TSTP Solution File: SWW334+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW334+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 : n019.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 00:13:49 EDT 2023
% Result : Theorem 18.55s 18.46s
% Output : CNFRefutation 18.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW334+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 22:47:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 18.25/18.31 %-------------------------------------------
% 18.25/18.31 % File :CSE---1.6
% 18.25/18.31 % Problem :theBenchmark
% 18.25/18.31 % Transform :cnf
% 18.25/18.31 % Format :tptp:raw
% 18.25/18.31 % Command :java -jar mcs_scs.jar %d %s
% 18.25/18.31
% 18.25/18.31 % Result :Theorem 14.880000s
% 18.25/18.31 % Output :CNFRefutation 14.880000s
% 18.25/18.31 %-------------------------------------------
% 18.25/18.32 %------------------------------------------------------------------------------
% 18.25/18.32 % File : SWW334+1 : TPTP v8.1.2. Released v5.2.0.
% 18.25/18.32 % Domain : Software Verification
% 18.25/18.32 % Problem : Hoare's Logic with Procedures 435150, 5000 axioms selected
% 18.25/18.32 % Version : Especial.
% 18.25/18.32 % English :
% 18.25/18.32
% 18.25/18.32 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 18.25/18.32 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 18.25/18.32 % Source : [Bla11]
% 18.25/18.32 % Names : hoare_435150.5000.p [Bla11]
% 18.25/18.32
% 18.25/18.32 % Status : ContradictoryAxioms
% 18.25/18.32 % Rating : 0.58 v8.1.0, 0.61 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, 0.73 v6.3.0, 0.62 v6.2.0, 0.72 v6.1.0, 0.77 v6.0.0, 0.65 v5.5.0, 0.78 v5.4.0, 0.75 v5.3.0, 0.81 v5.2.0
% 18.25/18.32 % Syntax : Number of formulae : 5209 (1689 unt; 0 def)
% 18.25/18.32 % Number of atoms : 12634 (4517 equ)
% 18.25/18.32 % Maximal formula atoms : 13 ( 2 avg)
% 18.25/18.32 % Number of connectives : 8510 (1085 ~; 158 |; 712 &)
% 18.25/18.32 % ( 884 <=>;5671 =>; 0 <=; 0 <~>)
% 18.25/18.32 % Maximal formula depth : 22 ( 6 avg)
% 18.25/18.32 % Maximal term depth : 19 ( 2 avg)
% 18.25/18.32 % Number of predicates : 139 ( 138 usr; 1 prp; 0-6 aty)
% 18.25/18.32 % Number of functors : 385 ( 385 usr; 58 con; 0-7 aty)
% 18.25/18.32 % Number of variables : 16593 (16467 !; 126 ?)
% 18.25/18.32 % SPC : FOF_CAX_RFO_SEQ
% 18.25/18.32
% 18.25/18.32 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 18.25/18.32 % 2011-03-01 12:05:43
% 18.25/18.32 %------------------------------------------------------------------------------
% 18.25/18.32 %----Relevant facts (4983)
% 18.25/18.32 fof(fact_ext,axiom,
% 18.25/18.32 ! [V_g_2,V_f_2] :
% 18.25/18.32 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 18.25/18.32 => V_f_2 = V_g_2 ) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_Body__triple__valid__Suc,axiom,
% 18.25/18.32 ! [V_Qa_2,V_pn_2,V_Pa_2,V_n_2,T_b] :
% 18.25/18.32 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
% 18.25/18.32 <=> 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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_triple_Oinject,axiom,
% 18.25/18.32 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 18.25/18.32 ( 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)
% 18.25/18.32 <=> ( V_fun1_2 = V_fun1_H_2
% 18.25/18.32 & V_com_2 = V_com_H_2
% 18.25/18.32 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_triple__valid__Suc,axiom,
% 18.25/18.32 ! [V_t,V_n,T_a] :
% 18.25/18.32 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 18.25/18.32 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_equalityCE,axiom,
% 18.25/18.32 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 18.25/18.32 ( V_A_2 = V_B_2
% 18.25/18.32 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.32 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 18.25/18.32 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_triple_Orecs,axiom,
% 18.25/18.32 ! [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) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_triple_Osimps_I2_J,axiom,
% 18.25/18.32 ! [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) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_Body__triple__valid__0,axiom,
% 18.25/18.32 ! [V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_evaln_OBody,axiom,
% 18.25/18.32 ! [V_s1,V_n,V_s0,V_pn] :
% 18.25/18.32 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
% 18.25/18.32 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_com_Osimps_I6_J,axiom,
% 18.25/18.32 ! [V_pname_H_2,V_pname_2] :
% 18.25/18.32 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 18.25/18.32 <=> V_pname_2 = V_pname_H_2 ) ).
% 18.25/18.32
% 18.25/18.32 fof(fact_evaln_Oequations_I9_J,axiom,
% 18.25/18.32 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 18.25/18.32 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
% 18.25/18.33 <=> 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) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_n__not__Suc__n,axiom,
% 18.25/18.33 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Suc__n__not__n,axiom,
% 18.25/18.33 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 18.25/18.33
% 18.25/18.33 fof(fact_nat_Oinject,axiom,
% 18.25/18.33 ! [V_nat_H_2,V_nat_2] :
% 18.25/18.33 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 18.25/18.33 <=> V_nat_2 = V_nat_H_2 ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Suc__inject,axiom,
% 18.25/18.33 ! [V_y,V_x] :
% 18.25/18.33 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 18.25/18.33 => V_x = V_y ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evaln__Suc,axiom,
% 18.25/18.33 ! [V_s_H,V_n,V_s,V_c] :
% 18.25/18.33 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
% 18.25/18.33 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Suc__neq__Zero,axiom,
% 18.25/18.33 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Zero__neq__Suc,axiom,
% 18.25/18.33 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_nat_Osimps_I3_J,axiom,
% 18.25/18.33 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Suc__not__Zero,axiom,
% 18.25/18.33 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_nat_Osimps_I2_J,axiom,
% 18.25/18.33 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Zero__not__Suc,axiom,
% 18.25/18.33 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_triple__valid__def2,axiom,
% 18.25/18.33 ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
% 18.25/18.33 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
% 18.25/18.33 <=> ! [B_Z,B_s] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 18.25/18.33 => ! [B_s_H] :
% 18.25/18.33 ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
% 18.25/18.33 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_eq__mem__trans,axiom,
% 18.25/18.33 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 18.25/18.33 ( V_a_2 = V_b_2
% 18.25/18.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 18.25/18.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_eqelem__imp__iff,axiom,
% 18.25/18.33 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 18.25/18.33 ( V_x_2 = V_y_2
% 18.25/18.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.25/18.33 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_eqset__imp__iff,axiom,
% 18.25/18.33 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 18.25/18.33 ( V_A_2 = V_B_2
% 18.25/18.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.25/18.33 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_mem__def,axiom,
% 18.25/18.33 ! [V_A_2,V_x_2,T_b] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.25/18.33 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_triple_Osize_I1_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_triple_Osize_I2_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evaln__elim__cases_I6_J,axiom,
% 18.25/18.33 ! [V_s1,V_n,V_s,V_P] :
% 18.25/18.33 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
% 18.25/18.33 => ~ ! [B_n] :
% 18.25/18.33 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 18.25/18.33 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evalc_OBody,axiom,
% 18.25/18.33 ! [V_s1,V_s0,V_pn] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 18.25/18.33 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evalc__elim__cases_I6_J,axiom,
% 18.25/18.33 ! [V_s1,V_s,V_P] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 18.25/18.33 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evalc_Oequations_I9_J,axiom,
% 18.25/18.33 ! [V_a3_2,V_a2_2,V_a1_2] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 18.25/18.33 <=> 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)) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Nats__0,axiom,
% 18.25/18.33 ! [T_b] :
% 18.25/18.33 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.33 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I7_J,axiom,
% 18.25/18.33 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I15_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_zero__reorient,axiom,
% 18.25/18.33 ! [V_x_2,T_b] :
% 18.25/18.33 ( class_Groups_Ozero(T_b)
% 18.25/18.33 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 18.25/18.33 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_eq__mem,axiom,
% 18.25/18.33 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 18.25/18.33 <=> V_x_2 = V_y_2 ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com__det,axiom,
% 18.25/18.33 ! [V_u,V_t,V_s,V_c] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 18.25/18.33 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 18.25/18.33 => V_u = V_t ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evaln__evalc,axiom,
% 18.25/18.33 ! [V_t,V_n,V_s,V_c] :
% 18.25/18.33 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 18.25/18.33 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_eval__eq,axiom,
% 18.25/18.33 ! [V_t_2,V_s_2,V_c_2] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
% 18.25/18.33 <=> ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 18.25/18.33 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 18.25/18.33 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.33 => 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)) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I9_J,axiom,
% 18.25/18.33 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I1_J,axiom,
% 18.25/18.33 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 18.25/18.33 ! [V_i_2,V_inc_2,T_b] :
% 18.25/18.33 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.33 => 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 ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evalc__evaln,axiom,
% 18.25/18.33 ! [V_t,V_s,V_c] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 18.25/18.33 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I16_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I8_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I10_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osize_I2_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_zero__less__Suc,axiom,
% 18.25/18.33 ! [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))) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_nat_Oexhaust,axiom,
% 18.25/18.33 ! [V_y] :
% 18.25/18.33 ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.33 => ~ ! [B_nat] : V_y != hAPP(c_Nat_OSuc,B_nat) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_zero__induct,axiom,
% 18.25/18.33 ! [V_k_2,V_Pa_2] :
% 18.25/18.33 ( hBOOL(hAPP(V_Pa_2,V_k_2))
% 18.25/18.33 => ( ! [B_n] :
% 18.25/18.33 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_OSuc,B_n)))
% 18.25/18.33 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 18.25/18.33 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_less__zeroE,axiom,
% 18.25/18.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_Suc__mono,axiom,
% 18.25/18.33 ! [V_n,V_m] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_lessI,axiom,
% 18.25/18.33 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evaln_OSkip,axiom,
% 18.25/18.33 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evaln__elim__cases_I1_J,axiom,
% 18.25/18.33 ! [V_t,V_n,V_s] :
% 18.25/18.33 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
% 18.25/18.33 => V_t = V_s ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evalc__elim__cases_I1_J,axiom,
% 18.25/18.33 ! [V_t,V_s] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 18.25/18.33 => V_t = V_s ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_evalc_OSkip,axiom,
% 18.25/18.33 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_nat__less__cases,axiom,
% 18.25/18.33 ! [V_Pa_2,V_n_2,V_m_2] :
% 18.25/18.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 18.25/18.33 => ( ( V_m_2 = V_n_2
% 18.25/18.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 18.25/18.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 18.25/18.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 18.25/18.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_less__not__refl3,axiom,
% 18.25/18.33 ! [V_t,V_s] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 18.25/18.33 => V_s != V_t ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_less__not__refl2,axiom,
% 18.25/18.33 ! [V_m,V_n] :
% 18.25/18.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 18.25/18.33 => V_m != V_n ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_less__irrefl__nat,axiom,
% 18.25/18.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_linorder__neqE__nat,axiom,
% 18.25/18.33 ! [V_y,V_x] :
% 18.25/18.33 ( V_x != V_y
% 18.25/18.33 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 18.25/18.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osimps_I7_J,axiom,
% 18.25/18.33 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 18.25/18.33 ( 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)
% 18.25/18.33 <=> ( V_vname_2 = V_vname_H_2
% 18.25/18.33 & V_pname_2 = V_pname_H_2
% 18.25/18.33 & V_fun_2 = V_fun_H_2 ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osimps_I1_J,axiom,
% 18.25/18.33 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 18.25/18.33 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 18.25/18.33 <=> ( V_vname_2 = V_vname_H_2
% 18.25/18.33 & V_fun_2 = V_fun_H_2 ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_nat__neq__iff,axiom,
% 18.25/18.33 ! [V_n_2,V_m_2] :
% 18.25/18.33 ( V_m_2 != V_n_2
% 18.25/18.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osimps_I33_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osimps_I21_J,axiom,
% 18.25/18.33 ! [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 ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osimps_I32_J,axiom,
% 18.25/18.33 ! [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) ).
