604)))
% 51.10/50.83 [8295]~P136(x82951)+~P113(x82951)+P1(f331(f331(f287(x82951),x82952),f331(f331(f87(x82951),f814(x82952,x82953,x82951)),f2(x82951))))+~P1(f331(x82953,f331(f331(f88(x82951),x82952),x82954)))
% 51.10/50.83 [8618]E(f331(f331(f3(a1),f471(x86181,x86182,x86183,x86184)),f464(x86181,x86182,x86183,x86184)),x86184)+~P1(f331(f331(f241(a1),f2(a1)),x86183))+~P1(f331(f331(f240(a1),x86181),x86184))+P1(f331(f331(f240(a1),x86181),f331(f331(f87(a1),x86184),x86183)))
% 51.10/50.83 [8619]E(f331(f331(f3(a1),f475(x86191,x86192,x86193,x86194)),f476(x86191,x86192,x86193,x86194)),x86194)+~P1(f331(f331(f241(a1),f2(a1)),x86193))+~P1(f331(f331(f241(a1),x86191),x86194))+P1(f331(f331(f241(a1),x86191),f331(f331(f87(a1),x86194),x86193)))
% 51.10/50.83 [8745]~E(f331(f331(f155(x87451),x87453),f757(x87454,x87453,x87451,x87452)),f331(f331(f155(x87451),x87454),f757(x87454,x87453,x87451,x87452)))+E(f331(f331(f164(x87451),x87452),x87453),f331(f331(f164(x87451),x87452),x87454))+~P1(f331(f331(f240(a847),x87452),f331(f185(f848(x87451)),x87453)))+~P1(f331(f331(f240(a847),x87452),f331(f185(f848(x87451)),x87454)))
% 51.10/50.83 [8796]~P1(f331(f331(f241(a1),f2(a1)),x87963))+~P1(f331(f331(f240(a1),x87961),x87964))+P1(f331(f331(f333(a1),f471(x87961,x87962,x87963,x87964)),x87962))+P1(f331(f331(f240(a1),x87961),f331(f331(f87(a1),x87964),x87963)))
% 51.10/50.83 [8797]~P1(f331(f331(f241(a1),f2(a1)),x87973))+~P1(f331(f331(f241(a1),x87971),x87974))+P1(f331(f331(f333(a1),f475(x87971,x87972,x87973,x87974)),x87972))+P1(f331(f331(f241(a1),x87971),f331(f331(f87(a1),x87974),x87973)))
% 51.10/50.83 [8834]~P102(x88341)+~P1(f331(f68(x88341),x88343))+~P1(f331(f331(f333(x88341),x88344),x88343))+P1(f331(f331(f240(x88341),f331(f331(f71(x88341,x88341,f244(x88341)),x88342),x88343)),f331(f331(f244(x88341),x88344),x88342)))
% 51.10/50.83 [8835]~P101(x88351)+~P1(f331(f68(x88351),x88353))+~P1(f331(f331(f333(x88351),x88354),x88353))+P1(f331(f331(f240(x88351),f331(f331(f71(x88351,x88351,f109(x88351)),x88352),x88353)),f331(f331(f109(x88351),x88354),x88352)))
% 51.10/50.83 [8843]~P10(x88432,x88433,x88434)+~P1(f331(f68(x88432),x88433))+P1(f331(f331(f287(a847),x88431),f331(f47(x88432),x88433)))+P1(f331(f331(f333(f854(x88432,a840)),f394(x88431,x88434,x88433,x88432)),f331(f331(f66(x88432),x88433),x88434)))
% 51.10/50.83 [8881]E(f331(f331(f164(x88811),x88812),x88813),f331(f331(f164(x88811),x88812),x88814))+P1(f331(f331(f241(a847),f757(x88813,x88814,x88811,x88812)),x88812))+~P1(f331(f331(f240(a847),x88812),f331(f185(f848(x88811)),x88813)))+~P1(f331(f331(f240(a847),x88812),f331(f185(f848(x88811)),x88814)))
% 51.10/50.83 [8886]~P1(f331(f331(f241(a1),f2(a1)),x88863))+~P1(f331(f331(f241(a1),x88861),x88862))+P1(f331(f331(f333(a1),f476(x88861,x88864,x88863,x88862)),f303(a1,f85(a1),x88863)))+P1(f331(f331(f241(a1),x88861),f331(f331(f87(a1),x88862),x88863)))
% 51.10/50.83 [8887]~P1(f331(f331(f241(a1),f2(a1)),x88873))+~P1(f331(f331(f240(a1),x88871),x88872))+P1(f331(f331(f333(a1),f464(x88871,x88874,x88873,x88872)),f303(a1,f85(a1),x88873)))+P1(f331(f331(f240(a1),x88871),f331(f331(f87(a1),x88872),x88873)))
% 51.10/50.83 [9048]~E(f171(x90481,x90482,x90483),f171(x90481,x90482,x90484))+E(f331(f163(f853(x90481,x90482)),x90483),f331(f163(f853(x90481,x90482)),x90484))+~P1(f331(f132(x90481),f331(f331(f147(f853(x90481,x90482),x90481),f248(x90481,x90482)),x90484)))+~P1(f331(f132(x90481),f331(f331(f147(f853(x90481,x90482),x90481),f248(x90481,x90482)),x90483)))
% 51.10/50.83 [9051]E(f171(x90511,x90512,x90513),f171(x90511,x90512,x90514))+~E(f331(f163(f853(x90511,x90512)),x90513),f331(f163(f853(x90511,x90512)),x90514))+~P1(f331(f132(x90511),f331(f331(f147(f853(x90511,x90512),x90511),f248(x90511,x90512)),x90514)))+~P1(f331(f132(x90511),f331(f331(f147(f853(x90511,x90512),x90511),f248(x90511,x90512)),x90513)))
% 51.10/50.83 [9167]~P102(x91671)+~P1(f331(f68(x91671),x91674))+P1(f331(f331(f333(x91671),f677(x91672,x91673,x91674,x91671)),x91674))+P1(f331(f331(f240(x91671),f331(f331(f71(x91671,x91671,f239(x91671)),x91672),x91674)),f331(f331(f239(x91671),x91673),x91672)))
% 51.10/50.83 [9168]~P100(x91681)+~P1(f331(f68(x91681),x91684))+P1(f331(f331(f333(x91681),f690(x91682,x91683,x91684,x91681)),x91684))+P1(f331(f331(f240(x91681),f331(f331(f71(x91681,x91681,f108(x91681)),x91682),x91684)),f331(f331(f108(x91681),x91683),x91682)))
% 51.10/50.83 [9295]~P102(x92951)+~P1(f331(f68(x92951),x92953))+~P1(f331(f331(f240(x92951),f677(x92952,x92954,x92953,x92951)),x92954))+P1(f331(f331(f240(x92951),f331(f331(f71(x92951,x92951,f239(x92951)),x92952),x92953)),f331(f331(f239(x92951),x92954),x92952)))
% 51.10/50.83 [9296]~P100(x92961)+~P1(f331(f68(x92961),x92963))+~P1(f331(f331(f240(x92961),f690(x92962,x92964,x92963,x92961)),x92964))+P1(f331(f331(f240(x92961),f331(f331(f71(x92961,x92961,f108(x92961)),x92962),x92963)),f331(f331(f108(x92961),x92964),x92962)))
% 51.10/50.83 [9298]~P1(f331(f331(f241(a1),f2(a1)),x92983))+~P1(f331(f331(f240(a1),f2(a1)),x92984))+~P1(f331(f331(f241(a1),x92984),x92981))+P1(f331(f331(f241(a1),f331(f331(f87(a1),f331(f331(f88(a1),x92981),f57(a1,x92982,x92983))),x92984)),f331(f331(f88(a1),x92981),x92983)))
% 51.10/50.83 [9567]~P88(x95671)+P1(f331(f331(f241(x95671),f331(x95672,x95673)),f331(x95672,x95674)))+~P1(f331(f331(f241(a847),x95673),x95674))+~P1(f331(f331(f241(x95671),f331(x95672,f604(x95674,x95673,x95672,x95671))),f331(x95672,f331(a119,f604(x95674,x95673,x95672,x95671)))))
% 51.10/50.83 [9568]~P88(x95681)+P1(f331(f331(f241(x95681),f331(x95682,x95683)),f331(x95682,x95684)))+~P1(f331(f331(f241(a847),x95683),x95684))+~P1(f331(f331(f241(x95681),f331(x95682,f610(x95684,x95683,x95682,x95681))),f331(x95682,f331(a119,f610(x95684,x95683,x95682,x95681)))))
% 51.10/50.83 [9569]~P88(x95693)+~P1(f331(f331(f241(x95693),f331(x95694,x95691)),f331(x95694,x95692)))+P1(f331(f331(f241(a847),x95691),x95692))+~P1(f331(f331(f241(x95693),f331(x95694,f604(x95692,x95691,x95694,x95693))),f331(x95694,f331(a119,f604(x95692,x95691,x95694,x95693)))))
% 51.10/50.83 [9665]E(x96651,x96652)+P1(f331(f331(f333(f853(f848(x96653),f848(x96653))),f331(f331(f249(f848(x96653),f848(x96653)),x96652),x96651)),f142(x96653,x96654)))+P1(f331(f331(f333(f853(f848(x96653),f848(x96653))),f331(f331(f249(f848(x96653),f848(x96653)),x96651),x96652)),f142(x96653,x96654)))+~P1(f331(f331(f333(f853(x96653,x96653)),f331(f331(f249(x96653,x96653),f752(x96651,x96652,x96654,x96653)),f754(x96651,x96652,x96654,x96653))),x96654))
% 51.10/50.83 [9666]E(x96661,x96662)+P1(f331(f331(f333(f853(f848(x96663),f848(x96663))),f331(f331(f249(f848(x96663),f848(x96663)),x96662),x96661)),f142(x96663,x96664)))+P1(f331(f331(f333(f853(f848(x96663),f848(x96663))),f331(f331(f249(f848(x96663),f848(x96663)),x96661),x96662)),f142(x96663,x96664)))+~P1(f331(f331(f333(f853(x96663,x96663)),f331(f331(f249(x96663,x96663),f754(x96661,x96662,x96664,x96663)),f752(x96661,x96662,x96664,x96663))),x96664))
% 51.10/50.83 [7347]~P102(x73471)+~P1(f331(f331(f241(x73471),x73473),x73474))+~P1(f331(f331(f241(x73471),x73472),x73474))+P1(f331(f331(f241(x73471),f331(f331(f239(x73471),x73472),x73473)),x73474))
% 51.10/50.83 [7348]~P102(x73481)+~P1(f331(f331(f240(x73481),x73483),x73484))+~P1(f331(f331(f240(x73481),x73482),x73484))+P1(f331(f331(f240(x73481),f331(f331(f239(x73481),x73482),x73483)),x73484))
% 51.10/50.83 [7349]~P102(x73491)+~P1(f331(f331(f240(x73491),x73493),x73494))+~P1(f331(f331(f240(x73491),x73492),x73494))+P1(f331(f331(f240(x73491),f331(f331(f239(x73491),x73492),x73493)),x73494))
% 51.10/50.83 [7350]~P102(x73501)+~P1(f331(f331(f240(x73501),x73503),x73504))+~P1(f331(f331(f240(x73501),x73502),x73504))+P1(f331(f331(f240(x73501),f331(f331(f239(x73501),x73502),x73503)),x73504))
% 51.10/50.83 [7351]~P100(x73511)+~P1(f331(f331(f240(x73511),x73513),x73514))+~P1(f331(f331(f240(x73511),x73512),x73514))+P1(f331(f331(f240(x73511),f331(f331(f108(x73511),x73512),x73513)),x73514))
% 51.10/50.83 [7352]~P100(x73521)+~P1(f331(f331(f240(x73521),x73523),x73524))+~P1(f331(f331(f240(x73521),x73522),x73524))+P1(f331(f331(f240(x73521),f331(f331(f108(x73521),x73522),x73523)),x73524))
% 51.10/50.83 [7353]~P100(x73531)+~P1(f331(f331(f240(x73531),x73533),x73534))+~P1(f331(f331(f240(x73531),x73532),x73534))+P1(f331(f331(f240(x73531),f331(f331(f108(x73531),x73532),x73533)),x73534))
% 51.10/50.83 [7595]~P5(x75951)+E(f331(f331(f87(x75951),f331(f331(f48(x75951),x75952),x75953)),f331(f331(f48(x75951),x75954),x75953)),f331(f331(f48(x75951),f331(f331(f87(x75951),x75952),x75954)),x75953))+~P1(f331(f331(f287(x75951),x75953),x75954))+~P1(f331(f331(f287(x75951),x75953),x75952))
% 51.10/50.83 [7673]~E(x76731,x76733)+E(f135(a847,f331(f302(a847,x76731),x76732)),f331(f331(f145(a847),x76733),x76734))+~E(f135(a847,f331(f302(a847,f331(f331(f87(a847),x76731),f85(a847))),x76732)),x76734)+~P1(f331(f331(f241(a847),x76731),x76732))
% 51.10/50.83 [7684]~P102(x76841)+P1(f331(f331(f241(x76841),x76842),x76843))+P1(f331(f331(f241(x76841),x76844),x76843))+~P1(f331(f331(f241(x76841),f331(f331(f244(x76841),x76844),x76842)),x76843))
% 51.10/50.83 [7685]~P102(x76851)+P1(f331(f331(f240(x76851),x76852),x76853))+P1(f331(f331(f240(x76851),x76854),x76853))+~P1(f331(f331(f240(x76851),f331(f331(f244(x76851),x76854),x76852)),x76853))
% 51.10/50.83 [7966]~P60(x79661)+~P1(f331(f331(f241(x79661),f2(x79661)),x79663))+~P1(f331(f331(f241(x79661),x79662),f331(f331(f291(x79661),x79664),x79663)))+P1(f331(f331(f241(x79661),f331(f331(f88(x79661),x79662),x79663)),x79664))
% 51.10/50.83 [7967]~P61(x79671)+~P1(f331(f331(f241(x79671),f2(x79671)),x79673))+~P1(f331(f331(f241(x79671),x79672),f331(f331(f291(x79671),x79674),x79673)))+P1(f331(f331(f241(x79671),f331(f331(f88(x79671),x79672),x79673)),x79674))
% 51.10/50.83 [7968]~P60(x79681)+~P1(f331(f331(f241(x79681),f2(x79681)),x79683))+~P1(f331(f331(f241(x79681),x79682),f331(f331(f88(x79681),x79684),x79683)))+P1(f331(f331(f241(x79681),f331(f331(f291(x79681),x79682),x79683)),x79684))
% 51.10/50.83 [7969]~P61(x79691)+~P1(f331(f331(f241(x79691),f2(x79691)),x79693))+~P1(f331(f331(f241(x79691),x79692),f331(f331(f88(x79691),x79694),x79693)))+P1(f331(f331(f241(x79691),f331(f331(f291(x79691),x79692),x79693)),x79694))
% 51.10/50.83 [7970]~P61(x79701)+~P1(f331(f331(f241(x79701),f2(x79701)),x79703))+~P1(f331(f331(f241(x79701),x79702),f331(f331(f88(x79701),x79704),x79703)))+P1(f331(f331(f241(x79701),f331(f331(f291(x79701),x79702),x79703)),x79704))
% 51.10/50.83 [7971]~P60(x79711)+~P1(f331(f331(f241(x79711),f2(x79711)),x79713))+~P1(f331(f331(f240(x79711),x79712),f331(f331(f291(x79711),x79714),x79713)))+P1(f331(f331(f240(x79711),f331(f331(f88(x79711),x79712),x79713)),x79714))
% 51.10/50.83 [7972]~P61(x79721)+~P1(f331(f331(f241(x79721),f2(x79721)),x79723))+~P1(f331(f331(f240(x79721),x79722),f331(f331(f291(x79721),x79724),x79723)))+P1(f331(f331(f240(x79721),f331(f331(f88(x79721),x79722),x79723)),x79724))
% 51.10/50.83 [7973]~P60(x79731)+~P1(f331(f331(f241(x79731),f2(x79731)),x79733))+~P1(f331(f331(f240(x79731),x79732),f331(f331(f88(x79731),x79734),x79733)))+P1(f331(f331(f240(x79731),f331(f331(f291(x79731),x79732),x79733)),x79734))
% 51.10/50.83 [7974]~P61(x79741)+~P1(f331(f331(f241(x79741),f2(x79741)),x79743))+~P1(f331(f331(f240(x79741),x79742),f331(f331(f88(x79741),x79744),x79743)))+P1(f331(f331(f240(x79741),f331(f331(f291(x79741),x79742),x79743)),x79744))
% 51.10/50.83 [7975]~P61(x79751)+~P1(f331(f331(f241(x79751),f2(x79751)),x79753))+~P1(f331(f331(f240(x79751),x79752),f331(f331(f88(x79751),x79754),x79753)))+P1(f331(f331(f240(x79751),f331(f331(f291(x79751),x79752),x79753)),x79754))
% 51.10/50.83 [8099]~P60(x80991)+~P1(f331(f331(f241(x80991),f2(x80991)),x80994))+P1(f331(f331(f241(x80991),x80992),f331(f331(f88(x80991),x80993),x80994)))+~P1(f331(f331(f241(x80991),f331(f331(f291(x80991),x80992),x80994)),x80993))
% 51.10/50.83 [8100]~P60(x81001)+~P1(f331(f331(f241(x81001),f2(x81001)),x81004))+P1(f331(f331(f241(x81001),x81002),f331(f331(f291(x81001),x81003),x81004)))+~P1(f331(f331(f241(x81001),f331(f331(f88(x81001),x81002),x81004)),x81003))
% 51.10/50.83 [8101]~P61(x81011)+~P1(f331(f331(f241(x81011),f2(x81011)),x81014))+P1(f331(f331(f241(x81011),x81012),f331(f331(f291(x81011),x81013),x81014)))+~P1(f331(f331(f241(x81011),f331(f331(f88(x81011),x81012),x81014)),x81013))
% 51.10/50.83 [8102]~P61(x81021)+~P1(f331(f331(f241(x81021),f2(x81021)),x81024))+P1(f331(f331(f241(x81021),x81022),f331(f331(f88(x81021),x81023),x81024)))+~P1(f331(f331(f241(x81021),f331(f331(f291(x81021),x81022),x81024)),x81023))
% 51.10/50.83 [8103]~P61(x81031)+~P1(f331(f331(f241(x81031),f2(x81031)),x81034))+P1(f331(f331(f241(x81031),x81032),f331(f331(f291(x81031),x81033),x81034)))+~P1(f331(f331(f241(x81031),f331(f331(f88(x81031),x81032),x81034)),x81033))
% 51.10/50.83 [8104]~P60(x81041)+~P1(f331(f331(f241(x81041),f2(x81041)),x81044))+P1(f331(f331(f240(x81041),x81042),f331(f331(f88(x81041),x81043),x81044)))+~P1(f331(f331(f240(x81041),f331(f331(f291(x81041),x81042),x81044)),x81043))
% 51.10/50.83 [8105]~P60(x81051)+~P1(f331(f331(f241(x81051),f2(x81051)),x81054))+P1(f331(f331(f240(x81051),x81052),f331(f331(f291(x81051),x81053),x81054)))+~P1(f331(f331(f240(x81051),f331(f331(f88(x81051),x81052),x81054)),x81053))
% 51.10/50.83 [8106]~P61(x81061)+~P1(f331(f331(f241(x81061),f2(x81061)),x81064))+P1(f331(f331(f240(x81061),x81062),f331(f331(f291(x81061),x81063),x81064)))+~P1(f331(f331(f240(x81061),f331(f331(f88(x81061),x81062),x81064)),x81063))
% 51.10/50.83 [8107]~P61(x81071)+~P1(f331(f331(f241(x81071),f2(x81071)),x81074))+P1(f331(f331(f240(x81071),x81072),f331(f331(f88(x81071),x81073),x81074)))+~P1(f331(f331(f240(x81071),f331(f331(f291(x81071),x81072),x81074)),x81073))
% 51.10/50.83 [8108]~P61(x81081)+~P1(f331(f331(f241(x81081),f2(x81081)),x81084))+P1(f331(f331(f240(x81081),x81082),f331(f331(f291(x81081),x81083),x81084)))+~P1(f331(f331(f240(x81081),f331(f331(f88(x81081),x81082),x81084)),x81083))
% 51.10/50.83 [8265]~P61(x82651)+~P1(f331(f331(f241(x82651),x82653),f2(x82651)))+~P1(f331(f331(f241(x82651),f331(f331(f291(x82651),x82654),x82653)),x82652))+P1(f331(f331(f241(x82651),f331(f331(f88(x82651),x82652),x82653)),x82654))
% 51.10/50.83 [8266]~P61(x82661)+~P1(f331(f331(f241(x82661),x82663),f2(x82661)))+~P1(f331(f331(f241(x82661),f331(f331(f88(x82661),x82664),x82663)),x82662))+P1(f331(f331(f241(x82661),f331(f331(f291(x82661),x82662),x82663)),x82664))
% 51.10/50.83 [8267]~P61(x82671)+~P1(f331(f331(f241(x82671),x82673),f2(x82671)))+~P1(f331(f331(f240(x82671),f331(f331(f291(x82671),x82674),x82673)),x82672))+P1(f331(f331(f240(x82671),f331(f331(f88(x82671),x82672),x82673)),x82674))
% 51.10/50.83 [8268]~P61(x82681)+~P1(f331(f331(f241(x82681),x82683),f2(x82681)))+~P1(f331(f331(f240(x82681),f331(f331(f88(x82681),x82684),x82683)),x82682))+P1(f331(f331(f240(x82681),f331(f331(f291(x82681),x82682),x82683)),x82684))
% 51.10/50.83 [8281]~P1(f331(x82811,x82814))+~P1(f331(f331(f241(a847),x82812),f331(f331(f88(a847),x82813),f331(a119,x82814))))+P1(f331(x82811,f331(f331(f48(a847),x82812),x82813)))+~P1(f331(f331(f240(a847),f331(f331(f88(a847),x82813),x82814)),x82812))
% 51.10/50.83 [8492]~P102(x84921)+~P1(f331(f68(x84921),x84924))+~P1(f331(f331(f333(x84921),x84922),x84924))+P1(f331(f331(f240(x84921),f331(f331(f239(x84921),x84922),x84923)),f331(f331(f71(x84921,x84921,f239(x84921)),x84923),x84924)))
% 51.10/50.83 [8493]~P100(x84931)+~P1(f331(f68(x84931),x84934))+~P1(f331(f331(f333(x84931),x84932),x84934))+P1(f331(f331(f240(x84931),f331(f331(f108(x84931),x84932),x84933)),f331(f331(f71(x84931,x84931,f108(x84931)),x84933),x84934)))
% 51.10/50.83 [8620]~P1(f331(f68(x86201),x86202))+E(f331(f47(x86201),f331(f331(f3(f854(x86201,a840)),x86202),f331(f331(f310(x86201),x86203),x86204))),f331(f331(f3(a847),f331(f47(x86201),f331(f331(f3(f854(x86201,a840)),x86202),x86204))),f85(a847)))+P1(f331(f331(f333(x86201),x86203),x86204))+~P1(f331(f331(f333(x86201),x86203),x86202))
% 51.10/50.83 [8684]E(f331(f331(f87(a1),f465(x86841,x86842,x86843,x86844)),f466(x86841,x86842,x86843,x86844)),x86844)+~P1(f331(f331(f241(a1),f2(a1)),x86843))+~P1(f331(f331(f240(a1),x86844),x86841))+P1(f331(f331(f240(a1),f331(f331(f3(a1),x86844),x86843)),x86841))
% 51.10/50.83 [8685]E(f331(f331(f87(a1),f477(x86851,x86852,x86853,x86854)),f478(x86851,x86852,x86853,x86854)),x86854)+~P1(f331(f331(f241(a1),f2(a1)),x86853))+~P1(f331(f331(f241(a1),x86854),x86851))+P1(f331(f331(f241(a1),f331(f331(f3(a1),x86854),x86853)),x86851))
% 51.10/50.83 [8866]~P1(f331(f331(f241(a1),f2(a1)),x88663))+~P1(f331(f331(f240(a1),x88664),x88661))+P1(f331(f331(f333(a1),f465(x88661,x88662,x88663,x88664)),x88662))+P1(f331(f331(f240(a1),f331(f331(f3(a1),x88664),x88663)),x88661))
% 51.10/50.83 [8867]~P1(f331(f331(f241(a1),f2(a1)),x88673))+~P1(f331(f331(f241(a1),x88674),x88671))+P1(f331(f331(f333(a1),f477(x88671,x88672,x88673,x88674)),x88672))+P1(f331(f331(f241(a1),f331(f331(f3(a1),x88674),x88673)),x88671))
% 51.10/50.83 [8946]~P1(f331(f331(f241(a1),f2(a1)),x89462))+~P1(f331(f331(f241(a1),x89461),x89463))+P1(f331(f331(f333(a1),f478(x89463,x89464,x89462,x89461)),f303(a1,f85(a1),x89462)))+P1(f331(f331(f241(a1),f331(f331(f3(a1),x89461),x89462)),x89463))
% 51.10/50.83 [8947]~P1(f331(f331(f241(a1),f2(a1)),x89472))+~P1(f331(f331(f240(a1),x89471),x89473))+P1(f331(f331(f333(a1),f466(x89473,x89474,x89472,x89471)),f303(a1,f85(a1),x89472)))+P1(f331(f331(f240(a1),f331(f331(f3(a1),x89471),x89472)),x89473))
% 51.10/50.83 [8965]~P1(f331(f331(f241(a1),f2(a1)),x89653))+~P1(f331(f331(f240(a1),f2(a1)),x89654))+~P1(f331(f331(f241(a1),x89654),x89651))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f331(f331(f88(a1),x89651),f57(a1,x89652,x89653))),x89654)))
% 51.10/50.83 [9024]~P102(x90241)+~P1(f331(f68(x90241),x90244))+~P1(f331(f331(f240(x90241),x90242),f676(x90243,x90242,x90244,x90241)))+P1(f331(f331(f240(x90241),f331(f331(f244(x90241),x90242),x90243)),f331(f331(f71(x90241,x90241,f244(x90241)),x90243),x90244)))
% 51.10/50.83 [9025]~P101(x90251)+~P1(f331(f68(x90251),x90254))+~P1(f331(f331(f240(x90251),x90252),f689(x90253,x90252,x90254,x90251)))+P1(f331(f331(f240(x90251),f331(f331(f109(x90251),x90252),x90253)),f331(f331(f71(x90251,x90251,f109(x90251)),x90253),x90254)))
% 51.10/50.83 [9038]~P1(f331(f331(f240(a1),x90384),f2(a1)))+~P1(f331(f331(f241(a1),f2(a1)),x90382))+~P1(f331(f331(f241(a1),x90381),x90384))+P1(f331(f331(f241(a1),f331(f331(f88(a1),x90381),x90382)),f331(f331(f87(a1),f331(f331(f88(a1),x90381),f57(a1,x90383,x90382))),x90384)))
% 51.10/50.83 [9060]P1(f331(f68(x90601),x90602))+~P1(f331(f68(x90601),x90603))+~P1(f331(f331(f333(f854(x90601,a840)),x90602),f331(f331(f66(x90601),x90603),x90604)))+~P1(f331(f331(f240(f854(f853(x90601,x90601),a840)),x90604),f331(f331(f256(x90601,x90601),x90603),f331(f18(f854(x90601,a840),x90601),x90603))))
% 51.10/50.83 [9083]~P102(x90831)+~P1(f331(f68(x90831),x90834))+P1(f331(f331(f333(x90831),f676(x90832,x90833,x90834,x90831)),x90834))+P1(f331(f331(f240(x90831),f331(f331(f244(x90831),x90833),x90832)),f331(f331(f71(x90831,x90831,f244(x90831)),x90832),x90834)))
% 51.10/50.83 [9084]~P101(x90841)+~P1(f331(f68(x90841),x90844))+P1(f331(f331(f333(x90841),f689(x90842,x90843,x90844,x90841)),x90844))+P1(f331(f331(f240(x90841),f331(f331(f109(x90841),x90843),x90842)),f331(f331(f71(x90841,x90841,f109(x90841)),x90842),x90844)))
% 51.10/50.83 [9461]~P1(f331(f68(x94612),x94614))+~P1(f331(f68(x94611),x94613))+~P1(f331(f331(f240(a847),f331(f47(x94612),x94614)),f331(f47(x94611),x94613)))+P1(f331(f331(f240(f854(x94611,a840)),f331(f311(x94612,x94611,f445(x94613,x94611,x94614,x94612)),x94614)),x94613))
% 51.10/50.83 [9120]~P1(f331(f331(f333(x91201),x91202),x91204))+P1(f331(f331(f333(x91201),x91202),x91203))+~P1(f331(f331(f241(f854(x91201,a840)),x91204),f331(f331(f310(x91201),x91202),x91203)))+P1(f331(f331(f241(f854(x91201,a840)),f331(f331(f3(f854(x91201,a840)),x91204),f331(f331(f310(x91201),x91202),f184(f854(x91201,a840))))),x91203))
% 51.10/50.83 [9273]~P1(f331(f331(f333(x92731),x92732),x92734))+P1(f331(f331(f333(x92731),x92732),x92733))+P1(f331(f331(f241(f854(x92731,a840)),x92734),f331(f331(f310(x92731),x92732),x92733)))+~P1(f331(f331(f241(f854(x92731,a840)),f331(f331(f3(f854(x92731,a840)),x92734),f331(f331(f310(x92731),x92732),f184(f854(x92731,a840))))),x92733))
% 51.10/50.83 [9301]P1(f331(f331(f333(x93011),x93012),x93013))+~P1(f331(f331(f240(f854(x93011,a840)),x93014),x93013))+P1(f331(f331(f241(f854(x93011,a840)),x93014),f331(f331(f310(x93011),x93012),x93013)))+~P1(f331(f331(f241(f854(x93011,a840)),f331(f331(f3(f854(x93011,a840)),x93014),f331(f331(f310(x93011),x93012),f184(f854(x93011,a840))))),x93013))
% 51.10/50.83 [9306]~P1(f331(f331(f333(x93061),x93063),x93062))+~P1(f331(f331(f241(f854(x93061,a840)),x93062),x93064))+P1(f331(f331(f241(f854(x93061,a840)),x93062),f331(f331(f310(x93061),x93063),x93064)))+~P1(f331(f331(f241(f854(x93061,a840)),f331(f331(f3(f854(x93061,a840)),x93062),f331(f331(f310(x93061),x93063),f184(f854(x93061,a840))))),x93064))
% 51.10/50.83 [9318]~P1(f331(f331(f240(f854(x93181,a840)),x93182),x93184))+~P1(f331(f331(f241(f854(x93181,a840)),x93182),x93184))+P1(f331(f331(f241(f854(x93181,a840)),x93182),f331(f331(f310(x93181),x93183),x93184)))+~P1(f331(f331(f241(f854(x93181,a840)),f331(f331(f3(f854(x93181,a840)),x93182),f331(f331(f310(x93181),x93183),f184(f854(x93181,a840))))),x93184))
% 51.10/50.83 [9657]E(f331(f331(f155(x96571),f331(f331(f155(f848(x96571)),f169(x96571,x96572)),x96573)),x96574),f331(f331(f155(x96571),f331(f331(f155(f848(x96571)),x96572),x96574)),x96573))+~P1(f331(f331(f241(a847),x96573),f331(f185(f848(f848(x96571))),f169(x96571,x96572))))+~P16(a847,f331(f160(a847),f331(f331(f147(f848(x96571),a847),f185(f848(x96571))),x96572)))+~P1(f331(f331(f241(a847),x96574),f331(f185(f848(f848(x96571))),f331(f131(f848(x96571),f331(f331(f10(a847,a840,f848(x96571)),f331(f241(a847),x96573)),f185(f848(x96571)))),x96572))))
% 51.10/50.83 [9678]~P1(f331(f331(f333(f853(a847,a847)),x96784),x96781))+~P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),x96784),x96782)),a45))+~P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x96781),x96783)),a75))+P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x96781),f331(f331(f310(f853(a847,a847)),x96782),x96783))),a75))
% 51.10/50.83 [9679]~P1(f331(f331(f333(f853(a847,a847)),x96794),x96791))+~P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),x96794),x96792)),a77))+~P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x96791),x96793)),a78))+P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x96791),f331(f331(f310(f853(a847,a847)),x96792),x96793))),a78))
% 51.10/50.83 [9692]~P1(f331(f331(f333(f853(a847,a847)),x96924),x96923))+~P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),x96921),x96924)),a45))+~P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x96922),x96923)),a46))+P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),f331(f331(f310(f853(a847,a847)),x96921),x96922)),x96923)),a46))
% 51.10/50.83 [9693]~P1(f331(f331(f333(f853(a847,a847)),x96934),x96933))+~P1(f331(f331(f333(f853(f853(a847,a847),f853(a847,a847))),f331(f331(f249(f853(a847,a847),f853(a847,a847)),x96931),x96934)),a77))+~P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),x96932),x96933)),a76))+P1(f331(f331(f333(f853(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840))),f331(f331(f249(f854(f853(a847,a847),a840),f854(f853(a847,a847),a840)),f331(f331(f310(f853(a847,a847)),x96931),x96932)),x96933)),a76))
% 51.10/50.83 [5880]~P9(x58804,x58801)+~P1(f331(f331(x58801,x58802),x58805))+P1(f331(f331(x58801,x58802),x58803))+~P1(f331(f331(x58801,x58805),x58803))
% 51.10/50.83 [5141]~P4(x51415)+E(x51411,x51412)+~E(x51413,x51414)+~E(f331(f331(f3(x51415),x51413),x51414),f331(f331(f3(x51415),x51411),x51412))
% 51.10/50.83 [5142]~P4(x51425)+E(x51421,x51422)+~E(x51423,x51424)+~E(f331(f331(f3(x51425),x51423),x51424),f331(f331(f3(x51425),x51421),x51422))
% 51.10/50.83 [5993]~P19(x59935,x59931,x59933)+E(f331(f331(x59931,x59932),f331(x59933,x59934)),f331(x59933,x59934))+~P1(f331(f68(x59935),x59934))+~P1(f331(f331(f333(x59935),x59932),x59934))
% 51.10/50.83 [6190]~P76(x61901)+~E(f331(f331(f3(x61901),x61904),x61905),f331(f331(f3(x61901),x61902),x61903))+~P1(f331(f331(f241(x61901),x61904),x61905))+P1(f331(f331(f241(x61901),x61902),x61903))
% 51.10/50.83 [6191]~P76(x61911)+~E(f331(f331(f3(x61911),x61914),x61915),f331(f331(f3(x61911),x61912),x61913))+~P1(f331(f331(f241(x61911),x61914),x61915))+P1(f331(f331(f241(x61911),x61912),x61913))
% 51.10/50.83 [6192]~P76(x61921)+~E(f331(f331(f3(x61921),x61924),x61925),f331(f331(f3(x61921),x61922),x61923))+~P1(f331(f331(f240(x61921),x61924),x61925))+P1(f331(f331(f240(x61921),x61922),x61923))
% 51.10/50.83 [6193]~P76(x61931)+~E(f331(f331(f3(x61931),x61934),x61935),f331(f331(f3(x61931),x61932),x61933))+~P1(f331(f331(f240(x61931),x61934),x61935))+P1(f331(f331(f240(x61931),x61932),x61933))
% 51.10/50.83 [7192]~E(x71922,f331(f331(f145(x71921),x71924),x71925))+P1(f331(f331(f333(f848(x71921)),x71922),f153(x71921,x71923)))+~P1(f331(f331(f333(f848(x71921)),x71925),f153(x71921,x71923)))+~P1(f331(f331(f333(x71921),x71924),x71923))
% 51.10/50.83 [7627]~E(f331(f185(f848(x76271)),x76273),f331(f185(f848(x76272)),x76274))+~E(f331(f331(f147(f853(x76271,x76272),x76272),f258(x76271,x76272)),x76275),x76274)+~E(f331(f331(f147(f853(x76271,x76272),x76271),f248(x76271,x76272)),x76275),x76273)+E(f331(f331(f172(x76271,x76272),x76273),x76274),x76275)
% 51.10/50.83 [7963]~P88(x79631)+P1(f331(f331(f241(f854(x79631,a840)),f303(x79631,x79632,x79633)),f303(x79631,x79634,x79635)))+~P1(f331(f331(f240(x79631),x79634),x79635))+P1(f331(f331(f240(x79631),x79632),x79633))
% 51.10/50.83 [8055]~P88(x80551)+P1(f331(f331(f240(f854(x80551,a840)),f303(x80551,x80552,x80553)),f303(x80551,x80554,x80555)))+~P1(f331(f331(f240(x80551),x80553),x80555))+~P1(f331(f331(f240(x80551),x80554),x80552))
% 51.10/50.83 [8174]~P102(x81741)+P1(f331(f331(f240(x81741),x81742),x81743))+P1(f331(f331(f240(x81741),x81744),x81743))+~P1(f331(f331(f240(f854(x81741,a840)),f331(f302(x81741,x81743),x81742)),f331(f302(x81741,x81744),x81745)))
% 51.10/50.83 [8175]~P102(x81751)+P1(f331(f331(f240(x81751),x81752),x81753))+P1(f331(f331(f240(x81751),x81752),x81754))+~P1(f331(f331(f240(f854(x81751,a840)),f331(f302(x81751,x81753),x81752)),f331(f302(x81751,x81755),x81754)))
% 51.10/50.83 [8415]~P88(x84151)+~P1(f331(f331(f241(f854(x84151,a840)),f303(x84151,x84154,x84152)),f303(x84151,x84155,x84153)))+P1(f331(f331(f240(x84151),x84152),x84153))+~P1(f331(f331(f240(x84151),x84154),x84152))
% 51.10/50.83 [8416]~P88(x84161)+~P1(f331(f331(f240(f854(x84161,a840)),f303(x84161,x84164,x84162)),f303(x84161,x84165,x84163)))+P1(f331(f331(f240(x84161),x84162),x84163))+~P1(f331(f331(f240(x84161),x84164),x84162))
% 51.10/50.83 [8417]~P88(x84171)+~P1(f331(f331(f241(f854(x84171,a840)),f303(x84171,x84173,x84174)),f303(x84171,x84172,x84175)))+P1(f331(f331(f240(x84171),x84172),x84173))+~P1(f331(f331(f240(x84171),x84173),x84174))
% 51.10/50.83 [8418]~P88(x84181)+~P1(f331(f331(f240(f854(x84181,a840)),f303(x84181,x84183,x84184)),f303(x84181,x84182,x84185)))+P1(f331(f331(f240(x84181),x84182),x84183))+~P1(f331(f331(f240(x84181),x84183),x84184))
% 51.10/50.83 [5879]~P19(x58792,x58795,x58793)+E(x58791,f184(f854(x58792,a840)))+~P1(f331(f68(x58792),x58791))+E(f331(x58793,f331(f331(f310(x58792),x58794),x58791)),f331(f331(x58795,x58794),f331(x58793,x58791)))
% 51.10/50.83 [6682]~E(x66821,x66822)+~E(f331(f331(f109(f854(x66823,a840)),x66824),x66825),f184(f854(x66823,a840)))+~P1(f331(f331(f333(x66823),x66822),x66825))+~P1(f331(f331(f333(x66823),x66821),x66824))
% 51.10/50.83 [6768]~P20(x67682,x67685,x67681)+~P1(f331(f68(x67682),x67684))+E(f331(x67681,f331(f331(f310(x67682),x67683),x67684)),f331(f331(f71(x67682,x67682,x67685),x67683),x67684))+P1(f331(f331(f333(x67682),x67683),x67684))
% 51.10/50.83 [6838]~P70(x68382)+~P1(f331(f68(x68381),x68385))+E(f331(f331(f11(x68381,x68382),x68383),f331(f331(f310(x68381),x68384),x68385)),f331(f331(f88(x68382),f331(x68383,x68384)),f331(f331(f11(x68381,x68382),x68383),x68385)))+P1(f331(f331(f333(x68381),x68384),x68385))
% 51.10/50.83 [6839]~P70(x68392)+~P1(f331(f68(x68391),x68395))+E(f331(f331(f11(x68391,x68392),x68393),f331(f331(f310(x68391),x68394),x68395)),f331(f331(f88(x68392),f331(x68393,x68394)),f331(f331(f11(x68391,x68392),x68393),x68395)))+P1(f331(f331(f333(x68391),x68394),x68395))
% 51.10/50.83 [6840]~P68(x68402)+~P1(f331(f68(x68401),x68405))+E(f331(f331(f8(x68401,x68402),x68403),f331(f331(f310(x68401),x68404),x68405)),f331(f331(f87(x68402),f331(x68403,x68404)),f331(f331(f8(x68401,x68402),x68403),x68405)))+P1(f331(f331(f333(x68401),x68404),x68405))
% 51.10/50.83 [6841]~P68(x68412)+~P1(f331(f68(x68411),x68415))+E(f331(f331(f8(x68411,x68412),x68413),f331(f331(f310(x68411),x68414),x68415)),f331(f331(f87(x68412),f331(x68413,x68414)),f331(f331(f8(x68411,x68412),x68413),x68415)))+P1(f331(f331(f333(x68411),x68414),x68415))
% 51.10/50.83 [7250]~P87(x72501)+~P1(f331(f68(x72504),x72505))+~P1(f331(f331(f333(x72504),x72503),x72505))+P1(f331(f331(f287(x72501),f331(x72502,x72503)),f331(f331(f11(x72504,x72501),x72502),x72505)))
% 51.10/50.83 [7363]~P20(x73632,x73635,x73631)+~P1(f331(f68(x73632),x73634))+E(f331(x73631,f331(f331(f310(x73632),x73633),x73634)),x73633)+~E(f331(f331(f3(f854(x73632,a840)),x73634),f331(f331(f310(x73632),x73633),f184(f854(x73632,a840)))),f184(f854(x73632,a840)))
% 51.10/50.83 [7676]~P1(f331(x76761,x76763))+~P1(f331(f331(f191(x76762),x76763),x76765))+~P1(f331(f331(f191(f37(x76761,x76762)),x76765),x76764))+P1(f331(f331(f191(f37(x76761,x76762)),x76763),x76764))
% 51.10/50.83 [7677]~P1(f331(x76771,x76773))+~P1(f331(f331(f191(x76772),x76773),x76775))+~P1(f331(f331(f191(f37(x76771,x76772)),x76775),x76774))+P1(f331(f331(f191(f37(x76771,x76772)),x76773),x76774))
% 51.10/50.83 [7695]~P87(x76951)+~P1(f331(f331(f287(x76951),x76952),x76954))+~P1(f331(f331(f240(a847),x76953),x76955))+P1(f331(f331(f287(x76951),f331(f331(f250(x76951),x76952),x76953)),f331(f331(f250(x76951),x76954),x76955)))
% 51.10/50.83 [7729]~P5(x77291)+E(f331(f331(f48(x77291),f331(f331(f88(x77291),x77292),x77293)),f331(f331(f88(x77291),x77294),x77295)),f331(f331(f88(x77291),f331(f331(f48(x77291),x77292),x77294)),f331(f331(f48(x77291),x77293),x77295)))+~P1(f331(f331(f287(x77291),x77295),x77293))+~P1(f331(f331(f287(x77291),x77294),x77292))
% 51.10/50.83 [7733]~P79(x77331)+~P1(f331(f331(f241(x77331),x77333),x77335))+~P1(f331(f331(f241(x77331),x77332),x77334))+P1(f331(f331(f241(x77331),f331(f331(f87(x77331),x77332),x77333)),f331(f331(f87(x77331),x77334),x77335)))
% 51.10/50.83 [7734]~P79(x77341)+~P1(f331(f331(f240(x77341),x77342),x77344))+~P1(f331(f331(f241(x77341),x77343),x77345))+P1(f331(f331(f241(x77341),f331(f331(f87(x77341),x77342),x77343)),f331(f331(f87(x77341),x77344),x77345)))
% 51.10/50.83 [7735]~P79(x77351)+~P1(f331(f331(f240(x77351),x77353),x77355))+~P1(f331(f331(f241(x77351),x77352),x77354))+P1(f331(f331(f241(x77351),f331(f331(f87(x77351),x77352),x77353)),f331(f331(f87(x77351),x77354),x77355)))
% 51.10/50.83 [7736]~P77(x77361)+~P1(f331(f331(f240(x77361),x77363),x77365))+~P1(f331(f331(f240(x77361),x77362),x77364))+P1(f331(f331(f240(x77361),f331(f331(f87(x77361),x77362),x77363)),f331(f331(f87(x77361),x77364),x77365)))
% 51.10/50.83 [7737]~P102(x77371)+~P1(f331(f331(f240(x77371),x77373),x77375))+~P1(f331(f331(f240(x77371),x77372),x77374))+P1(f331(f331(f240(x77371),f331(f331(f244(x77371),x77372),x77373)),f331(f331(f244(x77371),x77374),x77375)))
% 51.10/50.83 [7738]~P102(x77381)+~P1(f331(f331(f240(x77381),x77383),x77385))+~P1(f331(f331(f240(x77381),x77382),x77384))+P1(f331(f331(f240(x77381),f331(f331(f239(x77381),x77382),x77383)),f331(f331(f239(x77381),x77384),x77385)))
% 51.10/50.83 [7739]~P100(x77391)+~P1(f331(f331(f240(x77391),x77393),x77395))+~P1(f331(f331(f240(x77391),x77392),x77394))+P1(f331(f331(f240(x77391),f331(f331(f108(x77391),x77392),x77393)),f331(f331(f108(x77391),x77394),x77395)))
% 51.10/50.83 [7740]~P101(x77401)+~P1(f331(f331(f240(x77401),x77403),x77405))+~P1(f331(f331(f240(x77401),x77402),x77404))+P1(f331(f331(f240(x77401),f331(f331(f109(x77401),x77402),x77403)),f331(f331(f109(x77401),x77404),x77405)))
% 51.10/50.83 [7741]~P87(x77411)+~P1(f331(f331(f287(x77411),x77413),x77415))+~P1(f331(f331(f287(x77411),x77412),x77414))+P1(f331(f331(f287(x77411),f331(f331(f88(x77411),x77412),x77413)),f331(f331(f88(x77411),x77414),x77415)))
% 51.10/50.83 [7873]~P137(x78735)+E(x78731,x78732)+E(x78733,x78734)+~E(f331(f331(f87(x78735),f331(f331(f88(x78735),x78733),x78731)),f331(f331(f88(x78735),x78734),x78732)),f331(f331(f87(x78735),f331(f331(f88(x78735),x78733),x78732)),f331(f331(f88(x78735),x78734),x78731)))
% 51.10/50.83 [7874]~P137(x78745)+E(x78741,x78742)+E(x78743,x78744)+~E(f331(f331(f87(x78745),f331(f331(f88(x78745),x78743),x78741)),f331(f331(f88(x78745),x78744),x78742)),f331(f331(f87(x78745),f331(f331(f88(x78745),x78743),x78742)),f331(f331(f88(x78745),x78744),x78741)))
% 51.10/50.83 [8012]P29(x80121,x80122,x80123)+~P30(x80121,x80124,x80125)+~P29(x80121,x80122,f596(x80125,x80124,x80121,x80122))+~P1(f331(f331(f333(f846(x80121)),x80123),x80125))
% 51.10/50.83 [8075]~P102(x80754)+~P1(f331(f132(x80751),x80753))+P1(f331(f331(f333(x80751),x80752),f331(f163(x80751),x80753)))+P1(f331(f132(x80751),f331(f331(f143(x80751,x80754,x80755),x80752),x80753)))
% 51.10/50.83 [8220]~P68(x82201)+E(f331(f331(f87(x82201),f331(f331(f8(a847,x82201),x82202),f331(f302(a847,x82203),x82204))),f331(f331(f8(a847,x82201),x82202),f331(f302(a847,x82204),x82205))),f331(f331(f8(a847,x82201),x82202),f331(f302(a847,x82203),x82205)))+~P1(f331(f331(f240(a847),x82204),x82205))+~P1(f331(f331(f240(a847),x82203),x82204))
% 51.10/50.83 [8221]~P4(x82211)+E(f331(f331(f3(x82211),f331(f331(f8(a847,x82211),x82212),f331(f302(a847,x82213),x82214))),f331(f331(f8(a847,x82211),x82212),f331(f302(a847,x82213),x82215))),f331(f331(f8(a847,x82211),x82212),f331(f302(a847,x82215),x82214)))+~P1(f331(f331(f240(a847),x82215),x82214))+~P1(f331(f331(f240(a847),x82213),x82215))
% 51.10/50.83 [8537]~P59(x85372)+E(x85371,f2(x85372))+E(x85373,f2(x85372))+E(f331(f331(f291(x85372),f331(f331(f87(x85372),f331(f331(f88(x85372),x85374),x85371)),f331(f331(f88(x85372),x85375),x85373))),f331(f331(f88(x85372),x85373),x85371)),f331(f331(f87(x85372),f331(f331(f291(x85372),x85374),x85373)),f331(f331(f291(x85372),x85375),x85371)))
% 51.10/50.83 [8538]~P59(x85382)+E(x85381,f2(x85382))+E(x85383,f2(x85382))+E(f331(f331(f291(x85382),f331(f331(f3(x85382),f331(f331(f88(x85382),x85384),x85381)),f331(f331(f88(x85382),x85385),x85383))),f331(f331(f88(x85382),x85383),x85381)),f331(f331(f3(x85382),f331(f331(f291(x85382),x85384),x85383)),f331(f331(f291(x85382),x85385),x85381)))
% 51.10/50.83 [8547]~E(x85472,f331(x85473,x85471))+E(x85471,f516(x85472,x85473,x85474,x85475))+~P27(x85475,x85474,x85473,f247(f854(x85475,a840)))+~P1(f331(f331(f333(x85474),x85472),f331(f311(x85475,x85474,x85473),f247(f854(x85475,a840)))))
% 51.10/50.83 [8732]~P86(x87321)+~P1(f331(f331(f241(x87321),f331(f82(x87321),x87322)),x87324))+P1(f331(f331(f241(x87321),f331(f331(f88(x87321),f331(f82(x87321),x87322)),f331(f82(x87321),x87323))),f331(f331(f88(x87321),x87324),x87325)))+~P1(f331(f331(f241(x87321),f331(f82(x87321),x87323)),x87325))
% 51.10/50.83 [8746]~P30(x87461,x87465,x87464)+P29(x87461,x87462,x87463)+P1(f331(f331(f333(f846(x87461)),f596(x87464,x87465,x87461,x87462)),x87465))+~P1(f331(f331(f333(f846(x87461)),x87463),x87464))
% 51.10/50.83 [8826]~P27(x88261,x88263,x88265,x88262)+~P1(f331(f68(x88263),x88264))+P1(f331(f331(f240(a847),f331(f47(x88261),x88262)),f331(f47(x88263),x88264)))+~P1(f331(f331(f240(f854(x88263,a840)),f331(f311(x88261,x88263,x88265),x88262)),x88264))
% 51.10/50.83 [8893]~P70(x88932)+~P27(x88931,x88931,x88934,x88935)+~P1(f331(f68(x88931),x88935))+E(f331(f331(f11(x88931,x88932),f331(f80(x88931,x88932,x88931,x88933),x88934)),x88935),f331(f331(f11(x88931,x88932),x88933),f331(f311(x88931,x88931,x88934),x88935)))
% 51.10/50.83 [8894]~P68(x88942)+~P27(x88941,x88941,x88944,x88945)+~P1(f331(f68(x88941),x88945))+E(f331(f331(f8(x88941,x88942),f331(f80(x88941,x88942,x88941,x88943),x88944)),x88945),f331(f331(f8(x88941,x88942),x88943),f331(f311(x88941,x88941,x88944),x88945)))
% 51.10/50.83 [8971]~E(f518(x89712,x89714,x89711,x89713,x89715),x89715)+~E(x89712,f331(x89714,x89715))+~P27(x89713,x89711,x89714,f247(f854(x89713,a840)))+P1(f331(f331(f333(x89711),x89712),f331(f311(x89713,x89711,x89714),f247(f854(x89713,a840)))))
% 51.10/50.83 [9003]~P34(x90031,x90032)+~P1(f331(f331(f333(x90031),x90033),x90034))+~P1(f331(f331(f333(x90031),x90035),x90034))+~P1(f331(f331(f333(f853(x90031,x90031)),f331(f331(f249(x90031,x90031),x90035),f693(x90032,x90031,x90034))),x90032))
% 51.10/50.83 [9037]~P27(x90372,x90373,x90375,x90371)+E(x90371,f184(f854(x90372,a840)))+E(f331(f311(x90373,x90372,f447(x90374,x90373,x90372,x90371)),x90374),x90371)+~P1(f331(f331(f240(f854(x90373,a840)),f331(f311(x90372,x90373,x90375),x90371)),x90374))
% 51.10/50.83 [9076]~E(x90762,f331(x90761,x90765))+~P27(x90764,x90763,x90761,f247(f854(x90764,a840)))+E(f331(x90761,f518(x90762,x90761,x90763,x90764,x90765)),x90762)+P1(f331(f331(f333(x90763),x90762),f331(f311(x90764,x90763,x90761),f247(f854(x90764,a840)))))
% 51.10/50.83 [9484]~P102(x94845)+~P7(x94845)+P1(f331(f331(f333(x94841),f410(x94842,x94843,x94841,x94844,x94845)),x94843))+~P1(f331(f331(f241(x94845),x94844),f331(f331(f51(x94841,x94845),x94843),x94842)))
% 51.10/50.83 [9489]~P102(x94891)+~P7(x94891)+P1(f331(f331(f241(x94891),x94892),f331(x94893,f410(x94893,x94894,x94895,x94892,x94891))))+~P1(f331(f331(f241(x94891),x94892),f331(f331(f51(x94895,x94891),x94894),x94893)))
% 51.10/50.83 [9562]~P64(x95621)+~P1(f331(f73(x95621,x95621,f88(x95621),x95622,x95623),x95625))+P1(f331(f331(f333(x95621),x95622),x95623))+P1(f331(f73(x95621,x95621,f88(x95621),x95624,f331(f331(f310(x95621),x95622),x95623)),f331(f331(f88(x95621),x95624),x95625)))
% 51.10/50.83 [9775]~P70(x97752)+~P1(f331(f68(x97751),x97755))+E(f331(f331(f11(x97751,x97752),f331(f331(f9(x97751,x97752,x97752),f331(f331(f20(x97751,x97752,f854(x97752,x97752)),f331(f331(f10(a840,f854(x97752,f854(x97752,x97752)),x97751),f103(x97752)),f331(a328,x97753))),x97754)),f85(x97752))),x97755),f85(x97752))+P1(f331(f331(f333(x97751),x97753),x97755))
% 51.10/50.83 [9776]~P68(x97762)+~P1(f331(f68(x97761),x97765))+E(f331(f331(f8(x97761,x97762),f331(f331(f9(x97761,x97762,x97762),f331(f331(f20(x97761,x97762,f854(x97762,x97762)),f331(f331(f10(a840,f854(x97762,f854(x97762,x97762)),x97761),f103(x97762)),f331(a328,x97763))),x97764)),f2(x97762))),x97765),f2(x97762))+P1(f331(f331(f333(x97761),x97763),x97765))
% 51.10/50.83 [9777]~P70(x97772)+~P1(f331(f68(x97771),x97775))+E(f331(f331(f11(x97771,x97772),f331(f331(f9(x97771,x97772,x97772),f331(f331(f20(x97771,x97772,f854(x97772,x97772)),f331(f331(f10(a840,f854(x97772,f854(x97772,x97772)),x97771),f103(x97772)),f331(a328,x97773))),x97774)),f85(x97772))),x97775),f331(x97774,x97773))+~P1(f331(f331(f333(x97771),x97773),x97775))
% 51.10/50.83 [9778]~P68(x97782)+~P1(f331(f68(x97781),x97785))+E(f331(f331(f8(x97781,x97782),f331(f331(f9(x97781,x97782,x97782),f331(f331(f20(x97781,x97782,f854(x97782,x97782)),f331(f331(f10(a840,f854(x97782,f854(x97782,x97782)),x97781),f103(x97782)),f331(a328,x97783))),x97784)),f2(x97782))),x97785),f331(x97784,x97783))+~P1(f331(f331(f333(x97781),x97783),x97785))
% 51.10/50.83 [9843]~P70(x98432)+~P1(f331(f68(x98431),x98435))+E(f331(f331(f11(x98431,x98432),f331(f331(f9(x98431,x98432,x98432),f331(f331(f20(x98431,x98432,f854(x98432,x98432)),f331(f331(f10(a840,f854(x98432,f854(x98432,x98432)),x98431),f103(x98432)),f331(f331(f9(x98431,x98431,a840),a328),x98433))),x98434)),f85(x98432))),x98435),f85(x98432))+P1(f331(f331(f333(x98431),x98433),x98435))
% 51.10/50.83 [9844]~P68(x98442)+~P1(f331(f68(x98441),x98445))+E(f331(f331(f8(x98441,x98442),f331(f331(f9(x98441,x98442,x98442),f331(f331(f20(x98441,x98442,f854(x98442,x98442)),f331(f331(f10(a840,f854(x98442,f854(x98442,x98442)),x98441),f103(x98442)),f331(f331(f9(x98441,x98441,a840),a328),x98443))),x98444)),f2(x98442))),x98445),f2(x98442))+P1(f331(f331(f333(x98441),x98443),x98445))
% 51.10/50.83 [9846]~P70(x98462)+~P1(f331(f68(x98461),x98465))+E(f331(f331(f11(x98461,x98462),f331(f331(f9(x98461,x98462,x98462),f331(f331(f20(x98461,x98462,f854(x98462,x98462)),f331(f331(f10(a840,f854(x98462,f854(x98462,x98462)),x98461),f103(x98462)),f331(f331(f9(x98461,x98461,a840),a328),x98463))),x98464)),f85(x98462))),x98465),f331(x98464,x98463))+~P1(f331(f331(f333(x98461),x98463),x98465))
% 51.10/50.83 [9847]~P68(x98472)+~P1(f331(f68(x98471),x98475))+E(f331(f331(f8(x98471,x98472),f331(f331(f9(x98471,x98472,x98472),f331(f331(f20(x98471,x98472,f854(x98472,x98472)),f331(f331(f10(a840,f854(x98472,f854(x98472,x98472)),x98471),f103(x98472)),f331(f331(f9(x98471,x98471,a840),a328),x98473))),x98474)),f2(x98472))),x98475),f331(x98474,x98473))+~P1(f331(f331(f333(x98471),x98473),x98475))
% 51.10/50.83 [7732]~P4(x77322)+~P1(f331(f68(x77321),x77324))+E(f331(f331(f8(x77321,x77322),x77323),f331(f331(f3(f854(x77321,a840)),x77324),f331(f331(f310(x77321),x77325),f184(f854(x77321,a840))))),f331(f331(f8(x77321,x77322),x77323),x77324))+P1(f331(f331(f333(x77321),x77325),x77324))
% 51.10/50.83 [8227]~P121(x82272)+~P1(f331(f68(x82271),x82274))+E(f331(f331(f8(x82271,x82272),x82273),f331(f331(f3(f854(x82271,a840)),x82274),f331(f331(f310(x82271),x82275),f184(f854(x82271,a840))))),f331(f331(f3(x82272),f331(f331(f8(x82271,x82272),x82273),x82274)),f331(x82273,x82275)))+~P1(f331(f331(f333(x82271),x82275),x82274))
% 51.10/50.83 [8228]~P4(x82282)+~P1(f331(f68(x82281),x82284))+E(f331(f331(f8(x82281,x82282),x82283),f331(f331(f3(f854(x82281,a840)),x82284),f331(f331(f310(x82281),x82285),f184(f854(x82281,a840))))),f331(f331(f3(x82282),f331(f331(f8(x82281,x82282),x82283),x82284)),f331(x82283,x82285)))+~P1(f331(f331(f333(x82281),x82285),x82284))
% 51.10/50.83 [8239]~P87(x82391)+~P1(f331(f331(f240(a847),x82393),x82395))+~P1(f331(f331(f287(x82391),f331(f331(f250(x82391),x82392),x82395)),x82394))+P1(f331(f331(f287(x82391),f331(f331(f250(x82391),x82392),x82393)),x82394))
% 51.10/50.83 [8256]~P4(x82561)+~P1(f331(f68(x82562),x82564))+E(f331(f331(f3(x82561),f331(f331(f8(x82562,x82561),x82563),x82564)),f331(f331(f8(x82562,x82561),x82563),x82565)),f331(f331(f8(x82562,x82561),x82563),f331(f331(f3(f854(x82562,a840)),x82564),x82565)))+~P1(f331(f331(f240(f854(x82562,a840)),x82565),x82564))
% 51.10/50.83 [8277]P1(f331(f68(x82771),f331(x82772,x82773)))+~P1(f331(f68(x82774),x82775))+~P1(f331(f331(f333(x82774),x82773),x82775))+~P1(f331(f68(x82771),f331(f331(f51(x82774,f854(x82771,a840)),x82775),x82772)))
% 51.10/50.83 [8697]~P10(x86971,x86975,x86974)+~E(f331(f285(x86971,x86971,x86974),f331(f331(f310(x86971),x86972),f184(f854(x86971,a840)))),f331(f285(x86971,x86971,x86974),f331(f331(f310(x86971),x86973),f184(f854(x86971,a840)))))+~P1(f331(f331(f333(x86971),x86973),x86975))+P1(f331(f331(f333(f853(x86971,x86971)),f331(f331(f249(x86971,x86971),x86972),x86973)),x86974))
% 51.10/50.83 [8963]~P1(f331(x89631,x89635))+P1(f331(x89631,f349(x89631,x89632,x89633,x89634)))+P1(f331(x89631,f346(x89631,x89632,x89633,x89634)))+~P1(f331(f331(f333(x89634),x89635),f331(f331(f108(f854(x89634,a840)),x89633),x89632)))
% 51.10/50.83 [9124]~P1(f331(x91241,x91245))+P1(f331(x91241,f346(x91241,x91242,x91243,x91244)))+P1(f331(f331(f333(x91244),f349(x91241,x91242,x91243,x91244)),x91242))+~P1(f331(f331(f333(x91244),x91245),f331(f331(f108(f854(x91244,a840)),x91243),x91242)))
% 51.10/50.83 [9125]~P1(f331(x91251,x91255))+P1(f331(x91251,f349(x91251,x91252,x91253,x91254)))+P1(f331(f331(f333(x91254),f346(x91251,x91252,x91253,x91254)),x91253))+~P1(f331(f331(f333(x91254),x91255),f331(f331(f108(f854(x91254,a840)),x91253),x91252)))
% 51.10/50.83 [9129]P1(f331(x91291,x91292))+~P1(f331(x91291,f354(x91291,x91293,x91294,x91295)))+~P1(f331(x91291,f353(x91291,x91293,x91294,x91295)))+~P1(f331(f331(f333(x91295),x91292),f331(f331(f108(f854(x91295,a840)),x91294),x91293)))
% 51.10/50.83 [9162]E(x91621,x91622)+~P1(f331(f331(f333(f853(x91623,x91623)),f331(f331(f249(x91623,x91623),x91621),x91622)),f308(x91623,x91625)))+P1(f331(f331(f333(x91623),x91621),x91624))+~P1(f331(f331(f240(f854(f853(x91623,x91623),a840)),x91625),f331(f331(f256(x91623,x91623),x91624),f331(f18(f854(x91623,a840),x91623),x91624))))
% 51.10/50.83 [9179]P1(f331(x91791,x91792))+~P1(f331(x91791,f353(x91791,x91794,x91795,x91793)))+P1(f331(f331(f333(x91793),f354(x91791,x91794,x91795,x91793)),x91794))+~P1(f331(f331(f333(x91793),x91792),f331(f331(f108(f854(x91793,a840)),x91795),x91794)))
% 51.10/50.83 [9180]P1(f331(x91801,x91802))+~P1(f331(x91801,f354(x91801,x91804,x91805,x91803)))+P1(f331(f331(f333(x91803),f353(x91801,x91804,x91805,x91803)),x91805))+~P1(f331(f331(f333(x91803),x91802),f331(f331(f108(f854(x91803,a840)),x91805),x91804)))
% 51.10/50.83 [9243]P1(f331(x92431,x92432))+P1(f331(f331(f333(x92433),f354(x92431,x92434,x92435,x92433)),x92434))+P1(f331(f331(f333(x92433),f353(x92431,x92434,x92435,x92433)),x92435))+~P1(f331(f331(f333(x92433),x92432),f331(f331(f108(f854(x92433,a840)),x92435),x92434)))
% 51.10/50.83 [9245]~P1(f331(x92452,x92455))+P1(f331(f331(f333(x92451),f349(x92452,x92453,x92454,x92451)),x92453))+P1(f331(f331(f333(x92451),f346(x92452,x92453,x92454,x92451)),x92454))+~P1(f331(f331(f333(x92451),x92455),f331(f331(f108(f854(x92451,a840)),x92454),x92453)))
% 51.10/50.83 [9392]~P10(x93921,x93925,x93924)+~P1(f331(f331(f333(x93921),x93923),x93925))+P1(f331(f331(f333(f853(x93921,x93921)),f331(f331(f249(x93921,x93921),x93922),x93923)),x93924))+~P1(f331(f331(f240(f854(x93921,a840)),f331(f285(x93921,x93921,x93924),f331(f331(f310(x93921),x93923),f184(f854(x93921,a840))))),f331(f285(x93921,x93921,x93924),f331(f331(f310(x93921),x93922),f184(f854(x93921,a840))))))
% 51.10/50.83 [9514]~P102(x95145)+~P7(x95145)+P1(f331(f331(f333(x95141),f642(x95142,x95143,x95144,x95141,x95145)),x95144))+~P1(f331(f331(f241(x95145),f331(f331(f52(x95141,x95145),x95144),x95143)),x95142))
% 51.10/50.83 [9547]~P71(x95475)+~P77(x95475)+P1(f331(f331(f333(x95471),f753(x95472,x95473,x95474,x95471,x95475)),f331(f163(x95471),x95474)))+P1(f331(f331(f240(x95475),f331(f157(x95475),f331(f331(f147(x95471,x95475),x95473),x95474))),f331(f157(x95475),f331(f331(f147(x95471,x95475),x95472),x95474))))
% 51.10/50.83 [9647]~P102(x96471)+~P7(x96471)+P1(f331(f331(f241(x96471),f331(x96472,f642(x96473,x96472,x96474,x96475,x96471))),x96473))+~P1(f331(f331(f241(x96471),f331(f331(f52(x96475,x96471),x96474),x96472)),x96473))
% 51.10/50.83 [9792]~P71(x97921)+~P77(x97921)+~P1(f331(f331(f240(x97921),f331(x97923,f753(x97925,x97923,x97924,x97922,x97921))),f331(x97925,f753(x97925,x97923,x97924,x97922,x97921))))+P1(f331(f331(f240(x97921),f331(f157(x97921),f331(f331(f147(x97922,x97921),x97923),x97924))),f331(f157(x97921),f331(f331(f147(x97922,x97921),x97925),x97924))))
% 51.10/50.83 [8555]~P70(x85551)+~P1(f331(f68(x85554),x85555))+~P1(f331(f331(f333(x85554),x85553),x85555))+E(f331(f331(f88(x85551),f331(x85552,x85553)),f331(f331(f11(x85554,x85551),x85552),f331(f331(f3(f854(x85554,a840)),x85555),f331(f331(f310(x85554),x85553),f184(f854(x85554,a840)))))),f331(f331(f11(x85554,x85551),x85552),x85555))
% 51.10/50.83 [8556]~P68(x85561)+~P1(f331(f68(x85564),x85565))+~P1(f331(f331(f333(x85564),x85563),x85565))+E(f331(f331(f87(x85561),f331(x85562,x85563)),f331(f331(f8(x85564,x85561),x85562),f331(f331(f3(f854(x85564,a840)),x85565),f331(f331(f310(x85564),x85563),f184(f854(x85564,a840)))))),f331(f331(f8(x85564,x85561),x85562),x85565))
% 51.10/50.83 [8557]~P68(x85571)+~P1(f331(f68(x85574),x85575))+~P1(f331(f331(f333(x85574),x85573),x85575))+E(f331(f331(f87(x85571),f331(x85572,x85573)),f331(f331(f8(x85574,x85571),x85572),f331(f331(f3(f854(x85574,a840)),x85575),f331(f331(f310(x85574),x85573),f184(f854(x85574,a840)))))),f331(f331(f8(x85574,x85571),x85572),x85575))
% 51.10/50.83 [8610]~P20(x86101,x86104,x86105)+~P1(f331(f68(x86101),x86102))+E(f331(f331(f3(f854(x86101,a840)),x86102),f331(f331(f310(x86101),x86103),f184(f854(x86101,a840)))),f184(f854(x86101,a840)))+E(f331(f331(x86104,x86103),f331(x86105,f331(f331(f3(f854(x86101,a840)),x86102),f331(f331(f310(x86101),x86103),f184(f854(x86101,a840)))))),f331(x86105,f331(f331(f310(x86101),x86103),x86102)))
% 51.10/50.83 [8941]~P68(x89411)+~P1(f331(f68(x89412),x89415))+~P1(f331(f68(x89412),x89414))+E(f331(f331(f87(x89411),f331(f331(f8(x89412,x89411),x89413),f331(f331(f108(f854(x89412,a840)),x89414),x89415))),f331(f331(f8(x89412,x89411),x89413),f331(f331(f109(f854(x89412,a840)),x89414),x89415))),f331(f331(f87(x89411),f331(f331(f8(x89412,x89411),x89413),x89414)),f331(f331(f8(x89412,x89411),x89413),x89415)))
% 51.10/50.83 [8942]~P70(x89421)+~P1(f331(f68(x89422),x89425))+~P1(f331(f68(x89422),x89424))+E(f331(f331(f88(x89421),f331(f331(f11(x89422,x89421),x89423),f331(f331(f108(f854(x89422,a840)),x89424),x89425))),f331(f331(f11(x89422,x89421),x89423),f331(f331(f109(f854(x89422,a840)),x89424),x89425))),f331(f331(f88(x89421),f331(f331(f11(x89422,x89421),x89423),x89424)),f331(f331(f11(x89422,x89421),x89423),x89425)))
% 51.10/50.83 [8943]~P70(x89431)+~P1(f331(f68(x89432),x89435))+~P1(f331(f68(x89432),x89434))+E(f331(f331(f88(x89431),f331(f331(f11(x89432,x89431),x89433),f331(f331(f108(f854(x89432,a840)),x89434),x89435))),f331(f331(f11(x89432,x89431),x89433),f331(f331(f109(f854(x89432,a840)),x89434),x89435))),f331(f331(f88(x89431),f331(f331(f11(x89432,x89431),x89433),x89434)),f331(f331(f11(x89432,x89431),x89433),x89435)))
% 51.10/50.83 [9075]~P4(x90751)+~P1(f331(f68(x90752),x90755))+~P1(f331(f68(x90752),x90754))+E(f331(f331(f3(x90751),f331(f331(f87(x90751),f331(f331(f8(x90752,x90751),x90753),x90754)),f331(f331(f8(x90752,x90751),x90753),x90755))),f331(f331(f8(x90752,x90751),x90753),f331(f331(f109(f854(x90752,a840)),x90754),x90755))),f331(f331(f8(x90752,x90751),x90753),f331(f331(f108(f854(x90752,a840)),x90754),x90755)))
% 51.10/50.83 [9257]~P27(x92571,x92572,x92573,x92575)+~P27(x92571,x92572,x92573,x92574)+P27(x92571,x92572,x92573,f331(f331(f108(f854(x92571,a840)),x92574),x92575))+~E(f331(f331(f109(f854(x92572,a840)),f331(f311(x92571,x92572,x92573),f331(f331(f3(f854(x92571,a840)),x92574),x92575))),f331(f311(x92571,x92572,x92573),f331(f331(f3(f854(x92571,a840)),x92575),x92574))),f184(f854(x92572,a840)))
% 51.10/50.83 [9364]E(x93641,f2(a1))+~P1(f331(f331(f241(a1),f2(a1)),x93643))+~P1(f331(f61(x93642,x93641),f331(f331(f249(a1,a1),x93644),x93645)))+P1(f331(f61(x93642,f331(f331(f88(a1),x93641),x93643)),f331(f331(f249(a1,a1),f331(f331(f48(a1),x93644),x93643)),f331(f331(f87(a1),f331(f331(f88(a1),x93641),f57(a1,x93644,x93643))),x93645))))
% 51.10/50.83 [9373]~P1(f331(f331(f241(a847),f2(a847)),x93733))+~P1(f331(f331(f241(a847),f2(a847)),x93732))+~P1(f331(f60(x93731,x93732),f331(f331(f249(a847,a847),x93734),x93735)))+P1(f331(f60(x93731,f331(f331(f88(a847),x93732),x93733)),f331(f331(f249(a847,a847),f331(f331(f48(a847),x93734),x93733)),f331(f331(f87(a847),f331(f331(f88(a847),x93732),f57(a847,x93734,x93733))),x93735))))
% 51.10/50.83 [9426]E(f331(f331(f87(a1),f484(x94261,x94262,x94263,x94264,x94265)),f479(x94261,x94262,x94263,x94264,x94265)),x94265)+~P1(f331(f331(f287(a1),x94264),x94263))+~P1(f331(f331(f287(a1),x94264),f331(f331(f87(a1),x94265),x94261)))+P1(f331(f331(f287(a1),x94264),f331(f331(f87(a1),f331(f331(f3(a1),x94265),x94263)),x94261)))
% 51.10/50.83 [9427]E(f331(f331(f3(a1),f495(x94271,x94272,x94273,x94274,x94275)),f489(x94271,x94272,x94273,x94274,x94275)),x94275)+~P1(f331(f331(f287(a1),x94274),x94273))+~P1(f331(f331(f287(a1),x94274),f331(f331(f87(a1),x94275),x94271)))+P1(f331(f331(f287(a1),x94274),f331(f331(f87(a1),f331(f331(f87(a1),x94275),x94273)),x94271)))
% 51.10/50.83 [9428]~P70(x94281)+~P1(f331(f68(x94282),x94285))+~P1(f331(f68(x94282),x94284))+E(f331(f331(f88(x94281),f331(f331(f331(f72(x94281,x94282,f88(x94281)),x94283),f85(x94281)),f331(f331(f108(f854(x94282,a840)),x94284),x94285))),f331(f331(f331(f72(x94281,x94282,f88(x94281)),x94283),f85(x94281)),f331(f331(f109(f854(x94282,a840)),x94284),x94285))),f331(f331(f88(x94281),f331(f331(f331(f72(x94281,x94282,f88(x94281)),x94283),f85(x94281)),x94284)),f331(f331(f331(f72(x94281,x94282,f88(x94281)),x94283),f85(x94281)),x94285)))
% 51.10/50.83 [9430]~E(f331(f331(f164(x94301),x94305),x94302),f331(f331(f164(x94301),x94305),x94303))+P1(f331(f331(f333(f853(f848(x94301),f848(x94301))),f331(f331(f249(f848(x94301),f848(x94301)),x94302),x94303)),f142(x94301,x94304)))+~P1(f331(f331(f241(a847),x94305),f331(f331(f244(a847),f331(f185(f848(x94301)),x94302)),f331(f185(f848(x94301)),x94303))))+~P1(f331(f331(f333(f853(x94301,x94301)),f331(f331(f249(x94301,x94301),f331(f331(f155(x94301),x94302),x94305)),f331(f331(f155(x94301),x94303),x94305))),x94304))
% 51.10/50.83 [9439]E(f331(f331(f87(a1),f490(x94391,x94392,x94393,x94394,x94395)),f491(x94391,x94392,x94393,x94394,x94395)),x94395)+~P1(f331(f331(f287(a1),x94394),x94393))+P1(f331(f331(f287(a1),x94394),f331(f331(f87(a1),x94395),x94391)))+~P1(f331(f331(f287(a1),x94394),f331(f331(f87(a1),f331(f331(f3(a1),x94395),x94393)),x94391)))
% 51.10/50.83 [9440]E(f331(f331(f3(a1),f492(x94401,x94402,x94403,x94404,x94405)),f493(x94401,x94402,x94403,x94404,x94405)),x94405)+~P1(f331(f331(f287(a1),x94404),x94403))+P1(f331(f331(f287(a1),x94404),f331(f331(f87(a1),x94405),x94401)))+~P1(f331(f331(f287(a1),x94404),f331(f331(f87(a1),f331(f331(f87(a1),x94405),x94403)),x94401)))
% 51.10/50.83 [9523]~P1(f331(f331(f287(a1),x95234),x95233))+P1(f331(f331(f333(a1),f484(x95231,x95232,x95233,x95234,x95235)),x95232))+~P1(f331(f331(f287(a1),x95234),f331(f331(f87(a1),x95235),x95231)))+P1(f331(f331(f287(a1),x95234),f331(f331(f87(a1),f331(f331(f3(a1),x95235),x95233)),x95231)))
% 51.10/50.83 [9524]~P1(f331(f331(f287(a1),x95244),x95243))+P1(f331(f331(f333(a1),f495(x95241,x95242,x95243,x95244,x95245)),x95242))+~P1(f331(f331(f287(a1),x95244),f331(f331(f87(a1),x95245),x95241)))+P1(f331(f331(f287(a1),x95244),f331(f331(f87(a1),f331(f331(f87(a1),x95245),x95243)),x95241)))
% 51.10/50.83 [9532]~P1(f331(f331(f287(a1),x95324),x95323))+P1(f331(f331(f333(a1),f479(x95321,x95322,x95323,x95324,x95325)),f303(a1,f85(a1),x95323)))+~P1(f331(f331(f287(a1),x95324),f331(f331(f87(a1),x95325),x95321)))+P1(f331(f331(f287(a1),x95324),f331(f331(f87(a1),f331(f331(f3(a1),x95325),x95323)),x95321)))
% 51.10/50.83 [9533]~P1(f331(f331(f287(a1),x95334),x95333))+P1(f331(f331(f333(a1),f489(x95331,x95332,x95333,x95334,x95335)),f303(a1,f85(a1),x95333)))+~P1(f331(f331(f287(a1),x95334),f331(f331(f87(a1),x95335),x95331)))+P1(f331(f331(f287(a1),x95334),f331(f331(f87(a1),f331(f331(f87(a1),x95335),x95333)),x95331)))
% 51.10/50.83 [9534]~P84(x95345)+~P77(x95345)+P1(f331(f331(f333(x95341),f496(x95342,x95343,x95344,x95341,x95345)),x95344))+P1(f331(f331(f240(x95345),f331(f331(f8(x95341,x95345),x95343),x95344)),f331(f331(f88(x95345),f331(f107(x95345),f331(f47(x95341),x95344))),x95342)))
% 51.10/50.83 [9535]~P1(f331(f331(f287(a1),x95354),x95353))+P1(f331(f331(f333(a1),f492(x95351,x95352,x95353,x95354,x95355)),x95352))+P1(f331(f331(f287(a1),x95354),f331(f331(f87(a1),x95355),x95351)))+~P1(f331(f331(f287(a1),x95354),f331(f331(f87(a1),f331(f331(f87(a1),x95355),x95353)),x95351)))
% 51.10/50.83 [9536]~P1(f331(f331(f287(a1),x95364),x95363))+P1(f331(f331(f333(a1),f490(x95361,x95362,x95363,x95364,x95365)),x95362))+P1(f331(f331(f287(a1),x95364),f331(f331(f87(a1),x95365),x95361)))+~P1(f331(f331(f287(a1),x95364),f331(f331(f87(a1),f331(f331(f3(a1),x95365),x95363)),x95361)))
% 51.10/50.83 [9537]~P1(f331(f331(f287(a1),x95371),x95375))+P1(f331(f331(f333(a1),f493(x95373,x95374,x95375,x95371,x95372)),f303(a1,f85(a1),x95375)))+P1(f331(f331(f287(a1),x95371),f331(f331(f87(a1),x95372),x95373)))+~P1(f331(f331(f287(a1),x95371),f331(f331(f87(a1),f331(f331(f87(a1),x95372),x95375)),x95373)))
% 51.10/50.83 [9538]~P1(f331(f331(f287(a1),x95381),x95385))+P1(f331(f331(f333(a1),f491(x95383,x95384,x95385,x95381,x95382)),f303(a1,f85(a1),x95385)))+P1(f331(f331(f287(a1),x95381),f331(f331(f87(a1),x95382),x95383)))+~P1(f331(f331(f287(a1),x95381),f331(f331(f87(a1),f331(f331(f3(a1),x95382),x95385)),x95383)))
% 51.10/50.83 [9708]~P84(x97081)+~P77(x97081)+~P1(f331(f331(f240(x97081),f331(x97083,f496(x97085,x97083,x97084,x97082,x97081))),x97085))+P1(f331(f331(f240(x97081),f331(f331(f8(x97082,x97081),x97083),x97084)),f331(f331(f88(x97081),f331(f107(x97081),f331(f47(x97082),x97084))),x97085)))
% 51.10/50.83 [8582]E(f331(f331(f130(x85821),x85822),x85823),f331(f331(f130(x85821),x85824),x85825))+~E(f331(f331(f164(x85821),f331(f185(f848(x85821)),x85822)),x85824),x85822)+~E(f331(f331(f130(x85821),f331(f331(f133(x85821),f331(f185(f848(x85821)),x85822)),x85824)),x85825),x85823)+P1(f331(f331(f240(a847),f331(f185(f848(x85821)),x85824)),f331(f185(f848(x85821)),x85822)))
% 51.10/50.83 [8695]E(f331(f331(f130(x86951),x86952),x86953),f331(f331(f130(x86951),x86954),x86955))+~E(f331(f331(f164(x86951),f331(f185(f848(x86951)),x86952)),x86954),x86952)+~E(x86953,f331(f331(f130(x86951),f331(f331(f133(x86951),f331(f185(f848(x86951)),x86952)),x86954)),x86955))+~P1(f331(f331(f240(a847),f331(f185(f848(x86951)),x86952)),f331(f185(f848(x86951)),x86954)))
% 51.10/50.83 [9864]~P1(f331(x98645,x98644))+~P1(f331(f68(x98642),f331(f264(x98642),x98645)))+P1(f331(f68(x98641),f331(f264(x98641),f331(f331(f9(x98641,x98642,a840),x98643),x98644))))+~P1(f331(f68(x98641),f331(f264(x98641),f331(f331(f10(f854(x98642,a840),a840,x98641),f94(x98642)),f331(f331(f10(f854(x98642,a840),f854(x98642,a840),x98641),f331(f20(x98642,a840,a840),f331(f331(f10(a840,f854(a840,a840),x98642),a329),x98645))),x98643)))))
% 51.10/50.83 [7877]~P37(x78772,x78773,x78774,x78776)+~P37(f37(x78771,x78772),x78776,x78774,x78775)+P37(f37(x78771,x78772),x78773,x78774,x78775)+~P1(f331(x78771,x78773))
% 51.10/50.83 [7878]~P37(x78782,x78783,x78784,x78786)+~P37(f37(x78781,x78782),x78786,x78784,x78785)+P37(f37(x78781,x78782),x78783,x78784,x78785)+~P1(f331(x78781,x78783))
% 51.10/50.83 [8391]~P21(x83915,x83911,x83916,x83912)+E(f331(f80(x83911,x83911,x83911,f331(x83912,x83913)),f331(x83912,x83914)),f331(f80(x83911,x83911,x83911,f331(x83912,x83914)),f331(x83912,x83913)))+~P1(f331(f68(x83915),x83914))+~P1(f331(f68(x83915),x83913))
% 51.10/50.83 [7788]~P27(x77881,x77882,x77884,x77883)+~E(f331(x77884,x77886),x77885)+E(f331(f84(x77881,x77882,x77883,x77884),x77885),x77886)+~P1(f331(f331(f333(x77881),x77886),x77883))
% 51.10/50.83 [7981]~P22(x79816,x79811,x79814,x79812)+E(f331(f80(x79811,x79811,x79811,f331(x79812,x79813)),f331(x79814,x79815)),f331(x79812,x79813))+~P1(f331(f68(x79816),x79813))+~P1(f331(f331(f333(x79816),x79815),x79813))
% 51.10/50.83 [9112]~P21(x91123,x91121,x91126,x91122)+E(f331(f80(x91121,x91121,x91121,f331(x91122,f331(f331(f3(f854(x91123,a840)),x91124),f331(f331(f310(x91123),x91125),f184(f854(x91123,a840)))))),f331(x91126,x91125)),f331(x91122,x91124))+~P1(f331(f68(x91123),x91124))+~P1(f331(f331(f333(x91123),x91125),x91124))
% 51.10/50.83 [6846]~P5(x68461)+~E(f57(x68461,x68463,x68464),f57(x68461,x68466,x68464))+~E(f57(x68461,x68462,x68464),f57(x68461,x68465,x68464))+E(f57(x68461,f331(f331(f87(x68461),x68462),x68463),x68464),f57(x68461,f331(f331(f87(x68461),x68465),x68466),x68464))
% 51.10/50.83 [6847]~P5(x68471)+~E(f57(x68471,x68473,x68474),f57(x68471,x68476,x68474))+~E(f57(x68471,x68472,x68474),f57(x68471,x68475,x68474))+E(f57(x68471,f331(f331(f88(x68471),x68472),x68473),x68474),f57(x68471,f331(f331(f88(x68471),x68475),x68476),x68474))
% 51.10/50.83 [6848]~P6(x68481)+~E(f57(x68481,x68483,x68484),f57(x68481,x68486,x68484))+~E(f57(x68481,x68482,x68484),f57(x68481,x68485,x68484))+E(f57(x68481,f331(f331(f3(x68481),x68482),x68483),x68484),f57(x68481,f331(f331(f3(x68481),x68485),x68486),x68484))
% 51.10/50.83 [7679]~P18(x76791,x76792,x76793)+~P1(f331(f68(x76791),x76796))+E(f331(f331(f71(x76791,x76792,x76793),x76794),f331(f331(f310(x76791),x76795),x76796)),f331(f331(f71(x76791,x76792,x76793),f331(f331(x76793,x76795),x76794)),x76796))+P1(f331(f331(f333(x76791),x76795),x76796))
% 51.10/50.83 [7746]~P7(x77461)+P1(f331(f331(f240(x77461),x77462),f331(x77463,x77464)))+~P1(f331(f331(f333(x77465),x77464),x77466))+~P1(f331(f331(f240(x77461),x77462),f331(f331(f52(x77465,x77461),x77466),x77463)))
% 51.10/50.83 [7906]~P18(x79061,x79062,x79063)+~P1(f331(f68(x79061),x79066))+E(f331(f331(f71(x79061,x79062,x79063),x79064),f331(f331(f310(x79061),x79065),x79066)),f331(f331(x79063,x79065),f331(f331(f71(x79061,x79062,x79063),x79064),x79066)))+P1(f331(f331(f333(x79061),x79065),x79066))
% 51.10/50.83 [7997]~P102(x79973)+~P1(f331(x79972,x79975))+~P16(x79973,f331(f331(f147(x79971,x79973),x79974),x79976))+E(f331(f131(x79971,x79972),f331(f331(f143(x79971,x79973,x79974),x79975),x79976)),f331(f331(f143(x79971,x79973,x79974),x79975),f331(f131(x79971,x79972),x79976)))
% 51.10/50.83 [8020]E(x80201,x80202)+E(x80203,f2(a1))+~P1(f331(f61(x80204,x80203),f331(f331(f249(a1,a1),x80205),x80202)))+~P1(f331(f61(x80204,x80203),f331(f331(f249(a1,a1),x80206),x80201)))
% 51.10/50.83 [8021]E(x80211,x80212)+E(x80213,f2(a1))+~P1(f331(f61(x80214,x80213),f331(f331(f249(a1,a1),x80212),x80215)))+~P1(f331(f61(x80214,x80213),f331(f331(f249(a1,a1),x80211),x80216)))
% 51.10/50.83 [8043]~P21(x80432,x80435,x80436,x80431)+~P1(f331(f68(x80432),x80434))+E(f331(x80431,f331(f331(f310(x80432),x80433),x80434)),f331(f80(x80435,x80435,x80435,f331(x80431,x80434)),f331(x80436,x80433)))+P1(f331(f331(f333(x80432),x80433),x80434))
% 51.10/50.83 [8259]~P22(x82595,x82591,x82596,x82592)+E(f331(f80(x82591,x82591,x82591,f331(x82592,x82593)),f331(x82592,x82594)),f331(x82592,x82593))+~P1(f331(f68(x82595),x82593))+~P1(f331(f331(f240(f854(x82595,a840)),x82594),x82593))
% 51.10/50.83 [9303]~P27(x93031,x93032,x93034,x93033)+~P1(f331(f331(f333(x93032),x93035),f331(f311(x93031,x93032,x93034),x93033)))+P1(f331(f331(f333(x93031),f331(f84(x93031,x93032,x93033,x93034),x93035)),x93036))+~P1(f331(f331(f240(f854(x93031,a840)),x93033),x93036))
% 51.10/50.83 [9658]~P68(x96582)+~E(f611(x96581,x96583,x96585,x96586,x96584,x96582),f612(x96581,x96583,x96585,x96586,x96584,x96582))+~P1(f331(f68(x96584),x96586))+E(f331(f331(f8(x96581,x96582),x96583),f331(f311(x96584,x96581,x96585),x96586)),f331(f331(f8(x96584,x96582),f331(f80(x96581,x96582,x96584,x96583),x96585)),x96586))
% 51.10/50.83 [9688]~P68(x96886)+E(f331(x96881,f611(x96882,x96883,x96881,x96884,x96885,x96886)),f331(x96881,f612(x96882,x96883,x96881,x96884,x96885,x96886)))+E(f331(f331(f8(x96882,x96886),x96883),f331(f311(x96885,x96882,x96881),x96884)),f331(f331(f8(x96885,x96886),f331(f80(x96882,x96886,x96885,x96883),x96881)),x96884))+~P1(f331(f68(x96885),x96884))
% 51.10/50.83 [9742]~P68(x97422)+~E(f331(x97423,f331(x97425,f612(x97421,x97423,x97425,x97426,x97424,x97422))),f2(x97422))+~P1(f331(f68(x97424),x97426))+E(f331(f331(f8(x97421,x97422),x97423),f331(f311(x97424,x97421,x97425),x97426)),f331(f331(f8(x97424,x97422),f331(f80(x97421,x97422,x97424,x97423),x97425)),x97426))
% 51.10/50.83 [9805]~P68(x98052)+~P1(f331(f68(x98054),x98056))+E(f331(f331(f8(x98051,x98052),x98053),f331(f311(x98054,x98051,x98055),x98056)),f331(f331(f8(x98054,x98052),f331(f80(x98051,x98052,x98054,x98053),x98055)),x98056))+P1(f331(f331(f333(x98054),f612(x98051,x98053,x98055,x98056,x98054,x98052)),x98056))
% 51.10/50.83 [9806]~P68(x98062)+~P1(f331(f68(x98064),x98066))+E(f331(f331(f8(x98061,x98062),x98063),f331(f311(x98064,x98061,x98065),x98066)),f331(f331(f8(x98064,x98062),f331(f80(x98061,x98062,x98064,x98063),x98065)),x98066))+P1(f331(f331(f333(x98064),f611(x98061,x98063,x98065,x98066,x98064,x98062)),x98066))
% 51.10/50.83 [9929]~P70(x99291)+~P1(f331(f68(x99292),x99296))+E(f331(f331(f331(f72(x99291,x99292,f88(x99291)),f331(f331(f20(x99292,f854(x99293,a840),x99291),f331(f331(f9(x99292,x99291,f854(f854(x99293,a840),x99291)),f331(f331(f10(f854(x99293,x99291),f854(x99291,f854(f854(x99293,a840),x99291)),x99292),f72(x99291,x99293,f88(x99291))),x99294)),f85(x99291))),x99295)),f85(x99291)),x99296),f331(f331(f331(f72(x99291,f853(x99292,x99293),f88(x99291)),f331(f259(x99292,x99293,x99291),x99294)),f85(x99291)),f331(f331(f256(x99292,x99293),x99296),x99295)))+P1(f331(f331(f333(x99292),f544(x99294,x99295,x99293,x99296,x99292,x99291)),x99296))
% 51.10/50.83 [9947]~P70(x99471)+~P1(f331(f68(x99472),x99476))+E(f331(f331(f331(f72(x99471,x99472,f88(x99471)),f331(f331(f20(x99472,f854(x99473,a840),x99471),f331(f331(f9(x99472,x99471,f854(f854(x99473,a840),x99471)),f331(f331(f10(f854(x99473,x99471),f854(x99471,f854(f854(x99473,a840),x99471)),x99472),f72(x99471,x99473,f88(x99471))),x99474)),f85(x99471))),x99475)),f85(x99471)),x99476),f331(f331(f331(f72(x99471,f853(x99472,x99473),f88(x99471)),f331(f259(x99472,x99473,x99471),x99474)),f85(x99471)),f331(f331(f256(x99472,x99473),x99476),x99475)))+~P1(f331(f68(x99473),f331(x99475,f544(x99474,x99475,x99473,x99476,x99472,x99471))))
% 51.10/50.83 [8173]~P22(x81732,x81735,x81736,x81731)+~P1(f331(f68(x81732),x81734))+~P1(f331(f68(x81732),x81733))+E(f331(x81731,f331(f331(f108(f854(x81732,a840)),x81733),x81734)),f331(f80(x81735,x81735,x81735,f331(x81731,x81733)),f331(x81731,x81734)))
% 51.10/50.83 [8393]~P7(x83931)+P1(f331(f331(f240(x83931),f331(x83932,x83933)),x83934))+~P1(f331(f331(f333(x83935),x83933),x83936))+~P1(f331(f331(f240(x83931),f331(f331(f51(x83935,x83931),x83936),x83932)),x83934))
% 51.10/50.83 [8765]~P27(x87652,x87651,x87653,x87656)+E(f331(f331(f3(f854(x87651,a840)),f331(f311(x87652,x87651,x87653),x87654)),f331(f311(x87652,x87651,x87653),x87655)),f331(f311(x87652,x87651,x87653),f331(f331(f3(f854(x87652,a840)),x87654),x87655)))+~P1(f331(f331(f240(f854(x87652,a840)),x87655),x87656))+~P1(f331(f331(f240(f854(x87652,a840)),x87654),x87656))
% 51.10/50.83 [8766]~P27(x87662,x87661,x87663,x87666)+E(f331(f331(f109(f854(x87661,a840)),f331(f311(x87662,x87661,x87663),x87664)),f331(f311(x87662,x87661,x87663),x87665)),f331(f311(x87662,x87661,x87663),f331(f331(f109(f854(x87662,a840)),x87664),x87665)))+~P1(f331(f331(f240(f854(x87662,a840)),x87665),x87666))+~P1(f331(f331(f240(f854(x87662,a840)),x87664),x87666))
% 51.10/50.83 [9005]E(x90051,x90052)+~P51(x90053,x90054,x90055)+~P1(f331(f331(f333(f853(x90053,x90054)),f331(f331(f249(x90053,x90054),x90056),x90052)),x90055))+~P1(f331(f331(f333(f853(x90053,x90054)),f331(f331(f249(x90053,x90054),x90056),x90051)),x90055))
% 51.10/50.83 [9006]E(x90061,x90062)+~P51(x90063,x90064,x90065)+~P1(f331(f331(f333(f853(x90063,x90064)),f331(f331(f249(x90063,x90064),x90066),x90062)),x90065))+~P1(f331(f331(f333(f853(x90063,x90064)),f331(f331(f249(x90063,x90064),x90066),x90061)),x90065))
% 51.10/50.83 [9738]~P64(x97381)+~E(f331(x97383,f628(x97384,x97386,x97383,x97385,x97382,x97381)),f331(x97386,f628(x97384,x97386,x97383,x97385,x97382,x97381)))+~P1(f331(f68(x97382),x97385))+E(f331(f331(f331(f72(x97381,x97382,f88(x97381)),x97383),x97384),x97385),f331(f331(f331(f72(x97381,x97382,f88(x97381)),x97386),x97384),x97385))
% 51.10/50.83 [9800]~P64(x98001)+~P1(f331(f68(x98002),x98005))+E(f331(f331(f331(f72(x98001,x98002,f88(x98001)),x98003),x98004),x98005),f331(f331(f331(f72(x98001,x98002,f88(x98001)),x98006),x98004),x98005))+P1(f331(f331(f333(x98002),f628(x98004,x98003,x98006,x98005,x98002,x98001)),x98005))
% 51.10/50.83 [8595]~P64(x85951)+~P1(f331(f68(x85952),x85956))+P1(f331(f331(f333(x85952),x85955),x85956))+E(f331(f331(f331(f72(x85951,x85952,f88(x85951)),x85953),x85954),f331(f331(f310(x85952),x85955),x85956)),f331(f331(f88(x85951),f331(x85953,x85955)),f331(f331(f331(f72(x85951,x85952,f88(x85951)),x85953),x85954),x85956)))
% 51.10/50.83 [8639]~P10(x86391,x86396,x86393)+~P14(x86391,f854(x86392,a840),x86393,x86395)+~P1(f331(f331(f333(x86391),x86394),x86396))+E(f331(f331(f51(x86391,f854(x86392,a840)),f331(f285(x86391,x86391,x86393),f331(f331(f310(x86391),x86394),f184(f854(x86391,a840))))),x86395),f331(x86395,x86394))
% 51.10/50.83 [8747]~P18(x87473,x87474,x87471)+~P1(f331(f68(x87473),x87476))+~P1(f331(f331(f333(x87473),x87472),x87476))+E(f331(f331(x87471,x87472),f331(f331(f71(x87473,x87474,x87471),x87475),f331(f331(f3(f854(x87473,a840)),x87476),f331(f331(f310(x87473),x87472),f184(f854(x87473,a840)))))),f331(f331(f71(x87473,x87474,x87471),x87475),x87476))
% 51.10/50.83 [9016]~P21(x90163,x90161,x90166,x90162)+~P1(f331(f68(x90163),x90165))+~P1(f331(f68(x90163),x90164))+E(f331(f80(x90161,x90161,x90161,f331(x90162,f331(f331(f108(f854(x90163,a840)),x90164),x90165))),f331(x90162,f331(f331(f109(f854(x90163,a840)),x90164),x90165))),f331(f80(x90161,x90161,x90161,f331(x90162,x90164)),f331(x90162,x90165)))
% 51.10/50.83 [9323]~E(x93233,f331(f331(f152(x93231,x93232),x93235),x93236))+P1(f331(f331(f333(f853(f848(x93231),f848(x93231))),f331(f331(f249(f848(x93231),f848(x93231)),x93232),x93233)),f150(x93231,x93234)))+~P1(f331(f331(f241(a847),x93235),f331(f185(f848(x93231)),x93232)))+~P1(f331(f331(f333(f853(x93231,x93231)),f331(f331(f249(x93231,x93231),f331(f331(f155(x93231),x93232),x93235)),x93236)),x93234))
% 51.10/50.83 [9822]~P70(x98222)+~P1(f331(f68(x98221),x98226))+P1(f331(f331(f333(x98221),f543(x98224,x98225,x98223,x98226,x98221,x98222)),x98226))+E(f331(f331(f11(x98221,x98222),f331(f331(f20(x98221,f854(x98223,a840),x98222),f331(f331(f10(f854(x98223,x98222),f854(f854(x98223,a840),x98222),x98221),f11(x98223,x98222)),x98224)),x98225)),x98226),f331(f331(f11(f853(x98221,x98223),x98222),f331(f259(x98221,x98223,x98222),x98224)),f331(f331(f256(x98221,x98223),x98226),x98225)))
% 51.10/50.83 [9823]~P68(x98232)+~P1(f331(f68(x98231),x98236))+P1(f331(f331(f333(x98231),f545(x98234,x98235,x98233,x98236,x98231,x98232)),x98236))+E(f331(f331(f8(x98231,x98232),f331(f331(f20(x98231,f854(x98233,a840),x98232),f331(f331(f10(f854(x98233,x98232),f854(f854(x98233,a840),x98232),x98231),f8(x98233,x98232)),x98234)),x98235)),x98236),f331(f331(f8(f853(x98231,x98233),x98232),f331(f259(x98231,x98233,x98232),x98234)),f331(f331(f256(x98231,x98233),x98236),x98235)))
% 51.10/50.83 [9862]~P70(x98622)+~P1(f331(f68(x98621),x98626))+~P1(f331(f68(x98623),f331(x98625,f543(x98624,x98625,x98623,x98626,x98621,x98622))))+E(f331(f331(f11(x98621,x98622),f331(f331(f20(x98621,f854(x98623,a840),x98622),f331(f331(f10(f854(x98623,x98622),f854(f854(x98623,a840),x98622),x98621),f11(x98623,x98622)),x98624)),x98625)),x98626),f331(f331(f11(f853(x98621,x98623),x98622),f331(f259(x98621,x98623,x98622),x98624)),f331(f331(f256(x98621,x98623),x98626),x98625)))
% 51.10/50.83 [9863]~P68(x98632)+~P1(f331(f68(x98631),x98636))+~P1(f331(f68(x98633),f331(x98635,f545(x98634,x98635,x98633,x98636,x98631,x98632))))+E(f331(f331(f8(x98631,x98632),f331(f331(f20(x98631,f854(x98633,a840),x98632),f331(f331(f10(f854(x98633,x98632),f854(f854(x98633,a840),x98632),x98631),f8(x98633,x98632)),x98634)),x98635)),x98636),f331(f331(f8(f853(x98631,x98633),x98632),f331(f259(x98631,x98633,x98632),x98634)),f331(f331(f256(x98631,x98633),x98636),x98635)))
% 51.10/50.83 [9845]~P70(x98452)+~P1(f331(f68(x98451),x98456))+P1(f331(f331(f333(x98451),x98453),x98456))+E(f331(f331(f11(x98451,x98452),f331(f331(f9(x98451,x98452,x98452),f331(f331(f20(x98451,x98452,f854(x98452,x98452)),f331(f331(f10(a840,f854(x98452,f854(x98452,x98452)),x98451),f103(x98452)),f331(f331(f9(x98451,x98451,a840),a328),x98453))),x98454)),x98455)),x98456),f331(f331(f250(x98452),x98455),f331(f47(x98451),x98456)))