% 18.25/18.33
% 18.25/18.33 fof(fact_com_Osimps_I9_J,axiom,
% 18.25/18.33 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 18.25/18.33
% 18.25/18.33 fof(fact_less__not__refl,axiom,
% 18.25/18.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I20_J,axiom,
% 18.25/18.34 ! [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) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I8_J,axiom,
% 18.25/18.34 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_not__less0,axiom,
% 18.25/18.34 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_neq0__conv,axiom,
% 18.25/18.34 ! [V_n_2] :
% 18.25/18.34 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__nat__zero__code,axiom,
% 18.25/18.34 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_gr__implies__not0,axiom,
% 18.25/18.34 ! [V_n,V_m] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.34 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_gr0I,axiom,
% 18.25/18.34 ! [V_n] :
% 18.25/18.34 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_Suc__less__SucD,axiom,
% 18.25/18.34 ! [V_n,V_m] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_Suc__lessD,axiom,
% 18.25/18.34 ! [V_n,V_m] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__SucE,axiom,
% 18.25/18.34 ! [V_n,V_m] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 18.25/18.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.34 => V_m = V_n ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__trans__Suc,axiom,
% 18.25/18.34 ! [V_k,V_j,V_i] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_Suc__lessI,axiom,
% 18.25/18.34 ! [V_n,V_m] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.34 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__SucI,axiom,
% 18.25/18.34 ! [V_n,V_m] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__antisym,axiom,
% 18.25/18.34 ! [V_m,V_n] :
% 18.25/18.34 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 18.25/18.34 => V_m = V_n ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_not__less__less__Suc__eq,axiom,
% 18.25/18.34 ! [V_m_2,V_n_2] :
% 18.25/18.34 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 18.25/18.34 <=> V_n_2 = V_m_2 ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_Suc__less__eq,axiom,
% 18.25/18.34 ! [V_n_2,V_m_2] :
% 18.25/18.34 ( 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)))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__Suc__eq,axiom,
% 18.25/18.34 ! [V_n_2,V_m_2] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 18.25/18.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.34 | V_m_2 = V_n_2 ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_not__less__eq,axiom,
% 18.25/18.34 ! [V_n_2,V_m_2] :
% 18.25/18.34 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I30_J,axiom,
% 18.25/18.34 ! [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) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I31_J,axiom,
% 18.25/18.34 ! [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) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I63_J,axiom,
% 18.25/18.34 ! [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) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I62_J,axiom,
% 18.25/18.34 ! [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) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evaln_Oequations_I1_J,axiom,
% 18.25/18.34 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evalc_Oequations_I1_J,axiom,
% 18.25/18.34 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I19_J,axiom,
% 18.25/18.34 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 18.25/18.34
% 18.25/18.34 fof(fact_com_Osimps_I18_J,axiom,
% 18.25/18.34 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_gr0__conv__Suc,axiom,
% 18.25/18.34 ! [V_n_2] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 18.25/18.34 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__Suc0,axiom,
% 18.25/18.34 ! [V_n_2] :
% 18.25/18.34 ( 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))))
% 18.25/18.34 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__Suc__eq__0__disj,axiom,
% 18.25/18.34 ! [V_n_2,V_m_2] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 18.25/18.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.34 | ? [B_j] :
% 18.25/18.34 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 18.25/18.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_of__nat__0__less__iff,axiom,
% 18.25/18.34 ! [V_n_2,T_b] :
% 18.25/18.34 ( class_Rings_Olinordered__semidom(T_b)
% 18.25/18.34 => ( 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)))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_gr0__implies__Suc,axiom,
% 18.25/18.34 ! [V_n] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.34 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_lift__Suc__mono__less,axiom,
% 18.25/18.34 ! [V_n_H_2,V_n_2,V_f_2,T_b] :
% 18.25/18.34 ( class_Orderings_Oorder(T_b)
% 18.25/18.34 => ( ! [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))))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
% 18.25/18.34 => 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))) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_lift__Suc__mono__less__iff,axiom,
% 18.25/18.34 ! [V_m_2,V_n_2,V_f_2,T_b] :
% 18.25/18.34 ( class_Orderings_Oorder(T_b)
% 18.25/18.34 => ( ! [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))))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WTs__elim__cases_I8_J,axiom,
% 18.25/18.34 ! [V_a_2,V_Pa_2,V_X_2] :
% 18.25/18.34 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2)))
% 18.25/18.34 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evalc__elim__cases_I2_J,axiom,
% 18.25/18.34 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 18.25/18.34 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evalc_OAssign,axiom,
% 18.25/18.34 ! [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)))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evaln_OAssign,axiom,
% 18.25/18.34 ! [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))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evaln__elim__cases_I2_J,axiom,
% 18.25/18.34 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 18.25/18.34 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2)
% 18.25/18.34 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__irrefl,axiom,
% 18.25/18.34 ! [V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Opreorder(T_a)
% 18.25/18.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_linorder__neq__iff,axiom,
% 18.25/18.34 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.34 ( class_Orderings_Olinorder(T_b)
% 18.25/18.34 => ( V_x_2 != V_y_2
% 18.25/18.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_not__less__iff__gr__or__eq,axiom,
% 18.25/18.34 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.34 ( class_Orderings_Olinorder(T_b)
% 18.25/18.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 18.25/18.34 | V_x_2 = V_y_2 ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_of__nat__eq__iff,axiom,
% 18.25/18.34 ! [V_n_2,V_m_2,T_b] :
% 18.25/18.34 ( class_Nat_Osemiring__char__0(T_b)
% 18.25/18.34 => ( 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)
% 18.25/18.34 <=> V_m_2 = V_n_2 ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_psubsetD,axiom,
% 18.25/18.34 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 18.25/18.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WT_OAssign,axiom,
% 18.25/18.34 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WT_Oequations_I2_J,axiom,
% 18.25/18.34 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WT_OSkip,axiom,
% 18.25/18.34 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WT_Oequations_I1_J,axiom,
% 18.25/18.34 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_of__nat__less__0__iff,axiom,
% 18.25/18.34 ! [V_m,T_a] :
% 18.25/18.34 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.34 => ~ 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))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_of__nat__0,axiom,
% 18.25/18.34 ! [T_a] :
% 18.25/18.34 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.34 => 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) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_of__nat__less__iff,axiom,
% 18.25/18.34 ! [V_n_2,V_m_2,T_b] :
% 18.25/18.34 ( class_Rings_Olinordered__semidom(T_b)
% 18.25/18.34 => ( 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)))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__imp__of__nat__less,axiom,
% 18.25/18.34 ! [V_n,V_m,T_a] :
% 18.25/18.34 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.34 => 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))) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_of__nat__less__imp__less,axiom,
% 18.25/18.34 ! [V_n,V_m,T_a] :
% 18.25/18.34 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.34 => ( 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)))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_of__nat__in__Nats,axiom,
% 18.25/18.34 ! [V_n_2,T_b] :
% 18.25/18.34 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.34 => 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))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evaln_Oequations_I2_J,axiom,
% 18.25/18.34 ! [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))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_evalc_Oequations_I2_J,axiom,
% 18.25/18.34 ! [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)))) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WT_OCall,axiom,
% 18.25/18.34 ! [V_a_2,V_X_2,V_pn_2] :
% 18.25/18.34 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 18.25/18.34 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WT_Oequations_I8_J,axiom,
% 18.25/18.34 ! [V_a3_2,V_a1_2,V_a2_2] :
% 18.25/18.34 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 18.25/18.34 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_linorder__cases,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Olinorder(T_a)
% 18.25/18.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => ( V_x != V_y
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__asym,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Opreorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_xt1_I10_J,axiom,
% 18.25/18.34 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.34 ( class_Orderings_Oorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__trans,axiom,
% 18.25/18.34 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Opreorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_xt1_I2_J,axiom,
% 18.25/18.34 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.34 ( class_Orderings_Oorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 18.25/18.34 => ( V_b = V_c
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_ord__less__eq__trans,axiom,
% 18.25/18.34 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.34 ( class_Orderings_Oord(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.34 => ( V_b = V_c
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_xt1_I1_J,axiom,
% 18.25/18.34 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.34 ( class_Orderings_Oorder(T_a)
% 18.25/18.34 => ( V_a = V_b
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_ord__eq__less__trans,axiom,
% 18.25/18.34 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.34 ( class_Orderings_Oord(T_a)
% 18.25/18.34 => ( V_a = V_b
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_xt1_I9_J,axiom,
% 18.25/18.34 ! [V_a,V_b,T_a] :
% 18.25/18.34 ( class_Orderings_Oorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 18.25/18.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__asym_H,axiom,
% 18.25/18.34 ! [V_b,V_a,T_a] :
% 18.25/18.34 ( class_Orderings_Opreorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__imp__not__eq2,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Oorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => V_y != V_x ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__imp__not__eq,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Oorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => V_x != V_y ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__imp__not__less,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Opreorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_order__less__not__sym,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Opreorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_less__imp__neq,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Oorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => V_x != V_y ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_linorder__neqE,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Olinorder(T_a)
% 18.25/18.34 => ( V_x != V_y
% 18.25/18.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_linorder__antisym__conv3,axiom,
% 18.25/18.34 ! [V_x_2,V_y_2,T_b] :
% 18.25/18.34 ( class_Orderings_Olinorder(T_b)
% 18.25/18.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 18.25/18.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.34 <=> V_x_2 = V_y_2 ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_linorder__less__linear,axiom,
% 18.25/18.34 ! [V_y,V_x,T_a] :
% 18.25/18.34 ( class_Orderings_Olinorder(T_a)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.34 | V_x = V_y
% 18.25/18.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_zero__less__int__conv,axiom,
% 18.25/18.34 ! [V_n_2] :
% 18.25/18.34 ( 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)))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_Nats__induct,axiom,
% 18.25/18.34 ! [V_Pa_2,V_x_2,T_b] :
% 18.25/18.34 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 18.25/18.34 => ( ! [B_n] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),B_n)))
% 18.25/18.34 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_Nats__cases,axiom,
% 18.25/18.34 ! [V_x_2,T_b] :
% 18.25/18.34 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 18.25/18.34 => ~ ! [B_n] : V_x_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),B_n) ) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_WT_OBody,axiom,
% 18.25/18.34 ! [V_pn] :
% 18.25/18.34 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 18.25/18.34 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_zless__int,axiom,
% 18.25/18.34 ! [V_n_2,V_m_2] :
% 18.25/18.34 ( 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)))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 18.25/18.34 ! [V_y_2,V_x_2] :
% 18.25/18.34 ( 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)))
% 18.25/18.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 18.25/18.34 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)) ).
% 18.25/18.34
% 18.25/18.34 fof(fact_int__0,axiom,
% 18.25/18.34 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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_int__eq__0__conv,axiom,
% 18.25/18.35 ! [V_n_2] :
% 18.25/18.35 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.35 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_WT_Oequations_I7_J,axiom,
% 18.25/18.35 ! [V_a_2] :
% 18.25/18.35 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 18.25/18.35 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_linorder__neqE__linordered__idom,axiom,
% 18.25/18.35 ! [V_y,V_x,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.35 => ( V_x != V_y
% 18.25/18.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_int__less__0__conv,axiom,
% 18.25/18.35 ! [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))) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zless__linear,axiom,
% 18.25/18.35 ! [V_y,V_x] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 18.25/18.35 | V_x = V_y
% 18.25/18.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_psubset__trans,axiom,
% 18.25/18.35 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.25/18.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 18.25/18.35 ! [V_y_2,V_x_2] :
% 18.25/18.35 ( 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)
% 18.25/18.35 <=> V_x_2 = V_y_2 ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_int__int__eq,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2] :
% 18.25/18.35 ( 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)
% 18.25/18.35 <=> V_m_2 = V_n_2 ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_WT__bodiesD,axiom,
% 18.25/18.35 ! [V_b,V_pn] :
% 18.25/18.35 ( c_Com_OWT__bodies
% 18.25/18.35 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 18.25/18.35 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_WTs__elim__cases_I7_J,axiom,
% 18.25/18.35 ! [V_P] :
% 18.25/18.35 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 18.25/18.35 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_the_Osimps,axiom,
% 18.25/18.35 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 18.25/18.35
% 18.25/18.35 fof(fact_option_Osimps_I2_J,axiom,
% 18.25/18.35 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_option_Osimps_I3_J,axiom,
% 18.25/18.35 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_not__Some__eq,axiom,
% 18.25/18.35 ! [T_b,V_x_2] :
% 18.25/18.35 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 18.25/18.35 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_not__None__eq,axiom,
% 18.25/18.35 ! [T_b,V_x_2] :
% 18.25/18.35 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 18.25/18.35 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zero__less__imp__eq__int,axiom,
% 18.25/18.35 ! [V_k] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 18.25/18.35 => ? [B_n] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 18.25/18.35 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__0__less__iff,axiom,
% 18.25/18.35 ! [V_z_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__less__0__iff,axiom,
% 18.25/18.35 ! [V_z_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zmult__zless__mono2__lemma,axiom,
% 18.25/18.35 ! [V_k,V_j,V_i] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 18.25/18.35 => 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))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__mult,axiom,
% 18.25/18.35 ! [V_z,V_w,T_a] :
% 18.25/18.35 ( class_Rings_Oring__1(T_a)
% 18.25/18.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zmult__commute,axiom,
% 18.25/18.35 ! [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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__eq__iff,axiom,
% 18.25/18.35 ! [V_z_2,V_w_2,T_b] :
% 18.25/18.35 ( class_Int_Oring__char__0(T_b)
% 18.25/18.35 => ( 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)
% 18.25/18.35 <=> V_w_2 = V_z_2 ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zmult__assoc,axiom,
% 18.25/18.35 ! [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)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 18.25/18.35 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.35 ( class_Groups_Oab__semigroup__mult(T_a)
% 18.25/18.35 => 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)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__nat__mult,axiom,
% 18.25/18.35 ! [V_n,V_m,T_a] :
% 18.25/18.35 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.35 => 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)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_divisors__zero,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Ono__zero__divisors(T_a)
% 18.25/18.35 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.35 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.35 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_no__zero__divisors,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Ono__zero__divisors(T_a)
% 18.25/18.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__eq__0__iff,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Rings_Oring__no__zero__divisors(T_b)
% 18.25/18.35 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.35 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.35 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__zero__right,axiom,
% 18.25/18.35 ! [V_a,T_a] :
% 18.25/18.35 ( class_Rings_Omult__zero(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__zero__left,axiom,
% 18.25/18.35 ! [V_a,T_a] :
% 18.25/18.35 ( class_Rings_Omult__zero(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__int__eq,axiom,
% 18.25/18.35 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__strict__left__mono__neg,axiom,
% 18.25/18.35 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__ring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__strict__right__mono__neg,axiom,
% 18.25/18.35 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__ring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_comm__mult__strict__left__mono,axiom,
% 18.25/18.35 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__strict__left__mono,axiom,
% 18.25/18.35 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__strict__right__mono,axiom,
% 18.25/18.35 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__neg__neg,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__ring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__neg__pos,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__cancel__left__neg,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zero__less__mult__pos2,axiom,
% 18.25/18.35 ! [V_a,V_b,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zero__less__mult__pos,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__pos__neg2,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__pos__neg,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__pos__pos,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__cancel__left__pos,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__cancel__left__disj,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 18.25/18.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__cancel__right__disj,axiom,
% 18.25/18.35 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 18.25/18.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_not__square__less__zero,axiom,
% 18.25/18.35 ! [V_a,T_a] :
% 18.25/18.35 ( class_Rings_Olinordered__ring(T_a)
% 18.25/18.35 => ~ 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))) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zmult__zless__mono2,axiom,
% 18.25/18.35 ! [V_k,V_j,V_i] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 18.25/18.35 => 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))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__eq__0__iff,axiom,
% 18.25/18.35 ! [V_z_2,T_b] :
% 18.25/18.35 ( class_Int_Oring__char__0(T_b)
% 18.25/18.35 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.35 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__0__eq__iff,axiom,
% 18.25/18.35 ! [V_z_2,T_b] :
% 18.25/18.35 ( class_Int_Oring__char__0(T_b)
% 18.25/18.35 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 18.25/18.35 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__0,axiom,
% 18.25/18.35 ! [T_a] :
% 18.25/18.35 ( class_Rings_Oring__1(T_a)
% 18.25/18.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__less__iff,axiom,
% 18.25/18.35 ! [V_z_2,V_w_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_Nats__mult,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 18.25/18.35 => 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))) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__of__nat__eq,axiom,
% 18.25/18.35 ! [V_n,T_a] :
% 18.25/18.35 ( class_Rings_Oring__1(T_a)
% 18.25/18.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_option_Oinject,axiom,
% 18.25/18.35 ! [V_a_H_2,V_a_2,T_b] :
% 18.25/18.35 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 18.25/18.35 <=> V_a_2 = V_a_H_2 ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 18.25/18.35 ! [V_a,T_a] :
% 18.25/18.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 18.25/18.35 ! [V_a,T_a] :
% 18.25/18.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_elem__set,axiom,
% 18.25/18.35 ! [V_xo_2,V_x_2,T_b] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 18.25/18.35 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_option_Osimps_I5_J,axiom,
% 18.25/18.35 ! [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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_option_Orecs_I2_J,axiom,
% 18.25/18.35 ! [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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_option_Osimps_I4_J,axiom,
% 18.25/18.35 ! [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 ).