% 51.10/50.83 [9850]~P70(x98502)+~P1(f331(f68(x98501),x98506))+~P1(f331(f331(f333(x98501),x98503),x98506))+E(f331(f331(f11(x98501,x98502),f331(f331(f9(x98501,x98502,x98502),f331(f331(f20(x98501,x98502,f854(x98502,x98502)),f331(f331(f10(a840,f854(x98502,f854(x98502,x98502)),x98501),f103(x98502)),f331(f331(f9(x98501,x98501,a840),a328),x98503))),x98504)),x98505)),x98506),f331(f331(f88(x98502),f331(x98504,x98503)),f331(f331(f250(x98502),x98505),f331(f331(f3(a847),f331(f47(x98501),x98506)),f85(a847)))))
% 51.10/50.83 [9916]~P1(f331(f68(x99161),x99165))+~P1(f331(f68(x99162),x99163))+P1(f331(f331(f333(x99162),f567(x99166,x99164,x99163,x99162,x99165,x99161)),x99163))+E(f331(f331(f8(x99161,a847),f331(f331(f10(f854(x99162,a840),a847,x99161),f47(x99162)),f331(f331(f10(f854(x99162,a840),f854(x99162,a840),x99161),f264(x99162)),f331(f331(f10(f854(x99162,a840),f854(x99162,a840),x99161),f331(f20(x99162,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99162),a329),f331(f331(f9(x99162,f854(x99162,a840),a840),f333(x99162)),x99163)))),x99164)))),x99165),f331(f331(f88(a847),x99166),f331(f47(x99162),x99163)))
% 51.10/50.83 [9917]~P1(f331(f68(x99171),x99175))+~P1(f331(f68(x99172),x99173))+P1(f331(f331(f333(x99172),f568(x99176,x99174,x99173,x99172,x99175,x99171)),x99173))+E(f331(f331(f8(x99171,a847),f331(f331(f10(f854(x99172,a840),a847,x99171),f47(x99172)),f331(f331(f10(f854(x99172,a840),f854(x99172,a840),x99171),f264(x99172)),f331(f331(f10(f854(x99172,a840),f854(x99172,a840),x99171),f331(f20(x99172,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99172),a329),f331(f331(f9(x99172,f854(x99172,a840),a840),f333(x99172)),x99173)))),x99174)))),x99175),f331(f331(f8(x99172,a847),x99176),x99173))
% 51.10/50.83 [9953]~P1(f331(f68(x99532),x99533))+~P1(f331(f68(x99531),x99535))+~E(f331(f47(x99531),f331(f264(x99531),f331(f331(f20(x99531,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99531),a329),f331(f331(f9(x99531,f854(x99531,a840),a840),f333(x99531)),x99535))),f331(f331(f9(x99531,x99532,a840),x99534),f567(x99536,x99534,x99533,x99532,x99535,x99531))))),x99536)+E(f331(f331(f8(x99531,a847),f331(f331(f10(f854(x99532,a840),a847,x99531),f47(x99532)),f331(f331(f10(f854(x99532,a840),f854(x99532,a840),x99531),f264(x99532)),f331(f331(f10(f854(x99532,a840),f854(x99532,a840),x99531),f331(f20(x99532,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99532),a329),f331(f331(f9(x99532,f854(x99532,a840),a840),f333(x99532)),x99533)))),x99534)))),x99535),f331(f331(f88(a847),x99536),f331(f47(x99532),x99533)))
% 51.10/50.83 [9955]~P1(f331(f68(x99552),x99553))+~P1(f331(f68(x99551),x99555))+~E(f331(f47(x99551),f331(f264(x99551),f331(f331(f20(x99551,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99551),a329),f331(f331(f9(x99551,f854(x99551,a840),a840),f333(x99551)),x99555))),f331(f331(f9(x99551,x99552,a840),x99554),f568(x99556,x99554,x99553,x99552,x99555,x99551))))),f331(x99556,f568(x99556,x99554,x99553,x99552,x99555,x99551)))+E(f331(f331(f8(x99551,a847),f331(f331(f10(f854(x99552,a840),a847,x99551),f47(x99552)),f331(f331(f10(f854(x99552,a840),f854(x99552,a840),x99551),f264(x99552)),f331(f331(f10(f854(x99552,a840),f854(x99552,a840),x99551),f331(f20(x99552,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99552),a329),f331(f331(f9(x99552,f854(x99552,a840),a840),f333(x99552)),x99553)))),x99554)))),x99555),f331(f331(f8(x99552,a847),x99556),x99553))
% 51.10/50.83 [9597]E(x95971,x95972)+~P18(x95973,x95974,x95975)+~P1(f331(f73(x95973,x95974,x95975,x95976,x95977),x95972))+~P1(f331(f73(x95973,x95974,x95975,x95976,x95977),x95971))
% 51.10/50.83 [9397]P1(f331(x93971,x93972))+~P1(f331(f331(f333(x93977),x93972),f331(x93976,x93974)))+~P1(f331(x93971,f403(x93971,x93976,x93975,x93973,x93977)))+~P1(f331(f331(f333(x93973),x93974),x93975))
% 51.10/50.83 [9837]~P18(x98377,x98376,x98371)+E(f331(f331(x98371,x98372),f635(x98372,x98373,x98374,x98375,x98371,x98376,x98377)),x98373)+~P1(f331(f73(x98377,x98376,x98371,x98375,x98374),x98373))+~P1(f331(f331(f333(x98377),x98372),x98374))
% 51.10/50.83 [9901]~P18(x99011,x99012,x99013)+~P1(f331(f73(x99011,x99012,x99013,x99014,x99015),x99017))+P1(f331(f73(x99011,x99012,x99013,x99014,f331(f331(f3(f854(x99011,a840)),x99015),f331(f331(f310(x99011),x99016),f184(f854(x99011,a840))))),f635(x99016,x99017,x99015,x99014,x99013,x99012,x99011)))+~P1(f331(f331(f333(x99011),x99016),x99015))
% 51.10/50.83 [9299]~P64(x92991)+~P27(x92995,x92992,x92996,x92997)+~P1(f331(f68(x92995),x92997))+E(f331(f331(f331(f72(x92991,x92992,f88(x92991)),x92993),x92994),f331(f311(x92995,x92992,x92996),x92997)),f331(f331(f331(f72(x92991,x92995,f88(x92991)),f331(f80(x92992,x92991,x92995,x92993),x92996)),x92994),x92997))
% 51.10/50.83 [9420]~E(f331(f331(f310(x94201),x94205),x94206),f331(f331(f310(x94201),x94202),x94203))+~P1(f331(f73(x94201,x94201,x94204,x94202,x94203),x94207))+P1(f331(f331(f333(x94201),x94202),x94203))+P1(f331(f69(x94201,x94204,f331(f331(f310(x94201),x94205),x94206)),x94207))
% 51.10/50.83 [9502]P1(f331(x95021,x95022))+~P1(f331(f331(f333(x95023),x95022),f331(x95024,x95027)))+~P1(f331(f331(f333(x95026),x95027),x95025))+P1(f331(f331(f333(x95023),f403(x95021,x95024,x95025,x95026,x95023)),f331(f331(f51(x95026,f854(x95023,a840)),x95025),x95024)))
% 51.10/50.83 [9515]~P27(x95152,x95151,x95155,x95154)+~P27(x95151,x95153,x95156,f331(f311(x95152,x95151,x95155),x95154))+E(f331(f331(f80(x95151,x95152,x95153,f84(x95152,x95151,x95154,x95155)),f84(x95151,x95153,f331(f311(x95152,x95151,x95155),x95154),x95156)),x95157),f331(f84(x95152,x95153,x95154,f331(f80(x95151,x95153,x95152,x95156),x95155)),x95157))+~P1(f331(f331(f333(x95153),x95157),f331(f311(x95151,x95153,x95156),f331(f311(x95152,x95151,x95155),x95154))))
% 51.10/50.83 [9838]~P18(x98387,x98386,x98381)+E(f331(f331(x98381,x98382),f675(x98383,x98384,x98382,x98385,x98381,x98386,x98387)),x98383)+P1(f331(f331(f333(x98387),x98382),x98384))+~P1(f331(f73(x98387,x98386,x98381,x98385,f331(f331(f310(x98387),x98382),x98384)),x98383))
% 51.10/50.83 [9900]~P18(x99001,x99004,x99005)+P1(f331(f73(x99001,x99004,x99005,x99006,x99003),f675(x99007,x99003,x99002,x99006,x99005,x99004,x99001)))+P1(f331(f331(f333(x99001),x99002),x99003))+~P1(f331(f73(x99001,x99004,x99005,x99006,f331(f331(f310(x99001),x99002),x99003)),x99007))
% 51.10/50.83 [9580]E(x95801,f2(a1))+~P1(f331(f61(x95803,x95801),f331(f331(f249(a1,a1),x95805),x95807)))+~P1(f331(f61(x95802,x95801),f331(f331(f249(a1,a1),x95804),x95806)))+P1(f331(f61(f331(f331(f87(a1),x95802),x95803),x95801),f331(f331(f249(a1,a1),f331(f331(f87(a1),f331(f331(f87(a1),x95804),x95805)),f331(f331(f48(a1),f331(f331(f87(a1),x95806),x95807)),x95801))),f57(a1,f331(f331(f87(a1),x95806),x95807),x95801))))
% 51.10/50.83 [9582]~P1(f331(f331(f241(a847),f2(a847)),x95823))+~P1(f331(f60(x95822,x95823),f331(f331(f249(a847,a847),x95825),x95827)))+~P1(f331(f60(x95821,x95823),f331(f331(f249(a847,a847),x95824),x95826)))+P1(f331(f60(f331(f331(f87(a847),x95821),x95822),x95823),f331(f331(f249(a847,a847),f331(f331(f87(a847),f331(f331(f87(a847),x95824),x95825)),f331(f331(f48(a847),f331(f331(f87(a847),x95826),x95827)),x95823))),f57(a847,f331(f331(f87(a847),x95826),x95827),x95823))))
% 51.10/50.83 [9952]~P68(x99522)+~P1(f331(f68(x99523),x99525))+~P1(f331(f68(x99521),x99527))+E(f331(f331(f8(x99521,x99522),f331(f331(f20(x99521,f854(x99523,a840),x99522),f331(f331(f10(f854(x99523,x99522),f854(f854(x99523,a840),x99522),x99521),f8(x99523,x99522)),x99524)),f331(f331(f10(f854(x99523,a840),f854(x99523,a840),x99521),f264(x99523)),f331(f331(f10(f854(x99523,a840),f854(x99523,a840),x99521),f331(f20(x99523,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99523),a329),f331(f331(f9(x99523,f854(x99523,a840),a840),f333(x99523)),x99525)))),x99526)))),x99527),f331(f331(f8(x99523,x99522),f331(f331(f20(x99523,f854(x99521,a840),x99522),f331(f331(f10(f854(x99521,x99522),f854(f854(x99521,a840),x99522),x99523),f8(x99521,x99522)),f331(f9(x99521,x99523,x99522),x99524))),f331(f331(f10(f854(x99521,a840),f854(x99521,a840),x99523),f264(x99521)),f331(f331(f10(f854(x99521,a840),f854(x99521,a840),x99523),f331(f20(x99521,a840,a840),f331(f331(f10(a840,f854(a840,a840),x99521),a329),f331(f331(f9(x99521,f854(x99521,a840),a840),f333(x99521)),x99527)))),f331(f9(x99521,x99523,a840),x99526))))),x99525))
% 51.10/50.83 [9460]~P24(x94607,x94606,x94601,x94608,x94602,x94604)+E(f331(f331(x94601,f331(x94602,x94603)),f331(x94604,x94605)),f331(x94604,x94605))+~P1(f331(f68(x94606),x94605))+~P1(f331(f331(f333(x94606),x94603),x94605))
% 51.10/50.83 [9464]~P15(x94646,x94641,x94642,x94648,x94643,x94644)+~P10(x94646,x94647,x94648)+P14(x94641,x94642,x94643,f331(x94644,x94645))+~P1(f331(f331(f333(x94646),x94645),x94647))
% 51.10/50.83 [7706]~P37(x77064,x77065,x77066,x77063)+~P29(x77068,x77066,f331(f331(f331(f98(x77068),x77067),x77064),x77061))+P1(f331(f331(x77061,x77062),x77063))+~P1(f331(f331(x77067,x77062),x77065))
% 51.10/50.83 [9101]~P21(x91017,x91011,x91018,x91013)+~P1(f331(f68(x91017),x91015))+~P1(f331(f68(x91017),x91014))+E(f331(f80(x91011,x91011,x91012,f331(x91013,x91014)),f331(f80(x91011,x91011,x91012,f331(x91013,x91015)),x91016)),f331(f80(x91011,x91011,x91012,f331(x91013,x91015)),f331(f80(x91011,x91011,x91012,f331(x91013,x91014)),x91016)))
% 51.10/50.83 [9169]~P27(x91692,x91692,x91695,x91696)+~P23(x91693,x91692,x91697,x91698,x91691)+~P1(f331(f68(x91692),x91696))+E(f331(f331(x91691,f331(f80(x91692,x91693,x91692,x91694),x91695)),x91696),f331(f331(x91691,x91694),f331(f311(x91692,x91692,x91695),x91696)))
% 51.10/50.83 [9462]~P25(x94627,x94622,x94625,x94628,x94626,x94621)+~P1(f331(f68(x94622),x94624))+E(f331(x94621,f331(f331(f310(x94622),x94623),x94624)),f331(f331(x94625,f331(x94626,x94623)),f331(x94621,x94624)))+P1(f331(f331(f333(x94622),x94623),x94624))
% 51.10/50.83 [9469]~P24(x94696,x94695,x94691,x94697,x94698,x94692)+E(f331(f331(x94691,f331(x94692,x94693)),f331(x94692,x94694)),f331(x94692,x94694))+~P1(f331(f68(x94695),x94694))+~P1(f331(f331(f240(f854(x94695,a840)),x94693),x94694))
% 51.10/50.83 [9088]P1(f331(f331(f333(f853(f848(x90881),f848(x90881))),f331(f331(f249(f848(x90881),f848(x90881)),x90882),x90883)),f150(x90881,x90884)))+~E(x90883,f331(f331(f130(x90881),x90885),f331(f331(f145(x90881),x90886),x90887)))+~E(x90882,f331(f331(f130(x90881),x90885),f331(f331(f145(x90881),x90888),x90887)))+~P1(f331(f331(f333(f853(x90881,x90881)),f331(f331(f249(x90881,x90881),x90888),x90886)),x90884))
% 51.10/50.83 [9465]~P24(x94656,x94652,x94655,x94657,x94658,x94651)+~P1(f331(f68(x94652),x94654))+~P1(f331(f68(x94652),x94653))+E(f331(x94651,f331(f331(f108(f854(x94652,a840)),x94653),x94654)),f331(f331(x94655,f331(x94651,x94653)),f331(x94651,x94654)))
% 51.10/50.83 [9992]~P27(x99924,x99922,x99925,x99928)+E(f331(f331(f52(x99921,f854(x99922,a840)),x99923),f331(f331(f10(f854(x99924,a840),f854(x99922,a840),x99921),f311(x99924,x99922,x99925)),x99926)),f331(f311(x99924,x99922,x99925),f331(f331(f52(x99921,f854(x99924,a840)),x99923),x99926)))+~P1(f331(f331(f333(x99921),x99927),x99923))+P1(f331(f331(f333(x99921),f645(x99927,x99926,x99923,x99921,x99928,x99925,x99922,x99924)),x99923))
% 51.10/50.83 [10012]~P27(x100124,x100122,x100125,x100127)+E(f331(f331(f52(x100121,f854(x100122,a840)),x100123),f331(f331(f10(f854(x100124,a840),f854(x100122,a840),x100121),f311(x100124,x100122,x100125)),x100126)),f331(f311(x100124,x100122,x100125),f331(f331(f52(x100121,f854(x100124,a840)),x100123),x100126)))+~P1(f331(f331(f333(x100121),x100128),x100123))+~P1(f331(f331(f240(f854(x100124,a840)),f331(x100126,f645(x100128,x100126,x100123,x100121,x100127,x100125,x100122,x100124))),x100127))
% 51.10/50.83 [9520]~P25(x95207,x95205,x95201,x95208,x95202,x95204)+~P1(f331(f68(x95205),x95206))+~P1(f331(f331(f333(x95205),x95203),x95206))+E(f331(f331(x95201,f331(x95202,x95203)),f331(x95204,f331(f331(f3(f854(x95205,a840)),x95206),f331(f331(f310(x95205),x95203),f184(f854(x95205,a840)))))),f331(x95204,x95206))
% 51.10/50.83 [9530]~P25(x95306,x95303,x95301,x95307,x95308,x95302)+~P1(f331(f68(x95303),x95305))+~P1(f331(f68(x95303),x95304))+E(f331(f331(x95301,f331(x95302,f331(f331(f108(f854(x95303,a840)),x95304),x95305))),f331(x95302,f331(f331(f109(f854(x95303,a840)),x95304),x95305))),f331(f331(x95301,f331(x95302,x95304)),f331(x95302,x95305)))
% 51.10/50.83 [9617]P39(x96171,x96172,x96173,x96174,x96175,f331(f331(x96173,x96176),x96177))+~P39(x96171,x96172,x96173,x96174,f331(f331(f3(f854(x96171,a840)),x96175),f331(f331(f310(x96171),x96178),f184(f854(x96171,a840)))),x96179)+~E(f331(f331(x96173,x96176),x96177),f331(f331(x96173,x96178),x96179))+~P1(f331(f331(f333(x96171),x96178),x96175))
% 51.10/50.83 [10024]P26(x100241,x100242,f331(f331(f310(f846(x100241)),f331(f331(f331(f98(x100241),f331(x100243,f367(x100244,x100245,x100246,x100247,x100243,x100242,x100241,x100248,x100249))),f331(x100247,f367(x100244,x100245,x100246,x100247,x100243,x100242,x100241,x100248,x100249))),f331(x100246,f367(x100244,x100245,x100246,x100247,x100243,x100242,x100241,x100248,x100249)))),f184(f854(f846(x100241),a840))))+~P1(f331(f68(x100249),x100248))+~P26(x100241,x100242,f331(f311(x100249,f846(x100241),f331(f331(f20(x100249,f854(x100241,f854(a845,a840)),f846(x100241)),f331(f331(f20(x100249,a841,f854(f854(x100241,f854(a845,a840)),f846(x100241))),f331(f331(f10(f854(x100241,f854(a845,a840)),f854(a841,f854(f854(x100241,f854(a845,a840)),f846(x100241))),x100249),f98(x100241)),x100243)),x100247)),x100246)),x100248))+P26(x100241,x100242,f331(f311(x100249,f846(x100241),f331(f331(f20(x100249,f854(x100241,f854(a845,a840)),f846(x100241)),f331(f331(f20(x100249,a841,f854(f854(x100241,f854(a845,a840)),f846(x100241))),f331(f331(f10(f854(x100241,f854(a845,a840)),f854(a841,f854(f854(x100241,f854(a845,a840)),f846(x100241))),x100249),f98(x100241)),x100245)),x100247)),x100244)),x100248))
% 51.10/50.83 [10025]~P26(x100251,x100252,f331(f331(f310(f846(x100251)),f331(f331(f331(f98(x100251),f331(x100254,f367(x100256,x100254,x100258,x100255,x100259,x100252,x100251,x100257,x100253))),f331(x100255,f367(x100256,x100254,x100258,x100255,x100259,x100252,x100251,x100257,x100253))),f331(x100256,f367(x100256,x100254,x100258,x100255,x100259,x100252,x100251,x100257,x100253)))),f184(f854(f846(x100251),a840))))+~P1(f331(f68(x100253),x100257))+~P26(x100251,x100252,f331(f311(x100253,f846(x100251),f331(f331(f20(x100253,f854(x100251,f854(a845,a840)),f846(x100251)),f331(f331(f20(x100253,a841,f854(f854(x100251,f854(a845,a840)),f846(x100251))),f331(f331(f10(f854(x100251,f854(a845,a840)),f854(a841,f854(f854(x100251,f854(a845,a840)),f846(x100251))),x100253),f98(x100251)),x100259)),x100255)),x100258)),x100257))+P26(x100251,x100252,f331(f311(x100253,f846(x100251),f331(f331(f20(x100253,f854(x100251,f854(a845,a840)),f846(x100251)),f331(f331(f20(x100253,a841,f854(f854(x100251,f854(a845,a840)),f846(x100251))),f331(f331(f10(f854(x100251,f854(a845,a840)),f854(a841,f854(f854(x100251,f854(a845,a840)),f846(x100251))),x100253),f98(x100251)),x100254)),x100255)),x100256)),x100257))
% 51.10/50.83 [9555]~P15(x95556,x95557,x95558,x95559,x955510,x95551)+E(f331(f331(x95551,x95552),x95553),f331(f331(x95551,x95554),x95555))+~P1(f331(f331(f333(f853(x95557,x95557)),f331(f331(f249(x95557,x95557),x95553),x95555)),x955510))+~P1(f331(f331(f333(f853(x95556,x95556)),f331(f331(f249(x95556,x95556),x95552),x95554)),x95559))
% 51.10/50.83 [6775]E(x67751,x67752)+~P1(f331(f331(f240(a1),f2(a1)),x67752))+~P1(f331(f331(f240(a1),f2(a1)),x67751))+~P1(f331(f331(f287(a1),x67752),x67751))+~P1(f331(f331(f287(a1),x67751),x67752))
% 51.10/50.83 [9322]E(x93221,f2(a1))+E(x93222,f2(a1))+E(f331(f331(f93(a1,f853(a1,a1)),f331(f331(a219,x93222),x93221)),f331(f331(f20(a1,a1,f853(a1,a1)),f331(f331(f10(a1,f854(a1,f853(a1,a1)),a1),f249(a1,a1)),f331(f48(a1),x93222))),f331(f48(a1),x93221))),f217(x93222,x93221))+P1(f331(f331(f241(a1),x93221),f2(a1)))+~P1(f331(f320(f853(a1,a1),a223),f331(f331(f249(a1,a1),x93222),x93221)))
% 51.10/50.83 [9171]~P97(x91712)+E(x91711,f184(f854(x91712,a840)))+~P1(f331(f68(x91712),x91711))+P1(f331(f331(f333(x91712),f12(x91712,x91711)),x91711))+~P1(f331(f331(f333(x91712),f331(f331(f109(x91712),f376(x91711,x91712)),f379(x91711,x91712))),f331(f331(f310(x91712),f376(x91711,x91712)),f331(f331(f310(x91712),f379(x91711,x91712)),f184(f854(x91712,a840))))))
% 51.10/50.83 [9172]~P97(x91722)+E(x91721,f184(f854(x91722,a840)))+~P1(f331(f68(x91722),x91721))+P1(f331(f331(f333(x91722),f15(x91722,x91721)),x91721))+~P1(f331(f331(f333(x91722),f331(f331(f108(x91722),f380(x91721,x91722)),f381(x91721,x91722))),f331(f331(f310(x91722),f380(x91721,x91722)),f331(f331(f310(x91722),f381(x91721,x91722)),f184(f854(x91722,a840))))))
% 51.10/50.83 [9173]~P102(x91732)+E(x91731,f184(f854(x91732,a840)))+~P1(f331(f68(x91732),x91731))+P1(f331(f331(f333(x91732),f16(x91732,x91731)),x91731))+~P1(f331(f331(f333(x91732),f331(f331(f239(x91732),f377(x91731,x91732)),f378(x91731,x91732))),f331(f331(f310(x91732),f377(x91731,x91732)),f331(f331(f310(x91732),f378(x91731,x91732)),f184(f854(x91732,a840))))))
% 51.10/50.83 [9174]~P102(x91742)+E(x91741,f184(f854(x91742,a840)))+~P1(f331(f68(x91742),x91741))+P1(f331(f331(f333(x91742),f17(x91742,x91741)),x91741))+~P1(f331(f331(f333(x91742),f331(f331(f244(x91742),f382(x91741,x91742)),f383(x91741,x91742))),f331(f331(f310(x91742),f382(x91741,x91742)),f331(f331(f310(x91742),f383(x91741,x91742)),f184(f854(x91742,a840))))))
% 51.10/50.83 [9202]~P64(x92022)+E(x92021,f184(f854(x92022,a840)))+~P1(f331(f68(x92022),x92021))+P1(f331(f331(f333(x92022),f331(f70(x92022,f88(x92022)),x92021)),x92021))+~P1(f331(f331(f333(x92022),f331(f331(f88(x92022),f546(x92021,x92022)),f547(x92021,x92022))),f331(f331(f310(x92022),f546(x92021,x92022)),f331(f331(f310(x92022),f547(x92021,x92022)),f184(f854(x92022,a840))))))
% 51.10/50.83 [9208]~P102(x92082)+E(x92081,f184(f854(x92082,a840)))+~P1(f331(f68(x92082),x92081))+P1(f331(f331(f333(x92082),f13(x92082,f239(x92082),x92081)),x92081))+~P1(f331(f331(f333(x92082),f331(f331(f239(x92082),f384(x92081,x92082)),f388(x92081,x92082))),f331(f331(f310(x92082),f384(x92081,x92082)),f331(f331(f310(x92082),f388(x92081,x92082)),f184(f854(x92082,a840))))))
% 51.10/50.83 [9209]~P102(x92092)+E(x92091,f184(f854(x92092,a840)))+~P1(f331(f68(x92092),x92091))+P1(f331(f331(f333(x92092),f14(x92092,f244(x92092),x92091)),x92091))+~P1(f331(f331(f333(x92092),f331(f331(f244(x92092),f389(x92091,x92092)),f390(x92091,x92092))),f331(f331(f310(x92092),f389(x92091,x92092)),f331(f331(f310(x92092),f390(x92091,x92092)),f184(f854(x92092,a840))))))
% 51.10/50.83 [6390]~P80(x63902)+E(x63901,f2(x63902))+~E(f331(f331(f87(x63902),x63903),x63901),f2(x63902))+~P1(f331(f331(f240(x63902),f2(x63902)),x63903))+~P1(f331(f331(f240(x63902),f2(x63902)),x63901))
% 51.10/50.83 [6391]~P80(x63912)+E(x63911,f2(x63912))+~E(f331(f331(f87(x63912),x63911),x63913),f2(x63912))+~P1(f331(f331(f240(x63912),f2(x63912)),x63913))+~P1(f331(f331(f240(x63912),f2(x63912)),x63911))
% 51.10/50.83 [6592]~P1(f331(f331(f287(a847),x65922),x65921))+~P1(f331(f331(f287(a847),x65921),x65923))+P1(f331(f331(f287(a847),x65922),x65923))+P1(f331(f331(f287(a847),x65921),x65922))+P1(f331(f331(f287(a847),x65923),x65921))
% 51.10/50.83 [6774]~P1(f331(f331(f287(a847),x67741),x67743))+~P1(f331(f331(f287(a847),x67743),x67742))+~P1(f331(f331(f287(a847),x67742),x67741))+P1(f331(f331(f287(a847),x67741),x67742))+P1(f331(f331(f287(a847),x67743),x67741))
% 51.10/50.83 [7108]~P102(x71081)+E(f17(x71081,x71082),x71083)+~P1(f331(f68(x71081),x71082))+~P1(f331(f331(f240(x71081),x71083),f623(x71083,x71082,x71081)))+~P1(f331(f331(f333(x71081),x71083),x71082))
% 51.10/50.83 [7143]~P102(x71431)+~P16(x71431,x71432)+~P16(x71431,x71433)+P16(x71431,f331(f331(f130(x71431),x71432),x71433))+P1(f331(f331(f333(x71431),f764(x71433,x71432,x71431)),f331(f163(x71431),x71432)))
% 51.10/50.83 [7144]~P102(x71441)+~P16(x71441,x71442)+~P16(x71441,x71443)+P16(x71441,f331(f331(f130(x71441),x71442),x71443))+P1(f331(f331(f333(x71441),f765(x71443,x71442,x71441)),f331(f163(x71441),x71443)))
% 51.10/50.83 [7208]~P102(x72081)+E(f16(x72081,x72082),x72083)+~P1(f331(f68(x72081),x72082))+P1(f331(f331(f333(x72081),f624(x72083,x72082,x72081)),x72082))+~P1(f331(f331(f333(x72081),x72083),x72082))
% 51.10/50.83 [7209]~P102(x72091)+E(f17(x72091,x72092),x72093)+~P1(f331(f68(x72091),x72092))+P1(f331(f331(f333(x72091),f623(x72093,x72092,x72091)),x72092))+~P1(f331(f331(f333(x72091),x72093),x72092))
% 51.10/50.83 [7809]~P102(x78091)+E(f16(x78091,x78092),x78093)+~P1(f331(f68(x78091),x78092))+~P1(f331(f331(f333(x78091),x78093),x78092))+~P1(f331(f331(f240(x78091),f624(x78093,x78092,x78091)),x78093))
% 51.10/50.83 [8123]~P102(x81231)+~P16(x81231,x81232)+~P16(x81231,x81233)+P16(x81231,f331(f331(f130(x81231),x81232),x81233))+~P1(f331(f331(f240(x81231),f764(x81233,x81232,x81231)),f765(x81233,x81232,x81231)))
% 51.10/50.83 [8850]~P97(x88502)+E(x88501,f184(f854(x88502,a840)))+~E(f331(f331(f109(x88502),f331(x88503,f427(x88501,x88503,x88502))),f331(x88503,f432(x88501,x88503,x88502))),f331(x88503,f331(f331(f109(x88502),f427(x88501,x88503,x88502)),f432(x88501,x88503,x88502))))+E(f12(x88502,f331(f311(x88502,x88502,x88503),x88501)),f331(x88503,f12(x88502,x88501)))+~P1(f331(f68(x88502),x88501))
% 51.10/50.83 [8851]~P97(x88512)+E(x88511,f184(f854(x88512,a840)))+~E(f331(f331(f108(x88512),f331(x88513,f433(x88511,x88513,x88512))),f331(x88513,f434(x88511,x88513,x88512))),f331(x88513,f331(f331(f108(x88512),f433(x88511,x88513,x88512)),f434(x88511,x88513,x88512))))+E(f15(x88512,f331(f311(x88512,x88512,x88513),x88511)),f331(x88513,f15(x88512,x88511)))+~P1(f331(f68(x88512),x88511))
% 51.10/50.83 [8852]~P102(x88522)+E(x88521,f184(f854(x88522,a840)))+~E(f331(f331(f239(x88522),f331(x88523,f428(x88521,x88523,x88522))),f331(x88523,f429(x88521,x88523,x88522))),f331(x88523,f331(f331(f239(x88522),f428(x88521,x88523,x88522)),f429(x88521,x88523,x88522))))+E(f16(x88522,f331(f311(x88522,x88522,x88523),x88521)),f331(x88523,f16(x88522,x88521)))+~P1(f331(f68(x88522),x88521))
% 51.10/50.83 [8853]~P102(x88532)+E(x88531,f184(f854(x88532,a840)))+~E(f331(f331(f244(x88532),f331(x88533,f430(x88531,x88533,x88532))),f331(x88533,f431(x88531,x88533,x88532))),f331(x88533,f331(f331(f244(x88532),f430(x88531,x88533,x88532)),f431(x88531,x88533,x88532))))+E(f17(x88532,f331(f311(x88532,x88532,x88533),x88531)),f331(x88533,f17(x88532,x88531)))+~P1(f331(f68(x88532),x88531))
% 51.10/50.83 [8916]~P102(x89162)+E(x89161,f184(f854(x89162,a840)))+~E(f331(f331(f239(x89162),f331(x89163,f418(x89161,x89163,x89162))),f331(x89163,f423(x89161,x89163,x89162))),f331(x89163,f331(f331(f239(x89162),f418(x89161,x89163,x89162)),f423(x89161,x89163,x89162))))+E(f13(x89162,f239(x89162),f331(f311(x89162,x89162,x89163),x89161)),f331(x89163,f13(x89162,f239(x89162),x89161)))+~P1(f331(f68(x89162),x89161))
% 51.10/50.83 [8917]~P102(x89172)+E(x89171,f184(f854(x89172,a840)))+~E(f331(f331(f244(x89172),f331(x89173,f425(x89171,x89173,x89172))),f331(x89173,f426(x89171,x89173,x89172))),f331(x89173,f331(f331(f244(x89172),f425(x89171,x89173,x89172)),f426(x89171,x89173,x89172))))+E(f14(x89172,f244(x89172),f331(f311(x89172,x89172,x89173),x89171)),f331(x89173,f14(x89172,f244(x89172),x89171)))+~P1(f331(f68(x89172),x89171))
% 51.10/50.83 [6007]~P97(x60072)+E(x60071,f184(f854(x60072,a840)))+~P1(f331(f68(x60072),x60071))+E(f12(x60072,f331(f331(f310(x60072),x60073),x60071)),f331(f331(f109(x60072),x60073),f12(x60072,x60071)))+P1(f331(f331(f333(x60072),x60073),x60071))
% 51.10/50.83 [6008]~P97(x60082)+E(x60081,f184(f854(x60082,a840)))+~P1(f331(f68(x60082),x60081))+E(f15(x60082,f331(f331(f310(x60082),x60083),x60081)),f331(f331(f108(x60082),x60083),f15(x60082,x60081)))+P1(f331(f331(f333(x60082),x60083),x60081))
% 51.10/50.83 [6009]~P102(x60092)+E(x60091,f184(f854(x60092,a840)))+~P1(f331(f68(x60092),x60091))+E(f16(x60092,f331(f331(f310(x60092),x60093),x60091)),f331(f331(f239(x60092),x60093),f16(x60092,x60091)))+P1(f331(f331(f333(x60092),x60093),x60091))
% 51.10/50.83 [6010]~P102(x60102)+E(x60101,f184(f854(x60102,a840)))+~P1(f331(f68(x60102),x60101))+E(f17(x60102,f331(f331(f310(x60102),x60103),x60101)),f331(f331(f244(x60102),x60103),f17(x60102,x60101)))+P1(f331(f331(f333(x60102),x60103),x60101))
% 51.10/50.83 [6407]~P64(x64072)+E(x64071,f184(f854(x64072,a840)))+~P1(f331(f68(x64072),x64071))+E(f331(f70(x64072,f88(x64072)),f331(f331(f310(x64072),x64073),x64071)),f331(f331(f88(x64072),x64073),f331(f70(x64072,f88(x64072)),x64071)))+P1(f331(f331(f333(x64072),x64073),x64071))
% 51.10/50.83 [6496]~P102(x64962)+E(x64961,f184(f854(x64962,a840)))+~P1(f331(f68(x64962),x64961))+E(f13(x64962,f239(x64962),f331(f331(f310(x64962),x64963),x64961)),f331(f331(f239(x64962),x64963),f13(x64962,f239(x64962),x64961)))+P1(f331(f331(f333(x64962),x64963),x64961))
% 51.10/50.83 [6497]~P102(x64972)+E(x64971,f184(f854(x64972,a840)))+~P1(f331(f68(x64972),x64971))+E(f14(x64972,f244(x64972),f331(f331(f310(x64972),x64973),x64971)),f331(f331(f244(x64972),x64973),f14(x64972,f244(x64972),x64971)))+P1(f331(f331(f333(x64972),x64973),x64971))
% 51.10/50.83 [6946]~P102(x69462)+E(f331(f331(f244(x69462),f17(x69462,x69461)),f17(x69462,x69463)),f17(x69462,x69463))+E(x69461,f184(f854(x69462,a840)))+~P1(f331(f68(x69462),x69463))+~P1(f331(f331(f240(f854(x69462,a840)),x69461),x69463))
% 51.10/50.83 [6947]~P102(x69472)+E(f331(f331(f239(x69472),f16(x69472,x69471)),f16(x69472,x69473)),f16(x69472,x69473))+E(x69471,f184(f854(x69472,a840)))+~P1(f331(f68(x69472),x69473))+~P1(f331(f331(f240(f854(x69472,a840)),x69471),x69473))
% 51.10/50.83 [6948]~P97(x69482)+E(f331(f331(f108(x69482),f15(x69482,x69481)),f15(x69482,x69483)),f15(x69482,x69483))+E(x69481,f184(f854(x69482,a840)))+~P1(f331(f68(x69482),x69483))+~P1(f331(f331(f240(f854(x69482,a840)),x69481),x69483))
% 51.10/50.83 [6949]~P97(x69492)+E(f331(f331(f109(x69492),f12(x69492,x69491)),f12(x69492,x69493)),f12(x69492,x69493))+E(x69491,f184(f854(x69492,a840)))+~P1(f331(f68(x69492),x69493))+~P1(f331(f331(f240(f854(x69492,a840)),x69491),x69493))
% 51.10/50.83 [7264]~P102(x72642)+E(x72641,f184(f854(x72642,a840)))+~P1(f331(f68(x72642),x72643))+P1(f331(f331(f240(x72642),f16(x72642,x72641)),f16(x72642,x72643)))+~P1(f331(f331(f240(f854(x72642,a840)),x72641),x72643))
% 51.10/50.83 [7265]~P102(x72652)+E(x72651,f184(f854(x72652,a840)))+~P1(f331(f68(x72652),x72653))+P1(f331(f331(f240(x72652),f17(x72652,x72653)),f17(x72652,x72651)))+~P1(f331(f331(f240(f854(x72652,a840)),x72651),x72653))
% 51.10/50.83 [7327]~P97(x73271)+E(f12(x73271,x73272),x73273)+~P1(f331(f68(x73271),x73272))+~E(f331(f331(f3(f854(x73271,a840)),x73272),f331(f331(f310(x73271),x73273),f184(f854(x73271,a840)))),f184(f854(x73271,a840)))+~P1(f331(f331(f333(x73271),x73273),x73272))
% 51.10/50.83 [7328]~P97(x73281)+E(f15(x73281,x73282),x73283)+~P1(f331(f68(x73281),x73282))+~E(f331(f331(f3(f854(x73281,a840)),x73282),f331(f331(f310(x73281),x73283),f184(f854(x73281,a840)))),f184(f854(x73281,a840)))+~P1(f331(f331(f333(x73281),x73283),x73282))
% 51.10/50.83 [7329]~P102(x73291)+E(f16(x73291,x73292),x73293)+~P1(f331(f68(x73291),x73292))+~E(f331(f331(f3(f854(x73291,a840)),x73292),f331(f331(f310(x73291),x73293),f184(f854(x73291,a840)))),f184(f854(x73291,a840)))+~P1(f331(f331(f333(x73291),x73293),x73292))
% 51.10/50.83 [7330]~P102(x73301)+E(f17(x73301,x73302),x73303)+~P1(f331(f68(x73301),x73302))+~E(f331(f331(f3(f854(x73301,a840)),x73302),f331(f331(f310(x73301),x73303),f184(f854(x73301,a840)))),f184(f854(x73301,a840)))+~P1(f331(f331(f333(x73301),x73303),x73302))
% 51.10/50.83 [7430]~P102(x74301)+E(f13(x74301,f239(x74301),x74302),x74303)+~P1(f331(f68(x74301),x74302))+~E(f331(f331(f3(f854(x74301,a840)),x74302),f331(f331(f310(x74301),x74303),f184(f854(x74301,a840)))),f184(f854(x74301,a840)))+~P1(f331(f331(f333(x74301),x74303),x74302))
% 51.10/50.83 [7431]~P102(x74311)+E(f14(x74311,f244(x74311),x74312),x74313)+~P1(f331(f68(x74311),x74312))+~E(f331(f331(f3(f854(x74311,a840)),x74312),f331(f331(f310(x74311),x74313),f184(f854(x74311,a840)))),f184(f854(x74311,a840)))+~P1(f331(f331(f333(x74311),x74313),x74312))
% 51.10/50.83 [7469]~P102(x74692)+E(x74691,f184(f854(x74692,a840)))+~P1(f331(f68(x74692),x74691))+~P1(f331(f331(f241(x74692),x74693),f523(x74693,x74691,x74692)))+P1(f331(f331(f241(x74692),x74693),f331(f70(x74692,f244(x74692)),x74691)))
% 51.10/50.83 [7470]~P102(x74702)+E(x74701,f184(f854(x74702,a840)))+~P1(f331(f68(x74702),x74701))+~P1(f331(f331(f240(x74702),x74703),f524(x74703,x74701,x74702)))+P1(f331(f331(f240(x74702),x74703),f331(f70(x74702,f244(x74702)),x74701)))
% 51.10/50.83 [7471]~P101(x74712)+E(x74711,f184(f854(x74712,a840)))+~P1(f331(f68(x74712),x74711))+~P1(f331(f331(f240(x74712),x74713),f525(x74713,x74711,x74712)))+P1(f331(f331(f240(x74712),x74713),f331(f70(x74712,f109(x74712)),x74711)))
% 51.10/50.83 [7559]~P101(x75592)+E(x75591,f184(f854(x75592,a840)))+~P1(f331(f68(x75592),x75591))+P1(f331(f331(f333(x75592),f525(x75593,x75591,x75592)),x75591))+P1(f331(f331(f240(x75592),x75593),f331(f70(x75592,f109(x75592)),x75591)))
% 51.10/50.83 [7560]~P102(x75602)+E(x75601,f184(f854(x75602,a840)))+~P1(f331(f68(x75602),x75601))+P1(f331(f331(f333(x75602),f524(x75603,x75601,x75602)),x75601))+P1(f331(f331(f240(x75602),x75603),f331(f70(x75602,f244(x75602)),x75601)))
% 51.10/50.83 [7561]~P102(x75612)+E(x75611,f184(f854(x75612,a840)))+~P1(f331(f68(x75612),x75611))+P1(f331(f331(f333(x75612),f523(x75613,x75611,x75612)),x75611))+P1(f331(f331(f241(x75612),x75613),f331(f70(x75612,f244(x75612)),x75611)))
% 51.10/50.83 [7681]~P102(x76812)+E(x76811,f184(f854(x76812,a840)))+E(f331(f331(f244(x76812),f14(x76812,f244(x76812),x76811)),f14(x76812,f244(x76812),x76813)),f14(x76812,f244(x76812),x76813))+~P1(f331(f68(x76812),x76813))+~P1(f331(f331(f240(f854(x76812,a840)),x76811),x76813))
% 51.10/50.83 [7682]~P102(x76822)+E(x76821,f184(f854(x76822,a840)))+E(f331(f331(f239(x76822),f13(x76822,f239(x76822),x76821)),f13(x76822,f239(x76822),x76823)),f13(x76822,f239(x76822),x76823))+~P1(f331(f68(x76822),x76823))+~P1(f331(f331(f240(f854(x76822,a840)),x76821),x76823))
% 51.10/50.83 [7884]~E(f670(x78841,x78843,x78842),f671(x78841,x78843,x78842))+~E(f331(f47(x78842),f668(x78841,x78843,x78842)),x78841)+E(f331(f331(f88(a847),x78841),f331(f47(f854(x78842,a840)),x78843)),f331(f47(x78842),f49(f854(x78842,a840),x78843)))+~P1(f331(f68(x78842),f49(f854(x78842,a840),x78843)))+~P1(f331(f68(f854(x78842,a840)),x78843))
% 51.10/50.83 [8059]~P102(x80592)+E(x80591,f184(f854(x80592,a840)))+~P1(f331(f68(x80592),x80593))+P1(f331(f331(f240(x80592),f331(f70(x80592,f244(x80592)),x80593)),f331(f70(x80592,f244(x80592)),x80591)))+~P1(f331(f331(f240(f854(x80592,a840)),x80591),x80593))
% 51.10/50.83 [8363]~E(f670(x83631,x83633,x83632),f671(x83631,x83633,x83632))+E(f331(f331(f88(a847),x83631),f331(f47(f854(x83632,a840)),x83633)),f331(f47(x83632),f49(f854(x83632,a840),x83633)))+P1(f331(f331(f333(f854(x83632,a840)),f668(x83631,x83633,x83632)),x83633))+~P1(f331(f68(x83632),f49(f854(x83632,a840),x83633)))+~P1(f331(f68(f854(x83632,a840)),x83633))
% 51.10/50.83 [8388]~E(f331(f47(x83882),f668(x83881,x83883,x83882)),x83881)+E(f331(f331(f88(a847),x83881),f331(f47(f854(x83882,a840)),x83883)),f331(f47(x83882),f49(f854(x83882,a840),x83883)))+P1(f331(f331(f333(f854(x83882,a840)),f671(x83881,x83883,x83882)),x83883))+~P1(f331(f68(x83882),f49(f854(x83882,a840),x83883)))+~P1(f331(f68(f854(x83882,a840)),x83883))
% 51.10/50.83 [8389]~E(f331(f47(x83892),f668(x83891,x83893,x83892)),x83891)+E(f331(f331(f88(a847),x83891),f331(f47(f854(x83892,a840)),x83893)),f331(f47(x83892),f49(f854(x83892,a840),x83893)))+P1(f331(f331(f333(f854(x83892,a840)),f670(x83891,x83893,x83892)),x83893))+~P1(f331(f68(x83892),f49(f854(x83892,a840),x83893)))+~P1(f331(f68(f854(x83892,a840)),x83893))
% 51.10/50.83 [8419]~E(f331(f47(x84192),f668(x84191,x84193,x84192)),x84191)+~E(f331(f331(f109(f854(x84192,a840)),f671(x84191,x84193,x84192)),f670(x84191,x84193,x84192)),f184(f854(x84192,a840)))+E(f331(f331(f88(a847),x84191),f331(f47(f854(x84192,a840)),x84193)),f331(f47(x84192),f49(f854(x84192,a840),x84193)))+~P1(f331(f68(f854(x84192,a840)),x84193))+~P1(f331(f68(x84192),f49(f854(x84192,a840),x84193)))
% 51.10/50.83 [8643]E(f331(f331(f88(a847),x86431),f331(f47(f854(x86432,a840)),x86433)),f331(f47(x86432),f49(f854(x86432,a840),x86433)))+P1(f331(f331(f333(f854(x86432,a840)),f668(x86431,x86433,x86432)),x86433))+P1(f331(f331(f333(f854(x86432,a840)),f671(x86431,x86433,x86432)),x86433))+~P1(f331(f68(f854(x86432,a840)),x86433))+~P1(f331(f68(x86432),f49(f854(x86432,a840),x86433)))
% 51.10/50.83 [8644]E(f331(f331(f88(a847),x86441),f331(f47(f854(x86442,a840)),x86443)),f331(f47(x86442),f49(f854(x86442,a840),x86443)))+P1(f331(f331(f333(f854(x86442,a840)),f668(x86441,x86443,x86442)),x86443))+P1(f331(f331(f333(f854(x86442,a840)),f670(x86441,x86443,x86442)),x86443))+~P1(f331(f68(f854(x86442,a840)),x86443))+~P1(f331(f68(x86442),f49(f854(x86442,a840),x86443)))
% 51.10/50.83 [8669]~E(f331(f331(f109(f854(x86692,a840)),f671(x86691,x86693,x86692)),f670(x86691,x86693,x86692)),f184(f854(x86692,a840)))+E(f331(f331(f88(a847),x86691),f331(f47(f854(x86692,a840)),x86693)),f331(f47(x86692),f49(f854(x86692,a840),x86693)))+~P1(f331(f68(f854(x86692,a840)),x86693))+P1(f331(f331(f333(f854(x86692,a840)),f668(x86691,x86693,x86692)),x86693))+~P1(f331(f68(x86692),f49(f854(x86692,a840),x86693)))
% 51.10/50.83 [8895]~P94(x88952)+E(x88951,f184(f854(x88952,a840)))+~E(f331(f331(f88(x88952),f331(x88953,f550(x88951,x88953,x88952))),f331(x88953,f551(x88951,x88953,x88952))),f331(x88953,f331(f331(f88(x88952),f550(x88951,x88953,x88952)),f551(x88951,x88953,x88952))))+~P1(f331(f68(x88952),x88951))+E(f331(f70(x88952,f88(x88952)),f331(f311(x88952,x88952,x88953),x88951)),f331(x88953,f331(f70(x88952,f88(x88952)),x88951)))
% 51.10/50.83 [9773]P1(f331(f331(x97731,x97732),x97733))+P1(f331(f331(f241(a1),f819(x97731,x97733,x97732)),f820(x97731,x97733,x97732)))+P1(f331(f331(f240(a1),f820(x97731,x97733,x97732)),f2(a1)))+P1(f331(f331(x97731,f819(x97731,x97733,x97732)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f820(x97731,x97733,x97732))))+~P1(f331(f320(f853(a1,a1),a67),f331(f331(f249(a1,a1),x97732),x97733)))
% 51.10/50.83 [9779]P1(f331(f331(x97791,x97792),x97793))+P1(f331(f331(f240(a1),f817(x97791,x97793,x97792)),f2(a1)))+P1(f331(f331(x97791,f816(x97791,x97793,x97792)),f331(f331(f88(a1),f331(f111(a1),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f817(x97791,x97793,x97792))))+P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f816(x97791,x97793,x97792)),f817(x97791,x97793,x97792))))+~P1(f331(f320(f853(a1,a1),a64),f331(f331(f249(a1,a1),x97792),x97793)))
% 51.10/50.83 [7854]~P86(x78541)+~P1(f331(f331(f240(x78541),x78542),f85(x78541)))+~P1(f331(f331(f240(x78541),f2(x78541)),x78542))+~P1(f331(f331(f240(x78541),f2(x78541)),x78543))+P1(f331(f331(f240(x78541),f331(f331(f88(x78541),x78542),x78543)),x78543))
% 51.10/50.83 [7855]~P86(x78551)+~P1(f331(f331(f240(x78551),x78553),f85(x78551)))+~P1(f331(f331(f240(x78551),f2(x78551)),x78553))+~P1(f331(f331(f240(x78551),f2(x78551)),x78552))+P1(f331(f331(f240(x78551),f331(f331(f88(x78551),x78552),x78553)),x78552))
% 51.10/50.83 [8205]~P102(x82052)+E(x82051,f184(f854(x82052,a840)))+~P1(f331(f68(x82052),x82051))+P1(f331(f331(f241(x82052),f537(x82053,x82051,x82052)),x82053))+~P1(f331(f331(f241(x82052),f331(f70(x82052,f244(x82052)),x82051)),x82053))
% 51.10/50.83 [8206]~P102(x82062)+E(x82061,f184(f854(x82062,a840)))+~P1(f331(f68(x82062),x82061))+P1(f331(f331(f240(x82062),f535(x82063,x82061,x82062)),x82063))+~P1(f331(f331(f240(x82062),f331(f70(x82062,f244(x82062)),x82061)),x82063))
% 51.10/50.83 [8207]~P102(x82072)+E(x82071,f184(f854(x82072,a840)))+~P1(f331(f68(x82072),x82071))+P1(f331(f331(f333(x82072),f535(x82073,x82071,x82072)),x82071))+~P1(f331(f331(f240(x82072),f331(f70(x82072,f244(x82072)),x82071)),x82073))
% 51.10/50.83 [8208]~P102(x82082)+E(x82081,f184(f854(x82082,a840)))+~P1(f331(f68(x82082),x82081))+P1(f331(f331(f333(x82082),f537(x82083,x82081,x82082)),x82081))+~P1(f331(f331(f241(x82082),f331(f70(x82082,f244(x82082)),x82081)),x82083))
% 51.10/50.83 [8294]~P1(f331(x82941,x82943))+P1(f331(x82941,f472(x82941,x82942)))+P1(f331(x82941,f470(x82941,x82942)))+~P1(f331(f331(f241(a1),f2(a1)),x82942))+P1(f331(x82941,f331(f331(f3(a1),f470(x82941,x82942)),f331(f331(f88(a1),f473(x82941,x82942)),x82942))))
% 51.10/50.83 [8508]~P1(f331(x85081,x85083))+P1(f331(x85081,f470(x85081,x85082)))+~P1(f331(f331(f241(a1),f2(a1)),x85082))+P1(f331(f331(f333(a1),f472(x85081,x85082)),f303(a1,f85(a1),x85082)))+P1(f331(x85081,f331(f331(f3(a1),f470(x85081,x85082)),f331(f331(f88(a1),f473(x85081,x85082)),x85082))))
% 51.10/50.83 [8687]~P1(f331(x86871,x86873))+~P1(f331(x86871,f470(x86871,x86872)))+P1(f331(x86871,f472(x86871,x86872)))+~P1(f331(f331(f241(a1),f2(a1)),x86872))+~P1(f331(x86871,f331(f331(f3(a1),f470(x86871,x86872)),f331(f331(f88(a1),f473(x86871,x86872)),x86872))))
% 51.10/50.83 [8790]~P1(f331(x87901,x87903))+~P1(f331(x87901,f470(x87901,x87902)))+~P1(f331(f331(f241(a1),f2(a1)),x87902))+P1(f331(f331(f333(a1),f472(x87901,x87902)),f303(a1,f85(a1),x87902)))+~P1(f331(x87901,f331(f331(f3(a1),f470(x87901,x87902)),f331(f331(f88(a1),f473(x87901,x87902)),x87902))))
% 51.10/50.83 [8606]~P97(x86061)+~P1(f331(f68(x86061),x86062))+E(f331(f331(f3(f854(x86061,a840)),x86062),f331(f331(f310(x86061),x86063),f184(f854(x86061,a840)))),f184(f854(x86061,a840)))+~P1(f331(f331(f333(x86061),x86063),x86062))+E(f331(f331(f109(x86061),x86063),f12(x86061,f331(f331(f3(f854(x86061,a840)),x86062),f331(f331(f310(x86061),x86063),f184(f854(x86061,a840)))))),f12(x86061,x86062))
% 51.10/50.83 [8607]~P97(x86071)+~P1(f331(f68(x86071),x86072))+E(f331(f331(f3(f854(x86071,a840)),x86072),f331(f331(f310(x86071),x86073),f184(f854(x86071,a840)))),f184(f854(x86071,a840)))+~P1(f331(f331(f333(x86071),x86073),x86072))+E(f331(f331(f108(x86071),x86073),f15(x86071,f331(f331(f3(f854(x86071,a840)),x86072),f331(f331(f310(x86071),x86073),f184(f854(x86071,a840)))))),f15(x86071,x86072))
% 51.10/50.83 [8608]~P102(x86081)+~P1(f331(f68(x86081),x86082))+E(f331(f331(f3(f854(x86081,a840)),x86082),f331(f331(f310(x86081),x86083),f184(f854(x86081,a840)))),f184(f854(x86081,a840)))+~P1(f331(f331(f333(x86081),x86083),x86082))+E(f331(f331(f239(x86081),x86083),f16(x86081,f331(f331(f3(f854(x86081,a840)),x86082),f331(f331(f310(x86081),x86083),f184(f854(x86081,a840)))))),f16(x86081,x86082))
% 51.10/50.83 [8609]~P102(x86091)+~P1(f331(f68(x86091),x86092))+E(f331(f331(f3(f854(x86091,a840)),x86092),f331(f331(f310(x86091),x86093),f184(f854(x86091,a840)))),f184(f854(x86091,a840)))+~P1(f331(f331(f333(x86091),x86093),x86092))+E(f331(f331(f244(x86091),x86093),f17(x86091,f331(f331(f3(f854(x86091,a840)),x86092),f331(f331(f310(x86091),x86093),f184(f854(x86091,a840)))))),f17(x86091,x86092))
% 51.10/50.83 [8664]~P102(x86641)+~P1(f331(f68(x86641),x86642))+E(f331(f331(f3(f854(x86641,a840)),x86642),f331(f331(f310(x86641),x86643),f184(f854(x86641,a840)))),f184(f854(x86641,a840)))+~P1(f331(f331(f333(x86641),x86643),x86642))+E(f331(f331(f239(x86641),x86643),f13(x86641,f239(x86641),f331(f331(f3(f854(x86641,a840)),x86642),f331(f331(f310(x86641),x86643),f184(f854(x86641,a840)))))),f13(x86641,f239(x86641),x86642))
% 51.10/50.83 [8665]~P102(x86651)+~P1(f331(f68(x86651),x86652))+E(f331(f331(f3(f854(x86651,a840)),x86652),f331(f331(f310(x86651),x86653),f184(f854(x86651,a840)))),f184(f854(x86651,a840)))+~P1(f331(f331(f333(x86651),x86653),x86652))+E(f331(f331(f244(x86651),x86653),f14(x86651,f244(x86651),f331(f331(f3(f854(x86651,a840)),x86652),f331(f331(f310(x86651),x86653),f184(f854(x86651,a840)))))),f14(x86651,f244(x86651),x86652))
% 51.10/50.83 [8675]~P102(x86751)+~P1(f331(f68(x86751),x86753))+~P1(f331(f68(x86751),x86752))+E(f331(f331(f109(f854(x86751,a840)),x86752),x86753),f184(f854(x86751,a840)))+E(f331(f331(f244(x86751),f17(x86751,f331(f331(f108(f854(x86751,a840)),x86752),x86753))),f17(x86751,f331(f331(f109(f854(x86751,a840)),x86752),x86753))),f331(f331(f244(x86751),f17(x86751,x86752)),f17(x86751,x86753)))
% 51.10/50.83 [8676]~P102(x86761)+~P1(f331(f68(x86761),x86763))+~P1(f331(f68(x86761),x86762))+E(f331(f331(f109(f854(x86761,a840)),x86762),x86763),f184(f854(x86761,a840)))+E(f331(f331(f239(x86761),f16(x86761,f331(f331(f108(f854(x86761,a840)),x86762),x86763))),f16(x86761,f331(f331(f109(f854(x86761,a840)),x86762),x86763))),f331(f331(f239(x86761),f16(x86761,x86762)),f16(x86761,x86763)))
% 51.10/50.83 [8677]~P97(x86771)+~P1(f331(f68(x86771),x86773))+~P1(f331(f68(x86771),x86772))+E(f331(f331(f109(f854(x86771,a840)),x86772),x86773),f184(f854(x86771,a840)))+E(f331(f331(f108(x86771),f15(x86771,f331(f331(f108(f854(x86771,a840)),x86772),x86773))),f15(x86771,f331(f331(f109(f854(x86771,a840)),x86772),x86773))),f331(f331(f108(x86771),f15(x86771,x86772)),f15(x86771,x86773)))
% 51.10/50.83 [8678]~P97(x86781)+~P1(f331(f68(x86781),x86783))+~P1(f331(f68(x86781),x86782))+E(f331(f331(f109(f854(x86781,a840)),x86782),x86783),f184(f854(x86781,a840)))+E(f331(f331(f109(x86781),f12(x86781,f331(f331(f108(f854(x86781,a840)),x86782),x86783))),f12(x86781,f331(f331(f109(f854(x86781,a840)),x86782),x86783))),f331(f331(f109(x86781),f12(x86781,x86782)),f12(x86781,x86783)))
% 51.10/50.83 [8869]~P102(x88691)+~P1(f331(f68(x88691),x88693))+~P1(f331(f68(x88691),x88692))+E(f331(f331(f109(f854(x88691,a840)),x88692),x88693),f184(f854(x88691,a840)))+E(f331(f331(f244(x88691),f14(x88691,f244(x88691),f331(f331(f108(f854(x88691,a840)),x88692),x88693))),f14(x88691,f244(x88691),f331(f331(f109(f854(x88691,a840)),x88692),x88693))),f331(f331(f244(x88691),f14(x88691,f244(x88691),x88692)),f14(x88691,f244(x88691),x88693)))
% 51.10/50.83 [8870]~P102(x88701)+~P1(f331(f68(x88701),x88703))+~P1(f331(f68(x88701),x88702))+E(f331(f331(f109(f854(x88701,a840)),x88702),x88703),f184(f854(x88701,a840)))+E(f331(f331(f239(x88701),f13(x88701,f239(x88701),f331(f331(f108(f854(x88701,a840)),x88702),x88703))),f13(x88701,f239(x88701),f331(f331(f109(f854(x88701,a840)),x88702),x88703))),f331(f331(f239(x88701),f13(x88701,f239(x88701),x88702)),f13(x88701,f239(x88701),x88703)))
% 51.10/50.83 [9614]~P85(x96143)+E(x96141,x96142)+~P1(f331(f331(f240(x96143),f2(x96143)),x96142))+~P1(f331(f331(f240(x96143),f2(x96143)),x96141))+~E(f331(f331(f250(x96143),x96141),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))),f331(f331(f250(x96143),x96142),f331(f111(a847),f331(f331(f87(a1),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)),f331(f331(f3(a1),f331(f331(f87(a1),a90),a90)),a104)))))
% 51.10/50.83 [4946]~P92(x49461)+~P58(x49461)+~E(x49464,f2(x49461))+~E(f331(f111(x49461),x49462),f2(x49461))+E(f331(f111(x49461),x49462),f331(f331(f291(x49461),x49463),x49464))
% 51.10/50.83 [4947]~P92(x49471)+~P58(x49471)+~E(x49473,f2(x49471))+~E(f331(f111(x49471),x49474),f2(x49471))+E(f331(f331(f291(x49471),x49472),x49473),f331(f111(x49471),x49474))
% 51.10/50.83 [5043]~P92(x50432)+~P58(x50432)+~E(x50431,f2(x50432))+~E(f331(f111(x50432),x50434),f2(x50432))+E(x50431,f331(f331(f291(x50432),x50433),f331(f111(x50432),x50434)))
% 51.10/50.83 [5044]~P92(x50441)+~P58(x50441)+~E(x50444,f2(x50441))+~E(f331(f111(x50441),x50443),f2(x50441))+E(f331(f331(f291(x50441),x50442),f331(f111(x50441),x50443)),x50444)
% 51.10/50.83 [5069]~P92(x50691)+~P58(x50691)+~E(x50693,f2(x50691))+E(f331(f111(x50691),x50692),f2(x50691))+~E(f331(f111(x50691),x50692),f331(f331(f291(x50691),x50694),x50693))
% 51.10/50.83 [5070]~P92(x50701)+~P58(x50701)+~E(x50703,f2(x50701))+E(f331(f111(x50701),x50702),f2(x50701))+~E(f331(f331(f291(x50701),x50704),x50703),f331(f111(x50701),x50702))
% 51.10/50.83 [5229]~P92(x52292)+~P58(x52292)+E(x52291,f2(x52292))+~E(f331(f111(x52292),x52293),f2(x52292))+~E(x52291,f331(f331(f291(x52292),x52294),f331(f111(x52292),x52293)))
% 51.10/50.83 [5230]~P92(x52302)+~P58(x52302)+E(x52301,f2(x52302))+~E(f331(f111(x52302),x52303),f2(x52302))+~E(f331(f331(f291(x52302),x52304),f331(f111(x52302),x52303)),x52301)
% 51.10/50.83 [5451]~P92(x54512)+~P58(x54512)+~E(x54511,f2(x54512))+E(x54511,f331(f331(f291(x54512),x54513),f331(f111(x54512),x54514)))+~E(f331(f331(f88(x54512),x54511),f331(f111(x54512),x54514)),x54513)
% 51.10/50.83 [5452]~P92(x54521)+~P58(x54521)+~E(x54524,f2(x54521))+~E(x54522,f331(f331(f88(x54521),x54524),f331(f111(x54521),x54523)))+E(f331(f331(f291(x54521),x54522),f331(f111(x54521),x54523)),x54524)
% 51.10/50.83 [5515]~P92(x55151)+~P58(x55151)+E(f331(f111(x55151),x55152),f2(x55151))+~E(f331(f331(f291(x55151),x55153),f331(f111(x55151),x55152)),x55154)+E(x55153,f331(f331(f88(x55151),x55154),f331(f111(x55151),x55152)))
% 51.10/50.83 [5516]~P92(x55161)+~P58(x55161)+E(f331(f111(x55161),x55162),f2(x55161))+~E(f331(f331(f88(x55161),x55163),f331(f111(x55161),x55162)),x55164)+E(x55163,f331(f331(f291(x55161),x55164),f331(f111(x55161),x55162)))
% 51.10/50.83 [5517]~P92(x55171)+~P58(x55171)+E(f331(f111(x55171),x55172),f2(x55171))+~E(x55173,f331(f331(f291(x55171),x55174),f331(f111(x55171),x55172)))+E(f331(f331(f88(x55171),x55173),f331(f111(x55171),x55172)),x55174)
% 51.10/50.83 [5518]~P92(x55181)+~P58(x55181)+E(f331(f111(x55181),x55182),f2(x55181))+~E(x55183,f331(f331(f88(x55181),x55184),f331(f111(x55181),x55182)))+E(f331(f331(f291(x55181),x55183),f331(f111(x55181),x55182)),x55184)
% 51.10/50.83 [5727]~P5(x57272)+E(x57271,f2(x57272))+~E(f331(f331(f48(x57272),x57273),x57271),x57274)+E(x57273,f331(f331(f88(x57272),x57274),x57271))+~P1(f331(f331(f287(x57272),x57271),x57273))
% 51.10/50.83 [5728]~P5(x57282)+E(x57281,f2(x57282))+~E(x57283,f331(f331(f88(x57282),x57284),x57281))+E(f331(f331(f48(x57282),x57283),x57281),x57284)+~P1(f331(f331(f287(x57282),x57281),x57283))
% 51.10/50.83 [6195]E(f485(x61951,x61952,x61953),x61954)+E(f331(x61951,x61954),f2(a847))+~E(f331(f331(f8(x61953,a847),x61951),x61952),f85(a847))+~P1(f331(f68(x61953),x61952))+~P1(f331(f331(f333(x61953),x61954),x61952))
% 51.10/50.83 [6262]E(f498(x62621,x62622,x62623),x62624)+E(f331(x62621,x62624),f2(a847))+~E(f331(f331(f8(x62623,a847),x62621),x62622),f331(a119,f2(a847)))+~P1(f331(f68(x62623),x62622))+~P1(f331(f331(f333(x62623),x62624),x62622))
% 51.10/50.83 [6376]~P102(x63761)+~P7(x63761)+P1(f331(f331(f241(x63761),x63762),f49(x63761,x63763)))+~P1(f331(f331(f333(x63761),x63764),x63763))+~P1(f331(f331(f241(x63761),x63762),x63764))
% 51.10/50.83 [6553]~P102(x65531)+~P7(x65531)+~P1(f331(f331(f333(x65531),x65534),x65532))+P1(f331(f331(f241(x65531),f50(x65531,x65532)),x65533))+~P1(f331(f331(f241(x65531),x65534),x65533))
% 51.10/50.83 [6829]~P85(x68293)+E(x68291,x68292)+~E(f331(f331(f250(x68293),x68291),f331(a119,x68294)),f331(f331(f250(x68293),x68292),f331(a119,x68294)))+~P1(f331(f331(f240(x68293),f2(x68293)),x68292))+~P1(f331(f331(f240(x68293),f2(x68293)),x68291))
% 51.10/50.83 [7040]~E(f500(x70402,x70403,x70401,x70404),x70404)+~E(f331(x70402,x70404),f85(a847))+E(f331(f331(f8(x70401,a847),x70402),x70403),f85(a847))+~P1(f331(f68(x70401),x70403))+~P1(f331(f331(f333(x70401),x70404),x70403))
% 51.10/50.83 [7047]~P87(x70474)+~P127(x70474)+E(f331(x70471,f393(x70471,x70472,x70473,x70474)),f2(x70474))+~E(f331(f331(f11(x70473,x70474),x70471),x70472),f2(x70474))+~P1(f331(f68(x70473),x70472))
% 51.10/50.83 [7130]~E(f499(x71302,x71303,x71301,x71304),x71304)+~E(f331(x71302,x71304),f331(a119,f2(a847)))+E(f331(f331(f8(x71301,a847),x71302),x71303),f331(a119,f2(a847)))+~P1(f331(f68(x71301),x71303))+~P1(f331(f331(f333(x71301),x71304),x71303))
% 51.10/50.83 [7894]~E(f331(x78942,x78944),f85(a847))+~E(f331(x78942,f500(x78942,x78943,x78941,x78944)),f2(a847))+E(f331(f331(f8(x78941,a847),x78942),x78943),f85(a847))+~P1(f331(f68(x78941),x78943))+~P1(f331(f331(f333(x78941),x78944),x78943))
% 51.10/50.83 [7939]~E(f331(x79392,x79394),f331(a119,f2(a847)))+~E(f331(x79392,f499(x79392,x79393,x79391,x79394)),f2(a847))+E(f331(f331(f8(x79391,a847),x79392),x79393),f331(a119,f2(a847)))+~P1(f331(f68(x79391),x79393))+~P1(f331(f331(f333(x79391),x79394),x79393))
% 51.10/50.83 [8018]~P136(x80182)+~P113(x80182)+~P1(f331(x80181,x80184))+~P1(f331(f331(f287(x80182),x80183),f331(f331(f87(x80182),x80184),f2(x80182))))+P1(f331(x80181,f331(f331(f88(x80182),x80183),f830(x80183,x80181,x80182))))
% 51.10/50.83 [8511]E(x85111,x85112)+E(f331(f331(f87(a1),f461(x85113,x85112,x85114,x85111)),f456(x85113,x85112,x85114,x85111)),x85111)+~E(f331(f331(f3(a1),x85111),x85114),x85112)+~P1(f331(f331(f241(a1),f2(a1)),x85114))+~P1(f331(f331(f333(a1),x85112),x85113))
% 51.10/50.83 [8512]E(x85121,x85122)+E(f331(f331(f3(a1),f457(x85123,x85122,x85124,x85121)),f458(x85123,x85122,x85124,x85121)),x85121)+~E(f331(f331(f87(a1),x85121),x85124),x85122)+~P1(f331(f331(f241(a1),f2(a1)),x85124))+~P1(f331(f331(f333(a1),x85122),x85123))
% 51.10/50.83 [8674]E(f331(x86741,f811(x86742,x86741,x86743,x86744)),x86742)+P1(f331(f331(f240(a847),x86744),f812(x86742,x86741,x86743,x86744)))+~P1(f331(f331(f240(a1),x86742),f331(x86741,x86743)))+~P1(f331(f331(f241(a847),x86744),x86743))+~P1(f331(f331(f240(a1),f331(x86741,x86744)),x86742))
% 51.10/50.83 [8691]~P87(x86914)+~P127(x86914)+~E(f331(f331(f11(x86911,x86914),x86912),x86913),f2(x86914))+~P1(f331(f68(x86911),x86913))+P1(f331(f331(f333(x86911),f393(x86912,x86913,x86911,x86914)),x86913))
% 51.10/50.83 [8724]~E(f331(x87242,x87244),f85(a847))+E(f331(f331(f8(x87241,a847),x87242),x87243),f85(a847))+~P1(f331(f68(x87241),x87243))+~P1(f331(f331(f333(x87241),x87244),x87243))+P1(f331(f331(f333(x87241),f500(x87242,x87243,x87241,x87244)),x87243))
% 51.10/50.83 [8733]E(x87331,x87332)+~E(f331(f331(f87(a1),x87332),x87334),x87331)+~P1(f331(f331(f241(a1),f2(a1)),x87334))+~P1(f331(f331(f333(a1),x87331),x87333))+P1(f331(f331(f333(a1),f457(x87333,x87331,x87334,x87332)),x87333))
% 51.10/50.83 [8734]E(x87341,x87342)+~E(f331(f331(f3(a1),x87342),x87344),x87341)+~P1(f331(f331(f241(a1),f2(a1)),x87344))+~P1(f331(f331(f333(a1),x87341),x87343))+P1(f331(f331(f333(a1),f461(x87343,x87341,x87344,x87342)),x87343))
% 51.10/50.83 [8736]~E(f331(x87362,x87364),f331(a119,f2(a847)))+E(f331(f331(f8(x87361,a847),x87362),x87363),f331(a119,f2(a847)))+~P1(f331(f68(x87361),x87363))+~P1(f331(f331(f333(x87361),x87364),x87363))+P1(f331(f331(f333(x87361),f499(x87362,x87363,x87361,x87364)),x87363))
% 51.10/50.83 [8740]P55(x87402,x87403,x87404,x87401)+E(x87401,f184(f854(x87402,a840)))+~P1(f331(f68(x87402),x87404))+~P1(f331(f68(x87402),x87401))+P1(f331(f331(f333(x87402),f526(x87401,x87404,x87403,x87402)),x87404))
% 51.10/50.83 [8803]E(x88031,x88032)+~E(f331(f331(f87(a1),x88032),x88034),x88031)+~P1(f331(f331(f241(a1),f2(a1)),x88034))+~P1(f331(f331(f333(a1),x88031),x88033))+P1(f331(f331(f333(a1),f458(x88033,x88031,x88034,x88032)),f303(a1,f85(a1),x88034)))
% 51.10/50.83 [8804]E(x88041,x88042)+~E(f331(f331(f3(a1),x88042),x88044),x88041)+~P1(f331(f331(f241(a1),f2(a1)),x88044))+~P1(f331(f331(f333(a1),x88041),x88043))+P1(f331(f331(f333(a1),f456(x88043,x88041,x88044,x88042)),f303(a1,f85(a1),x88044)))
% 51.10/50.83 [8875]P1(f331(f331(f240(a847),x88751),f811(x88752,x88753,x88754,x88751)))+~P1(f331(f331(f240(a1),x88752),f331(x88753,x88754)))+P1(f331(f331(f240(a847),x88751),f812(x88752,x88753,x88754,x88751)))+~P1(f331(f331(f241(a847),x88751),x88754))+~P1(f331(f331(f240(a1),f331(x88753,x88751)),x88752))
% 51.10/50.83 [8979]E(f331(x89791,f811(x89792,x89791,x89793,x89794)),x89792)+~P1(f331(f331(f240(a1),x89792),f331(x89791,x89793)))+P1(f331(f331(f241(a847),f812(x89792,x89791,x89793,x89794)),x89793))+~P1(f331(f331(f241(a847),x89794),x89793))+~P1(f331(f331(f240(a1),f331(x89791,x89794)),x89792))
% 51.10/50.83 [9085]~P1(f331(f331(f287(a847),x90854),x90851))+~P1(f331(f331(f287(a847),x90854),x90853))+~P1(f331(f331(f287(a847),x90852),x90851))+P1(f331(f331(f287(a847),x90851),x90852))+P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x90853,x90852)),f290(a847,f287(a847),x90854,x90851)))
% 51.10/50.83 [9086]~P1(f331(f331(f287(a847),x90862),x90861))+~P1(f331(f331(f287(a847),x90863),x90864))+~P1(f331(f331(f287(a847),x90862),x90864))+P1(f331(f331(f287(a847),x90861),x90862))+P1(f331(f331(f241(f854(a847,a840)),f290(a847,f287(a847),x90861,x90863)),f290(a847,f287(a847),x90862,x90864)))
% 51.10/50.83 [9095]~P1(f331(f331(f240(a1),x90952),f331(x90953,x90954)))+P1(f331(f331(f240(a847),x90951),f812(x90952,x90953,x90954,x90951)))+P1(f331(f331(f240(a847),f811(x90952,x90953,x90954,x90951)),x90954))+~P1(f331(f331(f241(a847),x90951),x90954))+~P1(f331(f331(f240(a1),f331(x90953,x90951)),x90952))
% 51.10/50.83 [9096]~P1(f331(f331(f240(a1),x90962),f331(x90963,x90964)))+P1(f331(f331(f240(a847),x90961),f811(x90962,x90963,x90964,x90961)))+P1(f331(f331(f241(a847),f812(x90962,x90963,x90964,x90961)),x90964))+~P1(f331(f331(f241(a847),x90961),x90964))+~P1(f331(f331(f240(a1),f331(x90963,x90961)),x90962))
% 51.10/50.83 [9184]~P1(f331(f331(f240(a1),x91841),f331(x91842,x91843)))+P1(f331(f331(f240(a847),f811(x91841,x91842,x91843,x91844)),x91843))+~P1(f331(f331(f241(a847),x91844),x91843))+~P1(f331(f331(f240(a1),f331(x91842,x91844)),x91841))+P1(f331(f331(f241(a847),f812(x91841,x91842,x91843,x91844)),x91843))
% 51.10/50.83 [9269]E(x92691,f184(f854(x92692,a840)))+~P1(f331(f68(x92692),x92694))+~P1(f331(f68(x92692),x92691))+P1(f331(f331(f333(f853(f854(x92692,a840),f854(x92692,a840))),f331(f331(f249(f854(x92692,a840),f854(x92692,a840)),x92694),x92691)),f323(x92692,x92693)))+P1(f331(f331(f333(x92692),f530(x92693,x92691,x92694,x92692)),x92694))
% 51.10/50.83 [9270]E(x92701,f184(f854(x92702,a840)))+~P1(f331(f68(x92702),x92704))+~P1(f331(f68(x92702),x92701))+P1(f331(f331(f333(f853(f854(x92702,a840),f854(x92702,a840))),f331(f331(f249(f854(x92702,a840),f854(x92702,a840)),x92704),x92701)),f323(x92702,x92703)))+P1(f331(f331(f333(x92702),f626(x92703,x92701,x92704,x92702)),x92704))
% 51.10/50.83 [9930]E(f331(x99301,f811(x99302,x99301,x99303,x99304)),x99302)+~P1(f331(f331(f240(a1),x99302),f331(x99301,x99303)))+~P1(f331(f331(f240(a1),f331(f82(a1),f331(f331(f3(a1),f331(x99301,f331(f331(f87(a847),f812(x99302,x99301,x99303,x99304)),f85(a847)))),f331(x99301,f812(x99302,x99301,x99303,x99304))))),f85(a1)))+~P1(f331(f331(f241(a847),x99304),x99303))+~P1(f331(f331(f240(a1),f331(x99301,x99304)),x99302))
% 51.10/50.83 [9931]~P1(f331(f331(f240(a1),x99312),f331(x99313,x99314)))+P1(f331(f331(f240(a847),x99311),f811(x99312,x99313,x99314,x99311)))+~P1(f331(f331(f240(a1),f331(f82(a1),f331(f331(f3(a1),f331(x99313,f331(f331(f87(a847),f812(x99312,x99313,x99314,x99311)),f85(a847)))),f331(x99313,f812(x99312,x99313,x99314,x99311))))),f85(a1)))+~P1(f331(f331(f241(a847),x99311),x99314))+~P1(f331(f331(f240(a1),f331(x99313,x99311)),x99312))
% 51.10/50.83 [9932]~P1(f331(f331(f240(a1),x99321),f331(x99322,x99323)))+~P1(f331(f331(f240(a1),f331(f82(a1),f331(f331(f3(a1),f331(x99322,f331(f331(f87(a847),f812(x99321,x99322,x99323,x99324)),f85(a847)))),f331(x99322,f812(x99321,x99322,x99323,x99324))))),f85(a1)))+~P1(f331(f331(f241(a847),x99324),x99323))+~P1(f331(f331(f240(a1),f331(x99322,x99324)),x99321))+P1(f331(f331(f240(a847),f811(x99321,x99322,x99323,x99324)),x99323))
% 51.10/50.83 [5474]~P92(x54742)+~P58(x54742)+E(x54741,f2(x54742))+~E(f331(f331(f291(x54742),x54743),x54741),f331(f111(x54742),x54744))+E(x54743,f331(f331(f88(x54742),f331(f111(x54742),x54744)),x54741))
% 51.10/50.83 [5475]~P92(x54752)+~P58(x54752)+E(x54751,f2(x54752))+~E(f331(f111(x54752),x54753),f331(f331(f291(x54752),x54754),x54751))+E(f331(f331(f88(x54752),f331(f111(x54752),x54753)),x54751),x54754)
% 51.10/50.83 [5627]~P92(x56272)+~P58(x56272)+E(x56271,f2(x56272))+E(f331(f111(x56272),x56273),f331(f331(f291(x56272),x56274),x56271))+~E(f331(f331(f88(x56272),f331(f111(x56272),x56273)),x56271),x56274)
% 51.10/50.83 [5628]~P92(x56282)+~P58(x56282)+E(x56281,f2(x56282))+E(f331(f331(f291(x56282),x56283),x56281),f331(f111(x56282),x56284))+~E(x56283,f331(f331(f88(x56282),f331(f111(x56282),x56284)),x56281))
% 51.10/50.83 [5766]~P92(x57661)+~P58(x57661)+~E(f331(f111(x57661),x57662),f2(x57661))+E(f331(f111(x57661),x57662),f331(f331(f291(x57661),x57663),x57664))+~E(f331(f331(f88(x57661),f331(f111(x57661),x57662)),x57664),x57663)
% 51.10/50.83 [5767]~P92(x57671)+~P58(x57671)+~E(f331(f111(x57671),x57674),f2(x57671))+E(f331(f331(f291(x57671),x57672),x57673),f331(f111(x57671),x57674))+~E(x57672,f331(f331(f88(x57671),f331(f111(x57671),x57674)),x57673))
% 51.10/50.83 [7098]~P60(x70981)+P1(f331(f331(f241(x70981),x70982),f2(x70981)))+~P1(f331(f331(f241(x70981),x70983),f2(x70981)))+P1(f331(f331(f241(x70981),f2(x70981)),x70982))+P1(f331(f331(f241(x70981),x70983),f331(f331(f291(x70981),x70984),x70982)))
% 51.10/50.83 [7099]~P60(x70991)+P1(f331(f331(f241(x70991),x70992),f2(x70991)))+~P1(f331(f331(f240(x70991),x70993),f2(x70991)))+P1(f331(f331(f241(x70991),f2(x70991)),x70992))+P1(f331(f331(f240(x70991),x70993),f331(f331(f291(x70991),x70994),x70992)))
% 51.10/50.83 [7368]~P60(x73681)+P1(f331(f331(f241(x73681),x73682),f2(x73681)))+P1(f331(f331(f241(x73681),x73683),f2(x73681)))+P1(f331(f331(f241(x73681),f2(x73681)),x73683))+~P1(f331(f331(f241(x73681),x73682),f331(f331(f291(x73681),x73684),x73683)))
% 51.10/50.83 [7369]~P60(x73691)+P1(f331(f331(f241(x73691),x73692),f2(x73691)))+P1(f331(f331(f240(x73691),x73693),f2(x73691)))+P1(f331(f331(f241(x73691),f2(x73691)),x73692))+~P1(f331(f331(f240(x73691),x73693),f331(f331(f291(x73691),x73694),x73692)))
% 51.10/50.83 [7488]E(x74881,x74882)+~E(f331(f331(f155(x74883),x74884),x74881),f331(f331(f155(x74883),x74884),x74882))+~P1(f331(f132(x74883),x74884))+~P1(f331(f331(f241(a847),x74882),f331(f185(f848(x74883)),x74884)))+~P1(f331(f331(f241(a847),x74881),f331(f185(f848(x74883)),x74884)))
% 51.10/50.83 [7489]E(x74891,x74892)+~E(f331(f331(f155(x74893),x74894),x74891),f331(f331(f155(x74893),x74894),x74892))+~P1(f331(f132(x74893),x74894))+~P1(f331(f331(f241(a847),x74892),f331(f185(f848(x74893)),x74894)))+~P1(f331(f331(f241(a847),x74891),f331(f185(f848(x74893)),x74894)))
% 51.10/50.83 [7856]~P60(x78561)+~P1(f331(f331(f241(x78561),x78563),f2(x78561)))+P1(f331(f331(f241(x78561),f2(x78561)),x78562))+~P1(f331(f331(f241(x78561),x78564),f331(f331(f88(x78561),x78563),x78562)))+P1(f331(f331(f241(x78561),x78563),f331(f331(f291(x78561),x78564),x78562)))
% 51.10/50.83 [7857]~P60(x78571)+~P1(f331(f331(f240(x78571),x78573),f2(x78571)))+P1(f331(f331(f241(x78571),f2(x78571)),x78572))+~P1(f331(f331(f240(x78571),x78574),f331(f331(f88(x78571),x78573),x78572)))+P1(f331(f331(f240(x78571),x78573),f331(f331(f291(x78571),x78574),x78572)))
% 51.10/50.83 [7858]~P60(x78581)+~P1(f331(f331(f241(x78581),x78582),f2(x78581)))+P1(f331(f331(f241(x78581),f2(x78581)),x78582))+~P1(f331(f331(f241(x78581),x78584),f331(f331(f88(x78581),x78583),x78582)))+P1(f331(f331(f241(x78581),x78583),f331(f331(f291(x78581),x78584),x78582)))
% 51.10/50.83 [7859]~P60(x78591)+~P1(f331(f331(f241(x78591),x78592),f2(x78591)))+P1(f331(f331(f241(x78591),f2(x78591)),x78592))+~P1(f331(f331(f241(x78591),x78594),f331(f331(f291(x78591),x78593),x78592)))+P1(f331(f331(f241(x78591),x78593),f331(f331(f88(x78591),x78594),x78592)))
% 51.10/50.83 [7860]~P60(x78601)+~P1(f331(f331(f241(x78601),x78602),f2(x78601)))+P1(f331(f331(f241(x78601),f2(x78601)),x78602))+~P1(f331(f331(f240(x78601),x78604),f331(f331(f88(x78601),x78603),x78602)))+P1(f331(f331(f240(x78601),x78603),f331(f331(f291(x78601),x78604),x78602)))
% 51.10/50.83 [7861]~P60(x78611)+~P1(f331(f331(f241(x78611),x78612),f2(x78611)))+P1(f331(f331(f241(x78611),f2(x78611)),x78612))+~P1(f331(f331(f240(x78611),x78614),f331(f331(f291(x78611),x78613),x78612)))+P1(f331(f331(f240(x78611),x78613),f331(f331(f88(x78611),x78614),x78612)))
% 51.10/50.83 [7986]~P5(x79861)+~P1(f331(f331(f287(x79861),x79863),x79864))+~P1(f331(f331(f287(x79861),x79863),x79862))+~P1(f331(f331(f287(x79861),x79862),x79864))+P1(f331(f331(f287(x79861),f331(f331(f48(x79861),x79862),x79863)),f331(f331(f48(x79861),x79864),x79863)))
% 51.10/50.83 [8000]~P102(x80001)+~P16(x80001,x80002)+~P1(f331(f331(f240(a847),x80003),x80004))+P1(f331(f331(f240(x80001),f331(f331(f155(x80001),x80002),x80003)),f331(f331(f155(x80001),x80002),x80004)))+~P1(f331(f331(f241(a847),x80004),f331(f185(f848(x80001)),x80002)))
% 51.10/50.83 [8001]~P102(x80011)+~P16(x80011,x80012)+~P1(f331(f331(f240(a847),x80013),x80014))+P1(f331(f331(f240(x80011),f331(f331(f155(x80011),x80012),x80013)),f331(f331(f155(x80011),x80012),x80014)))+~P1(f331(f331(f241(a847),x80014),f331(f185(f848(x80011)),x80012)))
% 51.10/50.83 [8051]~P85(x80511)+~P1(f331(f331(f241(x80511),x80512),f85(x80511)))+~P1(f331(f331(f241(x80511),f2(x80511)),x80512))+~P1(f331(f331(f241(a847),x80514),x80513))+P1(f331(f331(f241(x80511),f331(f331(f250(x80511),x80512),x80513)),f331(f331(f250(x80511),x80512),x80514)))
% 51.10/50.83 [8052]~P85(x80521)+~P1(f331(f331(f240(x80521),x80522),f85(x80521)))+~P1(f331(f331(f240(x80521),f2(x80521)),x80522))+~P1(f331(f331(f240(a847),x80524),x80523))+P1(f331(f331(f240(x80521),f331(f331(f250(x80521),x80522),x80523)),f331(f331(f250(x80521),x80522),x80524)))
% 51.10/50.83 [8053]~P85(x80531)+~P1(f331(f331(f240(x80531),f2(x80531)),x80532))+~P1(f331(f331(f241(a847),f2(a847)),x80533))+~P1(f331(f331(f241(x80531),x80532),x80534))+P1(f331(f331(f241(x80531),f331(f331(f250(x80531),x80532),x80533)),f331(f331(f250(x80531),x80534),x80533)))
% 51.10/50.83 [8071]~P102(x80711)+~P16(x80711,f331(f160(x80711),x80712))+~P1(f331(f331(f240(a847),x80714),x80713))+P1(f331(f331(f240(x80711),f331(f331(f155(x80711),x80712),x80713)),f331(f331(f155(x80711),x80712),x80714)))+~P1(f331(f331(f241(a847),x80713),f331(f185(f848(x80711)),x80712)))
% 51.10/50.83 [8301]~P5(x83011)+P1(f331(f331(f287(x83011),x83012),x83013))+~P1(f331(f331(f287(x83011),x83014),x83013))+~P1(f331(f331(f287(x83011),x83014),x83012))+~P1(f331(f331(f287(x83011),f331(f331(f48(x83011),x83012),x83014)),f331(f331(f48(x83011),x83013),x83014)))
% 51.10/50.83 [8317]~P61(x83171)+~P1(f331(f331(f241(x83171),x83172),f2(x83171)))+~P1(f331(f331(f241(x83171),x83173),x83174))+~P1(f331(f331(f241(x83171),f2(x83171)),f331(f331(f88(x83171),x83173),x83174)))+P1(f331(f331(f241(x83171),f331(f331(f291(x83171),x83172),x83173)),f331(f331(f291(x83171),x83172),x83174)))
% 51.10/50.83 [8318]~P60(x83181)+~P1(f331(f331(f240(x83181),x83182),f2(x83181)))+~P1(f331(f331(f240(x83181),x83183),x83184))+~P1(f331(f331(f241(x83181),f2(x83181)),f331(f331(f88(x83181),x83183),x83184)))+P1(f331(f331(f240(x83181),f331(f331(f291(x83181),x83182),x83183)),f331(f331(f291(x83181),x83182),x83184)))
% 51.10/50.83 [8328]~P61(x83281)+~P1(f331(f331(f241(x83281),x83284),x83283))+~P1(f331(f331(f241(x83281),f2(x83281)),x83282))+~P1(f331(f331(f241(x83281),f2(x83281)),f331(f331(f88(x83281),x83283),x83284)))+P1(f331(f331(f241(x83281),f331(f331(f291(x83281),x83282),x83283)),f331(f331(f291(x83281),x83282),x83284)))
% 51.10/50.83 [8329]~P61(x83291)+~P1(f331(f331(f240(x83291),x83294),x83293))+~P1(f331(f331(f240(x83291),f2(x83291)),x83292))+~P1(f331(f331(f241(x83291),f2(x83291)),f331(f331(f88(x83291),x83293),x83294)))+P1(f331(f331(f240(x83291),f331(f331(f291(x83291),x83292),x83293)),f331(f331(f291(x83291),x83292),x83294)))
% 51.10/50.83 [8434]P1(f331(x84341,x84342))+~P1(f331(f68(x84344),x84342))+P1(f331(x84341,f504(x84341,x84343,x84342,x84344)))+~P1(f331(x84341,f184(f854(x84344,a840))))+~P1(f331(f331(f240(f854(x84344,a840)),x84342),x84343))
% 51.10/50.83 [8442]P1(f331(x84421,x84422))+P1(f331(f68(x84423),f504(x84421,x84424,x84422,x84423)))+~P1(f331(f68(x84423),x84422))+~P1(f331(x84421,f184(f854(x84423,a840))))+~P1(f331(f331(f240(f854(x84423,a840)),x84422),x84424))
% 51.10/50.83 [8671]E(f331(f331(f87(a1),f462(x86711,x86712,x86713,x86714)),f463(x86711,x86712,x86713,x86714)),x86714)+~P1(f331(f331(f241(a1),f2(a1)),x86713))+~P1(f331(f331(f241(a1),x86712),x86714))+~P1(f331(f331(f333(a1),x86712),x86711))+P1(f331(f331(f241(a1),x86712),f331(f331(f3(a1),x86714),x86713)))
% 51.10/50.83 [8856]~P1(f331(f331(f241(a1),f2(a1)),x88563))+~P1(f331(f331(f241(a1),x88562),x88564))+~P1(f331(f331(f333(a1),x88562),x88561))+P1(f331(f331(f333(a1),f462(x88561,x88562,x88563,x88564)),x88561))+P1(f331(f331(f241(a1),x88562),f331(f331(f3(a1),x88564),x88563)))
% 51.10/50.83 [8868]P1(f331(x88681,x88682))+~P1(f331(f68(x88683),x88682))+P1(f331(f331(f333(x88683),f505(x88681,x88684,x88682,x88683)),x88684))+~P1(f331(x88681,f184(f854(x88683,a840))))+~P1(f331(f331(f240(f854(x88683,a840)),x88682),x88684))
% 51.10/50.83 [8885]E(f331(f331(f87(a1),f452(x88851,x88852,x88853,x88854)),f453(x88851,x88852,x88853,x88854)),x88854)+~P1(f331(f331(f241(a1),f2(a1)),x88853))+~P1(f331(f331(f240(a1),x88852),x88854))+P1(f331(f331(f240(a1),x88852),f331(f331(f3(a1),x88854),x88853)))+~P1(f331(f331(f333(a1),f331(f331(f3(a1),x88852),f85(a1))),x88851))
% 51.10/50.83 [8932]~P1(f331(f331(f241(a1),f2(a1)),x89323))+~P1(f331(f331(f241(a1),x89321),x89322))+~P1(f331(f331(f333(a1),x89321),x89324))+P1(f331(f331(f333(a1),f463(x89324,x89321,x89323,x89322)),f303(a1,f85(a1),x89323)))+P1(f331(f331(f241(a1),x89321),f331(f331(f3(a1),x89322),x89323)))
% 51.10/50.83 [9023]~P1(f331(f331(f241(a1),f2(a1)),x90233))+~P1(f331(f331(f240(a1),x90232),x90234))+P1(f331(f331(f333(a1),f452(x90231,x90232,x90233,x90234)),x90231))+P1(f331(f331(f240(a1),x90232),f331(f331(f3(a1),x90234),x90233)))+~P1(f331(f331(f333(a1),f331(f331(f3(a1),x90232),f85(a1))),x90231))
% 51.10/50.83 [9061]~P1(f331(f331(f241(a1),f2(a1)),x90613))+~P1(f331(f331(f240(a1),x90611),x90612))+P1(f331(f331(f333(a1),f453(x90614,x90611,x90613,x90612)),f303(a1,f85(a1),x90613)))+P1(f331(f331(f240(a1),x90611),f331(f331(f3(a1),x90612),x90613)))+~P1(f331(f331(f333(a1),f331(f331(f3(a1),x90611),f85(a1))),x90614))
% 51.10/50.83 [9272]P1(f331(x92721,x92722))+~P1(f331(f331(f333(x92723),f505(x92721,x92724,x92722,x92723)),f504(x92721,x92724,x92722,x92723)))+~P1(f331(f68(x92723),x92722))+~P1(f331(x92721,f184(f854(x92723,a840))))+~P1(f331(f331(f240(f854(x92723,a840)),x92722),x92724))
% 51.10/50.83 [9481]P1(f331(x94811,x94812))+~P1(f331(f68(x94813),x94812))+~P1(f331(x94811,f331(f331(f310(x94813),f505(x94811,x94814,x94812,x94813)),f504(x94811,x94814,x94812,x94813))))+~P1(f331(x94811,f184(f854(x94813,a840))))+~P1(f331(f331(f240(f854(x94813,a840)),x94812),x94814))
% 51.10/50.83 [9811]~P88(x98113)+~P50(a847,x98113,f331(f331(f20(a847,f854(a847,a840),f854(a847,a840)),f331(f331(f10(f854(a847,f854(a840,a840)),f854(f854(a847,a840),f854(a847,a840)),a847),f20(a847,a840,a840)),f331(f331(f10(f854(a847,a840),f854(a847,f854(a840,a840)),a847),f331(f10(a840,f854(a840,a840),a847),a329)),f287(a847)))),f331(f331(f10(f854(a847,a840),f854(a847,a840),a847),f331(f10(a840,a840,a847),a327)),f331(f9(a847,a847,a840),f287(a847)))),x98114)+P1(f331(f331(f241(x98113),f331(x98114,x98112)),f331(x98114,x98111)))+~P1(f331(f331(f287(a847),x98112),x98111))+P1(f331(f331(f287(a847),x98111),x98112))
% 51.10/50.83 [7628]~P60(x76281)+P1(f331(f331(f241(x76281),x76282),f2(x76281)))+P1(f331(f331(f241(x76281),f2(x76281)),x76282))+~P1(f331(f331(f241(x76281),f2(x76281)),x76284))+P1(f331(f331(f241(x76281),f331(f331(f291(x76281),x76283),x76282)),x76284))
% 51.10/50.83 [7629]~P60(x76291)+P1(f331(f331(f241(x76291),x76292),f2(x76291)))+~P1(f331(f331(f240(x76291),f2(x76291)),x76294))+P1(f331(f331(f241(x76291),f2(x76291)),x76292))+P1(f331(f331(f240(x76291),f331(f331(f291(x76291),x76293),x76292)),x76294))
% 51.10/50.83 [7912]~P1(f331(f331(f240(a1),x79124),f2(a1)))+~E(x79122,f331(f331(f87(a1),f331(f331(f88(a1),x79121),x79123)),x79124))+P1(f331(f331(f241(a1),f2(a1)),x79121))+~P1(f331(f331(f241(a1),x79121),x79124))+P1(f331(f61(x79122,x79121),f331(f331(f249(a1,a1),x79123),x79124)))
% 51.10/50.83 [7949]~P1(f331(x79491,x79494))+P1(f331(x79491,f799(x79492,x79491,x79493)))+~P1(f331(f331(f241(a1),f2(a1)),x79493))+~P1(f331(f331(f240(a1),f2(a1)),x79492))+P1(f331(x79491,f331(f331(f87(a1),x79494),f331(f331(f88(a1),x79492),x79493))))
% 51.10/50.83 [7950]~P1(f331(x79501,x79504))+P1(f331(x79501,f804(x79502,x79501,x79503)))+~P1(f331(f331(f241(a1),f2(a1)),x79503))+~P1(f331(f331(f240(a1),f2(a1)),x79502))+P1(f331(x79501,f331(f331(f3(a1),x79504),f331(f331(f88(a1),x79502),x79503))))
% 51.10/50.83 [7951]~P60(x79511)+P1(f331(f331(f241(x79511),x79512),f2(x79511)))+P1(f331(f331(f241(x79511),f2(x79511)),x79512))+P1(f331(f331(f241(x79511),f2(x79511)),x79513))+~P1(f331(f331(f241(x79511),f331(f331(f291(x79511),x79514),x79512)),x79513))
% 51.10/50.83 [7952]~P60(x79521)+P1(f331(f331(f241(x79521),x79522),f2(x79521)))+P1(f331(f331(f241(x79521),f2(x79521)),x79522))+P1(f331(f331(f240(x79521),f2(x79521)),x79523))+~P1(f331(f331(f240(x79521),f331(f331(f291(x79521),x79524),x79522)),x79523))
% 51.10/50.83 [7996]~E(x79961,f331(f331(f87(a1),f331(f331(f88(a1),x79962),x79963)),x79964))+~P1(f331(f331(f241(a1),f2(a1)),x79962))+~P1(f331(f331(f240(a1),f2(a1)),x79964))+~P1(f331(f331(f241(a1),x79964),x79962))+P1(f331(f61(x79961,x79962),f331(f331(f249(a1,a1),x79963),x79964)))
% 51.10/50.83 [8113]~P60(x81131)+P1(f331(f331(f241(x81131),x81132),f2(x81131)))+~P1(f331(f331(f241(x81131),f2(x81131)),x81134))+~P1(f331(f331(f241(x81131),x81133),f331(f331(f88(x81131),x81134),x81132)))+P1(f331(f331(f241(x81131),f331(f331(f291(x81131),x81133),x81132)),x81134))
% 51.10/50.83 [8114]~P60(x81141)+P1(f331(f331(f241(x81141),x81142),f2(x81141)))+~P1(f331(f331(f240(x81141),f2(x81141)),x81144))+~P1(f331(f331(f240(x81141),x81143),f331(f331(f88(x81141),x81144),x81142)))+P1(f331(f331(f240(x81141),f331(f331(f291(x81141),x81143),x81142)),x81144))
% 51.10/50.83 [8193]~P60(x81931)+P1(f331(f331(f241(x81931),x81932),f2(x81931)))+~P1(f331(f331(f241(x81931),x81933),f2(x81931)))+P1(f331(f331(f241(x81931),x81933),f331(f331(f291(x81931),x81934),x81932)))+~P1(f331(f331(f241(x81931),f331(f331(f88(x81931),x81933),x81932)),x81934))
% 51.10/50.83 [8194]~P60(x81941)+P1(f331(f331(f241(x81941),x81942),f2(x81941)))+~P1(f331(f331(f240(x81941),x81943),f2(x81941)))+P1(f331(f331(f240(x81941),x81943),f331(f331(f291(x81941),x81944),x81942)))+~P1(f331(f331(f240(x81941),f331(f331(f88(x81941),x81943),x81942)),x81944))
% 51.10/50.83 [8352]~P60(x83521)+~P1(f331(f331(f241(x83521),x83522),f2(x83521)))+P1(f331(f331(f241(x83521),f2(x83521)),x83522))+~P1(f331(f331(f241(x83521),f331(f331(f291(x83521),x83524),x83522)),x83523))+P1(f331(f331(f241(x83521),f331(f331(f88(x83521),x83523),x83522)),x83524))
% 51.10/50.83 [8353]~P60(x83531)+~P1(f331(f331(f241(x83531),x83532),f2(x83531)))+P1(f331(f331(f241(x83531),f2(x83531)),x83532))+~P1(f331(f331(f241(x83531),f331(f331(f88(x83531),x83534),x83532)),x83533))+P1(f331(f331(f241(x83531),f331(f331(f291(x83531),x83533),x83532)),x83534))
% 51.10/50.83 [8354]~P60(x83541)+~P1(f331(f331(f241(x83541),x83542),f2(x83541)))+P1(f331(f331(f241(x83541),f2(x83541)),x83542))+~P1(f331(f331(f240(x83541),f331(f331(f291(x83541),x83544),x83542)),x83543))+P1(f331(f331(f240(x83541),f331(f331(f88(x83541),x83543),x83542)),x83544))
% 51.10/50.83 [8355]~P60(x83551)+~P1(f331(f331(f241(x83551),x83552),f2(x83551)))+P1(f331(f331(f241(x83551),f2(x83551)),x83552))+~P1(f331(f331(f240(x83551),f331(f331(f88(x83551),x83554),x83552)),x83553))+P1(f331(f331(f240(x83551),f331(f331(f291(x83551),x83553),x83552)),x83554))
% 51.10/50.83 [8374]~P60(x83741)+~P1(f331(f331(f241(x83741),f2(x83741)),x83744))+P1(f331(f331(f241(x83741),f2(x83741)),x83742))+~P1(f331(f331(f241(x83741),f331(f331(f88(x83741),x83744),x83742)),x83743))+P1(f331(f331(f241(x83741),f331(f331(f291(x83741),x83743),x83742)),x83744))
% 51.10/50.83 [8375]~P60(x83751)+~P1(f331(f331(f240(x83751),f2(x83751)),x83754))+P1(f331(f331(f241(x83751),f2(x83751)),x83752))+~P1(f331(f331(f240(x83751),f331(f331(f88(x83751),x83754),x83752)),x83753))+P1(f331(f331(f240(x83751),f331(f331(f291(x83751),x83753),x83752)),x83754))
% 51.10/50.83 [8428]~P60(x84281)+~P92(x84281)+~P1(f331(f331(f241(x84281),f2(x84281)),x84284))+~P1(f331(f331(f241(x84281),f331(f331(f291(x84281),x84282),x84284)),f331(f111(x84281),x84283)))+P1(f331(f331(f241(x84281),x84282),f331(f331(f88(x84281),f331(f111(x84281),x84283)),x84284)))
% 51.10/50.83 [8429]~P60(x84291)+~P92(x84291)+~P1(f331(f331(f241(x84291),f2(x84291)),x84294))+~P1(f331(f331(f240(x84291),f331(f331(f291(x84291),x84292),x84294)),f331(f111(x84291),x84293)))+P1(f331(f331(f240(x84291),x84292),f331(f331(f88(x84291),f331(f111(x84291),x84293)),x84294)))
% 51.10/50.83 [8435]~P60(x84351)+~P92(x84351)+~P1(f331(f331(f241(x84351),f2(x84351)),x84353))+P1(f331(f331(f241(x84351),f331(f331(f291(x84351),x84352),x84353)),f331(f111(x84351),x84354)))+~P1(f331(f331(f241(x84351),x84352),f331(f331(f88(x84351),f331(f111(x84351),x84354)),x84353)))
% 51.10/50.83 [8436]~P60(x84361)+~P92(x84361)+~P1(f331(f331(f241(x84361),f2(x84361)),x84363))+P1(f331(f331(f240(x84361),f331(f331(f291(x84361),x84362),x84363)),f331(f111(x84361),x84364)))+~P1(f331(f331(f240(x84361),x84362),f331(f331(f88(x84361),f331(f111(x84361),x84364)),x84363)))
% 51.10/50.83 [8450]~P60(x84501)+~P1(f331(f331(f241(x84501),x84504),f2(x84501)))+~P1(f331(f331(f241(x84501),x84503),f331(f331(f88(x84501),x84502),x84504)))+P1(f331(f331(f241(x84501),x84502),f331(f331(f291(x84501),x84503),x84504)))+~P1(f331(f331(f241(x84501),f331(f331(f88(x84501),x84502),x84504)),x84503))
% 51.10/50.83 [8451]~P60(x84511)+~P1(f331(f331(f241(x84511),x84512),f2(x84511)))+~P1(f331(f331(f241(x84511),x84513),f331(f331(f88(x84511),x84512),x84514)))+P1(f331(f331(f241(x84511),x84512),f331(f331(f291(x84511),x84513),x84514)))+~P1(f331(f331(f241(x84511),f331(f331(f88(x84511),x84512),x84514)),x84513))
% 51.10/50.83 [8452]~P60(x84521)+~P1(f331(f331(f241(x84521),x84524),f2(x84521)))+~P1(f331(f331(f240(x84521),x84523),f331(f331(f88(x84521),x84522),x84524)))+P1(f331(f331(f240(x84521),x84522),f331(f331(f291(x84521),x84523),x84524)))+~P1(f331(f331(f240(x84521),f331(f331(f88(x84521),x84522),x84524)),x84523))
% 51.10/50.83 [8453]~P60(x84531)+~P1(f331(f331(f240(x84531),x84532),f2(x84531)))+~P1(f331(f331(f240(x84531),x84533),f331(f331(f88(x84531),x84532),x84534)))+P1(f331(f331(f240(x84531),x84532),f331(f331(f291(x84531),x84533),x84534)))+~P1(f331(f331(f240(x84531),f331(f331(f88(x84531),x84532),x84534)),x84533))
% 51.10/50.83 [8498]~P60(x84981)+~P92(x84981)+~P1(f331(f331(f241(x84981),f2(x84981)),f331(f111(x84981),x84983)))+~P1(f331(f331(f241(x84981),x84982),f331(f331(f291(x84981),x84984),f331(f111(x84981),x84983))))+P1(f331(f331(f241(x84981),f331(f331(f88(x84981),x84982),f331(f111(x84981),x84983))),x84984))
% 51.10/50.83 [8499]~P60(x84991)+~P92(x84991)+~P1(f331(f331(f241(x84991),f2(x84991)),f331(f111(x84991),x84993)))+~P1(f331(f331(f241(x84991),x84992),f331(f331(f88(x84991),x84994),f331(f111(x84991),x84993))))+P1(f331(f331(f241(x84991),f331(f331(f291(x84991),x84992),f331(f111(x84991),x84993))),x84994))
% 51.10/50.83 [8500]~P60(x85001)+~P92(x85001)+~P1(f331(f331(f241(x85001),f2(x85001)),f331(f111(x85001),x85003)))+~P1(f331(f331(f240(x85001),x85002),f331(f331(f291(x85001),x85004),f331(f111(x85001),x85003))))+P1(f331(f331(f240(x85001),f331(f331(f88(x85001),x85002),f331(f111(x85001),x85003))),x85004))
% 51.10/50.83 [8501]~P60(x85011)+~P92(x85011)+~P1(f331(f331(f241(x85011),f2(x85011)),f331(f111(x85011),x85013)))+~P1(f331(f331(f240(x85011),x85012),f331(f331(f88(x85011),x85014),f331(f111(x85011),x85013))))+P1(f331(f331(f240(x85011),f331(f331(f291(x85011),x85012),f331(f111(x85011),x85013))),x85014))
% 51.10/50.83 [8553]~P60(x85531)+~P1(f331(f331(f241(x85531),x85533),f2(x85531)))+~P1(f331(f331(f241(x85531),x85532),f331(f331(f88(x85531),x85534),x85533)))+~P1(f331(f331(f241(x85531),f331(f331(f88(x85531),x85534),x85533)),x85532))+P1(f331(f331(f241(x85531),f331(f331(f291(x85531),x85532),x85533)),x85534))
% 51.10/50.83 [8554]~P60(x85541)+~P1(f331(f331(f241(x85541),x85543),f2(x85541)))+~P1(f331(f331(f240(x85541),x85542),f331(f331(f88(x85541),x85544),x85543)))+~P1(f331(f331(f240(x85541),f331(f331(f88(x85541),x85544),x85543)),x85542))+P1(f331(f331(f240(x85541),f331(f331(f291(x85541),x85542),x85543)),x85544))
% 51.10/50.83 [8568]~P60(x85681)+~P1(f331(f331(f241(x85681),f2(x85681)),x85684))+~P1(f331(f331(f241(x85681),x85682),f331(f331(f88(x85681),x85684),x85683)))+~P1(f331(f331(f241(x85681),f331(f331(f88(x85681),x85684),x85683)),x85682))+P1(f331(f331(f241(x85681),f331(f331(f291(x85681),x85682),x85683)),x85684))
% 51.10/50.83 [8569]~P60(x85691)+~P1(f331(f331(f240(x85691),f2(x85691)),x85694))+~P1(f331(f331(f240(x85691),x85692),f331(f331(f88(x85691),x85694),x85693)))+~P1(f331(f331(f240(x85691),f331(f331(f88(x85691),x85694),x85693)),x85692))+P1(f331(f331(f240(x85691),f331(f331(f291(x85691),x85692),x85693)),x85694))
% 51.10/50.83 [8599]~P60(x85991)+~P92(x85991)+~P1(f331(f331(f241(x85991),f2(x85991)),f331(f111(x85991),x85994)))+P1(f331(f331(f241(x85991),x85992),f331(f331(f88(x85991),x85993),f331(f111(x85991),x85994))))+~P1(f331(f331(f241(x85991),f331(f331(f291(x85991),x85992),f331(f111(x85991),x85994))),x85993))
% 51.10/50.83 [8600]~P60(x86001)+~P92(x86001)+~P1(f331(f331(f241(x86001),f2(x86001)),f331(f111(x86001),x86004)))+P1(f331(f331(f241(x86001),x86002),f331(f331(f291(x86001),x86003),f331(f111(x86001),x86004))))+~P1(f331(f331(f241(x86001),f331(f331(f88(x86001),x86002),f331(f111(x86001),x86004))),x86003))
% 51.10/50.83 [8601]~P60(x86011)+~P92(x86011)+~P1(f331(f331(f241(x86011),f2(x86011)),f331(f111(x86011),x86014)))+P1(f331(f331(f240(x86011),x86012),f331(f331(f88(x86011),x86013),f331(f111(x86011),x86014))))+~P1(f331(f331(f240(x86011),f331(f331(f291(x86011),x86012),f331(f111(x86011),x86014))),x86013))
% 51.10/50.83 [8602]~P60(x86021)+~P92(x86021)+~P1(f331(f331(f241(x86021),f2(x86021)),f331(f111(x86021),x86024)))+P1(f331(f331(f240(x86021),x86022),f331(f331(f291(x86021),x86023),f331(f111(x86021),x86024))))+~P1(f331(f331(f240(x86021),f331(f331(f88(x86021),x86022),f331(f111(x86021),x86024))),x86023))
% 51.10/50.83 [8726]E(f331(f331(f3(a1),f467(x87261,x87262,x87263,x87264)),f468(x87261,x87262,x87263,x87264)),x87264)+~P1(f331(f331(f241(a1),f2(a1)),x87263))+~P1(f331(f331(f241(a1),x87264),x87262))+~P1(f331(f331(f333(a1),x87262),x87261))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x87264),x87263)),x87262))
% 51.10/50.83 [8787]~P1(f331(x87871,x87872))+~P1(f331(f331(f241(a1),f2(a1)),x87874))+~P1(f331(f331(f240(a1),f2(a1)),x87873))+~P1(f331(x87871,f331(f331(f87(a1),f799(x87873,x87871,x87874)),x87874)))+P1(f331(x87871,f331(f331(f87(a1),x87872),f331(f331(f88(a1),x87873),x87874))))
% 51.10/50.83 [8788]~P1(f331(x87881,x87882))+~P1(f331(f331(f241(a1),f2(a1)),x87884))+~P1(f331(f331(f240(a1),f2(a1)),x87883))+~P1(f331(x87881,f331(f331(f3(a1),f804(x87883,x87881,x87884)),x87884)))+P1(f331(x87881,f331(f331(f3(a1),x87882),f331(f331(f88(a1),x87883),x87884))))
% 51.10/50.83 [8925]~P1(f331(f331(f241(a1),f2(a1)),x89253))+~P1(f331(f331(f241(a1),x89254),x89252))+~P1(f331(f331(f333(a1),x89252),x89251))+P1(f331(f331(f333(a1),f467(x89251,x89252,x89253,x89254)),x89251))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x89254),x89253)),x89252))
% 51.10/50.83 [8945]E(f331(f331(f3(a1),f454(x89451,x89452,x89453,x89454)),f455(x89451,x89452,x89453,x89454)),x89454)+~P1(f331(f331(f241(a1),f2(a1)),x89453))+~P1(f331(f331(f240(a1),x89454),x89452))+~P1(f331(f331(f333(a1),f331(f331(f87(a1),x89452),f85(a1))),x89451))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x89454),x89453)),x89452))
% 51.10/50.83 [8973]~P1(f331(f331(f241(a1),f2(a1)),x89732))+~P1(f331(f331(f241(a1),x89731),x89733))+~P1(f331(f331(f333(a1),x89733),x89734))+P1(f331(f331(f333(a1),f468(x89734,x89733,x89732,x89731)),f303(a1,f85(a1),x89732)))+P1(f331(f331(f241(a1),f331(f331(f87(a1),x89731),x89732)),x89733))
% 51.10/50.83 [9054]~P1(f331(f331(f241(a1),f2(a1)),x90543))+~P1(f331(f331(f240(a1),x90544),x90542))+P1(f331(f331(f333(a1),f454(x90541,x90542,x90543,x90544)),x90541))+~P1(f331(f331(f333(a1),f331(f331(f87(a1),x90542),f85(a1))),x90541))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x90544),x90543)),x90542))
% 51.10/50.83 [9091]~P1(f331(f331(f241(a1),f2(a1)),x90912))+~P1(f331(f331(f240(a1),x90911),x90913))+P1(f331(f331(f333(a1),f455(x90914,x90913,x90912,x90911)),f303(a1,f85(a1),x90912)))+~P1(f331(f331(f333(a1),f331(f331(f87(a1),x90913),f85(a1))),x90914))+P1(f331(f331(f240(a1),f331(f331(f87(a1),x90911),x90912)),x90913))
% 51.10/50.83 [9359]~P34(x93591,x93593)+~P28(x93591,x93594)+P34(x93591,f331(f331(f108(f854(f853(x93591,x93591),a840)),x93592),x93593))+~P1(f331(f331(f240(f854(f853(x93591,x93591),a840)),x93592),f331(f248(f854(f853(x93591,x93591),a840),f854(f853(x93591,x93591),a840)),x93594)))+~P1(f331(f331(f240(f854(f853(x93591,x93591),a840)),x93593),f331(f258(f854(f853(x93591,x93591),a840),f854(f853(x93591,x93591),a840)),x93594)))
% 51.10/50.83 [9639]~E(f331(f708(x96391,x96394,x96393,x96392),f710(x96391,x96394,x96393,x96392)),f187(f848(a838)))+P1(f331(f331(f241(a1),f709(x96391,x96394,x96393,x96392)),f710(x96391,x96394,x96393,x96392)))+P1(f331(f331(f331(x96391,x96392),x96393),x96394))+P1(f331(f331(f331(x96391,f708(x96391,x96394,x96393,x96392)),f709(x96391,x96394,x96393,x96392)),f331(f331(f87(a1),f710(x96391,x96394,x96393,x96392)),f85(a1))))+~P1(f331(f320(f853(f854(a1,f851(f848(a838))),f853(a1,a1)),a318),f331(f331(f249(f854(a1,f851(f848(a838))),f853(a1,a1)),x96392),f331(f331(f249(a1,a1),x96393),x96394))))
% 51.10/50.83 [9741]~P20(x97412,x97414,x97413)+E(x97411,f184(f854(x97412,a840)))+~P1(f331(f68(x97412),x97411))+P1(f331(f331(f333(x97412),f331(x97413,x97411)),x97411))+~P1(f331(f331(f333(x97412),f331(f331(x97414,f386(x97411,x97413,x97414,x97412)),f387(x97411,x97413,x97414,x97412))),f331(f331(f310(x97412),f386(x97411,x97413,x97414,x97412)),f331(f331(f310(x97412),f387(x97411,x97413,x97414,x97412)),f184(f854(x97412,a840))))))
% 51.10/50.83 [8589]~P60(x85891)+~P92(x85891)+~P1(f331(f331(f241(x85891),f2(x85891)),x85893))+~P1(f331(f331(f241(x85891),f331(f111(x85891),x85892)),f331(f331(f291(x85891),x85894),x85893)))+P1(f331(f331(f241(x85891),f331(f331(f88(x85891),f331(f111(x85891),x85892)),x85893)),x85894))
% 51.10/50.83 [8590]~P60(x85901)+~P92(x85901)+~P1(f331(f331(f241(x85901),f2(x85901)),x85903))+~P1(f331(f331(f240(x85901),f331(f111(x85901),x85902)),f331(f331(f291(x85901),x85904),x85903)))+P1(f331(f331(f240(x85901),f331(f331(f88(x85901),f331(f111(x85901),x85902)),x85903)),x85904))
% 51.10/50.83 [8729]~P60(x87291)+~P92(x87291)+~P1(f331(f331(f241(x87291),f2(x87291)),x87294))+P1(f331(f331(f241(x87291),f331(f111(x87291),x87292)),f331(f331(f291(x87291),x87293),x87294)))+~P1(f331(f331(f241(x87291),f331(f331(f88(x87291),f331(f111(x87291),x87292)),x87294)),x87293))
% 51.10/50.83 [8730]~P60(x87301)+~P92(x87301)+~P1(f331(f331(f241(x87301),f2(x87301)),x87304))+P1(f331(f331(f240(x87301),f331(f111(x87301),x87302)),f331(f331(f291(x87301),x87303),x87304)))+~P1(f331(f331(f240(x87301),f331(f331(f88(x87301),f331(f111(x87301),x87302)),x87304)),x87303))
% 51.10/50.83 [9279]~P51(x92791,x92791,x92794)+P1(f331(f331(f333(f853(x92791,x92791)),f331(f331(f249(x92791,x92791),x92792),x92793)),f308(x92791,x92794)))+P1(f331(f331(f333(f853(x92791,x92791)),f331(f331(f249(x92791,x92791),x92793),x92792)),f308(x92791,x92794)))+~P1(f331(f331(f333(f853(x92791,x92791)),f331(f331(f249(x92791,x92791),x92795),x92792)),f308(x92791,x92794)))+~P1(f331(f331(f333(f853(x92791,x92791)),f331(f331(f249(x92791,x92791),x92795),x92793)),f308(x92791,x92794)))
% 51.10/50.83 [5464]E(x54641,f2(a847))+~E(f331(f47(x54642),x54645),x54641)+E(f331(f47(x54642),x54643),f331(a119,x54641))+~E(x54643,f331(f331(f310(x54642),x54644),x54645))+P1(f331(f331(f333(x54642),x54644),x54645))
% 51.10/50.83 [5587]~P59(x55872)+E(x55871,f2(x55872))+E(x55873,f2(x55872))+~E(f331(f331(f291(x55872),x55874),x55873),f331(f331(f291(x55872),x55875),x55871))+E(f331(f331(f88(x55872),x55874),x55871),f331(f331(f88(x55872),x55875),x55873))
% 51.10/50.83 [5588]~P59(x55882)+E(x55881,f2(x55882))+E(x55883,f2(x55882))+~E(f331(f331(f88(x55882),x55884),x55883),f331(f331(f88(x55882),x55885),x55881))+E(f331(f331(f291(x55882),x55884),x55881),f331(f331(f291(x55882),x55885),x55883))
% 51.10/50.83 [5661]~E(f331(f47(x56611),x56615),x56613)+~E(x56615,f184(f854(x56611,a840)))+E(f331(f47(x56611),x56612),f331(a119,x56613))+~E(x56612,f331(f331(f310(x56611),x56614),x56615))+P1(f331(f331(f333(x56611),x56614),x56615))
% 51.10/50.83 [5889]~P87(x58892)+~E(f331(x58893,x58895),f2(x58892))+E(f331(f331(f11(x58891,x58892),x58893),x58894),f2(x58892))+~P1(f331(f68(x58891),x58894))+~P1(f331(f331(f333(x58891),x58895),x58894))
% 51.10/50.83 [6273]~P102(x62733)+E(x62731,x62732)+~E(f331(f302(x62733,x62734),x62731),f331(f302(x62733,x62735),x62732))+~P1(f331(f331(f241(x62733),x62735),x62732))+~P1(f331(f331(f241(x62733),x62734),x62731))
% 51.10/50.83 [6274]~P102(x62743)+E(x62741,x62742)+~E(f331(f302(x62743,x62741),x62744),f331(f302(x62743,x62742),x62745))+~P1(f331(f331(f241(x62743),x62742),x62745))+~P1(f331(f331(f241(x62743),x62741),x62744))
% 51.10/50.83 [6275]~P102(x62753)+E(x62751,x62752)+~E(f331(f302(x62753,x62754),x62751),f331(f302(x62753,x62755),x62752))+~P1(f331(f331(f241(x62753),x62755),x62752))+~P1(f331(f331(f241(x62753),x62754),x62751))
% 51.10/50.83 [6276]~P102(x62763)+E(x62761,x62762)+~E(f331(f302(x62763,x62761),x62764),f331(f302(x62763,x62762),x62765))+~P1(f331(f331(f241(x62763),x62762),x62765))+~P1(f331(f331(f241(x62763),x62761),x62764))
% 51.10/50.83 [7382]~P102(x73821)+~P16(x73821,f331(f331(f130(x73821),x73824),x73825))+~P1(f331(f331(f333(x73821),x73823),f331(f163(x73821),x73825)))+~P1(f331(f331(f333(x73821),x73822),f331(f163(x73821),x73824)))+P1(f331(f331(f240(x73821),x73822),x73823))
% 51.10/50.83 [8484]~P88(x84841)+~P1(f331(f331(f241(f854(x84841,a840)),f303(x84841,x84845,x84842)),f303(x84841,x84844,x84843)))+~P1(f331(f331(f240(x84841),x84845),x84842))+P1(f331(f331(f241(x84841),x84842),x84843))+P1(f331(f331(f241(x84841),x84844),x84845))
% 51.10/50.83 [9785]~P19(x97852,x97855,x97853)+E(x97851,f184(f854(x97852,a840)))+~E(f331(f331(x97855,f331(x97854,f561(x97851,x97854,x97853,x97855,x97852))),f331(x97854,f562(x97851,x97854,x97853,x97855,x97852))),f331(x97854,f331(f331(x97855,f561(x97851,x97854,x97853,x97855,x97852)),f562(x97851,x97854,x97853,x97855,x97852))))+E(f331(x97853,f331(f311(x97852,x97852,x97854),x97851)),f331(x97854,f331(x97853,x97851)))+~P1(f331(f68(x97852),x97851))
% 51.10/50.83 [6272]~P20(x62722,x62725,x62723)+E(x62721,f184(f854(x62722,a840)))+~P1(f331(f68(x62722),x62721))+E(f331(x62723,f331(f331(f310(x62722),x62724),x62721)),f331(f331(x62725,x62724),f331(x62723,x62721)))+P1(f331(f331(f333(x62722),x62724),x62721))
% 51.10/50.83 [7121]~P19(x71212,x71213,x71214)+E(f331(f331(x71213,f331(x71214,x71211)),f331(x71214,x71215)),f331(x71214,x71215))+E(x71211,f184(f854(x71212,a840)))+~P1(f331(f68(x71212),x71215))+~P1(f331(f331(f240(f854(x71212,a840)),x71211),x71215))
% 51.10/50.83 [7524]~P20(x75244,x75245,x75241)+E(f331(x75241,x75242),x75243)+~P1(f331(f68(x75244),x75242))+~E(f331(f331(f3(f854(x75244,a840)),x75242),f331(f331(f310(x75244),x75243),f184(f854(x75244,a840)))),f184(f854(x75244,a840)))+~P1(f331(f331(f333(x75244),x75243),x75242))
% 51.10/50.83 [7671]E(x76711,x76712)+~E(f331(f185(f848(x76713)),x76712),f331(f185(f848(x76714)),x76715))+~E(f331(f185(f848(x76713)),x76711),f331(f185(f848(x76714)),x76715))+~E(f171(x76714,x76713,f331(f331(f172(x76714,x76713),x76715),x76711)),f171(x76714,x76713,f331(f331(f172(x76714,x76713),x76715),x76712)))+~P1(f331(f132(x76714),x76715))
% 51.10/50.83 [8410]~P70(x84101)+~P113(x84101)+~P1(f331(f68(x84102),x84105))+P1(f331(f331(f287(x84101),f331(f331(f11(x84102,x84101),x84103),x84104)),f331(f331(f11(x84102,x84101),x84103),x84105)))+~P1(f331(f331(f240(f854(x84102,a840)),x84104),x84105))
% 51.10/50.83 [8457]E(x84571,x84572)+~P10(x84573,x84574,x84575)+E(f331(f331(f109(f854(x84573,a840)),x84571),x84572),f184(f854(x84573,a840)))+~P1(f331(f331(f333(f854(x84573,a840)),x84572),f331(f331(f66(x84573),x84574),x84575)))+~P1(f331(f331(f333(f854(x84573,a840)),x84571),f331(f331(f66(x84573),x84574),x84575)))
% 51.10/50.83 [8858]~P27(x88581,x88583,x88585,x88582)+~P1(f331(f68(x88583),x88584))+~P1(f331(f68(x88581),x88582))+P1(f331(f331(f240(a847),f331(f47(x88581),x88582)),f331(f47(x88583),x88584)))+~P1(f331(f331(f240(f854(x88583,a840)),f331(f311(x88581,x88583,x88585),x88582)),x88584))
% 51.10/50.83 [9156]~P70(x91562)+~E(f331(x91563,f435(x91563,x91564,x91565,x91561,x91562)),f85(x91562))+E(f331(f331(f11(x91561,x91562),x91563),x91564),f331(f331(f11(x91561,x91562),x91563),x91565))+~P1(f331(f68(x91561),x91565))+~P1(f331(f331(f240(f854(x91561,a840)),x91564),x91565))
% 51.10/50.83 [9157]~P70(x91572)+~E(f331(x91573,f436(x91573,x91574,x91575,x91571,x91572)),f85(x91572))+E(f331(f331(f11(x91571,x91572),x91573),x91574),f331(f331(f11(x91571,x91572),x91573),x91575))+~P1(f331(f68(x91571),x91575))+~P1(f331(f331(f240(f854(x91571,a840)),x91574),x91575))
% 51.10/50.83 [9158]~P68(x91582)+~E(f331(x91583,f506(x91583,x91584,x91585,x91581,x91582)),f2(x91582))+E(f331(f331(f8(x91581,x91582),x91583),x91584),f331(f331(f8(x91581,x91582),x91583),x91585))+~P1(f331(f68(x91581),x91585))+~P1(f331(f331(f240(f854(x91581,a840)),x91584),x91585))
% 51.10/50.83 [9159]~P68(x91592)+~E(f331(x91593,f512(x91593,x91594,x91595,x91591,x91592)),f2(x91592))+E(f331(f331(f8(x91591,x91592),x91593),x91594),f331(f331(f8(x91591,x91592),x91593),x91595))+~P1(f331(f68(x91591),x91595))+~P1(f331(f331(f240(f854(x91591,a840)),x91594),x91595))
% 51.10/50.83 [9622]~P80(x96221)+~P1(f331(f68(x96222),x96225))+~P1(f331(f331(f240(x96221),f2(x96221)),f331(x96223,f497(x96223,x96224,x96225,x96222,x96221))))+P1(f331(f331(f240(x96221),f331(f331(f8(x96222,x96221),x96223),x96224)),f331(f331(f8(x96222,x96221),x96223),x96225)))+~P1(f331(f331(f240(f854(x96222,a840)),x96224),x96225))
% 51.10/50.83 [7379]E(x73791,f2(a847))+P1(f331(x73792,x73793))+~E(x73794,f331(f331(f87(a847),f331(f331(f88(a847),x73791),x73793)),x73795))+~P1(f331(f331(f241(a847),x73795),x73791))+~P1(f331(x73792,f331(f331(f48(a847),x73794),x73791)))
% 51.10/50.83 [7463]E(x74631,f2(a847))+P1(f331(x74632,x74633))+~P1(f331(x74632,f57(a847,x74634,x74631)))+~E(x74634,f331(f331(f87(a847),f331(f331(f88(a847),x74631),x74635)),x74633))+~P1(f331(f331(f241(a847),x74633),x74631))
% 51.10/50.83 [7759]~P59(x77593)+E(f331(x77591,x77592),f2(x77593))+~P1(f331(f68(x77594),x77595))+E(f331(f331(f11(x77594,x77593),x77591),f331(f331(f3(f854(x77594,a840)),x77595),f331(f331(f310(x77594),x77592),f184(f854(x77594,a840))))),f331(f331(f11(x77594,x77593),x77591),x77595))+P1(f331(f331(f333(x77594),x77592),x77595))
% 51.10/50.83 [8153]~P70(x81531)+~P1(f331(f68(x81532),x81535))+~P1(f331(f68(x81532),x81534))+~E(f331(f331(f109(f854(x81532,a840)),x81534),x81535),f184(f854(x81532,a840)))+E(f331(f331(f88(x81531),f331(f331(f11(x81532,x81531),x81533),x81534)),f331(f331(f11(x81532,x81531),x81533),x81535)),f331(f331(f11(x81532,x81531),x81533),f331(f331(f108(f854(x81532,a840)),x81534),x81535)))
% 51.10/50.83 [8154]~P70(x81541)+~P1(f331(f68(x81542),x81545))+~P1(f331(f68(x81542),x81544))+~E(f331(f331(f109(f854(x81542,a840)),x81544),x81545),f184(f854(x81542,a840)))+E(f331(f331(f88(x81541),f331(f331(f11(x81542,x81541),x81543),x81544)),f331(f331(f11(x81542,x81541),x81543),x81545)),f331(f331(f11(x81542,x81541),x81543),f331(f331(f108(f854(x81542,a840)),x81544),x81545)))
% 51.10/50.83 [8155]~P68(x81551)+~P1(f331(f68(x81552),x81555))+~P1(f331(f68(x81552),x81554))+~E(f331(f331(f109(f854(x81552,a840)),x81554),x81555),f184(f854(x81552,a840)))+E(f331(f331(f87(x81551),f331(f331(f8(x81552,x81551),x81553),x81554)),f331(f331(f8(x81552,x81551),x81553),x81555)),f331(f331(f8(x81552,x81551),x81553),f331(f331(f108(f854(x81552,a840)),x81554),x81555)))
% 51.10/50.83 [8247]~P59(x82473)+E(f331(x82471,x82472),f2(x82473))+~P1(f331(f68(x82474),x82475))+E(f331(f331(f11(x82474,x82473),x82471),f331(f331(f3(f854(x82474,a840)),x82475),f331(f331(f310(x82474),x82472),f184(f854(x82474,a840))))),f331(f331(f291(x82473),f331(f331(f11(x82474,x82473),x82471),x82475)),f331(x82471,x82472)))+~P1(f331(f331(f333(x82474),x82472),x82475))
% 51.10/50.83 [8741]~P10(x87411,x87415,x87414)+~E(f331(f285(x87411,x87411,x87414),f331(f331(f310(x87411),x87412),f184(f854(x87411,a840)))),f331(f285(x87411,x87411,x87414),f331(f331(f310(x87411),x87413),f184(f854(x87411,a840)))))+~P1(f331(f331(f333(x87411),x87413),x87415))+~P1(f331(f331(f333(x87411),x87412),x87415))+P1(f331(f331(f333(f853(x87411,x87411)),f331(f331(f249(x87411,x87411),x87412),x87413)),x87414))
% 51.10/50.83 [8742]~P10(x87421,x87425,x87424)+~E(f331(f285(x87421,x87421,x87424),f331(f331(f310(x87421),x87422),f184(f854(x87421,a840)))),f331(f285(x87421,x87421,x87424),f331(f331(f310(x87421),x87423),f184(f854(x87421,a840)))))+~P1(f331(f331(f333(x87421),x87423),x87425))+~P1(f331(f331(f333(x87421),x87422),x87425))+P1(f331(f331(f333(f853(x87421,x87421)),f331(f331(f249(x87421,x87421),x87422),x87423)),x87424))
% 51.10/50.83 [8820]~P10(x88201,x88205,x88202)+E(f331(f285(x88201,x88201,x88202),f331(f331(f310(x88201),x88203),f184(f854(x88201,a840)))),f331(f285(x88201,x88201,x88202),f331(f331(f310(x88201),x88204),f184(f854(x88201,a840)))))+~P1(f331(f331(f333(x88201),x88204),x88205))+~P1(f331(f331(f333(x88201),x88203),x88205))+~P1(f331(f331(f333(f853(x88201,x88201)),f331(f331(f249(x88201,x88201),x88203),x88204)),x88202))
% 51.10/50.83 [8907]~P10(x89071,x89075,x89074)+~E(f331(f331(f66(x89071),f331(f331(f310(x89071),x89072),f184(f854(x89071,a840)))),x89074),f331(f331(f66(x89071),f331(f331(f310(x89071),x89073),f184(f854(x89071,a840)))),x89074))+~P1(f331(f331(f333(x89071),x89073),x89075))+~P1(f331(f331(f333(x89071),x89072),x89075))+P1(f331(f331(f333(f853(x89071,x89071)),f331(f331(f249(x89071,x89071),x89072),x89073)),x89074))
% 51.10/50.83 [8924]~P10(x89241,x89245,x89243)+E(f331(f331(f66(x89241),f331(f331(f310(x89241),x89242),f184(f854(x89241,a840)))),x89243),f331(f331(f66(x89241),f331(f331(f310(x89241),x89244),f184(f854(x89241,a840)))),x89243))+~P1(f331(f331(f333(x89241),x89244),x89245))+~P1(f331(f331(f333(x89241),x89242),x89245))+~P1(f331(f331(f333(f853(x89241,x89241)),f331(f331(f249(x89241,x89241),x89242),x89244)),x89243))
% 51.10/50.83 [9183]~P70(x91831)+~P1(f331(f68(x91832),x91835))+~P1(f331(f68(x91832),x91834))+~E(f331(f331(f109(f854(x91832,a840)),x91834),x91835),f184(f854(x91832,a840)))+E(f331(f331(f88(x91831),f331(f331(f331(f72(x91831,x91832,f88(x91831)),x91833),f85(x91831)),x91834)),f331(f331(f331(f72(x91831,x91832,f88(x91831)),x91833),f85(x91831)),x91835)),f331(f331(f331(f72(x91831,x91832,f88(x91831)),x91833),f85(x91831)),f331(f331(f108(f854(x91832,a840)),x91834),x91835)))
% 51.10/50.83 [9193]~P70(x91931)+~E(f331(x91933,f398(x91933,x91935,x91934,x91932,x91931)),f85(x91931))+~P1(f331(f68(x91932),x91934))+~P1(f331(f68(x91932),x91935))+E(f331(f331(f88(x91931),f331(f331(f11(x91932,x91931),x91933),x91934)),f331(f331(f11(x91932,x91931),x91933),x91935)),f331(f331(f11(x91932,x91931),x91933),f331(f331(f108(f854(x91932,a840)),x91934),x91935)))
% 51.10/50.83 [9194]~P70(x91941)+~E(f331(x91943,f400(x91943,x91945,x91944,x91942,x91941)),f85(x91941))+~P1(f331(f68(x91942),x91944))+~P1(f331(f68(x91942),x91945))+E(f331(f331(f88(x91941),f331(f331(f11(x91942,x91941),x91943),x91944)),f331(f331(f11(x91942,x91941),x91943),x91945)),f331(f331(f11(x91942,x91941),x91943),f331(f331(f108(f854(x91942,a840)),x91944),x91945)))
% 51.10/50.83 [9195]~P68(x91951)+~E(f331(x91953,f494(x91953,x91955,x91954,x91952,x91951)),f2(x91951))+~P1(f331(f68(x91952),x91954))+~P1(f331(f68(x91952),x91955))+E(f331(f331(f87(x91951),f331(f331(f8(x91952,x91951),x91953),x91954)),f331(f331(f8(x91952,x91951),x91953),x91955)),f331(f331(f8(x91952,x91951),x91953),f331(f331(f108(f854(x91952,a840)),x91954),x91955)))
% 51.10/50.83 [9196]~P68(x91961)+~E(f331(x91963,f507(x91963,x91965,x91964,x91962,x91961)),f2(x91961))+~P1(f331(f68(x91962),x91964))+~P1(f331(f68(x91962),x91965))+E(f331(f331(f87(x91961),f331(f331(f8(x91962,x91961),x91963),x91964)),f331(f331(f8(x91962,x91961),x91963),x91965)),f331(f331(f8(x91962,x91961),x91963),f331(f331(f108(f854(x91962,a840)),x91964),x91965)))
% 51.10/50.83 [9403]~P70(x94031)+~E(f331(x94033,f424(x94033,x94035,x94034,x94032,x94031)),f85(x94031))+~P1(f331(f68(x94032),x94034))+~P1(f331(f68(x94032),x94035))+E(f331(f331(f88(x94031),f331(f331(f331(f72(x94031,x94032,f88(x94031)),x94033),f85(x94031)),x94034)),f331(f331(f331(f72(x94031,x94032,f88(x94031)),x94033),f85(x94031)),x94035)),f331(f331(f331(f72(x94031,x94032,f88(x94031)),x94033),f85(x94031)),f331(f331(f108(f854(x94032,a840)),x94034),x94035)))
% 51.10/50.83 [9508]~P70(x95082)+E(f331(f331(f11(x95081,x95082),x95083),x95084),f331(f331(f11(x95081,x95082),x95083),x95085))+~P1(f331(f68(x95081),x95085))+~P1(f331(f331(f240(f854(x95081,a840)),x95084),x95085))+P1(f331(f331(f333(x95081),f435(x95083,x95084,x95085,x95081,x95082)),f331(f331(f3(f854(x95081,a840)),x95085),x95084)))
% 51.10/50.83 [9509]~P70(x95092)+E(f331(f331(f11(x95091,x95092),x95093),x95094),f331(f331(f11(x95091,x95092),x95093),x95095))+~P1(f331(f68(x95091),x95095))+~P1(f331(f331(f240(f854(x95091,a840)),x95094),x95095))+P1(f331(f331(f333(x95091),f436(x95093,x95094,x95095,x95091,x95092)),f331(f331(f3(f854(x95091,a840)),x95095),x95094)))
% 51.10/50.83 [9510]~P68(x95102)+E(f331(f331(f8(x95101,x95102),x95103),x95104),f331(f331(f8(x95101,x95102),x95103),x95105))+~P1(f331(f68(x95101),x95105))+~P1(f331(f331(f240(f854(x95101,a840)),x95104),x95105))+P1(f331(f331(f333(x95101),f506(x95103,x95104,x95105,x95101,x95102)),f331(f331(f3(f854(x95101,a840)),x95105),x95104)))
% 51.10/50.83 [9511]~P68(x95112)+E(f331(f331(f8(x95111,x95112),x95113),x95114),f331(f331(f8(x95111,x95112),x95113),x95115))+~P1(f331(f68(x95111),x95115))+~P1(f331(f331(f240(f854(x95111,a840)),x95114),x95115))+P1(f331(f331(f333(x95111),f512(x95113,x95114,x95115,x95111,x95112)),f331(f331(f3(f854(x95111,a840)),x95115),x95114)))
% 51.10/50.83 [9526]~P70(x95261)+~P1(f331(f68(x95262),x95264))+~P1(f331(f68(x95262),x95265))+E(f331(f331(f88(x95261),f331(f331(f11(x95262,x95261),x95263),x95264)),f331(f331(f11(x95262,x95261),x95263),x95265)),f331(f331(f11(x95262,x95261),x95263),f331(f331(f108(f854(x95262,a840)),x95264),x95265)))+P1(f331(f331(f333(x95262),f398(x95263,x95265,x95264,x95262,x95261)),f331(f331(f109(f854(x95262,a840)),x95264),x95265)))
% 51.10/50.83 [9527]~P70(x95271)+~P1(f331(f68(x95272),x95274))+~P1(f331(f68(x95272),x95275))+E(f331(f331(f88(x95271),f331(f331(f11(x95272,x95271),x95273),x95274)),f331(f331(f11(x95272,x95271),x95273),x95275)),f331(f331(f11(x95272,x95271),x95273),f331(f331(f108(f854(x95272,a840)),x95274),x95275)))+P1(f331(f331(f333(x95272),f400(x95273,x95275,x95274,x95272,x95271)),f331(f331(f109(f854(x95272,a840)),x95274),x95275)))
% 51.10/50.83 [9528]~P68(x95281)+~P1(f331(f68(x95282),x95284))+~P1(f331(f68(x95282),x95285))+E(f331(f331(f87(x95281),f331(f331(f8(x95282,x95281),x95283),x95284)),f331(f331(f8(x95282,x95281),x95283),x95285)),f331(f331(f8(x95282,x95281),x95283),f331(f331(f108(f854(x95282,a840)),x95284),x95285)))+P1(f331(f331(f333(x95282),f494(x95283,x95285,x95284,x95282,x95281)),f331(f331(f109(f854(x95282,a840)),x95284),x95285)))
% 51.10/50.83 [9529]~P68(x95291)+~P1(f331(f68(x95292),x95294))+~P1(f331(f68(x95292),x95295))+E(f331(f331(f87(x95291),f331(f331(f8(x95292,x95291),x95293),x95294)),f331(f331(f8(x95292,x95291),x95293),x95295)),f331(f331(f8(x95292,x95291),x95293),f331(f331(f108(f854(x95292,a840)),x95294),x95295)))+P1(f331(f331(f333(x95292),f507(x95293,x95295,x95294,x95292,x95291)),f331(f331(f109(f854(x95292,a840)),x95294),x95295)))
% 51.10/50.83 [9541]~P80(x95415)+~P1(f331(f68(x95411),x95414))+P1(f331(f331(f240(x95415),f331(f331(f8(x95411,x95415),x95412),x95413)),f331(f331(f8(x95411,x95415),x95412),x95414)))+~P1(f331(f331(f240(f854(x95411,a840)),x95413),x95414))+P1(f331(f331(f333(x95411),f497(x95412,x95413,x95414,x95411,x95415)),f331(f331(f3(f854(x95411,a840)),x95414),x95413)))
% 51.10/50.83 [9588]~P70(x95881)+~P1(f331(f68(x95882),x95884))+~P1(f331(f68(x95882),x95885))+E(f331(f331(f88(x95881),f331(f331(f331(f72(x95881,x95882,f88(x95881)),x95883),f85(x95881)),x95884)),f331(f331(f331(f72(x95881,x95882,f88(x95881)),x95883),f85(x95881)),x95885)),f331(f331(f331(f72(x95881,x95882,f88(x95881)),x95883),f85(x95881)),f331(f331(f108(f854(x95882,a840)),x95884),x95885)))+P1(f331(f331(f333(x95882),f424(x95883,x95885,x95884,x95882,x95881)),f331(f331(f109(f854(x95882,a840)),x95884),x95885)))
% 51.10/50.83 [8635]~P20(x86351,x86354,x86355)+~P1(f331(f68(x86351),x86352))+E(f331(f331(f3(f854(x86351,a840)),x86352),f331(f331(f310(x86351),x86353),f184(f854(x86351,a840)))),f184(f854(x86351,a840)))+~P1(f331(f331(f333(x86351),x86353),x86352))+E(f331(f331(x86354,x86353),f331(x86355,f331(f331(f3(f854(x86351,a840)),x86352),f331(f331(f310(x86351),x86353),f184(f854(x86351,a840)))))),f331(x86355,x86352))
% 51.10/50.83 [8702]~P20(x87021,x87024,x87025)+~P1(f331(f68(x87021),x87023))+~P1(f331(f68(x87021),x87022))+E(f331(f331(f109(f854(x87021,a840)),x87022),x87023),f184(f854(x87021,a840)))+E(f331(f331(x87024,f331(x87025,f331(f331(f108(f854(x87021,a840)),x87022),x87023))),f331(x87025,f331(f331(f109(f854(x87021,a840)),x87022),x87023))),f331(f331(x87024,f331(x87025,x87022)),f331(x87025,x87023)))
% 51.10/50.83 [9198]~P1(f331(f331(f240(a1),x91984),f2(a1)))+~P1(f331(f331(f241(a1),x91983),x91985))+P1(f331(f331(f240(a1),x91981),x91982))+~P1(f331(f331(f241(a1),x91983),x91984))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),f331(f331(f88(a1),x91983),x91982)),x91985)),f331(f331(f87(a1),f331(f331(f88(a1),x91983),x91981)),x91984)))
% 51.10/50.83 [9200]~P1(f331(f331(f240(a1),f2(a1)),x92005))+P1(f331(f331(f240(a1),x92001),x92002))+~P1(f331(f331(f241(a1),x92003),x92004))+~P1(f331(f331(f241(a1),x92005),x92004))+~P1(f331(f331(f240(a1),f331(f331(f87(a1),f331(f331(f88(a1),x92004),x92001)),x92005)),f331(f331(f87(a1),f331(f331(f88(a1),x92004),x92002)),x92003)))
% 51.10/50.83 [9314]~P59(x93145)+E(f331(x93141,f399(x93141,x93142,x93143,x93144,x93145)),f2(x93145))+~P1(f331(f68(x93144),x93143))+~P1(f331(f68(x93144),x93142))+E(f331(f331(f291(x93145),f331(f331(f88(x93145),f331(f331(f11(x93144,x93145),x93141),x93143)),f331(f331(f11(x93144,x93145),x93141),x93142))),f331(f331(f11(x93144,x93145),x93141),f331(f331(f109(f854(x93144,a840)),x93143),x93142))),f331(f331(f11(x93144,x93145),x93141),f331(f331(f108(f854(x93144,a840)),x93143),x93142)))
% 51.10/50.83 [9581]~P59(x95811)+~P1(f331(f68(x95812),x95814))+~P1(f331(f68(x95812),x95815))+E(f331(f331(f291(x95811),f331(f331(f88(x95811),f331(f331(f11(x95812,x95811),x95813),x95814)),f331(f331(f11(x95812,x95811),x95813),x95815))),f331(f331(f11(x95812,x95811),x95813),f331(f331(f109(f854(x95812,a840)),x95814),x95815))),f331(f331(f11(x95812,x95811),x95813),f331(f331(f108(f854(x95812,a840)),x95814),x95815)))+P1(f331(f331(f333(x95812),f399(x95813,x95815,x95814,x95812,x95811)),f331(f331(f109(f854(x95812,a840)),x95814),x95815)))
% 51.10/50.83 [8944]E(f331(f331(f130(x89441),x89442),x89443),f331(f331(f130(x89441),x89444),x89445))+~E(f331(f331(f164(x89441),f331(f185(f848(x89441)),x89444)),x89442),x89444)+~E(f331(f331(f164(x89441),f331(f185(f848(x89441)),x89442)),x89444),x89442)+~E(x89445,f331(f331(f130(x89441),f331(f331(f133(x89441),f331(f185(f848(x89441)),x89444)),x89442)),x89443))+~E(f331(f331(f130(x89441),f331(f331(f133(x89441),f331(f185(f848(x89441)),x89442)),x89444)),x89445),x89443)
% 51.10/50.83 [9312]~P102(x93122)+E(f331(f331(f143(x93121,x93122,x93123),x93124),f161(x93121,x93124,x93125)),x93125)+~P16(x93122,f331(f331(f147(x93121,x93122),x93123),x93125))+~P1(f331(f331(f333(x93121),x93124),f331(f163(x93121),x93125)))+~E(f331(f136(x93121),f331(f131(x93121,f331(f331(f10(x93122,a840,x93121),f331(a328,f331(x93123,x93124))),x93123)),x93125)),x93124)
% 51.10/50.83 [9636]~P64(x96361)+~P1(f331(f73(x96361,x96361,f88(x96361),x96362,x96363),x96365))+~P1(f331(f331(f333(x96361),x96364),x96363))+P1(f331(f331(f333(x96361),x96362),x96363))+P1(f331(f73(x96361,x96361,f88(x96361),x96364,f331(f331(f310(x96361),x96362),f331(f331(f3(f854(x96361,a840)),x96363),f331(f331(f310(x96361),x96364),f184(f854(x96361,a840)))))),x96365))
% 51.10/50.83 [7125]E(x71251,x71252)+~P27(x71254,x71255,x71253,x71256)+~E(f331(x71253,x71251),f331(x71253,x71252))+~P1(f331(f331(f333(x71254),x71252),x71256))+~P1(f331(f331(f333(x71254),x71251),x71256))
% 51.10/50.83 [7126]E(x71261,x71262)+~P27(x71264,x71265,x71263,x71266)+~E(f331(x71263,x71261),f331(x71263,x71262))+~P1(f331(f331(f333(x71264),x71262),x71266))+~P1(f331(f331(f333(x71264),x71261),x71266))
% 51.10/50.83 [7127]E(x71271,x71272)+~P27(x71274,x71275,x71273,x71276)+~E(f331(x71273,x71271),f331(x71273,x71272))+~P1(f331(f331(f333(x71274),x71272),x71276))+~P1(f331(f331(f333(x71274),x71271),x71276))
% 51.10/50.83 [7128]E(x71281,x71282)+~P27(x71284,x71285,x71283,x71286)+~E(f331(x71283,x71281),f331(x71283,x71282))+~P1(f331(f331(f333(x71284),x71282),x71286))+~P1(f331(f331(f333(x71284),x71281),x71286))
% 51.10/50.83 [6370]~P137(x63704)+E(x63701,x63702)+~E(x63705,x63706)+E(x63703,f2(x63704))+~E(f331(f331(f87(x63704),x63705),f331(f331(f88(x63704),x63703),x63701)),f331(f331(f87(x63704),x63706),f331(f331(f88(x63704),x63703),x63702)))
% 51.10/50.83 [7443]~P102(x74431)+~P7(x74431)+~P1(f331(f331(f241(x74431),x74432),f331(x74435,x74436)))+~P1(f331(f331(f333(x74433),x74436),x74434))+P1(f331(f331(f241(x74431),x74432),f331(f331(f51(x74433,x74431),x74434),x74435)))
% 51.10/50.83 [9802]~P87(x98026)+~P1(f331(f68(x98021),x98025))+P1(f331(f331(f333(x98021),f629(x98022,x98023,x98024,x98025,x98021,x98026)),x98024))+P1(f331(f331(f287(x98026),f331(f331(f11(x98021,x98026),x98023),x98024)),f331(f331(f11(x98021,x98026),x98022),x98025)))+~P1(f331(f331(f240(f854(x98021,a840)),x98024),x98025))
% 51.10/50.83 [9927]~P87(x99271)+~P1(f331(f68(x99272),x99276))+~P1(f331(f331(f287(x99271),f331(x99273,f629(x99275,x99273,x99274,x99276,x99272,x99271))),f331(x99275,f629(x99275,x99273,x99274,x99276,x99272,x99271))))+P1(f331(f331(f287(x99271),f331(f331(f11(x99272,x99271),x99273),x99274)),f331(f331(f11(x99272,x99271),x99275),x99276)))+~P1(f331(f331(f240(f854(x99272,a840)),x99274),x99276))
% 51.10/50.83 [8124]~P102(x81241)+~P7(x81241)+~P1(f331(f331(f241(x81241),f331(x81244,x81246)),x81245))+~P1(f331(f331(f333(x81242),x81246),x81243))+P1(f331(f331(f241(x81241),f331(f331(f52(x81242,x81241),x81243),x81244)),x81245))
% 51.10/50.83 [8381]~P21(x83812,x83815,x83816,x83811)+~P1(f331(f68(x83812),x83814))+~P1(f331(f68(x83812),x83813))+~E(f331(f331(f109(f854(x83812,a840)),x83813),x83814),f184(f854(x83812,a840)))+E(f331(x83811,f331(f331(f108(f854(x83812,a840)),x83813),x83814)),f331(f80(x83815,x83815,x83815,f331(x83811,x83813)),f331(x83811,x83814)))
% 51.10/50.83 [9028]~P113(x90281)+~P110(x90281)+~P1(f331(f331(f287(x90281),x90282),x90285))+~P1(f331(f331(f287(x90281),x90282),f331(f331(f87(x90281),x90283),x90286)))+P1(f331(f331(f287(x90281),x90282),f331(f331(f87(x90281),f331(f331(f3(x90281),x90283),f331(f331(f88(x90281),x90284),x90285))),x90286)))
% 51.10/50.83 [9029]~P113(x90291)+~P110(x90291)+~P1(f331(f331(f287(x90291),x90292),x90295))+~P1(f331(f331(f287(x90291),x90292),f331(f331(f87(x90291),x90293),x90296)))+P1(f331(f331(f287(x90291),x90292),f331(f331(f87(x90291),f331(f331(f3(x90291),x90293),f331(f331(f88(x90291),x90294),x90295))),x90296)))
% 51.10/50.83 [9187]~P113(x91871)+~P110(x91871)+~P1(f331(f331(f287(x91871),x91872),x91875))+P1(f331(f331(f287(x91871),x91872),f331(f331(f87(x91871),x91873),x91874)))+~P1(f331(f331(f287(x91871),x91872),f331(f331(f87(x91871),f331(f331(f3(x91871),x91873),f331(f331(f88(x91871),x91876),x91875))),x91874)))
% 51.10/50.83 [9188]~P113(x91881)+~P110(x91881)+~P1(f331(f331(f287(x91881),x91882),x91885))+P1(f331(f331(f287(x91881),x91882),f331(f331(f87(x91881),x91883),x91884)))+~P1(f331(f331(f287(x91881),x91882),f331(f331(f87(x91881),f331(f331(f3(x91881),x91883),f331(f331(f88(x91881),x91886),x91885))),x91884)))
% 51.10/50.83 [8673]E(x86731,x86732)+~P53(x86734,x86735,x86736,x86733,x86737)+~E(f331(x86733,x86731),f331(x86733,x86732))+~P1(f331(f331(f333(x86735),x86732),x86737))+~P1(f331(f331(f333(x86735),x86731),x86737))
% 51.10/50.83 [9936]~P10(x99361,x99367,x99366)+~P14(x99361,f854(x99365,a840),x99366,x99364)+P1(f331(f331(f333(x99361),f419(x99362,x99363,x99364,x99365,x99366,x99367,x99361)),x99367))+~P1(f331(f331(f333(f854(x99361,a840)),x99363),f331(f331(f66(x99361),x99367),x99366)))+P1(f331(f331(f333(f854(x99365,a840)),f331(f331(f51(x99361,f854(x99365,a840)),x99363),x99364)),x99362))
% 51.10/50.83 [9984]~P10(x99842,x99846,x99847)+~P14(x99842,f854(x99841,a840),x99847,x99844)+~P1(f331(f331(f333(f854(x99842,a840)),x99843),f331(f331(f66(x99842),x99846),x99847)))+~P1(f331(f331(f333(f854(x99841,a840)),f331(x99844,f419(x99845,x99843,x99844,x99841,x99847,x99846,x99842))),x99845))+P1(f331(f331(f333(f854(x99841,a840)),f331(f331(f51(x99842,f854(x99841,a840)),x99843),x99844)),x99845))
% 51.10/50.83 [8293]~P70(x82932)+~P27(x82931,x82935,x82938,x82934)+~E(x82933,f331(f80(x82935,x82932,x82931,x82936),x82938))+~E(x82937,f331(f311(x82931,x82935,x82938),x82934))+E(f331(f331(f11(x82931,x82932),x82933),x82934),f331(f331(f11(x82935,x82932),x82936),x82937))
% 51.10/50.83 [9987]~P70(x99872)+~P27(x99875,x99871,x99878,x99877)+~E(f331(x99876,f613(x99873,x99876,x99874,x99877,x99878,x99871,x99875,x99872)),f331(f331(f80(x99871,x99872,x99875,x99873),x99878),f613(x99873,x99876,x99874,x99877,x99878,x99871,x99875,x99872)))+~E(x99874,f331(f311(x99875,x99871,x99878),x99877))+E(f331(f331(f11(x99871,x99872),x99873),x99874),f331(f331(f11(x99875,x99872),x99876),x99877))
% 51.10/50.83 [9990]~P70(x99902)+~P27(x99901,x99905,x99908,x99904)+~E(x99907,f331(f311(x99901,x99905,x99908),x99904))+E(f331(f331(f11(x99901,x99902),x99903),x99904),f331(f331(f11(x99905,x99902),x99906),x99907))+P1(f331(f331(f333(x99901),f613(x99906,x99903,x99907,x99904,x99908,x99905,x99901,x99902)),x99904))
% 51.10/50.83 [9991]~P68(x99912)+~P27(x99911,x99915,x99918,x99914)+~E(x99917,f331(f311(x99911,x99915,x99918),x99914))+E(f331(f331(f8(x99911,x99912),x99913),x99914),f331(f331(f8(x99915,x99912),x99916),x99917))+P1(f331(f331(f333(x99911),f633(x99916,x99913,x99917,x99914,x99918,x99915,x99911,x99912)),x99914))
% 51.10/50.83 [9996]~P68(x99962)+~P27(x99965,x99961,x99968,x99967)+~E(x99964,f331(f311(x99965,x99961,x99968),x99967))+~E(f331(x99966,f633(x99963,x99966,x99964,x99967,x99968,x99961,x99965,x99962)),f331(x99963,f331(x99968,f633(x99963,x99966,x99964,x99967,x99968,x99961,x99965,x99962))))+E(f331(f331(f8(x99961,x99962),x99963),x99964),f331(f331(f8(x99965,x99962),x99966),x99967))
% 51.10/50.83 [9378]~E(f331(f185(f848(x93782)),x93785),f331(f185(f848(x93781)),x93783))+~E(f331(f185(f848(x93782)),x93784),f331(f185(f848(x93781)),x93783))+~E(f331(f331(f331(f79(x93781,f851(x93782)),f171(x93781,x93782,f331(f331(f172(x93781,x93782),x93783),x93784))),x93786),f331(f234(x93782),x93787)),f331(f331(f331(f79(x93781,f851(x93782)),f171(x93781,x93782,f331(f331(f172(x93781,x93782),x93783),x93785))),x93786),f331(f234(x93782),x93788)))+E(f171(x93781,x93782,f331(f331(f172(x93781,x93782),x93783),x93784)),f171(x93781,x93782,f331(f331(f172(x93781,x93782),x93783),x93785)))+P1(f331(f331(f333(x93781),x93786),f331(f163(x93781),x93783)))
% 51.10/50.83 [9477]~P25(x94776,x94772,x94775,x94777,x94778,x94771)+~P1(f331(f68(x94772),x94774))+~P1(f331(f68(x94772),x94773))+~E(f331(f331(f109(f854(x94772,a840)),x94773),x94774),f184(f854(x94772,a840)))+E(f331(x94771,f331(f331(f108(f854(x94772,a840)),x94773),x94774)),f331(f331(x94775,f331(x94771,x94773)),f331(x94771,x94774)))
% 51.10/50.83 [9879]~P25(x98798,x98792,x98795,x98797,x98796,x98791)+~E(f331(x98796,f563(x98794,x98793,x98791,x98796,x98797,x98795,x98792)),x98797)+~P1(f331(f68(x98792),x98793))+~P1(f331(f68(x98792),x98794))+E(f331(x98791,f331(f331(f108(f854(x98792,a840)),x98793),x98794)),f331(f331(x98795,f331(x98791,x98793)),f331(x98791,x98794)))
% 51.10/50.83 [9942]~P25(x99428,x99422,x99425,x99427,x99426,x99421)+~P1(f331(f68(x99422),x99423))+~P1(f331(f68(x99422),x99424))+E(f331(x99421,f331(f331(f108(f854(x99422,a840)),x99423),x99424)),f331(f331(x99425,f331(x99421,x99423)),f331(x99421,x99424)))+P1(f331(f331(f333(x99422),f563(x99424,x99423,x99421,x99426,x99427,x99425,x99422)),f331(f331(f109(f854(x99422,a840)),x99423),x99424)))
% 51.10/50.83 [9627]~P10(x96274,x96278,x96275)+~P10(x96271,x96279,x96273)+~P15(x96271,x96274,f854(x96272,a840),x96273,x96275,x96277)+P14(x96271,f854(x96272,a840),x96273,f331(f331(f10(f854(x96274,f854(x96272,a840)),f854(x96272,a840),x96271),f331(f51(x96274,f854(x96272,a840)),f331(f285(x96274,x96274,x96275),f331(f331(f310(x96274),x96276),f184(f854(x96274,a840)))))),x96277))+~P1(f331(f331(f333(x96274),x96276),x96278))
% 51.10/50.83 [4906]~P122(x49062)+~P127(x49062)+~P138(x49062)+~P107(x49062)+E(x49061,f2(x49062))+~E(f331(f331(f250(x49062),x49061),x49063),f2(x49062))
% 51.10/50.83 [4907]~P122(x49072)+~P127(x49072)+~P138(x49072)+~P107(x49072)+~E(x49071,f2(a847))+~E(f331(f331(f250(x49072),x49073),x49071),f2(x49072))
% 51.10/50.83 [6350]~P80(x63501)+~E(x63503,f2(x63501))+~E(x63502,f2(x63501))+E(f331(f331(f87(x63501),x63502),x63503),f2(x63501))+~P1(f331(f331(f240(x63501),f2(x63501)),x63503))+~P1(f331(f331(f240(x63501),f2(x63501)),x63502))
% 51.10/50.83 [8719]E(x87191,f2(a847))+~E(x87192,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x87193)),x87191)),f331(f258(a847,a847),x87193)))+P1(f331(f60(x87192,x87191),x87193))+~P1(f331(f331(f240(a847),f331(f258(a847,a847),x87193)),f2(a847)))+P1(f331(f331(f241(a847),f2(a847)),x87191))+~P1(f331(f331(f241(a847),x87191),f331(f258(a847,a847),x87193)))
% 51.10/50.83 [8731]~E(f331(f248(a847,a847),x87313),f2(a847))+~E(x87311,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x87313)),x87312)),f331(f258(a847,a847),x87313)))+P1(f331(f60(x87311,x87312),x87313))+~P1(f331(f331(f240(a847),f331(f258(a847,a847),x87313)),f2(a847)))+P1(f331(f331(f241(a847),f2(a847)),x87312))+~P1(f331(f331(f241(a847),x87312),f331(f258(a847,a847),x87313)))
% 51.10/50.83 [8738]E(x87381,f2(a847))+~E(x87382,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x87383)),x87381)),f331(f258(a847,a847),x87383)))+P1(f331(f60(x87382,x87381),x87383))+~P1(f331(f331(f241(a847),f2(a847)),x87381))+~P1(f331(f331(f240(a847),f2(a847)),f331(f258(a847,a847),x87383)))+~P1(f331(f331(f241(a847),f331(f258(a847,a847),x87383)),x87381))
% 51.10/50.83 [8752]~E(f331(f248(a847,a847),x87523),f2(a847))+~E(x87521,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x87523)),x87522)),f331(f258(a847,a847),x87523)))+P1(f331(f60(x87521,x87522),x87523))+~P1(f331(f331(f241(a847),f2(a847)),x87522))+~P1(f331(f331(f240(a847),f2(a847)),f331(f258(a847,a847),x87523)))+~P1(f331(f331(f241(a847),f331(f258(a847,a847),x87523)),x87522))
% 51.10/50.83 [6749]~P97(x67492)+E(x67491,f184(f854(x67492,a840)))+E(x67493,f184(f854(x67492,a840)))+~P1(f331(f68(x67492),x67491))+~P1(f331(f68(x67492),x67493))+E(f12(x67492,f331(f331(f108(f854(x67492,a840)),x67493),x67491)),f331(f331(f109(x67492),f12(x67492,x67493)),f12(x67492,x67491)))
% 51.10/50.83 [6750]~P97(x67502)+E(x67501,f184(f854(x67502,a840)))+E(x67503,f184(f854(x67502,a840)))+~P1(f331(f68(x67502),x67501))+~P1(f331(f68(x67502),x67503))+E(f15(x67502,f331(f331(f108(f854(x67502,a840)),x67503),x67501)),f331(f331(f108(x67502),f15(x67502,x67503)),f15(x67502,x67501)))
% 51.10/50.83 [6751]~P102(x67512)+E(x67511,f184(f854(x67512,a840)))+E(x67513,f184(f854(x67512,a840)))+~P1(f331(f68(x67512),x67511))+~P1(f331(f68(x67512),x67513))+E(f16(x67512,f331(f331(f108(f854(x67512,a840)),x67513),x67511)),f331(f331(f239(x67512),f16(x67512,x67513)),f16(x67512,x67511)))
% 51.10/50.83 [6752]~P102(x67522)+E(x67521,f184(f854(x67522,a840)))+E(x67523,f184(f854(x67522,a840)))+~P1(f331(f68(x67522),x67521))+~P1(f331(f68(x67522),x67523))+E(f17(x67522,f331(f331(f108(f854(x67522,a840)),x67523),x67521)),f331(f331(f244(x67522),f17(x67522,x67523)),f17(x67522,x67521)))
% 51.10/50.83 [7414]~P94(x74142)+E(x74141,f184(f854(x74142,a840)))+E(x74143,f184(f854(x74142,a840)))+~P1(f331(f68(x74142),x74141))+~P1(f331(f68(x74142),x74143))+E(f331(f331(f88(x74142),f331(f70(x74142,f88(x74142)),x74143)),f331(f70(x74142,f88(x74142)),x74141)),f331(f70(x74142,f88(x74142)),f331(f331(f108(f854(x74142,a840)),x74143),x74141)))
% 51.10/50.83 [7580]~P102(x75802)+E(x75801,f184(f854(x75802,a840)))+E(x75803,f184(f854(x75802,a840)))+~P1(f331(f68(x75802),x75801))+~P1(f331(f68(x75802),x75803))+E(f331(f331(f239(x75802),f13(x75802,f239(x75802),x75803)),f13(x75802,f239(x75802),x75801)),f13(x75802,f239(x75802),f331(f331(f108(f854(x75802,a840)),x75803),x75801)))
% 51.10/50.83 [7581]~P102(x75812)+E(x75811,f184(f854(x75812,a840)))+E(x75813,f184(f854(x75812,a840)))+~P1(f331(f68(x75812),x75811))+~P1(f331(f68(x75812),x75813))+E(f331(f331(f244(x75812),f14(x75812,f244(x75812),x75813)),f14(x75812,f244(x75812),x75811)),f14(x75812,f244(x75812),f331(f331(f108(f854(x75812,a840)),x75813),x75811)))
% 51.10/50.83 [8588]~P1(f331(x85881,x85883))+P1(f331(x85881,f474(x85881,x85882)))+P1(f331(x85881,f470(x85881,x85882)))+~P1(f331(f331(f241(a1),f2(a1)),x85882))+~P1(f331(f331(f333(a1),x85883),f303(a1,f85(a1),x85882)))+P1(f331(x85881,f331(f331(f3(a1),f470(x85881,x85882)),f331(f331(f88(a1),f473(x85881,x85882)),x85882))))
% 51.10/50.83 [8849]~P1(f331(x88491,x88493))+~P1(f331(x88491,f470(x88491,x88492)))+P1(f331(x88491,f474(x88491,x88492)))+~P1(f331(f331(f241(a1),f2(a1)),x88492))+~P1(f331(f331(f333(a1),x88493),f303(a1,f85(a1),x88492)))+~P1(f331(x88491,f331(f331(f3(a1),f470(x88491,x88492)),f331(f331(f88(a1),f473(x88491,x88492)),x88492))))
% 51.10/50.83 [10017]~P98(x100172)+E(x100171,f184(f854(x100172,a840)))+E(x100173,f184(f854(x100172,a840)))+~P1(f331(f68(x100172),x100171))+~P1(f331(f68(x100172),x100173))+E(f12(x100172,f331(f264(x100172),f331(f331(f10(f854(x100172,a840),a840,x100172),f94(x100172)),f331(f331(f10(f854(x100172,f854(x100172,a840)),f854(x100172,a840),x100172),f331(f10(f854(x100172,a840),a840,x100172),f94(x100172))),f331(f331(f9(x100172,f854(x100172,f854(x100172,a840)),f854(x100172,f854(x100172,a840))),f331(f331(f10(f854(x100172,f854(f854(x100172,a840),f854(x100172,a840))),f854(f854(x100172,f854(x100172,a840)),f854(x100172,f854(x100172,a840))),x100172),f20(x100172,f854(x100172,a840),f854(x100172,a840))),f331(f331(f10(f854(x100172,f854(x100172,f854(a840,a840))),f854(x100172,f854(f854(x100172,a840),f854(x100172,a840))),x100172),f331(f10(f854(x100172,f854(a840,a840)),f854(f854(x100172,a840),f854(x100172,a840)),x100172),f20(x100172,a840,a840))),f331(f331(f10(f854(x100172,f854(x100172,a840)),f854(x100172,f854(x100172,f854(a840,a840))),x100172),f331(f10(f854(x100172,a840),f854(x100172,f854(a840,a840)),x100172),f331(f10(a840,f854(a840,a840),x100172),a329))),f331(f331(f9(x100172,f854(x100172,f854(x100172,x100172)),f854(x100172,f854(x100172,a840))),f331(f331(f10(f854(f854(x100172,x100172),f854(x100172,a840)),f854(f854(x100172,f854(x100172,x100172)),f854(x100172,f854(x100172,a840))),x100172),f10(f854(x100172,x100172),f854(x100172,a840),x100172)),f331(f331(f10(f854(x100172,a840),f854(f854(x100172,x100172),f854(x100172,a840)),x100172),f10(x100172,a840,x100172)),a328))),f108(x100172)))))),f331(f331(f9(x100172,f854(x100172,a840),f854(x100172,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x100172,a840),f854(x100172,a840)),x100172),f10(a840,a840,x100172)),f331(f331(f10(a840,f854(a840,a840),x100172),a329),f331(f331(f9(x100172,f854(x100172,a840),a840),f333(x100172)),x100173)))),f331(f331(f9(x100172,f854(x100172,a840),a840),f333(x100172)),x100171))))))),f331(f331(f108(x100172),f12(x100172,x100173)),f12(x100172,x100171)))
% 51.10/50.83 [10018]~P98(x100182)+E(x100181,f184(f854(x100182,a840)))+E(x100183,f184(f854(x100182,a840)))+~P1(f331(f68(x100182),x100181))+~P1(f331(f68(x100182),x100183))+E(f15(x100182,f331(f264(x100182),f331(f331(f10(f854(x100182,a840),a840,x100182),f94(x100182)),f331(f331(f10(f854(x100182,f854(x100182,a840)),f854(x100182,a840),x100182),f331(f10(f854(x100182,a840),a840,x100182),f94(x100182))),f331(f331(f9(x100182,f854(x100182,f854(x100182,a840)),f854(x100182,f854(x100182,a840))),f331(f331(f10(f854(x100182,f854(f854(x100182,a840),f854(x100182,a840))),f854(f854(x100182,f854(x100182,a840)),f854(x100182,f854(x100182,a840))),x100182),f20(x100182,f854(x100182,a840),f854(x100182,a840))),f331(f331(f10(f854(x100182,f854(x100182,f854(a840,a840))),f854(x100182,f854(f854(x100182,a840),f854(x100182,a840))),x100182),f331(f10(f854(x100182,f854(a840,a840)),f854(f854(x100182,a840),f854(x100182,a840)),x100182),f20(x100182,a840,a840))),f331(f331(f10(f854(x100182,f854(x100182,a840)),f854(x100182,f854(x100182,f854(a840,a840))),x100182),f331(f10(f854(x100182,a840),f854(x100182,f854(a840,a840)),x100182),f331(f10(a840,f854(a840,a840),x100182),a329))),f331(f331(f9(x100182,f854(x100182,f854(x100182,x100182)),f854(x100182,f854(x100182,a840))),f331(f331(f10(f854(f854(x100182,x100182),f854(x100182,a840)),f854(f854(x100182,f854(x100182,x100182)),f854(x100182,f854(x100182,a840))),x100182),f10(f854(x100182,x100182),f854(x100182,a840),x100182)),f331(f331(f10(f854(x100182,a840),f854(f854(x100182,x100182),f854(x100182,a840)),x100182),f10(x100182,a840,x100182)),a328))),f109(x100182)))))),f331(f331(f9(x100182,f854(x100182,a840),f854(x100182,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x100182,a840),f854(x100182,a840)),x100182),f10(a840,a840,x100182)),f331(f331(f10(a840,f854(a840,a840),x100182),a329),f331(f331(f9(x100182,f854(x100182,a840),a840),f333(x100182)),x100183)))),f331(f331(f9(x100182,f854(x100182,a840),a840),f333(x100182)),x100181))))))),f331(f331(f109(x100182),f15(x100182,x100183)),f15(x100182,x100181)))
% 51.10/50.83 [10019]~P102(x100192)+E(x100191,f184(f854(x100192,a840)))+E(x100193,f184(f854(x100192,a840)))+~P1(f331(f68(x100192),x100191))+~P1(f331(f68(x100192),x100193))+E(f13(x100192,f239(x100192),f331(f264(x100192),f331(f331(f10(f854(x100192,a840),a840,x100192),f94(x100192)),f331(f331(f10(f854(x100192,f854(x100192,a840)),f854(x100192,a840),x100192),f331(f10(f854(x100192,a840),a840,x100192),f94(x100192))),f331(f331(f9(x100192,f854(x100192,f854(x100192,a840)),f854(x100192,f854(x100192,a840))),f331(f331(f10(f854(x100192,f854(f854(x100192,a840),f854(x100192,a840))),f854(f854(x100192,f854(x100192,a840)),f854(x100192,f854(x100192,a840))),x100192),f20(x100192,f854(x100192,a840),f854(x100192,a840))),f331(f331(f10(f854(x100192,f854(x100192,f854(a840,a840))),f854(x100192,f854(f854(x100192,a840),f854(x100192,a840))),x100192),f331(f10(f854(x100192,f854(a840,a840)),f854(f854(x100192,a840),f854(x100192,a840)),x100192),f20(x100192,a840,a840))),f331(f331(f10(f854(x100192,f854(x100192,a840)),f854(x100192,f854(x100192,f854(a840,a840))),x100192),f331(f10(f854(x100192,a840),f854(x100192,f854(a840,a840)),x100192),f331(f10(a840,f854(a840,a840),x100192),a329))),f331(f331(f9(x100192,f854(x100192,f854(x100192,x100192)),f854(x100192,f854(x100192,a840))),f331(f331(f10(f854(f854(x100192,x100192),f854(x100192,a840)),f854(f854(x100192,f854(x100192,x100192)),f854(x100192,f854(x100192,a840))),x100192),f10(f854(x100192,x100192),f854(x100192,a840),x100192)),f331(f331(f10(f854(x100192,a840),f854(f854(x100192,x100192),f854(x100192,a840)),x100192),f10(x100192,a840,x100192)),a328))),f244(x100192)))))),f331(f331(f9(x100192,f854(x100192,a840),f854(x100192,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x100192,a840),f854(x100192,a840)),x100192),f10(a840,a840,x100192)),f331(f331(f10(a840,f854(a840,a840),x100192),a329),f331(f331(f9(x100192,f854(x100192,a840),a840),f333(x100192)),x100193)))),f331(f331(f9(x100192,f854(x100192,a840),a840),f333(x100192)),x100191))))))),f331(f331(f244(x100192),f13(x100192,f239(x100192),x100193)),f13(x100192,f239(x100192),x100191)))
% 51.10/50.83 [10020]~P102(x100202)+E(x100201,f184(f854(x100202,a840)))+E(x100203,f184(f854(x100202,a840)))+~P1(f331(f68(x100202),x100201))+~P1(f331(f68(x100202),x100203))+E(f14(x100202,f244(x100202),f331(f264(x100202),f331(f331(f10(f854(x100202,a840),a840,x100202),f94(x100202)),f331(f331(f10(f854(x100202,f854(x100202,a840)),f854(x100202,a840),x100202),f331(f10(f854(x100202,a840),a840,x100202),f94(x100202))),f331(f331(f9(x100202,f854(x100202,f854(x100202,a840)),f854(x100202,f854(x100202,a840))),f331(f331(f10(f854(x100202,f854(f854(x100202,a840),f854(x100202,a840))),f854(f854(x100202,f854(x100202,a840)),f854(x100202,f854(x100202,a840))),x100202),f20(x100202,f854(x100202,a840),f854(x100202,a840))),f331(f331(f10(f854(x100202,f854(x100202,f854(a840,a840))),f854(x100202,f854(f854(x100202,a840),f854(x100202,a840))),x100202),f331(f10(f854(x100202,f854(a840,a840)),f854(f854(x100202,a840),f854(x100202,a840)),x100202),f20(x100202,a840,a840))),f331(f331(f10(f854(x100202,f854(x100202,a840)),f854(x100202,f854(x100202,f854(a840,a840))),x100202),f331(f10(f854(x100202,a840),f854(x100202,f854(a840,a840)),x100202),f331(f10(a840,f854(a840,a840),x100202),a329))),f331(f331(f9(x100202,f854(x100202,f854(x100202,x100202)),f854(x100202,f854(x100202,a840))),f331(f331(f10(f854(f854(x100202,x100202),f854(x100202,a840)),f854(f854(x100202,f854(x100202,x100202)),f854(x100202,f854(x100202,a840))),x100202),f10(f854(x100202,x100202),f854(x100202,a840),x100202)),f331(f331(f10(f854(x100202,a840),f854(f854(x100202,x100202),f854(x100202,a840)),x100202),f10(x100202,a840,x100202)),a328))),f239(x100202)))))),f331(f331(f9(x100202,f854(x100202,a840),f854(x100202,a840)),f331(f331(f10(f854(a840,a840),f854(f854(x100202,a840),f854(x100202,a840)),x100202),f10(a840,a840,x100202)),f331(f331(f10(a840,f854(a840,a840),x100202),a329),f331(f331(f9(x100202,f854(x100202,a840),a840),f333(x100202)),x100203)))),f331(f331(f9(x100202,f854(x100202,a840),a840),f333(x100202)),x100201))))))),f331(f331(f239(x100202),f14(x100202,f244(x100202),x100203)),f14(x100202,f244(x100202),x100201)))
% 51.10/50.83 [7081]~P85(x70813)+E(x70811,x70812)+~E(f331(f331(f250(x70813),x70811),x70814),f331(f331(f250(x70813),x70812),x70814))+~P1(f331(f331(f240(x70813),f2(x70813)),x70812))+~P1(f331(f331(f240(x70813),f2(x70813)),x70811))+~P1(f331(f331(f241(a847),f2(a847)),x70814))
% 51.10/50.83 [7935]~P60(x79351)+~P92(x79351)+P1(f331(f331(f241(x79351),x79352),f2(x79351)))+P1(f331(f331(f241(x79351),f2(x79351)),x79352))+P1(f331(f331(f241(x79351),f331(f331(f291(x79351),x79353),x79352)),f331(f111(x79351),x79354)))+~P1(f331(f331(f241(x79351),f2(x79351)),f331(f111(x79351),x79354)))
% 51.10/50.83 [7936]~P60(x79361)+~P92(x79361)+P1(f331(f331(f241(x79361),x79362),f2(x79361)))+P1(f331(f331(f241(x79361),f2(x79361)),x79362))+P1(f331(f331(f240(x79361),f331(f331(f291(x79361),x79363),x79362)),f331(f111(x79361),x79364)))+~P1(f331(f331(f240(x79361),f2(x79361)),f331(f111(x79361),x79364)))
% 51.10/50.83 [8171]~P60(x81711)+~P92(x81711)+P1(f331(f331(f241(x81711),x81712),f2(x81711)))+P1(f331(f331(f241(x81711),f2(x81711)),x81712))+~P1(f331(f331(f241(x81711),f331(f331(f291(x81711),x81714),x81712)),f331(f111(x81711),x81713)))+P1(f331(f331(f241(x81711),f2(x81711)),f331(f111(x81711),x81713)))
% 51.10/50.83 [8172]~P60(x81721)+~P92(x81721)+P1(f331(f331(f241(x81721),x81722),f2(x81721)))+P1(f331(f331(f241(x81721),f2(x81721)),x81722))+~P1(f331(f331(f240(x81721),f331(f331(f291(x81721),x81724),x81722)),f331(f111(x81721),x81723)))+P1(f331(f331(f240(x81721),f2(x81721)),f331(f111(x81721),x81723)))
% 51.10/50.83 [7374]~P102(x73742)+E(x73741,f184(f854(x73742,a840)))+~P1(f331(f68(x73742),x73741))+~P1(f331(f331(f333(x73742),x73744),x73741))+P1(f331(f331(f241(x73742),x73743),x73744))+~P1(f331(f331(f241(x73742),x73743),f331(f70(x73742,f244(x73742)),x73741)))
% 51.10/50.83 [7375]~P102(x73752)+E(x73751,f184(f854(x73752,a840)))+~P1(f331(f68(x73752),x73751))+~P1(f331(f331(f333(x73752),x73754),x73751))+P1(f331(f331(f240(x73752),x73753),x73754))+~P1(f331(f331(f240(x73752),x73753),f331(f70(x73752,f244(x73752)),x73751)))
% 51.10/50.83 [7376]~P101(x73762)+E(x73761,f184(f854(x73762,a840)))+~P1(f331(f68(x73762),x73761))+~P1(f331(f331(f333(x73762),x73764),x73761))+P1(f331(f331(f240(x73762),x73763),x73764))+~P1(f331(f331(f240(x73762),x73763),f331(f70(x73762,f109(x73762)),x73761)))
% 51.10/50.83 [7885]~P60(x78851)+~P92(x78851)+P1(f331(f331(f241(x78851),f331(f111(x78851),x78852)),f2(x78851)))+~P1(f331(f331(f241(x78851),x78853),f2(x78851)))+P1(f331(f331(f241(x78851),f2(x78851)),f331(f111(x78851),x78852)))+P1(f331(f331(f241(x78851),x78853),f331(f331(f291(x78851),x78854),f331(f111(x78851),x78852))))
% 51.10/50.83 [7886]~P60(x78861)+~P92(x78861)+P1(f331(f331(f241(x78861),f331(f111(x78861),x78862)),f2(x78861)))+~P1(f331(f331(f240(x78861),x78863),f2(x78861)))+P1(f331(f331(f241(x78861),f2(x78861)),f331(f111(x78861),x78862)))+P1(f331(f331(f240(x78861),x78863),f331(f331(f291(x78861),x78864),f331(f111(x78861),x78862))))
% 51.10/50.83 [7896]~P60(x78961)+~P92(x78961)+P1(f331(f331(f241(x78961),x78962),f2(x78961)))+~P1(f331(f331(f241(x78961),f331(f111(x78961),x78963)),f2(x78961)))+P1(f331(f331(f241(x78961),f2(x78961)),x78962))+P1(f331(f331(f241(x78961),f331(f111(x78961),x78963)),f331(f331(f291(x78961),x78964),x78962)))
% 51.10/50.83 [7897]~P60(x78971)+~P92(x78971)+P1(f331(f331(f241(x78971),x78972),f2(x78971)))+~P1(f331(f331(f240(x78971),f331(f111(x78971),x78973)),f2(x78971)))+P1(f331(f331(f241(x78971),f2(x78971)),x78972))+P1(f331(f331(f240(x78971),f331(f111(x78971),x78973)),f331(f331(f291(x78971),x78974),x78972)))
% 51.10/50.83 [8044]~P60(x80441)+~P92(x80441)+P1(f331(f331(f241(x80441),x80442),f2(x80441)))+P1(f331(f331(f241(x80441),f331(f111(x80441),x80443)),f2(x80441)))+P1(f331(f331(f241(x80441),f2(x80441)),x80442))+~P1(f331(f331(f241(x80441),f331(f111(x80441),x80443)),f331(f331(f291(x80441),x80444),x80442)))
% 51.10/50.83 [8045]~P60(x80451)+~P92(x80451)+P1(f331(f331(f241(x80451),x80452),f2(x80451)))+P1(f331(f331(f240(x80451),f331(f111(x80451),x80453)),f2(x80451)))+P1(f331(f331(f241(x80451),f2(x80451)),x80452))+~P1(f331(f331(f240(x80451),f331(f111(x80451),x80453)),f331(f331(f291(x80451),x80454),x80452)))
% 51.10/50.83 [8118]~P60(x81181)+~P92(x81181)+P1(f331(f331(f241(x81181),x81182),f2(x81181)))+P1(f331(f331(f241(x81181),f331(f111(x81181),x81183)),f2(x81181)))+P1(f331(f331(f241(x81181),f2(x81181)),f331(f111(x81181),x81183)))+~P1(f331(f331(f241(x81181),x81182),f331(f331(f291(x81181),x81184),f331(f111(x81181),x81183))))
% 51.10/50.83 [8119]~P60(x81191)+~P92(x81191)+P1(f331(f331(f240(x81191),x81192),f2(x81191)))+P1(f331(f331(f241(x81191),f331(f111(x81191),x81193)),f2(x81191)))+P1(f331(f331(f241(x81191),f2(x81191)),f331(f111(x81191),x81193)))+~P1(f331(f331(f240(x81191),x81192),f331(f331(f291(x81191),x81194),f331(f111(x81191),x81193))))
% 51.10/50.83 [8311]~P60(x83111)+~P92(x83111)+~P1(f331(f331(f241(x83111),x83113),f2(x83111)))+P1(f331(f331(f241(x83111),f2(x83111)),f331(f111(x83111),x83112)))+~P1(f331(f331(f241(x83111),x83114),f331(f331(f88(x83111),x83113),f331(f111(x83111),x83112))))+P1(f331(f331(f241(x83111),x83113),f331(f331(f291(x83111),x83114),f331(f111(x83111),x83112))))
% 51.10/50.83 [8312]~P60(x83121)+~P92(x83121)+~P1(f331(f331(f240(x83121),x83123),f2(x83121)))+P1(f331(f331(f241(x83121),f2(x83121)),f331(f111(x83121),x83122)))+~P1(f331(f331(f240(x83121),x83124),f331(f331(f88(x83121),x83123),f331(f111(x83121),x83122))))+P1(f331(f331(f240(x83121),x83123),f331(f331(f291(x83121),x83124),f331(f111(x83121),x83122))))
% 51.10/50.83 [8478]~P60(x84781)+~P92(x84781)+~P1(f331(f331(f241(x84781),f331(f111(x84781),x84782)),f2(x84781)))+P1(f331(f331(f241(x84781),f2(x84781)),f331(f111(x84781),x84782)))+~P1(f331(f331(f241(x84781),x84784),f331(f331(f88(x84781),x84783),f331(f111(x84781),x84782))))+P1(f331(f331(f241(x84781),x84783),f331(f331(f291(x84781),x84784),f331(f111(x84781),x84782))))
% 51.10/50.83 [8479]~P60(x84791)+~P92(x84791)+~P1(f331(f331(f241(x84791),f331(f111(x84791),x84792)),f2(x84791)))+P1(f331(f331(f241(x84791),f2(x84791)),f331(f111(x84791),x84792)))+~P1(f331(f331(f241(x84791),x84794),f331(f331(f291(x84791),x84793),f331(f111(x84791),x84792))))+P1(f331(f331(f241(x84791),x84793),f331(f331(f88(x84791),x84794),f331(f111(x84791),x84792))))
% 51.10/50.83 [8480]~P60(x84801)+~P92(x84801)+~P1(f331(f331(f241(x84801),f331(f111(x84801),x84802)),f2(x84801)))+P1(f331(f331(f241(x84801),f2(x84801)),f331(f111(x84801),x84802)))+~P1(f331(f331(f240(x84801),x84804),f331(f331(f88(x84801),x84803),f331(f111(x84801),x84802))))+P1(f331(f331(f240(x84801),x84803),f331(f331(f291(x84801),x84804),f331(f111(x84801),x84802))))
% 51.10/50.83 [8481]~P60(x84811)+~P92(x84811)+~P1(f331(f331(f241(x84811),f331(f111(x84811),x84812)),f2(x84811)))+P1(f331(f331(f241(x84811),f2(x84811)),f331(f111(x84811),x84812)))+~P1(f331(f331(f240(x84811),x84814),f331(f331(f291(x84811),x84813),f331(f111(x84811),x84812))))+P1(f331(f331(f240(x84811),x84813),f331(f331(f88(x84811),x84814),f331(f111(x84811),x84812))))
% 51.10/50.83 [7270]E(x72701,f2(a1))+E(f331(f331(f48(a1),x72702),x72701),x72703)+~P1(f331(f331(f240(a1),x72704),f2(a1)))+~E(x72702,f331(f331(f87(a1),f331(f331(f88(a1),x72701),x72703)),x72704))+P1(f331(f331(f241(a1),f2(a1)),x72701))+~P1(f331(f331(f241(a1),x72701),x72704))
% 51.10/50.83 [7286]E(f57(a1,x72862,x72861),x72863)+E(x72861,f2(a1))+~P1(f331(f331(f240(a1),x72863),f2(a1)))+~E(x72862,f331(f331(f87(a1),f331(f331(f88(a1),x72861),x72864)),x72863))+P1(f331(f331(f241(a1),f2(a1)),x72861))+~P1(f331(f331(f241(a1),x72861),x72863))
% 51.10/50.83 [7413]E(x74131,f2(a1))+E(f331(f331(f48(a1),x74132),x74131),x74133)+~E(x74132,f331(f331(f87(a1),f331(f331(f88(a1),x74131),x74133)),x74134))+~P1(f331(f331(f241(a1),f2(a1)),x74131))+~P1(f331(f331(f240(a1),f2(a1)),x74134))+~P1(f331(f331(f241(a1),x74134),x74131))
% 51.10/50.83 [7439]E(f57(a1,x74392,x74391),x74393)+E(x74391,f2(a1))+~E(x74392,f331(f331(f87(a1),f331(f331(f88(a1),x74391),x74394)),x74393))+~P1(f331(f331(f241(a1),f2(a1)),x74391))+~P1(f331(f331(f240(a1),f2(a1)),x74393))+~P1(f331(f331(f241(a1),x74393),x74391))
% 51.10/50.83 [7584]~P102(x75842)+E(x75841,f184(f854(x75842,a840)))+~P1(f331(f68(x75842),x75841))+~P1(f331(f331(f333(x75842),x75844),x75841))+~P1(f331(f331(f241(x75842),x75844),x75843))+P1(f331(f331(f241(x75842),f331(f70(x75842,f244(x75842)),x75841)),x75843))
% 51.10/50.83 [7585]~P102(x75852)+E(x75851,f184(f854(x75852,a840)))+~P1(f331(f68(x75852),x75851))+~P1(f331(f331(f333(x75852),x75854),x75851))+~P1(f331(f331(f240(x75852),x75854),x75853))+P1(f331(f331(f240(x75852),f331(f70(x75852,f244(x75852)),x75851)),x75853))
% 51.10/50.83 [8148]~P1(f331(f331(f240(a1),x81484),f2(a1)))+~E(x81481,f331(f331(f87(a1),f331(f331(f88(a1),x81482),x81483)),x81484))+~P1(f331(f331(f240(a1),f2(a1)),x81484))+~P1(f331(f331(f241(a1),x81484),x81482))+~P1(f331(f331(f241(a1),x81482),x81484))+P1(f331(f61(x81481,x81482),f331(f331(f249(a1,a1),x81483),x81484)))
% 51.10/50.83 [8269]~P60(x82691)+~P92(x82691)+P1(f331(f331(f241(x82691),f331(f111(x82691),x82692)),f2(x82691)))+~P1(f331(f331(f241(x82691),f2(x82691)),x82694))+P1(f331(f331(f241(x82691),f2(x82691)),f331(f111(x82691),x82692)))+P1(f331(f331(f241(x82691),f331(f331(f291(x82691),x82693),f331(f111(x82691),x82692))),x82694))
% 51.10/50.83 [8270]~P60(x82701)+~P92(x82701)+P1(f331(f331(f241(x82701),f331(f111(x82701),x82702)),f2(x82701)))+~P1(f331(f331(f240(x82701),f2(x82701)),x82704))+P1(f331(f331(f241(x82701),f2(x82701)),f331(f111(x82701),x82702)))+P1(f331(f331(f240(x82701),f331(f331(f291(x82701),x82703),f331(f111(x82701),x82702))),x82704))
% 51.10/50.83 [8384]~P60(x83841)+~P92(x83841)+~P1(f331(f331(f241(x83841),x83842),f2(x83841)))+P1(f331(f331(f241(x83841),f2(x83841)),x83842))+~P1(f331(f331(f241(x83841),f331(f111(x83841),x83844)),f331(f331(f291(x83841),x83843),x83842)))+P1(f331(f331(f241(x83841),x83843),f331(f331(f88(x83841),f331(f111(x83841),x83844)),x83842)))
% 51.10/50.83 [8385]~P60(x83851)+~P92(x83851)+~P1(f331(f331(f241(x83851),x83852),f2(x83851)))+P1(f331(f331(f241(x83851),f2(x83851)),x83852))+~P1(f331(f331(f240(x83851),f331(f111(x83851),x83854)),f331(f331(f291(x83851),x83853),x83852)))+P1(f331(f331(f240(x83851),x83853),f331(f331(f88(x83851),f331(f111(x83851),x83854)),x83852)))
% 51.10/50.83 [8426]~P60(x84261)+~P92(x84261)+~P1(f331(f331(f241(x84261),x84262),f2(x84261)))+P1(f331(f331(f241(x84261),f2(x84261)),x84262))+P1(f331(f331(f241(x84261),f331(f111(x84261),x84263)),f331(f331(f291(x84261),x84264),x84262)))+~P1(f331(f331(f241(x84261),x84264),f331(f331(f88(x84261),f331(f111(x84261),x84263)),x84262)))
% 51.10/50.83 [8427]~P60(x84271)+~P92(x84271)+~P1(f331(f331(f241(x84271),x84272),f2(x84271)))+P1(f331(f331(f241(x84271),f2(x84271)),x84272))+P1(f331(f331(f240(x84271),f331(f111(x84271),x84273)),f331(f331(f291(x84271),x84274),x84272)))+~P1(f331(f331(f240(x84271),x84274),f331(f331(f88(x84271),f331(f111(x84271),x84273)),x84272)))
% 51.10/50.83 [8509]~P60(x85091)+~P92(x85091)+P1(f331(f331(f241(x85091),f331(f111(x85091),x85093)),f2(x85091)))+P1(f331(f331(f241(x85091),f2(x85091)),x85092))+P1(f331(f331(f241(x85091),f2(x85091)),f331(f111(x85091),x85093)))+~P1(f331(f331(f241(x85091),f331(f331(f291(x85091),x85094),f331(f111(x85091),x85093))),x85092))
% 51.10/50.83 [8510]~P60(x85101)+~P92(x85101)+P1(f331(f331(f241(x85101),f331(f111(x85101),x85103)),f2(x85101)))+P1(f331(f331(f240(x85101),f2(x85101)),x85102))+P1(f331(f331(f241(x85101),f2(x85101)),f331(f111(x85101),x85103)))+~P1(f331(f331(f240(x85101),f331(f331(f291(x85101),x85104),f331(f111(x85101),x85103))),x85102))
% 51.10/50.83 [8550]~P60(x85501)+~P92(x85501)+~P1(f331(f331(f241(x85501),f331(f111(x85501),x85503)),f2(x85501)))+P1(f331(f331(f241(x85501),f2(x85501)),x85502))+P1(f331(f331(f241(x85501),f331(f111(x85501),x85503)),f331(f331(f291(x85501),x85504),x85502)))+~P1(f331(f331(f241(x85501),x85504),f331(f331(f88(x85501),f331(f111(x85501),x85503)),x85502)))
% 51.10/50.83 [8551]~P60(x85511)+~P92(x85511)+~P1(f331(f331(f240(x85511),f331(f111(x85511),x85513)),f2(x85511)))+P1(f331(f331(f241(x85511),f2(x85511)),x85512))+P1(f331(f331(f240(x85511),f331(f111(x85511),x85513)),f331(f331(f291(x85511),x85514),x85512)))+~P1(f331(f331(f240(x85511),x85514),f331(f331(f88(x85511),f331(f111(x85511),x85513)),x85512)))
% 51.10/50.83 [8558]~P60(x85581)+~P92(x85581)+P1(f331(f331(f241(x85581),x85582),f2(x85581)))+P1(f331(f331(f241(x85581),f331(f331(f291(x85581),x85583),x85582)),f331(f111(x85581),x85584)))+~P1(f331(f331(f241(x85581),f2(x85581)),f331(f111(x85581),x85584)))+~P1(f331(f331(f241(x85581),x85583),f331(f331(f88(x85581),f331(f111(x85581),x85584)),x85582)))
% 51.10/50.83 [8559]~P60(x85591)+~P92(x85591)+P1(f331(f331(f241(x85591),x85592),f2(x85591)))+P1(f331(f331(f240(x85591),f331(f331(f291(x85591),x85593),x85592)),f331(f111(x85591),x85594)))+~P1(f331(f331(f240(x85591),f2(x85591)),f331(f111(x85591),x85594)))+~P1(f331(f331(f240(x85591),x85593),f331(f331(f88(x85591),f331(f111(x85591),x85594)),x85592)))
% 51.10/50.83 [8576]~P60(x85761)+~P92(x85761)+P1(f331(f331(f241(x85761),f331(f111(x85761),x85762)),f2(x85761)))+~P1(f331(f331(f241(x85761),f2(x85761)),x85764))+~P1(f331(f331(f241(x85761),x85763),f331(f331(f88(x85761),x85764),f331(f111(x85761),x85762))))+P1(f331(f331(f241(x85761),f331(f331(f291(x85761),x85763),f331(f111(x85761),x85762))),x85764))
% 51.10/50.83 [8577]~P60(x85771)+~P92(x85771)+P1(f331(f331(f241(x85771),f331(f111(x85771),x85772)),f2(x85771)))+~P1(f331(f331(f240(x85771),f2(x85771)),x85774))+~P1(f331(f331(f240(x85771),x85773),f331(f331(f88(x85771),x85774),f331(f111(x85771),x85772))))+P1(f331(f331(f240(x85771),f331(f331(f291(x85771),x85773),f331(f111(x85771),x85772))),x85774))
% 51.10/50.83 [8658]~P60(x86581)+~P92(x86581)+P1(f331(f331(f241(x86581),f331(f111(x86581),x86582)),f2(x86581)))+~P1(f331(f331(f241(x86581),x86583),f2(x86581)))+P1(f331(f331(f241(x86581),x86583),f331(f331(f291(x86581),x86584),f331(f111(x86581),x86582))))+~P1(f331(f331(f241(x86581),f331(f331(f88(x86581),x86583),f331(f111(x86581),x86582))),x86584))
% 51.10/50.83 [8659]~P60(x86591)+~P92(x86591)+P1(f331(f331(f241(x86591),f331(f111(x86591),x86592)),f2(x86591)))+~P1(f331(f331(f240(x86591),x86593),f2(x86591)))+P1(f331(f331(f240(x86591),x86593),f331(f331(f291(x86591),x86594),f331(f111(x86591),x86592))))+~P1(f331(f331(f240(x86591),f331(f331(f88(x86591),x86593),f331(f111(x86591),x86592))),x86594))
% 51.10/50.83 [8756]~P60(x87561)+~P92(x87561)+~P1(f331(f331(f241(x87561),f2(x87561)),x87564))+P1(f331(f331(f241(x87561),f2(x87561)),f331(f111(x87561),x87562)))+~P1(f331(f331(f241(x87561),f331(f331(f88(x87561),x87564),f331(f111(x87561),x87562))),x87563))+P1(f331(f331(f241(x87561),f331(f331(f291(x87561),x87563),f331(f111(x87561),x87562))),x87564))
% 51.10/50.83 [8757]~P60(x87571)+~P92(x87571)+~P1(f331(f331(f240(x87571),f2(x87571)),x87574))+P1(f331(f331(f241(x87571),f2(x87571)),f331(f111(x87571),x87572)))+~P1(f331(f331(f240(x87571),f331(f331(f88(x87571),x87574),f331(f111(x87571),x87572))),x87573))+P1(f331(f331(f240(x87571),f331(f331(f291(x87571),x87573),f331(f111(x87571),x87572))),x87574))
% 51.10/50.83 [8805]~P60(x88051)+~P92(x88051)+~P1(f331(f331(f241(x88051),x88052),f2(x88051)))+P1(f331(f331(f241(x88051),x88052),f331(f331(f291(x88051),x88053),f331(f111(x88051),x88054))))+~P1(f331(f331(f241(x88051),x88053),f331(f331(f88(x88051),x88052),f331(f111(x88051),x88054))))+~P1(f331(f331(f241(x88051),f331(f331(f88(x88051),x88052),f331(f111(x88051),x88054))),x88053))
% 51.10/50.83 [8806]~P60(x88061)+~P92(x88061)+~P1(f331(f331(f240(x88061),x88062),f2(x88061)))+P1(f331(f331(f240(x88061),x88062),f331(f331(f291(x88061),x88063),f331(f111(x88061),x88064))))+~P1(f331(f331(f240(x88061),x88063),f331(f331(f88(x88061),x88062),f331(f111(x88061),x88064))))+~P1(f331(f331(f240(x88061),f331(f331(f88(x88061),x88062),f331(f111(x88061),x88064))),x88063))
% 51.10/50.83 [8830]~P60(x88301)+~P92(x88301)+~P1(f331(f331(f241(x88301),f331(f111(x88301),x88302)),f2(x88301)))+P1(f331(f331(f241(x88301),f2(x88301)),f331(f111(x88301),x88302)))+~P1(f331(f331(f241(x88301),f331(f331(f291(x88301),x88304),f331(f111(x88301),x88302))),x88303))+P1(f331(f331(f241(x88301),f331(f331(f88(x88301),x88303),f331(f111(x88301),x88302))),x88304))
% 51.10/50.83 [8831]~P60(x88311)+~P92(x88311)+~P1(f331(f331(f241(x88311),f331(f111(x88311),x88312)),f2(x88311)))+P1(f331(f331(f241(x88311),f2(x88311)),f331(f111(x88311),x88312)))+~P1(f331(f331(f241(x88311),f331(f331(f88(x88311),x88314),f331(f111(x88311),x88312))),x88313))+P1(f331(f331(f241(x88311),f331(f331(f291(x88311),x88313),f331(f111(x88311),x88312))),x88314))
% 51.10/50.83 [8832]~P60(x88321)+~P92(x88321)+~P1(f331(f331(f241(x88321),f331(f111(x88321),x88322)),f2(x88321)))+P1(f331(f331(f241(x88321),f2(x88321)),f331(f111(x88321),x88322)))+~P1(f331(f331(f240(x88321),f331(f331(f291(x88321),x88324),f331(f111(x88321),x88322))),x88323))+P1(f331(f331(f240(x88321),f331(f331(f88(x88321),x88323),f331(f111(x88321),x88322))),x88324))
% 51.10/50.83 [8833]~P60(x88331)+~P92(x88331)+~P1(f331(f331(f241(x88331),f331(f111(x88331),x88332)),f2(x88331)))+P1(f331(f331(f241(x88331),f2(x88331)),f331(f111(x88331),x88332)))+~P1(f331(f331(f240(x88331),f331(f331(f88(x88331),x88334),f331(f111(x88331),x88332))),x88333))+P1(f331(f331(f240(x88331),f331(f331(f291(x88331),x88333),f331(f111(x88331),x88332))),x88334))
% 51.10/50.83 [8908]~P60(x89081)+~P92(x89081)+~P1(f331(f331(f241(x89081),f331(f111(x89081),x89084)),f2(x89081)))+P1(f331(f331(f241(x89081),x89082),f331(f331(f291(x89081),x89083),f331(f111(x89081),x89084))))+~P1(f331(f331(f241(x89081),x89083),f331(f331(f88(x89081),x89082),f331(f111(x89081),x89084))))+~P1(f331(f331(f241(x89081),f331(f331(f88(x89081),x89082),f331(f111(x89081),x89084))),x89083))