% 18.25/18.35
% 18.25/18.35 fof(fact_option_Orecs_I1_J,axiom,
% 18.25/18.35 ! [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 ).
% 18.25/18.35
% 18.25/18.35 fof(fact_is__none__code_I2_J,axiom,
% 18.25/18.35 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_is__none__def,axiom,
% 18.25/18.35 ! [V_x_2,T_b] :
% 18.25/18.35 ( c_Option_Ois__none(T_b,V_x_2)
% 18.25/18.35 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_is__none__code_I1_J,axiom,
% 18.25/18.35 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_negative__zless__0,axiom,
% 18.25/18.35 ! [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))) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_negative__zless,axiom,
% 18.25/18.35 ! [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))) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_nat__mult__commute,axiom,
% 18.25/18.35 ! [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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_nat__mult__assoc,axiom,
% 18.25/18.35 ! [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)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__equal__iff__equal,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Ogroup__add(T_b)
% 18.25/18.35 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 18.25/18.35 <=> V_a_2 = V_b_2 ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__equation__iff,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Ogroup__add(T_b)
% 18.25/18.35 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 18.25/18.35 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_equation__minus__iff,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Ogroup__add(T_b)
% 18.25/18.35 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 18.25/18.35 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__minus,axiom,
% 18.25/18.35 ! [V_a,T_a] :
% 18.25/18.35 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.35 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zminus__zminus,axiom,
% 18.25/18.35 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 18.25/18.35
% 18.25/18.35 fof(fact_of__int__minus,axiom,
% 18.25/18.35 ! [V_z,T_a] :
% 18.25/18.35 ( class_Rings_Oring__1(T_a)
% 18.25/18.35 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__zero,axiom,
% 18.25/18.35 ! [T_a] :
% 18.25/18.35 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.35 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__0__equal__iff__equal,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Ogroup__add(T_b)
% 18.25/18.35 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 18.25/18.35 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_equal__neg__zero,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.35 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 18.25/18.35 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__equal__0__iff__equal,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Ogroup__add(T_b)
% 18.25/18.35 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.35 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__equal__zero,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.35 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 18.25/18.35 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__less__iff__less,axiom,
% 18.25/18.35 ! [V_a_2,V_b_2,T_b] :
% 18.25/18.35 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__less__iff,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_less__minus__iff,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_square__eq__iff,axiom,
% 18.25/18.35 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.35 ( class_Rings_Oidom(T_b)
% 18.25/18.35 => ( 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)
% 18.25/18.35 <=> ( V_a_2 = V_b_2
% 18.25/18.35 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__mult__minus,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Oring(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__mult__commute,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Oring(T_a)
% 18.25/18.35 => 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)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__mult__left,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Oring(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_minus__mult__right,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Oring(T_a)
% 18.25/18.35 => 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)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zminus__0,axiom,
% 18.25/18.35 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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__0,axiom,
% 18.25/18.35 ! [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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__0__right,axiom,
% 18.25/18.35 ! [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) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__is__0,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2] :
% 18.25/18.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.35 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.35 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__cancel1,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.35 ( 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)
% 18.25/18.35 <=> ( V_m_2 = V_n_2
% 18.25/18.35 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__cancel2,axiom,
% 18.25/18.35 ! [V_n_2,V_k_2,V_m_2] :
% 18.25/18.35 ( 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)
% 18.25/18.35 <=> ( V_m_2 = V_n_2
% 18.25/18.35 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zmult__zminus,axiom,
% 18.25/18.35 ! [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)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_Suc__mult__cancel1,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.35 ( 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)
% 18.25/18.35 <=> V_m_2 = V_n_2 ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_less__minus__self__iff,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__less__nonneg,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__less__0__iff__less,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_neg__0__less__iff__less,axiom,
% 18.25/18.35 ! [V_a_2,T_b] :
% 18.25/18.35 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.35 => ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_negative__eq__positive,axiom,
% 18.25/18.35 ! [V_m_2,V_n_2] :
% 18.25/18.35 ( 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)
% 18.25/18.35 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.35 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_not__int__zless__negative,axiom,
% 18.25/18.35 ! [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)))) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__eq__1__iff,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2] :
% 18.25/18.35 ( 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))
% 18.25/18.35 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 18.25/18.35 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_nat__0__less__mult__iff,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2] :
% 18.25/18.35 ( 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)))
% 18.25/18.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 18.25/18.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__cancel1,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.35 ( 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)))
% 18.25/18.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.25/18.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__cancel2,axiom,
% 18.25/18.35 ! [V_n_2,V_k_2,V_m_2] :
% 18.25/18.35 ( 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)))
% 18.25/18.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.25/18.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__mono1,axiom,
% 18.25/18.35 ! [V_k,V_j,V_i] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 18.25/18.35 => 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))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_mult__less__mono2,axiom,
% 18.25/18.35 ! [V_k,V_j,V_i] :
% 18.25/18.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.25/18.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 18.25/18.35 => 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))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_Suc__mult__less__cancel1,axiom,
% 18.25/18.35 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.35 ( 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)))
% 18.25/18.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 18.25/18.35 ! [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)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_zmult__int,axiom,
% 18.25/18.35 ! [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)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_int__mult,axiom,
% 18.25/18.35 ! [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)) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_n__less__m__mult__n,axiom,
% 18.25/18.35 ! [V_m,V_n] :
% 18.25/18.35 ( 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))
% 18.25/18.35 => ( 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))
% 18.25/18.35 => 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))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_n__less__n__mult__m,axiom,
% 18.25/18.35 ! [V_m,V_n] :
% 18.25/18.35 ( 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))
% 18.25/18.35 => ( 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))
% 18.25/18.35 => 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))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_one__less__mult,axiom,
% 18.25/18.35 ! [V_m,V_n] :
% 18.25/18.35 ( 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))
% 18.25/18.35 => ( 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))
% 18.25/18.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 18.25/18.35 ! [V_b,V_a,T_a] :
% 18.25/18.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 18.25/18.35 ! [V_ry,V_rx,V_lx,T_a] :
% 18.25/18.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.35 => 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)) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 18.25/18.35 ! [V_ry,V_rx,V_lx,T_a] :
% 18.25/18.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.35 => 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) ) ).
% 18.25/18.35
% 18.25/18.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 18.25/18.35 ! [V_rx,V_ly,V_lx,T_a] :
% 18.25/18.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 18.25/18.36 ! [V_rx,V_ly,V_lx,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 18.25/18.36 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 18.25/18.36 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 18.25/18.36 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__mult__eq__cancel1,axiom,
% 18.25/18.36 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.25/18.36 => ( 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)
% 18.25/18.36 <=> V_m_2 = V_n_2 ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__mult__less__cancel1,axiom,
% 18.25/18.36 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 18.25/18.36 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.36 ( 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)
% 18.25/18.36 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.36 | V_m_2 = V_n_2 ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_negD,axiom,
% 18.25/18.36 ! [V_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.36 => ? [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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_of__int__of__nat,axiom,
% 18.25/18.36 ! [V_k,T_a] :
% 18.25/18.36 ( class_Rings_Oring__1(T_a)
% 18.25/18.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.36 => 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)))) )
% 18.25/18.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.36 => 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)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_not__zle__0__negative,axiom,
% 18.25/18.36 ! [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))))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_split__nat,axiom,
% 18.25/18.36 ! [V_i_2,V_Pa_2] :
% 18.25/18.36 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 18.25/18.36 <=> ( ! [B_n] :
% 18.25/18.36 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 18.25/18.36 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 18.25/18.36 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.36 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zero__less__nat__eq,axiom,
% 18.25/18.36 ! [V_z_2] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_neg__zminus__int,axiom,
% 18.25/18.36 ! [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))))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_option_Osize_I1_J,axiom,
% 18.25/18.36 ! [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) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ospec,axiom,
% 18.25/18.36 ! [V_x_2,V_Pa_2,V_A_2,T_b] :
% 18.25/18.36 ( ! [B_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Option_Oset(T_b,V_A_2)))
% 18.25/18.36 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.25/18.36 => ( V_A_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 18.25/18.36 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__refl,axiom,
% 18.25/18.36 ! [V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Opreorder(T_a)
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ComplI,axiom,
% 18.25/18.36 ! [V_A_2,V_c_2,T_b] :
% 18.25/18.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_negative__zle,axiom,
% 18.25/18.36 ! [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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zle__refl,axiom,
% 18.25/18.36 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zle__linear,axiom,
% 18.25/18.36 ! [V_w,V_z] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 18.25/18.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zle__trans,axiom,
% 18.25/18.36 ! [V_k,V_j,V_i] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zle__antisym,axiom,
% 18.25/18.36 ! [V_w,V_z] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 18.25/18.36 => V_z = V_w ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__fun__def,axiom,
% 18.25/18.36 ! [V_g_2,V_f_2,T_b,T_c] :
% 18.25/18.36 ( class_Orderings_Oord(T_c)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 18.25/18.36 <=> ! [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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_linorder__linear,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__eq__iff,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Oorder(T_b)
% 18.25/18.36 => ( V_x_2 = V_y_2
% 18.25/18.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__eq__refl,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Opreorder(T_a)
% 18.25/18.36 => ( V_x = V_y
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__funD,axiom,
% 18.25/18.36 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 18.25/18.36 ( class_Orderings_Oord(T_c)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__antisym__conv,axiom,
% 18.25/18.36 ! [V_x_2,V_y_2,T_b] :
% 18.25/18.36 ( class_Orderings_Oorder(T_b)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> V_x_2 = V_y_2 ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ord__eq__le__trans,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Orderings_Oord(T_a)
% 18.25/18.36 => ( V_a = V_b
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I3_J,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( V_a = V_b
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ord__le__eq__trans,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Orderings_Oord(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( V_b = V_c
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I4_J,axiom,
% 18.25/18.36 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 18.25/18.36 => ( V_b = V_c
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__antisym,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.36 => V_x = V_y ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__trans,axiom,
% 18.25/18.36 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Opreorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I5_J,axiom,
% 18.25/18.36 ! [V_x,V_y,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 => V_x = V_y ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I6_J,axiom,
% 18.25/18.36 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__funE,axiom,
% 18.25/18.36 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 18.25/18.36 ( class_Orderings_Oord(T_c)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_linorder__le__cases,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_a)
% 18.25/18.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_eq__nat__nat__iff,axiom,
% 18.25/18.36 ! [V_z_H_2,V_z_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 18.25/18.36 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 18.25/18.36 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 18.25/18.36 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 18.25/18.36 <=> V_x_2 = V_y_2 ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_all__nat,axiom,
% 18.25/18.36 ! [V_Pa_2] :
% 18.25/18.36 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 18.25/18.36 <=> ! [B_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 18.25/18.36 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ex__nat,axiom,
% 18.25/18.36 ! [V_Pa_2] :
% 18.25/18.36 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 18.25/18.36 <=> ? [B_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 18.25/18.36 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_neg__nat,axiom,
% 18.25/18.36 ! [V_z] :
% 18.25/18.36 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 18.25/18.36 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_of__nat__le__iff,axiom,
% 18.25/18.36 ! [V_n_2,V_m_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__semidom(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_not__neg__nat,axiom,
% 18.25/18.36 ! [V_z] :
% 18.25/18.36 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 18.25/18.36 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_not__neg__eq__ge__0,axiom,
% 18.25/18.36 ! [V_x_2] :
% 18.25/18.36 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_of__int__le__iff,axiom,
% 18.25/18.36 ! [V_z_2,V_w_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__le__0,axiom,
% 18.25/18.36 ! [V_z] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.36 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__0__iff,axiom,
% 18.25/18.36 ! [V_i_2] :
% 18.25/18.36 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_int__nat__eq,axiom,
% 18.25/18.36 ! [V_z] :
% 18.25/18.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.36 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 18.25/18.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.36 => 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) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_int__eq__iff,axiom,
% 18.25/18.36 ! [V_z_2,V_m_2] :
% 18.25/18.36 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 18.25/18.36 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__0__le,axiom,
% 18.25/18.36 ! [V_z] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.36 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Compl__iff,axiom,
% 18.25/18.36 ! [V_A_2,V_c_2,T_b] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ComplD,axiom,
% 18.25/18.36 ! [V_A_2,V_c_2,T_b] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ComplE,axiom,
% 18.25/18.36 ! [V_A_2,V_c_2,T_b] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__int,axiom,
% 18.25/18.36 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I8_J,axiom,
% 18.25/18.36 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__le__less__trans,axiom,
% 18.25/18.36 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Opreorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I7_J,axiom,
% 18.25/18.36 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__less__le__trans,axiom,
% 18.25/18.36 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Opreorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I11_J,axiom,
% 18.25/18.36 ! [V_a,V_b,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 18.25/18.36 => ( V_a != V_b
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__le__neq__trans,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( V_a != V_b
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__le__imp__less__or__eq,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.36 | V_x = V_y ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_linorder__antisym__conv2,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_b)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> V_x_2 = V_y_2 ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__less__imp__le,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Opreorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_leD,axiom,
% 18.25/18.36 ! [V_x,V_y,T_a] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_xt1_I12_J,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( V_a != V_b
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__neq__le__trans,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Orderings_Oorder(T_a)
% 18.25/18.36 => ( V_a != V_b
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_linorder__antisym__conv1,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_b)
% 18.25/18.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> V_x_2 = V_y_2 ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_not__leE,axiom,
% 18.25/18.36 ! [V_x,V_y,T_a] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_a)
% 18.25/18.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_leI,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_a)
% 18.25/18.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__le__less,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Oorder(T_b)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.36 | V_x_2 = V_y_2 ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_less__le__not__le,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Opreorder(T_b)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_order__less__le,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Oorder(T_b)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 & V_x_2 != V_y_2 ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_linorder__le__less__linear,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_linorder__not__le,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_b)
% 18.25/18.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_linorder__not__less,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Orderings_Olinorder(T_b)
% 18.25/18.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__minus__iff,axiom,
% 18.25/18.36 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.36 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_minus__le__iff,axiom,
% 18.25/18.36 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.36 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.36 => ( 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))
% 18.25/18.36 <=> 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)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_neg__le__iff__le,axiom,
% 18.25/18.36 ! [V_a_2,V_b_2,T_b] :
% 18.25/18.36 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__imp__neg__le,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Groups_Oordered__ab__group__add(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 18.25/18.36 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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zless__le,axiom,
% 18.25/18.36 ! [V_w_2,V_z_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 18.25/18.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 18.25/18.36 & V_z_2 != V_w_2 ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_not__neg__0,axiom,
% 18.25/18.36 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_not__neg__int,axiom,
% 18.25/18.36 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__less__eq__zless,axiom,
% 18.25/18.36 ! [V_z_2,V_w_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__eq__iff2,axiom,
% 18.25/18.36 ! [V_w_2,V_m_2] :
% 18.25/18.36 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 18.25/18.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 18.25/18.36 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 18.25/18.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 18.25/18.36 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__eq__iff,axiom,
% 18.25/18.36 ! [V_m_2,V_w_2] :
% 18.25/18.36 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 18.25/18.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 18.25/18.36 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 18.25/18.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 18.25/18.36 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__mult__distrib,axiom,
% 18.25/18.36 ! [V_z_H,V_z] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 18.25/18.36 ! [V_y,V_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.36 => 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)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_of__nat__nat,axiom,
% 18.25/18.36 ! [V_z,T_a] :
% 18.25/18.36 ( class_Rings_Oring__1(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.36 => 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) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_of__int__le__0__iff,axiom,
% 18.25/18.36 ! [V_z_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_of__int__0__le__iff,axiom,
% 18.25/18.36 ! [V_z_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__less__iff,axiom,
% 18.25/18.36 ! [V_m_2,V_w_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 18.25/18.36 <=> 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__mult__distrib__neg,axiom,
% 18.25/18.36 ! [V_z_H,V_z] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 18.25/18.36 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__0,axiom,
% 18.25/18.36 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_split__mult__neg__le,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__cancel__semiring(T_a)
% 18.25/18.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 18.25/18.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_split__mult__pos__le,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__ring(T_a)
% 18.25/18.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 18.25/18.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__mono,axiom,
% 18.25/18.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__mono_H,axiom,
% 18.25/18.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__left__mono__neg,axiom,
% 18.25/18.36 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__ring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__right__mono__neg,axiom,
% 18.25/18.36 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__ring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__mult__left__mono,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__comm__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__left__mono,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__right__mono,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__nonpos__nonpos,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__ring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__nonpos__nonneg,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__cancel__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__nonneg__nonpos2,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__cancel__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__nonneg__nonpos,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__cancel__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__nonneg__nonneg,axiom,
% 18.25/18.36 ! [V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Oordered__cancel__semiring(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.36 => 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))) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__le__0__iff,axiom,
% 18.25/18.36 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 18.25/18.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zero__le__mult__iff,axiom,
% 18.25/18.36 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 18.25/18.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zero__le__square,axiom,
% 18.25/18.36 ! [V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__ring(T_a)
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_neg__0__le__iff__le,axiom,
% 18.25/18.36 ! [V_a_2,T_b] :
% 18.25/18.36 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__minus__self__iff,axiom,
% 18.25/18.36 ! [V_a_2,T_b] :
% 18.25/18.36 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_neg__le__0__iff__le,axiom,
% 18.25/18.36 ! [V_a_2,T_b] :
% 18.25/18.36 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_minus__le__self__iff,axiom,
% 18.25/18.36 ! [V_a_2,T_b] :
% 18.25/18.36 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.36 => ( 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))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_of__nat__0__le__iff,axiom,
% 18.25/18.36 ! [V_n,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zero__le__imp__of__nat,axiom,
% 18.25/18.36 ! [V_m,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zero__zle__int,axiom,
% 18.25/18.36 ! [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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 18.25/18.36 ! [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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 18.25/18.36 ! [V_Pa_2] :
% 18.25/18.36 ( ? [B_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 18.25/18.36 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.25/18.36 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 18.25/18.36 ! [V_Pa_2] :
% 18.25/18.36 ( ! [B_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 18.25/18.36 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.25/18.36 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 18.25/18.36 ! [V_y,V_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_neg__def,axiom,
% 18.25/18.36 ! [V_Z_2] :
% 18.25/18.36 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zless__nat__conj,axiom,
% 18.25/18.36 ! [V_z_2,V_w_2] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 18.25/18.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__mono__iff,axiom,
% 18.25/18.36 ! [V_w_2,V_z_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_zless__nat__eq__int__zless,axiom,
% 18.25/18.36 ! [V_z_2,V_m_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 18.25/18.36 <=> 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__zminus__int,axiom,
% 18.25/18.36 ! [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) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__left__le__imp__le,axiom,
% 18.25/18.36 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__right__le__imp__le,axiom,
% 18.25/18.36 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__less__imp__less__left,axiom,
% 18.25/18.36 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__left__less__imp__less,axiom,
% 18.25/18.36 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring(T_a)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__less__imp__less__right,axiom,
% 18.25/18.36 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__right__less__imp__less,axiom,
% 18.25/18.36 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring(T_a)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__le__less__imp__less,axiom,
% 18.25/18.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__less__le__imp__less,axiom,
% 18.25/18.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__strict__mono_H,axiom,
% 18.25/18.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__strict__mono,axiom,
% 18.25/18.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semiring__strict(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.36 => 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))) ) ) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__le__cancel__left__neg,axiom,
% 18.25/18.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_mult__le__cancel__left__pos,axiom,
% 18.25/18.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.36 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_int__le__0__conv,axiom,
% 18.25/18.36 ! [V_n_2] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_int__zle__neg,axiom,
% 18.25/18.36 ! [V_m_2,V_n_2] :
% 18.25/18.36 ( 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))))
% 18.25/18.36 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.36 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_negative__zle__0,axiom,
% 18.25/18.36 ! [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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_transfer__morphism__nat__int,axiom,