% 51.10/50.83 [8909]~P60(x89091)+~P92(x89091)+~P1(f331(f331(f241(x89091),f331(f111(x89091),x89094)),f2(x89091)))+P1(f331(f331(f240(x89091),x89092),f331(f331(f291(x89091),x89093),f331(f111(x89091),x89094))))+~P1(f331(f331(f240(x89091),x89093),f331(f331(f88(x89091),x89092),f331(f111(x89091),x89094))))+~P1(f331(f331(f240(x89091),f331(f331(f88(x89091),x89092),f331(f111(x89091),x89094))),x89093))
% 51.10/50.83 [8948]~P60(x89481)+~P92(x89481)+~P1(f331(f331(f241(x89481),f2(x89481)),x89484))+~P1(f331(f331(f241(x89481),x89482),f331(f331(f88(x89481),x89484),f331(f111(x89481),x89483))))+~P1(f331(f331(f241(x89481),f331(f331(f88(x89481),x89484),f331(f111(x89481),x89483))),x89482))+P1(f331(f331(f241(x89481),f331(f331(f291(x89481),x89482),f331(f111(x89481),x89483))),x89484))
% 51.10/50.83 [8949]~P60(x89491)+~P92(x89491)+~P1(f331(f331(f240(x89491),f2(x89491)),x89494))+~P1(f331(f331(f240(x89491),x89492),f331(f331(f88(x89491),x89494),f331(f111(x89491),x89493))))+~P1(f331(f331(f240(x89491),f331(f331(f88(x89491),x89494),f331(f111(x89491),x89493))),x89492))+P1(f331(f331(f240(x89491),f331(f331(f291(x89491),x89492),f331(f111(x89491),x89493))),x89494))
% 51.10/50.83 [8982]~P60(x89821)+~P92(x89821)+~P1(f331(f331(f241(x89821),f331(f111(x89821),x89823)),f2(x89821)))+~P1(f331(f331(f241(x89821),x89822),f331(f331(f88(x89821),x89824),f331(f111(x89821),x89823))))+~P1(f331(f331(f241(x89821),f331(f331(f88(x89821),x89824),f331(f111(x89821),x89823))),x89822))+P1(f331(f331(f241(x89821),f331(f331(f291(x89821),x89822),f331(f111(x89821),x89823))),x89824))
% 51.10/50.83 [8983]~P60(x89831)+~P92(x89831)+~P1(f331(f331(f241(x89831),f331(f111(x89831),x89833)),f2(x89831)))+~P1(f331(f331(f240(x89831),x89832),f331(f331(f88(x89831),x89834),f331(f111(x89831),x89833))))+~P1(f331(f331(f240(x89831),f331(f331(f88(x89831),x89834),f331(f111(x89831),x89833))),x89832))+P1(f331(f331(f240(x89831),f331(f331(f291(x89831),x89832),f331(f111(x89831),x89833))),x89834))
% 51.10/50.83 [8715]~P60(x87151)+~P92(x87151)+~P1(f331(f331(f241(x87151),x87152),f2(x87151)))+~P1(f331(f331(f241(x87151),f331(f331(f291(x87151),x87154),x87152)),f331(f111(x87151),x87153)))+P1(f331(f331(f241(x87151),f2(x87151)),x87152))+P1(f331(f331(f241(x87151),f331(f331(f88(x87151),f331(f111(x87151),x87153)),x87152)),x87154))
% 51.10/50.83 [8716]~P60(x87161)+~P92(x87161)+~P1(f331(f331(f241(x87161),x87162),f2(x87161)))+~P1(f331(f331(f240(x87161),f331(f331(f291(x87161),x87164),x87162)),f331(f111(x87161),x87163)))+P1(f331(f331(f241(x87161),f2(x87161)),x87162))+P1(f331(f331(f240(x87161),f331(f331(f88(x87161),f331(f111(x87161),x87163)),x87162)),x87164))
% 51.10/50.83 [8808]~P60(x88081)+~P92(x88081)+~P1(f331(f331(f241(x88081),x88082),f2(x88081)))+P1(f331(f331(f241(x88081),f2(x88081)),x88082))+P1(f331(f331(f241(x88081),f331(f331(f291(x88081),x88083),x88082)),f331(f111(x88081),x88084)))+~P1(f331(f331(f241(x88081),f331(f331(f88(x88081),f331(f111(x88081),x88084)),x88082)),x88083))
% 51.10/50.83 [8809]~P60(x88091)+~P92(x88091)+~P1(f331(f331(f241(x88091),x88092),f2(x88091)))+P1(f331(f331(f241(x88091),f2(x88091)),x88092))+P1(f331(f331(f240(x88091),f331(f331(f291(x88091),x88093),x88092)),f331(f111(x88091),x88094)))+~P1(f331(f331(f240(x88091),f331(f331(f88(x88091),f331(f111(x88091),x88094)),x88092)),x88093))
% 51.10/50.83 [8846]~P60(x88461)+~P92(x88461)+P1(f331(f331(f241(x88461),x88462),f2(x88461)))+~P1(f331(f331(f241(x88461),f331(f111(x88461),x88463)),f2(x88461)))+P1(f331(f331(f241(x88461),f331(f111(x88461),x88463)),f331(f331(f291(x88461),x88464),x88462)))+~P1(f331(f331(f241(x88461),f331(f331(f88(x88461),f331(f111(x88461),x88463)),x88462)),x88464))
% 51.10/50.83 [8847]~P60(x88471)+~P92(x88471)+P1(f331(f331(f241(x88471),x88472),f2(x88471)))+~P1(f331(f331(f240(x88471),f331(f111(x88471),x88473)),f2(x88471)))+P1(f331(f331(f240(x88471),f331(f111(x88471),x88473)),f331(f331(f291(x88471),x88474),x88472)))+~P1(f331(f331(f240(x88471),f331(f331(f88(x88471),f331(f111(x88471),x88473)),x88472)),x88474))
% 51.10/50.83 [8862]~P60(x88621)+~P92(x88621)+P1(f331(f331(f241(x88621),f2(x88621)),x88622))+P1(f331(f331(f241(x88621),f331(f331(f291(x88621),x88623),x88622)),f331(f111(x88621),x88624)))+~P1(f331(f331(f241(x88621),f2(x88621)),f331(f111(x88621),x88624)))+~P1(f331(f331(f241(x88621),f331(f331(f88(x88621),f331(f111(x88621),x88624)),x88622)),x88623))
% 51.10/50.83 [8863]~P60(x88631)+~P92(x88631)+P1(f331(f331(f241(x88631),f2(x88631)),x88632))+P1(f331(f331(f240(x88631),f331(f331(f291(x88631),x88633),x88632)),f331(f111(x88631),x88634)))+~P1(f331(f331(f240(x88631),f2(x88631)),f331(f111(x88631),x88634)))+~P1(f331(f331(f240(x88631),f331(f331(f88(x88631),f331(f111(x88631),x88634)),x88632)),x88633))
% 51.10/50.83 [9014]~P60(x90141)+~P92(x90141)+~P1(f331(f331(f241(x90141),x90144),f2(x90141)))+P1(f331(f331(f241(x90141),f331(f111(x90141),x90142)),f331(f331(f291(x90141),x90143),x90144)))+~P1(f331(f331(f241(x90141),x90143),f331(f331(f88(x90141),f331(f111(x90141),x90142)),x90144)))+~P1(f331(f331(f241(x90141),f331(f331(f88(x90141),f331(f111(x90141),x90142)),x90144)),x90143))
% 51.10/50.83 [9015]~P60(x90151)+~P92(x90151)+~P1(f331(f331(f241(x90151),x90154),f2(x90151)))+P1(f331(f331(f240(x90151),f331(f111(x90151),x90152)),f331(f331(f291(x90151),x90153),x90154)))+~P1(f331(f331(f240(x90151),x90153),f331(f331(f88(x90151),f331(f111(x90151),x90152)),x90154)))+~P1(f331(f331(f240(x90151),f331(f331(f88(x90151),f331(f111(x90151),x90152)),x90154)),x90153))
% 51.10/50.83 [9044]~P60(x90441)+~P92(x90441)+~P1(f331(f331(f241(x90441),x90443),f2(x90441)))+P1(f331(f331(f241(x90441),f331(f331(f291(x90441),x90442),x90443)),f331(f111(x90441),x90444)))+~P1(f331(f331(f241(x90441),x90442),f331(f331(f88(x90441),f331(f111(x90441),x90444)),x90443)))+~P1(f331(f331(f241(x90441),f331(f331(f88(x90441),f331(f111(x90441),x90444)),x90443)),x90442))
% 51.10/50.83 [9045]~P60(x90451)+~P92(x90451)+~P1(f331(f331(f241(x90451),x90453),f2(x90451)))+P1(f331(f331(f240(x90451),f331(f331(f291(x90451),x90452),x90453)),f331(f111(x90451),x90454)))+~P1(f331(f331(f240(x90451),x90452),f331(f331(f88(x90451),f331(f111(x90451),x90454)),x90453)))+~P1(f331(f331(f240(x90451),f331(f331(f88(x90451),f331(f111(x90451),x90454)),x90453)),x90452))
% 51.10/50.83 [9063]~P60(x90631)+~P92(x90631)+~P1(f331(f331(f241(x90631),f331(f111(x90631),x90632)),f2(x90631)))+P1(f331(f331(f241(x90631),f331(f111(x90631),x90632)),f331(f331(f291(x90631),x90633),x90634)))+~P1(f331(f331(f241(x90631),x90633),f331(f331(f88(x90631),f331(f111(x90631),x90632)),x90634)))+~P1(f331(f331(f241(x90631),f331(f331(f88(x90631),f331(f111(x90631),x90632)),x90634)),x90633))
% 51.10/50.83 [9064]~P60(x90641)+~P92(x90641)+~P1(f331(f331(f240(x90641),f331(f111(x90641),x90642)),f2(x90641)))+P1(f331(f331(f240(x90641),f331(f111(x90641),x90642)),f331(f331(f291(x90641),x90643),x90644)))+~P1(f331(f331(f240(x90641),x90643),f331(f331(f88(x90641),f331(f111(x90641),x90642)),x90644)))+~P1(f331(f331(f240(x90641),f331(f331(f88(x90641),f331(f111(x90641),x90642)),x90644)),x90643))
% 51.10/50.83 [9069]~P60(x90691)+~P92(x90691)+P1(f331(f331(f241(x90691),f331(f331(f291(x90691),x90692),x90693)),f331(f111(x90691),x90694)))+~P1(f331(f331(f241(x90691),f2(x90691)),f331(f111(x90691),x90694)))+~P1(f331(f331(f241(x90691),x90692),f331(f331(f88(x90691),f331(f111(x90691),x90694)),x90693)))+~P1(f331(f331(f241(x90691),f331(f331(f88(x90691),f331(f111(x90691),x90694)),x90693)),x90692))
% 51.10/50.83 [9070]~P60(x90701)+~P92(x90701)+P1(f331(f331(f240(x90701),f331(f331(f291(x90701),x90702),x90703)),f331(f111(x90701),x90704)))+~P1(f331(f331(f240(x90701),f2(x90701)),f331(f111(x90701),x90704)))+~P1(f331(f331(f240(x90701),x90702),f331(f331(f88(x90701),f331(f111(x90701),x90704)),x90703)))+~P1(f331(f331(f240(x90701),f331(f331(f88(x90701),f331(f111(x90701),x90704)),x90703)),x90702))
% 51.10/50.83 [5912]~P87(x59122)+~P127(x59122)+~E(f331(x59123,x59125),f2(x59122))+E(f331(f331(f11(x59121,x59122),x59123),x59124),f2(x59122))+~P1(f331(f68(x59121),x59124))+~P1(f331(f331(f333(x59121),x59125),x59124))
% 51.10/50.83 [8315]~P88(x83151)+P1(f331(f331(f241(f854(x83151,a840)),f303(x83151,x83152,x83153)),f303(x83151,x83154,x83155)))+~P1(f331(f331(f241(x83151),x83153),x83155))+~P1(f331(f331(f240(x83151),x83154),x83152))+~P1(f331(f331(f240(x83151),x83154),x83155))+~P1(f331(f331(f240(x83151),x83153),x83155))
% 51.10/50.83 [8316]~P88(x83161)+P1(f331(f331(f241(f854(x83161,a840)),f303(x83161,x83162,x83163)),f303(x83161,x83164,x83165)))+~P1(f331(f331(f241(x83161),x83164),x83162))+~P1(f331(f331(f240(x83161),x83163),x83165))+~P1(f331(f331(f240(x83161),x83164),x83165))+~P1(f331(f331(f240(x83161),x83164),x83162))
% 51.10/50.83 [9090]P55(x90902,x90903,x90904,x90901)+E(x90901,f184(f854(x90902,a840)))+~P1(f331(f68(x90902),x90904))+~P1(f331(f68(x90902),x90901))+~P1(f331(f331(x90903,f526(x90901,x90904,x90903,x90902)),x90905))+~P1(f331(f331(f333(x90902),x90905),x90901))
% 51.10/50.83 [9217]~E(x92173,x92175)+~P68(x92171)+~P70(x92171)+~P36(x92173)+E(f331(f331(f11(a1,x92171),x92172),x92173),f331(f331(f11(a1,x92171),x92174),x92175))+P1(f331(f331(f240(a1),f2(a1)),f515(x92172,x92174,x92173,x92175,x92171)))
% 51.10/50.83 [9218]~E(x92183,x92185)+~P68(x92181)+~P70(x92181)+~P36(x92183)+E(f331(f331(f8(a1,x92181),x92182),x92183),f331(f331(f8(a1,x92181),x92184),x92185))+P1(f331(f331(f240(a1),f2(a1)),f528(x92182,x92184,x92183,x92185,x92181)))
% 51.10/50.83 [9385]~E(x93855,x93853)+~P68(x93851)+~P70(x93851)+~P36(x93855)+~E(f331(x93852,f515(x93854,x93852,x93855,x93853,x93851)),f331(x93854,f515(x93854,x93852,x93855,x93853,x93851)))+E(f331(f331(f11(a1,x93851),x93852),x93853),f331(f331(f11(a1,x93851),x93854),x93855))
% 51.10/50.83 [9386]~E(x93865,x93863)+~P68(x93861)+~P70(x93861)+~P36(x93865)+~E(f331(x93862,f528(x93864,x93862,x93865,x93863,x93861)),f331(x93864,f528(x93864,x93862,x93865,x93863,x93861)))+E(f331(f331(f8(a1,x93861),x93862),x93863),f331(f331(f8(a1,x93861),x93864),x93865))
% 51.10/50.83 [9474]~P76(x94743)+E(f331(x94741,x94742),f2(x94743))+~E(f331(f331(f8(x94744,x94743),x94741),x94745),f2(x94743))+~P1(f331(f68(x94744),x94745))+P1(f331(f331(f333(x94744),f509(x94742,x94741,x94745,x94744,x94743)),x94745))+~P1(f331(f331(f333(x94744),x94742),x94745))
% 51.10/50.83 [9603]~P76(x96033)+E(f331(x96031,x96032),f2(x96033))+~E(f331(f331(f8(x96034,x96033),x96031),x96035),f2(x96033))+~P1(f331(f68(x96034),x96035))+~P1(f331(f331(f333(x96034),x96032),x96035))+~P1(f331(f331(f240(x96033),f2(x96033)),f331(x96031,f509(x96032,x96031,x96035,x96034,x96033))))
% 51.10/50.83 [8229]~P123(x82291)+~P1(f331(f331(f240(x82291),f2(x82291)),x82293))+~P1(f331(f331(f241(x82291),x82293),x82295))+~P1(f331(f331(f241(x82291),x82292),x82294))+~P1(f331(f331(f241(x82291),f2(x82291)),x82294))+P1(f331(f331(f241(x82291),f331(f331(f88(x82291),x82292),x82293)),f331(f331(f88(x82291),x82294),x82295)))
% 51.10/50.83 [8230]~P123(x82301)+~P1(f331(f331(f240(x82301),f2(x82301)),x82303))+~P1(f331(f331(f240(x82301),f2(x82301)),x82302))+~P1(f331(f331(f241(x82301),x82303),x82305))+~P1(f331(f331(f241(x82301),x82302),x82304))+P1(f331(f331(f241(x82301),f331(f331(f88(x82301),x82302),x82303)),f331(f331(f88(x82301),x82304),x82305)))
% 51.10/50.83 [8231]~P123(x82311)+~P1(f331(f331(f240(x82311),x82312),x82314))+~P1(f331(f331(f240(x82311),f2(x82311)),x82313))+~P1(f331(f331(f241(x82311),x82313),x82315))+~P1(f331(f331(f241(x82311),f2(x82311)),x82312))+P1(f331(f331(f241(x82311),f331(f331(f88(x82311),x82312),x82313)),f331(f331(f88(x82311),x82314),x82315)))
% 51.10/50.83 [8232]~P123(x82321)+~P1(f331(f331(f240(x82321),x82323),x82325))+~P1(f331(f331(f240(x82321),f2(x82321)),x82322))+~P1(f331(f331(f241(x82321),x82322),x82324))+~P1(f331(f331(f241(x82321),f2(x82321)),x82323))+P1(f331(f331(f241(x82321),f331(f331(f88(x82321),x82322),x82323)),f331(f331(f88(x82321),x82324),x82325)))
% 51.10/50.83 [8233]~P61(x82331)+~P1(f331(f331(f240(x82331),x82332),x82334))+~P1(f331(f331(f241(x82331),x82335),x82333))+~P1(f331(f331(f241(x82331),f2(x82331)),x82335))+~P1(f331(f331(f241(x82331),f2(x82331)),x82332))+P1(f331(f331(f241(x82331),f331(f331(f291(x82331),x82332),x82333)),f331(f331(f291(x82331),x82334),x82335)))
% 51.10/50.83 [8234]~P61(x82341)+~P1(f331(f331(f240(x82341),x82345),x82343))+~P1(f331(f331(f240(x82341),f2(x82341)),x82342))+~P1(f331(f331(f241(x82341),x82342),x82344))+~P1(f331(f331(f241(x82341),f2(x82341)),x82345))+P1(f331(f331(f241(x82341),f331(f331(f291(x82341),x82342),x82343)),f331(f331(f291(x82341),x82344),x82345)))
% 51.10/50.83 [8235]~P131(x82351)+~P1(f331(f331(f240(x82351),x82353),x82355))+~P1(f331(f331(f240(x82351),x82352),x82354))+~P1(f331(f331(f240(x82351),f2(x82351)),x82353))+~P1(f331(f331(f240(x82351),f2(x82351)),x82354))+P1(f331(f331(f240(x82351),f331(f331(f88(x82351),x82352),x82353)),f331(f331(f88(x82351),x82354),x82355)))
% 51.10/50.83 [8236]~P131(x82361)+~P1(f331(f331(f240(x82361),x82363),x82365))+~P1(f331(f331(f240(x82361),x82362),x82364))+~P1(f331(f331(f240(x82361),f2(x82361)),x82363))+~P1(f331(f331(f240(x82361),f2(x82361)),x82362))+P1(f331(f331(f240(x82361),f331(f331(f88(x82361),x82362),x82363)),f331(f331(f88(x82361),x82364),x82365)))
% 51.10/50.83 [8237]~P61(x82371)+~P1(f331(f331(f241(x82371),f2(x82371)),x82375))+~P1(f331(f331(f240(x82371),x82375),x82373))+~P1(f331(f331(f240(x82371),x82372),x82374))+~P1(f331(f331(f240(x82371),f2(x82371)),x82372))+P1(f331(f331(f240(x82371),f331(f331(f291(x82371),x82372),x82373)),f331(f331(f291(x82371),x82374),x82375)))
% 51.10/50.83 [9512]~P79(x95125)+~P68(x95125)+E(x95121,f184(f854(x95122,a840)))+~P1(f331(f68(x95122),x95121))+P1(f331(f331(f333(x95122),f513(x95123,x95124,x95121,x95122,x95125)),x95121))+P1(f331(f331(f241(x95125),f331(f331(f8(x95122,x95125),x95124),x95121)),f331(f331(f8(x95122,x95125),x95123),x95121)))
% 51.10/50.83 [9623]~P68(x96231)+~P77(x96231)+~P1(f331(f68(x96232),x96235))+~P1(f331(f331(f240(x96231),f2(x96231)),f331(x96233,f510(x96233,x96234,x96235,x96232,x96231))))+P1(f331(f331(f240(x96231),f331(f331(f8(x96232,x96231),x96233),x96234)),f331(f331(f8(x96232,x96231),x96233),x96235)))+~P1(f331(f331(f240(f854(x96232,a840)),x96234),x96235))
% 51.10/50.83 [9790]~P79(x97903)+~P68(x97903)+E(x97901,f184(f854(x97902,a840)))+~P1(f331(f68(x97902),x97901))+~P1(f331(f331(f241(x97903),f331(x97904,f513(x97905,x97904,x97901,x97902,x97903))),f331(x97905,f513(x97905,x97904,x97901,x97902,x97903))))+P1(f331(f331(f241(x97903),f331(f331(f8(x97902,x97903),x97904),x97901)),f331(f331(f8(x97902,x97903),x97905),x97901)))
% 51.10/50.83 [6941]~P19(x69412,x69415,x69414)+E(x69411,f184(f854(x69412,a840)))+E(x69413,f184(f854(x69412,a840)))+~P1(f331(f68(x69412),x69411))+~P1(f331(f68(x69412),x69413))+E(f331(x69414,f331(f331(f108(f854(x69412,a840)),x69413),x69411)),f331(f331(x69415,f331(x69414,x69413)),f331(x69414,x69411)))
% 51.10/50.83 [7549]~P141(x75491,x75494,x75493)+P1(f331(x75491,x75492))+~P1(f331(f331(f241(a1),x75494),f2(a1)))+~P1(f331(f331(f240(a1),x75495),f2(a1)))+~E(x75493,f331(f331(f87(a1),f331(f331(f88(a1),x75494),x75492)),x75495))+~P1(f331(f331(f241(a1),x75494),x75495))
% 51.10/50.83 [7550]~P140(x75501,x75504,x75503)+P1(f331(x75501,x75502))+~P1(f331(f331(f241(a1),x75504),f2(a1)))+~P1(f331(f331(f240(a1),x75502),f2(a1)))+~E(x75503,f331(f331(f87(a1),f331(f331(f88(a1),x75504),x75505)),x75502))+~P1(f331(f331(f241(a1),x75504),x75502))
% 51.10/50.83 [7593]~P141(x75931,x75934,x75933)+P1(f331(x75931,x75932))+~E(x75933,f331(f331(f87(a1),f331(f331(f88(a1),x75934),x75932)),x75935))+~P1(f331(f331(f241(a1),f2(a1)),x75934))+~P1(f331(f331(f240(a1),f2(a1)),x75935))+~P1(f331(f331(f241(a1),x75935),x75934))
% 51.10/50.83 [7594]~P140(x75941,x75944,x75943)+P1(f331(x75941,x75942))+~E(x75943,f331(f331(f87(a1),f331(f331(f88(a1),x75944),x75945)),x75942))+~P1(f331(f331(f241(a1),f2(a1)),x75944))+~P1(f331(f331(f240(a1),f2(a1)),x75942))+~P1(f331(f331(f241(a1),x75942),x75944))
% 51.10/50.83 [8517]P1(f331(f331(x85171,x85172),x85173))+~P1(f331(f331(x85171,f331(f331(f48(a1),x85174),x85175)),f57(a1,x85174,x85175)))+~P1(f331(f331(f241(a1),x85175),f2(a1)))+~P1(f331(f331(f240(a1),x85173),f2(a1)))+~E(x85174,f331(f331(f87(a1),f331(f331(f88(a1),x85175),x85172)),x85173))+~P1(f331(f331(f241(a1),x85175),x85173))
% 51.10/50.83 [8524]P1(f331(f331(x85241,x85242),x85243))+~P1(f331(f331(x85241,f331(f331(f48(a1),x85244),x85245)),f57(a1,x85244,x85245)))+~E(x85244,f331(f331(f87(a1),f331(f331(f88(a1),x85245),x85242)),x85243))+~P1(f331(f331(f241(a1),f2(a1)),x85245))+~P1(f331(f331(f240(a1),f2(a1)),x85243))+~P1(f331(f331(f241(a1),x85243),x85245))
% 51.10/50.83 [8744]E(x87441,x87442)+~P52(x87443,x87445,x87444)+~P1(f331(f331(f333(x87443),x87442),x87445))+~P1(f331(f331(f333(x87443),x87441),x87445))+P1(f331(f331(f333(f853(x87443,x87443)),f331(f331(f249(x87443,x87443),x87441),x87442)),x87444))+P1(f331(f331(f333(f853(x87443,x87443)),f331(f331(f249(x87443,x87443),x87442),x87441)),x87444))
% 51.10/50.83 [9542]~P68(x95425)+~P77(x95425)+~P1(f331(f68(x95421),x95424))+P1(f331(f331(f240(x95425),f331(f331(f8(x95421,x95425),x95422),x95423)),f331(f331(f8(x95421,x95425),x95422),x95424)))+~P1(f331(f331(f240(f854(x95421,a840)),x95423),x95424))+P1(f331(f331(f333(x95421),f510(x95422,x95423,x95424,x95421,x95425)),f331(f331(f3(f854(x95421,a840)),x95424),x95423)))
% 51.10/50.83 [9630]E(x96301,f184(f854(x96302,a840)))+~P1(f331(f68(x96302),x96303))+~P1(f331(f68(x96302),x96301))+P1(f331(f331(f333(f853(f854(x96302,a840),f854(x96302,a840))),f331(f331(f249(f854(x96302,a840),f854(x96302,a840)),x96303),x96301)),f323(x96302,x96304)))+~P1(f331(f331(f333(x96302),x96305),x96301))+~P1(f331(f331(f333(f853(x96302,x96302)),f331(f331(f249(x96302,x96302),f530(x96304,x96301,x96303,x96302)),x96305)),x96304))
% 51.10/50.83 [9631]E(x96311,f184(f854(x96312,a840)))+~P1(f331(f68(x96312),x96313))+~P1(f331(f68(x96312),x96311))+P1(f331(f331(f333(f853(f854(x96312,a840),f854(x96312,a840))),f331(f331(f249(f854(x96312,a840),f854(x96312,a840)),x96313),x96311)),f323(x96312,x96314)))+~P1(f331(f331(f333(x96312),x96315),x96311))+~P1(f331(f331(f333(f853(x96312,x96312)),f331(f331(f249(x96312,x96312),f626(x96314,x96311,x96313,x96312)),x96315)),x96314))
% 51.10/50.83 [9793]~P76(x97931)+~E(f331(f331(f8(x97935,x97931),x97932),x97936),x97934)+~P1(f331(f68(x97935),x97936))+P1(f331(f331(f333(x97935),f511(x97933,x97934,x97932,x97936,x97935,x97931)),x97936))+P1(f331(f331(f240(x97931),f331(x97932,x97933)),x97934))+~P1(f331(f331(f333(x97935),x97933),x97936))
% 51.10/50.83 [9851]~P76(x98511)+~E(f331(f331(f8(x98515,x98511),x98512),x98516),x98514)+~P1(f331(f68(x98515),x98516))+~P1(f331(f331(f333(x98515),x98513),x98516))+~P1(f331(f331(f240(x98511),f2(x98511)),f331(x98512,f511(x98513,x98514,x98512,x98516,x98515,x98511))))+P1(f331(f331(f240(x98511),f331(x98512,x98513)),x98514))
% 51.10/50.83 [9970]~E(x99705,x99708)+~E(x99704,x99707)+~P68(x99702)+~P104(x99701)+E(f331(f331(f8(x99701,x99702),x99703),f331(f302(x99701,x99704),x99705)),f331(f331(f8(x99701,x99702),x99706),f331(f302(x99701,x99707),x99708)))+P1(f331(f331(f240(x99701),x99704),f632(x99703,x99706,x99705,x99708,x99704,x99707,x99701,x99702)))
% 51.10/50.83 [9986]~E(x99867,x99864)+~E(x99868,x99865)+~P68(x99862)+~P104(x99861)+~E(f331(x99863,f632(x99866,x99863,x99868,x99865,x99867,x99864,x99861,x99862)),f331(x99866,f632(x99866,x99863,x99868,x99865,x99867,x99864,x99861,x99862)))+E(f331(f331(f8(x99861,x99862),x99863),f331(f302(x99861,x99864),x99865)),f331(f331(f8(x99861,x99862),x99866),f331(f302(x99861,x99867),x99868)))
% 51.10/50.83 [9989]~E(x99894,x99897)+~E(x99895,x99898)+~P68(x99892)+~P104(x99891)+E(f331(f331(f8(x99891,x99892),x99893),f331(f302(x99891,x99894),x99895)),f331(f331(f8(x99891,x99892),x99896),f331(f302(x99891,x99897),x99898)))+P1(f331(f331(f241(x99891),f632(x99893,x99896,x99895,x99898,x99894,x99897,x99891,x99892)),x99895))
% 51.10/50.83 [9635]~P10(x96355,x96359,x96356)+~P10(x96351,x963510,x96353)+~P15(x96351,x96355,f854(x96352,a840),x96353,x96356,x96358)+~P1(f331(f331(f333(x96355),x96357),x96359))+~P1(f331(f331(f333(x96351),x96354),x963510))+E(f331(f331(f51(x96351,f854(x96352,a840)),f331(f285(x96351,x96351,x96353),f331(f331(f310(x96351),x96354),f184(f854(x96351,a840))))),f331(f331(f10(f854(x96355,f854(x96352,a840)),f854(x96352,a840),x96351),f331(f51(x96355,f854(x96352,a840)),f331(f285(x96355,x96355,x96356),f331(f331(f310(x96355),x96357),f184(f854(x96355,a840)))))),x96358)),f331(f331(x96358,x96354),x96357))
% 51.10/50.83 [5435]~P102(x54353)+~P16(x54353,x54352)+~P16(x54353,x54351)+E(x54351,x54352)+~E(f331(f163(x54353),x54351),f331(f163(x54353),x54352))+~P1(f331(f132(x54353),x54352))+~P1(f331(f132(x54353),x54351))
% 51.10/50.83 [4790]~P122(x47902)+~P127(x47902)+~P138(x47902)+~P107(x47902)+~E(x47903,f2(x47902))+E(x47901,f2(a847))+E(f331(f331(f250(x47902),x47903),x47901),f2(x47902))
% 51.10/50.83 [8976]E(x89761,f2(a847))+~E(x89762,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x89763)),x89761)),f331(f258(a847,a847),x89763)))+P1(f331(f60(x89762,x89761),x89763))+~P1(f331(f331(f240(a847),f331(f258(a847,a847),x89763)),f2(a847)))+~P1(f331(f331(f240(a847),f2(a847)),f331(f258(a847,a847),x89763)))+~P1(f331(f331(f241(a847),x89761),f331(f258(a847,a847),x89763)))+~P1(f331(f331(f241(a847),f331(f258(a847,a847),x89763)),x89761))
% 51.10/50.83 [8985]~E(f331(f248(a847,a847),x89853),f2(a847))+~E(x89851,f331(f331(f87(a847),f331(f331(f88(a847),f331(f248(a847,a847),x89853)),x89852)),f331(f258(a847,a847),x89853)))+P1(f331(f60(x89851,x89852),x89853))+~P1(f331(f331(f240(a847),f331(f258(a847,a847),x89853)),f2(a847)))+~P1(f331(f331(f240(a847),f2(a847)),f331(f258(a847,a847),x89853)))+~P1(f331(f331(f241(a847),x89852),f331(f258(a847,a847),x89853)))+~P1(f331(f331(f241(a847),f331(f258(a847,a847),x89853)),x89852))
% 51.10/50.83 [7426]~P97(x74262)+E(x74261,f184(f854(x74262,a840)))+E(x74263,f184(f854(x74262,a840)))+~P1(f331(f68(x74262),x74261))+~P1(f331(f68(x74262),x74263))+~E(f331(f331(f109(f854(x74262,a840)),x74263),x74261),f184(f854(x74262,a840)))+E(f12(x74262,f331(f331(f108(f854(x74262,a840)),x74263),x74261)),f331(f331(f109(x74262),f12(x74262,x74263)),f12(x74262,x74261)))
% 51.10/50.83 [7427]~P97(x74272)+E(x74271,f184(f854(x74272,a840)))+E(x74273,f184(f854(x74272,a840)))+~P1(f331(f68(x74272),x74271))+~P1(f331(f68(x74272),x74273))+~E(f331(f331(f109(f854(x74272,a840)),x74273),x74271),f184(f854(x74272,a840)))+E(f15(x74272,f331(f331(f108(f854(x74272,a840)),x74273),x74271)),f331(f331(f108(x74272),f15(x74272,x74273)),f15(x74272,x74271)))
% 51.10/50.83 [7428]~P102(x74282)+E(x74281,f184(f854(x74282,a840)))+E(x74283,f184(f854(x74282,a840)))+~P1(f331(f68(x74282),x74281))+~P1(f331(f68(x74282),x74283))+~E(f331(f331(f109(f854(x74282,a840)),x74283),x74281),f184(f854(x74282,a840)))+E(f16(x74282,f331(f331(f108(f854(x74282,a840)),x74283),x74281)),f331(f331(f239(x74282),f16(x74282,x74283)),f16(x74282,x74281)))
% 51.10/50.83 [7429]~P102(x74292)+E(x74291,f184(f854(x74292,a840)))+E(x74293,f184(f854(x74292,a840)))+~P1(f331(f68(x74292),x74291))+~P1(f331(f68(x74292),x74293))+~E(f331(f331(f109(f854(x74292,a840)),x74293),x74291),f184(f854(x74292,a840)))+E(f17(x74292,f331(f331(f108(f854(x74292,a840)),x74293),x74291)),f331(f331(f244(x74292),f17(x74292,x74293)),f17(x74292,x74291)))
% 51.10/50.83 [7908]~P64(x79082)+E(x79081,f184(f854(x79082,a840)))+E(x79083,f184(f854(x79082,a840)))+~P1(f331(f68(x79082),x79081))+~P1(f331(f68(x79082),x79083))+~E(f331(f331(f109(f854(x79082,a840)),x79083),x79081),f184(f854(x79082,a840)))+E(f331(f331(f88(x79082),f331(f70(x79082,f88(x79082)),x79083)),f331(f70(x79082,f88(x79082)),x79081)),f331(f70(x79082,f88(x79082)),f331(f331(f108(f854(x79082,a840)),x79083),x79081)))
% 51.10/50.83 [7978]~P102(x79782)+E(x79781,f184(f854(x79782,a840)))+E(x79783,f184(f854(x79782,a840)))+~P1(f331(f68(x79782),x79781))+~P1(f331(f68(x79782),x79783))+~E(f331(f331(f109(f854(x79782,a840)),x79783),x79781),f184(f854(x79782,a840)))+E(f331(f331(f239(x79782),f13(x79782,f239(x79782),x79783)),f13(x79782,f239(x79782),x79781)),f13(x79782,f239(x79782),f331(f331(f108(f854(x79782,a840)),x79783),x79781)))
% 51.10/50.83 [7979]~P102(x79792)+E(x79791,f184(f854(x79792,a840)))+E(x79793,f184(f854(x79792,a840)))+~P1(f331(f68(x79792),x79791))+~P1(f331(f68(x79792),x79793))+~E(f331(f331(f109(f854(x79792,a840)),x79793),x79791),f184(f854(x79792,a840)))+E(f331(f331(f244(x79792),f14(x79792,f244(x79792),x79793)),f14(x79792,f244(x79792),x79791)),f14(x79792,f244(x79792),f331(f331(f108(f854(x79792,a840)),x79793),x79791)))
% 51.10/50.83 [7687]E(x76871,f2(a1))+E(f331(f331(f48(a1),x76872),x76871),x76873)+~P1(f331(f331(f240(a1),x76874),f2(a1)))+~E(x76872,f331(f331(f87(a1),f331(f331(f88(a1),x76871),x76873)),x76874))+~P1(f331(f331(f240(a1),f2(a1)),x76874))+~P1(f331(f331(f241(a1),x76874),x76871))+~P1(f331(f331(f241(a1),x76871),x76874))
% 51.10/50.83 [7693]E(f57(a1,x76932,x76931),x76933)+E(x76931,f2(a1))+~P1(f331(f331(f240(a1),x76933),f2(a1)))+~E(x76932,f331(f331(f87(a1),f331(f331(f88(a1),x76931),x76934)),x76933))+~P1(f331(f331(f240(a1),f2(a1)),x76933))+~P1(f331(f331(f241(a1),x76933),x76931))+~P1(f331(f331(f241(a1),x76931),x76933))
% 51.10/50.83 [6715]~P5(x67152)+E(x67151,f2(x67152))+E(x67153,f2(x67152))+~E(f331(f331(f48(x67152),x67154),x67153),f331(f331(f48(x67152),x67155),x67151))+E(f331(f331(f88(x67152),x67154),x67151),f331(f331(f88(x67152),x67153),x67155))+~P1(f331(f331(f287(x67152),x67151),x67155))+~P1(f331(f331(f287(x67152),x67153),x67154))
% 51.10/50.83 [6716]~P5(x67162)+E(x67161,f2(x67162))+E(x67163,f2(x67162))+~E(f331(f331(f88(x67162),x67164),x67163),f331(f331(f88(x67162),x67161),x67165))+E(f331(f331(f48(x67162),x67164),x67161),f331(f331(f48(x67162),x67165),x67163))+~P1(f331(f331(f287(x67162),x67161),x67164))+~P1(f331(f331(f287(x67162),x67163),x67165))
% 51.10/50.83 [7602]~P20(x76022,x76025,x76024)+E(x76021,f184(f854(x76022,a840)))+E(x76023,f184(f854(x76022,a840)))+~P1(f331(f68(x76022),x76021))+~P1(f331(f68(x76022),x76023))+~E(f331(f331(f109(f854(x76022,a840)),x76023),x76021),f184(f854(x76022,a840)))+E(f331(x76024,f331(f331(f108(f854(x76022,a840)),x76023),x76021)),f331(f331(x76025,f331(x76024,x76023)),f331(x76024,x76021)))
% 51.10/50.83 [9189]~P27(x91893,x91891,x91895,x91894)+~P27(x91891,x91893,x91896,x91892)+E(f331(f47(x91891),x91892),f331(f47(x91893),x91894))+~P1(f331(f68(x91893),x91894))+~P1(f331(f68(x91891),x91892))+~P1(f331(f331(f240(f854(x91893,a840)),f331(f311(x91891,x91893,x91896),x91892)),x91894))+~P1(f331(f331(f240(f854(x91891,a840)),f331(f311(x91893,x91891,x91895),x91894)),x91892))
% 51.10/50.83 [9137]~P1(f331(f331(f241(a1),f331(f331(f87(a1),f331(f331(f88(a1),x91375),x91371)),x91376)),f2(a1)))+~E(f331(f331(f87(a1),f331(f331(f88(a1),x91373),x91372)),x91374),f331(f331(f87(a1),f331(f331(f88(a1),x91375),x91371)),x91376))+~P1(f331(f331(f241(a1),f2(a1)),x91375))+~P1(f331(f331(f240(a1),f2(a1)),x91376))+~P1(f331(f331(f241(a1),x91374),x91373))+~P1(f331(f331(f240(a1),x91375),x91373))+P1(f331(f331(f240(a1),x91371),x91372))
% 51.10/50.83 [8931]~E(f331(f331(f87(a1),f331(f331(f88(a1),x89313),x89311)),x89314),f331(f331(f87(a1),f331(f331(f88(a1),x89315),x89312)),x89316))+~P1(f331(f331(f241(a1),f2(a1)),x89315))+~P1(f331(f331(f240(a1),f2(a1)),x89314))+~P1(f331(f331(f241(a1),x89316),x89315))+~P1(f331(f331(f240(a1),x89315),x89313))+P1(f331(f331(f240(a1),x89311),x89312))+~P1(f331(f331(f240(a1),f2(a1)),f331(f331(f87(a1),f331(f331(f88(a1),x89315),x89312)),x89316)))
% 51.10/50.83 [9092]~P124(x90921)+~E(f331(f331(f87(x90921),x90922),x90924),f85(x90921))+~P1(f331(f331(f240(x90921),f2(x90921)),x90924))+~P1(f331(f331(f240(x90921),f2(x90921)),x90922))+~P1(f331(f331(f241(x90921),x90925),x90926))+~P1(f331(f331(f241(x90921),x90923),x90926))+P1(f331(f331(f241(x90921),f331(f331(f87(x90921),f331(f331(f88(x90921),x90922),x90923)),f331(f331(f88(x90921),x90924),x90925))),x90926))
% 51.10/50.83 [9093]~P126(x90931)+~E(f331(f331(f87(x90931),x90932),x90934),f85(x90931))+~P1(f331(f331(f240(x90931),x90935),x90936))+~P1(f331(f331(f240(x90931),x90933),x90936))+~P1(f331(f331(f240(x90931),f2(x90931)),x90934))+~P1(f331(f331(f240(x90931),f2(x90931)),x90932))+P1(f331(f331(f240(x90931),f331(f331(f87(x90931),f331(f331(f88(x90931),x90932),x90933)),f331(f331(f88(x90931),x90934),x90935))),x90936))
% 51.10/50.83 [9893]~P10(x98937,x98936,x98935)+E(x98931,x98932)+~P14(x98937,f854(x98934,a840),x98935,x98933)+E(f331(x98933,f415(x98931,x98932,x98933,x98934,x98935,x98936,x98937)),f331(x98933,f416(x98931,x98932,x98933,x98934,x98935,x98936,x98937)))+~E(f331(f331(f51(x98937,f854(x98934,a840)),x98931),x98933),f331(f331(f51(x98937,f854(x98934,a840)),x98932),x98933))+~P1(f331(f331(f333(f854(x98937,a840)),x98932),f331(f331(f66(x98937),x98936),x98935)))+~P1(f331(f331(f333(f854(x98937,a840)),x98931),f331(f331(f66(x98937),x98936),x98935)))
% 51.10/50.83 [9934]~P10(x99343,x99347,x99346)+E(x99341,x99342)+~P14(x99343,f854(x99345,a840),x99346,x99344)+~E(f331(f331(f51(x99343,f854(x99345,a840)),x99341),x99344),f331(f331(f51(x99343,f854(x99345,a840)),x99342),x99344))+P1(f331(f331(f333(x99343),f416(x99341,x99342,x99344,x99345,x99346,x99347,x99343)),x99347))+~P1(f331(f331(f333(f854(x99343,a840)),x99342),f331(f331(f66(x99343),x99347),x99346)))+~P1(f331(f331(f333(f854(x99343,a840)),x99341),f331(f331(f66(x99343),x99347),x99346)))
% 51.10/50.83 [9935]~P10(x99353,x99357,x99356)+E(x99351,x99352)+~P14(x99353,f854(x99355,a840),x99356,x99354)+~E(f331(f331(f51(x99353,f854(x99355,a840)),x99351),x99354),f331(f331(f51(x99353,f854(x99355,a840)),x99352),x99354))+P1(f331(f331(f333(x99353),f415(x99351,x99352,x99354,x99355,x99356,x99357,x99353)),x99357))+~P1(f331(f331(f333(f854(x99353,a840)),x99352),f331(f331(f66(x99353),x99357),x99356)))+~P1(f331(f331(f333(f854(x99353,a840)),x99351),f331(f331(f66(x99353),x99357),x99356)))
% 51.10/50.83 [10004]E(x100041,x100042)+~P10(x100043,x100046,x100047)+~P14(x100043,f854(x100044,a840),x100047,x100045)+~E(f331(f331(f51(x100043,f854(x100044,a840)),x100041),x100045),f331(f331(f51(x100043,f854(x100044,a840)),x100042),x100045))+~P1(f331(f331(f333(f853(x100043,x100043)),f331(f331(f249(x100043,x100043),f416(x100041,x100042,x100045,x100044,x100047,x100046,x100043)),f415(x100041,x100042,x100045,x100044,x100047,x100046,x100043))),x100047))+~P1(f331(f331(f333(f854(x100043,a840)),x100042),f331(f331(f66(x100043),x100046),x100047)))+~P1(f331(f331(f333(f854(x100043,a840)),x100041),f331(f331(f66(x100043),x100046),x100047)))
% 51.10/50.83 [8930]~P10(x89301,x89307,x89304)+~E(x89305,x89306)+~P1(f331(f331(f333(x89301),x89303),x89306))+~P1(f331(f331(f333(x89301),x89302),x89305))+~P1(f331(f331(f333(f854(x89301,a840)),x89306),f331(f331(f66(x89301),x89307),x89304)))+~P1(f331(f331(f333(f854(x89301,a840)),x89305),f331(f331(f66(x89301),x89307),x89304)))+P1(f331(f331(f333(f853(x89301,x89301)),f331(f331(f249(x89301,x89301),x89302),x89303)),x89304))
% 51.10/50.83 [9058]E(x90581,x90582)+~P10(x90583,x90584,x90585)+~P1(f331(f331(f333(x90583),x90586),x90582))+~P1(f331(f331(f333(x90583),x90587),x90581))+~P1(f331(f331(f333(f854(x90583,a840)),x90582),f331(f331(f66(x90583),x90584),x90585)))+~P1(f331(f331(f333(f854(x90583,a840)),x90581),f331(f331(f66(x90583),x90584),x90585)))+~P1(f331(f331(f333(f853(x90583,x90583)),f331(f331(f249(x90583,x90583),x90587),x90586)),x90585))
% 51.10/50.83 [9059]E(x90591,x90592)+~P10(x90593,x90594,x90595)+~P1(f331(f331(f333(x90593),x90596),x90592))+~P1(f331(f331(f333(x90593),x90597),x90591))+~P1(f331(f331(f333(f854(x90593,a840)),x90592),f331(f331(f66(x90593),x90594),x90595)))+~P1(f331(f331(f333(f854(x90593,a840)),x90591),f331(f331(f66(x90593),x90594),x90595)))+~P1(f331(f331(f333(f853(x90593,x90593)),f331(f331(f249(x90593,x90593),x90597),x90596)),x90595))
% 51.10/50.83 [10022]~P10(x100229,x100228,x100227)+~P10(x100221,x1002211,x1002210)+~P15(x100221,x100229,f854(x100226,a840),x1002210,x100227,x100225)+P1(f331(f331(f333(x100221),f420(x100222,x100223,x100224,x100225,x100226,x100227,x100228,x100229,x1002210,x1002211,x100221)),x1002211))+~P1(f331(f331(f333(f854(x100229,a840)),x100223),f331(f331(f66(x100229),x100228),x100227)))+~P1(f331(f331(f333(f854(x100221,a840)),x100224),f331(f331(f66(x100221),x1002211),x1002210)))+P1(f331(f331(f333(f854(x100226,a840)),f331(f331(f51(x100221,f854(x100226,a840)),x100224),f331(f331(f10(f854(x100229,f854(x100226,a840)),f854(x100226,a840),x100221),f331(f51(x100229,f854(x100226,a840)),x100223)),x100225))),x100222))
% 51.10/50.83 [10023]~P10(x1002311,x1002310,x100239)+~P10(x100231,x100238,x100237)+~P15(x1002311,x100231,f854(x100236,a840),x100239,x100237,x100235)+P1(f331(f331(f333(x100231),f421(x100232,x100233,x100234,x100235,x100236,x100237,x100238,x100231,x100239,x1002310,x1002311)),x100238))+~P1(f331(f331(f333(f854(x1002311,a840)),x100234),f331(f331(f66(x1002311),x1002310),x100239)))+~P1(f331(f331(f333(f854(x100231,a840)),x100233),f331(f331(f66(x100231),x100238),x100237)))+P1(f331(f331(f333(f854(x100236,a840)),f331(f331(f51(x1002311,f854(x100236,a840)),x100234),f331(f331(f10(f854(x100231,f854(x100236,a840)),f854(x100236,a840),x1002311),f331(f51(x100231,f854(x100236,a840)),x100233)),x100235))),x100232))
% 51.10/50.83 [10026]~P10(x100262,x100268,x100269)+~P10(x100264,x1002610,x1002611)+~P15(x100262,x100264,f854(x100261,a840),x100269,x1002611,x100266)+~P1(f331(f331(f333(f854(x100262,a840)),x100263),f331(f331(f66(x100262),x100268),x100269)))+~P1(f331(f331(f333(f854(x100264,a840)),x100265),f331(f331(f66(x100264),x1002610),x1002611)))+~P1(f331(f331(f333(f854(x100261,a840)),f331(f331(x100266,f420(x100267,x100265,x100263,x100266,x100261,x1002611,x1002610,x100264,x100269,x100268,x100262)),f421(x100267,x100265,x100263,x100266,x100261,x1002611,x1002610,x100264,x100269,x100268,x100262))),x100267))+P1(f331(f331(f333(f854(x100261,a840)),f331(f331(f51(x100262,f854(x100261,a840)),x100263),f331(f331(f10(f854(x100264,f854(x100261,a840)),f854(x100261,a840),x100262),f331(f51(x100264,f854(x100261,a840)),x100265)),x100266))),x100267))
% 51.10/50.83 [8969]E(x89691,x89692)+~P102(x89694)+~P27(x89693,x89694,x89695,f331(f331(f108(f854(x89693,a840)),f331(f163(x89693),x89691)),f331(f163(x89693),x89692)))+~E(f331(f163(x89693),x89691),f331(f163(x89693),x89692))+~P16(x89694,f331(f331(f147(x89693,x89694),x89695),x89692))+~P16(x89694,f331(f331(f147(x89693,x89694),x89695),x89691))+~P1(f331(f132(x89694),f331(f331(f147(x89693,x89694),x89695),x89692)))+~P1(f331(f132(x89694),f331(f331(f147(x89693,x89694),x89695),x89691)))
% 51.10/50.83 %EqnAxiom
% 51.10/50.83 [1]E(x11,x11)
% 51.10/50.83 [2]E(x22,x21)+~E(x21,x22)
% 51.10/50.83 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 51.10/50.83 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 51.10/50.83 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 51.10/50.83 [6]~E(x61,x62)+E(f107(x61),f107(x62))
% 51.10/50.83 [7]~E(x71,x72)+E(f36(x71),f36(x72))
% 51.10/50.83 [8]~E(x81,x82)+E(f331(x81,x83),f331(x82,x83))
% 51.10/50.83 [9]~E(x91,x92)+E(f331(x93,x91),f331(x93,x92))
% 51.10/50.83 [10]~E(x101,x102)+E(f91(x101),f91(x102))
% 51.10/50.83 [11]~E(x111,x112)+E(f145(x111),f145(x112))
% 51.10/50.83 [12]~E(x121,x122)+E(f241(x121),f241(x122))
% 51.10/50.83 [13]~E(x131,x132)+E(f87(x131),f87(x132))
% 51.10/50.83 [14]~E(x141,x142)+E(f184(x141),f184(x142))
% 51.10/50.83 [15]~E(x151,x152)+E(f421(x151,x153,x154,x155,x156,x157,x158,x159,x1510,x1511,x1512),f421(x152,x153,x154,x155,x156,x157,x158,x159,x1510,x1511,x1512))
% 51.10/50.83 [16]~E(x161,x162)+E(f421(x163,x161,x164,x165,x166,x167,x168,x169,x1610,x1611,x1612),f421(x163,x162,x164,x165,x166,x167,x168,x169,x1610,x1611,x1612))
% 51.10/50.83 [17]~E(x171,x172)+E(f421(x173,x174,x171,x175,x176,x177,x178,x179,x1710,x1711,x1712),f421(x173,x174,x172,x175,x176,x177,x178,x179,x1710,x1711,x1712))
% 51.10/50.83 [18]~E(x181,x182)+E(f421(x183,x184,x185,x181,x186,x187,x188,x189,x1810,x1811,x1812),f421(x183,x184,x185,x182,x186,x187,x188,x189,x1810,x1811,x1812))
% 51.10/50.83 [19]~E(x191,x192)+E(f421(x193,x194,x195,x196,x191,x197,x198,x199,x1910,x1911,x1912),f421(x193,x194,x195,x196,x192,x197,x198,x199,x1910,x1911,x1912))
% 51.10/50.83 [20]~E(x201,x202)+E(f421(x203,x204,x205,x206,x207,x201,x208,x209,x2010,x2011,x2012),f421(x203,x204,x205,x206,x207,x202,x208,x209,x2010,x2011,x2012))
% 51.10/50.83 [21]~E(x211,x212)+E(f421(x213,x214,x215,x216,x217,x218,x211,x219,x2110,x2111,x2112),f421(x213,x214,x215,x216,x217,x218,x212,x219,x2110,x2111,x2112))
% 51.10/50.84 [22]~E(x221,x222)+E(f421(x223,x224,x225,x226,x227,x228,x229,x221,x2210,x2211,x2212),f421(x223,x224,x225,x226,x227,x228,x229,x222,x2210,x2211,x2212))
% 51.10/50.84 [23]~E(x231,x232)+E(f421(x233,x234,x235,x236,x237,x238,x239,x2310,x231,x2311,x2312),f421(x233,x234,x235,x236,x237,x238,x239,x2310,x232,x2311,x2312))
% 51.10/50.84 [24]~E(x241,x242)+E(f421(x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x241,x2412),f421(x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x242,x2412))
% 51.10/50.84 [25]~E(x251,x252)+E(f421(x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512,x251),f421(x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512,x252))
% 51.10/50.84 [26]~E(x261,x262)+E(f239(x261),f239(x262))
% 51.10/50.84 [27]~E(x271,x272)+E(f108(x271),f108(x272))
% 51.10/50.84 [28]~E(x281,x282)+E(f244(x281),f244(x282))
% 51.10/50.84 [29]~E(x291,x292)+E(f109(x291),f109(x292))
% 51.10/50.84 [30]~E(x301,x302)+E(f110(x301),f110(x302))
% 51.10/50.84 [31]~E(x311,x312)+E(f39(x311),f39(x312))
% 51.10/50.84 [32]~E(x321,x322)+E(f848(x321),f848(x322))
% 51.10/50.84 [33]~E(x331,x332)+E(f85(x331),f85(x332))
% 51.10/50.84 [34]~E(x341,x342)+E(f420(x341,x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412),f420(x342,x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412))
% 51.10/50.84 [35]~E(x351,x352)+E(f420(x353,x351,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f420(x353,x352,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512))
% 51.10/50.84 [36]~E(x361,x362)+E(f420(x363,x364,x361,x365,x366,x367,x368,x369,x3610,x3611,x3612),f420(x363,x364,x362,x365,x366,x367,x368,x369,x3610,x3611,x3612))
% 51.10/50.84 [37]~E(x371,x372)+E(f420(x373,x374,x375,x371,x376,x377,x378,x379,x3710,x3711,x3712),f420(x373,x374,x375,x372,x376,x377,x378,x379,x3710,x3711,x3712))
% 51.10/50.84 [38]~E(x381,x382)+E(f420(x383,x384,x385,x386,x381,x387,x388,x389,x3810,x3811,x3812),f420(x383,x384,x385,x386,x382,x387,x388,x389,x3810,x3811,x3812))
% 51.10/50.84 [39]~E(x391,x392)+E(f420(x393,x394,x395,x396,x397,x391,x398,x399,x3910,x3911,x3912),f420(x393,x394,x395,x396,x397,x392,x398,x399,x3910,x3911,x3912))
% 51.10/50.84 [40]~E(x401,x402)+E(f420(x403,x404,x405,x406,x407,x408,x401,x409,x4010,x4011,x4012),f420(x403,x404,x405,x406,x407,x408,x402,x409,x4010,x4011,x4012))
% 51.10/50.84 [41]~E(x411,x412)+E(f420(x413,x414,x415,x416,x417,x418,x419,x411,x4110,x4111,x4112),f420(x413,x414,x415,x416,x417,x418,x419,x412,x4110,x4111,x4112))
% 51.10/50.84 [42]~E(x421,x422)+E(f420(x423,x424,x425,x426,x427,x428,x429,x4210,x421,x4211,x4212),f420(x423,x424,x425,x426,x427,x428,x429,x4210,x422,x4211,x4212))
% 51.10/50.84 [43]~E(x431,x432)+E(f420(x433,x434,x435,x436,x437,x438,x439,x4310,x4311,x431,x4312),f420(x433,x434,x435,x436,x437,x438,x439,x4310,x4311,x432,x4312))
% 51.10/50.84 [44]~E(x441,x442)+E(f420(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412,x441),f420(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412,x442))
% 51.10/50.84 [45]~E(x451,x452)+E(f118(x451),f118(x452))
% 51.10/50.84 [46]~E(x461,x462)+E(f333(x461),f333(x462))
% 51.10/50.84 [47]~E(x471,x472)+E(f854(x471,x473),f854(x472,x473))
% 51.10/50.84 [48]~E(x481,x482)+E(f854(x483,x481),f854(x483,x482))
% 51.10/50.84 [49]~E(x491,x492)+E(f6(x491),f6(x492))
% 51.10/50.84 [50]~E(x501,x502)+E(f169(x501,x503),f169(x502,x503))
% 51.10/50.84 [51]~E(x511,x512)+E(f169(x513,x511),f169(x513,x512))
% 51.10/50.84 [52]~E(x521,x522)+E(f40(x521),f40(x522))
% 51.10/50.84 [53]~E(x531,x532)+E(f42(x531),f42(x532))
% 51.10/50.84 [54]~E(x541,x542)+E(f149(x541,x543,x544,x545),f149(x542,x543,x544,x545))
% 51.10/50.84 [55]~E(x551,x552)+E(f149(x553,x551,x554,x555),f149(x553,x552,x554,x555))
% 51.10/50.84 [56]~E(x561,x562)+E(f149(x563,x564,x561,x565),f149(x563,x564,x562,x565))
% 51.10/50.84 [57]~E(x571,x572)+E(f149(x573,x574,x575,x571),f149(x573,x574,x575,x572))
% 51.10/50.84 [58]~E(x581,x582)+E(f41(x581),f41(x582))
% 51.10/50.84 [59]~E(x591,x592)+E(f851(x591),f851(x592))
% 51.10/50.84 [60]~E(x601,x602)+E(f120(x601),f120(x602))
% 51.10/50.84 [61]~E(x611,x612)+E(f86(x611),f86(x612))
% 51.10/50.84 [62]~E(x621,x622)+E(f303(x621,x623,x624),f303(x622,x623,x624))
% 51.10/50.84 [63]~E(x631,x632)+E(f303(x633,x631,x634),f303(x633,x632,x634))
% 51.10/50.84 [64]~E(x641,x642)+E(f303(x643,x644,x641),f303(x643,x644,x642))
% 51.10/50.84 [65]~E(x651,x652)+E(f185(x651),f185(x652))
% 51.10/50.84 [66]~E(x661,x662)+E(f291(x661),f291(x662))
% 51.10/50.84 [67]~E(x671,x672)+E(f111(x671),f111(x672))
% 51.10/50.84 [68]~E(x681,x682)+E(f287(x681),f287(x682))
% 51.10/50.84 [69]~E(x691,x692)+E(f66(x691),f66(x692))
% 51.10/50.84 [70]~E(x701,x702)+E(f9(x701,x703,x704),f9(x702,x703,x704))
% 51.10/50.84 [71]~E(x711,x712)+E(f9(x713,x711,x714),f9(x713,x712,x714))
% 51.10/50.84 [72]~E(x721,x722)+E(f9(x723,x724,x721),f9(x723,x724,x722))
% 51.10/50.84 [73]~E(x731,x732)+E(f8(x731,x733),f8(x732,x733))
% 51.10/50.84 [74]~E(x741,x742)+E(f8(x743,x741),f8(x743,x742))
% 51.10/50.84 [75]~E(x751,x752)+E(f240(x751),f240(x752))
% 51.10/50.84 [76]~E(x761,x762)+E(f68(x761),f68(x762))
% 51.10/50.84 [77]~E(x771,x772)+E(f121(x771,x773),f121(x772,x773))
% 51.10/50.84 [78]~E(x781,x782)+E(f121(x783,x781),f121(x783,x782))
% 51.10/50.84 [79]~E(x791,x792)+E(f161(x791,x793,x794),f161(x792,x793,x794))
% 51.10/50.84 [80]~E(x801,x802)+E(f161(x803,x801,x804),f161(x803,x802,x804))
% 51.10/50.84 [81]~E(x811,x812)+E(f161(x813,x814,x811),f161(x813,x814,x812))
% 51.10/50.84 [82]~E(x821,x822)+E(f137(x821,x823,x824,x825),f137(x822,x823,x824,x825))
% 51.10/50.84 [83]~E(x831,x832)+E(f137(x833,x831,x834,x835),f137(x833,x832,x834,x835))
% 51.10/50.84 [84]~E(x841,x842)+E(f137(x843,x844,x841,x845),f137(x843,x844,x842,x845))
% 51.10/50.84 [85]~E(x851,x852)+E(f137(x853,x854,x855,x851),f137(x853,x854,x855,x852))
% 51.10/50.84 [86]~E(x861,x862)+E(f48(x861),f48(x862))
% 51.10/50.84 [87]~E(x871,x872)+E(f310(x871),f310(x872))
% 51.10/50.84 [88]~E(x881,x882)+E(f155(x881),f155(x882))
% 51.10/50.84 [89]~E(x891,x892)+E(f163(x891),f163(x892))
% 51.10/50.84 [90]~E(x901,x902)+E(f103(x901),f103(x902))
% 51.10/50.84 [91]~E(x911,x912)+E(f18(x911,x913),f18(x912,x913))
% 51.10/50.84 [92]~E(x921,x922)+E(f18(x923,x921),f18(x923,x922))
% 51.10/50.84 [93]~E(x931,x932)+E(f88(x931),f88(x932))
% 51.10/50.84 [94]~E(x941,x942)+E(f82(x941),f82(x942))
% 51.10/50.84 [95]~E(x951,x952)+E(f20(x951,x953,x954),f20(x952,x953,x954))
% 51.10/50.84 [96]~E(x961,x962)+E(f20(x963,x961,x964),f20(x963,x962,x964))
% 51.10/50.84 [97]~E(x971,x972)+E(f20(x973,x974,x971),f20(x973,x974,x972))
% 51.10/50.84 [98]~E(x981,x982)+E(f51(x981,x983),f51(x982,x983))
% 51.10/50.84 [99]~E(x991,x992)+E(f51(x993,x991),f51(x993,x992))
% 51.10/50.84 [100]~E(x1001,x1002)+E(f853(x1001,x1003),f853(x1002,x1003))
% 51.10/50.84 [101]~E(x1011,x1012)+E(f853(x1013,x1011),f853(x1013,x1012))
% 51.10/50.84 [102]~E(x1021,x1022)+E(f133(x1021),f133(x1022))
% 51.10/50.84 [103]~E(x1031,x1032)+E(f311(x1031,x1033,x1034),f311(x1032,x1033,x1034))
% 51.10/50.84 [104]~E(x1041,x1042)+E(f311(x1043,x1041,x1044),f311(x1043,x1042,x1044))
% 51.10/50.84 [105]~E(x1051,x1052)+E(f311(x1053,x1054,x1051),f311(x1053,x1054,x1052))
% 51.10/50.84 [106]~E(x1061,x1062)+E(f10(x1061,x1063,x1064),f10(x1062,x1063,x1064))
% 51.10/50.84 [107]~E(x1071,x1072)+E(f10(x1073,x1071,x1074),f10(x1073,x1072,x1074))
% 51.10/50.84 [108]~E(x1081,x1082)+E(f10(x1083,x1084,x1081),f10(x1083,x1084,x1082))
% 51.10/50.84 [109]~E(x1091,x1092)+E(f249(x1091,x1093),f249(x1092,x1093))
% 51.10/50.84 [110]~E(x1101,x1102)+E(f249(x1103,x1101),f249(x1103,x1102))
% 51.10/50.84 [111]~E(x1111,x1112)+E(f130(x1111),f130(x1112))
% 51.10/50.84 [112]~E(x1121,x1122)+E(f821(x1121,x1123,x1124),f821(x1122,x1123,x1124))
% 51.10/50.84 [113]~E(x1131,x1132)+E(f821(x1133,x1131,x1134),f821(x1133,x1132,x1134))
% 51.10/50.84 [114]~E(x1141,x1142)+E(f821(x1143,x1144,x1141),f821(x1143,x1144,x1142))
% 51.10/50.84 [115]~E(x1151,x1152)+E(f33(x1151,x1153,x1154),f33(x1152,x1153,x1154))
% 51.10/50.84 [116]~E(x1161,x1162)+E(f33(x1163,x1161,x1164),f33(x1163,x1162,x1164))
% 51.10/50.84 [117]~E(x1171,x1172)+E(f33(x1173,x1174,x1171),f33(x1173,x1174,x1172))
% 51.10/50.84 [118]~E(x1181,x1182)+E(f289(x1181,x1183,x1184),f289(x1182,x1183,x1184))
% 51.10/50.84 [119]~E(x1191,x1192)+E(f289(x1193,x1191,x1194),f289(x1193,x1192,x1194))
% 51.10/50.84 [120]~E(x1201,x1202)+E(f289(x1203,x1204,x1201),f289(x1203,x1204,x1202))
% 51.10/50.84 [121]~E(x1211,x1212)+E(f47(x1211),f47(x1212))
% 51.10/50.84 [122]~E(x1221,x1222)+E(f264(x1221),f264(x1222))
% 51.10/50.84 [123]~E(x1231,x1232)+E(f302(x1231,x1233),f302(x1232,x1233))
% 51.10/50.84 [124]~E(x1241,x1242)+E(f302(x1243,x1241),f302(x1243,x1242))
% 51.10/50.84 [125]~E(x1251,x1252)+E(f250(x1251),f250(x1252))
% 51.10/50.84 [126]~E(x1261,x1262)+E(f147(x1261,x1263),f147(x1262,x1263))
% 51.10/50.84 [127]~E(x1271,x1272)+E(f147(x1273,x1271),f147(x1273,x1272))
% 51.10/50.84 [128]~E(x1281,x1282)+E(f784(x1281,x1283,x1284),f784(x1282,x1283,x1284))
% 51.10/50.84 [129]~E(x1291,x1292)+E(f784(x1293,x1291,x1294),f784(x1293,x1292,x1294))
% 51.10/50.84 [130]~E(x1301,x1302)+E(f784(x1303,x1304,x1301),f784(x1303,x1304,x1302))
% 51.10/50.84 [131]~E(x1311,x1312)+E(f487(x1311,x1313),f487(x1312,x1313))
% 51.10/50.84 [132]~E(x1321,x1322)+E(f487(x1323,x1321),f487(x1323,x1322))
% 51.10/50.84 [133]~E(x1331,x1332)+E(f70(x1331,x1333),f70(x1332,x1333))
% 51.10/50.84 [134]~E(x1341,x1342)+E(f70(x1343,x1341),f70(x1343,x1342))
% 51.10/50.84 [135]~E(x1351,x1352)+E(f49(x1351,x1353),f49(x1352,x1353))
% 51.10/50.84 [136]~E(x1361,x1362)+E(f49(x1363,x1361),f49(x1363,x1362))
% 51.10/50.84 [137]~E(x1371,x1372)+E(f157(x1371),f157(x1372))
% 51.10/50.84 [138]~E(x1381,x1382)+E(f271(x1381,x1383),f271(x1382,x1383))
% 51.10/50.84 [139]~E(x1391,x1392)+E(f271(x1393,x1391),f271(x1393,x1392))
% 51.10/50.84 [140]~E(x1401,x1402)+E(f305(x1401,x1403,x1404),f305(x1402,x1403,x1404))
% 51.10/50.84 [141]~E(x1411,x1412)+E(f305(x1413,x1411,x1414),f305(x1413,x1412,x1414))
% 51.10/50.84 [142]~E(x1421,x1422)+E(f305(x1423,x1424,x1421),f305(x1423,x1424,x1422))
% 51.10/50.84 [143]~E(x1431,x1432)+E(f113(x1431),f113(x1432))
% 51.10/50.84 [144]~E(x1441,x1442)+E(f114(x1441),f114(x1442))
% 51.10/50.84 [145]~E(x1451,x1452)+E(f332(x1451),f332(x1452))
% 51.10/50.84 [146]~E(x1461,x1462)+E(f320(x1461,x1463),f320(x1462,x1463))
% 51.10/50.84 [147]~E(x1471,x1472)+E(f320(x1473,x1471),f320(x1473,x1472))
% 51.10/50.84 [148]~E(x1481,x1482)+E(f247(x1481),f247(x1482))
% 51.10/50.84 [149]~E(x1491,x1492)+E(f246(x1491,x1493),f246(x1492,x1493))
% 51.10/50.84 [150]~E(x1501,x1502)+E(f246(x1503,x1501),f246(x1503,x1502))
% 51.10/50.84 [151]~E(x1511,x1512)+E(f248(x1511,x1513),f248(x1512,x1513))
% 51.10/50.84 [152]~E(x1521,x1522)+E(f248(x1523,x1521),f248(x1523,x1522))
% 51.10/50.84 [153]~E(x1531,x1532)+E(f187(x1531),f187(x1532))
% 51.10/50.84 [154]~E(x1541,x1542)+E(f135(x1541,x1543),f135(x1542,x1543))
% 51.10/50.84 [155]~E(x1551,x1552)+E(f135(x1553,x1551),f135(x1553,x1552))
% 51.10/50.84 [156]~E(x1561,x1562)+E(f191(x1561),f191(x1562))
% 51.10/50.84 [157]~E(x1571,x1572)+E(f256(x1571,x1573),f256(x1572,x1573))
% 51.10/50.84 [158]~E(x1581,x1582)+E(f256(x1583,x1581),f256(x1583,x1582))
% 51.10/50.84 [159]~E(x1591,x1592)+E(f7(x1591),f7(x1592))
% 51.10/50.84 [160]~E(x1601,x1602)+E(f192(x1601,x1603),f192(x1602,x1603))
% 51.10/50.84 [161]~E(x1611,x1612)+E(f192(x1613,x1611),f192(x1613,x1612))
% 51.10/50.84 [162]~E(x1621,x1622)+E(f483(x1621,x1623),f483(x1622,x1623))
% 51.10/50.84 [163]~E(x1631,x1632)+E(f483(x1633,x1631),f483(x1633,x1632))
% 51.10/50.84 [164]~E(x1641,x1642)+E(f445(x1641,x1643,x1644,x1645),f445(x1642,x1643,x1644,x1645))
% 51.10/50.84 [165]~E(x1651,x1652)+E(f445(x1653,x1651,x1654,x1655),f445(x1653,x1652,x1654,x1655))
% 51.10/50.84 [166]~E(x1661,x1662)+E(f445(x1663,x1664,x1661,x1665),f445(x1663,x1664,x1662,x1665))
% 51.10/50.84 [167]~E(x1671,x1672)+E(f445(x1673,x1674,x1675,x1671),f445(x1673,x1674,x1675,x1672))
% 51.10/50.84 [168]~E(x1681,x1682)+E(f98(x1681),f98(x1682))
% 51.10/50.84 [169]~E(x1691,x1692)+E(f132(x1691),f132(x1692))
% 51.10/50.84 [170]~E(x1701,x1702)+E(f260(x1701,x1703,x1704,x1705,x1706,x1707),f260(x1702,x1703,x1704,x1705,x1706,x1707))
% 51.10/50.84 [171]~E(x1711,x1712)+E(f260(x1713,x1711,x1714,x1715,x1716,x1717),f260(x1713,x1712,x1714,x1715,x1716,x1717))
% 51.10/50.84 [172]~E(x1721,x1722)+E(f260(x1723,x1724,x1721,x1725,x1726,x1727),f260(x1723,x1724,x1722,x1725,x1726,x1727))
% 51.10/50.84 [173]~E(x1731,x1732)+E(f260(x1733,x1734,x1735,x1731,x1736,x1737),f260(x1733,x1734,x1735,x1732,x1736,x1737))
% 51.10/50.84 [174]~E(x1741,x1742)+E(f260(x1743,x1744,x1745,x1746,x1741,x1747),f260(x1743,x1744,x1745,x1746,x1742,x1747))
% 51.10/50.84 [175]~E(x1751,x1752)+E(f260(x1753,x1754,x1755,x1756,x1757,x1751),f260(x1753,x1754,x1755,x1756,x1757,x1752))
% 51.10/50.84 [176]~E(x1761,x1762)+E(f15(x1761,x1763),f15(x1762,x1763))
% 51.10/50.84 [177]~E(x1771,x1772)+E(f15(x1773,x1771),f15(x1773,x1772))
% 51.10/50.84 [178]~E(x1781,x1782)+E(f399(x1781,x1783,x1784,x1785,x1786),f399(x1782,x1783,x1784,x1785,x1786))
% 51.10/50.84 [179]~E(x1791,x1792)+E(f399(x1793,x1791,x1794,x1795,x1796),f399(x1793,x1792,x1794,x1795,x1796))
% 51.10/50.84 [180]~E(x1801,x1802)+E(f399(x1803,x1804,x1801,x1805,x1806),f399(x1803,x1804,x1802,x1805,x1806))
% 51.10/50.84 [181]~E(x1811,x1812)+E(f399(x1813,x1814,x1815,x1811,x1816),f399(x1813,x1814,x1815,x1812,x1816))
% 51.10/50.84 [182]~E(x1821,x1822)+E(f399(x1823,x1824,x1825,x1826,x1821),f399(x1823,x1824,x1825,x1826,x1822))
% 51.10/50.84 [183]~E(x1831,x1832)+E(f143(x1831,x1833,x1834),f143(x1832,x1833,x1834))
% 51.10/50.84 [184]~E(x1841,x1842)+E(f143(x1843,x1841,x1844),f143(x1843,x1842,x1844))
% 51.10/50.84 [185]~E(x1851,x1852)+E(f143(x1853,x1854,x1851),f143(x1853,x1854,x1852))
% 51.10/50.84 [186]~E(x1861,x1862)+E(f79(x1861,x1863),f79(x1862,x1863))
% 51.10/50.84 [187]~E(x1871,x1872)+E(f79(x1873,x1871),f79(x1873,x1872))
% 51.10/50.84 [188]~E(x1881,x1882)+E(f265(x1881),f265(x1882))
% 51.10/50.84 [189]~E(x1891,x1892)+E(f171(x1891,x1893,x1894),f171(x1892,x1893,x1894))
% 51.10/50.84 [190]~E(x1901,x1902)+E(f171(x1903,x1901,x1904),f171(x1903,x1902,x1904))
% 51.10/50.84 [191]~E(x1911,x1912)+E(f171(x1913,x1914,x1911),f171(x1913,x1914,x1912))
% 51.10/50.84 [192]~E(x1921,x1922)+E(f65(x1921,x1923),f65(x1922,x1923))
% 51.10/50.84 [193]~E(x1931,x1932)+E(f65(x1933,x1931),f65(x1933,x1932))
% 51.10/50.84 [194]~E(x1941,x1942)+E(f142(x1941,x1943),f142(x1942,x1943))
% 51.10/50.84 [195]~E(x1951,x1952)+E(f142(x1953,x1951),f142(x1953,x1952))
% 51.10/50.84 [196]~E(x1961,x1962)+E(f57(x1961,x1963,x1964),f57(x1962,x1963,x1964))
% 51.10/50.84 [197]~E(x1971,x1972)+E(f57(x1973,x1971,x1974),f57(x1973,x1972,x1974))
% 51.10/50.84 [198]~E(x1981,x1982)+E(f57(x1983,x1984,x1981),f57(x1983,x1984,x1982))
% 51.10/50.84 [199]~E(x1991,x1992)+E(f754(x1991,x1993,x1994,x1995),f754(x1992,x1993,x1994,x1995))
% 51.10/50.84 [200]~E(x2001,x2002)+E(f754(x2003,x2001,x2004,x2005),f754(x2003,x2002,x2004,x2005))
% 51.10/50.84 [201]~E(x2011,x2012)+E(f754(x2013,x2014,x2011,x2015),f754(x2013,x2014,x2012,x2015))
% 51.10/50.84 [202]~E(x2021,x2022)+E(f754(x2023,x2024,x2025,x2021),f754(x2023,x2024,x2025,x2022))
% 51.10/50.84 [203]~E(x2031,x2032)+E(f411(x2031,x2033,x2034,x2035,x2036),f411(x2032,x2033,x2034,x2035,x2036))
% 51.10/50.84 [204]~E(x2041,x2042)+E(f411(x2043,x2041,x2044,x2045,x2046),f411(x2043,x2042,x2044,x2045,x2046))
% 51.10/50.84 [205]~E(x2051,x2052)+E(f411(x2053,x2054,x2051,x2055,x2056),f411(x2053,x2054,x2052,x2055,x2056))
% 51.10/50.84 [206]~E(x2061,x2062)+E(f411(x2063,x2064,x2065,x2061,x2066),f411(x2063,x2064,x2065,x2062,x2066))
% 51.10/50.84 [207]~E(x2071,x2072)+E(f411(x2073,x2074,x2075,x2076,x2071),f411(x2073,x2074,x2075,x2076,x2072))
% 51.10/50.84 [208]~E(x2081,x2082)+E(f395(x2081,x2083,x2084,x2085,x2086,x2087),f395(x2082,x2083,x2084,x2085,x2086,x2087))
% 51.10/50.84 [209]~E(x2091,x2092)+E(f395(x2093,x2091,x2094,x2095,x2096,x2097),f395(x2093,x2092,x2094,x2095,x2096,x2097))
% 51.10/50.84 [210]~E(x2101,x2102)+E(f395(x2103,x2104,x2101,x2105,x2106,x2107),f395(x2103,x2104,x2102,x2105,x2106,x2107))
% 51.10/50.84 [211]~E(x2111,x2112)+E(f395(x2113,x2114,x2115,x2111,x2116,x2117),f395(x2113,x2114,x2115,x2112,x2116,x2117))
% 51.10/50.84 [212]~E(x2121,x2122)+E(f395(x2123,x2124,x2125,x2126,x2121,x2127),f395(x2123,x2124,x2125,x2126,x2122,x2127))
% 51.10/50.84 [213]~E(x2131,x2132)+E(f395(x2133,x2134,x2135,x2136,x2137,x2131),f395(x2133,x2134,x2135,x2136,x2137,x2132))
% 51.10/50.84 [214]~E(x2141,x2142)+E(f160(x2141),f160(x2142))
% 51.10/50.84 [215]~E(x2151,x2152)+E(f52(x2151,x2153),f52(x2152,x2153))
% 51.10/50.84 [216]~E(x2161,x2162)+E(f52(x2163,x2161),f52(x2163,x2162))
% 51.10/50.84 [217]~E(x2171,x2172)+E(f255(x2171,x2173,x2174),f255(x2172,x2173,x2174))
% 51.10/50.84 [218]~E(x2181,x2182)+E(f255(x2183,x2181,x2184),f255(x2183,x2182,x2184))
% 51.10/50.84 [219]~E(x2191,x2192)+E(f255(x2193,x2194,x2191),f255(x2193,x2194,x2192))
% 51.10/50.84 [220]~E(x2201,x2202)+E(f459(x2201,x2203,x2204),f459(x2202,x2203,x2204))
% 51.10/50.84 [221]~E(x2211,x2212)+E(f459(x2213,x2211,x2214),f459(x2213,x2212,x2214))
% 51.10/50.84 [222]~E(x2221,x2222)+E(f459(x2223,x2224,x2221),f459(x2223,x2224,x2222))
% 51.10/50.84 [223]~E(x2231,x2232)+E(f406(x2231,x2233,x2234),f406(x2232,x2233,x2234))
% 51.10/50.84 [224]~E(x2241,x2242)+E(f406(x2243,x2241,x2244),f406(x2243,x2242,x2244))
% 51.10/50.84 [225]~E(x2251,x2252)+E(f406(x2253,x2254,x2251),f406(x2253,x2254,x2252))
% 51.10/50.84 [226]~E(x2261,x2262)+E(f11(x2261,x2263),f11(x2262,x2263))
% 51.10/50.84 [227]~E(x2271,x2272)+E(f11(x2273,x2271),f11(x2273,x2272))
% 51.10/50.84 [228]~E(x2281,x2282)+E(f73(x2281,x2283,x2284,x2285,x2286),f73(x2282,x2283,x2284,x2285,x2286))
% 51.10/50.84 [229]~E(x2291,x2292)+E(f73(x2293,x2291,x2294,x2295,x2296),f73(x2293,x2292,x2294,x2295,x2296))
% 51.10/50.84 [230]~E(x2301,x2302)+E(f73(x2303,x2304,x2301,x2305,x2306),f73(x2303,x2304,x2302,x2305,x2306))
% 51.10/50.84 [231]~E(x2311,x2312)+E(f73(x2313,x2314,x2315,x2311,x2316),f73(x2313,x2314,x2315,x2312,x2316))
% 51.10/50.84 [232]~E(x2321,x2322)+E(f73(x2323,x2324,x2325,x2326,x2321),f73(x2323,x2324,x2325,x2326,x2322))
% 51.10/50.84 [233]~E(x2331,x2332)+E(f295(x2331,x2333,x2334),f295(x2332,x2333,x2334))
% 51.10/50.84 [234]~E(x2341,x2342)+E(f295(x2343,x2341,x2344),f295(x2343,x2342,x2344))
% 51.10/50.84 [235]~E(x2351,x2352)+E(f295(x2353,x2354,x2351),f295(x2353,x2354,x2352))
% 51.10/50.84 [236]~E(x2361,x2362)+E(f467(x2361,x2363,x2364,x2365),f467(x2362,x2363,x2364,x2365))
% 51.10/50.84 [237]~E(x2371,x2372)+E(f467(x2373,x2371,x2374,x2375),f467(x2373,x2372,x2374,x2375))
% 51.10/50.84 [238]~E(x2381,x2382)+E(f467(x2383,x2384,x2381,x2385),f467(x2383,x2384,x2382,x2385))
% 51.10/50.84 [239]~E(x2391,x2392)+E(f467(x2393,x2394,x2395,x2391),f467(x2393,x2394,x2395,x2392))
% 51.10/50.84 [240]~E(x2401,x2402)+E(f164(x2401),f164(x2402))
% 51.10/50.84 [241]~E(x2411,x2412)+E(f259(x2411,x2413,x2414),f259(x2412,x2413,x2414))
% 51.10/50.84 [242]~E(x2421,x2422)+E(f259(x2423,x2421,x2424),f259(x2423,x2422,x2424))
% 51.10/50.84 [243]~E(x2431,x2432)+E(f259(x2433,x2434,x2431),f259(x2433,x2434,x2432))
% 51.10/50.84 [244]~E(x2441,x2442)+E(f632(x2441,x2443,x2444,x2445,x2446,x2447,x2448,x2449),f632(x2442,x2443,x2444,x2445,x2446,x2447,x2448,x2449))
% 51.10/50.84 [245]~E(x2451,x2452)+E(f632(x2453,x2451,x2454,x2455,x2456,x2457,x2458,x2459),f632(x2453,x2452,x2454,x2455,x2456,x2457,x2458,x2459))
% 51.10/50.84 [246]~E(x2461,x2462)+E(f632(x2463,x2464,x2461,x2465,x2466,x2467,x2468,x2469),f632(x2463,x2464,x2462,x2465,x2466,x2467,x2468,x2469))
% 51.10/50.84 [247]~E(x2471,x2472)+E(f632(x2473,x2474,x2475,x2471,x2476,x2477,x2478,x2479),f632(x2473,x2474,x2475,x2472,x2476,x2477,x2478,x2479))
% 51.10/50.84 [248]~E(x2481,x2482)+E(f632(x2483,x2484,x2485,x2486,x2481,x2487,x2488,x2489),f632(x2483,x2484,x2485,x2486,x2482,x2487,x2488,x2489))
% 51.10/50.84 [249]~E(x2491,x2492)+E(f632(x2493,x2494,x2495,x2496,x2497,x2491,x2498,x2499),f632(x2493,x2494,x2495,x2496,x2497,x2492,x2498,x2499))
% 51.10/50.84 [250]~E(x2501,x2502)+E(f632(x2503,x2504,x2505,x2506,x2507,x2508,x2501,x2509),f632(x2503,x2504,x2505,x2506,x2507,x2508,x2502,x2509))
% 51.10/50.84 [251]~E(x2511,x2512)+E(f632(x2513,x2514,x2515,x2516,x2517,x2518,x2519,x2511),f632(x2513,x2514,x2515,x2516,x2517,x2518,x2519,x2512))
% 51.10/50.84 [252]~E(x2521,x2522)+E(f80(x2521,x2523,x2524,x2525),f80(x2522,x2523,x2524,x2525))
% 51.10/50.84 [253]~E(x2531,x2532)+E(f80(x2533,x2531,x2534,x2535),f80(x2533,x2532,x2534,x2535))
% 51.10/50.84 [254]~E(x2541,x2542)+E(f80(x2543,x2544,x2541,x2545),f80(x2543,x2544,x2542,x2545))
% 51.10/50.84 [255]~E(x2551,x2552)+E(f80(x2553,x2554,x2555,x2551),f80(x2553,x2554,x2555,x2552))
% 51.10/50.84 [256]~E(x2561,x2562)+E(f371(x2561,x2563,x2564),f371(x2562,x2563,x2564))
% 51.10/50.84 [257]~E(x2571,x2572)+E(f371(x2573,x2571,x2574),f371(x2573,x2572,x2574))
% 51.10/50.84 [258]~E(x2581,x2582)+E(f371(x2583,x2584,x2581),f371(x2583,x2584,x2582))
% 51.10/50.84 [259]~E(x2591,x2592)+E(f217(x2591,x2593),f217(x2592,x2593))
% 51.10/50.84 [260]~E(x2601,x2602)+E(f217(x2603,x2601),f217(x2603,x2602))
% 51.10/50.84 [261]~E(x2611,x2612)+E(f174(x2611,x2613,x2614),f174(x2612,x2613,x2614))
% 51.10/50.84 [262]~E(x2621,x2622)+E(f174(x2623,x2621,x2624),f174(x2623,x2622,x2624))
% 51.10/50.84 [263]~E(x2631,x2632)+E(f174(x2633,x2634,x2631),f174(x2633,x2634,x2632))
% 51.10/50.84 [264]~E(x2641,x2642)+E(f549(x2641,x2643,x2644,x2645),f549(x2642,x2643,x2644,x2645))
% 51.10/50.84 [265]~E(x2651,x2652)+E(f549(x2653,x2651,x2654,x2655),f549(x2653,x2652,x2654,x2655))
% 51.10/50.84 [266]~E(x2661,x2662)+E(f549(x2663,x2664,x2661,x2665),f549(x2663,x2664,x2662,x2665))
% 51.10/50.84 [267]~E(x2671,x2672)+E(f549(x2673,x2674,x2675,x2671),f549(x2673,x2674,x2675,x2672))
% 51.10/50.84 [268]~E(x2681,x2682)+E(f252(x2681,x2683,x2684),f252(x2682,x2683,x2684))
% 51.10/50.84 [269]~E(x2691,x2692)+E(f252(x2693,x2691,x2694),f252(x2693,x2692,x2694))
% 51.10/50.84 [270]~E(x2701,x2702)+E(f252(x2703,x2704,x2701),f252(x2703,x2704,x2702))
% 51.10/50.84 [271]~E(x2711,x2712)+E(f60(x2711,x2713),f60(x2712,x2713))
% 51.10/50.84 [272]~E(x2721,x2722)+E(f60(x2723,x2721),f60(x2723,x2722))
% 51.10/50.84 [273]~E(x2731,x2732)+E(f172(x2731,x2733),f172(x2732,x2733))
% 51.10/50.84 [274]~E(x2741,x2742)+E(f172(x2743,x2741),f172(x2743,x2742))
% 51.10/50.84 [275]~E(x2751,x2752)+E(f319(x2751,x2753,x2754,x2755),f319(x2752,x2753,x2754,x2755))
% 51.10/50.84 [276]~E(x2761,x2762)+E(f319(x2763,x2761,x2764,x2765),f319(x2763,x2762,x2764,x2765))
% 51.10/50.84 [277]~E(x2771,x2772)+E(f319(x2773,x2774,x2771,x2775),f319(x2773,x2774,x2772,x2775))
% 51.10/50.84 [278]~E(x2781,x2782)+E(f319(x2783,x2784,x2785,x2781),f319(x2783,x2784,x2785,x2782))
% 51.10/50.84 [279]~E(x2791,x2792)+E(f146(x2791,x2793),f146(x2792,x2793))
% 51.10/50.84 [280]~E(x2801,x2802)+E(f146(x2803,x2801),f146(x2803,x2802))
% 51.10/50.84 [281]~E(x2811,x2812)+E(f94(x2811),f94(x2812))
% 51.10/50.84 [282]~E(x2821,x2822)+E(f188(x2821),f188(x2822))
% 51.10/50.84 [283]~E(x2831,x2832)+E(f38(x2831,x2833),f38(x2832,x2833))
% 51.10/50.84 [284]~E(x2841,x2842)+E(f38(x2843,x2841),f38(x2843,x2842))
% 51.10/50.84 [285]~E(x2851,x2852)+E(f122(x2851),f122(x2852))
% 51.10/50.84 [286]~E(x2861,x2862)+E(f306(x2861,x2863,x2864),f306(x2862,x2863,x2864))
% 51.10/50.84 [287]~E(x2871,x2872)+E(f306(x2873,x2871,x2874),f306(x2873,x2872,x2874))
% 51.10/50.84 [288]~E(x2881,x2882)+E(f306(x2883,x2884,x2881),f306(x2883,x2884,x2882))
% 51.10/50.84 [289]~E(x2891,x2892)+E(f761(x2891,x2893),f761(x2892,x2893))
% 51.10/50.84 [290]~E(x2901,x2902)+E(f761(x2903,x2901),f761(x2903,x2902))
% 51.10/50.84 [291]~E(x2911,x2912)+E(f13(x2911,x2913,x2914),f13(x2912,x2913,x2914))
% 51.10/50.84 [292]~E(x2921,x2922)+E(f13(x2923,x2921,x2924),f13(x2923,x2922,x2924))
% 51.10/50.84 [293]~E(x2931,x2932)+E(f13(x2933,x2934,x2931),f13(x2933,x2934,x2932))
% 51.10/50.84 [294]~E(x2941,x2942)+E(f71(x2941,x2943,x2944),f71(x2942,x2943,x2944))
% 51.10/50.84 [295]~E(x2951,x2952)+E(f71(x2953,x2951,x2954),f71(x2953,x2952,x2954))
% 51.10/50.84 [296]~E(x2961,x2962)+E(f71(x2963,x2964,x2961),f71(x2963,x2964,x2962))
% 51.10/50.84 [297]~E(x2971,x2972)+E(f37(x2971,x2973),f37(x2972,x2973))
% 51.10/50.84 [298]~E(x2981,x2982)+E(f37(x2983,x2981),f37(x2983,x2982))
% 51.10/50.84 [299]~E(x2991,x2992)+E(f805(x2991,x2993,x2994),f805(x2992,x2993,x2994))
% 51.10/50.84 [300]~E(x3001,x3002)+E(f805(x3003,x3001,x3004),f805(x3003,x3002,x3004))
% 51.10/50.84 [301]~E(x3011,x3012)+E(f805(x3013,x3014,x3011),f805(x3013,x3014,x3012))
% 51.10/50.84 [302]~E(x3021,x3022)+E(f624(x3021,x3023,x3024),f624(x3022,x3023,x3024))
% 51.10/50.84 [303]~E(x3031,x3032)+E(f624(x3033,x3031,x3034),f624(x3033,x3032,x3034))
% 51.10/50.84 [304]~E(x3041,x3042)+E(f624(x3043,x3044,x3041),f624(x3043,x3044,x3042))
% 51.10/50.84 [305]~E(x3051,x3052)+E(f783(x3051,x3053,x3054),f783(x3052,x3053,x3054))
% 51.10/50.84 [306]~E(x3061,x3062)+E(f783(x3063,x3061,x3064),f783(x3063,x3062,x3064))
% 51.10/50.84 [307]~E(x3071,x3072)+E(f783(x3073,x3074,x3071),f783(x3073,x3074,x3072))
% 51.10/50.84 [308]~E(x3081,x3082)+E(f621(x3081,x3083,x3084,x3085),f621(x3082,x3083,x3084,x3085))
% 51.10/50.84 [309]~E(x3091,x3092)+E(f621(x3093,x3091,x3094,x3095),f621(x3093,x3092,x3094,x3095))
% 51.10/50.84 [310]~E(x3101,x3102)+E(f621(x3103,x3104,x3101,x3105),f621(x3103,x3104,x3102,x3105))
% 51.10/50.84 [311]~E(x3111,x3112)+E(f621(x3113,x3114,x3115,x3111),f621(x3113,x3114,x3115,x3112))
% 51.10/50.84 [312]~E(x3121,x3122)+E(f16(x3121,x3123),f16(x3122,x3123))
% 51.10/50.84 [313]~E(x3131,x3132)+E(f16(x3133,x3131),f16(x3133,x3132))
% 51.10/50.84 [314]~E(x3141,x3142)+E(f168(x3141,x3143),f168(x3142,x3143))
% 51.10/50.84 [315]~E(x3151,x3152)+E(f168(x3153,x3151),f168(x3153,x3152))
% 51.10/50.84 [316]~E(x3161,x3162)+E(f151(x3161,x3163),f151(x3162,x3163))
% 51.10/50.84 [317]~E(x3171,x3172)+E(f151(x3173,x3171),f151(x3173,x3172))
% 51.10/50.84 [318]~E(x3181,x3182)+E(f693(x3181,x3183,x3184),f693(x3182,x3183,x3184))
% 51.10/50.84 [319]~E(x3191,x3192)+E(f693(x3193,x3191,x3194),f693(x3193,x3192,x3194))
% 51.10/50.84 [320]~E(x3201,x3202)+E(f693(x3203,x3204,x3201),f693(x3203,x3204,x3202))
% 51.10/50.84 [321]~E(x3211,x3212)+E(f159(x3211),f159(x3212))
% 51.10/50.84 [322]~E(x3221,x3222)+E(f12(x3221,x3223),f12(x3222,x3223))
% 51.10/50.84 [323]~E(x3231,x3232)+E(f12(x3233,x3231),f12(x3233,x3232))
% 51.10/50.84 [324]~E(x3241,x3242)+E(f364(x3241,x3243),f364(x3242,x3243))
% 51.10/50.84 [325]~E(x3251,x3252)+E(f364(x3253,x3251),f364(x3253,x3252))
% 51.10/50.84 [326]~E(x3261,x3262)+E(f308(x3261,x3263),f308(x3262,x3263))
% 51.10/50.84 [327]~E(x3271,x3272)+E(f308(x3273,x3271),f308(x3273,x3272))
% 51.10/50.84 [328]~E(x3281,x3282)+E(f162(x3281),f162(x3282))
% 51.10/50.84 [329]~E(x3291,x3292)+E(f17(x3291,x3293),f17(x3292,x3293))
% 51.10/50.84 [330]~E(x3301,x3302)+E(f17(x3303,x3301),f17(x3303,x3302))
% 51.10/50.84 [331]~E(x3311,x3312)+E(f812(x3311,x3313,x3314,x3315),f812(x3312,x3313,x3314,x3315))
% 51.10/50.84 [332]~E(x3321,x3322)+E(f812(x3323,x3321,x3324,x3325),f812(x3323,x3322,x3324,x3325))
% 51.10/50.84 [333]~E(x3331,x3332)+E(f812(x3333,x3334,x3331,x3335),f812(x3333,x3334,x3332,x3335))
% 51.10/50.84 [334]~E(x3341,x3342)+E(f812(x3343,x3344,x3345,x3341),f812(x3343,x3344,x3345,x3342))
% 51.10/50.84 [335]~E(x3351,x3352)+E(f50(x3351,x3353),f50(x3352,x3353))
% 51.10/50.84 [336]~E(x3361,x3362)+E(f50(x3363,x3361),f50(x3363,x3362))
% 51.10/50.84 [337]~E(x3371,x3372)+E(f267(x3371,x3373),f267(x3372,x3373))
% 51.10/50.84 [338]~E(x3381,x3382)+E(f267(x3383,x3381),f267(x3383,x3382))
% 51.10/50.84 [339]~E(x3391,x3392)+E(f144(x3391,x3393,x3394,x3395,x3396),f144(x3392,x3393,x3394,x3395,x3396))
% 51.10/50.84 [340]~E(x3401,x3402)+E(f144(x3403,x3401,x3404,x3405,x3406),f144(x3403,x3402,x3404,x3405,x3406))
% 51.10/50.84 [341]~E(x3411,x3412)+E(f144(x3413,x3414,x3411,x3415,x3416),f144(x3413,x3414,x3412,x3415,x3416))
% 51.10/50.84 [342]~E(x3421,x3422)+E(f144(x3423,x3424,x3425,x3421,x3426),f144(x3423,x3424,x3425,x3422,x3426))
% 51.10/50.84 [343]~E(x3431,x3432)+E(f144(x3433,x3434,x3435,x3436,x3431),f144(x3433,x3434,x3435,x3436,x3432))
% 51.10/50.84 [344]~E(x3441,x3442)+E(f200(x3441,x3443,x3444,x3445),f200(x3442,x3443,x3444,x3445))
% 51.10/50.84 [345]~E(x3451,x3452)+E(f200(x3453,x3451,x3454,x3455),f200(x3453,x3452,x3454,x3455))
% 51.10/50.84 [346]~E(x3461,x3462)+E(f200(x3463,x3464,x3461,x3465),f200(x3463,x3464,x3462,x3465))
% 51.10/50.84 [347]~E(x3471,x3472)+E(f200(x3473,x3474,x3475,x3471),f200(x3473,x3474,x3475,x3472))
% 51.10/50.84 [348]~E(x3481,x3482)+E(f286(x3481,x3483),f286(x3482,x3483))
% 51.10/50.84 [349]~E(x3491,x3492)+E(f286(x3493,x3491),f286(x3493,x3492))
% 51.10/50.84 [350]~E(x3501,x3502)+E(f139(x3501,x3503),f139(x3502,x3503))
% 51.10/50.84 [351]~E(x3511,x3512)+E(f139(x3513,x3511),f139(x3513,x3512))
% 51.10/50.84 [352]~E(x3521,x3522)+E(f34(x3521,x3523,x3524),f34(x3522,x3523,x3524))
% 51.10/50.84 [353]~E(x3531,x3532)+E(f34(x3533,x3531,x3534),f34(x3533,x3532,x3534))
% 51.10/50.84 [354]~E(x3541,x3542)+E(f34(x3543,x3544,x3541),f34(x3543,x3544,x3542))
% 51.10/50.84 [355]~E(x3551,x3552)+E(f353(x3551,x3553,x3554,x3555),f353(x3552,x3553,x3554,x3555))
% 51.10/50.84 [356]~E(x3561,x3562)+E(f353(x3563,x3561,x3564,x3565),f353(x3563,x3562,x3564,x3565))
% 51.10/50.84 [357]~E(x3571,x3572)+E(f353(x3573,x3574,x3571,x3575),f353(x3573,x3574,x3572,x3575))
% 51.10/50.84 [358]~E(x3581,x3582)+E(f353(x3583,x3584,x3585,x3581),f353(x3583,x3584,x3585,x3582))
% 51.10/50.84 [359]~E(x3591,x3592)+E(f849(x3591),f849(x3592))
% 51.10/50.84 [360]~E(x3601,x3602)+E(f30(x3601,x3603),f30(x3602,x3603))
% 51.10/50.84 [361]~E(x3611,x3612)+E(f30(x3613,x3611),f30(x3613,x3612))
% 51.10/50.84 [362]~E(x3621,x3622)+E(f794(x3621,x3623,x3624),f794(x3622,x3623,x3624))
% 51.10/50.84 [363]~E(x3631,x3632)+E(f794(x3633,x3631,x3634),f794(x3633,x3632,x3634))
% 51.10/50.84 [364]~E(x3641,x3642)+E(f794(x3643,x3644,x3641),f794(x3643,x3644,x3642))
% 51.10/50.84 [365]~E(x3651,x3652)+E(f309(x3651),f309(x3652))
% 51.10/50.84 [366]~E(x3661,x3662)+E(f668(x3661,x3663,x3664),f668(x3662,x3663,x3664))
% 51.10/50.84 [367]~E(x3671,x3672)+E(f668(x3673,x3671,x3674),f668(x3673,x3672,x3674))
% 51.10/50.84 [368]~E(x3681,x3682)+E(f668(x3683,x3684,x3681),f668(x3683,x3684,x3682))
% 51.10/50.84 [369]~E(x3691,x3692)+E(f323(x3691,x3693),f323(x3692,x3693))
% 51.10/50.84 [370]~E(x3701,x3702)+E(f323(x3703,x3701),f323(x3703,x3702))
% 51.10/50.84 [371]~E(x3711,x3712)+E(f681(x3711,x3713,x3714,x3715,x3716),f681(x3712,x3713,x3714,x3715,x3716))
% 51.10/50.84 [372]~E(x3721,x3722)+E(f681(x3723,x3721,x3724,x3725,x3726),f681(x3723,x3722,x3724,x3725,x3726))
% 51.10/50.84 [373]~E(x3731,x3732)+E(f681(x3733,x3734,x3731,x3735,x3736),f681(x3733,x3734,x3732,x3735,x3736))
% 51.10/50.84 [374]~E(x3741,x3742)+E(f681(x3743,x3744,x3745,x3741,x3746),f681(x3743,x3744,x3745,x3742,x3746))
% 51.10/50.84 [375]~E(x3751,x3752)+E(f681(x3753,x3754,x3755,x3756,x3751),f681(x3753,x3754,x3755,x3756,x3752))
% 51.10/50.84 [376]~E(x3761,x3762)+E(f325(x3761,x3763),f325(x3762,x3763))
% 51.10/50.84 [377]~E(x3771,x3772)+E(f325(x3773,x3771),f325(x3773,x3772))
% 51.10/50.84 [378]~E(x3781,x3782)+E(f682(x3781,x3783,x3784,x3785,x3786),f682(x3782,x3783,x3784,x3785,x3786))
% 51.10/50.84 [379]~E(x3791,x3792)+E(f682(x3793,x3791,x3794,x3795,x3796),f682(x3793,x3792,x3794,x3795,x3796))
% 51.10/50.84 [380]~E(x3801,x3802)+E(f682(x3803,x3804,x3801,x3805,x3806),f682(x3803,x3804,x3802,x3805,x3806))
% 51.10/50.84 [381]~E(x3811,x3812)+E(f682(x3813,x3814,x3815,x3811,x3816),f682(x3813,x3814,x3815,x3812,x3816))
% 51.10/50.84 [382]~E(x3821,x3822)+E(f682(x3823,x3824,x3825,x3826,x3821),f682(x3823,x3824,x3825,x3826,x3822))
% 51.10/50.84 [383]~E(x3831,x3832)+E(f233(x3831,x3833),f233(x3832,x3833))
% 51.10/50.84 [384]~E(x3841,x3842)+E(f233(x3843,x3841),f233(x3843,x3842))
% 51.10/50.84 [385]~E(x3851,x3852)+E(f234(x3851),f234(x3852))
% 51.10/50.84 [386]~E(x3861,x3862)+E(f505(x3861,x3863,x3864,x3865),f505(x3862,x3863,x3864,x3865))
% 51.10/50.84 [387]~E(x3871,x3872)+E(f505(x3873,x3871,x3874,x3875),f505(x3873,x3872,x3874,x3875))
% 51.10/50.84 [388]~E(x3881,x3882)+E(f505(x3883,x3884,x3881,x3885),f505(x3883,x3884,x3882,x3885))
% 51.10/50.84 [389]~E(x3891,x3892)+E(f505(x3893,x3894,x3895,x3891),f505(x3893,x3894,x3895,x3892))
% 51.10/50.84 [390]~E(x3901,x3902)+E(f780(x3901,x3903,x3904),f780(x3902,x3903,x3904))
% 51.10/50.84 [391]~E(x3911,x3912)+E(f780(x3913,x3911,x3914),f780(x3913,x3912,x3914))
% 51.10/50.84 [392]~E(x3921,x3922)+E(f780(x3923,x3924,x3921),f780(x3923,x3924,x3922))
% 51.10/50.84 [393]~E(x3931,x3932)+E(f721(x3931,x3933),f721(x3932,x3933))
% 51.10/50.84 [394]~E(x3941,x3942)+E(f721(x3943,x3941),f721(x3943,x3942))
% 51.10/50.84 [395]~E(x3951,x3952)+E(f258(x3951,x3953),f258(x3952,x3953))
% 51.10/50.84 [396]~E(x3961,x3962)+E(f258(x3963,x3961),f258(x3963,x3962))
% 51.10/50.84 [397]~E(x3971,x3972)+E(f152(x3971,x3973),f152(x3972,x3973))
% 51.10/50.84 [398]~E(x3981,x3982)+E(f152(x3983,x3981),f152(x3983,x3982))
% 51.10/50.84 [399]~E(x3991,x3992)+E(f321(x3991,x3993),f321(x3992,x3993))
% 51.10/50.84 [400]~E(x4001,x4002)+E(f321(x4003,x4001),f321(x4003,x4002))
% 51.10/50.84 [401]~E(x4011,x4012)+E(f846(x4011),f846(x4012))
% 51.10/50.84 [402]~E(x4021,x4022)+E(f150(x4021,x4023),f150(x4022,x4023))
% 51.10/50.84 [403]~E(x4031,x4032)+E(f150(x4033,x4031),f150(x4033,x4032))
% 51.10/50.84 [404]~E(x4041,x4042)+E(f736(x4041,x4043,x4044,x4045),f736(x4042,x4043,x4044,x4045))
% 51.10/50.84 [405]~E(x4051,x4052)+E(f736(x4053,x4051,x4054,x4055),f736(x4053,x4052,x4054,x4055))
% 51.10/50.84 [406]~E(x4061,x4062)+E(f736(x4063,x4064,x4061,x4065),f736(x4063,x4064,x4062,x4065))
% 51.10/50.84 [407]~E(x4071,x4072)+E(f736(x4073,x4074,x4075,x4071),f736(x4073,x4074,x4075,x4072))
% 51.10/50.84 [408]~E(x4081,x4082)+E(f800(x4081,x4083,x4084),f800(x4082,x4083,x4084))
% 51.10/50.84 [409]~E(x4091,x4092)+E(f800(x4093,x4091,x4094),f800(x4093,x4092,x4094))
% 51.10/50.84 [410]~E(x4101,x4102)+E(f800(x4103,x4104,x4101),f800(x4103,x4104,x4102))
% 51.10/50.84 [411]~E(x4111,x4112)+E(f584(x4111,x4113,x4114,x4115),f584(x4112,x4113,x4114,x4115))
% 51.10/50.84 [412]~E(x4121,x4122)+E(f584(x4123,x4121,x4124,x4125),f584(x4123,x4122,x4124,x4125))
% 51.10/50.84 [413]~E(x4131,x4132)+E(f584(x4133,x4134,x4131,x4135),f584(x4133,x4134,x4132,x4135))
% 51.10/50.84 [414]~E(x4141,x4142)+E(f584(x4143,x4144,x4145,x4141),f584(x4143,x4144,x4145,x4142))
% 51.10/50.84 [415]~E(x4151,x4152)+E(f662(x4151,x4153,x4154),f662(x4152,x4153,x4154))
% 51.10/50.84 [416]~E(x4161,x4162)+E(f662(x4163,x4161,x4164),f662(x4163,x4162,x4164))
% 51.10/50.84 [417]~E(x4171,x4172)+E(f662(x4173,x4174,x4171),f662(x4173,x4174,x4172))
% 51.10/50.84 [418]~E(x4181,x4182)+E(f747(x4181,x4183),f747(x4182,x4183))
% 51.10/50.84 [419]~E(x4191,x4192)+E(f747(x4193,x4191),f747(x4193,x4192))
% 51.10/50.84 [420]~E(x4201,x4202)+E(f92(x4201,x4203),f92(x4202,x4203))
% 51.10/50.84 [421]~E(x4211,x4212)+E(f92(x4213,x4211),f92(x4213,x4212))
% 51.10/50.84 [422]~E(x4221,x4222)+E(f131(x4221,x4223),f131(x4222,x4223))
% 51.10/50.84 [423]~E(x4231,x4232)+E(f131(x4233,x4231),f131(x4233,x4232))
% 51.10/50.84 [424]~E(x4241,x4242)+E(f97(x4241,x4243),f97(x4242,x4243))
% 51.10/50.84 [425]~E(x4251,x4252)+E(f97(x4253,x4251),f97(x4253,x4252))
% 51.10/50.84 [426]~E(x4261,x4262)+E(f379(x4261,x4263),f379(x4262,x4263))
% 51.10/50.84 [427]~E(x4271,x4272)+E(f379(x4273,x4271),f379(x4273,x4272))
% 51.10/50.84 [428]~E(x4281,x4282)+E(f764(x4281,x4283,x4284),f764(x4282,x4283,x4284))