% 18.25/18.36 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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_option_Osize_I4_J,axiom,
% 18.25/18.36 ! [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) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_option_Osize_I3_J,axiom,
% 18.25/18.36 ! [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) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_compl__mono,axiom,
% 18.25/18.36 ! [V_y,V_x,T_a] :
% 18.25/18.36 ( class_Lattices_Oboolean__algebra(T_a)
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_compl__le__compl__iff,axiom,
% 18.25/18.36 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.36 ( class_Lattices_Oboolean__algebra(T_b)
% 18.25/18.36 => ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_one__less__nat__eq,axiom,
% 18.25/18.36 ! [V_z_2] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_option_Osize_I2_J,axiom,
% 18.25/18.36 ! [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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_bool_Osize_I2_J,axiom,
% 18.25/18.36 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_bool_Osize_I1_J,axiom,
% 18.25/18.36 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 18.25/18.36 ! [V_y,V_x] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_subsetD,axiom,
% 18.25/18.36 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le0,axiom,
% 18.25/18.36 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Compl__anti__mono,axiom,
% 18.25/18.36 ! [V_B_2,V_A_2,T_b] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Compl__subset__Compl__iff,axiom,
% 18.25/18.36 ! [V_B_2,V_A_2,T_b] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_Compl__eq__Compl__iff,axiom,
% 18.25/18.36 ! [V_B_2,V_A_2,T_b] :
% 18.25/18.36 ( 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)
% 18.25/18.36 <=> V_A_2 = V_B_2 ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_double__complement,axiom,
% 18.25/18.36 ! [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 ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__refl,axiom,
% 18.25/18.36 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__add2,axiom,
% 18.25/18.36 ! [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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__add1,axiom,
% 18.25/18.36 ! [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))) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__iff__add,axiom,
% 18.25/18.36 ! [V_n_2,V_m_2] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.36 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__le__linear,axiom,
% 18.25/18.36 ! [V_n,V_m] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__add__left__cancel__le,axiom,
% 18.25/18.36 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.36 ( 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)))
% 18.25/18.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_eq__imp__le,axiom,
% 18.25/18.36 ! [V_n,V_m] :
% 18.25/18.36 ( V_m = V_n
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_trans__le__add1,axiom,
% 18.25/18.36 ! [V_m,V_j,V_i] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_trans__le__add2,axiom,
% 18.25/18.36 ! [V_m,V_j,V_i] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__le__mono1,axiom,
% 18.25/18.36 ! [V_k,V_j,V_i] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.36 => 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))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__trans,axiom,
% 18.25/18.36 ! [V_k,V_j,V_i] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_le__antisym,axiom,
% 18.25/18.36 ! [V_n,V_m] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.36 => V_m = V_n ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__le__mono,axiom,
% 18.25/18.36 ! [V_l,V_k,V_j,V_i] :
% 18.25/18.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 18.25/18.36 => 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))) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__leD2,axiom,
% 18.25/18.36 ! [V_n,V_k,V_m] :
% 18.25/18.36 ( 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))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__leD1,axiom,
% 18.25/18.36 ! [V_n,V_k,V_m] :
% 18.25/18.36 ( 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))
% 18.25/18.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__leE,axiom,
% 18.25/18.36 ! [V_n,V_k,V_m] :
% 18.25/18.36 ( 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))
% 18.25/18.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_less__add__one,axiom,
% 18.25/18.36 ! [V_a,T_a] :
% 18.25/18.36 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.36 => 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)))) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__right__imp__eq,axiom,
% 18.25/18.36 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.36 ( class_Groups_Ocancel__semigroup__add(T_a)
% 18.25/18.36 => ( 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)
% 18.25/18.36 => V_b = V_c ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__imp__eq,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 18.25/18.36 => ( 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)
% 18.25/18.36 => V_b = V_c ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__left__imp__eq,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Groups_Ocancel__semigroup__add(T_a)
% 18.25/18.36 => ( 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)
% 18.25/18.36 => V_b = V_c ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__right__cancel,axiom,
% 18.25/18.36 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 18.25/18.36 ( class_Groups_Ocancel__semigroup__add(T_b)
% 18.25/18.36 => ( 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)
% 18.25/18.36 <=> V_b_2 = V_c_2 ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_add__left__cancel,axiom,
% 18.25/18.36 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.36 ( class_Groups_Ocancel__semigroup__add(T_b)
% 18.25/18.36 => ( 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)
% 18.25/18.36 <=> V_b_2 = V_c_2 ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Groups_Oab__semigroup__add(T_a)
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_one__reorient,axiom,
% 18.25/18.36 ! [V_x_2,T_b] :
% 18.25/18.36 ( class_Groups_Oone(T_b)
% 18.25/18.36 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 18.25/18.36 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__add__right__cancel,axiom,
% 18.25/18.36 ! [V_n_2,V_k_2,V_m_2] :
% 18.25/18.36 ( 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)
% 18.25/18.36 <=> V_m_2 = V_n_2 ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__add__left__cancel,axiom,
% 18.25/18.36 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.36 ( 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)
% 18.25/18.36 <=> V_m_2 = V_n_2 ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__add__assoc,axiom,
% 18.25/18.36 ! [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)) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__add__left__commute,axiom,
% 18.25/18.36 ! [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)) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_nat__add__commute,axiom,
% 18.25/18.36 ! [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) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 18.25/18.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 18.25/18.36 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 18.25/18.36 ! [V_d,V_c,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 18.25/18.36 ! [V_d,V_c,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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)) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 18.25/18.36 ! [V_c,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 18.25/18.36 ! [V_m,V_a,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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) ) ).
% 18.25/18.36
% 18.25/18.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 18.25/18.36 ! [V_a,V_m,T_a] :
% 18.25/18.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.36 => 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) ) ).
% 18.25/18.36
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 18.25/18.37 ! [V_m,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_of__nat__add,axiom,
% 18.25/18.37 ! [V_n,V_m,T_a] :
% 18.25/18.37 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_of__nat__1,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_of__int__add,axiom,
% 18.25/18.37 ! [V_z,V_w,T_a] :
% 18.25/18.37 ( class_Rings_Oring__1(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_of__int__1,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Oring__1(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zero__less__two,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.37 => 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)))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_of__nat__Suc,axiom,
% 18.25/18.37 ! [V_m,T_a] :
% 18.25/18.37 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__le__imp__le__left,axiom,
% 18.25/18.37 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__le__imp__le__right,axiom,
% 18.25/18.37 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__mono,axiom,
% 18.25/18.37 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__left__mono,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__right__mono,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__le__cancel__left,axiom,
% 18.25/18.37 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__le__cancel__right,axiom,
% 18.25/18.37 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__0__iff,axiom,
% 18.25/18.37 ! [V_a_2,V_b_2,T_b] :
% 18.25/18.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 18.25/18.37 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 18.25/18.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_double__eq__0__iff,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__0__left,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Omonoid__add(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__0,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ocomm__monoid__add(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_double__zero__sym,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.37 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 18.25/18.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__0__right,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Omonoid__add(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add_Ocomm__neutral,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ocomm__monoid__add(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__less__imp__less__left,axiom,
% 18.25/18.37 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__less__imp__less__right,axiom,
% 18.25/18.37 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__strict__mono,axiom,
% 18.25/18.37 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__strict__left__mono,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__strict__right__mono,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__less__cancel__left,axiom,
% 18.25/18.37 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__less__cancel__right,axiom,
% 18.25/18.37 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 18.25/18.37 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_crossproduct__noteq,axiom,
% 18.25/18.37 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 18.25/18.37 => ( ( V_a_2 != V_b_2
% 18.25/18.37 & V_c_2 != V_d_2 )
% 18.25/18.37 <=> 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)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 18.25/18.37 ! [V_b,V_m,V_a,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_crossproduct__eq,axiom,
% 18.25/18.37 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 18.25/18.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 18.25/18.37 => ( 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))
% 18.25/18.37 <=> ( V_w_2 = V_x_2
% 18.25/18.37 | V_y_2 = V_z_2 ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_combine__common__factor,axiom,
% 18.25/18.37 ! [V_c,V_b,V_e,V_a,T_a] :
% 18.25/18.37 ( class_Rings_Osemiring(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__class_Odistrib,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_one__neq__zero,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Ozero__neq__one(T_a)
% 18.25/18.37 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zero__neq__one,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Ozero__neq__one(T_a)
% 18.25/18.37 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult_Ocomm__neutral,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ocomm__monoid__mult(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__1__right,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__1,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ocomm__monoid__mult(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__1__left,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_minus__add__cancel,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.37 => 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 ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__minus__cancel,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.37 => 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 ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_minus__add,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_minus__add__distrib,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oab__group__add(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_set__mp,axiom,
% 18.25/18.37 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_set__rev__mp,axiom,
% 18.25/18.37 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_in__mono,axiom,
% 18.25/18.37 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_plus__nat_Oadd__0,axiom,
% 18.25/18.37 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Nat_Oadd__0__right,axiom,
% 18.25/18.37 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__is__0,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__eq__self__zero,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 18.25/18.37 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__Suc__shift,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__Suc,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__Suc__right,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__lessD1,axiom,
% 18.25/18.37 ! [V_k,V_j,V_i] :
% 18.25/18.37 ( 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))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__add__eq__less,axiom,
% 18.25/18.37 ! [V_n,V_m,V_l,V_k] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 18.25/18.37 => ( 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)
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__less__mono,axiom,
% 18.25/18.37 ! [V_l,V_k,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__less__mono1,axiom,
% 18.25/18.37 ! [V_k,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_trans__less__add2,axiom,
% 18.25/18.37 ! [V_m,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_trans__less__add1,axiom,
% 18.25/18.37 ! [V_m,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__add__left__cancel__less,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_not__add__less2,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_not__add__less1,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 18.25/18.37 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__0__eq,axiom,
% 18.25/18.37 ! [V_n_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 18.25/18.37 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__leD,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__SucE,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 18.25/18.37 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.37 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__SucI,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__le__mono,axiom,
% 18.25/18.37 ! [V_m_2,V_n_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__Suc__eq,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_not__less__eq__eq,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__n__not__le__n,axiom,
% 18.25/18.37 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__or__eq__imp__le,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.37 | V_m = V_n )
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__neq__implies__less,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.37 => ( V_m != V_n
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__imp__le__nat,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__eq__less__or__eq,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 | V_m_2 = V_n_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__less__le,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 & V_m_2 != V_n_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_int__0__neq__1,axiom,
% 18.25/18.37 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__mult__distrib2,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__mult__distrib,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_left__add__mult__distrib,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__square,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__cube,axiom,
% 18.25/18.37 ! [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)))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__le__mono1,axiom,
% 18.25/18.37 ! [V_k,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__le__mono2,axiom,
% 18.25/18.37 ! [V_k,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__le__mono,axiom,
% 18.25/18.37 ! [V_l,V_k,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmult__1__right,axiom,
% 18.25/18.37 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmult__1,axiom,
% 18.25/18.37 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__fun__def,axiom,
% 18.25/18.37 ! [V_g_2,V_f_2,T_b,T_c] :
% 18.25/18.37 ( class_Orderings_Oord(T_c)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 18.25/18.37 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evaln__nonstrict,axiom,
% 18.25/18.37 ! [V_m,V_t,V_n,V_s,V_c] :
% 18.25/18.37 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.37 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_not__neg__1,axiom,
% 18.25/18.37 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_subset__psubset__trans,axiom,
% 18.25/18.37 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_psubset__subset__trans,axiom,
% 18.25/18.37 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_psubset__imp__subset,axiom,
% 18.25/18.37 ! [V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_subset__iff__psubset__eq,axiom,
% 18.25/18.37 ! [V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 | V_A_2 = V_B_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_psubset__eq,axiom,
% 18.25/18.37 ! [V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 & V_A_2 != V_B_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_convex__bound__le,axiom,
% 18.25/18.37 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semiring__1(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 18.25/18.37 => 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)) ) ) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_convex__bound__lt,axiom,
% 18.25/18.37 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 18.25/18.37 => 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)) ) ) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__nonpos__nonpos,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__increasing2,axiom,
% 18.25/18.37 ! [V_a,V_b,V_c,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__increasing,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__nonneg__eq__0__iff,axiom,
% 18.25/18.37 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__nonneg__nonneg,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__le__less__mono,axiom,
% 18.25/18.37 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__less__le__mono,axiom,
% 18.25/18.37 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_even__less__0__iff,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_pos__add__strict,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__neg__neg,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__pos__pos,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__scale__eq__noteq,axiom,
% 18.25/18.37 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 18.25/18.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 18.25/18.37 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.37 => ( ( V_a = V_b
% 18.25/18.37 & V_c != V_d )
% 18.25/18.37 => 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)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sum__squares__eq__zero__iff,axiom,
% 18.25/18.37 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.37 => ( 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)
% 18.25/18.37 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_minus__unique,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_ab__left__minus,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oab__group__add(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_left__minus,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 18.25/18.37 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.37 ( class_Groups_Ogroup__add(T_b)
% 18.25/18.37 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 18.25/18.37 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_right__minus,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_not__one__le__zero,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.37 => ~ 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zero__le__one,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_not__one__less__zero,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zero__less__one,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__1__mult,axiom,
% 18.25/18.37 ! [V_n,V_m,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 18.25/18.37 ! [V_x,T_a] :
% 18.25/18.37 ( class_Rings_Ocomm__ring__1(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_square__eq__1__iff,axiom,
% 18.25/18.37 ! [V_x_2,T_b] :
% 18.25/18.37 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 18.25/18.37 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 18.25/18.37 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_one__is__add,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( 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)
% 18.25/18.37 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 18.25/18.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.25/18.37 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__is__1,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( 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))
% 18.25/18.37 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 18.25/18.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.25/18.37 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__gr__0,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 18.25/18.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__add__Suc1,axiom,
% 18.25/18.37 ! [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)))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__add__Suc2,axiom,
% 18.25/18.37 ! [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)))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__iff__Suc__add,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__Suc__right,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__Suc,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__eq__Suc__le,axiom,
% 18.25/18.37 ! [V_m_2,V_n_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_less__Suc__eq__le,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__le__eq,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__imp__less__Suc,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__leI,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__less__Suc__eq,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 18.25/18.37 <=> V_n_2 = V_m_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__le__lessD,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 18.25/18.37 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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__mult__le__cancel1,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_int__0__less__1,axiom,
% 18.25/18.37 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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 18.25/18.37 ! [V_y_2,V_x_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zle__int,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Nats__add,axiom,
% 18.25/18.37 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Nats__1,axiom,
% 18.25/18.37 ! [T_b] :
% 18.25/18.37 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__pos__nonneg,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__nonneg__pos,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__strict__increasing,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__strict__increasing2,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__neg__nonpos,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add__nonpos__neg,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sum__squares__le__zero__iff,axiom,
% 18.25/18.37 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sum__squares__ge__zero,axiom,
% 18.25/18.37 ! [V_y,V_x,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__ring(T_a)
% 18.25/18.37 => 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)))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_not__sum__squares__lt__zero,axiom,
% 18.25/18.37 ! [V_y,V_x,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__ring(T_a)
% 18.25/18.37 => ~ 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sum__squares__gt__zero__iff,axiom,
% 18.25/18.37 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__ring__strict(T_b)
% 18.25/18.37 => ( 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))))
% 18.25/18.37 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__left__le__one__le,axiom,
% 18.25/18.37 ! [V_y,V_x,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 18.25/18.37 => 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)) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__right__le__one__le,axiom,
% 18.25/18.37 ! [V_y,V_x,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 18.25/18.37 => 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)) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_one__le__mult__iff,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> ( 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))
% 18.25/18.37 & 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)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__le__cancel1,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__le__cancel2,axiom,
% 18.25/18.37 ! [V_n_2,V_k_2,V_m_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__mult__le__cancel1,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 18.25/18.37 ! [V_y_2,V_x_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_int__one__le__iff__zero__less,axiom,
% 18.25/18.37 ! [V_z_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_int__Suc0__eq__1,axiom,
% 18.25/18.37 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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__1,axiom,
% 18.25/18.37 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_pos__zmult__eq__1__iff,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 18.25/18.37 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 18.25/18.37 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_times_Oidem,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__idem,axiom,
% 18.25/18.37 ! [V_x,T_a] :
% 18.25/18.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 18.25/18.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__left__idem,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_double__compl,axiom,
% 18.25/18.37 ! [V_x,T_a] :
% 18.25/18.37 ( class_Lattices_Oboolean__algebra(T_a)
% 18.25/18.37 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_uminus__apply,axiom,
% 18.25/18.37 ! [V_x_2,V_A_2,T_c,T_b] :
% 18.25/18.37 ( class_Groups_Ouminus(T_b)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_compl__eq__compl__iff,axiom,
% 18.25/18.37 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.37 ( class_Lattices_Oboolean__algebra(T_b)
% 18.25/18.37 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 18.25/18.37 <=> V_x_2 = V_y_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__le__eq__zle,axiom,
% 18.25/18.37 ! [V_z_2,V_w_2] :
% 18.25/18.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 18.25/18.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__aux__def,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat_Osize_I2_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat_Osize_I4_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_termination__basic__simps_I4_J,axiom,
% 18.25/18.37 ! [V_y,V_z,V_x] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_termination__basic__simps_I3_J,axiom,
% 18.25/18.37 ! [V_z,V_y,V_x] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_termination__basic__simps_I5_J,axiom,
% 18.25/18.37 ! [V_y,V_x] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_termination__basic__simps_I1_J,axiom,
% 18.25/18.37 ! [V_z,V_y,V_x] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_termination__basic__simps_I2_J,axiom,
% 18.25/18.37 ! [V_y,V_z,V_x] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__odd__less__0,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__1__neg,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.37 => ( 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))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_equalityI,axiom,
% 18.25/18.37 ! [V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.25/18.37 => V_A_2 = V_B_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_subset__refl,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_set__eq__subset,axiom,
% 18.25/18.37 ! [T_b,V_B_2,V_A_2] :
% 18.25/18.37 ( V_A_2 = V_B_2
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_equalityD1,axiom,
% 18.25/18.37 ! [T_b,V_B_2,V_A_2] :
% 18.25/18.37 ( V_A_2 = V_B_2
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_equalityD2,axiom,
% 18.25/18.37 ! [T_b,V_B_2,V_A_2] :
% 18.25/18.37 ( V_A_2 = V_B_2
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_subset__trans,axiom,
% 18.25/18.37 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_equalityE,axiom,
% 18.25/18.37 ! [T_b,V_B_2,V_A_2] :
% 18.25/18.37 ( V_A_2 = V_B_2
% 18.25/18.37 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_rev__predicate1D,axiom,
% 18.25/18.37 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
% 18.25/18.37 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 18.25/18.37 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_predicate1D,axiom,
% 18.25/18.37 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 18.25/18.37 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.25/18.37 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__assoc,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__left__commute,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__commute,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__sgn,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__size,axiom,
% 18.25/18.37 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__0__right,axiom,
% 18.25/18.37 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__0,axiom,
% 18.25/18.37 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__left__mono,axiom,
% 18.25/18.37 ! [V_k,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__strict__right__mono,axiom,
% 18.25/18.37 ! [V_k,V_j,V_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__zmult__distrib2,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__zmult__distrib,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zminus__zadd__distrib,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__mult__eq__1__iff,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 18.25/18.37 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 18.25/18.37 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__mult__1__right,axiom,
% 18.25/18.37 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__1__eq__mult__iff,axiom,
% 18.25/18.37 ! [V_n_2,V_m_2] :
% 18.25/18.37 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 18.25/18.37 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 18.25/18.37 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__mult__1,axiom,
% 18.25/18.37 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn0,axiom,
% 18.25/18.37 ! [T_a] :
% 18.25/18.37 ( class_Groups_Osgn__if(T_a)
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__0__0,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.37 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__times,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 18.25/18.37 ! [V_y,V_x] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__zless__mono,axiom,