% 51.10/50.84 [429]~E(x4291,x4292)+E(f764(x4293,x4291,x4294),f764(x4293,x4292,x4294))
% 51.10/50.84 [430]~E(x4301,x4302)+E(f764(x4303,x4304,x4301),f764(x4303,x4304,x4302))
% 51.10/50.84 [431]~E(x4311,x4312)+E(f466(x4311,x4313,x4314,x4315),f466(x4312,x4313,x4314,x4315))
% 51.10/50.84 [432]~E(x4321,x4322)+E(f466(x4323,x4321,x4324,x4325),f466(x4323,x4322,x4324,x4325))
% 51.10/50.84 [433]~E(x4331,x4332)+E(f466(x4333,x4334,x4331,x4335),f466(x4333,x4334,x4332,x4335))
% 51.10/50.84 [434]~E(x4341,x4342)+E(f466(x4343,x4344,x4345,x4341),f466(x4343,x4344,x4345,x4342))
% 51.10/50.84 [435]~E(x4351,x4352)+E(f177(x4351,x4353,x4354,x4355),f177(x4352,x4353,x4354,x4355))
% 51.10/50.84 [436]~E(x4361,x4362)+E(f177(x4363,x4361,x4364,x4365),f177(x4363,x4362,x4364,x4365))
% 51.10/50.84 [437]~E(x4371,x4372)+E(f177(x4373,x4374,x4371,x4375),f177(x4373,x4374,x4372,x4375))
% 51.10/50.84 [438]~E(x4381,x4382)+E(f177(x4383,x4384,x4385,x4381),f177(x4383,x4384,x4385,x4382))
% 51.10/50.84 [439]~E(x4391,x4392)+E(f737(x4391,x4393,x4394,x4395),f737(x4392,x4393,x4394,x4395))
% 51.10/50.84 [440]~E(x4401,x4402)+E(f737(x4403,x4401,x4404,x4405),f737(x4403,x4402,x4404,x4405))
% 51.10/50.84 [441]~E(x4411,x4412)+E(f737(x4413,x4414,x4411,x4415),f737(x4413,x4414,x4412,x4415))
% 51.10/50.84 [442]~E(x4421,x4422)+E(f737(x4423,x4424,x4425,x4421),f737(x4423,x4424,x4425,x4422))
% 51.10/50.84 [443]~E(x4431,x4432)+E(f696(x4431,x4433,x4434),f696(x4432,x4433,x4434))
% 51.10/50.84 [444]~E(x4441,x4442)+E(f696(x4443,x4441,x4444),f696(x4443,x4442,x4444))
% 51.10/50.84 [445]~E(x4451,x4452)+E(f696(x4453,x4454,x4451),f696(x4453,x4454,x4452))
% 51.10/50.84 [446]~E(x4461,x4462)+E(f62(x4461,x4463),f62(x4462,x4463))
% 51.10/50.84 [447]~E(x4471,x4472)+E(f62(x4473,x4471),f62(x4473,x4472))
% 51.10/50.84 [448]~E(x4481,x4482)+E(f284(x4481),f284(x4482))
% 51.10/50.84 [449]~E(x4491,x4492)+E(f338(x4491,x4493),f338(x4492,x4493))
% 51.10/50.84 [450]~E(x4501,x4502)+E(f338(x4503,x4501),f338(x4503,x4502))
% 51.10/50.84 [451]~E(x4511,x4512)+E(f811(x4511,x4513,x4514,x4515),f811(x4512,x4513,x4514,x4515))
% 51.10/50.84 [452]~E(x4521,x4522)+E(f811(x4523,x4521,x4524,x4525),f811(x4523,x4522,x4524,x4525))
% 51.10/50.84 [453]~E(x4531,x4532)+E(f811(x4533,x4534,x4531,x4535),f811(x4533,x4534,x4532,x4535))
% 51.10/50.84 [454]~E(x4541,x4542)+E(f811(x4543,x4544,x4545,x4541),f811(x4543,x4544,x4545,x4542))
% 51.10/50.84 [455]~E(x4551,x4552)+E(f72(x4551,x4553,x4554),f72(x4552,x4553,x4554))
% 51.10/50.84 [456]~E(x4561,x4562)+E(f72(x4563,x4561,x4564),f72(x4563,x4562,x4564))
% 51.10/50.84 [457]~E(x4571,x4572)+E(f72(x4573,x4574,x4571),f72(x4573,x4574,x4572))
% 51.10/50.84 [458]~E(x4581,x4582)+E(f795(x4581,x4583,x4584),f795(x4582,x4583,x4584))
% 51.10/50.84 [459]~E(x4591,x4592)+E(f795(x4593,x4591,x4594),f795(x4593,x4592,x4594))
% 51.10/50.84 [460]~E(x4601,x4602)+E(f795(x4603,x4604,x4601),f795(x4603,x4604,x4602))
% 51.10/50.84 [461]~E(x4611,x4612)+E(f203(x4611,x4613),f203(x4612,x4613))
% 51.10/50.84 [462]~E(x4621,x4622)+E(f203(x4623,x4621),f203(x4623,x4622))
% 51.10/50.84 [463]~E(x4631,x4632)+E(f594(x4631,x4633,x4634),f594(x4632,x4633,x4634))
% 51.10/50.84 [464]~E(x4641,x4642)+E(f594(x4643,x4641,x4644),f594(x4643,x4642,x4644))
% 51.10/50.84 [465]~E(x4651,x4652)+E(f594(x4653,x4654,x4651),f594(x4653,x4654,x4652))
% 51.10/50.84 [466]~E(x4661,x4662)+E(f354(x4661,x4663,x4664,x4665),f354(x4662,x4663,x4664,x4665))
% 51.10/50.84 [467]~E(x4671,x4672)+E(f354(x4673,x4671,x4674,x4675),f354(x4673,x4672,x4674,x4675))
% 51.10/50.84 [468]~E(x4681,x4682)+E(f354(x4683,x4684,x4681,x4685),f354(x4683,x4684,x4682,x4685))
% 51.10/50.84 [469]~E(x4691,x4692)+E(f354(x4693,x4694,x4695,x4691),f354(x4693,x4694,x4695,x4692))
% 51.10/50.84 [470]~E(x4701,x4702)+E(f423(x4701,x4703,x4704),f423(x4702,x4703,x4704))
% 51.10/50.84 [471]~E(x4711,x4712)+E(f423(x4713,x4711,x4714),f423(x4713,x4712,x4714))
% 51.10/50.84 [472]~E(x4721,x4722)+E(f423(x4723,x4724,x4721),f423(x4723,x4724,x4722))
% 51.10/50.84 [473]~E(x4731,x4732)+E(f361(x4731,x4733,x4734,x4735,x4736),f361(x4732,x4733,x4734,x4735,x4736))
% 51.10/50.84 [474]~E(x4741,x4742)+E(f361(x4743,x4741,x4744,x4745,x4746),f361(x4743,x4742,x4744,x4745,x4746))
% 51.10/50.84 [475]~E(x4751,x4752)+E(f361(x4753,x4754,x4751,x4755,x4756),f361(x4753,x4754,x4752,x4755,x4756))
% 51.10/50.84 [476]~E(x4761,x4762)+E(f361(x4763,x4764,x4765,x4761,x4766),f361(x4763,x4764,x4765,x4762,x4766))
% 51.10/50.84 [477]~E(x4771,x4772)+E(f361(x4773,x4774,x4775,x4776,x4771),f361(x4773,x4774,x4775,x4776,x4772))
% 51.10/50.84 [478]~E(x4781,x4782)+E(f84(x4781,x4783,x4784,x4785),f84(x4782,x4783,x4784,x4785))
% 51.10/50.84 [479]~E(x4791,x4792)+E(f84(x4793,x4791,x4794,x4795),f84(x4793,x4792,x4794,x4795))
% 51.10/50.84 [480]~E(x4801,x4802)+E(f84(x4803,x4804,x4801,x4805),f84(x4803,x4804,x4802,x4805))
% 51.10/50.84 [481]~E(x4811,x4812)+E(f84(x4813,x4814,x4815,x4811),f84(x4813,x4814,x4815,x4812))
% 51.10/50.84 [482]~E(x4821,x4822)+E(f829(x4821,x4823,x4824,x4825,x4826,x4827,x4828),f829(x4822,x4823,x4824,x4825,x4826,x4827,x4828))
% 51.10/50.84 [483]~E(x4831,x4832)+E(f829(x4833,x4831,x4834,x4835,x4836,x4837,x4838),f829(x4833,x4832,x4834,x4835,x4836,x4837,x4838))
% 51.10/50.84 [484]~E(x4841,x4842)+E(f829(x4843,x4844,x4841,x4845,x4846,x4847,x4848),f829(x4843,x4844,x4842,x4845,x4846,x4847,x4848))
% 51.10/50.84 [485]~E(x4851,x4852)+E(f829(x4853,x4854,x4855,x4851,x4856,x4857,x4858),f829(x4853,x4854,x4855,x4852,x4856,x4857,x4858))
% 51.10/50.84 [486]~E(x4861,x4862)+E(f829(x4863,x4864,x4865,x4866,x4861,x4867,x4868),f829(x4863,x4864,x4865,x4866,x4862,x4867,x4868))
% 51.10/50.84 [487]~E(x4871,x4872)+E(f829(x4873,x4874,x4875,x4876,x4877,x4871,x4878),f829(x4873,x4874,x4875,x4876,x4877,x4872,x4878))
% 51.10/50.84 [488]~E(x4881,x4882)+E(f829(x4883,x4884,x4885,x4886,x4887,x4888,x4881),f829(x4883,x4884,x4885,x4886,x4887,x4888,x4882))
% 51.10/50.84 [489]~E(x4891,x4892)+E(f504(x4891,x4893,x4894,x4895),f504(x4892,x4893,x4894,x4895))
% 51.10/50.84 [490]~E(x4901,x4902)+E(f504(x4903,x4901,x4904,x4905),f504(x4903,x4902,x4904,x4905))
% 51.10/50.84 [491]~E(x4911,x4912)+E(f504(x4913,x4914,x4911,x4915),f504(x4913,x4914,x4912,x4915))
% 51.10/50.84 [492]~E(x4921,x4922)+E(f504(x4923,x4924,x4925,x4921),f504(x4923,x4924,x4925,x4922))
% 51.10/50.84 [493]~E(x4931,x4932)+E(f297(x4931,x4933,x4934,x4935,x4936),f297(x4932,x4933,x4934,x4935,x4936))
% 51.10/50.84 [494]~E(x4941,x4942)+E(f297(x4943,x4941,x4944,x4945,x4946),f297(x4943,x4942,x4944,x4945,x4946))
% 51.10/50.84 [495]~E(x4951,x4952)+E(f297(x4953,x4954,x4951,x4955,x4956),f297(x4953,x4954,x4952,x4955,x4956))
% 51.10/50.84 [496]~E(x4961,x4962)+E(f297(x4963,x4964,x4965,x4961,x4966),f297(x4963,x4964,x4965,x4962,x4966))
% 51.10/50.84 [497]~E(x4971,x4972)+E(f297(x4973,x4974,x4975,x4976,x4971),f297(x4973,x4974,x4975,x4976,x4972))
% 51.10/50.84 [498]~E(x4981,x4982)+E(f35(x4981,x4983,x4984),f35(x4982,x4983,x4984))
% 51.10/50.84 [499]~E(x4991,x4992)+E(f35(x4993,x4991,x4994),f35(x4993,x4992,x4994))
% 51.10/50.84 [500]~E(x5001,x5002)+E(f35(x5003,x5004,x5001),f35(x5003,x5004,x5002))
% 51.10/50.84 [501]~E(x5011,x5012)+E(f370(x5011,x5013,x5014),f370(x5012,x5013,x5014))
% 51.10/50.84 [502]~E(x5021,x5022)+E(f370(x5023,x5021,x5024),f370(x5023,x5022,x5024))
% 51.10/50.84 [503]~E(x5031,x5032)+E(f370(x5033,x5034,x5031),f370(x5033,x5034,x5032))
% 51.10/50.84 [504]~E(x5041,x5042)+E(f774(x5041,x5043,x5044),f774(x5042,x5043,x5044))
% 51.10/50.84 [505]~E(x5051,x5052)+E(f774(x5053,x5051,x5054),f774(x5053,x5052,x5054))
% 51.10/50.84 [506]~E(x5061,x5062)+E(f774(x5063,x5064,x5061),f774(x5063,x5064,x5062))
% 51.10/50.84 [507]~E(x5071,x5072)+E(f614(x5071,x5073),f614(x5072,x5073))
% 51.10/50.84 [508]~E(x5081,x5082)+E(f614(x5083,x5081),f614(x5083,x5082))
% 51.10/50.84 [509]~E(x5091,x5092)+E(f708(x5091,x5093,x5094,x5095),f708(x5092,x5093,x5094,x5095))
% 51.10/50.84 [510]~E(x5101,x5102)+E(f708(x5103,x5101,x5104,x5105),f708(x5103,x5102,x5104,x5105))
% 51.10/50.84 [511]~E(x5111,x5112)+E(f708(x5113,x5114,x5111,x5115),f708(x5113,x5114,x5112,x5115))
% 51.10/50.84 [512]~E(x5121,x5122)+E(f708(x5123,x5124,x5125,x5121),f708(x5123,x5124,x5125,x5122))
% 51.10/50.84 [513]~E(x5131,x5132)+E(f167(x5131,x5133,x5134),f167(x5132,x5133,x5134))
% 51.10/50.84 [514]~E(x5141,x5142)+E(f167(x5143,x5141,x5144),f167(x5143,x5142,x5144))
% 51.10/50.84 [515]~E(x5151,x5152)+E(f167(x5153,x5154,x5151),f167(x5153,x5154,x5152))
% 51.10/50.84 [516]~E(x5161,x5162)+E(f53(x5161),f53(x5162))
% 51.10/50.84 [517]~E(x5171,x5172)+E(f236(x5171,x5173,x5174,x5175),f236(x5172,x5173,x5174,x5175))
% 51.10/50.84 [518]~E(x5181,x5182)+E(f236(x5183,x5181,x5184,x5185),f236(x5183,x5182,x5184,x5185))
% 51.10/50.84 [519]~E(x5191,x5192)+E(f236(x5193,x5194,x5191,x5195),f236(x5193,x5194,x5192,x5195))
% 51.10/50.84 [520]~E(x5201,x5202)+E(f236(x5203,x5204,x5205,x5201),f236(x5203,x5204,x5205,x5202))
% 51.10/50.84 [521]~E(x5211,x5212)+E(f216(x5211,x5213),f216(x5212,x5213))
% 51.10/50.84 [522]~E(x5221,x5222)+E(f216(x5223,x5221),f216(x5223,x5222))
% 51.10/50.84 [523]~E(x5231,x5232)+E(f307(x5231),f307(x5232))
% 51.10/50.84 [524]~E(x5241,x5242)+E(f59(x5241,x5243),f59(x5242,x5243))
% 51.10/50.84 [525]~E(x5251,x5252)+E(f59(x5253,x5251),f59(x5253,x5252))
% 51.10/50.84 [526]~E(x5261,x5262)+E(f389(x5261,x5263),f389(x5262,x5263))
% 51.10/50.84 [527]~E(x5271,x5272)+E(f389(x5273,x5271),f389(x5273,x5272))
% 51.10/50.84 [528]~E(x5281,x5282)+E(f470(x5281,x5283),f470(x5282,x5283))
% 51.10/50.84 [529]~E(x5291,x5292)+E(f470(x5293,x5291),f470(x5293,x5292))
% 51.10/50.84 [530]~E(x5301,x5302)+E(f175(x5301,x5303,x5304,x5305),f175(x5302,x5303,x5304,x5305))
% 51.10/50.84 [531]~E(x5311,x5312)+E(f175(x5313,x5311,x5314,x5315),f175(x5313,x5312,x5314,x5315))
% 51.10/50.84 [532]~E(x5321,x5322)+E(f175(x5323,x5324,x5321,x5325),f175(x5323,x5324,x5322,x5325))
% 51.10/50.84 [533]~E(x5331,x5332)+E(f175(x5333,x5334,x5335,x5331),f175(x5333,x5334,x5335,x5332))
% 51.10/50.84 [534]~E(x5341,x5342)+E(f595(x5341,x5343,x5344),f595(x5342,x5343,x5344))
% 51.10/50.84 [535]~E(x5351,x5352)+E(f595(x5353,x5351,x5354),f595(x5353,x5352,x5354))
% 51.10/50.84 [536]~E(x5361,x5362)+E(f595(x5363,x5364,x5361),f595(x5363,x5364,x5362))
% 51.10/50.84 [537]~E(x5371,x5372)+E(f394(x5371,x5373,x5374,x5375),f394(x5372,x5373,x5374,x5375))
% 51.10/50.84 [538]~E(x5381,x5382)+E(f394(x5383,x5381,x5384,x5385),f394(x5383,x5382,x5384,x5385))
% 51.10/50.84 [539]~E(x5391,x5392)+E(f394(x5393,x5394,x5391,x5395),f394(x5393,x5394,x5392,x5395))
% 51.10/50.84 [540]~E(x5401,x5402)+E(f394(x5403,x5404,x5405,x5401),f394(x5403,x5404,x5405,x5402))
% 51.10/50.84 [541]~E(x5411,x5412)+E(f165(x5411,x5413,x5414),f165(x5412,x5413,x5414))
% 51.10/50.84 [542]~E(x5421,x5422)+E(f165(x5423,x5421,x5424),f165(x5423,x5422,x5424))
% 51.10/50.84 [543]~E(x5431,x5432)+E(f165(x5433,x5434,x5431),f165(x5433,x5434,x5432))
% 51.10/50.84 [544]~E(x5441,x5442)+E(f140(x5441,x5443),f140(x5442,x5443))
% 51.10/50.84 [545]~E(x5451,x5452)+E(f140(x5453,x5451),f140(x5453,x5452))
% 51.10/50.84 [546]~E(x5461,x5462)+E(f520(x5461,x5463,x5464,x5465),f520(x5462,x5463,x5464,x5465))
% 51.10/50.84 [547]~E(x5471,x5472)+E(f520(x5473,x5471,x5474,x5475),f520(x5473,x5472,x5474,x5475))
% 51.10/50.84 [548]~E(x5481,x5482)+E(f520(x5483,x5484,x5481,x5485),f520(x5483,x5484,x5482,x5485))
% 51.10/50.84 [549]~E(x5491,x5492)+E(f520(x5493,x5494,x5495,x5491),f520(x5493,x5494,x5495,x5492))
% 51.10/50.84 [550]~E(x5501,x5502)+E(f734(x5501,x5503,x5504,x5505,x5506),f734(x5502,x5503,x5504,x5505,x5506))
% 51.10/50.84 [551]~E(x5511,x5512)+E(f734(x5513,x5511,x5514,x5515,x5516),f734(x5513,x5512,x5514,x5515,x5516))
% 51.10/50.84 [552]~E(x5521,x5522)+E(f734(x5523,x5524,x5521,x5525,x5526),f734(x5523,x5524,x5522,x5525,x5526))
% 51.10/50.84 [553]~E(x5531,x5532)+E(f734(x5533,x5534,x5535,x5531,x5536),f734(x5533,x5534,x5535,x5532,x5536))
% 51.10/50.84 [554]~E(x5541,x5542)+E(f734(x5543,x5544,x5545,x5546,x5541),f734(x5543,x5544,x5545,x5546,x5542))
% 51.10/50.84 [555]~E(x5551,x5552)+E(f61(x5551,x5553),f61(x5552,x5553))
% 51.10/50.84 [556]~E(x5561,x5562)+E(f61(x5563,x5561),f61(x5563,x5562))
% 51.10/50.84 [557]~E(x5571,x5572)+E(f266(x5571),f266(x5572))
% 51.10/50.84 [558]~E(x5581,x5582)+E(f14(x5581,x5583,x5584),f14(x5582,x5583,x5584))
% 51.10/50.84 [559]~E(x5591,x5592)+E(f14(x5593,x5591,x5594),f14(x5593,x5592,x5594))
% 51.10/50.84 [560]~E(x5601,x5602)+E(f14(x5603,x5604,x5601),f14(x5603,x5604,x5602))
% 51.10/50.84 [561]~E(x5611,x5612)+E(f89(x5611,x5613),f89(x5612,x5613))
% 51.10/50.84 [562]~E(x5621,x5622)+E(f89(x5623,x5621),f89(x5623,x5622))
% 51.10/50.84 [563]~E(x5631,x5632)+E(f301(x5631),f301(x5632))
% 51.10/50.84 [564]~E(x5641,x5642)+E(f237(x5641,x5643,x5644,x5645,x5646),f237(x5642,x5643,x5644,x5645,x5646))
% 51.10/50.84 [565]~E(x5651,x5652)+E(f237(x5653,x5651,x5654,x5655,x5656),f237(x5653,x5652,x5654,x5655,x5656))
% 51.10/50.84 [566]~E(x5661,x5662)+E(f237(x5663,x5664,x5661,x5665,x5666),f237(x5663,x5664,x5662,x5665,x5666))
% 51.10/50.84 [567]~E(x5671,x5672)+E(f237(x5673,x5674,x5675,x5671,x5676),f237(x5673,x5674,x5675,x5672,x5676))
% 51.10/50.84 [568]~E(x5681,x5682)+E(f237(x5683,x5684,x5685,x5686,x5681),f237(x5683,x5684,x5685,x5686,x5682))
% 51.10/50.84 [569]~E(x5691,x5692)+E(f618(x5691,x5693,x5694),f618(x5692,x5693,x5694))
% 51.10/50.84 [570]~E(x5701,x5702)+E(f618(x5703,x5701,x5704),f618(x5703,x5702,x5704))
% 51.10/50.84 [571]~E(x5711,x5712)+E(f618(x5713,x5714,x5711),f618(x5713,x5714,x5712))
% 51.10/50.84 [572]~E(x5721,x5722)+E(f346(x5721,x5723,x5724,x5725),f346(x5722,x5723,x5724,x5725))
% 51.10/50.84 [573]~E(x5731,x5732)+E(f346(x5733,x5731,x5734,x5735),f346(x5733,x5732,x5734,x5735))
% 51.10/50.84 [574]~E(x5741,x5742)+E(f346(x5743,x5744,x5741,x5745),f346(x5743,x5744,x5742,x5745))
% 51.10/50.84 [575]~E(x5751,x5752)+E(f346(x5753,x5754,x5755,x5751),f346(x5753,x5754,x5755,x5752))
% 51.10/50.84 [576]~E(x5761,x5762)+E(f453(x5761,x5763,x5764,x5765),f453(x5762,x5763,x5764,x5765))
% 51.10/50.84 [577]~E(x5771,x5772)+E(f453(x5773,x5771,x5774,x5775),f453(x5773,x5772,x5774,x5775))
% 51.10/50.84 [578]~E(x5781,x5782)+E(f453(x5783,x5784,x5781,x5785),f453(x5783,x5784,x5782,x5785))
% 51.10/50.84 [579]~E(x5791,x5792)+E(f453(x5793,x5794,x5795,x5791),f453(x5793,x5794,x5795,x5792))
% 51.10/50.84 [580]~E(x5801,x5802)+E(f603(x5801,x5803,x5804),f603(x5802,x5803,x5804))
% 51.10/50.84 [581]~E(x5811,x5812)+E(f603(x5813,x5811,x5814),f603(x5813,x5812,x5814))
% 51.10/50.84 [582]~E(x5821,x5822)+E(f603(x5823,x5824,x5821),f603(x5823,x5824,x5822))
% 51.10/50.84 [583]~E(x5831,x5832)+E(f312(x5831,x5833,x5834),f312(x5832,x5833,x5834))
% 51.10/50.84 [584]~E(x5841,x5842)+E(f312(x5843,x5841,x5844),f312(x5843,x5842,x5844))
% 51.10/50.84 [585]~E(x5851,x5852)+E(f312(x5853,x5854,x5851),f312(x5853,x5854,x5852))
% 51.10/50.84 [586]~E(x5861,x5862)+E(f158(x5861,x5863,x5864),f158(x5862,x5863,x5864))
% 51.10/50.84 [587]~E(x5871,x5872)+E(f158(x5873,x5871,x5874),f158(x5873,x5872,x5874))
% 51.10/50.84 [588]~E(x5881,x5882)+E(f158(x5883,x5884,x5881),f158(x5883,x5884,x5882))
% 51.10/50.84 [589]~E(x5891,x5892)+E(f683(x5891,x5893,x5894,x5895,x5896),f683(x5892,x5893,x5894,x5895,x5896))
% 51.10/50.84 [590]~E(x5901,x5902)+E(f683(x5903,x5901,x5904,x5905,x5906),f683(x5903,x5902,x5904,x5905,x5906))
% 51.10/50.84 [591]~E(x5911,x5912)+E(f683(x5913,x5914,x5911,x5915,x5916),f683(x5913,x5914,x5912,x5915,x5916))
% 51.10/50.84 [592]~E(x5921,x5922)+E(f683(x5923,x5924,x5925,x5921,x5926),f683(x5923,x5924,x5925,x5922,x5926))
% 51.10/50.84 [593]~E(x5931,x5932)+E(f683(x5933,x5934,x5935,x5936,x5931),f683(x5933,x5934,x5935,x5936,x5932))
% 51.10/50.84 [594]~E(x5941,x5942)+E(f684(x5941,x5943,x5944,x5945,x5946),f684(x5942,x5943,x5944,x5945,x5946))
% 51.10/50.84 [595]~E(x5951,x5952)+E(f684(x5953,x5951,x5954,x5955,x5956),f684(x5953,x5952,x5954,x5955,x5956))
% 51.10/50.84 [596]~E(x5961,x5962)+E(f684(x5963,x5964,x5961,x5965,x5966),f684(x5963,x5964,x5962,x5965,x5966))
% 51.10/50.84 [597]~E(x5971,x5972)+E(f684(x5973,x5974,x5975,x5971,x5976),f684(x5973,x5974,x5975,x5972,x5976))
% 51.10/50.84 [598]~E(x5981,x5982)+E(f684(x5983,x5984,x5985,x5986,x5981),f684(x5983,x5984,x5985,x5986,x5982))
% 51.10/50.84 [599]~E(x5991,x5992)+E(f268(x5991,x5993),f268(x5992,x5993))
% 51.10/50.84 [600]~E(x6001,x6002)+E(f268(x6003,x6001),f268(x6003,x6002))
% 51.10/50.84 [601]~E(x6011,x6012)+E(f695(x6011,x6013,x6014),f695(x6012,x6013,x6014))
% 51.10/50.84 [602]~E(x6021,x6022)+E(f695(x6023,x6021,x6024),f695(x6023,x6022,x6024))
% 51.10/50.84 [603]~E(x6031,x6032)+E(f695(x6033,x6034,x6031),f695(x6033,x6034,x6032))
% 51.10/50.84 [604]~E(x6041,x6042)+E(f768(x6041,x6043,x6044),f768(x6042,x6043,x6044))
% 51.10/50.84 [605]~E(x6051,x6052)+E(f768(x6053,x6051,x6054),f768(x6053,x6052,x6054))
% 51.10/50.84 [606]~E(x6061,x6062)+E(f768(x6063,x6064,x6061),f768(x6063,x6064,x6062))
% 51.10/50.84 [607]~E(x6071,x6072)+E(f472(x6071,x6073),f472(x6072,x6073))
% 51.10/50.84 [608]~E(x6081,x6082)+E(f472(x6083,x6081),f472(x6083,x6082))
% 51.10/50.84 [609]~E(x6091,x6092)+E(f699(x6091,x6093,x6094,x6095,x6096,x6097),f699(x6092,x6093,x6094,x6095,x6096,x6097))
% 51.10/50.84 [610]~E(x6101,x6102)+E(f699(x6103,x6101,x6104,x6105,x6106,x6107),f699(x6103,x6102,x6104,x6105,x6106,x6107))
% 51.10/50.84 [611]~E(x6111,x6112)+E(f699(x6113,x6114,x6111,x6115,x6116,x6117),f699(x6113,x6114,x6112,x6115,x6116,x6117))
% 51.10/50.84 [612]~E(x6121,x6122)+E(f699(x6123,x6124,x6125,x6121,x6126,x6127),f699(x6123,x6124,x6125,x6122,x6126,x6127))
% 51.10/50.84 [613]~E(x6131,x6132)+E(f699(x6133,x6134,x6135,x6136,x6131,x6137),f699(x6133,x6134,x6135,x6136,x6132,x6137))
% 51.10/50.84 [614]~E(x6141,x6142)+E(f699(x6143,x6144,x6145,x6146,x6147,x6141),f699(x6143,x6144,x6145,x6146,x6147,x6142))
% 51.10/50.84 [615]~E(x6151,x6152)+E(f95(x6151),f95(x6152))
% 51.10/50.84 [616]~E(x6161,x6162)+E(f463(x6161,x6163,x6164,x6165),f463(x6162,x6163,x6164,x6165))
% 51.10/50.84 [617]~E(x6171,x6172)+E(f463(x6173,x6171,x6174,x6175),f463(x6173,x6172,x6174,x6175))
% 51.10/50.84 [618]~E(x6181,x6182)+E(f463(x6183,x6184,x6181,x6185),f463(x6183,x6184,x6182,x6185))
% 51.10/50.84 [619]~E(x6191,x6192)+E(f463(x6193,x6194,x6195,x6191),f463(x6193,x6194,x6195,x6192))
% 51.10/50.84 [620]~E(x6201,x6202)+E(f475(x6201,x6203,x6204,x6205),f475(x6202,x6203,x6204,x6205))
% 51.10/50.84 [621]~E(x6211,x6212)+E(f475(x6213,x6211,x6214,x6215),f475(x6213,x6212,x6214,x6215))
% 51.10/50.84 [622]~E(x6221,x6222)+E(f475(x6223,x6224,x6221,x6225),f475(x6223,x6224,x6222,x6225))
% 51.10/50.84 [623]~E(x6231,x6232)+E(f475(x6233,x6234,x6235,x6231),f475(x6233,x6234,x6235,x6232))
% 51.10/50.84 [624]~E(x6241,x6242)+E(f398(x6241,x6243,x6244,x6245,x6246),f398(x6242,x6243,x6244,x6245,x6246))
% 51.10/50.84 [625]~E(x6251,x6252)+E(f398(x6253,x6251,x6254,x6255,x6256),f398(x6253,x6252,x6254,x6255,x6256))
% 51.10/50.84 [626]~E(x6261,x6262)+E(f398(x6263,x6264,x6261,x6265,x6266),f398(x6263,x6264,x6262,x6265,x6266))
% 51.10/50.84 [627]~E(x6271,x6272)+E(f398(x6273,x6274,x6275,x6271,x6276),f398(x6273,x6274,x6275,x6272,x6276))
% 51.10/50.84 [628]~E(x6281,x6282)+E(f398(x6283,x6284,x6285,x6286,x6281),f398(x6283,x6284,x6285,x6286,x6282))
% 51.10/50.84 [629]~E(x6291,x6292)+E(f820(x6291,x6293,x6294),f820(x6292,x6293,x6294))
% 51.10/50.84 [630]~E(x6301,x6302)+E(f820(x6303,x6301,x6304),f820(x6303,x6302,x6304))
% 51.10/50.84 [631]~E(x6311,x6312)+E(f820(x6313,x6314,x6311),f820(x6313,x6314,x6312))
% 51.10/50.84 [632]~E(x6321,x6322)+E(f372(x6321,x6323,x6324,x6325,x6326),f372(x6322,x6323,x6324,x6325,x6326))
% 51.10/50.84 [633]~E(x6331,x6332)+E(f372(x6333,x6331,x6334,x6335,x6336),f372(x6333,x6332,x6334,x6335,x6336))
% 51.10/50.84 [634]~E(x6341,x6342)+E(f372(x6343,x6344,x6341,x6345,x6346),f372(x6343,x6344,x6342,x6345,x6346))
% 51.10/50.84 [635]~E(x6351,x6352)+E(f372(x6353,x6354,x6355,x6351,x6356),f372(x6353,x6354,x6355,x6352,x6356))
% 51.10/50.84 [636]~E(x6361,x6362)+E(f372(x6363,x6364,x6365,x6366,x6361),f372(x6363,x6364,x6365,x6366,x6362))
% 51.10/50.84 [637]~E(x6371,x6372)+E(f134(x6371,x6373,x6374),f134(x6372,x6373,x6374))
% 51.10/50.84 [638]~E(x6381,x6382)+E(f134(x6383,x6381,x6384),f134(x6383,x6382,x6384))
% 51.10/50.84 [639]~E(x6391,x6392)+E(f134(x6393,x6394,x6391),f134(x6393,x6394,x6392))
% 51.10/50.84 [640]~E(x6401,x6402)+E(f810(x6401,x6403,x6404),f810(x6402,x6403,x6404))
% 51.10/50.84 [641]~E(x6411,x6412)+E(f810(x6413,x6411,x6414),f810(x6413,x6412,x6414))
% 51.10/50.84 [642]~E(x6421,x6422)+E(f810(x6423,x6424,x6421),f810(x6423,x6424,x6422))
% 51.10/50.84 [643]~E(x6431,x6432)+E(f576(x6431,x6433,x6434,x6435),f576(x6432,x6433,x6434,x6435))
% 51.10/50.84 [644]~E(x6441,x6442)+E(f576(x6443,x6441,x6444,x6445),f576(x6443,x6442,x6444,x6445))
% 51.10/50.84 [645]~E(x6451,x6452)+E(f576(x6453,x6454,x6451,x6455),f576(x6453,x6454,x6452,x6455))
% 51.10/50.84 [646]~E(x6461,x6462)+E(f576(x6463,x6464,x6465,x6461),f576(x6463,x6464,x6465,x6462))
% 51.10/50.84 [647]~E(x6471,x6472)+E(f527(x6471,x6473,x6474,x6475,x6476),f527(x6472,x6473,x6474,x6475,x6476))
% 51.10/50.84 [648]~E(x6481,x6482)+E(f527(x6483,x6481,x6484,x6485,x6486),f527(x6483,x6482,x6484,x6485,x6486))
% 51.10/50.84 [649]~E(x6491,x6492)+E(f527(x6493,x6494,x6491,x6495,x6496),f527(x6493,x6494,x6492,x6495,x6496))
% 51.10/50.84 [650]~E(x6501,x6502)+E(f527(x6503,x6504,x6505,x6501,x6506),f527(x6503,x6504,x6505,x6502,x6506))
% 51.10/50.84 [651]~E(x6511,x6512)+E(f527(x6513,x6514,x6515,x6516,x6511),f527(x6513,x6514,x6515,x6516,x6512))
% 51.10/50.84 [652]~E(x6521,x6522)+E(f633(x6521,x6523,x6524,x6525,x6526,x6527,x6528,x6529),f633(x6522,x6523,x6524,x6525,x6526,x6527,x6528,x6529))
% 51.10/50.84 [653]~E(x6531,x6532)+E(f633(x6533,x6531,x6534,x6535,x6536,x6537,x6538,x6539),f633(x6533,x6532,x6534,x6535,x6536,x6537,x6538,x6539))
% 51.10/50.84 [654]~E(x6541,x6542)+E(f633(x6543,x6544,x6541,x6545,x6546,x6547,x6548,x6549),f633(x6543,x6544,x6542,x6545,x6546,x6547,x6548,x6549))
% 51.10/50.84 [655]~E(x6551,x6552)+E(f633(x6553,x6554,x6555,x6551,x6556,x6557,x6558,x6559),f633(x6553,x6554,x6555,x6552,x6556,x6557,x6558,x6559))
% 51.10/50.84 [656]~E(x6561,x6562)+E(f633(x6563,x6564,x6565,x6566,x6561,x6567,x6568,x6569),f633(x6563,x6564,x6565,x6566,x6562,x6567,x6568,x6569))
% 51.10/50.84 [657]~E(x6571,x6572)+E(f633(x6573,x6574,x6575,x6576,x6577,x6571,x6578,x6579),f633(x6573,x6574,x6575,x6576,x6577,x6572,x6578,x6579))
% 51.10/50.84 [658]~E(x6581,x6582)+E(f633(x6583,x6584,x6585,x6586,x6587,x6588,x6581,x6589),f633(x6583,x6584,x6585,x6586,x6587,x6588,x6582,x6589))
% 51.10/50.84 [659]~E(x6591,x6592)+E(f633(x6593,x6594,x6595,x6596,x6597,x6598,x6599,x6591),f633(x6593,x6594,x6595,x6596,x6597,x6598,x6599,x6592))
% 51.10/50.84 [660]~E(x6601,x6602)+E(f677(x6601,x6603,x6604,x6605),f677(x6602,x6603,x6604,x6605))
% 51.10/50.84 [661]~E(x6611,x6612)+E(f677(x6613,x6611,x6614,x6615),f677(x6613,x6612,x6614,x6615))
% 51.10/50.84 [662]~E(x6621,x6622)+E(f677(x6623,x6624,x6621,x6625),f677(x6623,x6624,x6622,x6625))
% 51.10/50.84 [663]~E(x6631,x6632)+E(f677(x6633,x6634,x6635,x6631),f677(x6633,x6634,x6635,x6632))
% 51.10/50.84 [664]~E(x6641,x6642)+E(f285(x6641,x6643,x6644),f285(x6642,x6643,x6644))
% 51.10/50.84 [665]~E(x6651,x6652)+E(f285(x6653,x6651,x6654),f285(x6653,x6652,x6654))
% 51.10/50.84 [666]~E(x6661,x6662)+E(f285(x6663,x6664,x6661),f285(x6663,x6664,x6662))
% 51.10/50.84 [667]~E(x6671,x6672)+E(f813(x6671,x6673,x6674),f813(x6672,x6673,x6674))
% 51.10/50.84 [668]~E(x6681,x6682)+E(f813(x6683,x6681,x6684),f813(x6683,x6682,x6684))
% 51.10/50.84 [669]~E(x6691,x6692)+E(f813(x6693,x6694,x6691),f813(x6693,x6694,x6692))
% 51.10/50.84 [670]~E(x6701,x6702)+E(f476(x6701,x6703,x6704,x6705),f476(x6702,x6703,x6704,x6705))
% 51.10/50.84 [671]~E(x6711,x6712)+E(f476(x6713,x6711,x6714,x6715),f476(x6713,x6712,x6714,x6715))
% 51.10/50.84 [672]~E(x6721,x6722)+E(f476(x6723,x6724,x6721,x6725),f476(x6723,x6724,x6722,x6725))
% 51.10/50.84 [673]~E(x6731,x6732)+E(f476(x6733,x6734,x6735,x6731),f476(x6733,x6734,x6735,x6732))
% 51.10/50.84 [674]~E(x6741,x6742)+E(f181(x6741),f181(x6742))
% 51.10/50.84 [675]~E(x6751,x6752)+E(f156(x6751,x6753,x6754,x6755),f156(x6752,x6753,x6754,x6755))
% 51.10/50.84 [676]~E(x6761,x6762)+E(f156(x6763,x6761,x6764,x6765),f156(x6763,x6762,x6764,x6765))
% 51.10/50.84 [677]~E(x6771,x6772)+E(f156(x6773,x6774,x6771,x6775),f156(x6773,x6774,x6772,x6775))
% 51.10/50.84 [678]~E(x6781,x6782)+E(f156(x6783,x6784,x6785,x6781),f156(x6783,x6784,x6785,x6782))
% 51.10/50.84 [679]~E(x6791,x6792)+E(f630(x6791,x6793),f630(x6792,x6793))
% 51.10/50.84 [680]~E(x6801,x6802)+E(f630(x6803,x6801),f630(x6803,x6802))
% 51.10/50.84 [681]~E(x6811,x6812)+E(f731(x6811,x6813,x6814,x6815),f731(x6812,x6813,x6814,x6815))
% 51.10/50.84 [682]~E(x6821,x6822)+E(f731(x6823,x6821,x6824,x6825),f731(x6823,x6822,x6824,x6825))
% 51.10/50.84 [683]~E(x6831,x6832)+E(f731(x6833,x6834,x6831,x6835),f731(x6833,x6834,x6832,x6835))
% 51.10/50.84 [684]~E(x6841,x6842)+E(f731(x6843,x6844,x6845,x6841),f731(x6843,x6844,x6845,x6842))
% 51.10/50.84 [685]~E(x6851,x6852)+E(f93(x6851,x6853),f93(x6852,x6853))
% 51.10/50.84 [686]~E(x6861,x6862)+E(f93(x6863,x6861),f93(x6863,x6862))
% 51.10/50.84 [687]~E(x6871,x6872)+E(f468(x6871,x6873,x6874,x6875),f468(x6872,x6873,x6874,x6875))
% 51.10/50.84 [688]~E(x6881,x6882)+E(f468(x6883,x6881,x6884,x6885),f468(x6883,x6882,x6884,x6885))
% 51.10/50.84 [689]~E(x6891,x6892)+E(f468(x6893,x6894,x6891,x6895),f468(x6893,x6894,x6892,x6895))
% 51.10/50.84 [690]~E(x6901,x6902)+E(f468(x6903,x6904,x6905,x6901),f468(x6903,x6904,x6905,x6902))
% 51.10/50.84 [691]~E(x6911,x6912)+E(f803(x6911,x6913,x6914),f803(x6912,x6913,x6914))
% 51.10/50.84 [692]~E(x6921,x6922)+E(f803(x6923,x6921,x6924),f803(x6923,x6922,x6924))
% 51.10/50.84 [693]~E(x6931,x6932)+E(f803(x6933,x6934,x6931),f803(x6933,x6934,x6932))
% 51.10/50.84 [694]~E(x6941,x6942)+E(f205(x6941,x6943),f205(x6942,x6943))
% 51.10/50.84 [695]~E(x6951,x6952)+E(f205(x6953,x6951),f205(x6953,x6952))
% 51.10/50.84 [696]~E(x6961,x6962)+E(f214(x6961),f214(x6962))
% 51.10/50.84 [697]~E(x6971,x6972)+E(f117(x6971),f117(x6972))
% 51.10/50.84 [698]~E(x6981,x6982)+E(f817(x6981,x6983,x6984),f817(x6982,x6983,x6984))
% 51.10/50.84 [699]~E(x6991,x6992)+E(f817(x6993,x6991,x6994),f817(x6993,x6992,x6994))
% 51.10/50.84 [700]~E(x7001,x7002)+E(f817(x7003,x7004,x7001),f817(x7003,x7004,x7002))
% 51.10/50.84 [701]~E(x7011,x7012)+E(f819(x7011,x7013,x7014),f819(x7012,x7013,x7014))
% 51.10/50.84 [702]~E(x7021,x7022)+E(f819(x7023,x7021,x7024),f819(x7023,x7022,x7024))
% 51.10/50.84 [703]~E(x7031,x7032)+E(f819(x7033,x7034,x7031),f819(x7033,x7034,x7032))
% 51.10/50.84 [704]~E(x7041,x7042)+E(f180(x7041,x7043,x7044,x7045),f180(x7042,x7043,x7044,x7045))
% 51.10/50.84 [705]~E(x7051,x7052)+E(f180(x7053,x7051,x7054,x7055),f180(x7053,x7052,x7054,x7055))
% 51.10/50.84 [706]~E(x7061,x7062)+E(f180(x7063,x7064,x7061,x7065),f180(x7063,x7064,x7062,x7065))
% 51.10/50.84 [707]~E(x7071,x7072)+E(f180(x7073,x7074,x7075,x7071),f180(x7073,x7074,x7075,x7072))
% 51.10/50.84 [708]~E(x7081,x7082)+E(f523(x7081,x7083,x7084),f523(x7082,x7083,x7084))
% 51.10/50.84 [709]~E(x7091,x7092)+E(f523(x7093,x7091,x7094),f523(x7093,x7092,x7094))
% 51.10/50.84 [710]~E(x7101,x7102)+E(f523(x7103,x7104,x7101),f523(x7103,x7104,x7102))
% 51.10/50.84 [711]~E(x7111,x7112)+E(f269(x7111,x7113),f269(x7112,x7113))
% 51.10/50.84 [712]~E(x7121,x7122)+E(f269(x7123,x7121),f269(x7123,x7122))
% 51.10/50.84 [713]~E(x7131,x7132)+E(f426(x7131,x7133,x7134),f426(x7132,x7133,x7134))
% 51.10/50.84 [714]~E(x7141,x7142)+E(f426(x7143,x7141,x7144),f426(x7143,x7142,x7144))
% 51.10/50.84 [715]~E(x7151,x7152)+E(f426(x7153,x7154,x7151),f426(x7153,x7154,x7152))
% 51.10/50.84 [716]~E(x7161,x7162)+E(f659(x7161,x7163),f659(x7162,x7163))
% 51.10/50.84 [717]~E(x7171,x7172)+E(f659(x7173,x7171),f659(x7173,x7172))
% 51.10/50.84 [718]~E(x7181,x7182)+E(f552(x7181,x7183,x7184),f552(x7182,x7183,x7184))
% 51.10/50.84 [719]~E(x7191,x7192)+E(f552(x7193,x7191,x7194),f552(x7193,x7192,x7194))
% 51.10/50.84 [720]~E(x7201,x7202)+E(f552(x7203,x7204,x7201),f552(x7203,x7204,x7202))
% 51.10/50.84 [721]~E(x7211,x7212)+E(f698(x7211,x7213,x7214,x7215,x7216),f698(x7212,x7213,x7214,x7215,x7216))
% 51.10/50.84 [722]~E(x7221,x7222)+E(f698(x7223,x7221,x7224,x7225,x7226),f698(x7223,x7222,x7224,x7225,x7226))
% 51.10/50.84 [723]~E(x7231,x7232)+E(f698(x7233,x7234,x7231,x7235,x7236),f698(x7233,x7234,x7232,x7235,x7236))
% 51.10/50.84 [724]~E(x7241,x7242)+E(f698(x7243,x7244,x7245,x7241,x7246),f698(x7243,x7244,x7245,x7242,x7246))
% 51.10/50.84 [725]~E(x7251,x7252)+E(f698(x7253,x7254,x7255,x7256,x7251),f698(x7253,x7254,x7255,x7256,x7252))
% 51.10/50.84 [726]~E(x7261,x7262)+E(f787(x7261,x7263,x7264),f787(x7262,x7263,x7264))
% 51.10/50.84 [727]~E(x7271,x7272)+E(f787(x7273,x7271,x7274),f787(x7273,x7272,x7274))
% 51.10/50.84 [728]~E(x7281,x7282)+E(f787(x7283,x7284,x7281),f787(x7283,x7284,x7282))
% 51.10/50.84 [729]~E(x7291,x7292)+E(f178(x7291,x7293),f178(x7292,x7293))
% 51.10/50.84 [730]~E(x7301,x7302)+E(f178(x7303,x7301),f178(x7303,x7302))
% 51.10/50.84 [731]~E(x7311,x7312)+E(f612(x7311,x7313,x7314,x7315,x7316,x7317),f612(x7312,x7313,x7314,x7315,x7316,x7317))
% 51.10/50.84 [732]~E(x7321,x7322)+E(f612(x7323,x7321,x7324,x7325,x7326,x7327),f612(x7323,x7322,x7324,x7325,x7326,x7327))
% 51.10/50.84 [733]~E(x7331,x7332)+E(f612(x7333,x7334,x7331,x7335,x7336,x7337),f612(x7333,x7334,x7332,x7335,x7336,x7337))
% 51.10/50.84 [734]~E(x7341,x7342)+E(f612(x7343,x7344,x7345,x7341,x7346,x7347),f612(x7343,x7344,x7345,x7342,x7346,x7347))
% 51.10/50.84 [735]~E(x7351,x7352)+E(f612(x7353,x7354,x7355,x7356,x7351,x7357),f612(x7353,x7354,x7355,x7356,x7352,x7357))
% 51.10/50.84 [736]~E(x7361,x7362)+E(f612(x7363,x7364,x7365,x7366,x7367,x7361),f612(x7363,x7364,x7365,x7366,x7367,x7362))
% 51.10/50.84 [737]~E(x7371,x7372)+E(f694(x7371),f694(x7372))
% 51.10/50.84 [738]~E(x7381,x7382)+E(f535(x7381,x7383,x7384),f535(x7382,x7383,x7384))
% 51.10/50.84 [739]~E(x7391,x7392)+E(f535(x7393,x7391,x7394),f535(x7393,x7392,x7394))
% 51.10/50.84 [740]~E(x7401,x7402)+E(f535(x7403,x7404,x7401),f535(x7403,x7404,x7402))
% 51.10/50.84 [741]~E(x7411,x7412)+E(f808(x7411,x7413,x7414),f808(x7412,x7413,x7414))
% 51.10/50.84 [742]~E(x7421,x7422)+E(f808(x7423,x7421,x7424),f808(x7423,x7422,x7424))
% 51.10/50.84 [743]~E(x7431,x7432)+E(f808(x7433,x7434,x7431),f808(x7433,x7434,x7432))
% 51.10/50.84 [744]~E(x7441,x7442)+E(f435(x7441,x7443,x7444,x7445,x7446),f435(x7442,x7443,x7444,x7445,x7446))
% 51.10/50.84 [745]~E(x7451,x7452)+E(f435(x7453,x7451,x7454,x7455,x7456),f435(x7453,x7452,x7454,x7455,x7456))
% 51.10/50.84 [746]~E(x7461,x7462)+E(f435(x7463,x7464,x7461,x7465,x7466),f435(x7463,x7464,x7462,x7465,x7466))
% 51.10/50.84 [747]~E(x7471,x7472)+E(f435(x7473,x7474,x7475,x7471,x7476),f435(x7473,x7474,x7475,x7472,x7476))
% 51.10/50.84 [748]~E(x7481,x7482)+E(f435(x7483,x7484,x7485,x7486,x7481),f435(x7483,x7484,x7485,x7486,x7482))
% 51.10/50.84 [749]~E(x7491,x7492)+E(f488(x7491,x7493,x7494,x7495,x7496),f488(x7492,x7493,x7494,x7495,x7496))
% 51.10/50.84 [750]~E(x7501,x7502)+E(f488(x7503,x7501,x7504,x7505,x7506),f488(x7503,x7502,x7504,x7505,x7506))
% 51.10/50.84 [751]~E(x7511,x7512)+E(f488(x7513,x7514,x7511,x7515,x7516),f488(x7513,x7514,x7512,x7515,x7516))
% 51.10/50.84 [752]~E(x7521,x7522)+E(f488(x7523,x7524,x7525,x7521,x7526),f488(x7523,x7524,x7525,x7522,x7526))
% 51.10/50.84 [753]~E(x7531,x7532)+E(f488(x7533,x7534,x7535,x7536,x7531),f488(x7533,x7534,x7535,x7536,x7532))
% 51.10/50.84 [754]~E(x7541,x7542)+E(f304(x7541),f304(x7542))
% 51.10/50.84 [755]~E(x7551,x7552)+E(f655(x7551,x7553,x7554,x7555,x7556),f655(x7552,x7553,x7554,x7555,x7556))
% 51.10/50.84 [756]~E(x7561,x7562)+E(f655(x7563,x7561,x7564,x7565,x7566),f655(x7563,x7562,x7564,x7565,x7566))
% 51.10/50.84 [757]~E(x7571,x7572)+E(f655(x7573,x7574,x7571,x7575,x7576),f655(x7573,x7574,x7572,x7575,x7576))
% 51.10/50.84 [758]~E(x7581,x7582)+E(f655(x7583,x7584,x7585,x7581,x7586),f655(x7583,x7584,x7585,x7582,x7586))
% 51.10/50.84 [759]~E(x7591,x7592)+E(f655(x7593,x7594,x7595,x7596,x7591),f655(x7593,x7594,x7595,x7596,x7592))
% 51.10/50.84 [760]~E(x7601,x7602)+E(f437(x7601,x7603),f437(x7602,x7603))
% 51.10/50.84 [761]~E(x7611,x7612)+E(f437(x7613,x7611),f437(x7613,x7612))
% 51.10/50.84 [762]~E(x7621,x7622)+E(f791(x7621,x7623,x7624),f791(x7622,x7623,x7624))
% 51.10/50.84 [763]~E(x7631,x7632)+E(f791(x7633,x7631,x7634),f791(x7633,x7632,x7634))
% 51.10/50.84 [764]~E(x7641,x7642)+E(f791(x7643,x7644,x7641),f791(x7643,x7644,x7642))
% 51.10/50.84 [765]~E(x7651,x7652)+E(f625(x7651,x7653,x7654,x7655,x7656),f625(x7652,x7653,x7654,x7655,x7656))
% 51.10/50.84 [766]~E(x7661,x7662)+E(f625(x7663,x7661,x7664,x7665,x7666),f625(x7663,x7662,x7664,x7665,x7666))
% 51.10/50.84 [767]~E(x7671,x7672)+E(f625(x7673,x7674,x7671,x7675,x7676),f625(x7673,x7674,x7672,x7675,x7676))
% 51.10/50.84 [768]~E(x7681,x7682)+E(f625(x7683,x7684,x7685,x7681,x7686),f625(x7683,x7684,x7685,x7682,x7686))
% 51.10/50.84 [769]~E(x7691,x7692)+E(f625(x7693,x7694,x7695,x7696,x7691),f625(x7693,x7694,x7695,x7696,x7692))
% 51.10/50.84 [770]~E(x7701,x7702)+E(f788(x7701,x7703,x7704),f788(x7702,x7703,x7704))
% 51.10/50.84 [771]~E(x7711,x7712)+E(f788(x7713,x7711,x7714),f788(x7713,x7712,x7714))
% 51.10/50.84 [772]~E(x7721,x7722)+E(f788(x7723,x7724,x7721),f788(x7723,x7724,x7722))
% 51.10/50.84 [773]~E(x7731,x7732)+E(f153(x7731,x7733),f153(x7732,x7733))
% 51.10/50.84 [774]~E(x7741,x7742)+E(f153(x7743,x7741),f153(x7743,x7742))
% 51.10/50.84 [775]~E(x7751,x7752)+E(f455(x7751,x7753,x7754,x7755),f455(x7752,x7753,x7754,x7755))
% 51.10/50.84 [776]~E(x7761,x7762)+E(f455(x7763,x7761,x7764,x7765),f455(x7763,x7762,x7764,x7765))
% 51.10/50.84 [777]~E(x7771,x7772)+E(f455(x7773,x7774,x7771,x7775),f455(x7773,x7774,x7772,x7775))
% 51.10/50.84 [778]~E(x7781,x7782)+E(f455(x7783,x7784,x7785,x7781),f455(x7783,x7784,x7785,x7782))
% 51.10/50.84 [779]~E(x7791,x7792)+E(f589(x7791,x7793,x7794,x7795),f589(x7792,x7793,x7794,x7795))
% 51.10/50.84 [780]~E(x7801,x7802)+E(f589(x7803,x7801,x7804,x7805),f589(x7803,x7802,x7804,x7805))
% 51.10/50.84 [781]~E(x7811,x7812)+E(f589(x7813,x7814,x7811,x7815),f589(x7813,x7814,x7812,x7815))
% 51.10/50.84 [782]~E(x7821,x7822)+E(f589(x7823,x7824,x7825,x7821),f589(x7823,x7824,x7825,x7822))
% 51.10/50.84 [783]~E(x7831,x7832)+E(f290(x7831,x7833,x7834,x7835),f290(x7832,x7833,x7834,x7835))
% 51.10/50.84 [784]~E(x7841,x7842)+E(f290(x7843,x7841,x7844,x7845),f290(x7843,x7842,x7844,x7845))
% 51.10/50.84 [785]~E(x7851,x7852)+E(f290(x7853,x7854,x7851,x7855),f290(x7853,x7854,x7852,x7855))
% 51.10/50.84 [786]~E(x7861,x7862)+E(f290(x7863,x7864,x7865,x7861),f290(x7863,x7864,x7865,x7862))
% 51.10/50.84 [787]~E(x7871,x7872)+E(f347(x7871,x7873,x7874,x7875,x7876,x7877,x7878),f347(x7872,x7873,x7874,x7875,x7876,x7877,x7878))
% 51.10/50.84 [788]~E(x7881,x7882)+E(f347(x7883,x7881,x7884,x7885,x7886,x7887,x7888),f347(x7883,x7882,x7884,x7885,x7886,x7887,x7888))
% 51.10/50.84 [789]~E(x7891,x7892)+E(f347(x7893,x7894,x7891,x7895,x7896,x7897,x7898),f347(x7893,x7894,x7892,x7895,x7896,x7897,x7898))
% 51.10/50.84 [790]~E(x7901,x7902)+E(f347(x7903,x7904,x7905,x7901,x7906,x7907,x7908),f347(x7903,x7904,x7905,x7902,x7906,x7907,x7908))
% 51.10/50.84 [791]~E(x7911,x7912)+E(f347(x7913,x7914,x7915,x7916,x7911,x7917,x7918),f347(x7913,x7914,x7915,x7916,x7912,x7917,x7918))
% 51.10/50.84 [792]~E(x7921,x7922)+E(f347(x7923,x7924,x7925,x7926,x7927,x7921,x7928),f347(x7923,x7924,x7925,x7926,x7927,x7922,x7928))
% 51.10/50.84 [793]~E(x7931,x7932)+E(f347(x7933,x7934,x7935,x7936,x7937,x7938,x7931),f347(x7933,x7934,x7935,x7936,x7937,x7938,x7932))
% 51.10/50.84 [794]~E(x7941,x7942)+E(f568(x7941,x7943,x7944,x7945,x7946,x7947),f568(x7942,x7943,x7944,x7945,x7946,x7947))
% 51.10/50.84 [795]~E(x7951,x7952)+E(f568(x7953,x7951,x7954,x7955,x7956,x7957),f568(x7953,x7952,x7954,x7955,x7956,x7957))
% 51.10/50.84 [796]~E(x7961,x7962)+E(f568(x7963,x7964,x7961,x7965,x7966,x7967),f568(x7963,x7964,x7962,x7965,x7966,x7967))
% 51.10/50.84 [797]~E(x7971,x7972)+E(f568(x7973,x7974,x7975,x7971,x7976,x7977),f568(x7973,x7974,x7975,x7972,x7976,x7977))
% 51.10/50.84 [798]~E(x7981,x7982)+E(f568(x7983,x7984,x7985,x7986,x7981,x7987),f568(x7983,x7984,x7985,x7986,x7982,x7987))
% 51.10/50.84 [799]~E(x7991,x7992)+E(f568(x7993,x7994,x7995,x7996,x7997,x7991),f568(x7993,x7994,x7995,x7996,x7997,x7992))
% 51.10/50.84 [800]~E(x8001,x8002)+E(f557(x8001,x8003,x8004),f557(x8002,x8003,x8004))
% 51.10/50.84 [801]~E(x8011,x8012)+E(f557(x8013,x8011,x8014),f557(x8013,x8012,x8014))
% 51.10/50.84 [802]~E(x8021,x8022)+E(f557(x8023,x8024,x8021),f557(x8023,x8024,x8022))
% 51.10/50.84 [803]~E(x8031,x8032)+E(f828(x8031,x8033,x8034,x8035,x8036,x8037,x8038),f828(x8032,x8033,x8034,x8035,x8036,x8037,x8038))
% 51.10/50.84 [804]~E(x8041,x8042)+E(f828(x8043,x8041,x8044,x8045,x8046,x8047,x8048),f828(x8043,x8042,x8044,x8045,x8046,x8047,x8048))
% 51.10/50.84 [805]~E(x8051,x8052)+E(f828(x8053,x8054,x8051,x8055,x8056,x8057,x8058),f828(x8053,x8054,x8052,x8055,x8056,x8057,x8058))
% 51.10/50.84 [806]~E(x8061,x8062)+E(f828(x8063,x8064,x8065,x8061,x8066,x8067,x8068),f828(x8063,x8064,x8065,x8062,x8066,x8067,x8068))
% 51.10/50.84 [807]~E(x8071,x8072)+E(f828(x8073,x8074,x8075,x8076,x8071,x8077,x8078),f828(x8073,x8074,x8075,x8076,x8072,x8077,x8078))
% 51.10/50.84 [808]~E(x8081,x8082)+E(f828(x8083,x8084,x8085,x8086,x8087,x8081,x8088),f828(x8083,x8084,x8085,x8086,x8087,x8082,x8088))
% 51.10/50.84 [809]~E(x8091,x8092)+E(f828(x8093,x8094,x8095,x8096,x8097,x8098,x8091),f828(x8093,x8094,x8095,x8096,x8097,x8098,x8092))
% 51.10/50.84 [810]~E(x8101,x8102)+E(f782(x8101,x8103,x8104),f782(x8102,x8103,x8104))
% 51.10/50.84 [811]~E(x8111,x8112)+E(f782(x8113,x8111,x8114),f782(x8113,x8112,x8114))
% 51.10/50.84 [812]~E(x8121,x8122)+E(f782(x8123,x8124,x8121),f782(x8123,x8124,x8122))
% 51.10/50.84 [813]~E(x8131,x8132)+E(f565(x8131,x8133),f565(x8132,x8133))
% 51.10/50.84 [814]~E(x8141,x8142)+E(f565(x8143,x8141),f565(x8143,x8142))
% 51.10/50.84 [815]~E(x8151,x8152)+E(f650(x8151,x8153,x8154),f650(x8152,x8153,x8154))
% 51.10/50.84 [816]~E(x8161,x8162)+E(f650(x8163,x8161,x8164),f650(x8163,x8162,x8164))
% 51.10/50.84 [817]~E(x8171,x8172)+E(f650(x8173,x8174,x8171),f650(x8173,x8174,x8172))
% 51.10/50.84 [818]~E(x8181,x8182)+E(f755(x8181,x8183,x8184),f755(x8182,x8183,x8184))
% 51.10/50.84 [819]~E(x8191,x8192)+E(f755(x8193,x8191,x8194),f755(x8193,x8192,x8194))
% 51.10/50.84 [820]~E(x8201,x8202)+E(f755(x8203,x8204,x8201),f755(x8203,x8204,x8202))
% 51.10/50.84 [821]~E(x8211,x8212)+E(f58(x8211,x8213),f58(x8212,x8213))
% 51.10/50.84 [822]~E(x8221,x8222)+E(f58(x8223,x8221),f58(x8223,x8222))
% 51.10/50.84 [823]~E(x8231,x8232)+E(f837(x8231,x8233,x8234,x8235,x8236,x8237),f837(x8232,x8233,x8234,x8235,x8236,x8237))
% 51.10/50.84 [824]~E(x8241,x8242)+E(f837(x8243,x8241,x8244,x8245,x8246,x8247),f837(x8243,x8242,x8244,x8245,x8246,x8247))
% 51.10/50.84 [825]~E(x8251,x8252)+E(f837(x8253,x8254,x8251,x8255,x8256,x8257),f837(x8253,x8254,x8252,x8255,x8256,x8257))
% 51.10/50.84 [826]~E(x8261,x8262)+E(f837(x8263,x8264,x8265,x8261,x8266,x8267),f837(x8263,x8264,x8265,x8262,x8266,x8267))
% 51.10/50.84 [827]~E(x8271,x8272)+E(f837(x8273,x8274,x8275,x8276,x8271,x8277),f837(x8273,x8274,x8275,x8276,x8272,x8277))
% 51.10/50.84 [828]~E(x8281,x8282)+E(f837(x8283,x8284,x8285,x8286,x8287,x8281),f837(x8283,x8284,x8285,x8286,x8287,x8282))
% 51.10/50.84 [829]~E(x8291,x8292)+E(f69(x8291,x8293,x8294),f69(x8292,x8293,x8294))
% 51.10/50.84 [830]~E(x8301,x8302)+E(f69(x8303,x8301,x8304),f69(x8303,x8302,x8304))
% 51.10/50.84 [831]~E(x8311,x8312)+E(f69(x8313,x8314,x8311),f69(x8313,x8314,x8312))
% 51.10/50.84 [832]~E(x8321,x8322)+E(f352(x8321,x8323,x8324,x8325,x8326),f352(x8322,x8323,x8324,x8325,x8326))
% 51.10/50.84 [833]~E(x8331,x8332)+E(f352(x8333,x8331,x8334,x8335,x8336),f352(x8333,x8332,x8334,x8335,x8336))
% 51.10/50.84 [834]~E(x8341,x8342)+E(f352(x8343,x8344,x8341,x8345,x8346),f352(x8343,x8344,x8342,x8345,x8346))
% 51.10/50.84 [835]~E(x8351,x8352)+E(f352(x8353,x8354,x8355,x8351,x8356),f352(x8353,x8354,x8355,x8352,x8356))
% 51.10/50.84 [836]~E(x8361,x8362)+E(f352(x8363,x8364,x8365,x8366,x8361),f352(x8363,x8364,x8365,x8366,x8362))
% 51.10/50.84 [837]~E(x8371,x8372)+E(f769(x8371,x8373),f769(x8372,x8373))
% 51.10/50.84 [838]~E(x8381,x8382)+E(f769(x8383,x8381),f769(x8383,x8382))
% 51.10/50.84 [839]~E(x8391,x8392)+E(f276(x8391,x8393,x8394,x8395),f276(x8392,x8393,x8394,x8395))
% 51.10/50.84 [840]~E(x8401,x8402)+E(f276(x8403,x8401,x8404,x8405),f276(x8403,x8402,x8404,x8405))
% 51.10/50.84 [841]~E(x8411,x8412)+E(f276(x8413,x8414,x8411,x8415),f276(x8413,x8414,x8412,x8415))
% 51.10/50.84 [842]~E(x8421,x8422)+E(f276(x8423,x8424,x8425,x8421),f276(x8423,x8424,x8425,x8422))
% 51.10/50.84 [843]~E(x8431,x8432)+E(f375(x8431,x8433,x8434,x8435),f375(x8432,x8433,x8434,x8435))
% 51.10/50.84 [844]~E(x8441,x8442)+E(f375(x8443,x8441,x8444,x8445),f375(x8443,x8442,x8444,x8445))
% 51.10/50.84 [845]~E(x8451,x8452)+E(f375(x8453,x8454,x8451,x8455),f375(x8453,x8454,x8452,x8455))
% 51.10/50.84 [846]~E(x8461,x8462)+E(f375(x8463,x8464,x8465,x8461),f375(x8463,x8464,x8465,x8462))
% 51.10/50.84 [847]~E(x8471,x8472)+E(f272(x8471),f272(x8472))
% 51.10/50.84 [848]~E(x8481,x8482)+E(f243(x8481,x8483),f243(x8482,x8483))
% 51.10/50.84 [849]~E(x8491,x8492)+E(f243(x8493,x8491),f243(x8493,x8492))
% 51.10/50.84 [850]~E(x8501,x8502)+E(f368(x8501,x8503),f368(x8502,x8503))
% 51.10/50.84 [851]~E(x8511,x8512)+E(f368(x8513,x8511),f368(x8513,x8512))
% 51.10/50.84 [852]~E(x8521,x8522)+E(f611(x8521,x8523,x8524,x8525,x8526,x8527),f611(x8522,x8523,x8524,x8525,x8526,x8527))
% 51.10/50.84 [853]~E(x8531,x8532)+E(f611(x8533,x8531,x8534,x8535,x8536,x8537),f611(x8533,x8532,x8534,x8535,x8536,x8537))
% 51.10/50.84 [854]~E(x8541,x8542)+E(f611(x8543,x8544,x8541,x8545,x8546,x8547),f611(x8543,x8544,x8542,x8545,x8546,x8547))
% 51.10/50.84 [855]~E(x8551,x8552)+E(f611(x8553,x8554,x8555,x8551,x8556,x8557),f611(x8553,x8554,x8555,x8552,x8556,x8557))
% 51.10/50.84 [856]~E(x8561,x8562)+E(f611(x8563,x8564,x8565,x8566,x8561,x8567),f611(x8563,x8564,x8565,x8566,x8562,x8567))
% 51.10/50.84 [857]~E(x8571,x8572)+E(f611(x8573,x8574,x8575,x8576,x8577,x8571),f611(x8573,x8574,x8575,x8576,x8577,x8572))
% 51.10/50.84 [858]~E(x8581,x8582)+E(f438(x8581,x8583),f438(x8582,x8583))
% 51.10/50.84 [859]~E(x8591,x8592)+E(f438(x8593,x8591),f438(x8593,x8592))
% 51.10/50.84 [860]~E(x8601,x8602)+E(f789(x8601,x8603,x8604),f789(x8602,x8603,x8604))
% 51.10/50.84 [861]~E(x8611,x8612)+E(f789(x8613,x8611,x8614),f789(x8613,x8612,x8614))
% 51.10/50.84 [862]~E(x8621,x8622)+E(f789(x8623,x8624,x8621),f789(x8623,x8624,x8622))
% 51.10/50.84 [863]~E(x8631,x8632)+E(f653(x8631,x8633,x8634,x8635,x8636),f653(x8632,x8633,x8634,x8635,x8636))
% 51.10/50.84 [864]~E(x8641,x8642)+E(f653(x8643,x8641,x8644,x8645,x8646),f653(x8643,x8642,x8644,x8645,x8646))
% 51.10/50.84 [865]~E(x8651,x8652)+E(f653(x8653,x8654,x8651,x8655,x8656),f653(x8653,x8654,x8652,x8655,x8656))
% 51.10/50.84 [866]~E(x8661,x8662)+E(f653(x8663,x8664,x8665,x8661,x8666),f653(x8663,x8664,x8665,x8662,x8666))
% 51.10/50.84 [867]~E(x8671,x8672)+E(f653(x8673,x8674,x8675,x8676,x8671),f653(x8673,x8674,x8675,x8676,x8672))
% 51.10/50.84 [868]~E(x8681,x8682)+E(f635(x8681,x8683,x8684,x8685,x8686,x8687,x8688),f635(x8682,x8683,x8684,x8685,x8686,x8687,x8688))
% 51.10/50.84 [869]~E(x8691,x8692)+E(f635(x8693,x8691,x8694,x8695,x8696,x8697,x8698),f635(x8693,x8692,x8694,x8695,x8696,x8697,x8698))
% 51.10/50.84 [870]~E(x8701,x8702)+E(f635(x8703,x8704,x8701,x8705,x8706,x8707,x8708),f635(x8703,x8704,x8702,x8705,x8706,x8707,x8708))
% 51.10/50.84 [871]~E(x8711,x8712)+E(f635(x8713,x8714,x8715,x8711,x8716,x8717,x8718),f635(x8713,x8714,x8715,x8712,x8716,x8717,x8718))
% 51.10/50.84 [872]~E(x8721,x8722)+E(f635(x8723,x8724,x8725,x8726,x8721,x8727,x8728),f635(x8723,x8724,x8725,x8726,x8722,x8727,x8728))
% 51.10/50.84 [873]~E(x8731,x8732)+E(f635(x8733,x8734,x8735,x8736,x8737,x8731,x8738),f635(x8733,x8734,x8735,x8736,x8737,x8732,x8738))
% 51.10/50.84 [874]~E(x8741,x8742)+E(f635(x8743,x8744,x8745,x8746,x8747,x8748,x8741),f635(x8743,x8744,x8745,x8746,x8747,x8748,x8742))
% 51.10/50.84 [875]~E(x8751,x8752)+E(f253(x8751,x8753),f253(x8752,x8753))
% 51.10/50.84 [876]~E(x8761,x8762)+E(f253(x8763,x8761),f253(x8763,x8762))
% 51.10/50.84 [877]~E(x8771,x8772)+E(f723(x8771,x8773,x8774),f723(x8772,x8773,x8774))
% 51.10/50.84 [878]~E(x8781,x8782)+E(f723(x8783,x8781,x8784),f723(x8783,x8782,x8784))
% 51.10/50.84 [879]~E(x8791,x8792)+E(f723(x8793,x8794,x8791),f723(x8793,x8794,x8792))
% 51.10/50.84 [880]~E(x8801,x8802)+E(f732(x8801,x8803,x8804,x8805),f732(x8802,x8803,x8804,x8805))
% 51.10/50.84 [881]~E(x8811,x8812)+E(f732(x8813,x8811,x8814,x8815),f732(x8813,x8812,x8814,x8815))
% 51.10/50.84 [882]~E(x8821,x8822)+E(f732(x8823,x8824,x8821,x8825),f732(x8823,x8824,x8822,x8825))
% 51.10/50.84 [883]~E(x8831,x8832)+E(f732(x8833,x8834,x8835,x8831),f732(x8833,x8834,x8835,x8832))
% 51.10/50.84 [884]~E(x8841,x8842)+E(f776(x8841,x8843,x8844),f776(x8842,x8843,x8844))
% 51.10/50.84 [885]~E(x8851,x8852)+E(f776(x8853,x8851,x8854),f776(x8853,x8852,x8854))
% 51.10/50.84 [886]~E(x8861,x8862)+E(f776(x8863,x8864,x8861),f776(x8863,x8864,x8862))
% 51.10/50.84 [887]~E(x8871,x8872)+E(f408(x8871,x8873,x8874,x8875,x8876),f408(x8872,x8873,x8874,x8875,x8876))
% 51.10/50.84 [888]~E(x8881,x8882)+E(f408(x8883,x8881,x8884,x8885,x8886),f408(x8883,x8882,x8884,x8885,x8886))
% 51.10/50.84 [889]~E(x8891,x8892)+E(f408(x8893,x8894,x8891,x8895,x8896),f408(x8893,x8894,x8892,x8895,x8896))
% 51.10/50.84 [890]~E(x8901,x8902)+E(f408(x8903,x8904,x8905,x8901,x8906),f408(x8903,x8904,x8905,x8902,x8906))
% 51.10/50.84 [891]~E(x8911,x8912)+E(f408(x8913,x8914,x8915,x8916,x8911),f408(x8913,x8914,x8915,x8916,x8912))
% 51.10/50.84 [892]~E(x8921,x8922)+E(f658(x8921),f658(x8922))
% 51.10/50.84 [893]~E(x8931,x8932)+E(f531(x8931,x8933,x8934,x8935,x8936),f531(x8932,x8933,x8934,x8935,x8936))
% 51.10/50.84 [894]~E(x8941,x8942)+E(f531(x8943,x8941,x8944,x8945,x8946),f531(x8943,x8942,x8944,x8945,x8946))
% 51.10/50.84 [895]~E(x8951,x8952)+E(f531(x8953,x8954,x8951,x8955,x8956),f531(x8953,x8954,x8952,x8955,x8956))
% 51.10/50.84 [896]~E(x8961,x8962)+E(f531(x8963,x8964,x8965,x8961,x8966),f531(x8963,x8964,x8965,x8962,x8966))
% 51.10/50.84 [897]~E(x8971,x8972)+E(f531(x8973,x8974,x8975,x8976,x8971),f531(x8973,x8974,x8975,x8976,x8972))
% 51.10/50.84 [898]~E(x8981,x8982)+E(f218(x8981,x8983),f218(x8982,x8983))
% 51.10/50.84 [899]~E(x8991,x8992)+E(f218(x8993,x8991),f218(x8993,x8992))
% 51.10/50.84 [900]~E(x9001,x9002)+E(f360(x9001),f360(x9002))
% 51.10/50.84 [901]~E(x9011,x9012)+E(f727(x9011),f727(x9012))
% 51.10/50.84 [902]~E(x9021,x9022)+E(f826(x9021,x9023,x9024),f826(x9022,x9023,x9024))
% 51.10/50.84 [903]~E(x9031,x9032)+E(f826(x9033,x9031,x9034),f826(x9033,x9032,x9034))
% 51.10/50.84 [904]~E(x9041,x9042)+E(f826(x9043,x9044,x9041),f826(x9043,x9044,x9042))
% 51.10/50.84 [905]~E(x9051,x9052)+E(f348(x9051,x9053,x9054,x9055,x9056,x9057,x9058),f348(x9052,x9053,x9054,x9055,x9056,x9057,x9058))
% 51.10/50.84 [906]~E(x9061,x9062)+E(f348(x9063,x9061,x9064,x9065,x9066,x9067,x9068),f348(x9063,x9062,x9064,x9065,x9066,x9067,x9068))
% 51.10/50.84 [907]~E(x9071,x9072)+E(f348(x9073,x9074,x9071,x9075,x9076,x9077,x9078),f348(x9073,x9074,x9072,x9075,x9076,x9077,x9078))
% 51.10/50.84 [908]~E(x9081,x9082)+E(f348(x9083,x9084,x9085,x9081,x9086,x9087,x9088),f348(x9083,x9084,x9085,x9082,x9086,x9087,x9088))
% 51.10/50.84 [909]~E(x9091,x9092)+E(f348(x9093,x9094,x9095,x9096,x9091,x9097,x9098),f348(x9093,x9094,x9095,x9096,x9092,x9097,x9098))
% 51.10/50.84 [910]~E(x9101,x9102)+E(f348(x9103,x9104,x9105,x9106,x9107,x9101,x9108),f348(x9103,x9104,x9105,x9106,x9107,x9102,x9108))
% 51.10/50.84 [911]~E(x9111,x9112)+E(f348(x9113,x9114,x9115,x9116,x9117,x9118,x9111),f348(x9113,x9114,x9115,x9116,x9117,x9118,x9112))
% 51.10/50.84 [912]~E(x9121,x9122)+E(f564(x9121),f564(x9122))
% 51.10/50.84 [913]~E(x9131,x9132)+E(f773(x9131,x9133,x9134),f773(x9132,x9133,x9134))
% 51.10/50.84 [914]~E(x9141,x9142)+E(f773(x9143,x9141,x9144),f773(x9143,x9142,x9144))
% 51.10/50.84 [915]~E(x9151,x9152)+E(f773(x9153,x9154,x9151),f773(x9153,x9154,x9152))
% 51.10/50.84 [916]~E(x9161,x9162)+E(f532(x9161,x9163,x9164,x9165,x9166),f532(x9162,x9163,x9164,x9165,x9166))
% 51.10/50.84 [917]~E(x9171,x9172)+E(f532(x9173,x9171,x9174,x9175,x9176),f532(x9173,x9172,x9174,x9175,x9176))
% 51.10/50.84 [918]~E(x9181,x9182)+E(f532(x9183,x9184,x9181,x9185,x9186),f532(x9183,x9184,x9182,x9185,x9186))
% 51.10/50.84 [919]~E(x9191,x9192)+E(f532(x9193,x9194,x9195,x9191,x9196),f532(x9193,x9194,x9195,x9192,x9196))
% 51.10/50.84 [920]~E(x9201,x9202)+E(f532(x9203,x9204,x9205,x9206,x9201),f532(x9203,x9204,x9205,x9206,x9202))
% 51.10/50.84 [921]~E(x9211,x9212)+E(f273(x9211,x9213),f273(x9212,x9213))
% 51.10/50.84 [922]~E(x9221,x9222)+E(f273(x9223,x9221),f273(x9223,x9222))
% 51.10/50.84 [923]~E(x9231,x9232)+E(f344(x9231,x9233,x9234,x9235),f344(x9232,x9233,x9234,x9235))
% 51.10/50.84 [924]~E(x9241,x9242)+E(f344(x9243,x9241,x9244,x9245),f344(x9243,x9242,x9244,x9245))
% 51.10/50.84 [925]~E(x9251,x9252)+E(f344(x9253,x9254,x9251,x9255),f344(x9253,x9254,x9252,x9255))
% 51.10/50.84 [926]~E(x9261,x9262)+E(f344(x9263,x9264,x9265,x9261),f344(x9263,x9264,x9265,x9262))
% 51.10/50.84 [927]~E(x9271,x9272)+E(f676(x9271,x9273,x9274,x9275),f676(x9272,x9273,x9274,x9275))
% 51.10/50.84 [928]~E(x9281,x9282)+E(f676(x9283,x9281,x9284,x9285),f676(x9283,x9282,x9284,x9285))
% 51.10/50.84 [929]~E(x9291,x9292)+E(f676(x9293,x9294,x9291,x9295),f676(x9293,x9294,x9292,x9295))
% 51.10/50.84 [930]~E(x9301,x9302)+E(f676(x9303,x9304,x9305,x9301),f676(x9303,x9304,x9305,x9302))
% 51.10/50.84 [931]~E(x9311,x9312)+E(f508(x9311,x9313,x9314),f508(x9312,x9313,x9314))
% 51.10/50.84 [932]~E(x9321,x9322)+E(f508(x9323,x9321,x9324),f508(x9323,x9322,x9324))
% 51.10/50.84 [933]~E(x9331,x9332)+E(f508(x9333,x9334,x9331),f508(x9333,x9334,x9332))
% 51.10/50.84 [934]~E(x9341,x9342)+E(f561(x9341,x9343,x9344,x9345,x9346),f561(x9342,x9343,x9344,x9345,x9346))
% 51.10/50.84 [935]~E(x9351,x9352)+E(f561(x9353,x9351,x9354,x9355,x9356),f561(x9353,x9352,x9354,x9355,x9356))
% 51.10/50.84 [936]~E(x9361,x9362)+E(f561(x9363,x9364,x9361,x9365,x9366),f561(x9363,x9364,x9362,x9365,x9366))
% 51.10/50.84 [937]~E(x9371,x9372)+E(f561(x9373,x9374,x9375,x9371,x9376),f561(x9373,x9374,x9375,x9372,x9376))
% 51.10/50.84 [938]~E(x9381,x9382)+E(f561(x9383,x9384,x9385,x9386,x9381),f561(x9383,x9384,x9385,x9386,x9382))
% 51.10/50.84 [939]~E(x9391,x9392)+E(f767(x9391),f767(x9392))
% 51.10/50.84 [940]~E(x9401,x9402)+E(f351(x9401,x9403,x9404,x9405),f351(x9402,x9403,x9404,x9405))
% 51.10/50.84 [941]~E(x9411,x9412)+E(f351(x9413,x9411,x9414,x9415),f351(x9413,x9412,x9414,x9415))
% 51.10/50.84 [942]~E(x9421,x9422)+E(f351(x9423,x9424,x9421,x9425),f351(x9423,x9424,x9422,x9425))
% 51.10/50.84 [943]~E(x9431,x9432)+E(f351(x9433,x9434,x9435,x9431),f351(x9433,x9434,x9435,x9432))
% 51.10/50.84 [944]~E(x9441,x9442)+E(f99(x9441,x9443,x9444),f99(x9442,x9443,x9444))
% 51.10/50.84 [945]~E(x9451,x9452)+E(f99(x9453,x9451,x9454),f99(x9453,x9452,x9454))
% 51.10/50.84 [946]~E(x9461,x9462)+E(f99(x9463,x9464,x9461),f99(x9463,x9464,x9462))
% 51.10/50.84 [947]~E(x9471,x9472)+E(f189(x9471,x9473),f189(x9472,x9473))
% 51.10/50.84 [948]~E(x9481,x9482)+E(f189(x9483,x9481),f189(x9483,x9482))
% 51.10/50.84 [949]~E(x9491,x9492)+E(f509(x9491,x9493,x9494,x9495,x9496),f509(x9492,x9493,x9494,x9495,x9496))
% 51.10/50.84 [950]~E(x9501,x9502)+E(f509(x9503,x9501,x9504,x9505,x9506),f509(x9503,x9502,x9504,x9505,x9506))
% 51.10/50.84 [951]~E(x9511,x9512)+E(f509(x9513,x9514,x9511,x9515,x9516),f509(x9513,x9514,x9512,x9515,x9516))
% 51.10/50.84 [952]~E(x9521,x9522)+E(f509(x9523,x9524,x9525,x9521,x9526),f509(x9523,x9524,x9525,x9522,x9526))
% 51.10/50.84 [953]~E(x9531,x9532)+E(f509(x9533,x9534,x9535,x9536,x9531),f509(x9533,x9534,x9535,x9536,x9532))
% 51.10/50.84 [954]~E(x9541,x9542)+E(f125(x9541,x9543),f125(x9542,x9543))
% 51.10/50.84 [955]~E(x9551,x9552)+E(f125(x9553,x9551),f125(x9553,x9552))
% 51.10/50.84 [956]~E(x9561,x9562)+E(f201(x9561,x9563),f201(x9562,x9563))
% 51.10/50.84 [957]~E(x9571,x9572)+E(f201(x9573,x9571),f201(x9573,x9572))
% 51.10/50.84 [958]~E(x9581,x9582)+E(f238(x9581),f238(x9582))
% 51.10/50.84 [959]~E(x9591,x9592)+E(f128(x9591,x9593),f128(x9592,x9593))
% 51.10/50.84 [960]~E(x9601,x9602)+E(f128(x9603,x9601),f128(x9603,x9602))
% 51.10/50.84 [961]~E(x9611,x9612)+E(f543(x9611,x9613,x9614,x9615,x9616,x9617),f543(x9612,x9613,x9614,x9615,x9616,x9617))
% 51.10/50.84 [962]~E(x9621,x9622)+E(f543(x9623,x9621,x9624,x9625,x9626,x9627),f543(x9623,x9622,x9624,x9625,x9626,x9627))
% 51.10/50.84 [963]~E(x9631,x9632)+E(f543(x9633,x9634,x9631,x9635,x9636,x9637),f543(x9633,x9634,x9632,x9635,x9636,x9637))
% 51.10/50.84 [964]~E(x9641,x9642)+E(f543(x9643,x9644,x9645,x9641,x9646,x9647),f543(x9643,x9644,x9645,x9642,x9646,x9647))
% 51.10/50.84 [965]~E(x9651,x9652)+E(f543(x9653,x9654,x9655,x9656,x9651,x9657),f543(x9653,x9654,x9655,x9656,x9652,x9657))
% 51.10/50.84 [966]~E(x9661,x9662)+E(f543(x9663,x9664,x9665,x9666,x9667,x9661),f543(x9663,x9664,x9665,x9666,x9667,x9662))
% 51.10/50.84 [967]~E(x9671,x9672)+E(f540(x9671,x9673),f540(x9672,x9673))
% 51.10/50.84 [968]~E(x9681,x9682)+E(f540(x9683,x9681),f540(x9683,x9682))
% 51.10/50.84 [969]~E(x9691,x9692)+E(f775(x9691,x9693,x9694),f775(x9692,x9693,x9694))
% 51.10/50.84 [970]~E(x9701,x9702)+E(f775(x9703,x9701,x9704),f775(x9703,x9702,x9704))
% 51.10/50.84 [971]~E(x9711,x9712)+E(f775(x9713,x9714,x9711),f775(x9713,x9714,x9712))
% 51.10/50.84 [972]~E(x9721,x9722)+E(f176(x9721,x9723,x9724),f176(x9722,x9723,x9724))
% 51.10/50.84 [973]~E(x9731,x9732)+E(f176(x9733,x9731,x9734),f176(x9733,x9732,x9734))
% 51.10/50.84 [974]~E(x9741,x9742)+E(f176(x9743,x9744,x9741),f176(x9743,x9744,x9742))
% 51.10/50.84 [975]~E(x9751,x9752)+E(f424(x9751,x9753,x9754,x9755,x9756),f424(x9752,x9753,x9754,x9755,x9756))
% 51.10/50.84 [976]~E(x9761,x9762)+E(f424(x9763,x9761,x9764,x9765,x9766),f424(x9763,x9762,x9764,x9765,x9766))
% 51.10/50.84 [977]~E(x9771,x9772)+E(f424(x9773,x9774,x9771,x9775,x9776),f424(x9773,x9774,x9772,x9775,x9776))
% 51.10/50.84 [978]~E(x9781,x9782)+E(f424(x9783,x9784,x9785,x9781,x9786),f424(x9783,x9784,x9785,x9782,x9786))
% 51.10/50.84 [979]~E(x9791,x9792)+E(f424(x9793,x9794,x9795,x9796,x9791),f424(x9793,x9794,x9795,x9796,x9792))
% 51.10/50.84 [980]~E(x9801,x9802)+E(f581(x9801,x9803,x9804),f581(x9802,x9803,x9804))
% 51.10/50.84 [981]~E(x9811,x9812)+E(f581(x9813,x9811,x9814),f581(x9813,x9812,x9814))
% 51.10/50.84 [982]~E(x9821,x9822)+E(f581(x9823,x9824,x9821),f581(x9823,x9824,x9822))
% 51.10/50.84 [983]~E(x9831,x9832)+E(f714(x9831,x9833,x9834,x9835,x9836),f714(x9832,x9833,x9834,x9835,x9836))
% 51.10/50.84 [984]~E(x9841,x9842)+E(f714(x9843,x9841,x9844,x9845,x9846),f714(x9843,x9842,x9844,x9845,x9846))
% 51.10/50.84 [985]~E(x9851,x9852)+E(f714(x9853,x9854,x9851,x9855,x9856),f714(x9853,x9854,x9852,x9855,x9856))
% 51.10/50.84 [986]~E(x9861,x9862)+E(f714(x9863,x9864,x9865,x9861,x9866),f714(x9863,x9864,x9865,x9862,x9866))
% 51.10/50.84 [987]~E(x9871,x9872)+E(f714(x9873,x9874,x9875,x9876,x9871),f714(x9873,x9874,x9875,x9876,x9872))
% 51.10/50.84 [988]~E(x9881,x9882)+E(f136(x9881),f136(x9882))
% 51.10/50.84 [989]~E(x9891,x9892)+E(f735(x9891,x9893,x9894,x9895,x9896),f735(x9892,x9893,x9894,x9895,x9896))
% 51.10/50.84 [990]~E(x9901,x9902)+E(f735(x9903,x9901,x9904,x9905,x9906),f735(x9903,x9902,x9904,x9905,x9906))
% 51.10/50.84 [991]~E(x9911,x9912)+E(f735(x9913,x9914,x9911,x9915,x9916),f735(x9913,x9914,x9912,x9915,x9916))
% 51.10/50.84 [992]~E(x9921,x9922)+E(f735(x9923,x9924,x9925,x9921,x9926),f735(x9923,x9924,x9925,x9922,x9926))
% 51.10/50.84 [993]~E(x9931,x9932)+E(f735(x9933,x9934,x9935,x9936,x9931),f735(x9933,x9934,x9935,x9936,x9932))
% 51.10/50.84 [994]~E(x9941,x9942)+E(f166(x9941,x9943,x9944),f166(x9942,x9943,x9944))
% 51.10/50.84 [995]~E(x9951,x9952)+E(f166(x9953,x9951,x9954),f166(x9953,x9952,x9954))
% 51.10/50.84 [996]~E(x9961,x9962)+E(f166(x9963,x9964,x9961),f166(x9963,x9964,x9962))
% 51.10/50.84 [997]~E(x9971,x9972)+E(f671(x9971,x9973,x9974),f671(x9972,x9973,x9974))
% 51.10/50.84 [998]~E(x9981,x9982)+E(f671(x9983,x9981,x9984),f671(x9983,x9982,x9984))
% 51.10/50.84 [999]~E(x9991,x9992)+E(f671(x9993,x9994,x9991),f671(x9993,x9994,x9992))
% 51.10/50.84 [1000]~E(x10001,x10002)+E(f278(x10001,x10003),f278(x10002,x10003))
% 51.10/50.84 [1001]~E(x10011,x10012)+E(f278(x10013,x10011),f278(x10013,x10012))
% 51.10/50.84 [1002]~E(x10021,x10022)+E(f686(x10021,x10023,x10024,x10025,x10026),f686(x10022,x10023,x10024,x10025,x10026))
% 51.10/50.84 [1003]~E(x10031,x10032)+E(f686(x10033,x10031,x10034,x10035,x10036),f686(x10033,x10032,x10034,x10035,x10036))
% 51.10/50.84 [1004]~E(x10041,x10042)+E(f686(x10043,x10044,x10041,x10045,x10046),f686(x10043,x10044,x10042,x10045,x10046))
% 51.10/50.84 [1005]~E(x10051,x10052)+E(f686(x10053,x10054,x10055,x10051,x10056),f686(x10053,x10054,x10055,x10052,x10056))
% 51.10/50.84 [1006]~E(x10061,x10062)+E(f686(x10063,x10064,x10065,x10066,x10061),f686(x10063,x10064,x10065,x10066,x10062))
% 51.10/50.84 [1007]~E(x10071,x10072)+E(f579(x10071,x10073),f579(x10072,x10073))
% 51.10/50.84 [1008]~E(x10081,x10082)+E(f579(x10083,x10081),f579(x10083,x10082))
% 51.10/50.84 [1009]~E(x10091,x10092)+E(f222(x10091,x10093,x10094,x10095),f222(x10092,x10093,x10094,x10095))
% 51.10/50.84 [1010]~E(x10101,x10102)+E(f222(x10103,x10101,x10104,x10105),f222(x10103,x10102,x10104,x10105))
% 51.10/50.84 [1011]~E(x10111,x10112)+E(f222(x10113,x10114,x10111,x10115),f222(x10113,x10114,x10112,x10115))
% 51.10/50.84 [1012]~E(x10121,x10122)+E(f222(x10123,x10124,x10125,x10121),f222(x10123,x10124,x10125,x10122))
% 51.10/50.84 [1013]~E(x10131,x10132)+E(f298(x10131,x10133,x10134),f298(x10132,x10133,x10134))
% 51.10/50.84 [1014]~E(x10141,x10142)+E(f298(x10143,x10141,x10144),f298(x10143,x10142,x10144))
% 51.10/50.84 [1015]~E(x10151,x10152)+E(f298(x10153,x10154,x10151),f298(x10153,x10154,x10152))
% 51.10/50.84 [1016]~E(x10161,x10162)+E(f299(x10161,x10163,x10164,x10165),f299(x10162,x10163,x10164,x10165))
% 51.10/50.84 [1017]~E(x10171,x10172)+E(f299(x10173,x10171,x10174,x10175),f299(x10173,x10172,x10174,x10175))
% 51.10/50.84 [1018]~E(x10181,x10182)+E(f299(x10183,x10184,x10181,x10185),f299(x10183,x10184,x10182,x10185))
% 51.10/50.84 [1019]~E(x10191,x10192)+E(f299(x10193,x10194,x10195,x10191),f299(x10193,x10194,x10195,x10192))
% 51.10/50.84 [1020]~E(x10201,x10202)+E(f376(x10201,x10203),f376(x10202,x10203))
% 51.10/50.84 [1021]~E(x10211,x10212)+E(f376(x10213,x10211),f376(x10213,x10212))
% 51.10/50.84 [1022]~E(x10221,x10222)+E(f827(x10221,x10223,x10224,x10225),f827(x10222,x10223,x10224,x10225))
% 51.10/50.84 [1023]~E(x10231,x10232)+E(f827(x10233,x10231,x10234,x10235),f827(x10233,x10232,x10234,x10235))
% 51.10/50.84 [1024]~E(x10241,x10242)+E(f827(x10243,x10244,x10241,x10245),f827(x10243,x10244,x10242,x10245))
% 51.10/50.84 [1025]~E(x10251,x10252)+E(f827(x10253,x10254,x10255,x10251),f827(x10253,x10254,x10255,x10252))
% 51.10/50.84 [1026]~E(x10261,x10262)+E(f261(x10261,x10263,x10264,x10265),f261(x10262,x10263,x10264,x10265))
% 51.10/50.84 [1027]~E(x10271,x10272)+E(f261(x10273,x10271,x10274,x10275),f261(x10273,x10272,x10274,x10275))
% 51.10/50.84 [1028]~E(x10281,x10282)+E(f261(x10283,x10284,x10281,x10285),f261(x10283,x10284,x10282,x10285))
% 51.10/50.84 [1029]~E(x10291,x10292)+E(f261(x10293,x10294,x10295,x10291),f261(x10293,x10294,x10295,x10292))
% 51.10/50.84 [1030]~E(x10301,x10302)+E(f324(x10301,x10303,x10304,x10305),f324(x10302,x10303,x10304,x10305))
% 51.10/50.84 [1031]~E(x10311,x10312)+E(f324(x10313,x10311,x10314,x10315),f324(x10313,x10312,x10314,x10315))
% 51.10/50.84 [1032]~E(x10321,x10322)+E(f324(x10323,x10324,x10321,x10325),f324(x10323,x10324,x10322,x10325))
% 51.10/50.84 [1033]~E(x10331,x10332)+E(f324(x10333,x10334,x10335,x10331),f324(x10333,x10334,x10335,x10332))
% 51.10/50.84 [1034]~E(x10341,x10342)+E(f570(x10341,x10343),f570(x10342,x10343))
% 51.10/50.84 [1035]~E(x10351,x10352)+E(f570(x10353,x10351),f570(x10353,x10352))
% 51.10/50.84 [1036]~E(x10361,x10362)+E(f482(x10361,x10363),f482(x10362,x10363))
% 51.10/50.84 [1037]~E(x10371,x10372)+E(f482(x10373,x10371),f482(x10373,x10372))
% 51.10/50.84 [1038]~E(x10381,x10382)+E(f410(x10381,x10383,x10384,x10385,x10386),f410(x10382,x10383,x10384,x10385,x10386))
% 51.10/50.84 [1039]~E(x10391,x10392)+E(f410(x10393,x10391,x10394,x10395,x10396),f410(x10393,x10392,x10394,x10395,x10396))
% 51.10/50.84 [1040]~E(x10401,x10402)+E(f410(x10403,x10404,x10401,x10405,x10406),f410(x10403,x10404,x10402,x10405,x10406))
% 51.10/50.84 [1041]~E(x10411,x10412)+E(f410(x10413,x10414,x10415,x10411,x10416),f410(x10413,x10414,x10415,x10412,x10416))
% 51.10/50.84 [1042]~E(x10421,x10422)+E(f410(x10423,x10424,x10425,x10426,x10421),f410(x10423,x10424,x10425,x10426,x10422))
% 51.10/50.84 [1043]~E(x10431,x10432)+E(f760(x10431),f760(x10432))
% 51.10/50.84 [1044]~E(x10441,x10442)+E(f528(x10441,x10443,x10444,x10445,x10446),f528(x10442,x10443,x10444,x10445,x10446))
% 51.10/50.84 [1045]~E(x10451,x10452)+E(f528(x10453,x10451,x10454,x10455,x10456),f528(x10453,x10452,x10454,x10455,x10456))
% 51.10/50.84 [1046]~E(x10461,x10462)+E(f528(x10463,x10464,x10461,x10465,x10466),f528(x10463,x10464,x10462,x10465,x10466))
% 51.10/50.84 [1047]~E(x10471,x10472)+E(f528(x10473,x10474,x10475,x10471,x10476),f528(x10473,x10474,x10475,x10472,x10476))
% 51.10/50.84 [1048]~E(x10481,x10482)+E(f528(x10483,x10484,x10485,x10486,x10481),f528(x10483,x10484,x10485,x10486,x10482))
% 51.10/50.84 [1049]~E(x10491,x10492)+E(f757(x10491,x10493,x10494,x10495),f757(x10492,x10493,x10494,x10495))
% 51.10/50.84 [1050]~E(x10501,x10502)+E(f757(x10503,x10501,x10504,x10505),f757(x10503,x10502,x10504,x10505))
% 51.10/50.84 [1051]~E(x10511,x10512)+E(f757(x10513,x10514,x10511,x10515),f757(x10513,x10514,x10512,x10515))
% 51.10/50.84 [1052]~E(x10521,x10522)+E(f757(x10523,x10524,x10525,x10521),f757(x10523,x10524,x10525,x10522))
% 51.10/50.84 [1053]~E(x10531,x10532)+E(f493(x10531,x10533,x10534,x10535,x10536),f493(x10532,x10533,x10534,x10535,x10536))
% 51.10/50.84 [1054]~E(x10541,x10542)+E(f493(x10543,x10541,x10544,x10545,x10546),f493(x10543,x10542,x10544,x10545,x10546))
% 51.10/50.84 [1055]~E(x10551,x10552)+E(f493(x10553,x10554,x10551,x10555,x10556),f493(x10553,x10554,x10552,x10555,x10556))
% 51.10/50.84 [1056]~E(x10561,x10562)+E(f493(x10563,x10564,x10565,x10561,x10566),f493(x10563,x10564,x10565,x10562,x10566))
% 51.10/50.84 [1057]~E(x10571,x10572)+E(f493(x10573,x10574,x10575,x10576,x10571),f493(x10573,x10574,x10575,x10576,x10572))
% 51.10/50.84 [1058]~E(x10581,x10582)+E(f752(x10581,x10583,x10584,x10585),f752(x10582,x10583,x10584,x10585))
% 51.10/50.84 [1059]~E(x10591,x10592)+E(f752(x10593,x10591,x10594,x10595),f752(x10593,x10592,x10594,x10595))
% 51.10/50.84 [1060]~E(x10601,x10602)+E(f752(x10603,x10604,x10601,x10605),f752(x10603,x10604,x10602,x10605))
% 51.10/50.84 [1061]~E(x10611,x10612)+E(f752(x10613,x10614,x10615,x10611),f752(x10613,x10614,x10615,x10612))
% 51.10/50.84 [1062]~E(x10621,x10622)+E(f430(x10621,x10623,x10624),f430(x10622,x10623,x10624))
% 51.10/50.84 [1063]~E(x10631,x10632)+E(f430(x10633,x10631,x10634),f430(x10633,x10632,x10634))
% 51.10/50.84 [1064]~E(x10641,x10642)+E(f430(x10643,x10644,x10641),f430(x10643,x10644,x10642))
% 51.10/50.84 [1065]~E(x10651,x10652)+E(f345(x10651,x10653),f345(x10652,x10653))
% 51.10/50.84 [1066]~E(x10661,x10662)+E(f345(x10663,x10661),f345(x10663,x10662))
% 51.10/50.84 [1067]~E(x10671,x10672)+E(f666(x10671,x10673,x10674),f666(x10672,x10673,x10674))
% 51.10/50.84 [1068]~E(x10681,x10682)+E(f666(x10683,x10681,x10684),f666(x10683,x10682,x10684))
% 51.10/50.84 [1069]~E(x10691,x10692)+E(f666(x10693,x10694,x10691),f666(x10693,x10694,x10692))
% 51.10/50.84 [1070]~E(x10701,x10702)+E(f554(x10701,x10703,x10704,x10705,x10706),f554(x10702,x10703,x10704,x10705,x10706))
% 51.10/50.84 [1071]~E(x10711,x10712)+E(f554(x10713,x10711,x10714,x10715,x10716),f554(x10713,x10712,x10714,x10715,x10716))
% 51.10/50.84 [1072]~E(x10721,x10722)+E(f554(x10723,x10724,x10721,x10725,x10726),f554(x10723,x10724,x10722,x10725,x10726))
% 51.10/50.84 [1073]~E(x10731,x10732)+E(f554(x10733,x10734,x10735,x10731,x10736),f554(x10733,x10734,x10735,x10732,x10736))
% 51.10/50.84 [1074]~E(x10741,x10742)+E(f554(x10743,x10744,x10745,x10746,x10741),f554(x10743,x10744,x10745,x10746,x10742))
% 51.10/50.84 [1075]~E(x10751,x10752)+E(f382(x10751,x10753),f382(x10752,x10753))
% 51.10/50.84 [1076]~E(x10761,x10762)+E(f382(x10763,x10761),f382(x10763,x10762))
% 51.10/50.84 [1077]~E(x10771,x10772)+E(f855(x10771,x10773),f855(x10772,x10773))
% 51.10/50.84 [1078]~E(x10781,x10782)+E(f855(x10783,x10781),f855(x10783,x10782))
% 51.10/50.84 [1079]~E(x10791,x10792)+E(f660(x10791,x10793,x10794),f660(x10792,x10793,x10794))
% 51.10/50.84 [1080]~E(x10801,x10802)+E(f660(x10803,x10801,x10804),f660(x10803,x10802,x10804))
% 51.10/50.84 [1081]~E(x10811,x10812)+E(f660(x10813,x10814,x10811),f660(x10813,x10814,x10812))
% 51.10/50.84 [1082]~E(x10821,x10822)+E(f198(x10821,x10823,x10824,x10825),f198(x10822,x10823,x10824,x10825))
% 51.10/50.84 [1083]~E(x10831,x10832)+E(f198(x10833,x10831,x10834,x10835),f198(x10833,x10832,x10834,x10835))
% 51.10/50.84 [1084]~E(x10841,x10842)+E(f198(x10843,x10844,x10841,x10845),f198(x10843,x10844,x10842,x10845))
% 51.10/50.84 [1085]~E(x10851,x10852)+E(f198(x10853,x10854,x10855,x10851),f198(x10853,x10854,x10855,x10852))
% 51.10/50.84 [1086]~E(x10861,x10862)+E(f343(x10861,x10863,x10864,x10865),f343(x10862,x10863,x10864,x10865))
% 51.10/50.84 [1087]~E(x10871,x10872)+E(f343(x10873,x10871,x10874,x10875),f343(x10873,x10872,x10874,x10875))
% 51.10/50.84 [1088]~E(x10881,x10882)+E(f343(x10883,x10884,x10881,x10885),f343(x10883,x10884,x10882,x10885))
% 51.10/50.84 [1089]~E(x10891,x10892)+E(f343(x10893,x10894,x10895,x10891),f343(x10893,x10894,x10895,x10892))
% 51.10/50.84 [1090]~E(x10901,x10902)+E(f275(x10901,x10903),f275(x10902,x10903))
% 51.10/50.84 [1091]~E(x10911,x10912)+E(f275(x10913,x10911),f275(x10913,x10912))
% 51.10/50.84 [1092]~E(x10921,x10922)+E(f566(x10921,x10923,x10924,x10925),f566(x10922,x10923,x10924,x10925))
% 51.10/50.84 [1093]~E(x10931,x10932)+E(f566(x10933,x10931,x10934,x10935),f566(x10933,x10932,x10934,x10935))
% 51.10/50.84 [1094]~E(x10941,x10942)+E(f566(x10943,x10944,x10941,x10945),f566(x10943,x10944,x10942,x10945))
% 51.10/50.84 [1095]~E(x10951,x10952)+E(f566(x10953,x10954,x10955,x10951),f566(x10953,x10954,x10955,x10952))
% 51.10/50.84 [1096]~E(x10961,x10962)+E(f212(x10961,x10963,x10964,x10965),f212(x10962,x10963,x10964,x10965))
% 51.10/50.84 [1097]~E(x10971,x10972)+E(f212(x10973,x10971,x10974,x10975),f212(x10973,x10972,x10974,x10975))
% 51.10/50.84 [1098]~E(x10981,x10982)+E(f212(x10983,x10984,x10981,x10985),f212(x10983,x10984,x10982,x10985))
% 51.10/50.84 [1099]~E(x10991,x10992)+E(f212(x10993,x10994,x10995,x10991),f212(x10993,x10994,x10995,x10992))
% 51.10/50.84 [1100]~E(x11001,x11002)+E(f739(x11001,x11003,x11004,x11005,x11006),f739(x11002,x11003,x11004,x11005,x11006))
% 51.10/50.84 [1101]~E(x11011,x11012)+E(f739(x11013,x11011,x11014,x11015,x11016),f739(x11013,x11012,x11014,x11015,x11016))
% 51.10/50.84 [1102]~E(x11021,x11022)+E(f739(x11023,x11024,x11021,x11025,x11026),f739(x11023,x11024,x11022,x11025,x11026))
% 51.10/50.84 [1103]~E(x11031,x11032)+E(f739(x11033,x11034,x11035,x11031,x11036),f739(x11033,x11034,x11035,x11032,x11036))
% 51.10/50.84 [1104]~E(x11041,x11042)+E(f739(x11043,x11044,x11045,x11046,x11041),f739(x11043,x11044,x11045,x11046,x11042))
% 51.10/50.84 [1105]~E(x11051,x11052)+E(f409(x11051,x11053,x11054,x11055,x11056),f409(x11052,x11053,x11054,x11055,x11056))
% 51.10/50.84 [1106]~E(x11061,x11062)+E(f409(x11063,x11061,x11064,x11065,x11066),f409(x11063,x11062,x11064,x11065,x11066))
% 51.10/50.84 [1107]~E(x11071,x11072)+E(f409(x11073,x11074,x11071,x11075,x11076),f409(x11073,x11074,x11072,x11075,x11076))
% 51.10/50.84 [1108]~E(x11081,x11082)+E(f409(x11083,x11084,x11085,x11081,x11086),f409(x11083,x11084,x11085,x11082,x11086))
% 51.10/50.84 [1109]~E(x11091,x11092)+E(f409(x11093,x11094,x11095,x11096,x11091),f409(x11093,x11094,x11095,x11096,x11092))
% 51.10/50.84 [1110]~E(x11101,x11102)+E(f615(x11101),f615(x11102))
% 51.10/50.84 [1111]~E(x11111,x11112)+E(f604(x11111,x11113,x11114,x11115),f604(x11112,x11113,x11114,x11115))
% 51.10/50.84 [1112]~E(x11121,x11122)+E(f604(x11123,x11121,x11124,x11125),f604(x11123,x11122,x11124,x11125))
% 51.10/50.84 [1113]~E(x11131,x11132)+E(f604(x11133,x11134,x11131,x11135),f604(x11133,x11134,x11132,x11135))
% 51.10/50.84 [1114]~E(x11141,x11142)+E(f604(x11143,x11144,x11145,x11141),f604(x11143,x11144,x11145,x11142))
% 51.10/50.84 [1115]~E(x11151,x11152)+E(f515(x11151,x11153,x11154,x11155,x11156),f515(x11152,x11153,x11154,x11155,x11156))
% 51.10/50.84 [1116]~E(x11161,x11162)+E(f515(x11163,x11161,x11164,x11165,x11166),f515(x11163,x11162,x11164,x11165,x11166))
% 51.10/50.84 [1117]~E(x11171,x11172)+E(f515(x11173,x11174,x11171,x11175,x11176),f515(x11173,x11174,x11172,x11175,x11176))
% 51.10/50.84 [1118]~E(x11181,x11182)+E(f515(x11183,x11184,x11185,x11181,x11186),f515(x11183,x11184,x11185,x11182,x11186))
% 51.10/50.84 [1119]~E(x11191,x11192)+E(f515(x11193,x11194,x11195,x11196,x11191),f515(x11193,x11194,x11195,x11196,x11192))
% 51.10/50.84 [1120]~E(x11201,x11202)+E(f786(x11201,x11203),f786(x11202,x11203))
% 51.10/50.84 [1121]~E(x11211,x11212)+E(f786(x11213,x11211),f786(x11213,x11212))
% 51.10/50.84 [1122]~E(x11221,x11222)+E(f785(x11221,x11223,x11224),f785(x11222,x11223,x11224))
% 51.10/50.84 [1123]~E(x11231,x11232)+E(f785(x11233,x11231,x11234),f785(x11233,x11232,x11234))
% 51.10/50.84 [1124]~E(x11241,x11242)+E(f785(x11243,x11244,x11241),f785(x11243,x11244,x11242))
% 51.10/50.84 [1125]~E(x11251,x11252)+E(f758(x11251,x11253,x11254,x11255),f758(x11252,x11253,x11254,x11255))
% 51.10/50.84 [1126]~E(x11261,x11262)+E(f758(x11263,x11261,x11264,x11265),f758(x11263,x11262,x11264,x11265))
% 51.10/50.84 [1127]~E(x11271,x11272)+E(f758(x11273,x11274,x11271,x11275),f758(x11273,x11274,x11272,x11275))
% 51.10/50.84 [1128]~E(x11281,x11282)+E(f758(x11283,x11284,x11285,x11281),f758(x11283,x11284,x11285,x11282))
% 51.10/50.84 [1129]~E(x11291,x11292)+E(f316(x11291,x11293,x11294),f316(x11292,x11293,x11294))
% 51.10/50.84 [1130]~E(x11301,x11302)+E(f316(x11303,x11301,x11304),f316(x11303,x11302,x11304))
% 51.10/50.84 [1131]~E(x11311,x11312)+E(f316(x11313,x11314,x11311),f316(x11313,x11314,x11312))
% 51.10/50.84 [1132]~E(x11321,x11322)+E(f377(x11321,x11323),f377(x11322,x11323))
% 51.10/50.84 [1133]~E(x11331,x11332)+E(f377(x11333,x11331),f377(x11333,x11332))
% 51.10/50.84 [1134]~E(x11341,x11342)+E(f373(x11341,x11343,x11344),f373(x11342,x11343,x11344))
% 51.10/50.84 [1135]~E(x11351,x11352)+E(f373(x11353,x11351,x11354),f373(x11353,x11352,x11354))
% 51.10/50.84 [1136]~E(x11361,x11362)+E(f373(x11363,x11364,x11361),f373(x11363,x11364,x11362))
% 51.10/50.84 [1137]~E(x11371,x11372)+E(f349(x11371,x11373,x11374,x11375),f349(x11372,x11373,x11374,x11375))
% 51.10/50.84 [1138]~E(x11381,x11382)+E(f349(x11383,x11381,x11384,x11385),f349(x11383,x11382,x11384,x11385))
% 51.10/50.84 [1139]~E(x11391,x11392)+E(f349(x11393,x11394,x11391,x11395),f349(x11393,x11394,x11392,x11395))
% 51.10/50.84 [1140]~E(x11401,x11402)+E(f349(x11403,x11404,x11405,x11401),f349(x11403,x11404,x11405,x11402))
% 51.10/50.84 [1141]~E(x11411,x11412)+E(f685(x11411,x11413,x11414,x11415,x11416),f685(x11412,x11413,x11414,x11415,x11416))
% 51.10/50.84 [1142]~E(x11421,x11422)+E(f685(x11423,x11421,x11424,x11425,x11426),f685(x11423,x11422,x11424,x11425,x11426))
% 51.10/50.84 [1143]~E(x11431,x11432)+E(f685(x11433,x11434,x11431,x11435,x11436),f685(x11433,x11434,x11432,x11435,x11436))
% 51.10/50.84 [1144]~E(x11441,x11442)+E(f685(x11443,x11444,x11445,x11441,x11446),f685(x11443,x11444,x11445,x11442,x11446))
% 51.10/50.84 [1145]~E(x11451,x11452)+E(f685(x11453,x11454,x11455,x11456,x11451),f685(x11453,x11454,x11455,x11456,x11452))
% 51.10/50.84 [1146]~E(x11461,x11462)+E(f674(x11461,x11463,x11464,x11465,x11466,x11467),f674(x11462,x11463,x11464,x11465,x11466,x11467))
% 51.10/50.84 [1147]~E(x11471,x11472)+E(f674(x11473,x11471,x11474,x11475,x11476,x11477),f674(x11473,x11472,x11474,x11475,x11476,x11477))
% 51.10/50.84 [1148]~E(x11481,x11482)+E(f674(x11483,x11484,x11481,x11485,x11486,x11487),f674(x11483,x11484,x11482,x11485,x11486,x11487))
% 51.10/50.84 [1149]~E(x11491,x11492)+E(f674(x11493,x11494,x11495,x11491,x11496,x11497),f674(x11493,x11494,x11495,x11492,x11496,x11497))
% 51.10/50.84 [1150]~E(x11501,x11502)+E(f674(x11503,x11504,x11505,x11506,x11501,x11507),f674(x11503,x11504,x11505,x11506,x11502,x11507))
% 51.10/50.84 [1151]~E(x11511,x11512)+E(f674(x11513,x11514,x11515,x11516,x11517,x11511),f674(x11513,x11514,x11515,x11516,x11517,x11512))
% 51.10/50.84 [1152]~E(x11521,x11522)+E(f501(x11521,x11523,x11524,x11525),f501(x11522,x11523,x11524,x11525))
% 51.10/50.84 [1153]~E(x11531,x11532)+E(f501(x11533,x11531,x11534,x11535),f501(x11533,x11532,x11534,x11535))
% 51.10/50.84 [1154]~E(x11541,x11542)+E(f501(x11543,x11544,x11541,x11545),f501(x11543,x11544,x11542,x11545))
% 51.10/50.84 [1155]~E(x11551,x11552)+E(f501(x11553,x11554,x11555,x11551),f501(x11553,x11554,x11555,x11552))
% 51.10/50.84 [1156]~E(x11561,x11562)+E(f517(x11561,x11563,x11564,x11565,x11566),f517(x11562,x11563,x11564,x11565,x11566))
% 51.10/50.84 [1157]~E(x11571,x11572)+E(f517(x11573,x11571,x11574,x11575,x11576),f517(x11573,x11572,x11574,x11575,x11576))
% 51.10/50.84 [1158]~E(x11581,x11582)+E(f517(x11583,x11584,x11581,x11585,x11586),f517(x11583,x11584,x11582,x11585,x11586))
% 51.10/50.84 [1159]~E(x11591,x11592)+E(f517(x11593,x11594,x11595,x11591,x11596),f517(x11593,x11594,x11595,x11592,x11596))
% 51.10/50.84 [1160]~E(x11601,x11602)+E(f517(x11603,x11604,x11605,x11606,x11601),f517(x11603,x11604,x11605,x11606,x11602))
% 51.10/50.84 [1161]~E(x11611,x11612)+E(f314(x11611,x11613,x11614),f314(x11612,x11613,x11614))
% 51.10/50.84 [1162]~E(x11621,x11622)+E(f314(x11623,x11621,x11624),f314(x11623,x11622,x11624))
% 51.10/50.84 [1163]~E(x11631,x11632)+E(f314(x11633,x11634,x11631),f314(x11633,x11634,x11632))
% 51.10/50.84 [1164]~E(x11641,x11642)+E(f567(x11641,x11643,x11644,x11645,x11646,x11647),f567(x11642,x11643,x11644,x11645,x11646,x11647))
% 51.10/50.84 [1165]~E(x11651,x11652)+E(f567(x11653,x11651,x11654,x11655,x11656,x11657),f567(x11653,x11652,x11654,x11655,x11656,x11657))
% 51.10/50.84 [1166]~E(x11661,x11662)+E(f567(x11663,x11664,x11661,x11665,x11666,x11667),f567(x11663,x11664,x11662,x11665,x11666,x11667))
% 51.10/50.84 [1167]~E(x11671,x11672)+E(f567(x11673,x11674,x11675,x11671,x11676,x11677),f567(x11673,x11674,x11675,x11672,x11676,x11677))
% 51.10/50.84 [1168]~E(x11681,x11682)+E(f567(x11683,x11684,x11685,x11686,x11681,x11687),f567(x11683,x11684,x11685,x11686,x11682,x11687))
% 51.10/50.84 [1169]~E(x11691,x11692)+E(f567(x11693,x11694,x11695,x11696,x11697,x11691),f567(x11693,x11694,x11695,x11696,x11697,x11692))
% 51.10/50.84 [1170]~E(x11701,x11702)+E(f444(x11701,x11703,x11704,x11705),f444(x11702,x11703,x11704,x11705))
% 51.10/50.84 [1171]~E(x11711,x11712)+E(f444(x11713,x11711,x11714,x11715),f444(x11713,x11712,x11714,x11715))
% 51.10/50.84 [1172]~E(x11721,x11722)+E(f444(x11723,x11724,x11721,x11725),f444(x11723,x11724,x11722,x11725))
% 51.10/50.84 [1173]~E(x11731,x11732)+E(f444(x11733,x11734,x11735,x11731),f444(x11733,x11734,x11735,x11732))
% 51.10/50.84 [1174]~E(x11741,x11742)+E(f651(x11741,x11743,x11744),f651(x11742,x11743,x11744))
% 51.10/50.84 [1175]~E(x11751,x11752)+E(f651(x11753,x11751,x11754),f651(x11753,x11752,x11754))
% 51.10/50.84 [1176]~E(x11761,x11762)+E(f651(x11763,x11764,x11761),f651(x11763,x11764,x11762))
% 51.10/50.84 [1177]~E(x11771,x11772)+E(f616(x11771,x11773,x11774),f616(x11772,x11773,x11774))
% 51.10/50.84 [1178]~E(x11781,x11782)+E(f616(x11783,x11781,x11784),f616(x11783,x11782,x11784))
% 51.10/50.84 [1179]~E(x11791,x11792)+E(f616(x11793,x11794,x11791),f616(x11793,x11794,x11792))
% 51.10/50.84 [1180]~E(x11801,x11802)+E(f510(x11801,x11803,x11804,x11805,x11806),f510(x11802,x11803,x11804,x11805,x11806))
% 51.10/50.84 [1181]~E(x11811,x11812)+E(f510(x11813,x11811,x11814,x11815,x11816),f510(x11813,x11812,x11814,x11815,x11816))
% 51.10/50.84 [1182]~E(x11821,x11822)+E(f510(x11823,x11824,x11821,x11825,x11826),f510(x11823,x11824,x11822,x11825,x11826))
% 51.10/50.84 [1183]~E(x11831,x11832)+E(f510(x11833,x11834,x11835,x11831,x11836),f510(x11833,x11834,x11835,x11832,x11836))
% 51.10/50.84 [1184]~E(x11841,x11842)+E(f510(x11843,x11844,x11845,x11846,x11841),f510(x11843,x11844,x11845,x11846,x11842))
% 51.10/50.84 [1185]~E(x11851,x11852)+E(f816(x11851,x11853,x11854),f816(x11852,x11853,x11854))
% 51.10/50.84 [1186]~E(x11861,x11862)+E(f816(x11863,x11861,x11864),f816(x11863,x11862,x11864))
% 51.10/50.84 [1187]~E(x11871,x11872)+E(f816(x11873,x11874,x11871),f816(x11873,x11874,x11872))
% 51.10/50.84 [1188]~E(x11881,x11882)+E(f511(x11881,x11883,x11884,x11885,x11886,x11887),f511(x11882,x11883,x11884,x11885,x11886,x11887))
% 51.10/50.84 [1189]~E(x11891,x11892)+E(f511(x11893,x11891,x11894,x11895,x11896,x11897),f511(x11893,x11892,x11894,x11895,x11896,x11897))
% 51.10/50.84 [1190]~E(x11901,x11902)+E(f511(x11903,x11904,x11901,x11905,x11906,x11907),f511(x11903,x11904,x11902,x11905,x11906,x11907))
% 51.10/50.84 [1191]~E(x11911,x11912)+E(f511(x11913,x11914,x11915,x11911,x11916,x11917),f511(x11913,x11914,x11915,x11912,x11916,x11917))
% 51.10/50.84 [1192]~E(x11921,x11922)+E(f511(x11923,x11924,x11925,x11926,x11921,x11927),f511(x11923,x11924,x11925,x11926,x11922,x11927))
% 51.10/50.84 [1193]~E(x11931,x11932)+E(f511(x11933,x11934,x11935,x11936,x11937,x11931),f511(x11933,x11934,x11935,x11936,x11937,x11932))
% 51.10/50.84 [1194]~E(x11941,x11942)+E(f24(x11941,x11943),f24(x11942,x11943))
% 51.10/50.84 [1195]~E(x11951,x11952)+E(f24(x11953,x11951),f24(x11953,x11952))
% 51.10/50.84 [1196]~E(x11961,x11962)+E(f384(x11961,x11963),f384(x11962,x11963))
% 51.10/50.84 [1197]~E(x11971,x11972)+E(f384(x11973,x11971),f384(x11973,x11972))
% 51.10/50.84 [1198]~E(x11981,x11982)+E(f367(x11981,x11983,x11984,x11985,x11986,x11987,x11988,x11989,x119810),f367(x11982,x11983,x11984,x11985,x11986,x11987,x11988,x11989,x119810))
% 51.10/50.84 [1199]~E(x11991,x11992)+E(f367(x11993,x11991,x11994,x11995,x11996,x11997,x11998,x11999,x119910),f367(x11993,x11992,x11994,x11995,x11996,x11997,x11998,x11999,x119910))
% 51.10/50.84 [1200]~E(x12001,x12002)+E(f367(x12003,x12004,x12001,x12005,x12006,x12007,x12008,x12009,x120010),f367(x12003,x12004,x12002,x12005,x12006,x12007,x12008,x12009,x120010))
% 51.10/50.84 [1201]~E(x12011,x12012)+E(f367(x12013,x12014,x12015,x12011,x12016,x12017,x12018,x12019,x120110),f367(x12013,x12014,x12015,x12012,x12016,x12017,x12018,x12019,x120110))
% 51.10/50.84 [1202]~E(x12021,x12022)+E(f367(x12023,x12024,x12025,x12026,x12021,x12027,x12028,x12029,x120210),f367(x12023,x12024,x12025,x12026,x12022,x12027,x12028,x12029,x120210))
% 51.10/50.84 [1203]~E(x12031,x12032)+E(f367(x12033,x12034,x12035,x12036,x12037,x12031,x12038,x12039,x120310),f367(x12033,x12034,x12035,x12036,x12037,x12032,x12038,x12039,x120310))
% 51.10/50.84 [1204]~E(x12041,x12042)+E(f367(x12043,x12044,x12045,x12046,x12047,x12048,x12041,x12049,x120410),f367(x12043,x12044,x12045,x12046,x12047,x12048,x12042,x12049,x120410))
% 51.10/50.84 [1205]~E(x12051,x12052)+E(f367(x12053,x12054,x12055,x12056,x12057,x12058,x12059,x12051,x120510),f367(x12053,x12054,x12055,x12056,x12057,x12058,x12059,x12052,x120510))
% 51.10/50.84 [1206]~E(x12061,x12062)+E(f367(x12063,x12064,x12065,x12066,x12067,x12068,x12069,x120610,x12061),f367(x12063,x12064,x12065,x12066,x12067,x12068,x12069,x120610,x12062))
% 51.10/50.84 [1207]~E(x12071,x12072)+E(f383(x12071,x12073),f383(x12072,x12073))
% 51.10/50.84 [1208]~E(x12081,x12082)+E(f383(x12083,x12081),f383(x12083,x12082))
% 51.10/50.84 [1209]~E(x12091,x12092)+E(f442(x12091,x12093),f442(x12092,x12093))
% 51.10/50.84 [1210]~E(x12101,x12102)+E(f442(x12103,x12101),f442(x12103,x12102))
% 51.10/50.84 [1211]~E(x12111,x12112)+E(f154(x12111,x12113),f154(x12112,x12113))
% 51.10/50.84 [1212]~E(x12121,x12122)+E(f154(x12123,x12121),f154(x12123,x12122))
% 51.10/50.84 [1213]~E(x12131,x12132)+E(f644(x12131,x12133,x12134,x12135,x12136,x12137,x12138),f644(x12132,x12133,x12134,x12135,x12136,x12137,x12138))
% 51.10/50.84 [1214]~E(x12141,x12142)+E(f644(x12143,x12141,x12144,x12145,x12146,x12147,x12148),f644(x12143,x12142,x12144,x12145,x12146,x12147,x12148))
% 51.10/50.84 [1215]~E(x12151,x12152)+E(f644(x12153,x12154,x12151,x12155,x12156,x12157,x12158),f644(x12153,x12154,x12152,x12155,x12156,x12157,x12158))
% 51.10/50.84 [1216]~E(x12161,x12162)+E(f644(x12163,x12164,x12165,x12161,x12166,x12167,x12168),f644(x12163,x12164,x12165,x12162,x12166,x12167,x12168))
% 51.10/50.84 [1217]~E(x12171,x12172)+E(f644(x12173,x12174,x12175,x12176,x12171,x12177,x12178),f644(x12173,x12174,x12175,x12176,x12172,x12177,x12178))
% 51.10/50.84 [1218]~E(x12181,x12182)+E(f644(x12183,x12184,x12185,x12186,x12187,x12181,x12188),f644(x12183,x12184,x12185,x12186,x12187,x12182,x12188))
% 51.10/50.84 [1219]~E(x12191,x12192)+E(f644(x12193,x12194,x12195,x12196,x12197,x12198,x12191),f644(x12193,x12194,x12195,x12196,x12197,x12198,x12192))
% 51.10/50.84 [1220]~E(x12201,x12202)+E(f613(x12201,x12203,x12204,x12205,x12206,x12207,x12208,x12209),f613(x12202,x12203,x12204,x12205,x12206,x12207,x12208,x12209))
% 51.10/50.84 [1221]~E(x12211,x12212)+E(f613(x12213,x12211,x12214,x12215,x12216,x12217,x12218,x12219),f613(x12213,x12212,x12214,x12215,x12216,x12217,x12218,x12219))
% 51.10/50.84 [1222]~E(x12221,x12222)+E(f613(x12223,x12224,x12221,x12225,x12226,x12227,x12228,x12229),f613(x12223,x12224,x12222,x12225,x12226,x12227,x12228,x12229))
% 51.10/50.84 [1223]~E(x12231,x12232)+E(f613(x12233,x12234,x12235,x12231,x12236,x12237,x12238,x12239),f613(x12233,x12234,x12235,x12232,x12236,x12237,x12238,x12239))
% 51.10/50.84 [1224]~E(x12241,x12242)+E(f613(x12243,x12244,x12245,x12246,x12241,x12247,x12248,x12249),f613(x12243,x12244,x12245,x12246,x12242,x12247,x12248,x12249))
% 51.10/50.84 [1225]~E(x12251,x12252)+E(f613(x12253,x12254,x12255,x12256,x12257,x12251,x12258,x12259),f613(x12253,x12254,x12255,x12256,x12257,x12252,x12258,x12259))
% 51.10/50.84 [1226]~E(x12261,x12262)+E(f613(x12263,x12264,x12265,x12266,x12267,x12268,x12261,x12269),f613(x12263,x12264,x12265,x12266,x12267,x12268,x12262,x12269))
% 51.10/50.84 [1227]~E(x12271,x12272)+E(f613(x12273,x12274,x12275,x12276,x12277,x12278,x12279,x12271),f613(x12273,x12274,x12275,x12276,x12277,x12278,x12279,x12272))
% 51.10/50.84 [1228]~E(x12281,x12282)+E(f251(x12281,x12283,x12284),f251(x12282,x12283,x12284))
% 51.10/50.84 [1229]~E(x12291,x12292)+E(f251(x12293,x12291,x12294),f251(x12293,x12292,x12294))
% 51.10/50.84 [1230]~E(x12301,x12302)+E(f251(x12303,x12304,x12301),f251(x12303,x12304,x12302))
% 51.10/50.84 [1231]~E(x12311,x12312)+E(f148(x12311,x12313,x12314),f148(x12312,x12313,x12314))
% 51.10/50.84 [1232]~E(x12321,x12322)+E(f148(x12323,x12321,x12324),f148(x12323,x12322,x12324))
% 51.10/50.84 [1233]~E(x12331,x12332)+E(f148(x12333,x12334,x12331),f148(x12333,x12334,x12332))
% 51.10/50.84 [1234]~E(x12341,x12342)+E(f500(x12341,x12343,x12344,x12345),f500(x12342,x12343,x12344,x12345))
% 51.10/50.84 [1235]~E(x12351,x12352)+E(f500(x12353,x12351,x12354,x12355),f500(x12353,x12352,x12354,x12355))
% 51.10/50.84 [1236]~E(x12361,x12362)+E(f500(x12363,x12364,x12361,x12365),f500(x12363,x12364,x12362,x12365))
% 51.10/50.84 [1237]~E(x12371,x12372)+E(f500(x12373,x12374,x12375,x12371),f500(x12373,x12374,x12375,x12372))
% 51.10/50.84 [1238]~E(x12381,x12382)+E(f596(x12381,x12383,x12384,x12385),f596(x12382,x12383,x12384,x12385))
% 51.10/50.84 [1239]~E(x12391,x12392)+E(f596(x12393,x12391,x12394,x12395),f596(x12393,x12392,x12394,x12395))
% 51.10/50.84 [1240]~E(x12401,x12402)+E(f596(x12403,x12404,x12401,x12405),f596(x12403,x12404,x12402,x12405))
% 51.10/50.84 [1241]~E(x12411,x12412)+E(f596(x12413,x12414,x12415,x12411),f596(x12413,x12414,x12415,x12412))
% 51.10/50.84 [1242]~E(x12421,x12422)+E(f623(x12421,x12423,x12424),f623(x12422,x12423,x12424))
% 51.10/50.84 [1243]~E(x12431,x12432)+E(f623(x12433,x12431,x12434),f623(x12433,x12432,x12434))
% 51.10/50.84 [1244]~E(x12441,x12442)+E(f623(x12443,x12444,x12441),f623(x12443,x12444,x12442))
% 51.10/50.84 [1245]~E(x12451,x12452)+E(f499(x12451,x12453,x12454,x12455),f499(x12452,x12453,x12454,x12455))
% 51.10/50.84 [1246]~E(x12461,x12462)+E(f499(x12463,x12461,x12464,x12465),f499(x12463,x12462,x12464,x12465))
% 51.10/50.84 [1247]~E(x12471,x12472)+E(f499(x12473,x12474,x12471,x12475),f499(x12473,x12474,x12472,x12475))
% 51.10/50.84 [1248]~E(x12481,x12482)+E(f499(x12483,x12484,x12485,x12481),f499(x12483,x12484,x12485,x12482))
% 51.10/50.84 [1249]~E(x12491,x12492)+E(f690(x12491,x12493,x12494,x12495),f690(x12492,x12493,x12494,x12495))
% 51.10/50.84 [1250]~E(x12501,x12502)+E(f690(x12503,x12501,x12504,x12505),f690(x12503,x12502,x12504,x12505))
% 51.10/50.84 [1251]~E(x12511,x12512)+E(f690(x12513,x12514,x12511,x12515),f690(x12513,x12514,x12512,x12515))
% 51.10/50.84 [1252]~E(x12521,x12522)+E(f690(x12523,x12524,x12525,x12521),f690(x12523,x12524,x12525,x12522))
% 51.10/50.84 [1253]~E(x12531,x12532)+E(f652(x12531,x12533,x12534,x12535,x12536),f652(x12532,x12533,x12534,x12535,x12536))
% 51.10/50.84 [1254]~E(x12541,x12542)+E(f652(x12543,x12541,x12544,x12545,x12546),f652(x12543,x12542,x12544,x12545,x12546))
% 51.10/50.84 [1255]~E(x12551,x12552)+E(f652(x12553,x12554,x12551,x12555,x12556),f652(x12553,x12554,x12552,x12555,x12556))
% 51.10/50.84 [1256]~E(x12561,x12562)+E(f652(x12563,x12564,x12565,x12561,x12566),f652(x12563,x12564,x12565,x12562,x12566))
% 51.10/50.84 [1257]~E(x12571,x12572)+E(f652(x12573,x12574,x12575,x12576,x12571),f652(x12573,x12574,x12575,x12576,x12572))
% 51.10/50.84 [1258]~E(x12581,x12582)+E(f456(x12581,x12583,x12584,x12585),f456(x12582,x12583,x12584,x12585))
% 51.10/50.84 [1259]~E(x12591,x12592)+E(f456(x12593,x12591,x12594,x12595),f456(x12593,x12592,x12594,x12595))
% 51.10/50.84 [1260]~E(x12601,x12602)+E(f456(x12603,x12604,x12601,x12605),f456(x12603,x12604,x12602,x12605))
% 51.10/50.84 [1261]~E(x12611,x12612)+E(f456(x12613,x12614,x12615,x12611),f456(x12613,x12614,x12615,x12612))
% 51.10/50.84 [1262]~E(x12621,x12622)+E(f425(x12621,x12623,x12624),f425(x12622,x12623,x12624))
% 51.10/50.84 [1263]~E(x12631,x12632)+E(f425(x12633,x12631,x12634),f425(x12633,x12632,x12634))
% 51.10/50.84 [1264]~E(x12641,x12642)+E(f425(x12643,x12644,x12641),f425(x12643,x12644,x12642))
% 51.10/50.84 [1265]~E(x12651,x12652)+E(f759(x12651,x12653,x12654),f759(x12652,x12653,x12654))
% 51.10/50.84 [1266]~E(x12661,x12662)+E(f759(x12663,x12661,x12664),f759(x12663,x12662,x12664))
% 51.10/50.84 [1267]~E(x12671,x12672)+E(f759(x12673,x12674,x12671),f759(x12673,x12674,x12672))
% 51.10/50.84 [1268]~E(x12681,x12682)+E(f288(x12681,x12683),f288(x12682,x12683))
% 51.10/50.84 [1269]~E(x12691,x12692)+E(f288(x12693,x12691),f288(x12693,x12692))
% 51.10/50.84 [1270]~E(x12701,x12702)+E(f454(x12701,x12703,x12704,x12705),f454(x12702,x12703,x12704,x12705))
% 51.10/50.84 [1271]~E(x12711,x12712)+E(f454(x12713,x12711,x12714,x12715),f454(x12713,x12712,x12714,x12715))
% 51.10/50.84 [1272]~E(x12721,x12722)+E(f454(x12723,x12724,x12721,x12725),f454(x12723,x12724,x12722,x12725))
% 51.10/50.84 [1273]~E(x12731,x12732)+E(f454(x12733,x12734,x12735,x12731),f454(x12733,x12734,x12735,x12732))
% 51.10/50.84 [1274]~E(x12741,x12742)+E(f378(x12741,x12743),f378(x12742,x12743))
% 51.10/50.84 [1275]~E(x12751,x12752)+E(f378(x12753,x12751),f378(x12753,x12752))
% 51.10/50.84 [1276]~E(x12761,x12762)+E(f211(x12761,x12763,x12764,x12765),f211(x12762,x12763,x12764,x12765))
% 51.10/50.84 [1277]~E(x12771,x12772)+E(f211(x12773,x12771,x12774,x12775),f211(x12773,x12772,x12774,x12775))
% 51.10/50.84 [1278]~E(x12781,x12782)+E(f211(x12783,x12784,x12781,x12785),f211(x12783,x12784,x12782,x12785))
% 51.10/50.84 [1279]~E(x12791,x12792)+E(f211(x12793,x12794,x12795,x12791),f211(x12793,x12794,x12795,x12792))
% 51.10/50.84 [1280]~E(x12801,x12802)+E(f300(x12801,x12803,x12804,x12805,x12806),f300(x12802,x12803,x12804,x12805,x12806))
% 51.10/50.84 [1281]~E(x12811,x12812)+E(f300(x12813,x12811,x12814,x12815,x12816),f300(x12813,x12812,x12814,x12815,x12816))
% 51.10/50.84 [1282]~E(x12821,x12822)+E(f300(x12823,x12824,x12821,x12825,x12826),f300(x12823,x12824,x12822,x12825,x12826))
% 51.10/50.84 [1283]~E(x12831,x12832)+E(f300(x12833,x12834,x12835,x12831,x12836),f300(x12833,x12834,x12835,x12832,x12836))
% 51.10/50.84 [1284]~E(x12841,x12842)+E(f300(x12843,x12844,x12845,x12846,x12841),f300(x12843,x12844,x12845,x12846,x12842))
% 51.10/50.84 [1285]~E(x12851,x12852)+E(f179(x12851,x12853,x12854),f179(x12852,x12853,x12854))
% 51.10/50.84 [1286]~E(x12861,x12862)+E(f179(x12863,x12861,x12864),f179(x12863,x12862,x12864))
% 51.10/50.84 [1287]~E(x12871,x12872)+E(f179(x12873,x12874,x12871),f179(x12873,x12874,x12872))
% 51.10/50.84 [1288]~E(x12881,x12882)+E(f485(x12881,x12883,x12884),f485(x12882,x12883,x12884))
% 51.10/50.84 [1289]~E(x12891,x12892)+E(f485(x12893,x12891,x12894),f485(x12893,x12892,x12894))
% 51.10/50.84 [1290]~E(x12901,x12902)+E(f485(x12903,x12904,x12901),f485(x12903,x12904,x12902))
% 51.10/50.84 [1291]~E(x12911,x12912)+E(f481(x12911,x12913),f481(x12912,x12913))
% 51.10/50.84 [1292]~E(x12921,x12922)+E(f481(x12923,x12921),f481(x12923,x12922))
% 51.10/50.84 [1293]~E(x12931,x12932)+E(f617(x12931,x12933),f617(x12932,x12933))
% 51.10/50.84 [1294]~E(x12941,x12942)+E(f617(x12943,x12941),f617(x12943,x12942))
% 51.10/50.84 [1295]~E(x12951,x12952)+E(f186(x12951,x12953,x12954,x12955),f186(x12952,x12953,x12954,x12955))
% 51.10/50.84 [1296]~E(x12961,x12962)+E(f186(x12963,x12961,x12964,x12965),f186(x12963,x12962,x12964,x12965))
% 51.10/50.84 [1297]~E(x12971,x12972)+E(f186(x12973,x12974,x12971,x12975),f186(x12973,x12974,x12972,x12975))
% 51.10/50.84 [1298]~E(x12981,x12982)+E(f186(x12983,x12984,x12985,x12981),f186(x12983,x12984,x12985,x12982))
% 51.10/50.84 [1299]~E(x12991,x12992)+E(f667(x12991,x12993,x12994),f667(x12992,x12993,x12994))
% 51.10/50.84 [1300]~E(x13001,x13002)+E(f667(x13003,x13001,x13004),f667(x13003,x13002,x13004))
% 51.10/50.84 [1301]~E(x13011,x13012)+E(f667(x13013,x13014,x13011),f667(x13013,x13014,x13012))
% 51.10/50.84 [1302]~E(x13021,x13022)+E(f680(x13021,x13023,x13024,x13025),f680(x13022,x13023,x13024,x13025))
% 51.10/50.84 [1303]~E(x13031,x13032)+E(f680(x13033,x13031,x13034,x13035),f680(x13033,x13032,x13034,x13035))
% 51.10/50.84 [1304]~E(x13041,x13042)+E(f680(x13043,x13044,x13041,x13045),f680(x13043,x13044,x13042,x13045))
% 51.10/50.84 [1305]~E(x13051,x13052)+E(f680(x13053,x13054,x13055,x13051),f680(x13053,x13054,x13055,x13052))
% 51.10/50.84 [1306]~E(x13061,x13062)+E(f574(x13061,x13063),f574(x13062,x13063))
% 51.10/50.84 [1307]~E(x13071,x13072)+E(f574(x13073,x13071),f574(x13073,x13072))
% 51.10/50.84 [1308]~E(x13081,x13082)+E(f533(x13081,x13083,x13084,x13085,x13086),f533(x13082,x13083,x13084,x13085,x13086))
% 51.10/50.84 [1309]~E(x13091,x13092)+E(f533(x13093,x13091,x13094,x13095,x13096),f533(x13093,x13092,x13094,x13095,x13096))
% 51.10/50.84 [1310]~E(x13101,x13102)+E(f533(x13103,x13104,x13101,x13105,x13106),f533(x13103,x13104,x13102,x13105,x13106))
% 51.10/50.84 [1311]~E(x13111,x13112)+E(f533(x13113,x13114,x13115,x13111,x13116),f533(x13113,x13114,x13115,x13112,x13116))
% 51.10/50.84 [1312]~E(x13121,x13122)+E(f533(x13123,x13124,x13125,x13126,x13121),f533(x13123,x13124,x13125,x13126,x13122))
% 51.10/50.84 [1313]~E(x13131,x13132)+E(f809(x13131,x13133,x13134),f809(x13132,x13133,x13134))
% 51.10/50.84 [1314]~E(x13141,x13142)+E(f809(x13143,x13141,x13144),f809(x13143,x13142,x13144))
% 51.10/50.84 [1315]~E(x13151,x13152)+E(f809(x13153,x13154,x13151),f809(x13153,x13154,x13152))
% 51.10/50.84 [1316]~E(x13161,x13162)+E(f669(x13161,x13163,x13164),f669(x13162,x13163,x13164))
% 51.10/50.84 [1317]~E(x13171,x13172)+E(f669(x13173,x13171,x13174),f669(x13173,x13172,x13174))
% 51.10/50.84 [1318]~E(x13181,x13182)+E(f669(x13183,x13184,x13181),f669(x13183,x13184,x13182))
% 51.10/50.84 [1319]~E(x13191,x13192)+E(f709(x13191,x13193,x13194,x13195),f709(x13192,x13193,x13194,x13195))
% 51.10/50.84 [1320]~E(x13201,x13202)+E(f709(x13203,x13201,x13204,x13205),f709(x13203,x13202,x13204,x13205))
% 51.10/50.84 [1321]~E(x13211,x13212)+E(f709(x13213,x13214,x13211,x13215),f709(x13213,x13214,x13212,x13215))
% 51.10/50.84 [1322]~E(x13221,x13222)+E(f709(x13223,x13224,x13225,x13221),f709(x13223,x13224,x13225,x13222))
% 51.10/50.84 [1323]~E(x13231,x13232)+E(f497(x13231,x13233,x13234,x13235,x13236),f497(x13232,x13233,x13234,x13235,x13236))
% 51.10/50.84 [1324]~E(x13241,x13242)+E(f497(x13243,x13241,x13244,x13245,x13246),f497(x13243,x13242,x13244,x13245,x13246))
% 51.10/50.84 [1325]~E(x13251,x13252)+E(f497(x13253,x13254,x13251,x13255,x13256),f497(x13253,x13254,x13252,x13255,x13256))
% 51.10/50.84 [1326]~E(x13261,x13262)+E(f497(x13263,x13264,x13265,x13261,x13266),f497(x13263,x13264,x13265,x13262,x13266))
% 51.10/50.84 [1327]~E(x13271,x13272)+E(f497(x13273,x13274,x13275,x13276,x13271),f497(x13273,x13274,x13275,x13276,x13272))
% 51.10/50.84 [1328]~E(x13281,x13282)+E(f210(x13281),f210(x13282))
% 51.10/50.84 [1329]~E(x13291,x13292)+E(f534(x13291,x13293,x13294,x13295,x13296),f534(x13292,x13293,x13294,x13295,x13296))
% 51.10/50.84 [1330]~E(x13301,x13302)+E(f534(x13303,x13301,x13304,x13305,x13306),f534(x13303,x13302,x13304,x13305,x13306))
% 51.10/50.84 [1331]~E(x13311,x13312)+E(f534(x13313,x13314,x13311,x13315,x13316),f534(x13313,x13314,x13312,x13315,x13316))
% 51.10/50.84 [1332]~E(x13321,x13322)+E(f534(x13323,x13324,x13325,x13321,x13326),f534(x13323,x13324,x13325,x13322,x13326))
% 51.10/50.84 [1333]~E(x13331,x13332)+E(f534(x13333,x13334,x13335,x13336,x13331),f534(x13333,x13334,x13335,x13336,x13332))
% 51.10/50.84 [1334]~E(x13341,x13342)+E(f417(x13341,x13343,x13344),f417(x13342,x13343,x13344))
% 51.10/50.84 [1335]~E(x13351,x13352)+E(f417(x13353,x13351,x13354),f417(x13353,x13352,x13354))
% 51.10/50.84 [1336]~E(x13361,x13362)+E(f417(x13363,x13364,x13361),f417(x13363,x13364,x13362))
% 51.10/50.84 [1337]~E(x13371,x13372)+E(f474(x13371,x13373),f474(x13372,x13373))
% 51.10/50.84 [1338]~E(x13381,x13382)+E(f474(x13383,x13381),f474(x13383,x13382))
% 51.10/50.84 [1339]~E(x13391,x13392)+E(f852(x13391,x13393),f852(x13392,x13393))
% 51.10/50.84 [1340]~E(x13401,x13402)+E(f852(x13403,x13401),f852(x13403,x13402))
% 51.10/50.84 [1341]~E(x13411,x13412)+E(f587(x13411,x13413,x13414,x13415),f587(x13412,x13413,x13414,x13415))
% 51.10/50.84 [1342]~E(x13421,x13422)+E(f587(x13423,x13421,x13424,x13425),f587(x13423,x13422,x13424,x13425))
% 51.10/50.84 [1343]~E(x13431,x13432)+E(f587(x13433,x13434,x13431,x13435),f587(x13433,x13434,x13432,x13435))
% 51.10/50.84 [1344]~E(x13441,x13442)+E(f587(x13443,x13444,x13445,x13441),f587(x13443,x13444,x13445,x13442))
% 51.10/50.84 [1345]~E(x13451,x13452)+E(f512(x13451,x13453,x13454,x13455,x13456),f512(x13452,x13453,x13454,x13455,x13456))
% 51.10/50.84 [1346]~E(x13461,x13462)+E(f512(x13463,x13461,x13464,x13465,x13466),f512(x13463,x13462,x13464,x13465,x13466))
% 51.10/50.84 [1347]~E(x13471,x13472)+E(f512(x13473,x13474,x13471,x13475,x13476),f512(x13473,x13474,x13472,x13475,x13476))
% 51.10/50.84 [1348]~E(x13481,x13482)+E(f512(x13483,x13484,x13485,x13481,x13486),f512(x13483,x13484,x13485,x13482,x13486))
% 51.10/50.84 [1349]~E(x13491,x13492)+E(f512(x13493,x13494,x13495,x13496,x13491),f512(x13493,x13494,x13495,x13496,x13492))
% 51.10/50.84 [1350]~E(x13501,x13502)+E(f446(x13501,x13503,x13504,x13505),f446(x13502,x13503,x13504,x13505))
% 51.10/50.84 [1351]~E(x13511,x13512)+E(f446(x13513,x13511,x13514,x13515),f446(x13513,x13512,x13514,x13515))
% 51.10/50.84 [1352]~E(x13521,x13522)+E(f446(x13523,x13524,x13521,x13525),f446(x13523,x13524,x13522,x13525))
% 51.10/50.84 [1353]~E(x13531,x13532)+E(f446(x13533,x13534,x13535,x13531),f446(x13533,x13534,x13535,x13532))
% 51.10/50.84 [1354]~E(x13541,x13542)+E(f480(x13541),f480(x13542))
% 51.10/50.84 [1355]~E(x13551,x13552)+E(f689(x13551,x13553,x13554,x13555),f689(x13552,x13553,x13554,x13555))
% 51.10/50.84 [1356]~E(x13561,x13562)+E(f689(x13563,x13561,x13564,x13565),f689(x13563,x13562,x13564,x13565))
% 51.10/50.84 [1357]~E(x13571,x13572)+E(f689(x13573,x13574,x13571,x13575),f689(x13573,x13574,x13572,x13575))
% 51.10/50.84 [1358]~E(x13581,x13582)+E(f689(x13583,x13584,x13585,x13581),f689(x13583,x13584,x13585,x13582))
% 51.10/50.84 [1359]~E(x13591,x13592)+E(f465(x13591,x13593,x13594,x13595),f465(x13592,x13593,x13594,x13595))
% 51.10/50.84 [1360]~E(x13601,x13602)+E(f465(x13603,x13601,x13604,x13605),f465(x13603,x13602,x13604,x13605))
% 51.10/50.84 [1361]~E(x13611,x13612)+E(f465(x13613,x13614,x13611,x13615),f465(x13613,x13614,x13612,x13615))
% 51.10/50.84 [1362]~E(x13621,x13622)+E(f465(x13623,x13624,x13625,x13621),f465(x13623,x13624,x13625,x13622))
% 51.10/50.84 [1363]~E(x13631,x13632)+E(f326(x13631,x13633,x13634),f326(x13632,x13633,x13634))
% 51.10/50.84 [1364]~E(x13641,x13642)+E(f326(x13643,x13641,x13644),f326(x13643,x13642,x13644))
% 51.10/50.84 [1365]~E(x13651,x13652)+E(f326(x13653,x13654,x13651),f326(x13653,x13654,x13652))
% 51.10/50.84 [1366]~E(x13661,x13662)+E(f675(x13661,x13663,x13664,x13665,x13666,x13667,x13668),f675(x13662,x13663,x13664,x13665,x13666,x13667,x13668))
% 51.10/50.84 [1367]~E(x13671,x13672)+E(f675(x13673,x13671,x13674,x13675,x13676,x13677,x13678),f675(x13673,x13672,x13674,x13675,x13676,x13677,x13678))
% 51.10/50.84 [1368]~E(x13681,x13682)+E(f675(x13683,x13684,x13681,x13685,x13686,x13687,x13688),f675(x13683,x13684,x13682,x13685,x13686,x13687,x13688))
% 51.10/50.84 [1369]~E(x13691,x13692)+E(f675(x13693,x13694,x13695,x13691,x13696,x13697,x13698),f675(x13693,x13694,x13695,x13692,x13696,x13697,x13698))
% 51.10/50.84 [1370]~E(x13701,x13702)+E(f675(x13703,x13704,x13705,x13706,x13701,x13707,x13708),f675(x13703,x13704,x13705,x13706,x13702,x13707,x13708))
% 51.10/50.84 [1371]~E(x13711,x13712)+E(f675(x13713,x13714,x13715,x13716,x13717,x13711,x13718),f675(x13713,x13714,x13715,x13716,x13717,x13712,x13718))
% 51.10/50.84 [1372]~E(x13721,x13722)+E(f675(x13723,x13724,x13725,x13726,x13727,x13728,x13721),f675(x13723,x13724,x13725,x13726,x13727,x13728,x13722))
% 51.10/50.84 [1373]~E(x13731,x13732)+E(f257(x13731,x13733,x13734,x13735),f257(x13732,x13733,x13734,x13735))
% 51.10/50.84 [1374]~E(x13741,x13742)+E(f257(x13743,x13741,x13744,x13745),f257(x13743,x13742,x13744,x13745))
% 51.10/50.84 [1375]~E(x13751,x13752)+E(f257(x13753,x13754,x13751,x13755),f257(x13753,x13754,x13752,x13755))
% 51.10/50.84 [1376]~E(x13761,x13762)+E(f257(x13763,x13764,x13765,x13761),f257(x13763,x13764,x13765,x13762))
% 51.10/50.84 [1377]~E(x13771,x13772)+E(f556(x13771,x13773,x13774,x13775,x13776,x13777,x13778,x13779),f556(x13772,x13773,x13774,x13775,x13776,x13777,x13778,x13779))
% 51.10/50.84 [1378]~E(x13781,x13782)+E(f556(x13783,x13781,x13784,x13785,x13786,x13787,x13788,x13789),f556(x13783,x13782,x13784,x13785,x13786,x13787,x13788,x13789))
% 51.10/50.84 [1379]~E(x13791,x13792)+E(f556(x13793,x13794,x13791,x13795,x13796,x13797,x13798,x13799),f556(x13793,x13794,x13792,x13795,x13796,x13797,x13798,x13799))
% 51.10/50.84 [1380]~E(x13801,x13802)+E(f556(x13803,x13804,x13805,x13801,x13806,x13807,x13808,x13809),f556(x13803,x13804,x13805,x13802,x13806,x13807,x13808,x13809))
% 51.10/50.84 [1381]~E(x13811,x13812)+E(f556(x13813,x13814,x13815,x13816,x13811,x13817,x13818,x13819),f556(x13813,x13814,x13815,x13816,x13812,x13817,x13818,x13819))
% 51.10/50.84 [1382]~E(x13821,x13822)+E(f556(x13823,x13824,x13825,x13826,x13827,x13821,x13828,x13829),f556(x13823,x13824,x13825,x13826,x13827,x13822,x13828,x13829))
% 51.10/50.84 [1383]~E(x13831,x13832)+E(f556(x13833,x13834,x13835,x13836,x13837,x13838,x13831,x13839),f556(x13833,x13834,x13835,x13836,x13837,x13838,x13832,x13839))
% 51.10/50.84 [1384]~E(x13841,x13842)+E(f556(x13843,x13844,x13845,x13846,x13847,x13848,x13849,x13841),f556(x13843,x13844,x13845,x13846,x13847,x13848,x13849,x13842))
% 51.10/50.84 [1385]~E(x13851,x13852)+E(f697(x13851,x13853),f697(x13852,x13853))
% 51.10/50.84 [1386]~E(x13861,x13862)+E(f697(x13863,x13861),f697(x13863,x13862))
% 51.10/50.84 [1387]~E(x13871,x13872)+E(f54(x13871),f54(x13872))
% 51.10/50.84 [1388]~E(x13881,x13882)+E(f21(x13881,x13883,x13884,x13885),f21(x13882,x13883,x13884,x13885))
% 51.10/50.84 [1389]~E(x13891,x13892)+E(f21(x13893,x13891,x13894,x13895),f21(x13893,x13892,x13894,x13895))
% 51.10/50.84 [1390]~E(x13901,x13902)+E(f21(x13903,x13904,x13901,x13905),f21(x13903,x13904,x13902,x13905))
% 51.10/50.84 [1391]~E(x13911,x13912)+E(f21(x13913,x13914,x13915,x13911),f21(x13913,x13914,x13915,x13912))
% 51.10/50.84 [1392]~E(x13921,x13922)+E(f634(x13921,x13923,x13924,x13925,x13926),f634(x13922,x13923,x13924,x13925,x13926))
% 51.10/50.84 [1393]~E(x13931,x13932)+E(f634(x13933,x13931,x13934,x13935,x13936),f634(x13933,x13932,x13934,x13935,x13936))
% 51.10/50.84 [1394]~E(x13941,x13942)+E(f634(x13943,x13944,x13941,x13945,x13946),f634(x13943,x13944,x13942,x13945,x13946))
% 51.10/50.84 [1395]~E(x13951,x13952)+E(f634(x13953,x13954,x13955,x13951,x13956),f634(x13953,x13954,x13955,x13952,x13956))
% 51.10/50.84 [1396]~E(x13961,x13962)+E(f634(x13963,x13964,x13965,x13966,x13961),f634(x13963,x13964,x13965,x13966,x13962))
% 51.10/50.84 [1397]~E(x13971,x13972)+E(f199(x13971,x13973,x13974,x13975),f199(x13972,x13973,x13974,x13975))
% 51.10/50.84 [1398]~E(x13981,x13982)+E(f199(x13983,x13981,x13984,x13985),f199(x13983,x13982,x13984,x13985))
% 51.10/50.84 [1399]~E(x13991,x13992)+E(f199(x13993,x13994,x13991,x13995),f199(x13993,x13994,x13992,x13995))
% 51.10/50.84 [1400]~E(x14001,x14002)+E(f199(x14003,x14004,x14005,x14001),f199(x14003,x14004,x14005,x14002))
% 51.10/50.84 [1401]~E(x14011,x14012)+E(f748(x14011,x14013,x14014),f748(x14012,x14013,x14014))
% 51.10/50.84 [1402]~E(x14021,x14022)+E(f748(x14023,x14021,x14024),f748(x14023,x14022,x14024))
% 51.10/50.84 [1403]~E(x14031,x14032)+E(f748(x14033,x14034,x14031),f748(x14033,x14034,x14032))
% 51.10/50.84 [1404]~E(x14041,x14042)+E(f81(x14041,x14043),f81(x14042,x14043))
% 51.10/50.84 [1405]~E(x14051,x14052)+E(f81(x14053,x14051),f81(x14053,x14052))
% 51.10/50.84 [1406]~E(x14061,x14062)+E(f553(x14061,x14063,x14064,x14065,x14066),f553(x14062,x14063,x14064,x14065,x14066))
% 51.10/50.84 [1407]~E(x14071,x14072)+E(f553(x14073,x14071,x14074,x14075,x14076),f553(x14073,x14072,x14074,x14075,x14076))
% 51.10/50.84 [1408]~E(x14081,x14082)+E(f553(x14083,x14084,x14081,x14085,x14086),f553(x14083,x14084,x14082,x14085,x14086))
% 51.10/50.84 [1409]~E(x14091,x14092)+E(f553(x14093,x14094,x14095,x14091,x14096),f553(x14093,x14094,x14095,x14092,x14096))
% 51.10/50.84 [1410]~E(x14101,x14102)+E(f553(x14103,x14104,x14105,x14106,x14101),f553(x14103,x14104,x14105,x14106,x14102))
% 51.10/50.84 [1411]~E(x14111,x14112)+E(f460(x14111,x14113,x14114),f460(x14112,x14113,x14114))
% 51.10/50.84 [1412]~E(x14121,x14122)+E(f460(x14123,x14121,x14124),f460(x14123,x14122,x14124))
% 51.10/50.84 [1413]~E(x14131,x14132)+E(f460(x14133,x14134,x14131),f460(x14133,x14134,x14132))
% 51.10/50.84 [1414]~E(x14141,x14142)+E(f461(x14141,x14143,x14144,x14145),f461(x14142,x14143,x14144,x14145))
% 51.10/50.84 [1415]~E(x14151,x14152)+E(f461(x14153,x14151,x14154,x14155),f461(x14153,x14152,x14154,x14155))
% 51.10/50.84 [1416]~E(x14161,x14162)+E(f461(x14163,x14164,x14161,x14165),f461(x14163,x14164,x14162,x14165))
% 51.10/50.84 [1417]~E(x14171,x14172)+E(f461(x14173,x14174,x14175,x14171),f461(x14173,x14174,x14175,x14172))
% 51.10/50.84 [1418]~E(x14181,x14182)+E(f124(x14181,x14183,x14184,x14185),f124(x14182,x14183,x14184,x14185))
% 51.10/50.84 [1419]~E(x14191,x14192)+E(f124(x14193,x14191,x14194,x14195),f124(x14193,x14192,x14194,x14195))
% 51.10/50.84 [1420]~E(x14201,x14202)+E(f124(x14203,x14204,x14201,x14205),f124(x14203,x14204,x14202,x14205))
% 51.10/50.84 [1421]~E(x14211,x14212)+E(f124(x14213,x14214,x14215,x14211),f124(x14213,x14214,x14215,x14212))
% 51.10/50.84 [1422]~E(x14221,x14222)+E(f293(x14221,x14223),f293(x14222,x14223))
% 51.10/50.84 [1423]~E(x14231,x14232)+E(f293(x14233,x14231),f293(x14233,x14232))
% 51.10/50.84 [1424]~E(x14241,x14242)+E(f716(x14241,x14243,x14244,x14245,x14246),f716(x14242,x14243,x14244,x14245,x14246))
% 51.10/50.84 [1425]~E(x14251,x14252)+E(f716(x14253,x14251,x14254,x14255,x14256),f716(x14253,x14252,x14254,x14255,x14256))
% 51.10/50.84 [1426]~E(x14261,x14262)+E(f716(x14263,x14264,x14261,x14265,x14266),f716(x14263,x14264,x14262,x14265,x14266))
% 51.10/50.84 [1427]~E(x14271,x14272)+E(f716(x14273,x14274,x14275,x14271,x14276),f716(x14273,x14274,x14275,x14272,x14276))
% 51.10/50.84 [1428]~E(x14281,x14282)+E(f716(x14283,x14284,x14285,x14286,x14281),f716(x14283,x14284,x14285,x14286,x14282))
% 51.10/50.84 [1429]~E(x14291,x14292)+E(f770(x14291,x14293,x14294),f770(x14292,x14293,x14294))
% 51.10/50.84 [1430]~E(x14301,x14302)+E(f770(x14303,x14301,x14304),f770(x14303,x14302,x14304))
% 51.10/50.84 [1431]~E(x14311,x14312)+E(f770(x14313,x14314,x14311),f770(x14313,x14314,x14312))
% 51.10/50.84 [1432]~E(x14321,x14322)+E(f451(x14321,x14323,x14324),f451(x14322,x14323,x14324))
% 51.10/50.84 [1433]~E(x14331,x14332)+E(f451(x14333,x14331,x14334),f451(x14333,x14332,x14334))
% 51.10/50.84 [1434]~E(x14341,x14342)+E(f451(x14343,x14344,x14341),f451(x14343,x14344,x14342))
% 51.10/50.84 [1435]~E(x14351,x14352)+E(f719(x14351,x14353,x14354,x14355,x14356),f719(x14352,x14353,x14354,x14355,x14356))
% 51.10/50.84 [1436]~E(x14361,x14362)+E(f719(x14363,x14361,x14364,x14365,x14366),f719(x14363,x14362,x14364,x14365,x14366))
% 51.10/50.84 [1437]~E(x14371,x14372)+E(f719(x14373,x14374,x14371,x14375,x14376),f719(x14373,x14374,x14372,x14375,x14376))
% 51.10/50.84 [1438]~E(x14381,x14382)+E(f719(x14383,x14384,x14385,x14381,x14386),f719(x14383,x14384,x14385,x14382,x14386))
% 51.10/50.84 [1439]~E(x14391,x14392)+E(f719(x14393,x14394,x14395,x14396,x14391),f719(x14393,x14394,x14395,x14396,x14392))
% 51.10/50.84 [1440]~E(x14401,x14402)+E(f431(x14401,x14403,x14404),f431(x14402,x14403,x14404))
% 51.10/50.84 [1441]~E(x14411,x14412)+E(f431(x14413,x14411,x14414),f431(x14413,x14412,x14414))
% 51.10/50.84 [1442]~E(x14421,x14422)+E(f431(x14423,x14424,x14421),f431(x14423,x14424,x14422))
% 51.10/50.84 [1443]~E(x14431,x14432)+E(f772(x14431,x14433,x14434),f772(x14432,x14433,x14434))
% 51.10/50.84 [1444]~E(x14441,x14442)+E(f772(x14443,x14441,x14444),f772(x14443,x14442,x14444))
% 51.10/50.84 [1445]~E(x14451,x14452)+E(f772(x14453,x14454,x14451),f772(x14453,x14454,x14452))
% 51.10/50.84 [1446]~E(x14461,x14462)+E(f645(x14461,x14463,x14464,x14465,x14466,x14467,x14468,x14469),f645(x14462,x14463,x14464,x14465,x14466,x14467,x14468,x14469))
% 51.10/50.84 [1447]~E(x14471,x14472)+E(f645(x14473,x14471,x14474,x14475,x14476,x14477,x14478,x14479),f645(x14473,x14472,x14474,x14475,x14476,x14477,x14478,x14479))
% 51.10/50.84 [1448]~E(x14481,x14482)+E(f645(x14483,x14484,x14481,x14485,x14486,x14487,x14488,x14489),f645(x14483,x14484,x14482,x14485,x14486,x14487,x14488,x14489))
% 51.10/50.84 [1449]~E(x14491,x14492)+E(f645(x14493,x14494,x14495,x14491,x14496,x14497,x14498,x14499),f645(x14493,x14494,x14495,x14492,x14496,x14497,x14498,x14499))
% 51.10/50.84 [1450]~E(x14501,x14502)+E(f645(x14503,x14504,x14505,x14506,x14501,x14507,x14508,x14509),f645(x14503,x14504,x14505,x14506,x14502,x14507,x14508,x14509))
% 51.10/50.84 [1451]~E(x14511,x14512)+E(f645(x14513,x14514,x14515,x14516,x14517,x14511,x14518,x14519),f645(x14513,x14514,x14515,x14516,x14517,x14512,x14518,x14519))
% 51.10/50.84 [1452]~E(x14521,x14522)+E(f645(x14523,x14524,x14525,x14526,x14527,x14528,x14521,x14529),f645(x14523,x14524,x14525,x14526,x14527,x14528,x14522,x14529))
% 51.10/50.84 [1453]~E(x14531,x14532)+E(f645(x14533,x14534,x14535,x14536,x14537,x14538,x14539,x14531),f645(x14533,x14534,x14535,x14536,x14537,x14538,x14539,x14532))
% 51.10/50.84 [1454]~E(x14541,x14542)+E(f433(x14541,x14543,x14544),f433(x14542,x14543,x14544))
% 51.10/50.84 [1455]~E(x14551,x14552)+E(f433(x14553,x14551,x14554),f433(x14553,x14552,x14554))
% 51.10/50.84 [1456]~E(x14561,x14562)+E(f433(x14563,x14564,x14561),f433(x14563,x14564,x14562))
% 51.10/50.84 [1457]~E(x14571,x14572)+E(f763(x14571,x14573,x14574),f763(x14572,x14573,x14574))
% 51.10/50.84 [1458]~E(x14581,x14582)+E(f763(x14583,x14581,x14584),f763(x14583,x14582,x14584))
% 51.10/50.84 [1459]~E(x14591,x14592)+E(f763(x14593,x14594,x14591),f763(x14593,x14594,x14592))
% 51.10/50.84 [1460]~E(x14601,x14602)+E(f235(x14601,x14603,x14604),f235(x14602,x14603,x14604))
% 51.10/50.84 [1461]~E(x14611,x14612)+E(f235(x14613,x14611,x14614),f235(x14613,x14612,x14614))
% 51.10/50.84 [1462]~E(x14621,x14622)+E(f235(x14623,x14624,x14621),f235(x14623,x14624,x14622))
% 51.10/50.84 [1463]~E(x14631,x14632)+E(f432(x14631,x14633,x14634),f432(x14632,x14633,x14634))
% 51.10/50.84 [1464]~E(x14641,x14642)+E(f432(x14643,x14641,x14644),f432(x14643,x14642,x14644))
% 51.10/50.84 [1465]~E(x14651,x14652)+E(f432(x14653,x14654,x14651),f432(x14653,x14654,x14652))
% 51.10/50.84 [1466]~E(x14661,x14662)+E(f452(x14661,x14663,x14664,x14665),f452(x14662,x14663,x14664,x14665))
% 51.10/50.84 [1467]~E(x14671,x14672)+E(f452(x14673,x14671,x14674,x14675),f452(x14673,x14672,x14674,x14675))
% 51.10/50.84 [1468]~E(x14681,x14682)+E(f452(x14683,x14684,x14681,x14685),f452(x14683,x14684,x14682,x14685))
% 51.10/50.84 [1469]~E(x14691,x14692)+E(f452(x14693,x14694,x14695,x14691),f452(x14693,x14694,x14695,x14692))
% 51.10/50.84 [1470]~E(x14701,x14702)+E(f835(x14701,x14703,x14704,x14705,x14706,x14707),f835(x14702,x14703,x14704,x14705,x14706,x14707))
% 51.10/50.84 [1471]~E(x14711,x14712)+E(f835(x14713,x14711,x14714,x14715,x14716,x14717),f835(x14713,x14712,x14714,x14715,x14716,x14717))
% 51.10/50.84 [1472]~E(x14721,x14722)+E(f835(x14723,x14724,x14721,x14725,x14726,x14727),f835(x14723,x14724,x14722,x14725,x14726,x14727))
% 51.10/50.84 [1473]~E(x14731,x14732)+E(f835(x14733,x14734,x14735,x14731,x14736,x14737),f835(x14733,x14734,x14735,x14732,x14736,x14737))
% 51.10/50.84 [1474]~E(x14741,x14742)+E(f835(x14743,x14744,x14745,x14746,x14741,x14747),f835(x14743,x14744,x14745,x14746,x14742,x14747))
% 51.10/50.84 [1475]~E(x14751,x14752)+E(f835(x14753,x14754,x14755,x14756,x14757,x14751),f835(x14753,x14754,x14755,x14756,x14757,x14752))
% 51.10/50.84 [1476]~E(x14761,x14762)+E(f730(x14761,x14763,x14764),f730(x14762,x14763,x14764))
% 51.10/50.84 [1477]~E(x14771,x14772)+E(f730(x14773,x14771,x14774),f730(x14773,x14772,x14774))
% 51.10/50.84 [1478]~E(x14781,x14782)+E(f730(x14783,x14784,x14781),f730(x14783,x14784,x14782))
% 51.10/50.84 [1479]~E(x14791,x14792)+E(f462(x14791,x14793,x14794,x14795),f462(x14792,x14793,x14794,x14795))
% 51.10/50.84 [1480]~E(x14801,x14802)+E(f462(x14803,x14801,x14804,x14805),f462(x14803,x14802,x14804,x14805))
% 51.10/50.84 [1481]~E(x14811,x14812)+E(f462(x14813,x14814,x14811,x14815),f462(x14813,x14814,x14812,x14815))
% 51.10/50.84 [1482]~E(x14821,x14822)+E(f462(x14823,x14824,x14825,x14821),f462(x14823,x14824,x14825,x14822))
% 51.10/50.84 [1483]~E(x14831,x14832)+E(f802(x14831,x14833,x14834),f802(x14832,x14833,x14834))
% 51.10/50.84 [1484]~E(x14841,x14842)+E(f802(x14843,x14841,x14844),f802(x14843,x14842,x14844))
% 51.10/50.84 [1485]~E(x14851,x14852)+E(f802(x14853,x14854,x14851),f802(x14853,x14854,x14852))
% 51.10/50.84 [1486]~E(x14861,x14862)+E(f170(x14861),f170(x14862))
% 51.10/50.84 [1487]~E(x14871,x14872)+E(f138(x14871,x14873),f138(x14872,x14873))
% 51.10/50.84 [1488]~E(x14881,x14882)+E(f138(x14883,x14881),f138(x14883,x14882))
% 51.10/50.84 [1489]~E(x14891,x14892)+E(f722(x14891),f722(x14892))
% 51.10/50.84 [1490]~E(x14901,x14902)+E(f530(x14901,x14903,x14904,x14905),f530(x14902,x14903,x14904,x14905))
% 51.10/50.84 [1491]~E(x14911,x14912)+E(f530(x14913,x14911,x14914,x14915),f530(x14913,x14912,x14914,x14915))
% 51.10/50.84 [1492]~E(x14921,x14922)+E(f530(x14923,x14924,x14921,x14925),f530(x14923,x14924,x14922,x14925))
% 51.10/50.84 [1493]~E(x14931,x14932)+E(f530(x14933,x14934,x14935,x14931),f530(x14933,x14934,x14935,x14932))
% 51.10/50.84 [1494]~E(x14941,x14942)+E(f627(x14941,x14943,x14944,x14945,x14946),f627(x14942,x14943,x14944,x14945,x14946))
% 51.10/50.84 [1495]~E(x14951,x14952)+E(f627(x14953,x14951,x14954,x14955,x14956),f627(x14953,x14952,x14954,x14955,x14956))
% 51.10/50.84 [1496]~E(x14961,x14962)+E(f627(x14963,x14964,x14961,x14965,x14966),f627(x14963,x14964,x14962,x14965,x14966))
% 51.10/50.84 [1497]~E(x14971,x14972)+E(f627(x14973,x14974,x14975,x14971,x14976),f627(x14973,x14974,x14975,x14972,x14976))
% 51.10/50.84 [1498]~E(x14981,x14982)+E(f627(x14983,x14984,x14985,x14986,x14981),f627(x14983,x14984,x14985,x14986,x14982))
% 51.10/50.84 [1499]~E(x14991,x14992)+E(f713(x14991,x14993,x14994,x14995,x14996),f713(x14992,x14993,x14994,x14995,x14996))
% 51.10/50.84 [1500]~E(x15001,x15002)+E(f713(x15003,x15001,x15004,x15005,x15006),f713(x15003,x15002,x15004,x15005,x15006))
% 51.10/50.84 [1501]~E(x15011,x15012)+E(f713(x15013,x15014,x15011,x15015,x15016),f713(x15013,x15014,x15012,x15015,x15016))
% 51.10/50.84 [1502]~E(x15021,x15022)+E(f713(x15023,x15024,x15025,x15021,x15026),f713(x15023,x15024,x15025,x15022,x15026))
% 51.10/50.84 [1503]~E(x15031,x15032)+E(f713(x15033,x15034,x15035,x15036,x15031),f713(x15033,x15034,x15035,x15036,x15032))
% 51.10/50.84 [1504]~E(x15041,x15042)+E(f413(x15041,x15043,x15044,x15045),f413(x15042,x15043,x15044,x15045))
% 51.10/50.84 [1505]~E(x15051,x15052)+E(f413(x15053,x15051,x15054,x15055),f413(x15053,x15052,x15054,x15055))
% 51.10/50.84 [1506]~E(x15061,x15062)+E(f413(x15063,x15064,x15061,x15065),f413(x15063,x15064,x15062,x15065))
% 51.10/50.84 [1507]~E(x15071,x15072)+E(f413(x15073,x15074,x15075,x15071),f413(x15073,x15074,x15075,x15072))
% 51.10/50.84 [1508]~E(x15081,x15082)+E(f100(x15081,x15083,x15084),f100(x15082,x15083,x15084))
% 51.10/50.84 [1509]~E(x15091,x15092)+E(f100(x15093,x15091,x15094),f100(x15093,x15092,x15094))
% 51.10/50.84 [1510]~E(x15101,x15102)+E(f100(x15103,x15104,x15101),f100(x15103,x15104,x15102))
% 51.10/50.84 [1511]~E(x15111,x15112)+E(f436(x15111,x15113,x15114,x15115,x15116),f436(x15112,x15113,x15114,x15115,x15116))
% 51.10/50.84 [1512]~E(x15121,x15122)+E(f436(x15123,x15121,x15124,x15125,x15126),f436(x15123,x15122,x15124,x15125,x15126))
% 51.10/50.84 [1513]~E(x15131,x15132)+E(f436(x15133,x15134,x15131,x15135,x15136),f436(x15133,x15134,x15132,x15135,x15136))
% 51.10/50.84 [1514]~E(x15141,x15142)+E(f436(x15143,x15144,x15145,x15141,x15146),f436(x15143,x15144,x15145,x15142,x15146))
% 51.10/50.84 [1515]~E(x15151,x15152)+E(f436(x15153,x15154,x15155,x15156,x15151),f436(x15153,x15154,x15155,x15156,x15152))
% 51.10/50.84 [1516]~E(x15161,x15162)+E(f495(x15161,x15163,x15164,x15165,x15166),f495(x15162,x15163,x15164,x15165,x15166))
% 51.10/50.84 [1517]~E(x15171,x15172)+E(f495(x15173,x15171,x15174,x15175,x15176),f495(x15173,x15172,x15174,x15175,x15176))
% 51.10/50.84 [1518]~E(x15181,x15182)+E(f495(x15183,x15184,x15181,x15185,x15186),f495(x15183,x15184,x15182,x15185,x15186))
% 51.10/50.84 [1519]~E(x15191,x15192)+E(f495(x15193,x15194,x15195,x15191,x15196),f495(x15193,x15194,x15195,x15192,x15196))
% 51.10/50.84 [1520]~E(x15201,x15202)+E(f495(x15203,x15204,x15205,x15206,x15201),f495(x15203,x15204,x15205,x15206,x15202))
% 51.10/50.84 [1521]~E(x15211,x15212)+E(f599(x15211,x15213),f599(x15212,x15213))
% 51.10/50.84 [1522]~E(x15221,x15222)+E(f599(x15223,x15221),f599(x15223,x15222))
% 51.10/50.84 [1523]~E(x15231,x15232)+E(f797(x15231,x15233,x15234,x15235,x15236),f797(x15232,x15233,x15234,x15235,x15236))
% 51.10/50.84 [1524]~E(x15241,x15242)+E(f797(x15243,x15241,x15244,x15245,x15246),f797(x15243,x15242,x15244,x15245,x15246))
% 51.10/50.84 [1525]~E(x15251,x15252)+E(f797(x15253,x15254,x15251,x15255,x15256),f797(x15253,x15254,x15252,x15255,x15256))
% 51.10/50.84 [1526]~E(x15261,x15262)+E(f797(x15263,x15264,x15265,x15261,x15266),f797(x15263,x15264,x15265,x15262,x15266))
% 51.10/50.84 [1527]~E(x15271,x15272)+E(f797(x15273,x15274,x15275,x15276,x15271),f797(x15273,x15274,x15275,x15276,x15272))
% 51.10/50.84 [1528]~E(x15281,x15282)+E(f229(x15281,x15283,x15284),f229(x15282,x15283,x15284))
% 51.10/50.84 [1529]~E(x15291,x15292)+E(f229(x15293,x15291,x15294),f229(x15293,x15292,x15294))
% 51.10/50.84 [1530]~E(x15301,x15302)+E(f229(x15303,x15304,x15301),f229(x15303,x15304,x15302))
% 51.10/50.84 [1531]~E(x15311,x15312)+E(f279(x15311,x15313,x15314,x15315),f279(x15312,x15313,x15314,x15315))
% 51.10/50.84 [1532]~E(x15321,x15322)+E(f279(x15323,x15321,x15324,x15325),f279(x15323,x15322,x15324,x15325))
% 51.10/50.84 [1533]~E(x15331,x15332)+E(f279(x15333,x15334,x15331,x15335),f279(x15333,x15334,x15332,x15335))
% 51.10/50.84 [1534]~E(x15341,x15342)+E(f279(x15343,x15344,x15345,x15341),f279(x15343,x15344,x15345,x15342))
% 51.10/50.84 [1535]~E(x15351,x15352)+E(f55(x15351),f55(x15352))
% 51.10/50.84 [1536]~E(x15361,x15362)+E(f804(x15361,x15363,x15364),f804(x15362,x15363,x15364))
% 51.10/50.84 [1537]~E(x15371,x15372)+E(f804(x15373,x15371,x15374),f804(x15373,x15372,x15374))
% 51.10/50.84 [1538]~E(x15381,x15382)+E(f804(x15383,x15384,x15381),f804(x15383,x15384,x15382))
% 51.10/50.84 [1539]~E(x15391,x15392)+E(f317(x15391),f317(x15392))
% 51.10/50.84 [1540]~E(x15401,x15402)+E(f502(x15401,x15403,x15404,x15405),f502(x15402,x15403,x15404,x15405))
% 51.10/50.84 [1541]~E(x15411,x15412)+E(f502(x15413,x15411,x15414,x15415),f502(x15413,x15412,x15414,x15415))
% 51.10/50.84 [1542]~E(x15421,x15422)+E(f502(x15423,x15424,x15421,x15425),f502(x15423,x15424,x15422,x15425))
% 51.10/50.84 [1543]~E(x15431,x15432)+E(f502(x15433,x15434,x15435,x15431),f502(x15433,x15434,x15435,x15432))
% 51.10/50.84 [1544]~E(x15441,x15442)+E(f441(x15441,x15443,x15444),f441(x15442,x15443,x15444))
% 51.10/50.84 [1545]~E(x15451,x15452)+E(f441(x15453,x15451,x15454),f441(x15453,x15452,x15454))
% 51.10/50.84 [1546]~E(x15461,x15462)+E(f441(x15463,x15464,x15461),f441(x15463,x15464,x15462))
% 51.10/50.84 [1547]~E(x15471,x15472)+E(f601(x15471,x15473,x15474),f601(x15472,x15473,x15474))
% 51.10/50.84 [1548]~E(x15481,x15482)+E(f601(x15483,x15481,x15484),f601(x15483,x15482,x15484))
% 51.10/50.84 [1549]~E(x15491,x15492)+E(f601(x15493,x15494,x15491),f601(x15493,x15494,x15492))
% 51.10/50.84 [1550]~E(x15501,x15502)+E(f479(x15501,x15503,x15504,x15505,x15506),f479(x15502,x15503,x15504,x15505,x15506))
% 51.10/50.84 [1551]~E(x15511,x15512)+E(f479(x15513,x15511,x15514,x15515,x15516),f479(x15513,x15512,x15514,x15515,x15516))
% 51.10/50.84 [1552]~E(x15521,x15522)+E(f479(x15523,x15524,x15521,x15525,x15526),f479(x15523,x15524,x15522,x15525,x15526))
% 51.10/50.84 [1553]~E(x15531,x15532)+E(f479(x15533,x15534,x15535,x15531,x15536),f479(x15533,x15534,x15535,x15532,x15536))
% 51.10/50.84 [1554]~E(x15541,x15542)+E(f479(x15543,x15544,x15545,x15546,x15541),f479(x15543,x15544,x15545,x15546,x15542))
% 51.10/50.84 [1555]~E(x15551,x15552)+E(f414(x15551,x15553,x15554,x15555,x15556),f414(x15552,x15553,x15554,x15555,x15556))
% 51.10/50.84 [1556]~E(x15561,x15562)+E(f414(x15563,x15561,x15564,x15565,x15566),f414(x15563,x15562,x15564,x15565,x15566))
% 51.10/50.84 [1557]~E(x15571,x15572)+E(f414(x15573,x15574,x15571,x15575,x15576),f414(x15573,x15574,x15572,x15575,x15576))
% 51.10/50.84 [1558]~E(x15581,x15582)+E(f414(x15583,x15584,x15585,x15581,x15586),f414(x15583,x15584,x15585,x15582,x15586))
% 51.10/50.84 [1559]~E(x15591,x15592)+E(f414(x15593,x15594,x15595,x15596,x15591),f414(x15593,x15594,x15595,x15596,x15592))
% 51.10/50.84 [1560]~E(x15601,x15602)+E(f590(x15601),f590(x15602))
% 51.10/50.84 [1561]~E(x15611,x15612)+E(f542(x15611,x15613,x15614,x15615),f542(x15612,x15613,x15614,x15615))
% 51.10/50.84 [1562]~E(x15621,x15622)+E(f542(x15623,x15621,x15624,x15625),f542(x15623,x15622,x15624,x15625))
% 51.10/50.84 [1563]~E(x15631,x15632)+E(f542(x15633,x15634,x15631,x15635),f542(x15633,x15634,x15632,x15635))
% 51.10/50.84 [1564]~E(x15641,x15642)+E(f542(x15643,x15644,x15645,x15641),f542(x15643,x15644,x15645,x15642))
% 51.10/50.84 [1565]~E(x15651,x15652)+E(f380(x15651,x15653),f380(x15652,x15653))
% 51.10/50.84 [1566]~E(x15661,x15662)+E(f380(x15663,x15661),f380(x15663,x15662))
% 51.10/50.84 [1567]~E(x15671,x15672)+E(f656(x15671),f656(x15672))
% 51.10/50.84 [1568]~E(x15681,x15682)+E(f575(x15681,x15683,x15684),f575(x15682,x15683,x15684))
% 51.10/50.84 [1569]~E(x15691,x15692)+E(f575(x15693,x15691,x15694),f575(x15693,x15692,x15694))
% 51.10/50.84 [1570]~E(x15701,x15702)+E(f575(x15703,x15704,x15701),f575(x15703,x15704,x15702))
% 51.10/50.84 [1571]~E(x15711,x15712)+E(f283(x15711,x15713,x15714,x15715),f283(x15712,x15713,x15714,x15715))
% 51.10/50.84 [1572]~E(x15721,x15722)+E(f283(x15723,x15721,x15724,x15725),f283(x15723,x15722,x15724,x15725))
% 51.10/50.84 [1573]~E(x15731,x15732)+E(f283(x15733,x15734,x15731,x15735),f283(x15733,x15734,x15732,x15735))
% 51.10/50.84 [1574]~E(x15741,x15742)+E(f283(x15743,x15744,x15745,x15741),f283(x15743,x15744,x15745,x15742))
% 51.10/50.84 [1575]~E(x15751,x15752)+E(f647(x15751,x15753,x15754),f647(x15752,x15753,x15754))
% 51.10/50.84 [1576]~E(x15761,x15762)+E(f647(x15763,x15761,x15764),f647(x15763,x15762,x15764))
% 51.10/50.84 [1577]~E(x15771,x15772)+E(f647(x15773,x15774,x15771),f647(x15773,x15774,x15772))
% 51.10/50.84 [1578]~E(x15781,x15782)+E(f586(x15781,x15783,x15784),f586(x15782,x15783,x15784))
% 51.10/50.84 [1579]~E(x15791,x15792)+E(f586(x15793,x15791,x15794),f586(x15793,x15792,x15794))
% 51.10/50.84 [1580]~E(x15801,x15802)+E(f586(x15803,x15804,x15801),f586(x15803,x15804,x15802))
% 51.10/50.84 [1581]~E(x15811,x15812)+E(f771(x15811,x15813),f771(x15812,x15813))
% 51.10/50.84 [1582]~E(x15821,x15822)+E(f771(x15823,x15821),f771(x15823,x15822))
% 51.10/50.84 [1583]~E(x15831,x15832)+E(f366(x15831,x15833,x15834),f366(x15832,x15833,x15834))
% 51.10/50.84 [1584]~E(x15841,x15842)+E(f366(x15843,x15841,x15844),f366(x15843,x15842,x15844))
% 51.10/50.84 [1585]~E(x15851,x15852)+E(f366(x15853,x15854,x15851),f366(x15853,x15854,x15852))
% 51.10/50.84 [1586]~E(x15861,x15862)+E(f726(x15861,x15863),f726(x15862,x15863))
% 51.10/50.84 [1587]~E(x15871,x15872)+E(f726(x15873,x15871),f726(x15873,x15872))
% 51.10/50.84 [1588]~E(x15881,x15882)+E(f548(x15881,x15883,x15884),f548(x15882,x15883,x15884))
% 51.10/50.84 [1589]~E(x15891,x15892)+E(f548(x15893,x15891,x15894),f548(x15893,x15892,x15894))
% 51.10/50.84 [1590]~E(x15901,x15902)+E(f548(x15903,x15904,x15901),f548(x15903,x15904,x15902))
% 51.10/50.84 [1591]~E(x15911,x15912)+E(f558(x15911),f558(x15912))
% 51.10/50.84 [1592]~E(x15921,x15922)+E(f369(x15921),f369(x15922))
% 51.10/50.84 [1593]~E(x15931,x15932)+E(f715(x15931,x15933,x15934,x15935),f715(x15932,x15933,x15934,x15935))
% 51.10/50.84 [1594]~E(x15941,x15942)+E(f715(x15943,x15941,x15944,x15945),f715(x15943,x15942,x15944,x15945))
% 51.10/50.84 [1595]~E(x15951,x15952)+E(f715(x15953,x15954,x15951,x15955),f715(x15953,x15954,x15952,x15955))
% 51.10/50.84 [1596]~E(x15961,x15962)+E(f715(x15963,x15964,x15965,x15961),f715(x15963,x15964,x15965,x15962))
% 51.10/50.84 [1597]~E(x15971,x15972)+E(f228(x15971,x15973),f228(x15972,x15973))
% 51.10/50.84 [1598]~E(x15981,x15982)+E(f228(x15983,x15981),f228(x15983,x15982))
% 51.10/50.84 [1599]~E(x15991,x15992)+E(f492(x15991,x15993,x15994,x15995,x15996),f492(x15992,x15993,x15994,x15995,x15996))
% 51.10/50.84 [1600]~E(x16001,x16002)+E(f492(x16003,x16001,x16004,x16005,x16006),f492(x16003,x16002,x16004,x16005,x16006))
% 51.10/50.84 [1601]~E(x16011,x16012)+E(f492(x16013,x16014,x16011,x16015,x16016),f492(x16013,x16014,x16012,x16015,x16016))
% 51.10/50.84 [1602]~E(x16021,x16022)+E(f492(x16023,x16024,x16025,x16021,x16026),f492(x16023,x16024,x16025,x16022,x16026))
% 51.10/50.84 [1603]~E(x16031,x16032)+E(f492(x16033,x16034,x16035,x16036,x16031),f492(x16033,x16034,x16035,x16036,x16032))
% 51.10/50.84 [1604]~E(x16041,x16042)+E(f550(x16041,x16043,x16044),f550(x16042,x16043,x16044))
% 51.10/50.84 [1605]~E(x16051,x16052)+E(f550(x16053,x16051,x16054),f550(x16053,x16052,x16054))
% 51.10/50.84 [1606]~E(x16061,x16062)+E(f550(x16063,x16064,x16061),f550(x16063,x16064,x16062))
% 51.10/50.84 [1607]~E(x16071,x16072)+E(f340(x16071,x16073),f340(x16072,x16073))
% 51.10/50.84 [1608]~E(x16081,x16082)+E(f340(x16083,x16081),f340(x16083,x16082))
% 51.10/50.84 [1609]~E(x16091,x16092)+E(f313(x16091,x16093),f313(x16092,x16093))
% 51.10/50.84 [1610]~E(x16101,x16102)+E(f313(x16103,x16101),f313(x16103,x16102))
% 51.10/50.84 [1611]~E(x16111,x16112)+E(f522(x16111),f522(x16112))
% 51.10/50.84 [1612]~E(x16121,x16122)+E(f263(x16121,x16123,x16124,x16125,x16126),f263(x16122,x16123,x16124,x16125,x16126))
% 51.10/50.84 [1613]~E(x16131,x16132)+E(f263(x16133,x16131,x16134,x16135,x16136),f263(x16133,x16132,x16134,x16135,x16136))
% 51.10/50.84 [1614]~E(x16141,x16142)+E(f263(x16143,x16144,x16141,x16145,x16146),f263(x16143,x16144,x16142,x16145,x16146))
% 51.10/50.84 [1615]~E(x16151,x16152)+E(f263(x16153,x16154,x16155,x16151,x16156),f263(x16153,x16154,x16155,x16152,x16156))
% 51.10/50.84 [1616]~E(x16161,x16162)+E(f263(x16163,x16164,x16165,x16166,x16161),f263(x16163,x16164,x16165,x16166,x16162))
% 51.10/50.84 [1617]~E(x16171,x16172)+E(f725(x16171,x16173,x16174),f725(x16172,x16173,x16174))
% 51.10/50.84 [1618]~E(x16181,x16182)+E(f725(x16183,x16181,x16184),f725(x16183,x16182,x16184))
% 51.10/50.84 [1619]~E(x16191,x16192)+E(f725(x16193,x16194,x16191),f725(x16193,x16194,x16192))
% 51.10/50.84 [1620]~E(x16201,x16202)+E(f74(x16201,x16203,x16204),f74(x16202,x16203,x16204))
% 51.10/50.84 [1621]~E(x16211,x16212)+E(f74(x16213,x16211,x16214),f74(x16213,x16212,x16214))
% 51.10/50.84 [1622]~E(x16221,x16222)+E(f74(x16223,x16224,x16221),f74(x16223,x16224,x16222))
% 51.10/50.84 [1623]~E(x16231,x16232)+E(f729(x16231,x16233,x16234),f729(x16232,x16233,x16234))
% 51.10/50.84 [1624]~E(x16241,x16242)+E(f729(x16243,x16241,x16244),f729(x16243,x16242,x16244))
% 51.10/50.84 [1625]~E(x16251,x16252)+E(f729(x16253,x16254,x16251),f729(x16253,x16254,x16252))
% 51.10/50.84 [1626]~E(x16261,x16262)+E(f720(x16261,x16263),f720(x16262,x16263))
% 51.10/50.84 [1627]~E(x16271,x16272)+E(f720(x16273,x16271),f720(x16273,x16272))
% 51.10/50.84 [1628]~E(x16281,x16282)+E(f597(x16281,x16283,x16284),f597(x16282,x16283,x16284))
% 51.10/50.84 [1629]~E(x16291,x16292)+E(f597(x16293,x16291,x16294),f597(x16293,x16292,x16294))
% 51.10/50.84 [1630]~E(x16301,x16302)+E(f597(x16303,x16304,x16301),f597(x16303,x16304,x16302))
% 51.10/50.84 [1631]~E(x16311,x16312)+E(f254(x16311,x16313,x16314),f254(x16312,x16313,x16314))
% 51.10/50.84 [1632]~E(x16321,x16322)+E(f254(x16323,x16321,x16324),f254(x16323,x16322,x16324))
% 51.10/50.84 [1633]~E(x16331,x16332)+E(f254(x16333,x16334,x16331),f254(x16333,x16334,x16332))
% 51.10/50.84 [1634]~E(x16341,x16342)+E(f231(x16341,x16343,x16344),f231(x16342,x16343,x16344))
% 51.10/50.84 [1635]~E(x16351,x16352)+E(f231(x16353,x16351,x16354),f231(x16353,x16352,x16354))
% 51.10/50.84 [1636]~E(x16361,x16362)+E(f231(x16363,x16364,x16361),f231(x16363,x16364,x16362))
% 51.10/50.84 [1637]~E(x16371,x16372)+E(f356(x16371,x16373,x16374,x16375,x16376),f356(x16372,x16373,x16374,x16375,x16376))
% 51.10/50.84 [1638]~E(x16381,x16382)+E(f356(x16383,x16381,x16384,x16385,x16386),f356(x16383,x16382,x16384,x16385,x16386))
% 51.10/50.84 [1639]~E(x16391,x16392)+E(f356(x16393,x16394,x16391,x16395,x16396),f356(x16393,x16394,x16392,x16395,x16396))
% 51.10/50.84 [1640]~E(x16401,x16402)+E(f356(x16403,x16404,x16405,x16401,x16406),f356(x16403,x16404,x16405,x16402,x16406))
% 51.10/50.84 [1641]~E(x16411,x16412)+E(f356(x16413,x16414,x16415,x16416,x16411),f356(x16413,x16414,x16415,x16416,x16412))
% 51.10/50.84 [1642]~E(x16421,x16422)+E(f440(x16421,x16423,x16424),f440(x16422,x16423,x16424))
% 51.10/50.84 [1643]~E(x16431,x16432)+E(f440(x16433,x16431,x16434),f440(x16433,x16432,x16434))
% 51.10/50.84 [1644]~E(x16441,x16442)+E(f440(x16443,x16444,x16441),f440(x16443,x16444,x16442))
% 51.10/50.84 [1645]~E(x16451,x16452)+E(f141(x16451,x16453),f141(x16452,x16453))
% 51.10/50.84 [1646]~E(x16461,x16462)+E(f141(x16463,x16461),f141(x16463,x16462))
% 51.10/50.84 [1647]~E(x16471,x16472)+E(f712(x16471,x16473,x16474),f712(x16472,x16473,x16474))
% 51.10/50.84 [1648]~E(x16481,x16482)+E(f712(x16483,x16481,x16484),f712(x16483,x16482,x16484))
% 51.10/50.84 [1649]~E(x16491,x16492)+E(f712(x16493,x16494,x16491),f712(x16493,x16494,x16492))
% 51.10/50.84 [1650]~E(x16501,x16502)+E(f756(x16501,x16503,x16504),f756(x16502,x16503,x16504))
% 51.10/50.84 [1651]~E(x16511,x16512)+E(f756(x16513,x16511,x16514),f756(x16513,x16512,x16514))
% 51.10/50.84 [1652]~E(x16521,x16522)+E(f756(x16523,x16524,x16521),f756(x16523,x16524,x16522))
% 51.10/50.84 [1653]~E(x16531,x16532)+E(f519(x16531,x16533,x16534),f519(x16532,x16533,x16534))
% 51.10/50.84 [1654]~E(x16541,x16542)+E(f519(x16543,x16541,x16544),f519(x16543,x16542,x16544))
% 51.10/50.84 [1655]~E(x16551,x16552)+E(f519(x16553,x16554,x16551),f519(x16553,x16554,x16552))
% 51.10/50.84 [1656]~E(x16561,x16562)+E(f710(x16561,x16563,x16564,x16565),f710(x16562,x16563,x16564,x16565))
% 51.10/50.84 [1657]~E(x16571,x16572)+E(f710(x16573,x16571,x16574,x16575),f710(x16573,x16572,x16574,x16575))
% 51.10/50.84 [1658]~E(x16581,x16582)+E(f710(x16583,x16584,x16581,x16585),f710(x16583,x16584,x16582,x16585))
% 51.10/50.84 [1659]~E(x16591,x16592)+E(f710(x16593,x16594,x16595,x16591),f710(x16593,x16594,x16595,x16592))
% 51.10/50.84 [1660]~E(x16601,x16602)+E(f744(x16601,x16603,x16604,x16605),f744(x16602,x16603,x16604,x16605))
% 51.10/50.84 [1661]~E(x16611,x16612)+E(f744(x16613,x16611,x16614,x16615),f744(x16613,x16612,x16614,x16615))
% 51.10/50.84 [1662]~E(x16621,x16622)+E(f744(x16623,x16624,x16621,x16625),f744(x16623,x16624,x16622,x16625))
% 51.10/50.84 [1663]~E(x16631,x16632)+E(f744(x16633,x16634,x16635,x16631),f744(x16633,x16634,x16635,x16632))
% 51.10/50.84 [1664]~E(x16641,x16642)+E(f825(x16641,x16643,x16644),f825(x16642,x16643,x16644))
% 51.10/50.84 [1665]~E(x16651,x16652)+E(f825(x16653,x16651,x16654),f825(x16653,x16652,x16654))
% 51.10/50.84 [1666]~E(x16661,x16662)+E(f825(x16663,x16664,x16661),f825(x16663,x16664,x16662))
% 51.10/50.84 [1667]~E(x16671,x16672)+E(f412(x16671,x16673,x16674,x16675,x16676),f412(x16672,x16673,x16674,x16675,x16676))
% 51.10/50.84 [1668]~E(x16681,x16682)+E(f412(x16683,x16681,x16684,x16685,x16686),f412(x16683,x16682,x16684,x16685,x16686))
% 51.10/50.84 [1669]~E(x16691,x16692)+E(f412(x16693,x16694,x16691,x16695,x16696),f412(x16693,x16694,x16692,x16695,x16696))
% 51.10/50.84 [1670]~E(x16701,x16702)+E(f412(x16703,x16704,x16705,x16701,x16706),f412(x16703,x16704,x16705,x16702,x16706))
% 51.10/50.84 [1671]~E(x16711,x16712)+E(f412(x16713,x16714,x16715,x16716,x16711),f412(x16713,x16714,x16715,x16716,x16712))
% 51.10/50.84 [1672]~E(x16721,x16722)+E(f339(x16721,x16723),f339(x16722,x16723))
% 51.10/50.84 [1673]~E(x16731,x16732)+E(f339(x16733,x16731),f339(x16733,x16732))
% 51.10/50.84 [1674]~E(x16741,x16742)+E(f807(x16741,x16743,x16744),f807(x16742,x16743,x16744))
% 51.10/50.84 [1675]~E(x16751,x16752)+E(f807(x16753,x16751,x16754),f807(x16753,x16752,x16754))
% 51.10/50.84 [1676]~E(x16761,x16762)+E(f807(x16763,x16764,x16761),f807(x16763,x16764,x16762))
% 51.10/50.84 [1677]~E(x16771,x16772)+E(f262(x16771,x16773,x16774,x16775,x16776),f262(x16772,x16773,x16774,x16775,x16776))
% 51.10/50.84 [1678]~E(x16781,x16782)+E(f262(x16783,x16781,x16784,x16785,x16786),f262(x16783,x16782,x16784,x16785,x16786))
% 51.10/50.84 [1679]~E(x16791,x16792)+E(f262(x16793,x16794,x16791,x16795,x16796),f262(x16793,x16794,x16792,x16795,x16796))
% 51.10/50.84 [1680]~E(x16801,x16802)+E(f262(x16803,x16804,x16805,x16801,x16806),f262(x16803,x16804,x16805,x16802,x16806))
% 51.10/50.84 [1681]~E(x16811,x16812)+E(f262(x16813,x16814,x16815,x16816,x16811),f262(x16813,x16814,x16815,x16816,x16812))
% 51.10/50.84 [1682]~E(x16821,x16822)+E(f521(x16821,x16823,x16824,x16825),f521(x16822,x16823,x16824,x16825))
% 51.10/50.84 [1683]~E(x16831,x16832)+E(f521(x16833,x16831,x16834,x16835),f521(x16833,x16832,x16834,x16835))
% 51.10/50.84 [1684]~E(x16841,x16842)+E(f521(x16843,x16844,x16841,x16845),f521(x16843,x16844,x16842,x16845))
% 51.10/50.84 [1685]~E(x16851,x16852)+E(f521(x16853,x16854,x16855,x16851),f521(x16853,x16854,x16855,x16852))
% 51.10/50.84 [1686]~E(x16861,x16862)+E(f464(x16861,x16863,x16864,x16865),f464(x16862,x16863,x16864,x16865))
% 51.10/50.84 [1687]~E(x16871,x16872)+E(f464(x16873,x16871,x16874,x16875),f464(x16873,x16872,x16874,x16875))
% 51.10/50.84 [1688]~E(x16881,x16882)+E(f464(x16883,x16884,x16881,x16885),f464(x16883,x16884,x16882,x16885))
% 51.10/50.84 [1689]~E(x16891,x16892)+E(f464(x16893,x16894,x16895,x16891),f464(x16893,x16894,x16895,x16892))
% 51.10/50.84 [1690]~E(x16901,x16902)+E(f498(x16901,x16903,x16904),f498(x16902,x16903,x16904))
% 51.10/50.84 [1691]~E(x16911,x16912)+E(f498(x16913,x16911,x16914),f498(x16913,x16912,x16914))
% 51.10/50.84 [1692]~E(x16921,x16922)+E(f498(x16923,x16924,x16921),f498(x16923,x16924,x16922))
% 51.10/50.84 [1693]~E(x16931,x16932)+E(f728(x16931),f728(x16932))
% 51.10/50.84 [1694]~E(x16941,x16942)+E(f705(x16941,x16943,x16944,x16945,x16946),f705(x16942,x16943,x16944,x16945,x16946))
% 51.10/50.84 [1695]~E(x16951,x16952)+E(f705(x16953,x16951,x16954,x16955,x16956),f705(x16953,x16952,x16954,x16955,x16956))
% 51.10/50.84 [1696]~E(x16961,x16962)+E(f705(x16963,x16964,x16961,x16965,x16966),f705(x16963,x16964,x16962,x16965,x16966))
% 51.10/50.84 [1697]~E(x16971,x16972)+E(f705(x16973,x16974,x16975,x16971,x16976),f705(x16973,x16974,x16975,x16972,x16976))
% 51.10/50.84 [1698]~E(x16981,x16982)+E(f705(x16983,x16984,x16985,x16986,x16981),f705(x16983,x16984,x16985,x16986,x16982))
% 51.10/50.84 [1699]~E(x16991,x16992)+E(f416(x16991,x16993,x16994,x16995,x16996,x16997,x16998),f416(x16992,x16993,x16994,x16995,x16996,x16997,x16998))
% 51.10/50.84 [1700]~E(x17001,x17002)+E(f416(x17003,x17001,x17004,x17005,x17006,x17007,x17008),f416(x17003,x17002,x17004,x17005,x17006,x17007,x17008))
% 51.10/50.84 [1701]~E(x17011,x17012)+E(f416(x17013,x17014,x17011,x17015,x17016,x17017,x17018),f416(x17013,x17014,x17012,x17015,x17016,x17017,x17018))
% 51.10/50.84 [1702]~E(x17021,x17022)+E(f416(x17023,x17024,x17025,x17021,x17026,x17027,x17028),f416(x17023,x17024,x17025,x17022,x17026,x17027,x17028))
% 51.10/50.84 [1703]~E(x17031,x17032)+E(f416(x17033,x17034,x17035,x17036,x17031,x17037,x17038),f416(x17033,x17034,x17035,x17036,x17032,x17037,x17038))
% 51.10/50.84 [1704]~E(x17041,x17042)+E(f416(x17043,x17044,x17045,x17046,x17047,x17041,x17048),f416(x17043,x17044,x17045,x17046,x17047,x17042,x17048))
% 51.10/50.84 [1705]~E(x17051,x17052)+E(f416(x17053,x17054,x17055,x17056,x17057,x17058,x17051),f416(x17053,x17054,x17055,x17056,x17057,x17058,x17052))
% 51.10/50.84 [1706]~E(x17061,x17062)+E(f640(x17061,x17063,x17064,x17065,x17066),f640(x17062,x17063,x17064,x17065,x17066))
% 51.10/50.84 [1707]~E(x17071,x17072)+E(f640(x17073,x17071,x17074,x17075,x17076),f640(x17073,x17072,x17074,x17075,x17076))
% 51.10/50.84 [1708]~E(x17081,x17082)+E(f640(x17083,x17084,x17081,x17085,x17086),f640(x17083,x17084,x17082,x17085,x17086))
% 51.10/50.84 [1709]~E(x17091,x17092)+E(f640(x17093,x17094,x17095,x17091,x17096),f640(x17093,x17094,x17095,x17092,x17096))
% 51.10/50.84 [1710]~E(x17101,x17102)+E(f640(x17103,x17104,x17105,x17106,x17101),f640(x17103,x17104,x17105,x17106,x17102))
% 51.10/50.84 [1711]~E(x17111,x17112)+E(f766(x17111,x17113,x17114),f766(x17112,x17113,x17114))
% 51.10/50.84 [1712]~E(x17121,x17122)+E(f766(x17123,x17121,x17124),f766(x17123,x17122,x17124))
% 51.10/50.84 [1713]~E(x17131,x17132)+E(f766(x17133,x17134,x17131),f766(x17133,x17134,x17132))
% 51.10/50.84 [1714]~E(x17141,x17142)+E(f296(x17141,x17143,x17144),f296(x17142,x17143,x17144))
% 51.10/50.84 [1715]~E(x17151,x17152)+E(f296(x17153,x17151,x17154),f296(x17153,x17152,x17154))
% 51.10/50.84 [1716]~E(x17161,x17162)+E(f296(x17163,x17164,x17161),f296(x17163,x17164,x17162))
% 51.10/50.84 [1717]~E(x17171,x17172)+E(f526(x17171,x17173,x17174,x17175),f526(x17172,x17173,x17174,x17175))
% 51.10/50.84 [1718]~E(x17181,x17182)+E(f526(x17183,x17181,x17184,x17185),f526(x17183,x17182,x17184,x17185))
% 51.10/50.84 [1719]~E(x17191,x17192)+E(f526(x17193,x17194,x17191,x17195),f526(x17193,x17194,x17192,x17195))
% 51.10/50.84 [1720]~E(x17201,x17202)+E(f526(x17203,x17204,x17205,x17201),f526(x17203,x17204,x17205,x17202))
% 51.10/50.84 [1721]~E(x17211,x17212)+E(f551(x17211,x17213,x17214),f551(x17212,x17213,x17214))
% 51.10/50.84 [1722]~E(x17221,x17222)+E(f551(x17223,x17221,x17224),f551(x17223,x17222,x17224))
% 51.10/50.84 [1723]~E(x17231,x17232)+E(f551(x17233,x17234,x17231),f551(x17233,x17234,x17232))
% 51.10/50.84 [1724]~E(x17241,x17242)+E(f546(x17241,x17243),f546(x17242,x17243))
% 51.10/50.84 [1725]~E(x17251,x17252)+E(f546(x17253,x17251),f546(x17253,x17252))
% 51.10/50.84 [1726]~E(x17261,x17262)+E(f793(x17261,x17263,x17264),f793(x17262,x17263,x17264))
% 51.10/50.84 [1727]~E(x17271,x17272)+E(f793(x17273,x17271,x17274),f793(x17273,x17272,x17274))
% 51.10/50.84 [1728]~E(x17281,x17282)+E(f793(x17283,x17284,x17281),f793(x17283,x17284,x17282))
% 51.10/50.84 [1729]~E(x17291,x17292)+E(f513(x17291,x17293,x17294,x17295,x17296),f513(x17292,x17293,x17294,x17295,x17296))
% 51.10/50.84 [1730]~E(x17301,x17302)+E(f513(x17303,x17301,x17304,x17305,x17306),f513(x17303,x17302,x17304,x17305,x17306))
% 51.10/50.84 [1731]~E(x17311,x17312)+E(f513(x17313,x17314,x17311,x17315,x17316),f513(x17313,x17314,x17312,x17315,x17316))
% 51.10/50.84 [1732]~E(x17321,x17322)+E(f513(x17323,x17324,x17325,x17321,x17326),f513(x17323,x17324,x17325,x17322,x17326))
% 51.10/50.84 [1733]~E(x17331,x17332)+E(f513(x17333,x17334,x17335,x17336,x17331),f513(x17333,x17334,x17335,x17336,x17332))
% 51.10/50.84 [1734]~E(x17341,x17342)+E(f643(x17341,x17343,x17344,x17345,x17346),f643(x17342,x17343,x17344,x17345,x17346))
% 51.10/50.84 [1735]~E(x17351,x17352)+E(f643(x17353,x17351,x17354,x17355,x17356),f643(x17353,x17352,x17354,x17355,x17356))
% 51.10/50.84 [1736]~E(x17361,x17362)+E(f643(x17363,x17364,x17361,x17365,x17366),f643(x17363,x17364,x17362,x17365,x17366))
% 51.10/50.84 [1737]~E(x17371,x17372)+E(f643(x17373,x17374,x17375,x17371,x17376),f643(x17373,x17374,x17375,x17372,x17376))
% 51.10/50.84 [1738]~E(x17381,x17382)+E(f643(x17383,x17384,x17385,x17386,x17381),f643(x17383,x17384,x17385,x17386,x17382))
% 51.10/50.84 [1739]~E(x17391,x17392)+E(f404(x17391),f404(x17392))
% 51.10/50.84 [1740]~E(x17401,x17402)+E(f392(x17401,x17403,x17404),f392(x17402,x17403,x17404))
% 51.10/50.84 [1741]~E(x17411,x17412)+E(f392(x17413,x17411,x17414),f392(x17413,x17412,x17414))
% 51.10/50.84 [1742]~E(x17421,x17422)+E(f392(x17423,x17424,x17421),f392(x17423,x17424,x17422))
% 51.10/50.84 [1743]~E(x17431,x17432)+E(f572(x17431,x17433,x17434,x17435),f572(x17432,x17433,x17434,x17435))
% 51.10/50.84 [1744]~E(x17441,x17442)+E(f572(x17443,x17441,x17444,x17445),f572(x17443,x17442,x17444,x17445))
% 51.10/50.84 [1745]~E(x17451,x17452)+E(f572(x17453,x17454,x17451,x17455),f572(x17453,x17454,x17452,x17455))
% 51.10/50.84 [1746]~E(x17461,x17462)+E(f572(x17463,x17464,x17465,x17461),f572(x17463,x17464,x17465,x17462))
% 51.10/50.84 [1747]~E(x17471,x17472)+E(f631(x17471,x17473,x17474),f631(x17472,x17473,x17474))
% 51.10/50.84 [1748]~E(x17481,x17482)+E(f631(x17483,x17481,x17484),f631(x17483,x17482,x17484))
% 51.10/50.84 [1749]~E(x17491,x17492)+E(f631(x17493,x17494,x17491),f631(x17493,x17494,x17492))
% 51.10/50.84 [1750]~E(x17501,x17502)+E(f781(x17501,x17503,x17504,x17505),f781(x17502,x17503,x17504,x17505))
% 51.10/50.84 [1751]~E(x17511,x17512)+E(f781(x17513,x17511,x17514,x17515),f781(x17513,x17512,x17514,x17515))
% 51.10/50.84 [1752]~E(x17521,x17522)+E(f781(x17523,x17524,x17521,x17525),f781(x17523,x17524,x17522,x17525))
% 51.10/50.84 [1753]~E(x17531,x17532)+E(f781(x17533,x17534,x17535,x17531),f781(x17533,x17534,x17535,x17532))
% 51.10/50.84 [1754]~E(x17541,x17542)+E(f537(x17541,x17543,x17544),f537(x17542,x17543,x17544))
% 51.10/50.84 [1755]~E(x17551,x17552)+E(f537(x17553,x17551,x17554),f537(x17553,x17552,x17554))
% 51.10/50.84 [1756]~E(x17561,x17562)+E(f537(x17563,x17564,x17561),f537(x17563,x17564,x17562))
% 51.10/50.84 [1757]~E(x17571,x17572)+E(f391(x17571),f391(x17572))
% 51.10/50.84 [1758]~E(x17581,x17582)+E(f43(x17581,x17583,x17584,x17585),f43(x17582,x17583,x17584,x17585))
% 51.10/50.84 [1759]~E(x17591,x17592)+E(f43(x17593,x17591,x17594,x17595),f43(x17593,x17592,x17594,x17595))
% 51.10/50.84 [1760]~E(x17601,x17602)+E(f43(x17603,x17604,x17601,x17605),f43(x17603,x17604,x17602,x17605))
% 51.10/50.84 [1761]~E(x17611,x17612)+E(f43(x17613,x17614,x17615,x17611),f43(x17613,x17614,x17615,x17612))
% 51.10/50.84 [1762]~E(x17621,x17622)+E(f387(x17621,x17623,x17624,x17625),f387(x17622,x17623,x17624,x17625))
% 51.10/50.84 [1763]~E(x17631,x17632)+E(f387(x17633,x17631,x17634,x17635),f387(x17633,x17632,x17634,x17635))
% 51.10/50.84 [1764]~E(x17641,x17642)+E(f387(x17643,x17644,x17641,x17645),f387(x17643,x17644,x17642,x17645))
% 51.10/50.84 [1765]~E(x17651,x17652)+E(f387(x17653,x17654,x17655,x17651),f387(x17653,x17654,x17655,x17652))
% 51.10/50.84 [1766]~E(x17661,x17662)+E(f415(x17661,x17663,x17664,x17665,x17666,x17667,x17668),f415(x17662,x17663,x17664,x17665,x17666,x17667,x17668))
% 51.10/50.84 [1767]~E(x17671,x17672)+E(f415(x17673,x17671,x17674,x17675,x17676,x17677,x17678),f415(x17673,x17672,x17674,x17675,x17676,x17677,x17678))
% 51.10/50.84 [1768]~E(x17681,x17682)+E(f415(x17683,x17684,x17681,x17685,x17686,x17687,x17688),f415(x17683,x17684,x17682,x17685,x17686,x17687,x17688))
% 51.10/50.84 [1769]~E(x17691,x17692)+E(f415(x17693,x17694,x17695,x17691,x17696,x17697,x17698),f415(x17693,x17694,x17695,x17692,x17696,x17697,x17698))
% 51.10/50.84 [1770]~E(x17701,x17702)+E(f415(x17703,x17704,x17705,x17706,x17701,x17707,x17708),f415(x17703,x17704,x17705,x17706,x17702,x17707,x17708))
% 51.10/50.84 [1771]~E(x17711,x17712)+E(f415(x17713,x17714,x17715,x17716,x17717,x17711,x17718),f415(x17713,x17714,x17715,x17716,x17717,x17712,x17718))
% 51.10/50.84 [1772]~E(x17721,x17722)+E(f415(x17723,x17724,x17725,x17726,x17727,x17728,x17721),f415(x17723,x17724,x17725,x17726,x17727,x17728,x17722))
% 51.10/50.84 [1773]~E(x17731,x17732)+E(f381(x17731,x17733),f381(x17732,x17733))
% 51.10/50.84 [1774]~E(x17741,x17742)+E(f381(x17743,x17741),f381(x17743,x17742))
% 51.10/50.84 [1775]~E(x17751,x17752)+E(f639(x17751,x17753,x17754),f639(x17752,x17753,x17754))
% 51.10/50.84 [1776]~E(x17761,x17762)+E(f639(x17763,x17761,x17764),f639(x17763,x17762,x17764))
% 51.10/50.84 [1777]~E(x17771,x17772)+E(f639(x17773,x17774,x17771),f639(x17773,x17774,x17772))
% 51.10/50.84 [1778]~E(x17781,x17782)+E(f225(x17781,x17783,x17784,x17785,x17786),f225(x17782,x17783,x17784,x17785,x17786))
% 51.10/50.84 [1779]~E(x17791,x17792)+E(f225(x17793,x17791,x17794,x17795,x17796),f225(x17793,x17792,x17794,x17795,x17796))
% 51.10/50.84 [1780]~E(x17801,x17802)+E(f225(x17803,x17804,x17801,x17805,x17806),f225(x17803,x17804,x17802,x17805,x17806))
% 51.10/50.84 [1781]~E(x17811,x17812)+E(f225(x17813,x17814,x17815,x17811,x17816),f225(x17813,x17814,x17815,x17812,x17816))
% 51.10/50.84 [1782]~E(x17821,x17822)+E(f225(x17823,x17824,x17825,x17826,x17821),f225(x17823,x17824,x17825,x17826,x17822))
% 51.10/50.84 [1783]~E(x17831,x17832)+E(f341(x17831,x17833),f341(x17832,x17833))
% 51.10/50.84 [1784]~E(x17841,x17842)+E(f341(x17843,x17841),f341(x17843,x17842))
% 51.10/50.84 [1785]~E(x17851,x17852)+E(f654(x17851,x17853,x17854,x17855,x17856),f654(x17852,x17853,x17854,x17855,x17856))
% 51.10/50.84 [1786]~E(x17861,x17862)+E(f654(x17863,x17861,x17864,x17865,x17866),f654(x17863,x17862,x17864,x17865,x17866))
% 51.10/50.84 [1787]~E(x17871,x17872)+E(f654(x17873,x17874,x17871,x17875,x17876),f654(x17873,x17874,x17872,x17875,x17876))
% 51.10/50.84 [1788]~E(x17881,x17882)+E(f654(x17883,x17884,x17885,x17881,x17886),f654(x17883,x17884,x17885,x17882,x17886))
% 51.10/50.84 [1789]~E(x17891,x17892)+E(f654(x17893,x17894,x17895,x17896,x17891),f654(x17893,x17894,x17895,x17896,x17892))
% 51.10/50.84 [1790]~E(x17901,x17902)+E(f126(x17901,x17903,x17904,x17905),f126(x17902,x17903,x17904,x17905))
% 51.10/50.84 [1791]~E(x17911,x17912)+E(f126(x17913,x17911,x17914,x17915),f126(x17913,x17912,x17914,x17915))
% 51.10/50.84 [1792]~E(x17921,x17922)+E(f126(x17923,x17924,x17921,x17925),f126(x17923,x17924,x17922,x17925))
% 51.10/50.84 [1793]~E(x17931,x17932)+E(f126(x17933,x17934,x17935,x17931),f126(x17933,x17934,x17935,x17932))
% 51.10/50.84 [1794]~E(x17941,x17942)+E(f541(x17941,x17943,x17944),f541(x17942,x17943,x17944))
% 51.10/50.84 [1795]~E(x17951,x17952)+E(f541(x17953,x17951,x17954),f541(x17953,x17952,x17954))
% 51.10/50.84 [1796]~E(x17961,x17962)+E(f541(x17963,x17964,x17961),f541(x17963,x17964,x17962))
% 51.10/50.84 [1797]~E(x17971,x17972)+E(f790(x17971,x17973,x17974),f790(x17972,x17973,x17974))
% 51.10/50.84 [1798]~E(x17981,x17982)+E(f790(x17983,x17981,x17984),f790(x17983,x17982,x17984))
% 51.10/50.84 [1799]~E(x17991,x17992)+E(f790(x17993,x17994,x17991),f790(x17993,x17994,x17992))
% 51.10/50.84 [1800]~E(x18001,x18002)+E(f473(x18001,x18003),f473(x18002,x18003))
% 51.10/50.84 [1801]~E(x18011,x18012)+E(f473(x18013,x18011),f473(x18013,x18012))
% 51.10/50.84 [1802]~E(x18021,x18022)+E(f242(x18021,x18023),f242(x18022,x18023))
% 51.10/50.84 [1803]~E(x18031,x18032)+E(f242(x18033,x18031),f242(x18033,x18032))
% 51.10/50.84 [1804]~E(x18041,x18042)+E(f518(x18041,x18043,x18044,x18045,x18046),f518(x18042,x18043,x18044,x18045,x18046))
% 51.10/50.84 [1805]~E(x18051,x18052)+E(f518(x18053,x18051,x18054,x18055,x18056),f518(x18053,x18052,x18054,x18055,x18056))
% 51.10/50.84 [1806]~E(x18061,x18062)+E(f518(x18063,x18064,x18061,x18065,x18066),f518(x18063,x18064,x18062,x18065,x18066))
% 51.10/50.84 [1807]~E(x18071,x18072)+E(f518(x18073,x18074,x18075,x18071,x18076),f518(x18073,x18074,x18075,x18072,x18076))
% 51.10/50.84 [1808]~E(x18081,x18082)+E(f518(x18083,x18084,x18085,x18086,x18081),f518(x18083,x18084,x18085,x18086,x18082))
% 51.10/50.84 [1809]~E(x18091,x18092)+E(f664(x18091,x18093,x18094),f664(x18092,x18093,x18094))
% 51.10/50.84 [1810]~E(x18101,x18102)+E(f664(x18103,x18101,x18104),f664(x18103,x18102,x18104))
% 51.10/50.84 [1811]~E(x18111,x18112)+E(f664(x18113,x18114,x18111),f664(x18113,x18114,x18112))
% 51.10/50.84 [1812]~E(x18121,x18122)+E(f280(x18121,x18123,x18124,x18125),f280(x18122,x18123,x18124,x18125))
% 51.10/50.84 [1813]~E(x18131,x18132)+E(f280(x18133,x18131,x18134,x18135),f280(x18133,x18132,x18134,x18135))
% 51.10/50.84 [1814]~E(x18141,x18142)+E(f280(x18143,x18144,x18141,x18145),f280(x18143,x18144,x18142,x18145))
% 51.10/50.84 [1815]~E(x18151,x18152)+E(f280(x18153,x18154,x18155,x18151),f280(x18153,x18154,x18155,x18152))
% 51.10/50.84 [1816]~E(x18161,x18162)+E(f717(x18161,x18163,x18164,x18165,x18166),f717(x18162,x18163,x18164,x18165,x18166))
% 51.10/50.84 [1817]~E(x18171,x18172)+E(f717(x18173,x18171,x18174,x18175,x18176),f717(x18173,x18172,x18174,x18175,x18176))
% 51.10/50.84 [1818]~E(x18181,x18182)+E(f717(x18183,x18184,x18181,x18185,x18186),f717(x18183,x18184,x18182,x18185,x18186))
% 51.10/50.84 [1819]~E(x18191,x18192)+E(f717(x18193,x18194,x18195,x18191,x18196),f717(x18193,x18194,x18195,x18192,x18196))
% 51.10/50.84 [1820]~E(x18201,x18202)+E(f717(x18203,x18204,x18205,x18206,x18201),f717(x18203,x18204,x18205,x18206,x18202))
% 51.10/50.84 [1821]~E(x18211,x18212)+E(f746(x18211),f746(x18212))
% 51.10/50.84 [1822]~E(x18221,x18222)+E(f402(x18221,x18223,x18224,x18225,x18226),f402(x18222,x18223,x18224,x18225,x18226))
% 51.10/50.84 [1823]~E(x18231,x18232)+E(f402(x18233,x18231,x18234,x18235,x18236),f402(x18233,x18232,x18234,x18235,x18236))
% 51.10/50.84 [1824]~E(x18241,x18242)+E(f402(x18243,x18244,x18241,x18245,x18246),f402(x18243,x18244,x18242,x18245,x18246))
% 51.10/50.84 [1825]~E(x18251,x18252)+E(f402(x18253,x18254,x18255,x18251,x18256),f402(x18253,x18254,x18255,x18252,x18256))
% 51.10/50.84 [1826]~E(x18261,x18262)+E(f402(x18263,x18264,x18265,x18266,x18261),f402(x18263,x18264,x18265,x18266,x18262))
% 51.10/50.84 [1827]~E(x18271,x18272)+E(f641(x18271,x18273,x18274,x18275,x18276),f641(x18272,x18273,x18274,x18275,x18276))
% 51.10/50.84 [1828]~E(x18281,x18282)+E(f641(x18283,x18281,x18284,x18285,x18286),f641(x18283,x18282,x18284,x18285,x18286))
% 51.10/50.84 [1829]~E(x18291,x18292)+E(f641(x18293,x18294,x18291,x18295,x18296),f641(x18293,x18294,x18292,x18295,x18296))
% 51.10/50.84 [1830]~E(x18301,x18302)+E(f641(x18303,x18304,x18305,x18301,x18306),f641(x18303,x18304,x18305,x18302,x18306))
% 51.10/50.84 [1831]~E(x18311,x18312)+E(f641(x18313,x18314,x18315,x18316,x18311),f641(x18313,x18314,x18315,x18316,x18312))
% 51.10/50.84 [1832]~E(x18321,x18322)+E(f700(x18321,x18323,x18324,x18325,x18326,x18327),f700(x18322,x18323,x18324,x18325,x18326,x18327))
% 51.10/50.84 [1833]~E(x18331,x18332)+E(f700(x18333,x18331,x18334,x18335,x18336,x18337),f700(x18333,x18332,x18334,x18335,x18336,x18337))
% 51.10/50.84 [1834]~E(x18341,x18342)+E(f700(x18343,x18344,x18341,x18345,x18346,x18347),f700(x18343,x18344,x18342,x18345,x18346,x18347))
% 51.10/50.84 [1835]~E(x18351,x18352)+E(f700(x18353,x18354,x18355,x18351,x18356,x18357),f700(x18353,x18354,x18355,x18352,x18356,x18357))
% 51.10/50.84 [1836]~E(x18361,x18362)+E(f700(x18363,x18364,x18365,x18366,x18361,x18367),f700(x18363,x18364,x18365,x18366,x18362,x18367))
% 51.10/50.84 [1837]~E(x18371,x18372)+E(f700(x18373,x18374,x18375,x18376,x18377,x18371),f700(x18373,x18374,x18375,x18376,x18377,x18372))
% 51.10/50.84 [1838]~E(x18381,x18382)+E(f701(x18381,x18383,x18384,x18385,x18386,x18387),f701(x18382,x18383,x18384,x18385,x18386,x18387))
% 51.10/50.84 [1839]~E(x18391,x18392)+E(f701(x18393,x18391,x18394,x18395,x18396,x18397),f701(x18393,x18392,x18394,x18395,x18396,x18397))
% 51.10/50.84 [1840]~E(x18401,x18402)+E(f701(x18403,x18404,x18401,x18405,x18406,x18407),f701(x18403,x18404,x18402,x18405,x18406,x18407))
% 51.10/50.84 [1841]~E(x18411,x18412)+E(f701(x18413,x18414,x18415,x18411,x18416,x18417),f701(x18413,x18414,x18415,x18412,x18416,x18417))
% 51.10/50.84 [1842]~E(x18421,x18422)+E(f701(x18423,x18424,x18425,x18426,x18421,x18427),f701(x18423,x18424,x18425,x18426,x18422,x18427))
% 51.10/50.84 [1843]~E(x18431,x18432)+E(f701(x18433,x18434,x18435,x18436,x18437,x18431),f701(x18433,x18434,x18435,x18436,x18437,x18432))
% 51.10/50.84 [1844]~E(x18441,x18442)+E(f585(x18441,x18443,x18444),f585(x18442,x18443,x18444))
% 51.10/50.84 [1845]~E(x18451,x18452)+E(f585(x18453,x18451,x18454),f585(x18453,x18452,x18454))
% 51.10/50.84 [1846]~E(x18461,x18462)+E(f585(x18463,x18464,x18461),f585(x18463,x18464,x18462))
% 51.10/50.84 [1847]~E(x18471,x18472)+E(f765(x18471,x18473,x18474),f765(x18472,x18473,x18474))
% 51.10/50.84 [1848]~E(x18481,x18482)+E(f765(x18483,x18481,x18484),f765(x18483,x18482,x18484))
% 51.10/50.84 [1849]~E(x18491,x18492)+E(f765(x18493,x18494,x18491),f765(x18493,x18494,x18492))
% 51.10/50.84 [1850]~E(x18501,x18502)+E(f447(x18501,x18503,x18504,x18505),f447(x18502,x18503,x18504,x18505))
% 51.10/50.84 [1851]~E(x18511,x18512)+E(f447(x18513,x18511,x18514,x18515),f447(x18513,x18512,x18514,x18515))
% 51.10/50.84 [1852]~E(x18521,x18522)+E(f447(x18523,x18524,x18521,x18525),f447(x18523,x18524,x18522,x18525))
% 51.10/50.84 [1853]~E(x18531,x18532)+E(f447(x18533,x18534,x18535,x18531),f447(x18533,x18534,x18535,x18532))
% 51.10/50.84 [1854]~E(x18541,x18542)+E(f688(x18541,x18543),f688(x18542,x18543))
% 51.10/50.84 [1855]~E(x18551,x18552)+E(f688(x18553,x18551),f688(x18553,x18552))
% 51.10/50.84 [1856]~E(x18561,x18562)+E(f646(x18561,x18563,x18564),f646(x18562,x18563,x18564))
% 51.10/50.84 [1857]~E(x18571,x18572)+E(f646(x18573,x18571,x18574),f646(x18573,x18572,x18574))
% 51.10/50.84 [1858]~E(x18581,x18582)+E(f646(x18583,x18584,x18581),f646(x18583,x18584,x18582))
% 51.10/50.84 [1859]~E(x18591,x18592)+E(f294(x18591,x18593,x18594),f294(x18592,x18593,x18594))
% 51.10/50.84 [1860]~E(x18601,x18602)+E(f294(x18603,x18601,x18604),f294(x18603,x18602,x18604))
% 51.10/50.84 [1861]~E(x18611,x18612)+E(f294(x18613,x18614,x18611),f294(x18613,x18614,x18612))
% 51.10/50.84 [1862]~E(x18621,x18622)+E(f649(x18621,x18623,x18624),f649(x18622,x18623,x18624))
% 51.10/50.84 [1863]~E(x18631,x18632)+E(f649(x18633,x18631,x18634),f649(x18633,x18632,x18634))
% 51.10/50.84 [1864]~E(x18641,x18642)+E(f649(x18643,x18644,x18641),f649(x18643,x18644,x18642))
% 51.10/50.84 [1865]~E(x18651,x18652)+E(f833(x18651,x18653,x18654,x18655,x18656),f833(x18652,x18653,x18654,x18655,x18656))
% 51.10/50.84 [1866]~E(x18661,x18662)+E(f833(x18663,x18661,x18664,x18665,x18666),f833(x18663,x18662,x18664,x18665,x18666))
% 51.10/50.84 [1867]~E(x18671,x18672)+E(f833(x18673,x18674,x18671,x18675,x18676),f833(x18673,x18674,x18672,x18675,x18676))
% 51.10/50.84 [1868]~E(x18681,x18682)+E(f833(x18683,x18684,x18685,x18681,x18686),f833(x18683,x18684,x18685,x18682,x18686))
% 51.10/50.84 [1869]~E(x18691,x18692)+E(f833(x18693,x18694,x18695,x18696,x18691),f833(x18693,x18694,x18695,x18696,x18692))
% 51.10/50.84 [1870]~E(x18701,x18702)+E(f489(x18701,x18703,x18704,x18705,x18706),f489(x18702,x18703,x18704,x18705,x18706))
% 51.10/50.84 [1871]~E(x18711,x18712)+E(f489(x18713,x18711,x18714,x18715,x18716),f489(x18713,x18712,x18714,x18715,x18716))
% 51.10/50.84 [1872]~E(x18721,x18722)+E(f489(x18723,x18724,x18721,x18725,x18726),f489(x18723,x18724,x18722,x18725,x18726))
% 51.10/50.84 [1873]~E(x18731,x18732)+E(f489(x18733,x18734,x18735,x18731,x18736),f489(x18733,x18734,x18735,x18732,x18736))
% 51.10/50.84 [1874]~E(x18741,x18742)+E(f489(x18743,x18744,x18745,x18746,x18741),f489(x18743,x18744,x18745,x18746,x18742))
% 51.10/50.84 [1875]~E(x18751,x18752)+E(f206(x18751),f206(x18752))
% 51.10/50.84 [1876]~E(x18761,x18762)+E(f678(x18761,x18763,x18764,x18765),f678(x18762,x18763,x18764,x18765))
% 51.10/50.84 [1877]~E(x18771,x18772)+E(f678(x18773,x18771,x18774,x18775),f678(x18773,x18772,x18774,x18775))
% 51.10/50.84 [1878]~E(x18781,x18782)+E(f678(x18783,x18784,x18781,x18785),f678(x18783,x18784,x18782,x18785))
% 51.10/50.84 [1879]~E(x18791,x18792)+E(f678(x18793,x18794,x18795,x18791),f678(x18793,x18794,x18795,x18792))
% 51.10/50.84 [1880]~E(x18801,x18802)+E(f670(x18801,x18803,x18804),f670(x18802,x18803,x18804))
% 51.10/50.84 [1881]~E(x18811,x18812)+E(f670(x18813,x18811,x18814),f670(x18813,x18812,x18814))
% 51.10/50.84 [1882]~E(x18821,x18822)+E(f670(x18823,x18824,x18821),f670(x18823,x18824,x18822))
% 51.10/50.84 [1883]~E(x18831,x18832)+E(f208(x18831,x18833,x18834,x18835),f208(x18832,x18833,x18834,x18835))
% 51.10/50.84 [1884]~E(x18841,x18842)+E(f208(x18843,x18841,x18844,x18845),f208(x18843,x18842,x18844,x18845))
% 51.10/50.84 [1885]~E(x18851,x18852)+E(f208(x18853,x18854,x18851,x18855),f208(x18853,x18854,x18852,x18855))
% 51.10/50.84 [1886]~E(x18861,x18862)+E(f208(x18863,x18864,x18865,x18861),f208(x18863,x18864,x18865,x18862))
% 51.10/50.84 [1887]~E(x18871,x18872)+E(f753(x18871,x18873,x18874,x18875,x18876),f753(x18872,x18873,x18874,x18875,x18876))
% 51.10/50.84 [1888]~E(x18881,x18882)+E(f753(x18883,x18881,x18884,x18885,x18886),f753(x18883,x18882,x18884,x18885,x18886))
% 51.10/50.84 [1889]~E(x18891,x18892)+E(f753(x18893,x18894,x18891,x18895,x18896),f753(x18893,x18894,x18892,x18895,x18896))
% 51.10/50.84 [1890]~E(x18901,x18902)+E(f753(x18903,x18904,x18905,x18901,x18906),f753(x18903,x18904,x18905,x18902,x18906))
% 51.10/50.84 [1891]~E(x18911,x18912)+E(f753(x18913,x18914,x18915,x18916,x18911),f753(x18913,x18914,x18915,x18916,x18912))
% 51.10/50.84 [1892]~E(x18921,x18922)+E(f778(x18921,x18923),f778(x18922,x18923))
% 51.10/50.84 [1893]~E(x18931,x18932)+E(f778(x18933,x18931),f778(x18933,x18932))
% 51.10/50.84 [1894]~E(x18941,x18942)+E(f525(x18941,x18943,x18944),f525(x18942,x18943,x18944))
% 51.10/50.84 [1895]~E(x18951,x18952)+E(f525(x18953,x18951,x18954),f525(x18953,x18952,x18954))
% 51.10/50.84 [1896]~E(x18961,x18962)+E(f525(x18963,x18964,x18961),f525(x18963,x18964,x18962))
% 51.10/50.84 [1897]~E(x18971,x18972)+E(f83(x18971,x18973,x18974,x18975,x18976),f83(x18972,x18973,x18974,x18975,x18976))
% 51.10/50.84 [1898]~E(x18981,x18982)+E(f83(x18983,x18981,x18984,x18985,x18986),f83(x18983,x18982,x18984,x18985,x18986))
% 51.10/50.84 [1899]~E(x18991,x18992)+E(f83(x18993,x18994,x18991,x18995,x18996),f83(x18993,x18994,x18992,x18995,x18996))
% 51.10/50.84 [1900]~E(x19001,x19002)+E(f83(x19003,x19004,x19005,x19001,x19006),f83(x19003,x19004,x19005,x19002,x19006))
% 51.10/50.84 [1901]~E(x19011,x19012)+E(f83(x19013,x19014,x19015,x19016,x19011),f83(x19013,x19014,x19015,x19016,x19012))
% 51.10/50.84 [1902]~E(x19021,x19022)+E(f129(x19021),f129(x19022))
% 51.10/50.84 [1903]~E(x19031,x19032)+E(f514(x19031,x19033,x19034,x19035),f514(x19032,x19033,x19034,x19035))
% 51.10/50.84 [1904]~E(x19041,x19042)+E(f514(x19043,x19041,x19044,x19045),f514(x19043,x19042,x19044,x19045))
% 51.10/50.84 [1905]~E(x19051,x19052)+E(f514(x19053,x19054,x19051,x19055),f514(x19053,x19054,x19052,x19055))
% 51.10/50.84 [1906]~E(x19061,x19062)+E(f514(x19063,x19064,x19065,x19061),f514(x19063,x19064,x19065,x19062))
% 51.10/50.84 [1907]~E(x19071,x19072)+E(f608(x19071,x19073,x19074,x19075,x19076,x19077),f608(x19072,x19073,x19074,x19075,x19076,x19077))
% 51.10/50.84 [1908]~E(x19081,x19082)+E(f608(x19083,x19081,x19084,x19085,x19086,x19087),f608(x19083,x19082,x19084,x19085,x19086,x19087))
% 51.10/50.84 [1909]~E(x19091,x19092)+E(f608(x19093,x19094,x19091,x19095,x19096,x19097),f608(x19093,x19094,x19092,x19095,x19096,x19097))
% 51.10/50.84 [1910]~E(x19101,x19102)+E(f608(x19103,x19104,x19105,x19101,x19106,x19107),f608(x19103,x19104,x19105,x19102,x19106,x19107))
% 51.10/50.84 [1911]~E(x19111,x19112)+E(f608(x19113,x19114,x19115,x19116,x19111,x19117),f608(x19113,x19114,x19115,x19116,x19112,x19117))
% 51.10/50.84 [1912]~E(x19121,x19122)+E(f608(x19123,x19124,x19125,x19126,x19127,x19121),f608(x19123,x19124,x19125,x19126,x19127,x19122))
% 51.10/50.84 [1913]~E(x19131,x19132)+E(f629(x19131,x19133,x19134,x19135,x19136,x19137),f629(x19132,x19133,x19134,x19135,x19136,x19137))
% 51.10/50.84 [1914]~E(x19141,x19142)+E(f629(x19143,x19141,x19144,x19145,x19146,x19147),f629(x19143,x19142,x19144,x19145,x19146,x19147))
% 51.10/50.84 [1915]~E(x19151,x19152)+E(f629(x19153,x19154,x19151,x19155,x19156,x19157),f629(x19153,x19154,x19152,x19155,x19156,x19157))
% 51.10/50.84 [1916]~E(x19161,x19162)+E(f629(x19163,x19164,x19165,x19161,x19166,x19167),f629(x19163,x19164,x19165,x19162,x19166,x19167))
% 51.10/50.84 [1917]~E(x19171,x19172)+E(f629(x19173,x19174,x19175,x19176,x19171,x19177),f629(x19173,x19174,x19175,x19176,x19172,x19177))
% 51.10/50.84 [1918]~E(x19181,x19182)+E(f629(x19183,x19184,x19185,x19186,x19187,x19181),f629(x19183,x19184,x19185,x19186,x19187,x19182))
% 51.10/50.84 [1919]~E(x19191,x19192)+E(f724(x19191,x19193,x19194),f724(x19192,x19193,x19194))
% 51.10/50.84 [1920]~E(x19201,x19202)+E(f724(x19203,x19201,x19204),f724(x19203,x19202,x19204))
% 51.10/50.84 [1921]~E(x19211,x19212)+E(f724(x19213,x19214,x19211),f724(x19213,x19214,x19212))
% 51.10/50.84 [1922]~E(x19221,x19222)+E(f281(x19221),f281(x19222))
% 51.10/50.84 [1923]~E(x19231,x19232)+E(f741(x19231,x19233,x19234,x19235),f741(x19232,x19233,x19234,x19235))
% 51.10/50.84 [1924]~E(x19241,x19242)+E(f741(x19243,x19241,x19244,x19245),f741(x19243,x19242,x19244,x19245))
% 51.10/50.84 [1925]~E(x19251,x19252)+E(f741(x19253,x19254,x19251,x19255),f741(x19253,x19254,x19252,x19255))
% 51.10/50.84 [1926]~E(x19261,x19262)+E(f741(x19263,x19264,x19265,x19261),f741(x19263,x19264,x19265,x19262))
% 51.10/50.84 [1927]~E(x19271,x19272)+E(f648(x19271,x19273,x19274),f648(x19272,x19273,x19274))
% 51.10/50.84 [1928]~E(x19281,x19282)+E(f648(x19283,x19281,x19284),f648(x19283,x19282,x19284))
% 51.10/50.84 [1929]~E(x19291,x19292)+E(f648(x19293,x19294,x19291),f648(x19293,x19294,x19292))
% 51.10/50.84 [1930]~E(x19301,x19302)+E(f102(x19301,x19303,x19304,x19305),f102(x19302,x19303,x19304,x19305))
% 51.10/50.84 [1931]~E(x19311,x19312)+E(f102(x19313,x19311,x19314,x19315),f102(x19313,x19312,x19314,x19315))
% 51.10/50.84 [1932]~E(x19321,x19322)+E(f102(x19323,x19324,x19321,x19325),f102(x19323,x19324,x19322,x19325))
% 51.10/50.84 [1933]~E(x19331,x19332)+E(f102(x19333,x19334,x19335,x19331),f102(x19333,x19334,x19335,x19332))
% 51.10/50.84 [1934]~E(x19341,x19342)+E(f478(x19341,x19343,x19344,x19345),f478(x19342,x19343,x19344,x19345))
% 51.10/50.84 [1935]~E(x19351,x19352)+E(f478(x19353,x19351,x19354,x19355),f478(x19353,x19352,x19354,x19355))
% 51.10/50.84 [1936]~E(x19361,x19362)+E(f478(x19363,x19364,x19361,x19365),f478(x19363,x19364,x19362,x19365))
% 51.10/50.84 [1937]~E(x19371,x19372)+E(f478(x19373,x19374,x19375,x19371),f478(x19373,x19374,x19375,x19372))
% 51.10/50.84 [1938]~E(x19381,x19382)+E(f834(x19381,x19383,x19384,x19385,x19386,x19387),f834(x19382,x19383,x19384,x19385,x19386,x19387))
% 51.10/50.84 [1939]~E(x19391,x19392)+E(f834(x19393,x19391,x19394,x19395,x19396,x19397),f834(x19393,x19392,x19394,x19395,x19396,x19397))
% 51.10/50.84 [1940]~E(x19401,x19402)+E(f834(x19403,x19404,x19401,x19405,x19406,x19407),f834(x19403,x19404,x19402,x19405,x19406,x19407))
% 51.10/50.84 [1941]~E(x19411,x19412)+E(f834(x19413,x19414,x19415,x19411,x19416,x19417),f834(x19413,x19414,x19415,x19412,x19416,x19417))
% 51.10/50.84 [1942]~E(x19421,x19422)+E(f834(x19423,x19424,x19425,x19426,x19421,x19427),f834(x19423,x19424,x19425,x19426,x19422,x19427))
% 51.10/50.84 [1943]~E(x19431,x19432)+E(f834(x19433,x19434,x19435,x19436,x19437,x19431),f834(x19433,x19434,x19435,x19436,x19437,x19432))
% 51.10/50.84 [1944]~E(x19441,x19442)+E(f449(x19441,x19443),f449(x19442,x19443))
% 51.10/50.84 [1945]~E(x19451,x19452)+E(f449(x19453,x19451),f449(x19453,x19452))
% 51.10/50.84 [1946]~E(x19461,x19462)+E(f224(x19461,x19463,x19464),f224(x19462,x19463,x19464))
% 51.10/50.84 [1947]~E(x19471,x19472)+E(f224(x19473,x19471,x19474),f224(x19473,x19472,x19474))
% 51.10/50.84 [1948]~E(x19481,x19482)+E(f224(x19483,x19484,x19481),f224(x19483,x19484,x19482))
% 51.10/50.84 [1949]~E(x19491,x19492)+E(f506(x19491,x19493,x19494,x19495,x19496),f506(x19492,x19493,x19494,x19495,x19496))
% 51.10/50.84 [1950]~E(x19501,x19502)+E(f506(x19503,x19501,x19504,x19505,x19506),f506(x19503,x19502,x19504,x19505,x19506))
% 51.10/50.84 [1951]~E(x19511,x19512)+E(f506(x19513,x19514,x19511,x19515,x19516),f506(x19513,x19514,x19512,x19515,x19516))
% 51.10/50.84 [1952]~E(x19521,x19522)+E(f506(x19523,x19524,x19525,x19521,x19526),f506(x19523,x19524,x19525,x19522,x19526))
% 51.10/50.84 [1953]~E(x19531,x19532)+E(f506(x19533,x19534,x19535,x19536,x19531),f506(x19533,x19534,x19535,x19536,x19532))
% 51.10/50.84 [1954]~E(x19541,x19542)+E(f742(x19541,x19543,x19544,x19545),f742(x19542,x19543,x19544,x19545))
% 51.10/50.84 [1955]~E(x19551,x19552)+E(f742(x19553,x19551,x19554,x19555),f742(x19553,x19552,x19554,x19555))
% 51.10/50.84 [1956]~E(x19561,x19562)+E(f742(x19563,x19564,x19561,x19565),f742(x19563,x19564,x19562,x19565))
% 51.10/50.84 [1957]~E(x19571,x19572)+E(f742(x19573,x19574,x19575,x19571),f742(x19573,x19574,x19575,x19572))
% 51.10/50.84 [1958]~E(x19581,x19582)+E(f363(x19581,x19583,x19584),f363(x19582,x19583,x19584))
% 51.10/50.84 [1959]~E(x19591,x19592)+E(f363(x19593,x19591,x19594),f363(x19593,x19592,x19594))
% 51.10/50.84 [1960]~E(x19601,x19602)+E(f363(x19603,x19604,x19601),f363(x19603,x19604,x19602))
% 51.10/50.84 [1961]~E(x19611,x19612)+E(f661(x19611,x19613,x19614),f661(x19612,x19613,x19614))
% 51.10/50.84 [1962]~E(x19621,x19622)+E(f661(x19623,x19621,x19624),f661(x19623,x19622,x19624))
% 51.10/50.84 [1963]~E(x19631,x19632)+E(f661(x19633,x19634,x19631),f661(x19633,x19634,x19632))
% 51.10/50.84 [1964]~E(x19641,x19642)+E(f743(x19641,x19643,x19644,x19645),f743(x19642,x19643,x19644,x19645))
% 51.10/50.84 [1965]~E(x19651,x19652)+E(f743(x19653,x19651,x19654,x19655),f743(x19653,x19652,x19654,x19655))
% 51.10/50.84 [1966]~E(x19661,x19662)+E(f743(x19663,x19664,x19661,x19665),f743(x19663,x19664,x19662,x19665))
% 51.10/50.84 [1967]~E(x19671,x19672)+E(f743(x19673,x19674,x19675,x19671),f743(x19673,x19674,x19675,x19672))
% 51.10/50.84 [1968]~E(x19681,x19682)+E(f622(x19681,x19683),f622(x19682,x19683))
% 51.10/50.84 [1969]~E(x19691,x19692)+E(f622(x19693,x19691),f622(x19693,x19692))
% 51.10/50.84 [1970]~E(x19701,x19702)+E(f427(x19701,x19703,x19704),f427(x19702,x19703,x19704))
% 51.10/50.84 [1971]~E(x19711,x19712)+E(f427(x19713,x19711,x19714),f427(x19713,x19712,x19714))
% 51.10/50.84 [1972]~E(x19721,x19722)+E(f427(x19723,x19724,x19721),f427(x19723,x19724,x19722))
% 51.10/50.84 [1973]~E(x19731,x19732)+E(f491(x19731,x19733,x19734,x19735,x19736),f491(x19732,x19733,x19734,x19735,x19736))
% 51.10/50.84 [1974]~E(x19741,x19742)+E(f491(x19743,x19741,x19744,x19745,x19746),f491(x19743,x19742,x19744,x19745,x19746))
% 51.10/50.84 [1975]~E(x19751,x19752)+E(f491(x19753,x19754,x19751,x19755,x19756),f491(x19753,x19754,x19752,x19755,x19756))
% 51.10/50.84 [1976]~E(x19761,x19762)+E(f491(x19763,x19764,x19765,x19761,x19766),f491(x19763,x19764,x19765,x19762,x19766))
% 51.10/50.84 [1977]~E(x19771,x19772)+E(f491(x19773,x19774,x19775,x19776,x19771),f491(x19773,x19774,x19775,x19776,x19772))
% 51.10/50.84 [1978]~E(x19781,x19782)+E(f388(x19781,x19783),f388(x19782,x19783))
% 51.10/50.84 [1979]~E(x19791,x19792)+E(f388(x19793,x19791),f388(x19793,x19792))
% 51.10/50.84 [1980]~E(x19801,x19802)+E(f204(x19801),f204(x19802))
% 51.10/50.84 [1981]~E(x19811,x19812)+E(f687(x19811,x19813,x19814,x19815,x19816),f687(x19812,x19813,x19814,x19815,x19816))
% 51.10/50.84 [1982]~E(x19821,x19822)+E(f687(x19823,x19821,x19824,x19825,x19826),f687(x19823,x19822,x19824,x19825,x19826))
% 51.10/50.84 [1983]~E(x19831,x19832)+E(f687(x19833,x19834,x19831,x19835,x19836),f687(x19833,x19834,x19832,x19835,x19836))
% 51.10/50.84 [1984]~E(x19841,x19842)+E(f687(x19843,x19844,x19845,x19841,x19846),f687(x19843,x19844,x19845,x19842,x19846))
% 51.10/50.84 [1985]~E(x19851,x19852)+E(f687(x19853,x19854,x19855,x19856,x19851),f687(x19853,x19854,x19855,x19856,x19852))
% 51.10/50.84 [1986]~E(x19861,x19862)+E(f536(x19861,x19863,x19864,x19865),f536(x19862,x19863,x19864,x19865))
% 51.10/50.84 [1987]~E(x19871,x19872)+E(f536(x19873,x19871,x19874,x19875),f536(x19873,x19872,x19874,x19875))
% 51.10/50.84 [1988]~E(x19881,x19882)+E(f536(x19883,x19884,x19881,x19885),f536(x19883,x19884,x19882,x19885))
% 51.10/50.84 [1989]~E(x19891,x19892)+E(f536(x19893,x19894,x19895,x19891),f536(x19893,x19894,x19895,x19892))
% 51.10/50.84 [1990]~E(x19901,x19902)+E(f806(x19901,x19903,x19904),f806(x19902,x19903,x19904))
% 51.10/50.84 [1991]~E(x19911,x19912)+E(f806(x19913,x19911,x19914),f806(x19913,x19912,x19914))
% 51.10/50.84 [1992]~E(x19921,x19922)+E(f806(x19923,x19924,x19921),f806(x19923,x19924,x19922))
% 51.10/50.84 [1993]~E(x19931,x19932)+E(f679(x19931,x19933,x19934,x19935),f679(x19932,x19933,x19934,x19935))
% 51.10/50.84 [1994]~E(x19941,x19942)+E(f679(x19943,x19941,x19944,x19945),f679(x19943,x19942,x19944,x19945))
% 51.10/50.84 [1995]~E(x19951,x19952)+E(f679(x19953,x19954,x19951,x19955),f679(x19953,x19954,x19952,x19955))
% 51.10/50.84 [1996]~E(x19961,x19962)+E(f679(x19963,x19964,x19965,x19961),f679(x19963,x19964,x19965,x19962))
% 51.10/50.84 [1997]~E(x19971,x19972)+E(f503(x19971,x19973,x19974),f503(x19972,x19973,x19974))
% 51.10/50.84 [1998]~E(x19981,x19982)+E(f503(x19983,x19981,x19984),f503(x19983,x19982,x19984))
% 51.10/50.84 [1999]~E(x19991,x19992)+E(f503(x19993,x19994,x19991),f503(x19993,x19994,x19992))
% 51.10/50.84 [2000]~E(x20001,x20002)+E(f439(x20001,x20003),f439(x20002,x20003))
% 51.10/50.84 [2001]~E(x20011,x20012)+E(f439(x20013,x20011),f439(x20013,x20012))
% 51.10/50.84 [2002]~E(x20021,x20022)+E(f457(x20021,x20023,x20024,x20025),f457(x20022,x20023,x20024,x20025))
% 51.10/50.84 [2003]~E(x20031,x20032)+E(f457(x20033,x20031,x20034,x20035),f457(x20033,x20032,x20034,x20035))
% 51.10/50.84 [2004]~E(x20041,x20042)+E(f457(x20043,x20044,x20041,x20045),f457(x20043,x20044,x20042,x20045))
% 51.10/50.84 [2005]~E(x20051,x20052)+E(f457(x20053,x20054,x20055,x20051),f457(x20053,x20054,x20055,x20052))
% 51.10/50.84 [2006]~E(x20061,x20062)+E(f591(x20061,x20063),f591(x20062,x20063))
% 51.10/50.84 [2007]~E(x20071,x20072)+E(f591(x20073,x20071),f591(x20073,x20072))
% 51.10/50.84 [2008]~E(x20081,x20082)+E(f592(x20081,x20083),f592(x20082,x20083))
% 51.10/50.84 [2009]~E(x20091,x20092)+E(f592(x20093,x20091),f592(x20093,x20092))
% 51.10/50.84 [2010]~E(x20101,x20102)+E(f824(x20101,x20103,x20104),f824(x20102,x20103,x20104))
% 51.10/50.84 [2011]~E(x20111,x20112)+E(f824(x20113,x20111,x20114),f824(x20113,x20112,x20114))
% 51.10/50.84 [2012]~E(x20121,x20122)+E(f824(x20123,x20124,x20121),f824(x20123,x20124,x20122))
% 51.10/50.84 [2013]~E(x20131,x20132)+E(f740(x20131,x20133,x20134,x20135,x20136),f740(x20132,x20133,x20134,x20135,x20136))
% 51.10/50.84 [2014]~E(x20141,x20142)+E(f740(x20143,x20141,x20144,x20145,x20146),f740(x20143,x20142,x20144,x20145,x20146))
% 51.10/50.84 [2015]~E(x20151,x20152)+E(f740(x20153,x20154,x20151,x20155,x20156),f740(x20153,x20154,x20152,x20155,x20156))
% 51.10/50.84 [2016]~E(x20161,x20162)+E(f740(x20163,x20164,x20165,x20161,x20166),f740(x20163,x20164,x20165,x20162,x20166))
% 51.10/50.84 [2017]~E(x20171,x20172)+E(f740(x20173,x20174,x20175,x20176,x20171),f740(x20173,x20174,x20175,x20176,x20172))
% 51.10/50.84 [2018]~E(x20181,x20182)+E(f706(x20181,x20183,x20184,x20185,x20186),f706(x20182,x20183,x20184,x20185,x20186))
% 51.10/50.84 [2019]~E(x20191,x20192)+E(f706(x20193,x20191,x20194,x20195,x20196),f706(x20193,x20192,x20194,x20195,x20196))
% 51.10/50.84 [2020]~E(x20201,x20202)+E(f706(x20203,x20204,x20201,x20205,x20206),f706(x20203,x20204,x20202,x20205,x20206))
% 51.10/50.84 [2021]~E(x20211,x20212)+E(f706(x20213,x20214,x20215,x20211,x20216),f706(x20213,x20214,x20215,x20212,x20216))
% 51.10/50.84 [2022]~E(x20221,x20222)+E(f706(x20223,x20224,x20225,x20226,x20221),f706(x20223,x20224,x20225,x20226,x20222))
% 51.10/50.84 [2023]~E(x20231,x20232)+E(f342(x20231,x20233),f342(x20232,x20233))
% 51.10/50.84 [2024]~E(x20241,x20242)+E(f342(x20243,x20241),f342(x20243,x20242))
% 51.10/50.84 [2025]~E(x20251,x20252)+E(f692(x20251,x20253),f692(x20252,x20253))
% 51.10/50.84 [2026]~E(x20261,x20262)+E(f692(x20263,x20261),f692(x20263,x20262))
% 51.10/50.84 [2027]~E(x20271,x20272)+E(f815(x20271,x20273,x20274),f815(x20272,x20273,x20274))
% 51.10/50.84 [2028]~E(x20281,x20282)+E(f815(x20283,x20281,x20284),f815(x20283,x20282,x20284))
% 51.10/50.84 [2029]~E(x20291,x20292)+E(f815(x20293,x20294,x20291),f815(x20293,x20294,x20292))
% 51.10/50.84 [2030]~E(x20301,x20302)+E(f562(x20301,x20303,x20304,x20305,x20306),f562(x20302,x20303,x20304,x20305,x20306))
% 51.10/50.84 [2031]~E(x20311,x20312)+E(f562(x20313,x20311,x20314,x20315,x20316),f562(x20313,x20312,x20314,x20315,x20316))
% 51.10/50.84 [2032]~E(x20321,x20322)+E(f562(x20323,x20324,x20321,x20325,x20326),f562(x20323,x20324,x20322,x20325,x20326))
% 51.10/50.84 [2033]~E(x20331,x20332)+E(f562(x20333,x20334,x20335,x20331,x20336),f562(x20333,x20334,x20335,x20332,x20336))
% 51.10/50.84 [2034]~E(x20341,x20342)+E(f562(x20343,x20344,x20345,x20346,x20341),f562(x20343,x20344,x20345,x20346,x20342))
% 51.10/50.84 [2035]~E(x20351,x20352)+E(f448(x20351),f448(x20352))
% 51.10/50.84 [2036]~E(x20361,x20362)+E(f230(x20361,x20363,x20364,x20365),f230(x20362,x20363,x20364,x20365))
% 51.10/50.84 [2037]~E(x20371,x20372)+E(f230(x20373,x20371,x20374,x20375),f230(x20373,x20372,x20374,x20375))
% 51.10/50.84 [2038]~E(x20381,x20382)+E(f230(x20383,x20384,x20381,x20385),f230(x20383,x20384,x20382,x20385))
% 51.10/50.84 [2039]~E(x20391,x20392)+E(f230(x20393,x20394,x20395,x20391),f230(x20393,x20394,x20395,x20392))
% 51.10/50.84 [2040]~E(x20401,x20402)+E(f434(x20401,x20403,x20404),f434(x20402,x20403,x20404))
% 51.10/50.84 [2041]~E(x20411,x20412)+E(f434(x20413,x20411,x20414),f434(x20413,x20412,x20414))
% 51.10/50.84 [2042]~E(x20421,x20422)+E(f434(x20423,x20424,x20421),f434(x20423,x20424,x20422))
% 51.10/50.84 [2043]~E(x20431,x20432)+E(f401(x20431,x20433,x20434,x20435),f401(x20432,x20433,x20434,x20435))
% 51.10/50.84 [2044]~E(x20441,x20442)+E(f401(x20443,x20441,x20444,x20445),f401(x20443,x20442,x20444,x20445))
% 51.10/50.84 [2045]~E(x20451,x20452)+E(f401(x20453,x20454,x20451,x20455),f401(x20453,x20454,x20452,x20455))
% 51.10/50.84 [2046]~E(x20461,x20462)+E(f401(x20463,x20464,x20465,x20461),f401(x20463,x20464,x20465,x20462))
% 51.10/50.84 [2047]~E(x20471,x20472)+E(f580(x20471,x20473),f580(x20472,x20473))
% 51.10/50.84 [2048]~E(x20481,x20482)+E(f580(x20483,x20481),f580(x20483,x20482))
% 51.10/50.84 [2049]~E(x20491,x20492)+E(f610(x20491,x20493,x20494,x20495),f610(x20492,x20493,x20494,x20495))
% 51.10/50.84 [2050]~E(x20501,x20502)+E(f610(x20503,x20501,x20504,x20505),f610(x20503,x20502,x20504,x20505))
% 51.10/50.84 [2051]~E(x20511,x20512)+E(f610(x20513,x20514,x20511,x20515),f610(x20513,x20514,x20512,x20515))
% 51.10/50.84 [2052]~E(x20521,x20522)+E(f610(x20523,x20524,x20525,x20521),f610(x20523,x20524,x20525,x20522))
% 51.10/50.84 [2053]~E(x20531,x20532)+E(f638(x20531,x20533,x20534,x20535),f638(x20532,x20533,x20534,x20535))
% 51.10/50.84 [2054]~E(x20541,x20542)+E(f638(x20543,x20541,x20544,x20545),f638(x20543,x20542,x20544,x20545))
% 51.10/50.84 [2055]~E(x20551,x20552)+E(f638(x20553,x20554,x20551,x20555),f638(x20553,x20554,x20552,x20555))
% 51.10/50.84 [2056]~E(x20561,x20562)+E(f638(x20563,x20564,x20565,x20561),f638(x20563,x20564,x20565,x20562))
% 51.10/50.84 [2057]~E(x20571,x20572)+E(f220(x20571,x20573),f220(x20572,x20573))
% 51.10/50.84 [2058]~E(x20581,x20582)+E(f220(x20583,x20581),f220(x20583,x20582))
% 51.10/50.84 [2059]~E(x20591,x20592)+E(f544(x20591,x20593,x20594,x20595,x20596,x20597),f544(x20592,x20593,x20594,x20595,x20596,x20597))
% 51.10/50.84 [2060]~E(x20601,x20602)+E(f544(x20603,x20601,x20604,x20605,x20606,x20607),f544(x20603,x20602,x20604,x20605,x20606,x20607))
% 51.10/50.84 [2061]~E(x20611,x20612)+E(f544(x20613,x20614,x20611,x20615,x20616,x20617),f544(x20613,x20614,x20612,x20615,x20616,x20617))
% 51.10/50.84 [2062]~E(x20621,x20622)+E(f544(x20623,x20624,x20625,x20621,x20626,x20627),f544(x20623,x20624,x20625,x20622,x20626,x20627))
% 51.10/50.84 [2063]~E(x20631,x20632)+E(f544(x20633,x20634,x20635,x20636,x20631,x20637),f544(x20633,x20634,x20635,x20636,x20632,x20637))
% 51.10/50.84 [2064]~E(x20641,x20642)+E(f544(x20643,x20644,x20645,x20646,x20647,x20641),f544(x20643,x20644,x20645,x20646,x20647,x20642))
% 51.10/50.84 [2065]~E(x20651,x20652)+E(f704(x20651,x20653,x20654,x20655),f704(x20652,x20653,x20654,x20655))
% 51.10/50.84 [2066]~E(x20661,x20662)+E(f704(x20663,x20661,x20664,x20665),f704(x20663,x20662,x20664,x20665))
% 51.10/50.84 [2067]~E(x20671,x20672)+E(f704(x20673,x20674,x20671,x20675),f704(x20673,x20674,x20672,x20675))
% 51.10/50.84 [2068]~E(x20681,x20682)+E(f704(x20683,x20684,x20685,x20681),f704(x20683,x20684,x20685,x20682))
% 51.10/50.84 [2069]~E(x20691,x20692)+E(f836(x20691,x20693,x20694,x20695,x20696,x20697),f836(x20692,x20693,x20694,x20695,x20696,x20697))
% 51.10/50.84 [2070]~E(x20701,x20702)+E(f836(x20703,x20701,x20704,x20705,x20706,x20707),f836(x20703,x20702,x20704,x20705,x20706,x20707))
% 51.10/50.84 [2071]~E(x20711,x20712)+E(f836(x20713,x20714,x20711,x20715,x20716,x20717),f836(x20713,x20714,x20712,x20715,x20716,x20717))
% 51.10/50.84 [2072]~E(x20721,x20722)+E(f836(x20723,x20724,x20725,x20721,x20726,x20727),f836(x20723,x20724,x20725,x20722,x20726,x20727))
% 51.10/50.84 [2073]~E(x20731,x20732)+E(f836(x20733,x20734,x20735,x20736,x20731,x20737),f836(x20733,x20734,x20735,x20736,x20732,x20737))
% 51.10/50.84 [2074]~E(x20741,x20742)+E(f836(x20743,x20744,x20745,x20746,x20747,x20741),f836(x20743,x20744,x20745,x20746,x20747,x20742))
% 51.10/50.84 [2075]~E(x20751,x20752)+E(f718(x20751,x20753,x20754,x20755,x20756),f718(x20752,x20753,x20754,x20755,x20756))
% 51.10/50.84 [2076]~E(x20761,x20762)+E(f718(x20763,x20761,x20764,x20765,x20766),f718(x20763,x20762,x20764,x20765,x20766))
% 51.10/50.84 [2077]~E(x20771,x20772)+E(f718(x20773,x20774,x20771,x20775,x20776),f718(x20773,x20774,x20772,x20775,x20776))
% 51.10/50.84 [2078]~E(x20781,x20782)+E(f718(x20783,x20784,x20785,x20781,x20786),f718(x20783,x20784,x20785,x20782,x20786))
% 51.10/50.84 [2079]~E(x20791,x20792)+E(f718(x20793,x20794,x20795,x20796,x20791),f718(x20793,x20794,x20795,x20796,x20792))
% 51.10/50.84 [2080]~E(x20801,x20802)+E(f642(x20801,x20803,x20804,x20805,x20806),f642(x20802,x20803,x20804,x20805,x20806))
% 51.10/50.84 [2081]~E(x20811,x20812)+E(f642(x20813,x20811,x20814,x20815,x20816),f642(x20813,x20812,x20814,x20815,x20816))
% 51.10/50.84 [2082]~E(x20821,x20822)+E(f642(x20823,x20824,x20821,x20825,x20826),f642(x20823,x20824,x20822,x20825,x20826))
% 51.10/50.84 [2083]~E(x20831,x20832)+E(f642(x20833,x20834,x20835,x20831,x20836),f642(x20833,x20834,x20835,x20832,x20836))
% 51.10/50.84 [2084]~E(x20841,x20842)+E(f642(x20843,x20844,x20845,x20846,x20841),f642(x20843,x20844,x20845,x20846,x20842))
% 51.10/50.84 [2085]~E(x20851,x20852)+E(f796(x20851,x20853,x20854),f796(x20852,x20853,x20854))
% 51.10/50.84 [2086]~E(x20861,x20862)+E(f796(x20863,x20861,x20864),f796(x20863,x20862,x20864))
% 51.10/50.84 [2087]~E(x20871,x20872)+E(f796(x20873,x20874,x20871),f796(x20873,x20874,x20872))
% 51.10/50.84 [2088]~E(x20881,x20882)+E(f396(x20881,x20883,x20884),f396(x20882,x20883,x20884))
% 51.10/50.84 [2089]~E(x20891,x20892)+E(f396(x20893,x20891,x20894),f396(x20893,x20892,x20894))
% 51.10/50.84 [2090]~E(x20901,x20902)+E(f396(x20903,x20904,x20901),f396(x20903,x20904,x20902))
% 51.10/50.84 [2091]~E(x20911,x20912)+E(f573(x20911,x20913,x20914,x20915),f573(x20912,x20913,x20914,x20915))
% 51.10/50.84 [2092]~E(x20921,x20922)+E(f573(x20923,x20921,x20924,x20925),f573(x20923,x20922,x20924,x20925))
% 51.10/50.84 [2093]~E(x20931,x20932)+E(f573(x20933,x20934,x20931,x20935),f573(x20933,x20934,x20932,x20935))
% 51.10/50.84 [2094]~E(x20941,x20942)+E(f573(x20943,x20944,x20945,x20941),f573(x20943,x20944,x20945,x20942))
% 51.10/50.84 [2095]~E(x20951,x20952)+E(f818(x20951,x20953,x20954,x20955,x20956),f818(x20952,x20953,x20954,x20955,x20956))
% 51.10/50.84 [2096]~E(x20961,x20962)+E(f818(x20963,x20961,x20964,x20965,x20966),f818(x20963,x20962,x20964,x20965,x20966))
% 51.10/50.84 [2097]~E(x20971,x20972)+E(f818(x20973,x20974,x20971,x20975,x20976),f818(x20973,x20974,x20972,x20975,x20976))
% 51.10/50.84 [2098]~E(x20981,x20982)+E(f818(x20983,x20984,x20985,x20981,x20986),f818(x20983,x20984,x20985,x20982,x20986))
% 51.10/50.84 [2099]~E(x20991,x20992)+E(f818(x20993,x20994,x20995,x20996,x20991),f818(x20993,x20994,x20995,x20996,x20992))
% 51.10/50.84 [2100]~E(x21001,x21002)+E(f588(x21001,x21003,x21004,x21005),f588(x21002,x21003,x21004,x21005))
% 51.10/50.84 [2101]~E(x21011,x21012)+E(f588(x21013,x21011,x21014,x21015),f588(x21013,x21012,x21014,x21015))
% 51.10/50.84 [2102]~E(x21021,x21022)+E(f588(x21023,x21024,x21021,x21025),f588(x21023,x21024,x21022,x21025))
% 51.10/50.84 [2103]~E(x21031,x21032)+E(f588(x21033,x21034,x21035,x21031),f588(x21033,x21034,x21035,x21032))
% 51.10/50.84 [2104]~E(x21041,x21042)+E(f559(x21041,x21043),f559(x21042,x21043))
% 51.10/50.84 [2105]~E(x21051,x21052)+E(f559(x21053,x21051),f559(x21053,x21052))
% 51.10/50.84 [2106]~E(x21061,x21062)+E(f350(x21061,x21063,x21064,x21065),f350(x21062,x21063,x21064,x21065))
% 51.10/50.84 [2107]~E(x21071,x21072)+E(f350(x21073,x21071,x21074,x21075),f350(x21073,x21072,x21074,x21075))
% 51.10/50.84 [2108]~E(x21081,x21082)+E(f350(x21083,x21084,x21081,x21085),f350(x21083,x21084,x21082,x21085))
% 51.10/50.84 [2109]~E(x21091,x21092)+E(f350(x21093,x21094,x21095,x21091),f350(x21093,x21094,x21095,x21092))
% 51.10/50.84 [2110]~E(x21101,x21102)+E(f202(x21101),f202(x21102))
% 51.10/50.84 [2111]~E(x21111,x21112)+E(f577(x21111,x21113,x21114,x21115),f577(x21112,x21113,x21114,x21115))
% 51.10/50.84 [2112]~E(x21121,x21122)+E(f577(x21123,x21121,x21124,x21125),f577(x21123,x21122,x21124,x21125))
% 51.10/50.84 [2113]~E(x21131,x21132)+E(f577(x21133,x21134,x21131,x21135),f577(x21133,x21134,x21132,x21135))
% 51.10/50.84 [2114]~E(x21141,x21142)+E(f577(x21143,x21144,x21145,x21141),f577(x21143,x21144,x21145,x21142))
% 51.10/50.84 [2115]~E(x21151,x21152)+E(f798(x21151,x21153,x21154),f798(x21152,x21153,x21154))
% 51.10/50.84 [2116]~E(x21161,x21162)+E(f798(x21163,x21161,x21164),f798(x21163,x21162,x21164))
% 51.10/50.84 [2117]~E(x21171,x21172)+E(f798(x21173,x21174,x21171),f798(x21173,x21174,x21172))
% 51.10/50.84 [2118]~E(x21181,x21182)+E(f336(x21181),f336(x21182))
% 51.10/50.84 [2119]~E(x21191,x21192)+E(f832(x21191,x21193,x21194,x21195,x21196),f832(x21192,x21193,x21194,x21195,x21196))
% 51.10/50.84 [2120]~E(x21201,x21202)+E(f832(x21203,x21201,x21204,x21205,x21206),f832(x21203,x21202,x21204,x21205,x21206))
% 51.10/50.84 [2121]~E(x21211,x21212)+E(f832(x21213,x21214,x21211,x21215,x21216),f832(x21213,x21214,x21212,x21215,x21216))
% 51.10/50.84 [2122]~E(x21221,x21222)+E(f832(x21223,x21224,x21225,x21221,x21226),f832(x21223,x21224,x21225,x21222,x21226))
% 51.10/50.84 [2123]~E(x21231,x21232)+E(f832(x21233,x21234,x21235,x21236,x21231),f832(x21233,x21234,x21235,x21236,x21232))
% 51.10/50.84 [2124]~E(x21241,x21242)+E(f458(x21241,x21243,x21244,x21245),f458(x21242,x21243,x21244,x21245))
% 51.10/50.84 [2125]~E(x21251,x21252)+E(f458(x21253,x21251,x21254,x21255),f458(x21253,x21252,x21254,x21255))
% 51.10/50.84 [2126]~E(x21261,x21262)+E(f458(x21263,x21264,x21261,x21265),f458(x21263,x21264,x21262,x21265))
% 51.10/50.84 [2127]~E(x21271,x21272)+E(f458(x21273,x21274,x21275,x21271),f458(x21273,x21274,x21275,x21272))
% 51.10/50.84 [2128]~E(x21281,x21282)+E(f390(x21281,x21283),f390(x21282,x21283))
% 51.10/50.84 [2129]~E(x21291,x21292)+E(f390(x21293,x21291),f390(x21293,x21292))
% 51.10/50.84 [2130]~E(x21301,x21302)+E(f477(x21301,x21303,x21304,x21305),f477(x21302,x21303,x21304,x21305))
% 51.10/50.84 [2131]~E(x21311,x21312)+E(f477(x21313,x21311,x21314,x21315),f477(x21313,x21312,x21314,x21315))
% 51.10/50.84 [2132]~E(x21321,x21322)+E(f477(x21323,x21324,x21321,x21325),f477(x21323,x21324,x21322,x21325))
% 51.10/50.84 [2133]~E(x21331,x21332)+E(f477(x21333,x21334,x21335,x21331),f477(x21333,x21334,x21335,x21332))
% 51.10/50.84 [2134]~E(x21341,x21342)+E(f443(x21341,x21343,x21344,x21345),f443(x21342,x21343,x21344,x21345))
% 51.10/50.84 [2135]~E(x21351,x21352)+E(f443(x21353,x21351,x21354,x21355),f443(x21353,x21352,x21354,x21355))
% 51.10/50.84 [2136]~E(x21361,x21362)+E(f443(x21363,x21364,x21361,x21365),f443(x21363,x21364,x21362,x21365))
% 51.10/50.84 [2137]~E(x21371,x21372)+E(f443(x21373,x21374,x21375,x21371),f443(x21373,x21374,x21375,x21372))
% 51.10/50.84 [2138]~E(x21381,x21382)+E(f484(x21381,x21383,x21384,x21385,x21386),f484(x21382,x21383,x21384,x21385,x21386))
% 51.10/50.84 [2139]~E(x21391,x21392)+E(f484(x21393,x21391,x21394,x21395,x21396),f484(x21393,x21392,x21394,x21395,x21396))
% 51.10/50.84 [2140]~E(x21401,x21402)+E(f484(x21403,x21404,x21401,x21405,x21406),f484(x21403,x21404,x21402,x21405,x21406))
% 51.10/50.84 [2141]~E(x21411,x21412)+E(f484(x21413,x21414,x21415,x21411,x21416),f484(x21413,x21414,x21415,x21412,x21416))
% 51.10/50.84 [2142]~E(x21421,x21422)+E(f484(x21423,x21424,x21425,x21426,x21421),f484(x21423,x21424,x21425,x21426,x21422))
% 51.10/50.84 [2143]~E(x21431,x21432)+E(f578(x21431,x21433,x21434,x21435),f578(x21432,x21433,x21434,x21435))
% 51.10/50.84 [2144]~E(x21441,x21442)+E(f578(x21443,x21441,x21444,x21445),f578(x21443,x21442,x21444,x21445))
% 51.10/50.84 [2145]~E(x21451,x21452)+E(f578(x21453,x21454,x21451,x21455),f578(x21453,x21454,x21452,x21455))
% 51.10/50.84 [2146]~E(x21461,x21462)+E(f578(x21463,x21464,x21465,x21461),f578(x21463,x21464,x21465,x21462))
% 51.10/50.84 [2147]~E(x21471,x21472)+E(f609(x21471,x21473,x21474,x21475,x21476,x21477),f609(x21472,x21473,x21474,x21475,x21476,x21477))
% 51.10/50.84 [2148]~E(x21481,x21482)+E(f609(x21483,x21481,x21484,x21485,x21486,x21487),f609(x21483,x21482,x21484,x21485,x21486,x21487))
% 51.10/50.84 [2149]~E(x21491,x21492)+E(f609(x21493,x21494,x21491,x21495,x21496,x21497),f609(x21493,x21494,x21492,x21495,x21496,x21497))
% 51.10/50.84 [2150]~E(x21501,x21502)+E(f609(x21503,x21504,x21505,x21501,x21506,x21507),f609(x21503,x21504,x21505,x21502,x21506,x21507))
% 51.10/50.84 [2151]~E(x21511,x21512)+E(f609(x21513,x21514,x21515,x21516,x21511,x21517),f609(x21513,x21514,x21515,x21516,x21512,x21517))
% 51.10/50.84 [2152]~E(x21521,x21522)+E(f609(x21523,x21524,x21525,x21526,x21527,x21521),f609(x21523,x21524,x21525,x21526,x21527,x21522))
% 51.10/50.84 [2153]~E(x21531,x21532)+E(f44(x21531,x21533,x21534,x21535),f44(x21532,x21533,x21534,x21535))
% 51.10/50.84 [2154]~E(x21541,x21542)+E(f44(x21543,x21541,x21544,x21545),f44(x21543,x21542,x21544,x21545))
% 51.10/50.84 [2155]~E(x21551,x21552)+E(f44(x21553,x21554,x21551,x21555),f44(x21553,x21554,x21552,x21555))
% 51.10/50.84 [2156]~E(x21561,x21562)+E(f44(x21563,x21564,x21565,x21561),f44(x21563,x21564,x21565,x21562))
% 51.10/50.84 [2157]~E(x21571,x21572)+E(f665(x21571,x21573,x21574,x21575),f665(x21572,x21573,x21574,x21575))
% 51.10/50.84 [2158]~E(x21581,x21582)+E(f665(x21583,x21581,x21584,x21585),f665(x21583,x21582,x21584,x21585))
% 51.10/50.84 [2159]~E(x21591,x21592)+E(f665(x21593,x21594,x21591,x21595),f665(x21593,x21594,x21592,x21595))
% 51.10/50.84 [2160]~E(x21601,x21602)+E(f665(x21603,x21604,x21605,x21601),f665(x21603,x21604,x21605,x21602))
% 51.10/50.84 [2161]~E(x21611,x21612)+E(f560(x21611,x21613,x21614,x21615,x21616,x21617),f560(x21612,x21613,x21614,x21615,x21616,x21617))
% 51.10/50.84 [2162]~E(x21621,x21622)+E(f560(x21623,x21621,x21624,x21625,x21626,x21627),f560(x21623,x21622,x21624,x21625,x21626,x21627))
% 51.10/50.84 [2163]~E(x21631,x21632)+E(f560(x21633,x21634,x21631,x21635,x21636,x21637),f560(x21633,x21634,x21632,x21635,x21636,x21637))
% 51.10/50.84 [2164]~E(x21641,x21642)+E(f560(x21643,x21644,x21645,x21641,x21646,x21647),f560(x21643,x21644,x21645,x21642,x21646,x21647))
% 51.10/50.84 [2165]~E(x21651,x21652)+E(f560(x21653,x21654,x21655,x21656,x21651,x21657),f560(x21653,x21654,x21655,x21656,x21652,x21657))
% 51.10/50.84 [2166]~E(x21661,x21662)+E(f560(x21663,x21664,x21665,x21666,x21667,x21661),f560(x21663,x21664,x21665,x21666,x21667,x21662))
% 51.10/50.84 [2167]~E(x21671,x21672)+E(f602(x21671,x21673,x21674),f602(x21672,x21673,x21674))
% 51.10/50.84 [2168]~E(x21681,x21682)+E(f602(x21683,x21681,x21684),f602(x21683,x21682,x21684))
% 51.10/50.84 [2169]~E(x21691,x21692)+E(f602(x21693,x21694,x21691),f602(x21693,x21694,x21692))
% 51.10/50.84 [2170]~E(x21701,x21702)+E(f428(x21701,x21703,x21704),f428(x21702,x21703,x21704))
% 51.10/50.84 [2171]~E(x21711,x21712)+E(f428(x21713,x21711,x21714),f428(x21713,x21712,x21714))
% 51.10/50.84 [2172]~E(x21721,x21722)+E(f428(x21723,x21724,x21721),f428(x21723,x21724,x21722))
% 51.10/50.84 [2173]~E(x21731,x21732)+E(f545(x21731,x21733,x21734,x21735,x21736,x21737),f545(x21732,x21733,x21734,x21735,x21736,x21737))
% 51.10/50.84 [2174]~E(x21741,x21742)+E(f545(x21743,x21741,x21744,x21745,x21746,x21747),f545(x21743,x21742,x21744,x21745,x21746,x21747))
% 51.10/50.84 [2175]~E(x21751,x21752)+E(f545(x21753,x21754,x21751,x21755,x21756,x21757),f545(x21753,x21754,x21752,x21755,x21756,x21757))
% 51.10/50.84 [2176]~E(x21761,x21762)+E(f545(x21763,x21764,x21765,x21761,x21766,x21767),f545(x21763,x21764,x21765,x21762,x21766,x21767))
% 51.10/50.84 [2177]~E(x21771,x21772)+E(f545(x21773,x21774,x21775,x21776,x21771,x21777),f545(x21773,x21774,x21775,x21776,x21772,x21777))
% 51.10/50.84 [2178]~E(x21781,x21782)+E(f545(x21783,x21784,x21785,x21786,x21787,x21781),f545(x21783,x21784,x21785,x21786,x21787,x21782))
% 51.10/50.84 [2179]~E(x21791,x21792)+E(f814(x21791,x21793,x21794),f814(x21792,x21793,x21794))
% 51.10/50.84 [2180]~E(x21801,x21802)+E(f814(x21803,x21801,x21804),f814(x21803,x21802,x21804))
% 51.10/50.84 [2181]~E(x21811,x21812)+E(f814(x21813,x21814,x21811),f814(x21813,x21814,x21812))
% 51.10/50.84 [2182]~E(x21821,x21822)+E(f823(x21821,x21823,x21824),f823(x21822,x21823,x21824))
% 51.10/50.84 [2183]~E(x21831,x21832)+E(f823(x21833,x21831,x21834),f823(x21833,x21832,x21834))
% 51.10/50.84 [2184]~E(x21841,x21842)+E(f823(x21843,x21844,x21841),f823(x21843,x21844,x21842))
% 51.10/50.84 [2185]~E(x21851,x21852)+E(f801(x21851,x21853,x21854),f801(x21852,x21853,x21854))
% 51.10/50.84 [2186]~E(x21861,x21862)+E(f801(x21863,x21861,x21864),f801(x21863,x21862,x21864))
% 51.10/50.84 [2187]~E(x21871,x21872)+E(f801(x21873,x21874,x21871),f801(x21873,x21874,x21872))
% 51.10/50.84 [2188]~E(x21881,x21882)+E(f733(x21881,x21883,x21884),f733(x21882,x21883,x21884))
% 51.10/50.84 [2189]~E(x21891,x21892)+E(f733(x21893,x21891,x21894),f733(x21893,x21892,x21894))
% 51.10/50.84 [2190]~E(x21901,x21902)+E(f733(x21903,x21904,x21901),f733(x21903,x21904,x21902))
% 51.10/50.84 [2191]~E(x21911,x21912)+E(f277(x21911,x21913,x21914),f277(x21912,x21913,x21914))
% 51.10/50.84 [2192]~E(x21921,x21922)+E(f277(x21923,x21921,x21924),f277(x21923,x21922,x21924))
% 51.10/50.84 [2193]~E(x21931,x21932)+E(f277(x21933,x21934,x21931),f277(x21933,x21934,x21932))
% 51.10/50.84 [2194]~E(x21941,x21942)+E(f792(x21941,x21943,x21944),f792(x21942,x21943,x21944))
% 51.10/50.84 [2195]~E(x21951,x21952)+E(f792(x21953,x21951,x21954),f792(x21953,x21952,x21954))
% 51.10/50.84 [2196]~E(x21961,x21962)+E(f792(x21963,x21964,x21961),f792(x21963,x21964,x21962))
% 51.10/50.84 [2197]~E(x21971,x21972)+E(f292(x21971,x21973),f292(x21972,x21973))
% 51.10/50.84 [2198]~E(x21981,x21982)+E(f292(x21983,x21981),f292(x21983,x21982))
% 51.10/50.84 [2199]~E(x21991,x21992)+E(f429(x21991,x21993,x21994),f429(x21992,x21993,x21994))
% 51.10/50.84 [2200]~E(x22001,x22002)+E(f429(x22003,x22001,x22004),f429(x22003,x22002,x22004))
% 51.10/50.84 [2201]~E(x22011,x22012)+E(f429(x22013,x22014,x22011),f429(x22013,x22014,x22012))
% 51.10/50.84 [2202]~E(x22021,x22022)+E(f450(x22021,x22023,x22024),f450(x22022,x22023,x22024))
% 51.10/50.84 [2203]~E(x22031,x22032)+E(f450(x22033,x22031,x22034),f450(x22033,x22032,x22034))
% 51.10/50.84 [2204]~E(x22041,x22042)+E(f450(x22043,x22044,x22041),f450(x22043,x22044,x22042))
% 51.10/50.84 [2205]~E(x22051,x22052)+E(f362(x22051,x22053),f362(x22052,x22053))
% 51.10/50.84 [2206]~E(x22061,x22062)+E(f362(x22063,x22061),f362(x22063,x22062))
% 51.10/50.84 [2207]~E(x22071,x22072)+E(f422(x22071,x22073,x22074,x22075,x22076,x22077,x22078),f422(x22072,x22073,x22074,x22075,x22076,x22077,x22078))
% 51.10/50.84 [2208]~E(x22081,x22082)+E(f422(x22083,x22081,x22084,x22085,x22086,x22087,x22088),f422(x22083,x22082,x22084,x22085,x22086,x22087,x22088))
% 51.10/50.84 [2209]~E(x22091,x22092)+E(f422(x22093,x22094,x22091,x22095,x22096,x22097,x22098),f422(x22093,x22094,x22092,x22095,x22096,x22097,x22098))
% 51.10/50.84 [2210]~E(x22101,x22102)+E(f422(x22103,x22104,x22105,x22101,x22106,x22107,x22108),f422(x22103,x22104,x22105,x22102,x22106,x22107,x22108))
% 51.10/50.84 [2211]~E(x22111,x22112)+E(f422(x22113,x22114,x22115,x22116,x22111,x22117,x22118),f422(x22113,x22114,x22115,x22116,x22112,x22117,x22118))
% 51.10/50.84 [2212]~E(x22121,x22122)+E(f422(x22123,x22124,x22125,x22126,x22127,x22121,x22128),f422(x22123,x22124,x22125,x22126,x22127,x22122,x22128))
% 51.10/50.84 [2213]~E(x22131,x22132)+E(f422(x22133,x22134,x22135,x22136,x22137,x22138,x22131),f422(x22133,x22134,x22135,x22136,x22137,x22138,x22132))
% 51.10/50.84 [2214]~E(x22141,x22142)+E(f605(x22141,x22143,x22144,x22145),f605(x22142,x22143,x22144,x22145))
% 51.10/50.84 [2215]~E(x22151,x22152)+E(f605(x22153,x22151,x22154,x22155),f605(x22153,x22152,x22154,x22155))
% 51.10/50.84 [2216]~E(x22161,x22162)+E(f605(x22163,x22164,x22161,x22165),f605(x22163,x22164,x22162,x22165))
% 51.10/50.84 [2217]~E(x22171,x22172)+E(f605(x22173,x22174,x22175,x22171),f605(x22173,x22174,x22175,x22172))
% 51.10/50.84 [2218]~E(x22181,x22182)+E(f418(x22181,x22183,x22184),f418(x22182,x22183,x22184))
% 51.10/50.84 [2219]~E(x22191,x22192)+E(f418(x22193,x22191,x22194),f418(x22193,x22192,x22194))
% 51.10/50.84 [2220]~E(x22201,x22202)+E(f418(x22203,x22204,x22201),f418(x22203,x22204,x22202))
% 51.10/50.84 [2221]~E(x22211,x22212)+E(f582(x22211,x22213),f582(x22212,x22213))
% 51.10/50.84 [2222]~E(x22221,x22222)+E(f582(x22223,x22221),f582(x22223,x22222))
% 51.10/50.84 [2223]~E(x22231,x22232)+E(f56(x22231),f56(x22232))
% 51.10/50.84 [2224]~E(x22241,x22242)+E(f672(x22241,x22243,x22244,x22245,x22246,x22247),f672(x22242,x22243,x22244,x22245,x22246,x22247))
% 51.10/50.84 [2225]~E(x22251,x22252)+E(f672(x22253,x22251,x22254,x22255,x22256,x22257),f672(x22253,x22252,x22254,x22255,x22256,x22257))
% 51.10/50.84 [2226]~E(x22261,x22262)+E(f672(x22263,x22264,x22261,x22265,x22266,x22267),f672(x22263,x22264,x22262,x22265,x22266,x22267))
% 51.10/50.84 [2227]~E(x22271,x22272)+E(f672(x22273,x22274,x22275,x22271,x22276,x22277),f672(x22273,x22274,x22275,x22272,x22276,x22277))
% 51.10/50.84 [2228]~E(x22281,x22282)+E(f672(x22283,x22284,x22285,x22286,x22281,x22287),f672(x22283,x22284,x22285,x22286,x22282,x22287))
% 51.10/50.84 [2229]~E(x22291,x22292)+E(f672(x22293,x22294,x22295,x22296,x22297,x22291),f672(x22293,x22294,x22295,x22296,x22297,x22292))
% 51.10/50.84 [2230]~E(x22301,x22302)+E(f516(x22301,x22303,x22304,x22305),f516(x22302,x22303,x22304,x22305))
% 51.10/50.84 [2231]~E(x22311,x22312)+E(f516(x22313,x22311,x22314,x22315),f516(x22313,x22312,x22314,x22315))
% 51.10/50.84 [2232]~E(x22321,x22322)+E(f516(x22323,x22324,x22321,x22325),f516(x22323,x22324,x22322,x22325))
% 51.10/50.84 [2233]~E(x22331,x22332)+E(f516(x22333,x22334,x22335,x22331),f516(x22333,x22334,x22335,x22332))
% 51.10/50.84 [2234]~E(x22341,x22342)+E(f637(x22341,x22343,x22344,x22345),f637(x22342,x22343,x22344,x22345))
% 51.10/50.84 [2235]~E(x22351,x22352)+E(f637(x22353,x22351,x22354,x22355),f637(x22353,x22352,x22354,x22355))
% 51.10/50.84 [2236]~E(x22361,x22362)+E(f637(x22363,x22364,x22361,x22365),f637(x22363,x22364,x22362,x22365))
% 51.10/50.84 [2237]~E(x22371,x22372)+E(f637(x22373,x22374,x22375,x22371),f637(x22373,x22374,x22375,x22372))
% 51.10/50.84 [2238]~E(x22381,x22382)+E(f831(x22381,x22383,x22384,x22385),f831(x22382,x22383,x22384,x22385))
% 51.10/50.84 [2239]~E(x22391,x22392)+E(f831(x22393,x22391,x22394,x22395),f831(x22393,x22392,x22394,x22395))
% 51.10/50.84 [2240]~E(x22401,x22402)+E(f831(x22403,x22404,x22401,x22405),f831(x22403,x22404,x22402,x22405))
% 51.10/50.84 [2241]~E(x22411,x22412)+E(f831(x22413,x22414,x22415,x22411),f831(x22413,x22414,x22415,x22412))
% 51.10/50.84 [2242]~E(x22421,x22422)+E(f691(x22421,x22423),f691(x22422,x22423))
% 51.10/50.84 [2243]~E(x22431,x22432)+E(f691(x22433,x22431),f691(x22433,x22432))
% 51.10/50.84 [2244]~E(x22441,x22442)+E(f19(x22441,x22443,x22444,x22445),f19(x22442,x22443,x22444,x22445))
% 51.10/50.84 [2245]~E(x22451,x22452)+E(f19(x22453,x22451,x22454,x22455),f19(x22453,x22452,x22454,x22455))
% 51.10/50.84 [2246]~E(x22461,x22462)+E(f19(x22463,x22464,x22461,x22465),f19(x22463,x22464,x22462,x22465))
% 51.10/50.84 [2247]~E(x22471,x22472)+E(f19(x22473,x22474,x22475,x22471),f19(x22473,x22474,x22475,x22472))
% 51.10/50.84 [2248]~E(x22481,x22482)+E(f529(x22481,x22483,x22484,x22485,x22486),f529(x22482,x22483,x22484,x22485,x22486))
% 51.10/50.84 [2249]~E(x22491,x22492)+E(f529(x22493,x22491,x22494,x22495,x22496),f529(x22493,x22492,x22494,x22495,x22496))
% 51.10/50.84 [2250]~E(x22501,x22502)+E(f529(x22503,x22504,x22501,x22505,x22506),f529(x22503,x22504,x22502,x22505,x22506))
% 51.10/50.84 [2251]~E(x22511,x22512)+E(f529(x22513,x22514,x22515,x22511,x22516),f529(x22513,x22514,x22515,x22512,x22516))
% 51.10/50.84 [2252]~E(x22521,x22522)+E(f529(x22523,x22524,x22525,x22526,x22521),f529(x22523,x22524,x22525,x22526,x22522))
% 51.10/50.84 [2253]~E(x22531,x22532)+E(f600(x22531,x22533,x22534,x22535),f600(x22532,x22533,x22534,x22535))
% 51.10/50.84 [2254]~E(x22541,x22542)+E(f600(x22543,x22541,x22544,x22545),f600(x22543,x22542,x22544,x22545))
% 51.10/50.84 [2255]~E(x22551,x22552)+E(f600(x22553,x22554,x22551,x22555),f600(x22553,x22554,x22552,x22555))
% 51.10/50.84 [2256]~E(x22561,x22562)+E(f600(x22563,x22564,x22565,x22561),f600(x22563,x22564,x22565,x22562))
% 51.10/50.84 [2257]~E(x22571,x22572)+E(f799(x22571,x22573,x22574),f799(x22572,x22573,x22574))
% 51.10/50.84 [2258]~E(x22581,x22582)+E(f799(x22583,x22581,x22584),f799(x22583,x22582,x22584))
% 51.10/50.84 [2259]~E(x22591,x22592)+E(f799(x22593,x22594,x22591),f799(x22593,x22594,x22592))
% 51.10/50.84 [2260]~E(x22601,x22602)+E(f335(x22601,x22603,x22604,x22605),f335(x22602,x22603,x22604,x22605))
% 51.10/50.84 [2261]~E(x22611,x22612)+E(f335(x22613,x22611,x22614,x22615),f335(x22613,x22612,x22614,x22615))
% 51.10/50.84 [2262]~E(x22621,x22622)+E(f335(x22623,x22624,x22621,x22625),f335(x22623,x22624,x22622,x22625))
% 51.10/50.84 [2263]~E(x22631,x22632)+E(f335(x22633,x22634,x22635,x22631),f335(x22633,x22634,x22635,x22632))
% 51.10/50.84 [2264]~E(x22641,x22642)+E(f490(x22641,x22643,x22644,x22645,x22646),f490(x22642,x22643,x22644,x22645,x22646))
% 51.10/50.84 [2265]~E(x22651,x22652)+E(f490(x22653,x22651,x22654,x22655,x22656),f490(x22653,x22652,x22654,x22655,x22656))
% 51.10/50.84 [2266]~E(x22661,x22662)+E(f490(x22663,x22664,x22661,x22665,x22666),f490(x22663,x22664,x22662,x22665,x22666))
% 51.10/50.84 [2267]~E(x22671,x22672)+E(f490(x22673,x22674,x22675,x22671,x22676),f490(x22673,x22674,x22675,x22672,x22676))
% 51.10/50.84 [2268]~E(x22681,x22682)+E(f490(x22683,x22684,x22685,x22686,x22681),f490(x22683,x22684,x22685,x22686,x22682))
% 51.10/50.84 [2269]~E(x22691,x22692)+E(f407(x22691,x22693,x22694,x22695),f407(x22692,x22693,x22694,x22695))
% 51.10/50.84 [2270]~E(x22701,x22702)+E(f407(x22703,x22701,x22704,x22705),f407(x22703,x22702,x22704,x22705))
% 51.10/50.84 [2271]~E(x22711,x22712)+E(f407(x22713,x22714,x22711,x22715),f407(x22713,x22714,x22712,x22715))
% 51.10/50.84 [2272]~E(x22721,x22722)+E(f407(x22723,x22724,x22725,x22721),f407(x22723,x22724,x22725,x22722))
% 51.10/50.84 [2273]~E(x22731,x22732)+E(f571(x22731,x22733),f571(x22732,x22733))
% 51.10/50.84 [2274]~E(x22741,x22742)+E(f571(x22743,x22741),f571(x22743,x22742))
% 51.10/50.84 [2275]~E(x22751,x22752)+E(f393(x22751,x22753,x22754,x22755),f393(x22752,x22753,x22754,x22755))
% 51.10/50.84 [2276]~E(x22761,x22762)+E(f393(x22763,x22761,x22764,x22765),f393(x22763,x22762,x22764,x22765))
% 51.10/50.84 [2277]~E(x22771,x22772)+E(f393(x22773,x22774,x22771,x22775),f393(x22773,x22774,x22772,x22775))
% 51.10/50.84 [2278]~E(x22781,x22782)+E(f393(x22783,x22784,x22785,x22781),f393(x22783,x22784,x22785,x22782))
% 51.10/50.84 [2279]~E(x22791,x22792)+E(f751(x22791,x22793,x22794),f751(x22792,x22793,x22794))
% 51.10/50.84 [2280]~E(x22801,x22802)+E(f751(x22803,x22801,x22804),f751(x22803,x22802,x22804))
% 51.10/50.84 [2281]~E(x22811,x22812)+E(f751(x22813,x22814,x22811),f751(x22813,x22814,x22812))
% 51.10/50.84 [2282]~E(x22821,x22822)+E(f197(x22821,x22823,x22824,x22825),f197(x22822,x22823,x22824,x22825))
% 51.10/50.84 [2283]~E(x22831,x22832)+E(f197(x22833,x22831,x22834,x22835),f197(x22833,x22832,x22834,x22835))
% 51.10/50.84 [2284]~E(x22841,x22842)+E(f197(x22843,x22844,x22841,x22845),f197(x22843,x22844,x22842,x22845))
% 51.10/50.84 [2285]~E(x22851,x22852)+E(f197(x22853,x22854,x22855,x22851),f197(x22853,x22854,x22855,x22852))
% 51.10/50.84 [2286]~E(x22861,x22862)+E(f547(x22861,x22863),f547(x22862,x22863))
% 51.10/50.84 [2287]~E(x22871,x22872)+E(f547(x22873,x22871),f547(x22873,x22872))
% 51.10/50.84 [2288]~E(x22881,x22882)+E(f606(x22881,x22883,x22884,x22885,x22886,x22887),f606(x22882,x22883,x22884,x22885,x22886,x22887))
% 51.10/50.84 [2289]~E(x22891,x22892)+E(f606(x22893,x22891,x22894,x22895,x22896,x22897),f606(x22893,x22892,x22894,x22895,x22896,x22897))
% 51.10/50.84 [2290]~E(x22901,x22902)+E(f606(x22903,x22904,x22901,x22905,x22906,x22907),f606(x22903,x22904,x22902,x22905,x22906,x22907))
% 51.10/50.84 [2291]~E(x22911,x22912)+E(f606(x22913,x22914,x22915,x22911,x22916,x22917),f606(x22913,x22914,x22915,x22912,x22916,x22917))
% 51.10/50.84 [2292]~E(x22921,x22922)+E(f606(x22923,x22924,x22925,x22926,x22921,x22927),f606(x22923,x22924,x22925,x22926,x22922,x22927))
% 51.10/50.84 [2293]~E(x22931,x22932)+E(f606(x22933,x22934,x22935,x22936,x22937,x22931),f606(x22933,x22934,x22935,x22936,x22937,x22932))
% 51.10/50.84 [2294]~E(x22941,x22942)+E(f207(x22941,x22943,x22944,x22945),f207(x22942,x22943,x22944,x22945))
% 51.10/50.84 [2295]~E(x22951,x22952)+E(f207(x22953,x22951,x22954,x22955),f207(x22953,x22952,x22954,x22955))
% 51.10/50.84 [2296]~E(x22961,x22962)+E(f207(x22963,x22964,x22961,x22965),f207(x22963,x22964,x22962,x22965))
% 51.10/50.84 [2297]~E(x22971,x22972)+E(f207(x22973,x22974,x22975,x22971),f207(x22973,x22974,x22975,x22972))
% 51.10/50.84 [2298]~E(x22981,x22982)+E(f127(x22981),f127(x22982))
% 51.10/50.84 [2299]~E(x22991,x22992)+E(f673(x22991,x22993),f673(x22992,x22993))
% 51.10/50.84 [2300]~E(x23001,x23002)+E(f673(x23003,x23001),f673(x23003,x23002))
% 51.10/50.84 [2301]~E(x23011,x23012)+E(f419(x23011,x23013,x23014,x23015,x23016,x23017,x23018),f419(x23012,x23013,x23014,x23015,x23016,x23017,x23018))
% 51.10/50.84 [2302]~E(x23021,x23022)+E(f419(x23023,x23021,x23024,x23025,x23026,x23027,x23028),f419(x23023,x23022,x23024,x23025,x23026,x23027,x23028))
% 51.10/50.84 [2303]~E(x23031,x23032)+E(f419(x23033,x23034,x23031,x23035,x23036,x23037,x23038),f419(x23033,x23034,x23032,x23035,x23036,x23037,x23038))
% 51.10/50.84 [2304]~E(x23041,x23042)+E(f419(x23043,x23044,x23045,x23041,x23046,x23047,x23048),f419(x23043,x23044,x23045,x23042,x23046,x23047,x23048))
% 51.10/50.84 [2305]~E(x23051,x23052)+E(f419(x23053,x23054,x23055,x23056,x23051,x23057,x23058),f419(x23053,x23054,x23055,x23056,x23052,x23057,x23058))
% 51.10/50.84 [2306]~E(x23061,x23062)+E(f419(x23063,x23064,x23065,x23066,x23067,x23061,x23068),f419(x23063,x23064,x23065,x23066,x23067,x23062,x23068))
% 51.10/50.84 [2307]~E(x23071,x23072)+E(f419(x23073,x23074,x23075,x23076,x23077,x23078,x23071),f419(x23073,x23074,x23075,x23076,x23077,x23078,x23072))
% 51.10/50.84 [2308]~E(x23081,x23082)+E(f282(x23081,x23083,x23084,x23085),f282(x23082,x23083,x23084,x23085))
% 51.10/50.84 [2309]~E(x23091,x23092)+E(f282(x23093,x23091,x23094,x23095),f282(x23093,x23092,x23094,x23095))
% 51.10/50.84 [2310]~E(x23101,x23102)+E(f282(x23103,x23104,x23101,x23105),f282(x23103,x23104,x23102,x23105))
% 51.10/50.84 [2311]~E(x23111,x23112)+E(f282(x23113,x23114,x23115,x23111),f282(x23113,x23114,x23115,x23112))
% 51.10/50.84 [2312]~E(x23121,x23122)+E(f749(x23121,x23123,x23124),f749(x23122,x23123,x23124))
% 51.10/50.84 [2313]~E(x23131,x23132)+E(f749(x23133,x23131,x23134),f749(x23133,x23132,x23134))
% 51.10/50.84 [2314]~E(x23141,x23142)+E(f749(x23143,x23144,x23141),f749(x23143,x23144,x23142))
% 51.10/50.84 [2315]~E(x23151,x23152)+E(f101(x23151,x23153,x23154,x23155),f101(x23152,x23153,x23154,x23155))
% 51.10/50.84 [2316]~E(x23161,x23162)+E(f101(x23163,x23161,x23164,x23165),f101(x23163,x23162,x23164,x23165))
% 51.10/50.84 [2317]~E(x23171,x23172)+E(f101(x23173,x23174,x23171,x23175),f101(x23173,x23174,x23172,x23175))
% 51.10/50.84 [2318]~E(x23181,x23182)+E(f101(x23183,x23184,x23185,x23181),f101(x23183,x23184,x23185,x23182))
% 51.10/50.84 [2319]~E(x23191,x23192)+E(f524(x23191,x23193,x23194),f524(x23192,x23193,x23194))
% 51.10/50.84 [2320]~E(x23201,x23202)+E(f524(x23203,x23201,x23204),f524(x23203,x23202,x23204))
% 51.10/50.84 [2321]~E(x23211,x23212)+E(f524(x23213,x23214,x23211),f524(x23213,x23214,x23212))
% 51.10/50.84 [2322]~E(x23221,x23222)+E(f355(x23221,x23223),f355(x23222,x23223))
% 51.10/50.84 [2323]~E(x23231,x23232)+E(f355(x23233,x23231),f355(x23233,x23232))
% 51.10/50.84 [2324]~E(x23241,x23242)+E(f337(x23241,x23243),f337(x23242,x23243))
% 51.10/50.84 [2325]~E(x23251,x23252)+E(f337(x23253,x23251),f337(x23253,x23252))
% 51.10/50.84 [2326]~E(x23261,x23262)+E(f365(x23261),f365(x23262))
% 51.10/50.84 [2327]~E(x23271,x23272)+E(f359(x23271,x23273),f359(x23272,x23273))
% 51.10/50.84 [2328]~E(x23281,x23282)+E(f359(x23283,x23281),f359(x23283,x23282))
% 51.10/50.84 [2329]~E(x23291,x23292)+E(f471(x23291,x23293,x23294,x23295),f471(x23292,x23293,x23294,x23295))
% 51.10/50.84 [2330]~E(x23301,x23302)+E(f471(x23303,x23301,x23304,x23305),f471(x23303,x23302,x23304,x23305))
% 51.10/50.84 [2331]~E(x23311,x23312)+E(f471(x23313,x23314,x23311,x23315),f471(x23313,x23314,x23312,x23315))
% 51.10/50.84 [2332]~E(x23321,x23322)+E(f471(x23323,x23324,x23325,x23321),f471(x23323,x23324,x23325,x23322))
% 51.10/50.84 [2333]~E(x23331,x23332)+E(f555(x23331,x23333,x23334,x23335,x23336,x23337,x23338,x23339),f555(x23332,x23333,x23334,x23335,x23336,x23337,x23338,x23339))
% 51.10/50.84 [2334]~E(x23341,x23342)+E(f555(x23343,x23341,x23344,x23345,x23346,x23347,x23348,x23349),f555(x23343,x23342,x23344,x23345,x23346,x23347,x23348,x23349))
% 51.10/50.84 [2335]~E(x23351,x23352)+E(f555(x23353,x23354,x23351,x23355,x23356,x23357,x23358,x23359),f555(x23353,x23354,x23352,x23355,x23356,x23357,x23358,x23359))
% 51.10/50.84 [2336]~E(x23361,x23362)+E(f555(x23363,x23364,x23365,x23361,x23366,x23367,x23368,x23369),f555(x23363,x23364,x23365,x23362,x23366,x23367,x23368,x23369))
% 51.10/50.84 [2337]~E(x23371,x23372)+E(f555(x23373,x23374,x23375,x23376,x23371,x23377,x23378,x23379),f555(x23373,x23374,x23375,x23376,x23372,x23377,x23378,x23379))
% 51.10/50.84 [2338]~E(x23381,x23382)+E(f555(x23383,x23384,x23385,x23386,x23387,x23381,x23388,x23389),f555(x23383,x23384,x23385,x23386,x23387,x23382,x23388,x23389))
% 51.10/50.84 [2339]~E(x23391,x23392)+E(f555(x23393,x23394,x23395,x23396,x23397,x23398,x23391,x23399),f555(x23393,x23394,x23395,x23396,x23397,x23398,x23392,x23399))
% 51.10/50.84 [2340]~E(x23401,x23402)+E(f555(x23403,x23404,x23405,x23406,x23407,x23408,x23409,x23401),f555(x23403,x23404,x23405,x23406,x23407,x23408,x23409,x23402))
% 51.10/50.84 [2341]~E(x23411,x23412)+E(f507(x23411,x23413,x23414,x23415,x23416),f507(x23412,x23413,x23414,x23415,x23416))
% 51.10/50.84 [2342]~E(x23421,x23422)+E(f507(x23423,x23421,x23424,x23425,x23426),f507(x23423,x23422,x23424,x23425,x23426))
% 51.10/50.84 [2343]~E(x23431,x23432)+E(f507(x23433,x23434,x23431,x23435,x23436),f507(x23433,x23434,x23432,x23435,x23436))
% 51.10/50.84 [2344]~E(x23441,x23442)+E(f507(x23443,x23444,x23445,x23441,x23446),f507(x23443,x23444,x23445,x23442,x23446))
% 51.10/50.84 [2345]~E(x23451,x23452)+E(f507(x23453,x23454,x23455,x23456,x23451),f507(x23453,x23454,x23455,x23456,x23452))
% 51.10/50.84 [2346]~E(x23461,x23462)+E(f745(x23461,x23463,x23464),f745(x23462,x23463,x23464))
% 51.10/50.84 [2347]~E(x23471,x23472)+E(f745(x23473,x23471,x23474),f745(x23473,x23472,x23474))
% 51.10/50.84 [2348]~E(x23481,x23482)+E(f745(x23483,x23484,x23481),f745(x23483,x23484,x23482))
% 51.10/50.84 [2349]~E(x23491,x23492)+E(f777(x23491,x23493),f777(x23492,x23493))
% 51.10/50.84 [2350]~E(x23501,x23502)+E(f777(x23503,x23501),f777(x23503,x23502))
% 51.10/50.84 [2351]~E(x23511,x23512)+E(f762(x23511,x23513),f762(x23512,x23513))
% 51.10/50.84 [2352]~E(x23521,x23522)+E(f762(x23523,x23521),f762(x23523,x23522))
% 51.10/50.84 [2353]~E(x23531,x23532)+E(f707(x23531,x23533,x23534,x23535,x23536,x23537),f707(x23532,x23533,x23534,x23535,x23536,x23537))
% 51.10/50.84 [2354]~E(x23541,x23542)+E(f707(x23543,x23541,x23544,x23545,x23546,x23547),f707(x23543,x23542,x23544,x23545,x23546,x23547))
% 51.10/50.84 [2355]~E(x23551,x23552)+E(f707(x23553,x23554,x23551,x23555,x23556,x23557),f707(x23553,x23554,x23552,x23555,x23556,x23557))
% 51.10/50.84 [2356]~E(x23561,x23562)+E(f707(x23563,x23564,x23565,x23561,x23566,x23567),f707(x23563,x23564,x23565,x23562,x23566,x23567))
% 51.10/50.84 [2357]~E(x23571,x23572)+E(f707(x23573,x23574,x23575,x23576,x23571,x23577),f707(x23573,x23574,x23575,x23576,x23572,x23577))
% 51.10/50.84 [2358]~E(x23581,x23582)+E(f707(x23583,x23584,x23585,x23586,x23587,x23581),f707(x23583,x23584,x23585,x23586,x23587,x23582))
% 51.10/50.84 [2359]~E(x23591,x23592)+E(f626(x23591,x23593,x23594,x23595),f626(x23592,x23593,x23594,x23595))
% 51.10/50.84 [2360]~E(x23601,x23602)+E(f626(x23603,x23601,x23604,x23605),f626(x23603,x23602,x23604,x23605))
% 51.10/50.84 [2361]~E(x23611,x23612)+E(f626(x23613,x23614,x23611,x23615),f626(x23613,x23614,x23612,x23615))
% 51.10/50.84 [2362]~E(x23621,x23622)+E(f626(x23623,x23624,x23625,x23621),f626(x23623,x23624,x23625,x23622))
% 51.10/50.84 [2363]~E(x23631,x23632)+E(f703(x23631,x23633,x23634,x23635),f703(x23632,x23633,x23634,x23635))
% 51.10/50.84 [2364]~E(x23641,x23642)+E(f703(x23643,x23641,x23644,x23645),f703(x23643,x23642,x23644,x23645))
% 51.10/50.84 [2365]~E(x23651,x23652)+E(f703(x23653,x23654,x23651,x23655),f703(x23653,x23654,x23652,x23655))
% 51.10/50.84 [2366]~E(x23661,x23662)+E(f703(x23663,x23664,x23665,x23661),f703(x23663,x23664,x23665,x23662))
% 51.10/50.84 [2367]~E(x23671,x23672)+E(f496(x23671,x23673,x23674,x23675,x23676),f496(x23672,x23673,x23674,x23675,x23676))
% 51.10/50.84 [2368]~E(x23681,x23682)+E(f496(x23683,x23681,x23684,x23685,x23686),f496(x23683,x23682,x23684,x23685,x23686))
% 51.10/50.84 [2369]~E(x23691,x23692)+E(f496(x23693,x23694,x23691,x23695,x23696),f496(x23693,x23694,x23692,x23695,x23696))
% 51.10/50.84 [2370]~E(x23701,x23702)+E(f496(x23703,x23704,x23705,x23701,x23706),f496(x23703,x23704,x23705,x23702,x23706))
% 51.10/50.84 [2371]~E(x23711,x23712)+E(f496(x23713,x23714,x23715,x23716,x23711),f496(x23713,x23714,x23715,x23716,x23712))
% 51.10/50.84 [2372]~E(x23721,x23722)+E(f563(x23721,x23723,x23724,x23725,x23726,x23727,x23728),f563(x23722,x23723,x23724,x23725,x23726,x23727,x23728))
% 51.10/50.84 [2373]~E(x23731,x23732)+E(f563(x23733,x23731,x23734,x23735,x23736,x23737,x23738),f563(x23733,x23732,x23734,x23735,x23736,x23737,x23738))
% 51.10/50.84 [2374]~E(x23741,x23742)+E(f563(x23743,x23744,x23741,x23745,x23746,x23747,x23748),f563(x23743,x23744,x23742,x23745,x23746,x23747,x23748))
% 51.10/50.84 [2375]~E(x23751,x23752)+E(f563(x23753,x23754,x23755,x23751,x23756,x23757,x23758),f563(x23753,x23754,x23755,x23752,x23756,x23757,x23758))
% 51.10/50.84 [2376]~E(x23761,x23762)+E(f563(x23763,x23764,x23765,x23766,x23761,x23767,x23768),f563(x23763,x23764,x23765,x23766,x23762,x23767,x23768))
% 51.10/50.84 [2377]~E(x23771,x23772)+E(f563(x23773,x23774,x23775,x23776,x23777,x23771,x23778),f563(x23773,x23774,x23775,x23776,x23777,x23772,x23778))
% 51.10/50.84 [2378]~E(x23781,x23782)+E(f563(x23783,x23784,x23785,x23786,x23787,x23788,x23781),f563(x23783,x23784,x23785,x23786,x23787,x23788,x23782))
% 51.10/50.84 [2379]~E(x23791,x23792)+E(f227(x23791,x23793,x23794,x23795,x23796),f227(x23792,x23793,x23794,x23795,x23796))
% 51.10/50.84 [2380]~E(x23801,x23802)+E(f227(x23803,x23801,x23804,x23805,x23806),f227(x23803,x23802,x23804,x23805,x23806))
% 51.10/50.84 [2381]~E(x23811,x23812)+E(f227(x23813,x23814,x23811,x23815,x23816),f227(x23813,x23814,x23812,x23815,x23816))
% 51.10/50.84 [2382]~E(x23821,x23822)+E(f227(x23823,x23824,x23825,x23821,x23826),f227(x23823,x23824,x23825,x23822,x23826))
% 51.10/50.84 [2383]~E(x23831,x23832)+E(f227(x23833,x23834,x23835,x23836,x23831),f227(x23833,x23834,x23835,x23836,x23832))
% 51.10/50.84 [2384]~E(x23841,x23842)+E(f539(x23841),f539(x23842))
% 51.10/50.84 [2385]~E(x23851,x23852)+E(f750(x23851,x23853,x23854),f750(x23852,x23853,x23854))
% 51.10/50.84 [2386]~E(x23861,x23862)+E(f750(x23863,x23861,x23864),f750(x23863,x23862,x23864))
% 51.10/50.84 [2387]~E(x23871,x23872)+E(f750(x23873,x23874,x23871),f750(x23873,x23874,x23872))
% 51.10/50.84 [2388]~E(x23881,x23882)+E(f657(x23881,x23883),f657(x23882,x23883))
% 51.10/50.84 [2389]~E(x23891,x23892)+E(f657(x23893,x23891),f657(x23893,x23892))
% 51.10/50.84 [2390]~E(x23901,x23902)+E(f779(x23901,x23903),f779(x23902,x23903))
% 51.10/50.84 [2391]~E(x23911,x23912)+E(f779(x23913,x23911),f779(x23913,x23912))
% 51.10/50.84 [2392]~E(x23921,x23922)+E(f386(x23921,x23923,x23924,x23925),f386(x23922,x23923,x23924,x23925))
% 51.10/50.84 [2393]~E(x23931,x23932)+E(f386(x23933,x23931,x23934,x23935),f386(x23933,x23932,x23934,x23935))
% 51.10/50.84 [2394]~E(x23941,x23942)+E(f386(x23943,x23944,x23941,x23945),f386(x23943,x23944,x23942,x23945))
% 51.10/50.84 [2395]~E(x23951,x23952)+E(f386(x23953,x23954,x23955,x23951),f386(x23953,x23954,x23955,x23952))
% 51.10/50.84 [2396]~E(x23961,x23962)+E(f738(x23961,x23963,x23964,x23965,x23966),f738(x23962,x23963,x23964,x23965,x23966))
% 51.10/50.84 [2397]~E(x23971,x23972)+E(f738(x23973,x23971,x23974,x23975,x23976),f738(x23973,x23972,x23974,x23975,x23976))
% 51.10/50.84 [2398]~E(x23981,x23982)+E(f738(x23983,x23984,x23981,x23985,x23986),f738(x23983,x23984,x23982,x23985,x23986))
% 51.10/50.84 [2399]~E(x23991,x23992)+E(f738(x23993,x23994,x23995,x23991,x23996),f738(x23993,x23994,x23995,x23992,x23996))
% 51.10/50.84 [2400]~E(x24001,x24002)+E(f738(x24003,x24004,x24005,x24006,x24001),f738(x24003,x24004,x24005,x24006,x24002))
% 51.10/50.84 [2401]~E(x24011,x24012)+E(f397(x24011,x24013,x24014),f397(x24012,x24013,x24014))
% 51.10/50.84 [2402]~E(x24021,x24022)+E(f397(x24023,x24021,x24024),f397(x24023,x24022,x24024))
% 51.10/50.84 [2403]~E(x24031,x24032)+E(f397(x24033,x24034,x24031),f397(x24033,x24034,x24032))
% 51.10/50.84 [2404]~E(x24041,x24042)+E(f315(x24041,x24043,x24044),f315(x24042,x24043,x24044))
% 51.10/50.84 [2405]~E(x24051,x24052)+E(f315(x24053,x24051,x24054),f315(x24053,x24052,x24054))
% 51.10/50.84 [2406]~E(x24061,x24062)+E(f315(x24063,x24064,x24061),f315(x24063,x24064,x24062))
% 51.10/50.84 [2407]~E(x24071,x24072)+E(f711(x24071,x24073,x24074,x24075,x24076,x24077,x24078),f711(x24072,x24073,x24074,x24075,x24076,x24077,x24078))
% 51.10/50.84 [2408]~E(x24081,x24082)+E(f711(x24083,x24081,x24084,x24085,x24086,x24087,x24088),f711(x24083,x24082,x24084,x24085,x24086,x24087,x24088))
% 51.10/50.84 [2409]~E(x24091,x24092)+E(f711(x24093,x24094,x24091,x24095,x24096,x24097,x24098),f711(x24093,x24094,x24092,x24095,x24096,x24097,x24098))
% 51.10/50.84 [2410]~E(x24101,x24102)+E(f711(x24103,x24104,x24105,x24101,x24106,x24107,x24108),f711(x24103,x24104,x24105,x24102,x24106,x24107,x24108))
% 51.10/50.84 [2411]~E(x24111,x24112)+E(f711(x24113,x24114,x24115,x24116,x24111,x24117,x24118),f711(x24113,x24114,x24115,x24116,x24112,x24117,x24118))
% 51.10/50.84 [2412]~E(x24121,x24122)+E(f711(x24123,x24124,x24125,x24126,x24127,x24121,x24128),f711(x24123,x24124,x24125,x24126,x24127,x24122,x24128))
% 51.10/50.84 [2413]~E(x24131,x24132)+E(f711(x24133,x24134,x24135,x24136,x24137,x24138,x24131),f711(x24133,x24134,x24135,x24136,x24137,x24138,x24132))
% 51.10/50.84 [2414]~E(x24141,x24142)+E(f494(x24141,x24143,x24144,x24145,x24146),f494(x24142,x24143,x24144,x24145,x24146))
% 51.10/50.84 [2415]~E(x24151,x24152)+E(f494(x24153,x24151,x24154,x24155,x24156),f494(x24153,x24152,x24154,x24155,x24156))
% 51.10/50.84 [2416]~E(x24161,x24162)+E(f494(x24163,x24164,x24161,x24165,x24166),f494(x24163,x24164,x24162,x24165,x24166))
% 51.10/50.84 [2417]~E(x24171,x24172)+E(f494(x24173,x24174,x24175,x24171,x24176),f494(x24173,x24174,x24175,x24172,x24176))
% 51.10/50.84 [2418]~E(x24181,x24182)+E(f494(x24183,x24184,x24185,x24186,x24181),f494(x24183,x24184,x24185,x24186,x24182))
% 51.10/50.84 [2419]~E(x24191,x24192)+E(f607(x24191,x24193,x24194,x24195,x24196,x24197),f607(x24192,x24193,x24194,x24195,x24196,x24197))
% 51.10/50.84 [2420]~E(x24201,x24202)+E(f607(x24203,x24201,x24204,x24205,x24206,x24207),f607(x24203,x24202,x24204,x24205,x24206,x24207))
% 51.10/50.84 [2421]~E(x24211,x24212)+E(f607(x24213,x24214,x24211,x24215,x24216,x24217),f607(x24213,x24214,x24212,x24215,x24216,x24217))
% 51.10/50.84 [2422]~E(x24221,x24222)+E(f607(x24223,x24224,x24225,x24221,x24226,x24227),f607(x24223,x24224,x24225,x24222,x24226,x24227))
% 51.10/50.84 [2423]~E(x24231,x24232)+E(f607(x24233,x24234,x24235,x24236,x24231,x24237),f607(x24233,x24234,x24235,x24236,x24232,x24237))
% 51.10/50.84 [2424]~E(x24241,x24242)+E(f607(x24243,x24244,x24245,x24246,x24247,x24241),f607(x24243,x24244,x24245,x24246,x24247,x24242))
% 51.10/50.84 [2425]~E(x24251,x24252)+E(f628(x24251,x24253,x24254,x24255,x24256,x24257),f628(x24252,x24253,x24254,x24255,x24256,x24257))
% 51.10/50.84 [2426]~E(x24261,x24262)+E(f628(x24263,x24261,x24264,x24265,x24266,x24267),f628(x24263,x24262,x24264,x24265,x24266,x24267))
% 51.10/50.84 [2427]~E(x24271,x24272)+E(f628(x24273,x24274,x24271,x24275,x24276,x24277),f628(x24273,x24274,x24272,x24275,x24276,x24277))
% 51.10/50.84 [2428]~E(x24281,x24282)+E(f628(x24283,x24284,x24285,x24281,x24286,x24287),f628(x24283,x24284,x24285,x24282,x24286,x24287))
% 51.10/50.84 [2429]~E(x24291,x24292)+E(f628(x24293,x24294,x24295,x24296,x24291,x24297),f628(x24293,x24294,x24295,x24296,x24292,x24297))
% 51.10/50.84 [2430]~E(x24301,x24302)+E(f628(x24303,x24304,x24305,x24306,x24307,x24301),f628(x24303,x24304,x24305,x24306,x24307,x24302))
% 51.10/50.84 [2431]~E(x24311,x24312)+E(f209(x24311,x24313,x24314,x24315,x24316,x24317,x24318),f209(x24312,x24313,x24314,x24315,x24316,x24317,x24318))
% 51.10/50.84 [2432]~E(x24321,x24322)+E(f209(x24323,x24321,x24324,x24325,x24326,x24327,x24328),f209(x24323,x24322,x24324,x24325,x24326,x24327,x24328))
% 51.10/50.84 [2433]~E(x24331,x24332)+E(f209(x24333,x24334,x24331,x24335,x24336,x24337,x24338),f209(x24333,x24334,x24332,x24335,x24336,x24337,x24338))
% 51.10/50.84 [2434]~E(x24341,x24342)+E(f209(x24343,x24344,x24345,x24341,x24346,x24347,x24348),f209(x24343,x24344,x24345,x24342,x24346,x24347,x24348))
% 51.10/50.84 [2435]~E(x24351,x24352)+E(f209(x24353,x24354,x24355,x24356,x24351,x24357,x24358),f209(x24353,x24354,x24355,x24356,x24352,x24357,x24358))
% 51.10/50.84 [2436]~E(x24361,x24362)+E(f209(x24363,x24364,x24365,x24366,x24367,x24361,x24368),f209(x24363,x24364,x24365,x24366,x24367,x24362,x24368))
% 51.10/50.84 [2437]~E(x24371,x24372)+E(f209(x24373,x24374,x24375,x24376,x24377,x24378,x24371),f209(x24373,x24374,x24375,x24376,x24377,x24378,x24372))
% 51.10/50.84 [2438]~E(x24381,x24382)+E(f213(x24381,x24383,x24384,x24385,x24386,x24387,x24388),f213(x24382,x24383,x24384,x24385,x24386,x24387,x24388))
% 51.10/50.84 [2439]~E(x24391,x24392)+E(f213(x24393,x24391,x24394,x24395,x24396,x24397,x24398),f213(x24393,x24392,x24394,x24395,x24396,x24397,x24398))
% 51.10/50.84 [2440]~E(x24401,x24402)+E(f213(x24403,x24404,x24401,x24405,x24406,x24407,x24408),f213(x24403,x24404,x24402,x24405,x24406,x24407,x24408))
% 51.10/50.84 [2441]~E(x24411,x24412)+E(f213(x24413,x24414,x24415,x24411,x24416,x24417,x24418),f213(x24413,x24414,x24415,x24412,x24416,x24417,x24418))
% 51.10/50.84 [2442]~E(x24421,x24422)+E(f213(x24423,x24424,x24425,x24426,x24421,x24427,x24428),f213(x24423,x24424,x24425,x24426,x24422,x24427,x24428))
% 51.10/50.84 [2443]~E(x24431,x24432)+E(f213(x24433,x24434,x24435,x24436,x24437,x24431,x24438),f213(x24433,x24434,x24435,x24436,x24437,x24432,x24438))
% 51.10/50.84 [2444]~E(x24441,x24442)+E(f213(x24443,x24444,x24445,x24446,x24447,x24448,x24441),f213(x24443,x24444,x24445,x24446,x24447,x24448,x24442))
% 51.10/50.84 [2445]~E(x24451,x24452)+E(f830(x24451,x24453,x24454),f830(x24452,x24453,x24454))
% 51.10/50.84 [2446]~E(x24461,x24462)+E(f830(x24463,x24461,x24464),f830(x24463,x24462,x24464))
% 51.10/50.84 [2447]~E(x24471,x24472)+E(f830(x24473,x24474,x24471),f830(x24473,x24474,x24472))
% 51.10/50.84 [2448]~E(x24481,x24482)+E(f270(x24481,x24483,x24484),f270(x24482,x24483,x24484))
% 51.10/50.84 [2449]~E(x24491,x24492)+E(f270(x24493,x24491,x24494),f270(x24493,x24492,x24494))
% 51.10/50.84 [2450]~E(x24501,x24502)+E(f270(x24503,x24504,x24501),f270(x24503,x24504,x24502))
% 51.10/50.84 [2451]~E(x24511,x24512)+E(f663(x24511,x24513,x24514),f663(x24512,x24513,x24514))
% 51.10/50.84 [2452]~E(x24521,x24522)+E(f663(x24523,x24521,x24524),f663(x24523,x24522,x24524))
% 51.10/50.84 [2453]~E(x24531,x24532)+E(f663(x24533,x24534,x24531),f663(x24533,x24534,x24532))
% 51.10/50.84 [2454]~E(x24541,x24542)+E(f860(x24541),f860(x24542))
% 51.10/50.84 [2455]~E(x24551,x24552)+E(f123(x24551,x24553,x24554,x24555),f123(x24552,x24553,x24554,x24555))
% 51.10/50.84 [2456]~E(x24561,x24562)+E(f123(x24563,x24561,x24564,x24565),f123(x24563,x24562,x24564,x24565))
% 51.10/50.84 [2457]~E(x24571,x24572)+E(f123(x24573,x24574,x24571,x24575),f123(x24573,x24574,x24572,x24575))
% 51.10/50.84 [2458]~E(x24581,x24582)+E(f123(x24583,x24584,x24585,x24581),f123(x24583,x24584,x24585,x24582))
% 51.10/50.84 [2459]~E(x24591,x24592)+E(f598(x24591,x24593,x24594),f598(x24592,x24593,x24594))
% 51.10/50.84 [2460]~E(x24601,x24602)+E(f598(x24603,x24601,x24604),f598(x24603,x24602,x24604))
% 51.10/50.84 [2461]~E(x24611,x24612)+E(f598(x24613,x24614,x24611),f598(x24613,x24614,x24612))
% 51.10/50.84 [2462]~E(x24621,x24622)+E(f569(x24621,x24623),f569(x24622,x24623))
% 51.10/50.84 [2463]~E(x24631,x24632)+E(f569(x24633,x24631),f569(x24633,x24632))
% 51.10/50.84 [2464]~E(x24641,x24642)+E(f636(x24641,x24643,x24644,x24645,x24646),f636(x24642,x24643,x24644,x24645,x24646))
% 51.10/50.84 [2465]~E(x24651,x24652)+E(f636(x24653,x24651,x24654,x24655,x24656),f636(x24653,x24652,x24654,x24655,x24656))
% 51.10/50.84 [2466]~E(x24661,x24662)+E(f636(x24663,x24664,x24661,x24665,x24666),f636(x24663,x24664,x24662,x24665,x24666))
% 51.10/50.84 [2467]~E(x24671,x24672)+E(f636(x24673,x24674,x24675,x24671,x24676),f636(x24673,x24674,x24675,x24672,x24676))
% 51.10/50.84 [2468]~E(x24681,x24682)+E(f636(x24683,x24684,x24685,x24686,x24681),f636(x24683,x24684,x24685,x24686,x24682))
% 51.10/50.84 [2469]~E(x24691,x24692)+E(f232(x24691,x24693,x24694,x24695),f232(x24692,x24693,x24694,x24695))
% 51.10/50.84 [2470]~E(x24701,x24702)+E(f232(x24703,x24701,x24704,x24705),f232(x24703,x24702,x24704,x24705))
% 51.10/50.84 [2471]~E(x24711,x24712)+E(f232(x24713,x24714,x24711,x24715),f232(x24713,x24714,x24712,x24715))
% 51.10/50.84 [2472]~E(x24721,x24722)+E(f232(x24723,x24724,x24725,x24721),f232(x24723,x24724,x24725,x24722))
% 51.10/50.84 [2473]~E(x24731,x24732)+E(f385(x24731,x24733,x24734,x24735,x24736),f385(x24732,x24733,x24734,x24735,x24736))
% 51.10/50.84 [2474]~E(x24741,x24742)+E(f385(x24743,x24741,x24744,x24745,x24746),f385(x24743,x24742,x24744,x24745,x24746))
% 51.10/50.84 [2475]~E(x24751,x24752)+E(f385(x24753,x24754,x24751,x24755,x24756),f385(x24753,x24754,x24752,x24755,x24756))
% 51.10/50.84 [2476]~E(x24761,x24762)+E(f385(x24763,x24764,x24765,x24761,x24766),f385(x24763,x24764,x24765,x24762,x24766))
% 51.10/50.84 [2477]~E(x24771,x24772)+E(f385(x24773,x24774,x24775,x24776,x24771),f385(x24773,x24774,x24775,x24776,x24772))
% 51.10/50.84 [2478]~E(x24781,x24782)+E(f274(x24781,x24783),f274(x24782,x24783))
% 51.10/50.84 [2479]~E(x24791,x24792)+E(f274(x24793,x24791),f274(x24793,x24792))
% 51.10/50.84 [2480]~E(x24801,x24802)+E(f405(x24801,x24803),f405(x24802,x24803))
% 51.10/50.84 [2481]~E(x24811,x24812)+E(f405(x24813,x24811),f405(x24813,x24812))
% 51.10/50.84 [2482]~E(x24821,x24822)+E(f226(x24821,x24823,x24824,x24825,x24826),f226(x24822,x24823,x24824,x24825,x24826))
% 51.10/50.84 [2483]~E(x24831,x24832)+E(f226(x24833,x24831,x24834,x24835,x24836),f226(x24833,x24832,x24834,x24835,x24836))
% 51.10/50.84 [2484]~E(x24841,x24842)+E(f226(x24843,x24844,x24841,x24845,x24846),f226(x24843,x24844,x24842,x24845,x24846))
% 51.10/50.84 [2485]~E(x24851,x24852)+E(f226(x24853,x24854,x24855,x24851,x24856),f226(x24853,x24854,x24855,x24852,x24856))
% 51.10/50.84 [2486]~E(x24861,x24862)+E(f226(x24863,x24864,x24865,x24866,x24861),f226(x24863,x24864,x24865,x24866,x24862))
% 51.10/50.84 [2487]~E(x24871,x24872)+E(f619(x24871,x24873,x24874,x24875,x24876,x24877),f619(x24872,x24873,x24874,x24875,x24876,x24877))
% 51.10/50.84 [2488]~E(x24881,x24882)+E(f619(x24883,x24881,x24884,x24885,x24886,x24887),f619(x24883,x24882,x24884,x24885,x24886,x24887))
% 51.10/50.84 [2489]~E(x24891,x24892)+E(f619(x24893,x24894,x24891,x24895,x24896,x24897),f619(x24893,x24894,x24892,x24895,x24896,x24897))
% 51.10/50.84 [2490]~E(x24901,x24902)+E(f619(x24903,x24904,x24905,x24901,x24906,x24907),f619(x24903,x24904,x24905,x24902,x24906,x24907))
% 51.10/50.84 [2491]~E(x24911,x24912)+E(f619(x24913,x24914,x24915,x24916,x24911,x24917),f619(x24913,x24914,x24915,x24916,x24912,x24917))
% 51.10/50.84 [2492]~E(x24921,x24922)+E(f619(x24923,x24924,x24925,x24926,x24927,x24921),f619(x24923,x24924,x24925,x24926,x24927,x24922))
% 51.10/50.84 [2493]~E(x24931,x24932)+E(f822(x24931,x24933,x24934),f822(x24932,x24933,x24934))
% 51.10/50.84 [2494]~E(x24941,x24942)+E(f822(x24943,x24941,x24944),f822(x24943,x24942,x24944))
% 51.10/50.84 [2495]~E(x24951,x24952)+E(f822(x24953,x24954,x24951),f822(x24953,x24954,x24952))
% 51.10/50.84 [2496]~E(x24961,x24962)+E(f538(x24961),f538(x24962))
% 51.10/50.84 [2497]~E(x24971,x24972)+E(f486(x24971,x24973,x24974),f486(x24972,x24973,x24974))
% 51.10/50.84 [2498]~E(x24981,x24982)+E(f486(x24983,x24981,x24984),f486(x24983,x24982,x24984))
% 51.10/50.84 [2499]~E(x24991,x24992)+E(f486(x24993,x24994,x24991),f486(x24993,x24994,x24992))
% 51.10/50.84 [2500]~E(x25001,x25002)+E(f593(x25001,x25003),f593(x25002,x25003))
% 51.10/50.84 [2501]~E(x25011,x25012)+E(f593(x25013,x25011),f593(x25013,x25012))
% 51.10/50.84 [2502]~E(x25021,x25022)+E(f403(x25021,x25023,x25024,x25025,x25026),f403(x25022,x25023,x25024,x25025,x25026))
% 51.10/50.84 [2503]~E(x25031,x25032)+E(f403(x25033,x25031,x25034,x25035,x25036),f403(x25033,x25032,x25034,x25035,x25036))
% 51.10/50.84 [2504]~E(x25041,x25042)+E(f403(x25043,x25044,x25041,x25045,x25046),f403(x25043,x25044,x25042,x25045,x25046))
% 51.10/50.84 [2505]~E(x25051,x25052)+E(f403(x25053,x25054,x25055,x25051,x25056),f403(x25053,x25054,x25055,x25052,x25056))
% 51.10/50.84 [2506]~E(x25061,x25062)+E(f403(x25063,x25064,x25065,x25066,x25061),f403(x25063,x25064,x25065,x25066,x25062))
% 51.10/50.84 [2507]~E(x25071,x25072)+E(f620(x25071,x25073,x25074),f620(x25072,x25073,x25074))
% 51.10/50.84 [2508]~E(x25081,x25082)+E(f620(x25083,x25081,x25084),f620(x25083,x25082,x25084))
% 51.10/50.84 [2509]~E(x25091,x25092)+E(f620(x25093,x25094,x25091),f620(x25093,x25094,x25092))
% 51.10/50.84 [2510]~E(x25101,x25102)+E(f358(x25101,x25103,x25104,x25105,x25106,x25107),f358(x25102,x25103,x25104,x25105,x25106,x25107))
% 51.10/50.84 [2511]~E(x25111,x25112)+E(f358(x25113,x25111,x25114,x25115,x25116,x25117),f358(x25113,x25112,x25114,x25115,x25116,x25117))
% 51.10/50.84 [2512]~E(x25121,x25122)+E(f358(x25123,x25124,x25121,x25125,x25126,x25127),f358(x25123,x25124,x25122,x25125,x25126,x25127))
% 51.10/50.84 [2513]~E(x25131,x25132)+E(f358(x25133,x25134,x25135,x25131,x25136,x25137),f358(x25133,x25134,x25135,x25132,x25136,x25137))
% 51.10/50.84 [2514]~E(x25141,x25142)+E(f358(x25143,x25144,x25145,x25146,x25141,x25147),f358(x25143,x25144,x25145,x25146,x25142,x25147))
% 51.10/50.84 [2515]~E(x25151,x25152)+E(f358(x25153,x25154,x25155,x25156,x25157,x25151),f358(x25153,x25154,x25155,x25156,x25157,x25152))
% 51.10/50.84 [2516]~E(x25161,x25162)+E(f374(x25161,x25163,x25164),f374(x25162,x25163,x25164))
% 51.10/50.84 [2517]~E(x25171,x25172)+E(f374(x25173,x25171,x25174),f374(x25173,x25172,x25174))
% 51.10/50.84 [2518]~E(x25181,x25182)+E(f374(x25183,x25184,x25181),f374(x25183,x25184,x25182))
% 51.10/50.84 [2519]~E(x25191,x25192)+E(f357(x25191),f357(x25192))
% 51.10/50.84 [2520]~E(x25201,x25202)+E(f583(x25201,x25203,x25204,x25205),f583(x25202,x25203,x25204,x25205))
% 51.10/50.84 [2521]~E(x25211,x25212)+E(f583(x25213,x25211,x25214,x25215),f583(x25213,x25212,x25214,x25215))
% 51.10/50.84 [2522]~E(x25221,x25222)+E(f583(x25223,x25224,x25221,x25225),f583(x25223,x25224,x25222,x25225))
% 51.10/50.84 [2523]~E(x25231,x25232)+E(f583(x25233,x25234,x25235,x25231),f583(x25233,x25234,x25235,x25232))
% 51.10/50.84 [2524]~E(x25241,x25242)+E(f400(x25241,x25243,x25244,x25245,x25246),f400(x25242,x25243,x25244,x25245,x25246))
% 51.10/50.84 [2525]~E(x25251,x25252)+E(f400(x25253,x25251,x25254,x25255,x25256),f400(x25253,x25252,x25254,x25255,x25256))
% 51.10/50.84 [2526]~E(x25261,x25262)+E(f400(x25263,x25264,x25261,x25265,x25266),f400(x25263,x25264,x25262,x25265,x25266))
% 51.10/50.84 [2527]~E(x25271,x25272)+E(f400(x25273,x25274,x25275,x25271,x25276),f400(x25273,x25274,x25275,x25272,x25276))
% 51.10/50.84 [2528]~E(x25281,x25282)+E(f400(x25283,x25284,x25285,x25286,x25281),f400(x25283,x25284,x25285,x25286,x25282))
% 51.10/50.84 [2529]~E(x25291,x25292)+E(f469(x25291,x25293),f469(x25292,x25293))
% 51.10/50.84 [2530]~E(x25301,x25302)+E(f469(x25303,x25301),f469(x25303,x25302))
% 51.10/50.84 [2531]~P1(x25311)+P1(x25312)+~E(x25311,x25312)
% 51.10/50.84 [2532]~P2(x25321)+P2(x25322)+~E(x25321,x25322)
% 51.10/50.84 [2533]P34(x25332,x25333)+~E(x25331,x25332)+~P34(x25331,x25333)
% 51.10/50.84 [2534]P34(x25343,x25342)+~E(x25341,x25342)+~P34(x25343,x25341)
% 51.10/50.84 [2535]~P91(x25351)+P91(x25352)+~E(x25351,x25352)
% 51.10/50.84 [2536]~P84(x25361)+P84(x25362)+~E(x25361,x25362)
% 51.10/50.84 [2537]~P68(x25371)+P68(x25372)+~E(x25371,x25372)
% 51.10/50.84 [2538]P26(x25382,x25383,x25384)+~E(x25381,x25382)+~P26(x25381,x25383,x25384)
% 51.10/50.84 [2539]P26(x25393,x25392,x25394)+~E(x25391,x25392)+~P26(x25393,x25391,x25394)
% 51.10/50.84 [2540]P26(x25403,x25404,x25402)+~E(x25401,x25402)+~P26(x25403,x25404,x25401)
% 51.10/50.84 [2541]~P3(x25411)+P3(x25412)+~E(x25411,x25412)
% 51.10/50.84 [2542]~P76(x25421)+P76(x25422)+~E(x25421,x25422)
% 51.10/50.84 [2543]P21(x25432,x25433,x25434,x25435)+~E(x25431,x25432)+~P21(x25431,x25433,x25434,x25435)
% 51.10/50.84 [2544]P21(x25443,x25442,x25444,x25445)+~E(x25441,x25442)+~P21(x25443,x25441,x25444,x25445)
% 51.10/50.84 [2545]P21(x25453,x25454,x25452,x25455)+~E(x25451,x25452)+~P21(x25453,x25454,x25451,x25455)
% 51.10/50.84 [2546]P21(x25463,x25464,x25465,x25462)+~E(x25461,x25462)+~P21(x25463,x25464,x25465,x25461)
% 51.10/50.84 [2547]~P62(x25471)+P62(x25472)+~E(x25471,x25472)
% 51.10/50.84 [2548]~P104(x25481)+P104(x25482)+~E(x25481,x25482)
% 51.10/50.84 [2549]~P80(x25491)+P80(x25492)+~E(x25491,x25492)
% 51.10/50.84 [2550]~P66(x25501)+P66(x25502)+~E(x25501,x25502)
% 51.10/50.84 [2551]~P60(x25511)+P60(x25512)+~E(x25511,x25512)
% 51.10/50.84 [2552]~P102(x25521)+P102(x25522)+~E(x25521,x25522)
% 51.10/50.84 [2553]~P79(x25531)+P79(x25532)+~E(x25531,x25532)
% 51.10/50.84 [2554]~P85(x25541)+P85(x25542)+~E(x25541,x25542)
% 51.10/50.84 [2555]P27(x25552,x25553,x25554,x25555)+~E(x25551,x25552)+~P27(x25551,x25553,x25554,x25555)
% 51.10/50.84 [2556]P27(x25563,x25562,x25564,x25565)+~E(x25561,x25562)+~P27(x25563,x25561,x25564,x25565)
% 51.10/50.84 [2557]P27(x25573,x25574,x25572,x25575)+~E(x25571,x25572)+~P27(x25573,x25574,x25571,x25575)
% 51.10/50.84 [2558]P27(x25583,x25584,x25585,x25582)+~E(x25581,x25582)+~P27(x25583,x25584,x25585,x25581)
% 51.10/50.84 [2559]~P63(x25591)+P63(x25592)+~E(x25591,x25592)
% 51.10/50.84 [2560]~P74(x25601)+P74(x25602)+~E(x25601,x25602)
% 51.10/50.84 [2561]P16(x25612,x25613)+~E(x25611,x25612)+~P16(x25611,x25613)
% 51.10/50.84 [2562]P16(x25623,x25622)+~E(x25621,x25622)+~P16(x25623,x25621)
% 51.10/50.84 [2563]~P97(x25631)+P97(x25632)+~E(x25631,x25632)
% 51.10/50.84 [2564]P141(x25642,x25643,x25644)+~E(x25641,x25642)+~P141(x25641,x25643,x25644)
% 51.10/50.84 [2565]P141(x25653,x25652,x25654)+~E(x25651,x25652)+~P141(x25653,x25651,x25654)
% 51.10/50.84 [2566]P141(x25663,x25664,x25662)+~E(x25661,x25662)+~P141(x25663,x25664,x25661)
% 51.10/50.84 [2567]~P118(x25671)+P118(x25672)+~E(x25671,x25672)
% 51.10/50.84 [2568]~P67(x25681)+P67(x25682)+~E(x25681,x25682)
% 51.10/50.84 [2569]~P71(x25691)+P71(x25692)+~E(x25691,x25692)
% 51.10/50.84 [2570]~P101(x25701)+P101(x25702)+~E(x25701,x25702)
% 51.10/50.84 [2571]P140(x25712,x25713,x25714)+~E(x25711,x25712)+~P140(x25711,x25713,x25714)
% 51.10/50.84 [2572]P140(x25723,x25722,x25724)+~E(x25721,x25722)+~P140(x25723,x25721,x25724)
% 51.10/50.84 [2573]P140(x25733,x25734,x25732)+~E(x25731,x25732)+~P140(x25733,x25734,x25731)
% 51.10/50.84 [2574]P29(x25742,x25743,x25744)+~E(x25741,x25742)+~P29(x25741,x25743,x25744)
% 51.10/50.84 [2575]P29(x25753,x25752,x25754)+~E(x25751,x25752)+~P29(x25753,x25751,x25754)
% 51.10/50.84 [2576]P29(x25763,x25764,x25762)+~E(x25761,x25762)+~P29(x25763,x25764,x25761)
% 51.10/50.84 [2577]P30(x25772,x25773,x25774)+~E(x25771,x25772)+~P30(x25771,x25773,x25774)
% 51.10/50.84 [2578]P30(x25783,x25782,x25784)+~E(x25781,x25782)+~P30(x25783,x25781,x25784)
% 51.10/50.84 [2579]P30(x25793,x25794,x25792)+~E(x25791,x25792)+~P30(x25793,x25794,x25791)
% 51.10/50.84 [2580]~P5(x25801)+P5(x25802)+~E(x25801,x25802)
% 51.10/50.84 [2581]~P87(x25811)+P87(x25812)+~E(x25811,x25812)
% 51.10/50.84 [2582]~P36(x25821)+P36(x25822)+~E(x25821,x25822)
% 51.10/50.84 [2583]~P133(x25831)+P133(x25832)+~E(x25831,x25832)
% 51.10/50.84 [2584]~P86(x25841)+P86(x25842)+~E(x25841,x25842)
% 51.10/50.84 [2585]~P137(x25851)+P137(x25852)+~E(x25851,x25852)
% 51.10/50.84 [2586]P52(x25862,x25863,x25864)+~E(x25861,x25862)+~P52(x25861,x25863,x25864)
% 51.10/50.84 [2587]P52(x25873,x25872,x25874)+~E(x25871,x25872)+~P52(x25873,x25871,x25874)
% 51.10/50.84 [2588]P52(x25883,x25884,x25882)+~E(x25881,x25882)+~P52(x25883,x25884,x25881)
% 51.10/50.84 [2589]~P78(x25891)+P78(x25892)+~E(x25891,x25892)
% 51.10/50.84 [2590]P37(x25902,x25903,x25904,x25905)+~E(x25901,x25902)+~P37(x25901,x25903,x25904,x25905)
% 51.10/50.84 [2591]P37(x25913,x25912,x25914,x25915)+~E(x25911,x25912)+~P37(x25913,x25911,x25914,x25915)
% 51.10/50.84 [2592]P37(x25923,x25924,x25922,x25925)+~E(x25921,x25922)+~P37(x25923,x25924,x25921,x25925)
% 51.10/50.84 [2593]P37(x25933,x25934,x25935,x25932)+~E(x25931,x25932)+~P37(x25933,x25934,x25935,x25931)
% 51.10/50.84 [2594]~P132(x25941)+P132(x25942)+~E(x25941,x25942)
% 51.10/50.84 [2595]~P88(x25951)+P88(x25952)+~E(x25951,x25952)
% 51.10/50.84 [2596]P32(x25962,x25963,x25964,x25965)+~E(x25961,x25962)+~P32(x25961,x25963,x25964,x25965)
% 51.10/50.84 [2597]P32(x25973,x25972,x25974,x25975)+~E(x25971,x25972)+~P32(x25973,x25971,x25974,x25975)
% 51.10/50.84 [2598]P32(x25983,x25984,x25982,x25985)+~E(x25981,x25982)+~P32(x25983,x25984,x25981,x25985)
% 51.10/50.84 [2599]P32(x25993,x25994,x25995,x25992)+~E(x25991,x25992)+~P32(x25993,x25994,x25995,x25991)
% 51.10/50.84 [2600]~P7(x26001)+P7(x26002)+~E(x26001,x26002)
% 51.10/50.84 [2601]~P92(x26011)+P92(x26012)+~E(x26011,x26012)
% 51.10/50.84 [2602]~P89(x26021)+P89(x26022)+~E(x26021,x26022)
% 51.10/50.84 [2603]~P4(x26031)+P4(x26032)+~E(x26031,x26032)
% 51.10/50.84 [2604]P56(x26042,x26043)+~E(x26041,x26042)+~P56(x26041,x26043)
% 51.10/50.84 [2605]P56(x26053,x26052)+~E(x26051,x26052)+~P56(x26053,x26051)
% 51.10/50.84 [2606]~P105(x26061)+P105(x26062)+~E(x26061,x26062)
% 51.10/50.84 [2607]P10(x26072,x26073,x26074)+~E(x26071,x26072)+~P10(x26071,x26073,x26074)
% 51.10/50.84 [2608]P10(x26083,x26082,x26084)+~E(x26081,x26082)+~P10(x26083,x26081,x26084)
% 51.10/50.84 [2609]P10(x26093,x26094,x26092)+~E(x26091,x26092)+~P10(x26093,x26094,x26091)
% 51.10/50.84 [2610]~P70(x26101)+P70(x26102)+~E(x26101,x26102)
% 51.10/50.84 [2611]~P64(x26111)+P64(x26112)+~E(x26111,x26112)
% 51.10/50.84 [2612]~P94(x26121)+P94(x26122)+~E(x26121,x26122)
% 51.10/50.84 [2613]~P119(x26131)+P119(x26132)+~E(x26131,x26132)
% 51.10/50.84 [2614]~P100(x26141)+P100(x26142)+~E(x26141,x26142)
% 51.10/50.84 [2615]~P11(x26151)+P11(x26152)+~E(x26151,x26152)
% 51.10/50.84 [2616]P18(x26162,x26163,x26164)+~E(x26161,x26162)+~P18(x26161,x26163,x26164)
% 51.10/50.84 [2617]P18(x26173,x26172,x26174)+~E(x26171,x26172)+~P18(x26173,x26171,x26174)
% 51.10/50.84 [2618]P18(x26183,x26184,x26182)+~E(x26181,x26182)+~P18(x26183,x26184,x26181)
% 51.10/50.84 [2619]P25(x26192,x26193,x26194,x26195,x26196,x26197)+~E(x26191,x26192)+~P25(x26191,x26193,x26194,x26195,x26196,x26197)
% 51.10/50.84 [2620]P25(x26203,x26202,x26204,x26205,x26206,x26207)+~E(x26201,x26202)+~P25(x26203,x26201,x26204,x26205,x26206,x26207)
% 51.10/50.84 [2621]P25(x26213,x26214,x26212,x26215,x26216,x26217)+~E(x26211,x26212)+~P25(x26213,x26214,x26211,x26215,x26216,x26217)
% 51.10/50.84 [2622]P25(x26223,x26224,x26225,x26222,x26226,x26227)+~E(x26221,x26222)+~P25(x26223,x26224,x26225,x26221,x26226,x26227)
% 51.10/50.84 [2623]P25(x26233,x26234,x26235,x26236,x26232,x26237)+~E(x26231,x26232)+~P25(x26233,x26234,x26235,x26236,x26231,x26237)
% 51.10/50.84 [2624]P25(x26243,x26244,x26245,x26246,x26247,x26242)+~E(x26241,x26242)+~P25(x26243,x26244,x26245,x26246,x26247,x26241)
% 51.10/50.84 [2625]P13(x26252,x26253,x26254,x26255,x26256)+~E(x26251,x26252)+~P13(x26251,x26253,x26254,x26255,x26256)
% 51.10/50.84 [2626]P13(x26263,x26262,x26264,x26265,x26266)+~E(x26261,x26262)+~P13(x26263,x26261,x26264,x26265,x26266)
% 51.10/50.84 [2627]P13(x26273,x26274,x26272,x26275,x26276)+~E(x26271,x26272)+~P13(x26273,x26274,x26271,x26275,x26276)
% 51.10/50.84 [2628]P13(x26283,x26284,x26285,x26282,x26286)+~E(x26281,x26282)+~P13(x26283,x26284,x26285,x26281,x26286)
% 51.10/50.84 [2629]P13(x26293,x26294,x26295,x26296,x26292)+~E(x26291,x26292)+~P13(x26293,x26294,x26295,x26296,x26291)
% 51.10/50.84 [2630]~P112(x26301)+P112(x26302)+~E(x26301,x26302)
% 51.10/50.84 [2631]~P120(x26311)+P120(x26312)+~E(x26311,x26312)
% 51.10/50.84 [2632]~P121(x26321)+P121(x26322)+~E(x26321,x26322)
% 51.10/50.84 [2633]~P90(x26331)+P90(x26332)+~E(x26331,x26332)
% 51.10/50.84 [2634]P45(x26342,x26343,x26344)+~E(x26341,x26342)+~P45(x26341,x26343,x26344)
% 51.10/50.84 [2635]P45(x26353,x26352,x26354)+~E(x26351,x26352)+~P45(x26353,x26351,x26354)
% 51.10/50.84 [2636]P45(x26363,x26364,x26362)+~E(x26361,x26362)+~P45(x26363,x26364,x26361)
% 51.10/50.84 [2637]~P128(x26371)+P128(x26372)+~E(x26371,x26372)
% 51.10/50.84 [2638]P51(x26382,x26383,x26384)+~E(x26381,x26382)+~P51(x26381,x26383,x26384)
% 51.10/50.84 [2639]P51(x26393,x26392,x26394)+~E(x26391,x26392)+~P51(x26393,x26391,x26394)
% 51.10/50.84 [2640]P51(x26403,x26404,x26402)+~E(x26401,x26402)+~P51(x26403,x26404,x26401)
% 51.10/50.84 [2641]~P58(x26411)+P58(x26412)+~E(x26411,x26412)
% 51.10/50.84 [2642]~P69(x26421)+P69(x26422)+~E(x26421,x26422)
% 51.10/50.84 [2643]P9(x26432,x26433)+~E(x26431,x26432)+~P9(x26431,x26433)
% 51.10/50.84 [2644]P9(x26443,x26442)+~E(x26441,x26442)+~P9(x26443,x26441)
% 51.10/50.84 [2645]P54(x26452,x26453)+~E(x26451,x26452)+~P54(x26451,x26453)
% 51.10/50.84 [2646]P54(x26463,x26462)+~E(x26461,x26462)+~P54(x26463,x26461)
% 51.10/50.84 [2647]~P123(x26471)+P123(x26472)+~E(x26471,x26472)
% 51.10/50.84 [2648]~P61(x26481)+P61(x26482)+~E(x26481,x26482)
% 51.10/50.84 [2649]~P131(x26491)+P131(x26492)+~E(x26491,x26492)
% 51.10/50.84 [2650]P31(x26502,x26503)+~E(x26501,x26502)+~P31(x26501,x26503)
% 51.10/50.84 [2651]P31(x26513,x26512)+~E(x26511,x26512)+~P31(x26513,x26511)
% 51.10/50.84 [2652]~P75(x26521)+P75(x26522)+~E(x26521,x26522)
% 51.10/50.84 [2653]~P59(x26531)+P59(x26532)+~E(x26531,x26532)
% 51.10/50.84 [2654]P55(x26542,x26543,x26544,x26545)+~E(x26541,x26542)+~P55(x26541,x26543,x26544,x26545)
% 51.10/50.84 [2655]P55(x26553,x26552,x26554,x26555)+~E(x26551,x26552)+~P55(x26553,x26551,x26554,x26555)
% 51.10/50.84 [2656]P55(x26563,x26564,x26562,x26565)+~E(x26561,x26562)+~P55(x26563,x26564,x26561,x26565)
% 51.10/50.84 [2657]P55(x26573,x26574,x26575,x26572)+~E(x26571,x26572)+~P55(x26573,x26574,x26575,x26571)
% 51.10/50.84 [2658]~P106(x26581)+P106(x26582)+~E(x26581,x26582)
% 51.10/50.84 [2659]P22(x26592,x26593,x26594,x26595)+~E(x26591,x26592)+~P22(x26591,x26593,x26594,x26595)
% 51.10/50.84 [2660]P22(x26603,x26602,x26604,x26605)+~E(x26601,x26602)+~P22(x26603,x26601,x26604,x26605)
% 51.10/50.84 [2661]P22(x26613,x26614,x26612,x26615)+~E(x26611,x26612)+~P22(x26613,x26614,x26611,x26615)
% 51.10/50.84 [2662]P22(x26623,x26624,x26625,x26622)+~E(x26621,x26622)+~P22(x26623,x26624,x26625,x26621)
% 51.10/50.84 [2663]~P99(x26631)+P99(x26632)+~E(x26631,x26632)
% 51.10/50.84 [2664]~P122(x26641)+P122(x26642)+~E(x26641,x26642)
% 51.10/50.84 [2665]~P57(x26651)+P57(x26652)+~E(x26651,x26652)
% 51.10/50.84 [2666]~P8(x26661)+P8(x26662)+~E(x26661,x26662)
% 51.10/50.84 [2667]~P134(x26671)+P134(x26672)+~E(x26671,x26672)
% 51.10/50.84 [2668]~P127(x26681)+P127(x26682)+~E(x26681,x26682)
% 51.10/50.84 [2669]~P114(x26691)+P114(x26692)+~E(x26691,x26692)
% 51.10/50.84 [2670]P19(x26702,x26703,x26704)+~E(x26701,x26702)+~P19(x26701,x26703,x26704)
% 51.10/50.84 [2671]P19(x26713,x26712,x26714)+~E(x26711,x26712)+~P19(x26713,x26711,x26714)
% 51.10/50.84 [2672]P19(x26723,x26724,x26722)+~E(x26721,x26722)+~P19(x26723,x26724,x26721)
% 51.10/50.84 [2673]~P138(x26731)+P138(x26732)+~E(x26731,x26732)
% 51.10/50.84 [2674]P43(x26742,x26743,x26744)+~E(x26741,x26742)+~P43(x26741,x26743,x26744)
% 51.10/50.84 [2675]P43(x26753,x26752,x26754)+~E(x26751,x26752)+~P43(x26753,x26751,x26754)
% 51.10/50.84 [2676]P43(x26763,x26764,x26762)+~E(x26761,x26762)+~P43(x26763,x26764,x26761)
% 51.10/50.84 [2677]~P98(x26771)+P98(x26772)+~E(x26771,x26772)
% 51.10/50.84 [2678]~P111(x26781)+P111(x26782)+~E(x26781,x26782)
% 51.10/50.84 [2679]P143(x26792,x26793)+~E(x26791,x26792)+~P143(x26791,x26793)
% 51.10/50.84 [2680]P143(x26803,x26802)+~E(x26801,x26802)+~P143(x26803,x26801)
% 51.10/50.84 [2681]~P113(x26811)+P113(x26812)+~E(x26811,x26812)
% 51.10/50.84 [2682]~P135(x26821)+P135(x26822)+~E(x26821,x26822)
% 51.10/50.84 [2683]~P125(x26831)+P125(x26832)+~E(x26831,x26832)
% 51.10/50.84 [2684]P20(x26842,x26843,x26844)+~E(x26841,x26842)+~P20(x26841,x26843,x26844)
% 51.10/50.84 [2685]P20(x26853,x26852,x26854)+~E(x26851,x26852)+~P20(x26853,x26851,x26854)
% 51.10/50.84 [2686]P20(x26863,x26864,x26862)+~E(x26861,x26862)+~P20(x26863,x26864,x26861)
% 51.10/50.84 [2687]~P93(x26871)+P93(x26872)+~E(x26871,x26872)
% 51.10/50.84 [2688]~P116(x26881)+P116(x26882)+~E(x26881,x26882)
% 51.10/50.84 [2689]~P95(x26891)+P95(x26892)+~E(x26891,x26892)
% 51.10/50.84 [2690]P50(x26902,x26903,x26904,x26905)+~E(x26901,x26902)+~P50(x26901,x26903,x26904,x26905)
% 51.10/50.84 [2691]P50(x26913,x26912,x26914,x26915)+~E(x26911,x26912)+~P50(x26913,x26911,x26914,x26915)
% 51.10/50.84 [2692]P50(x26923,x26924,x26922,x26925)+~E(x26921,x26922)+~P50(x26923,x26924,x26921,x26925)
% 51.10/50.84 [2693]P50(x26933,x26934,x26935,x26932)+~E(x26931,x26932)+~P50(x26933,x26934,x26935,x26931)
% 51.10/50.84 [2694]P46(x26942,x26943)+~E(x26941,x26942)+~P46(x26941,x26943)
% 51.10/50.84 [2695]P46(x26953,x26952)+~E(x26951,x26952)+~P46(x26953,x26951)
% 51.10/50.84 [2696]~P83(x26961)+P83(x26962)+~E(x26961,x26962)
% 51.10/50.84 [2697]~P136(x26971)+P136(x26972)+~E(x26971,x26972)
% 51.10/50.84 [2698]P15(x26982,x26983,x26984,x26985,x26986,x26987)+~E(x26981,x26982)+~P15(x26981,x26983,x26984,x26985,x26986,x26987)
% 51.10/50.84 [2699]P15(x26993,x26992,x26994,x26995,x26996,x26997)+~E(x26991,x26992)+~P15(x26993,x26991,x26994,x26995,x26996,x26997)
% 51.10/50.84 [2700]P15(x27003,x27004,x27002,x27005,x27006,x27007)+~E(x27001,x27002)+~P15(x27003,x27004,x27001,x27005,x27006,x27007)
% 51.10/50.84 [2701]P15(x27013,x27014,x27015,x27012,x27016,x27017)+~E(x27011,x27012)+~P15(x27013,x27014,x27015,x27011,x27016,x27017)
% 51.10/50.84 [2702]P15(x27023,x27024,x27025,x27026,x27022,x27027)+~E(x27021,x27022)+~P15(x27023,x27024,x27025,x27026,x27021,x27027)
% 51.10/50.84 [2703]P15(x27033,x27034,x27035,x27036,x27037,x27032)+~E(x27031,x27032)+~P15(x27033,x27034,x27035,x27036,x27037,x27031)
% 51.10/50.84 [2704]~P81(x27041)+P81(x27042)+~E(x27041,x27042)
% 51.10/50.84 [2705]~P124(x27051)+P124(x27052)+~E(x27051,x27052)
% 51.10/50.84 [2706]~P77(x27061)+P77(x27062)+~E(x27061,x27062)
% 51.10/50.84 [2707]~P107(x27071)+P107(x27072)+~E(x27071,x27072)
% 51.10/50.84 [2708]P48(x27082,x27083,x27084,x27085)+~E(x27081,x27082)+~P48(x27081,x27083,x27084,x27085)
% 51.10/50.84 [2709]P48(x27093,x27092,x27094,x27095)+~E(x27091,x27092)+~P48(x27093,x27091,x27094,x27095)
% 51.10/50.84 [2710]P48(x27103,x27104,x27102,x27105)+~E(x27101,x27102)+~P48(x27103,x27104,x27101,x27105)
% 51.10/50.84 [2711]P48(x27113,x27114,x27115,x27112)+~E(x27111,x27112)+~P48(x27113,x27114,x27115,x27111)
% 51.10/50.84 [2712]P49(x27122,x27123,x27124,x27125,x27126,x27127,x27128)+~E(x27121,x27122)+~P49(x27121,x27123,x27124,x27125,x27126,x27127,x27128)
% 51.10/50.84 [2713]P49(x27133,x27132,x27134,x27135,x27136,x27137,x27138)+~E(x27131,x27132)+~P49(x27133,x27131,x27134,x27135,x27136,x27137,x27138)
% 51.10/50.84 [2714]P49(x27143,x27144,x27142,x27145,x27146,x27147,x27148)+~E(x27141,x27142)+~P49(x27143,x27144,x27141,x27145,x27146,x27147,x27148)
% 51.10/50.84 [2715]P49(x27153,x27154,x27155,x27152,x27156,x27157,x27158)+~E(x27151,x27152)+~P49(x27153,x27154,x27155,x27151,x27156,x27157,x27158)
% 51.10/50.84 [2716]P49(x27163,x27164,x27165,x27166,x27162,x27167,x27168)+~E(x27161,x27162)+~P49(x27163,x27164,x27165,x27166,x27161,x27167,x27168)
% 51.10/50.84 [2717]P49(x27173,x27174,x27175,x27176,x27177,x27172,x27178)+~E(x27171,x27172)+~P49(x27173,x27174,x27175,x27176,x27177,x27171,x27178)
% 51.10/50.84 [2718]P49(x27183,x27184,x27185,x27186,x27187,x27188,x27182)+~E(x27181,x27182)+~P49(x27183,x27184,x27185,x27186,x27187,x27188,x27181)
% 51.10/50.84 [2719]~P6(x27191)+P6(x27192)+~E(x27191,x27192)
% 51.10/50.84 [2720]~P109(x27201)+P109(x27202)+~E(x27201,x27202)
% 51.10/50.84 [2721]~P129(x27211)+P129(x27212)+~E(x27211,x27212)
% 51.10/50.84 [2722]P17(x27222,x27223,x27224)+~E(x27221,x27222)+~P17(x27221,x27223,x27224)
% 51.10/50.84 [2723]P17(x27233,x27232,x27234)+~E(x27231,x27232)+~P17(x27233,x27231,x27234)
% 51.10/50.84 [2724]P17(x27243,x27244,x27242)+~E(x27241,x27242)+~P17(x27243,x27244,x27241)
% 51.10/50.84 [2725]P14(x27252,x27253,x27254,x27255)+~E(x27251,x27252)+~P14(x27251,x27253,x27254,x27255)
% 51.10/50.84 [2726]P14(x27263,x27262,x27264,x27265)+~E(x27261,x27262)+~P14(x27263,x27261,x27264,x27265)
% 51.10/50.84 [2727]P14(x27273,x27274,x27272,x27275)+~E(x27271,x27272)+~P14(x27273,x27274,x27271,x27275)
% 51.10/50.84 [2728]P14(x27283,x27284,x27285,x27282)+~E(x27281,x27282)+~P14(x27283,x27284,x27285,x27281)
% 51.10/50.84 [2729]P39(x27292,x27293,x27294,x27295,x27296,x27297)+~E(x27291,x27292)+~P39(x27291,x27293,x27294,x27295,x27296,x27297)
% 51.10/50.84 [2730]P39(x27303,x27302,x27304,x27305,x27306,x27307)+~E(x27301,x27302)+~P39(x27303,x27301,x27304,x27305,x27306,x27307)
% 51.10/50.84 [2731]P39(x27313,x27314,x27312,x27315,x27316,x27317)+~E(x27311,x27312)+~P39(x27313,x27314,x27311,x27315,x27316,x27317)
% 51.10/50.84 [2732]P39(x27323,x27324,x27325,x27322,x27326,x27327)+~E(x27321,x27322)+~P39(x27323,x27324,x27325,x27321,x27326,x27327)
% 51.10/50.84 [2733]P39(x27333,x27334,x27335,x27336,x27332,x27337)+~E(x27331,x27332)+~P39(x27333,x27334,x27335,x27336,x27331,x27337)
% 51.10/50.84 [2734]P39(x27343,x27344,x27345,x27346,x27347,x27342)+~E(x27341,x27342)+~P39(x27343,x27344,x27345,x27346,x27347,x27341)
% 51.10/50.84 [2735]~P130(x27351)+P130(x27352)+~E(x27351,x27352)
% 51.10/50.84 [2736]P24(x27362,x27363,x27364,x27365,x27366,x27367)+~E(x27361,x27362)+~P24(x27361,x27363,x27364,x27365,x27366,x27367)
% 51.10/50.84 [2737]P24(x27373,x27372,x27374,x27375,x27376,x27377)+~E(x27371,x27372)+~P24(x27373,x27371,x27374,x27375,x27376,x27377)
% 51.10/50.84 [2738]P24(x27383,x27384,x27382,x27385,x27386,x27387)+~E(x27381,x27382)+~P24(x27383,x27384,x27381,x27385,x27386,x27387)
% 51.10/50.84 [2739]P24(x27393,x27394,x27395,x27392,x27396,x27397)+~E(x27391,x27392)+~P24(x27393,x27394,x27395,x27391,x27396,x27397)
% 51.10/50.84 [2740]P24(x27403,x27404,x27405,x27406,x27402,x27407)+~E(x27401,x27402)+~P24(x27403,x27404,x27405,x27406,x27401,x27407)
% 51.10/50.84 [2741]P24(x27413,x27414,x27415,x27416,x27417,x27412)+~E(x27411,x27412)+~P24(x27413,x27414,x27415,x27416,x27417,x27411)
% 51.10/50.84 [2742]P40(x27422,x27423)+~E(x27421,x27422)+~P40(x27421,x27423)
% 51.10/50.84 [2743]P40(x27433,x27432)+~E(x27431,x27432)+~P40(x27433,x27431)
% 51.10/50.84 [2744]P47(x27442,x27443)+~E(x27441,x27442)+~P47(x27441,x27443)
% 51.10/50.84 [2745]P47(x27453,x27452)+~E(x27451,x27452)+~P47(x27453,x27451)
% 51.10/50.84 [2746]~P33(x27461)+P33(x27462)+~E(x27461,x27462)
% 51.10/50.84 [2747]~P115(x27471)+P115(x27472)+~E(x27471,x27472)
% 51.10/50.84 [2748]~P126(x27481)+P126(x27482)+~E(x27481,x27482)
% 51.10/50.84 [2749]P42(x27492,x27493)+~E(x27491,x27492)+~P42(x27491,x27493)
% 51.10/50.84 [2750]P42(x27503,x27502)+~E(x27501,x27502)+~P42(x27503,x27501)
% 51.10/50.84 [2751]P53(x27512,x27513,x27514,x27515,x27516)+~E(x27511,x27512)+~P53(x27511,x27513,x27514,x27515,x27516)
% 51.10/50.84 [2752]P53(x27523,x27522,x27524,x27525,x27526)+~E(x27521,x27522)+~P53(x27523,x27521,x27524,x27525,x27526)
% 51.10/50.84 [2753]P53(x27533,x27534,x27532,x27535,x27536)+~E(x27531,x27532)+~P53(x27533,x27534,x27531,x27535,x27536)
% 51.10/50.84 [2754]P53(x27543,x27544,x27545,x27542,x27546)+~E(x27541,x27542)+~P53(x27543,x27544,x27545,x27541,x27546)
% 51.10/50.84 [2755]P53(x27553,x27554,x27555,x27556,x27552)+~E(x27551,x27552)+~P53(x27553,x27554,x27555,x27556,x27551)
% 51.10/50.84 [2756]~P108(x27561)+P108(x27562)+~E(x27561,x27562)
% 51.10/50.84 [2757]~P103(x27571)+P103(x27572)+~E(x27571,x27572)
% 51.10/50.84 [2758]~P110(x27581)+P110(x27582)+~E(x27581,x27582)
% 51.10/50.84 [2759]~P41(x27591)+P41(x27592)+~E(x27591,x27592)
% 51.10/50.84 [2760]~P72(x27601)+P72(x27602)+~E(x27601,x27602)
% 51.10/50.84 [2761]P28(x27612,x27613)+~E(x27611,x27612)+~P28(x27611,x27613)
% 51.10/50.84 [2762]P28(x27623,x27622)+~E(x27621,x27622)+~P28(x27623,x27621)
% 51.10/50.84 [2763]P23(x27632,x27633,x27634,x27635,x27636)+~E(x27631,x27632)+~P23(x27631,x27633,x27634,x27635,x27636)
% 51.10/50.84 [2764]P23(x27643,x27642,x27644,x27645,x27646)+~E(x27641,x27642)+~P23(x27643,x27641,x27644,x27645,x27646)
% 51.10/50.84 [2765]P23(x27653,x27654,x27652,x27655,x27656)+~E(x27651,x27652)+~P23(x27653,x27654,x27651,x27655,x27656)
% 51.10/50.84 [2766]P23(x27663,x27664,x27665,x27662,x27666)+~E(x27661,x27662)+~P23(x27663,x27664,x27665,x27661,x27666)
% 51.10/50.84 [2767]P23(x27673,x27674,x27675,x27676,x27672)+~E(x27671,x27672)+~P23(x27673,x27674,x27675,x27676,x27671)
% 51.10/50.84 [2768]~P96(x27681)+P96(x27682)+~E(x27681,x27682)
% 51.10/50.84 [2769]~P139(x27691)+P139(x27692)+~E(x27691,x27692)
% 51.10/50.84 [2770]P142(x27702,x27703)+~E(x27701,x27702)+~P142(x27701,x27703)
% 51.10/50.84 [2771]P142(x27713,x27712)+~E(x27711,x27712)+~P142(x27713,x27711)
% 51.10/50.84 [2772]~P82(x27721)+P82(x27722)+~E(x27721,x27722)
% 51.10/50.84 [2773]~P73(x27731)+P73(x27732)+~E(x27731,x27732)
% 51.10/50.84 [2774]P44(x27742,x27743,x27744)+~E(x27741,x27742)+~P44(x27741,x27743,x27744)
% 51.10/50.84 [2775]P44(x27753,x27752,x27754)+~E(x27751,x27752)+~P44(x27753,x27751,x27754)
% 51.10/50.84 [2776]P44(x27763,x27764,x27762)+~E(x27761,x27762)+~P44(x27763,x27764,x27761)
% 51.10/50.84 [2777]P35(x27772,x27773)+~E(x27771,x27772)+~P35(x27771,x27773)
% 51.10/50.84 [2778]P35(x27783,x27782)+~E(x27781,x27782)+~P35(x27783,x27781)
% 51.10/50.84 [2779]~P65(x27791)+P65(x27792)+~E(x27791,x27792)
% 51.10/50.84 [2780]P12(x27802,x27803,x27804)+~E(x27801,x27802)+~P12(x27801,x27803,x27804)
% 51.10/50.84 [2781]P12(x27813,x27812,x27814)+~E(x27811,x27812)+~P12(x27813,x27811,x27814)
% 51.10/50.84 [2782]P12(x27823,x27824,x27822)+~E(x27821,x27822)+~P12(x27823,x27824,x27821)
% 51.10/50.84 [2783]P38(x27832,x27833,x27834,x27835)+~E(x27831,x27832)+~P38(x27831,x27833,x27834,x27835)
% 51.10/50.84 [2784]P38(x27843,x27842,x27844,x27845)+~E(x27841,x27842)+~P38(x27843,x27841,x27844,x27845)
% 51.10/50.84 [2785]P38(x27853,x27854,x27852,x27855)+~E(x27851,x27852)+~P38(x27853,x27854,x27851,x27855)
% 51.10/50.84 [2786]P38(x27863,x27864,x27865,x27862)+~E(x27861,x27862)+~P38(x27863,x27864,x27865,x27861)
% 51.10/50.84 [2787]~P117(x27871)+P117(x27872)+~E(x27871,x27872)
% 51.10/50.84
% 51.10/50.84 %-------------------------------------------
% 51.10/50.86 cnf(10029,plain,
% 51.10/50.86 (~E(f331(f331(f145(x100291),x100292),x100293),x100293)),
% 51.10/50.86 inference(rename_variables,[],[4367])).
% 51.10/50.86 cnf(10036,plain,
% 51.10/50.86 (~E(f331(f331(f145(x100361),x100362),x100363),x100363)),
% 51.10/50.86 inference(rename_variables,[],[4367])).
% 51.10/50.86 cnf(10045,plain,
% 51.10/50.86 (~E(f331(a119,x100451),x100451)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10052,plain,
% 51.10/50.86 (~E(f331(a119,x100521),x100521)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10055,plain,
% 51.10/50.86 (E(f331(f7(x100551),x100552),x100552)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(10058,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),f57(a847,x100581,x100582)),x100581))),
% 51.10/50.86 inference(rename_variables,[],[3627])).
% 51.10/50.86 cnf(10061,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),f331(f331(f87(a847),x100611),x100612)),x100612))),
% 51.10/50.86 inference(rename_variables,[],[4442])).
% 51.10/50.86 cnf(10064,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),f331(f331(f87(a847),x100641),x100642)),x100642))),
% 51.10/50.86 inference(rename_variables,[],[4442])).
% 51.10/50.86 cnf(10067,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x100671),x100671))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10079,plain,
% 51.10/50.86 (P1(f331(f331(f333(x100791),x100792),f247(f854(x100791,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(10082,plain,
% 51.10/50.86 (~E(f331(a119,x100821),x100821)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10085,plain,
% 51.10/50.86 (~E(f331(a29,x100851),a25)),
% 51.10/50.86 inference(rename_variables,[],[4331])).
% 51.10/50.86 cnf(10090,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x100901),x100901))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10107,plain,
% 51.10/50.86 (P1(f331(f331(f333(x101071),x101072),f247(f854(x101071,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(10112,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x101121),f331(a119,x101121)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10136,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x101361),f331(a119,x101361)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10145,plain,
% 51.10/50.86 (P1(f331(f331(f191(a25),x101451),x101451))),
% 51.10/50.86 inference(rename_variables,[],[3172])).
% 51.10/50.86 cnf(10160,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x101601),x101601))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10175,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x101751),f331(a119,x101751)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10178,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x101781),f331(a119,x101781)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10205,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),f331(f331(f87(a847),x102051),x102052)),x102052))),
% 51.10/50.86 inference(rename_variables,[],[4442])).
% 51.10/50.86 cnf(10210,plain,
% 51.10/50.86 (~P1(f331(f331(f240(a847),f331(a119,x102101)),x102101))),
% 51.10/50.86 inference(rename_variables,[],[4427])).
% 51.10/50.86 cnf(10213,plain,
% 51.10/50.86 (E(f331(f264(x102131),x102132),x102132)),
% 51.10/50.86 inference(rename_variables,[],[3011])).
% 51.10/50.86 cnf(10224,plain,
% 51.10/50.86 (E(f331(f7(x102241),x102242),x102242)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(10227,plain,
% 51.10/50.86 (E(f331(f264(x102271),x102272),x102272)),
% 51.10/50.86 inference(rename_variables,[],[3011])).
% 51.10/50.86 cnf(10236,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x102361),x102362),f184(f854(x102361,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(10239,plain,
% 51.10/50.86 (E(f331(f7(x102391),x102392),x102392)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(10242,plain,
% 51.10/50.86 (E(f331(f264(x102421),x102422),x102422)),
% 51.10/50.86 inference(rename_variables,[],[3011])).
% 51.10/50.86 cnf(10253,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x102531,a840)),x102532),x102532))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(10258,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x102581),f331(a119,x102581)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10277,plain,
% 51.10/50.86 (P1(f331(f331(f191(a25),x102771),x102771))),
% 51.10/50.86 inference(rename_variables,[],[3172])).
% 51.10/50.86 cnf(10280,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x102801),f331(a119,x102801)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10287,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x102871),f331(a119,x102871)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10290,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x102901),f331(a119,x102901)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10295,plain,
% 51.10/50.86 (P1(f331(f331(f191(a25),x102951),x102951))),
% 51.10/50.86 inference(rename_variables,[],[3172])).
% 51.10/50.86 cnf(10308,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x103081),x103081))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10315,plain,
% 51.10/50.86 (~E(f331(a29,x103151),a25)),
% 51.10/50.86 inference(rename_variables,[],[4331])).
% 51.10/50.86 cnf(10324,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x103241),x103241))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10333,plain,
% 51.10/50.86 (~E(f331(a119,x103331),x103331)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10336,plain,
% 51.10/50.86 (~E(f331(f331(f145(x103361),x103362),x103363),x103363)),
% 51.10/50.86 inference(rename_variables,[],[4367])).
% 51.10/50.86 cnf(10343,plain,
% 51.10/50.86 (~E(f331(f331(f145(x103431),x103432),x103433),x103433)),
% 51.10/50.86 inference(rename_variables,[],[4367])).
% 51.10/50.86 cnf(10364,plain,
% 51.10/50.86 (P1(f331(f331(f191(a25),x103641),x103641))),
% 51.10/50.86 inference(rename_variables,[],[3172])).
% 51.10/50.86 cnf(10369,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x103691),x103691))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10379,plain,
% 51.10/50.86 (E(f331(f7(x103791),x103792),x103792)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(10382,plain,
% 51.10/50.86 (E(f331(f7(x103821),x103822),x103822)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(10385,plain,
% 51.10/50.86 (~E(f331(a119,x103851),x103851)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10388,plain,
% 51.10/50.86 (~P1(f331(f69(x103881,x103882,f184(f854(x103881,a840))),x103883))),
% 51.10/50.86 inference(rename_variables,[],[4441])).
% 51.10/50.86 cnf(10393,plain,
% 51.10/50.86 (~P1(f331(f69(x103931,x103932,f184(f854(x103931,a840))),x103933))),
% 51.10/50.86 inference(rename_variables,[],[4441])).
% 51.10/50.86 cnf(10412,plain,
% 51.10/50.86 (~P1(f331(f331(f241(f854(x104121,a840)),x104122),f184(f854(x104121,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4439])).
% 51.10/50.86 cnf(10417,plain,
% 51.10/50.86 (~P1(f331(f331(f240(a847),f331(a119,x104171)),x104171))),
% 51.10/50.86 inference(rename_variables,[],[4427])).
% 51.10/50.86 cnf(10420,plain,
% 51.10/50.86 (~P1(f331(f331(f240(a847),f331(a119,x104201)),x104201))),
% 51.10/50.86 inference(rename_variables,[],[4427])).
% 51.10/50.86 cnf(10425,plain,
% 51.10/50.86 (~E(f331(f311(x104251,f854(x104251,a840),x104252),x104253),f331(f309(x104251),x104253))),
% 51.10/50.86 inference(rename_variables,[],[4428])).
% 51.10/50.86 cnf(10434,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),f2(a847)),x104341))),
% 51.10/50.86 inference(rename_variables,[],[3196])).
% 51.10/50.86 cnf(10437,plain,
% 51.10/50.86 (P1(f331(f331(f287(a847),x104371),x104371))),
% 51.10/50.86 inference(rename_variables,[],[3176])).
% 51.10/50.86 cnf(10440,plain,
% 51.10/50.86 (P1(f331(f331(f240(a1),x104401),x104401))),
% 51.10/50.86 inference(rename_variables,[],[3175])).
% 51.10/50.86 cnf(10445,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x104451),f331(f331(f88(a847),x104451),x104451)))),
% 51.10/50.86 inference(rename_variables,[],[3444])).
% 51.10/50.86 cnf(10448,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x104481),f331(f331(f88(a847),x104481),x104481)))),
% 51.10/50.86 inference(rename_variables,[],[3444])).
% 51.10/50.86 cnf(10451,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x104511),f331(f331(f87(a847),x104512),x104511)))),
% 51.10/50.86 inference(rename_variables,[],[3442])).
% 51.10/50.86 cnf(10454,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x104541),f331(f331(f87(a847),x104542),x104541)))),
% 51.10/50.86 inference(rename_variables,[],[3442])).
% 51.10/50.86 cnf(10457,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x104571),f331(a119,f331(f331(f87(a847),x104572),x104571))))),
% 51.10/50.86 inference(rename_variables,[],[3620])).
% 51.10/50.86 cnf(10462,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x104621,a840)),f331(f311(x104622,x104621,x104623),f331(f312(x104622,x104621,x104623),x104624))),x104624))),
% 51.10/50.86 inference(rename_variables,[],[4053])).
% 51.10/50.86 cnf(10465,plain,
% 51.10/50.86 (P1(f331(f331(f287(a847),x104651),x104651))),
% 51.10/50.86 inference(rename_variables,[],[3176])).
% 51.10/50.86 cnf(10470,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x104701),x104701))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10477,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x104771),x104771))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10484,plain,
% 51.10/50.86 (P1(f331(f331(f240(a1),x104841),x104841))),
% 51.10/50.86 inference(rename_variables,[],[3175])).
% 51.10/50.86 cnf(10501,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x105011),f331(f331(f88(a847),x105011),x105011)))),
% 51.10/50.86 inference(rename_variables,[],[3444])).
% 51.10/50.86 cnf(10504,plain,
% 51.10/50.86 (~P1(f331(f331(f240(a847),f331(a119,x105041)),x105041))),
% 51.10/50.86 inference(rename_variables,[],[4427])).
% 51.10/50.86 cnf(10509,plain,
% 51.10/50.86 (~P1(f331(f331(f240(a847),f331(a119,x105091)),x105091))),
% 51.10/50.86 inference(rename_variables,[],[4427])).
% 51.10/50.86 cnf(10514,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),f331(f331(f87(a847),x105141),x105142)),x105142))),
% 51.10/50.86 inference(rename_variables,[],[4442])).
% 51.10/50.86 cnf(10517,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),f331(f331(f87(a847),x105171),x105172)),x105171))),
% 51.10/50.86 inference(rename_variables,[],[4443])).
% 51.10/50.86 cnf(10520,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),f331(f331(f87(a847),x105201),x105202)),x105202))),
% 51.10/50.86 inference(rename_variables,[],[4442])).
% 51.10/50.86 cnf(10526,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x105261),x105261))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10529,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x105291),f331(f331(f88(a847),x105291),x105291)))),
% 51.10/50.86 inference(rename_variables,[],[3444])).
% 51.10/50.86 cnf(10538,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x105381),f331(a119,x105381)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10663,plain,
% 51.10/50.86 (~E(f331(a119,x106631),x106631)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10666,plain,
% 51.10/50.86 (~E(f331(a119,x106661),x106661)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10682,plain,
% 51.10/50.86 (P1(f331(f331(f333(x106821),x106822),f247(f854(x106821,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(10685,plain,
% 51.10/50.86 (P1(f331(f331(f333(x106851),x106852),f331(f331(f310(x106851),x106852),x106853)))),
% 51.10/50.86 inference(rename_variables,[],[3486])).
% 51.10/50.86 cnf(10688,plain,
% 51.10/50.86 (P1(f331(f331(f333(x106881),x106882),f247(f854(x106881,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(10691,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x106911),x106912),f184(f854(x106911,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(10699,plain,
% 51.10/50.86 (~E(f331(a119,x106991),x106991)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10706,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x107061),x107062),f184(f854(x107061,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(10752,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x107521),f2(a847)))),
% 51.10/50.86 inference(rename_variables,[],[4416])).
% 51.10/50.86 cnf(10755,plain,
% 51.10/50.86 (~P1(f331(f331(f184(f854(x107551,f854(x107552,a840))),x107553),x107554))),
% 51.10/50.86 inference(rename_variables,[],[4445])).
% 51.10/50.86 cnf(10779,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x107791),x107791))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10782,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x107821),f331(a119,x107821)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10787,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x107871),x107871))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10790,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x107901),x107901))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10797,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x107971),x107971))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10818,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x108181),x108181))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10829,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x108291),f2(a847)))),
% 51.10/50.86 inference(rename_variables,[],[4416])).
% 51.10/50.86 cnf(10832,plain,
% 51.10/50.86 (~E(f331(a119,x108321),x108321)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10839,plain,
% 51.10/50.86 (~P1(f331(f331(f184(f854(x108391,f854(x108392,a840))),x108393),x108394))),
% 51.10/50.86 inference(rename_variables,[],[4445])).
% 51.10/50.86 cnf(10856,plain,
% 51.10/50.86 (E(f331(f331(f130(x108561),f120(x108561)),x108562),x108562)),
% 51.10/50.86 inference(rename_variables,[],[3127])).
% 51.10/50.86 cnf(10870,plain,
% 51.10/50.86 (E(f331(f7(x108701),x108702),x108702)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(10873,plain,
% 51.10/50.86 (E(f331(f7(x108731),x108732),x108732)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(10876,plain,
% 51.10/50.86 (~E(f331(a119,x108761),x108761)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10879,plain,
% 51.10/50.86 (~E(f331(a119,x108791),x108791)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(10901,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x109011),x109012),f184(f854(x109011,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(10908,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x109081,a840)),f184(f854(x109081,a840))),x109082))),
% 51.10/50.86 inference(rename_variables,[],[3619])).
% 51.10/50.86 cnf(10913,plain,
% 51.10/50.86 (P1(f331(f331(f241(a847),x109131),f331(a119,x109131)))),
% 51.10/50.86 inference(rename_variables,[],[3242])).
% 51.10/50.86 cnf(10918,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x109181,a840)),x109182),f331(f331(f310(x109181),x109183),x109182)))),
% 51.10/50.86 inference(rename_variables,[],[3615])).
% 51.10/50.86 cnf(10923,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x109231,a840)),x109232),f331(f331(f310(x109231),x109233),x109232)))),
% 51.10/50.86 inference(rename_variables,[],[3615])).
% 51.10/50.86 cnf(10929,plain,
% 51.10/50.86 (P1(f331(f331(f333(x109291),x109292),f247(f854(x109291,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(10938,plain,
% 51.10/50.86 (P1(f331(f331(f333(x109381),x109382),f247(f854(x109381,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(10945,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x109451),x109451))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(10960,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x109601),x109601))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10966,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x109661),x109661))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(10973,plain,
% 51.10/50.86 (P1(f331(f247(f854(x109731,a840)),x109732))),
% 51.10/50.86 inference(rename_variables,[],[3236])).
% 51.10/50.86 cnf(10978,plain,
% 51.10/50.86 (P1(f331(f247(f854(x109781,a840)),x109782))),
% 51.10/50.86 inference(rename_variables,[],[3236])).
% 51.10/50.86 cnf(10995,plain,
% 51.10/50.86 (~E(f331(a119,x109951),x109951)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(11000,plain,
% 51.10/50.86 (E(f331(f47(a847),f331(f265(a847),x110001)),x110001)),
% 51.10/50.86 inference(rename_variables,[],[3069])).
% 51.10/50.86 cnf(11005,plain,
% 51.10/50.86 (~P1(f331(f331(f333(f853(f848(x110051),f848(x110051))),f331(f331(f249(f848(x110051),f848(x110051)),x110052),f120(x110051))),f142(x110051,x110053)))),
% 51.10/50.86 inference(rename_variables,[],[4448])).
% 51.10/50.86 cnf(11008,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x110081,a840)),f184(f854(x110081,a840))),x110082))),
% 51.10/50.86 inference(rename_variables,[],[3619])).
% 51.10/50.86 cnf(11014,plain,
% 51.10/50.86 (~E(f331(f311(x110141,f854(x110141,a840),x110142),x110143),f331(f309(x110141),x110143))),
% 51.10/50.86 inference(rename_variables,[],[4428])).
% 51.10/50.86 cnf(11025,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x110251,a840)),x110252),x110252))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(11031,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x110311),x110312),f184(f854(x110311,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11055,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x110551),x110552),f184(f854(x110551,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11061,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x110611),x110612),f184(f854(x110611,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11066,plain,
% 51.10/50.86 (~P1(f331(f69(x110661,x110662,f184(f854(x110661,a840))),x110663))),
% 51.10/50.86 inference(rename_variables,[],[4441])).
% 51.10/50.86 cnf(11073,plain,
% 51.10/50.86 (~E(f331(a119,x110731),x110731)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(11081,plain,
% 51.10/50.86 (P1(f331(f331(f333(x110811),x110812),f247(f854(x110811,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11088,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x110881),x110882),f184(f854(x110881,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11091,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x110911,a840)),x110912),f247(f854(x110911,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11094,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x110941,a840)),x110942),f247(f854(x110941,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11101,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x111011),x111011))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(11112,plain,
% 51.10/50.86 (P1(f331(f331(f333(x111121),x111122),f247(f854(x111121,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11118,plain,
% 51.10/50.86 (P1(f331(f331(f333(x111181),x111182),f247(f854(x111181,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11141,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x111411),x111411))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(11147,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x111471,a840)),x111472),x111472))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(11150,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x111501),x111502),f184(f854(x111501,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11156,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x111561,a840)),x111562),f247(f854(x111561,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11159,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x111591,a840)),x111592),f247(f854(x111591,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11162,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x111621),x111622),f184(f854(x111621,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11167,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x111671,a840)),x111672),f247(f854(x111671,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11172,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x111721),x111722),f184(f854(x111721,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11175,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x111751),x111752),f184(f854(x111751,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11180,plain,
% 51.10/50.86 (P1(f331(f331(f240(a847),x111801),x111801))),
% 51.10/50.86 inference(rename_variables,[],[3174])).
% 51.10/50.86 cnf(11190,plain,
% 51.10/50.86 (P1(f331(f331(f333(x111901),x111902),f247(f854(x111901,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11195,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x111951),x111952),f184(f854(x111951,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11202,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x112021),x112022),f184(f854(x112021,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11207,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x112071,a840)),x112072),f247(f854(x112071,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11210,plain,
% 51.10/50.86 (P1(f331(f331(f333(x112101),x112102),f247(f854(x112101,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11213,plain,
% 51.10/50.86 (P1(f331(f331(f333(x112131),x112132),f331(f331(f310(x112131),x112132),x112133)))),
% 51.10/50.86 inference(rename_variables,[],[3486])).
% 51.10/50.86 cnf(11216,plain,
% 51.10/50.86 (P1(f331(f331(f333(x112161),x112162),f247(f854(x112161,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11219,plain,
% 51.10/50.86 (P1(f331(f331(f333(x112191),x112192),f331(f331(f310(x112191),x112192),x112193)))),
% 51.10/50.86 inference(rename_variables,[],[3486])).
% 51.10/50.86 cnf(11222,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x112221,a840)),x112222),f247(f854(x112221,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11246,plain,
% 51.10/50.86 (~P1(f331(f331(f241(a847),x112461),x112461))),
% 51.10/50.86 inference(rename_variables,[],[4413])).
% 51.10/50.86 cnf(11252,plain,
% 51.10/50.86 (E(f331(f7(x112521),x112522),x112522)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(11255,plain,
% 51.10/50.86 (~E(f331(a119,x112551),x112551)),
% 51.10/50.86 inference(rename_variables,[],[4333])).
% 51.10/50.86 cnf(11258,plain,
% 51.10/50.86 (~P1(f331(f331(f184(f854(x112581,f854(x112582,a840))),x112583),x112584))),
% 51.10/50.86 inference(rename_variables,[],[4445])).
% 51.10/50.86 cnf(11269,plain,
% 51.10/50.86 (P1(f331(f331(f333(x112691),x112692),f247(f854(x112691,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11272,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x112721),x112722),f184(f854(x112721,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11286,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x112861),x112862),f184(f854(x112861,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11291,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x112911,a840)),x112912),x112912))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(11296,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x112961),x112962),f184(f854(x112961,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11299,plain,
% 51.10/50.86 (~P1(f331(f331(f333(f853(f848(x112991),f848(x112991))),f331(f331(f249(f848(x112991),f848(x112991)),x112992),f120(x112991))),f140(x112991,x112993)))),
% 51.10/50.86 inference(rename_variables,[],[4447])).
% 51.10/50.86 cnf(11305,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113051),x113052),f247(f854(x113051,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11311,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113111),x113112),f247(f854(x113111,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11314,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113141),x113142),f247(f854(x113141,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11317,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113171),x113172),f184(f854(x113171,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11320,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x113201,a840)),x113202),x113202))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(11323,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113231),x113232),f184(f854(x113231,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11329,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113291),x113292),f184(f854(x113291,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11332,plain,
% 51.10/50.86 (~P1(f331(f331(f333(f853(f848(x113321),f848(x113321))),f331(f331(f249(f848(x113321),f848(x113321)),x113322),f120(x113321))),f140(x113321,x113323)))),
% 51.10/50.86 inference(rename_variables,[],[4447])).
% 51.10/50.86 cnf(11335,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113351),x113352),f184(f854(x113351,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11338,plain,
% 51.10/50.86 (~P1(f331(f331(f333(f853(f848(x113381),f848(x113381))),f331(f331(f249(f848(x113381),f848(x113381)),f120(x113381)),x113382)),f140(x113381,x113383)))),
% 51.10/50.86 inference(rename_variables,[],[4450])).
% 51.10/50.86 cnf(11341,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x113411,a840)),x113412),x113412))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(11344,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x113441,a840)),x113442),x113442))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(11347,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113471),x113472),f184(f854(x113471,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11352,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113521),x113522),f247(f854(x113521,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11355,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113551),x113552),f331(f331(f310(x113551),x113552),x113553)))),
% 51.10/50.86 inference(rename_variables,[],[3486])).
% 51.10/50.86 cnf(11362,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113621),x113622),f184(f854(x113621,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11371,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113711),x113712),f247(f854(x113711,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11374,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113741),x113742),f247(f854(x113741,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11377,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113771),x113772),f247(f854(x113771,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11382,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113821),x113822),f184(f854(x113821,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11385,plain,
% 51.10/50.86 (P1(f331(f331(f333(x113851),x113852),f247(f854(x113851,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3327])).
% 51.10/50.86 cnf(11388,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x113881),x113882),f184(f854(x113881,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11396,plain,
% 51.10/50.86 (~E(f331(f311(x113961,f854(x113961,a840),x113962),x113963),f331(f309(x113961),x113963))),
% 51.10/50.86 inference(rename_variables,[],[4428])).
% 51.10/50.86 cnf(11407,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x114071),x114072),f184(f854(x114071,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11410,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x114101),x114102),f184(f854(x114101,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11413,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x114131),x114132),f184(f854(x114131,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11416,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x114161),x114162),f184(f854(x114161,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11419,plain,
% 51.10/50.86 (P1(f331(f331(f333(f853(f848(x114191),f848(x114191))),f331(f331(f249(f848(x114191),f848(x114191)),x114192),x114192)),f151(x114191,f308(x114191,x114193))))),
% 51.10/50.86 inference(rename_variables,[],[3946])).
% 51.10/50.86 cnf(11422,plain,
% 51.10/50.86 (P1(f331(f331(f333(f853(f848(x114221),f848(x114221))),f331(f331(f249(f848(x114221),f848(x114221)),x114222),x114222)),f151(x114221,f308(x114221,x114223))))),
% 51.10/50.86 inference(rename_variables,[],[3946])).
% 51.10/50.86 cnf(11425,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x114251,a840)),x114252),x114252))),
% 51.10/50.86 inference(rename_variables,[],[3473])).
% 51.10/50.86 cnf(11430,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x114301),x114302),f184(f854(x114301,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11449,plain,
% 51.10/50.86 (~P1(f331(f331(f333(x114491),x114492),f184(f854(x114491,a840))))),
% 51.10/50.86 inference(rename_variables,[],[4429])).
% 51.10/50.86 cnf(11455,plain,
% 51.10/50.86 (P1(f331(f331(f240(f854(x114551,a840)),x114552),f247(f854(x114551,a840))))),
% 51.10/50.86 inference(rename_variables,[],[3550])).
% 51.10/50.86 cnf(11477,plain,
% 51.10/50.86 (E(f331(f7(x114771),x114772),x114772)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(11494,plain,
% 51.10/50.86 (E(f331(f7(x114941),x114942),x114942)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(11497,plain,
% 51.10/50.86 (E(f331(f7(x114971),x114972),x114972)),
% 51.10/50.86 inference(rename_variables,[],[3010])).
% 51.10/50.86 cnf(11505,plain,
% 51.20/50.86 (E(f331(f7(x115051),x115052),x115052)),
% 51.20/50.86 inference(rename_variables,[],[3010])).
% 51.20/50.86 cnf(11540,plain,
% 51.20/50.86 (~E(f331(a119,x115401),x115401)),
% 51.20/50.86 inference(rename_variables,[],[4333])).
% 51.20/50.86 cnf(11551,plain,
% 51.20/50.86 (~E(f331(a119,x115511),x115511)),
% 51.20/50.86 inference(rename_variables,[],[4333])).
% 51.20/50.86 cnf(11562,plain,
% 51.20/50.86 ($false),
% 51.20/50.86 inference(scs_inference,[],[4446,3388,2985,3379,2795,2796,2983,4327,2788,2789,2979,2972,4328,3837,4362,4363,3485,2993,2997,3369,4406,4407,4409,3151,3152,3154,4408,4410,3153,3014,3177,4415,4426,4425,3056,3204,3202,3203,3685,3267,3723,3792,3973,4175,3413,3144,3145,3008,4333,10045,10052,10082,10333,10385,10663,10666,10699,10832,10876,10879,10995,11073,11255,11540,11551,3045,4331,10085,10315,3420,4114,4115,3148,3475,3194,4341,3010,10055,10224,10239,10379,10382,10870,10873,11252,11477,11494,11497,11505,3011,10213,10227,10242,4366,3630,3229,3232,4367,10029,10036,10336,10343,3277,3089,3158,3380,3172,10145,10277,10295,10364,3174,10090,10526,10779,10790,10797,10818,10960,10966,11101,11180,3175,10440,10484,3176,10437,10465,4413,10067,10160,10308,10324,10369,10470,10477,10787,10945,11141,11246,3236,10973,10978,3037,3730,3106,3127,10856,3081,3069,11000,3242,10112,10136,10175,10178,10258,10280,10287,10290,10538,10782,10913,4416,10752,10829,3196,10434,3627,10058,4427,10210,10417,10420,10504,10509,4441,10388,10393,11066,3473,10253,11025,11147,11291,11320,11341,11344,11425,4428,10425,11014,11396,3497,3254,3496,3327,10079,10107,10682,10688,10929,10938,11081,11112,11118,11190,11210,11216,11269,11305,11311,11314,11352,11371,11374,11377,11385,4429,10236,10691,10706,10901,11031,11055,11061,11088,11150,11162,11172,11175,11195,11202,11272,11286,11296,11317,11323,11329,11335,11347,11362,11382,11388,11407,11410,11413,11416,11430,11449,3329,3534,4445,10755,10839,11258,3543,3245,3370,4434,3550,11091,11094,11156,11159,11167,11207,11222,11455,4439,10412,3697,3486,10685,11213,11219,11355,3619,10908,11008,4431,3444,10445,10448,10501,10529,3442,10451,10454,3443,4442,10061,10064,10205,10514,10520,4443,10517,3568,3622,3615,10918,10923,3620,10457,3621,3276,3806,3776,4053,10462,3477,3754,3732,3759,3873,3902,4444,4438,3896,3470,3689,4126,4447,11299,11332,4448,11005,4449,4450,11338,3946,11419,11422,3996,4154,2,9456,6147,5113,4919,4872,4830,4829,4661,4564,4563,4470,4463,5074,5064,4984,4921,4458,4949,4869,9,8,9700,9457,8518,7610,6991,6593,6307,6287,6140,6139,6132,6115,5986,5900,5770,5745,5678,5667,5666,5611,5596,5595,5591,5589,5537,5531,5530,5525,5511,5492,5481,5478,5461,5460,5450,5362,5270,5263,5254,5253,5210,5196,5188,5180,5179,5171,5105,5082,5048,5042,5041,5040,5039,5038,5037,4995,4987,4974,4973,4915,4898,4892,4655,4588,4536,4534,4533,4527,4526,9642,8605,8439,8438,8431,7409,7237,7147,6849,6635,6449,6448,6446,6445,6333,6308,6241,6240,6141,6121,6109,6033,5991,5985,5984,5978,5958,5955,5954,5870,5869,5797,5754,5731,5687,5682,5675,5674,5646,5640,5615,5612,5547,5463,5462,5446,5433,5421,5410,5387,5340,5295,5267,5266,5265,5239,5200,5189,5099,5072,5061,5059,4965,4927,4926,4806,4768,4645,4769,9771,9728,9727,9726,9725,9713,9377,8953,8920,8750,8717,8672,8627,8587,8583,8290,7777,7588,7343,7324,7263,7245,7244,7243,7242,7241,7201,6796,6793,6685,6672,6584,6583,6563,6514,6513,6503,6233,6232,6230,6229,6228,6227,6187,6180,6094,6093,6092,6091,6090,6089,6088,6087,5964,5963,5962,5961,5960,5941,5939,5938,5937,5936,5935,5897,5788,5787,5786,5780,5708,5681,5647,5602,5601,5600,5599,5598,5597,5550,5504,5422,5419,5418,5417,5416,5415,5414,5390,5389,5386,5336,5328,5262,5232,5231,5221,5215,5214,5213,5183,5163,5146,5108,5086,5085,5083,5050,4989,4855,4854,4853,4743,4742,4625,4624,4623,4589,4582,4581,4485,4484,4481,8468,8467,8466,8465,8360,8359,8358,7742,7649,7538,7334,7216,6875,6779,6688,6687,6528,6224,5921,5918,5917,5673,5672,5626,5625,5586,5585,5584,5542,5432,5368,5313,5312,5301,5187,9797,9791,9390,9389,9388,9387,8540,8448,8447,8446,8445,8372,7640,7639,7558,7404,7271,6933,6797,6773,6702,6701,6658,6657,6656,6655,6654,6653,6652,6634,6605,6604,6603,6602,6568,6495,6427,6426,6404,6389,6388,6387,6124,5989,5988,5815,5539,5538,5311,5252,5251,5205,5202,5201,5170,5169,4920,8957,8956,8955,8954,8781,8780,8759,8758,8753,8641,8640,8449,8440,8347,8313,8159,8097,7961,7933,7688,7564,7545,7544,7408,7269,7268,7137,7079,7078,6910,6909,6758,6757,6646,6645,6348,6337,6278,6173,6117,6104,6052,6043,6034,5818,5758,5605,5604,5468,5404,5156,5063,8489,8423,8422,8378,8377,8308,8116,8049,7901,7872,7867,7866,7752,7690,7657,7457,7456,7401,7231,6771,6742,6699,6628,6627,6349,5594,5493,5287,5166,5165,9066,8789,8776,8679,8382,8327,8284,8253,8182,7946,7882,7881,7880,7879,7698,7437,7356,6834,6833,6772,6649,6648,6591,6590,6357,6356,9256,9056,9055,8959,8926,8798,8706,8705,8663,8570,8539,8469,7835,7686,7475,6960,6842,6106,5847,9283,9282,9068,9067,8683,8682,8630,8626,8507,8506,8505,8504,8491,8309,8287,8286,8282,7624,7340,7339,7214,7076,7075,7048,6877,6223,5855,8994,8854,8782,8779,8763,8629,8477,8407,8140,6369,5924,9560,9495,9494,9111,8997,8892,8891,8890,8513,8458,9871,9113,9100,9077,9566,9452,9450,9449,9255,9254,9358,9324,8906,8905,8861,8860,8690,9821,9745,9744,9602,9486,9290,9289,9126,9574,9496,9317,9132,9087,9733,9732,9215,9154,9770,9765,9682,9598,9549,9521,9300,9735,9546,9407,9337,9336,9675,9548,9412,9335,9950,9949,9890,9889,10003,10016,9906,9870,9956,9925,2786,2778,2777,2756,2754,2749,2734,2733,2732,2729,2727,2725,2724,2722,2717,2715,2695,2694,2666,2665,2644,2642,2639,2638,2636,2635,2634,2604,2603,2599,2598,2596,2593,2591,2590,2587,2586,2582,2579,2577,2576,2575,2574,2573,2572,2571,2566,2565,2564,2562,2558,2557,2556,2555,2540,2539,2538,2534,2533,2531,3,4924,5066,4491,4473,4945,4944,4918,4917,4905,8387]),
% 51.20/50.86 ['proof']).
% 51.20/50.86 % SZS output end Proof
% 51.20/50.86 % Total time :47.330000s
%------------------------------------------------------------------------------