% 18.25/18.37 ! [V_z,V_z_H,V_w,V_w_H] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_odd__nonzero,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_One__nat__def,axiom,
% 18.25/18.37 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__int,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__int__left,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zle__iff__zadd,axiom,
% 18.25/18.37 ! [V_z_2,V_w_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 18.25/18.37 <=> ? [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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zless__add1__eq,axiom,
% 18.25/18.37 ! [V_z_2,V_w_2] :
% 18.25/18.37 ( 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))))
% 18.25/18.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 18.25/18.37 | V_w_2 = V_z_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zadd__zminus__inverse2,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__eq__plus1,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__eq__plus1__left,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mult__eq__self__implies__10,axiom,
% 18.25/18.37 ! [V_n,V_m] :
% 18.25/18.37 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 18.25/18.37 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 18.25/18.37 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 18.25/18.37 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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_int__1,axiom,
% 18.25/18.37 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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 18.25/18.37 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__0,axiom,
% 18.25/18.37 ! [T_b] :
% 18.25/18.37 ( class_Rings_Oring__1(T_b)
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__add,axiom,
% 18.25/18.37 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Oring__1(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__mult,axiom,
% 18.25/18.37 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Oring__1(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat_Osize_I3_J,axiom,
% 18.25/18.37 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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__1,axiom,
% 18.25/18.37 ! [T_b] :
% 18.25/18.37 ( class_Rings_Oring__1(T_b)
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__minus,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Oring__1(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => 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))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__of__nat,axiom,
% 18.25/18.37 ! [V_n_2,T_b] :
% 18.25/18.37 ( class_Rings_Oring__1(T_b)
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__less,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__greater,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zless__iff__Suc__zadd,axiom,
% 18.25/18.37 ! [V_z_2,V_w_2] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 18.25/18.37 <=> ? [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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_odd__less__0,axiom,
% 18.25/18.37 ! [V_z_2] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__of__int,axiom,
% 18.25/18.37 ! [V_z_2,T_b] :
% 18.25/18.37 ( class_Rings_Oring__1(T_b)
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zle__add1__eq__le,axiom,
% 18.25/18.37 ! [V_z_2,V_w_2] :
% 18.25/18.37 ( 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))))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_add1__zle__eq,axiom,
% 18.25/18.37 ! [V_z_2,V_w_2] :
% 18.25/18.37 ( 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))
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zless__imp__add1__zle,axiom,
% 18.25/18.37 ! [V_z,V_w] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_int__Suc,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat_Osize_I1_J,axiom,
% 18.25/18.37 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_nat__add__distrib,axiom,
% 18.25/18.37 ! [V_z_H,V_z] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 18.25/18.37 => 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)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 18.25/18.37 ! [V_y,V_x] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.37 => 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)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_le__imp__0__less,axiom,
% 18.25/18.37 ! [V_z] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.37 => 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))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__double__eq__0__iff,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Int_Oring__char__0(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__pos,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__1__pos,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.37 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 18.25/18.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 18.25/18.37 ! [V_z] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_Ints__odd__nonzero,axiom,
% 18.25/18.37 ! [V_a_2,T_b] :
% 18.25/18.37 ( class_Int_Oring__char__0(T_b)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.37 => 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) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zsgn__def,axiom,
% 18.25/18.37 ! [V_i] :
% 18.25/18.37 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 18.25/18.37 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 18.25/18.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 18.25/18.37 => 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)) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__if,axiom,
% 18.25/18.37 ! [V_x,T_a] :
% 18.25/18.37 ( class_Groups_Osgn__if(T_a)
% 18.25/18.37 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 18.25/18.37 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 18.25/18.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_sgn__neg,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.37 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_self__quotient__aux2,axiom,
% 18.25/18.37 ! [V_q,V_r,V_a] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.37 => ( 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))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_self__quotient__aux1,axiom,
% 18.25/18.37 ! [V_q,V_r,V_a] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.37 => ( 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))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 18.25/18.37 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 18.25/18.37 ( 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)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_unique__quotient__lemma__neg,axiom,
% 18.25/18.37 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zdiv__mono2__lemma,axiom,
% 18.25/18.37 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 18.25/18.37 ( 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)
% 18.25/18.37 => ( 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)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_unique__quotient__lemma,axiom,
% 18.25/18.37 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_q__neg__lemma,axiom,
% 18.25/18.37 ! [V_r_H,V_q_H,V_b_H] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_q__pos__lemma,axiom,
% 18.25/18.37 ! [V_r_H,V_q_H,V_b_H] :
% 18.25/18.37 ( 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)))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_ex__least__nat__less,axiom,
% 18.25/18.37 ! [V_n_2,V_Pa_2] :
% 18.25/18.37 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 18.25/18.37 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 18.25/18.37 => ? [B_k] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 18.25/18.37 & ! [B_i] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 18.25/18.37 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 18.25/18.37 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osize_I4_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osize_I12_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osize_I5_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osize_I13_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osize_I3_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osize_I11_J,axiom,
% 18.25/18.37 ! [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))) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_divmod__int__rel__mod__eq,axiom,
% 18.25/18.37 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 18.25/18.37 ( 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)
% 18.25/18.37 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 18.25/18.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 18.25/18.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 18.25/18.37 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.37 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmult2__lemma__aux2,axiom,
% 18.25/18.37 ! [V_q,V_r,V_b,V_c] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.37 => 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))) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evaln__elim__cases_I5_J,axiom,
% 18.25/18.37 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 18.25/18.37 ( 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)
% 18.25/18.37 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
% 18.25/18.37 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evaln_OIfTrue,axiom,
% 18.25/18.37 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 18.25/18.37 ( hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
% 18.25/18.37 => 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) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evaln_OIfFalse,axiom,
% 18.25/18.37 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 18.25/18.37 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
% 18.25/18.37 => 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) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evalc_OIfFalse,axiom,
% 18.25/18.37 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 18.25/18.37 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 18.25/18.37 => 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)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evalc_OIfTrue,axiom,
% 18.25/18.37 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 18.25/18.37 ( hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 18.25/18.37 => 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)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evalc__elim__cases_I5_J,axiom,
% 18.25/18.37 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 18.25/18.37 ( 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))
% 18.25/18.37 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 18.25/18.37 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.37 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evaln_OSemi,axiom,
% 18.25/18.37 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 18.25/18.37 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
% 18.25/18.37 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
% 18.25/18.37 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evalc_OSemi,axiom,
% 18.25/18.37 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 18.25/18.37 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 18.25/18.37 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 18.25/18.37 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_WTs__elim__cases_I5_J,axiom,
% 18.25/18.37 ! [V_c2_2,V_c1_2,V_b_2] :
% 18.25/18.37 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 18.25/18.37 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 18.25/18.37 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_WTs__elim__cases_I3_J,axiom,
% 18.25/18.37 ! [V_c_2,V_a_2,V_Y_2] :
% 18.25/18.37 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
% 18.25/18.37 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_WTs__elim__cases_I4_J,axiom,
% 18.25/18.37 ! [V_c2,V_c1] :
% 18.25/18.37 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 18.25/18.37 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 18.25/18.37 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__mod__trivial,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I44_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I35_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I45_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I34_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I37_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I36_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I3_J,axiom,
% 18.25/18.37 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 18.25/18.37 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 18.25/18.37 <=> ( V_com1_2 = V_com1_H_2
% 18.25/18.37 & V_com2_2 = V_com2_H_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I4_J,axiom,
% 18.25/18.37 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 18.25/18.37 ( 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)
% 18.25/18.37 <=> ( V_fun_2 = V_fun_H_2
% 18.25/18.37 & V_com1_2 = V_com1_H_2
% 18.25/18.37 & V_com2_2 = V_com2_H_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I2_J,axiom,
% 18.25/18.37 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 18.25/18.37 ( 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)
% 18.25/18.37 <=> ( V_loc_2 = V_loc_H_2
% 18.25/18.37 & V_fun_2 = V_fun_H_2
% 18.25/18.37 & V_com_2 = V_com_H_2 ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__0,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__by__0,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__self,axiom,
% 18.25/18.37 ! [V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__add__cong,axiom,
% 18.25/18.37 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 18.25/18.37 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 18.25/18.37 => 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) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__simps_I1_J,axiom,
% 18.25/18.37 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__simps_I2_J,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__add__eq,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__add__left__eq,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__add__right__eq,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__add__self1,axiom,
% 18.25/18.37 ! [V_a,V_b,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__add__self2,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__mult__right__eq,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__mult__left__eq,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__mult__eq,axiom,
% 18.25/18.37 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__mult__mult1,axiom,
% 18.25/18.37 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__mult__mult2,axiom,
% 18.25/18.37 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__simps_I4_J,axiom,
% 18.25/18.37 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__mult__cong,axiom,
% 18.25/18.37 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.37 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 18.25/18.37 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 18.25/18.37 => 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) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__minus__eq,axiom,
% 18.25/18.37 ! [V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Oring__div(T_a)
% 18.25/18.37 => 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) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_mod__minus__cong,axiom,
% 18.25/18.37 ! [V_a_H,V_b,V_a,T_a] :
% 18.25/18.37 ( class_Divides_Oring__div(T_a)
% 18.25/18.37 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 18.25/18.37 => 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) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__zero,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__self,axiom,
% 18.25/18.37 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__zmult1__eq,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__simps_I3_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zminus__zmod,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__zminus__zminus,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_zmod__zminus2,axiom,
% 18.25/18.37 ! [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)) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_WT_Oequations_I3_J,axiom,
% 18.25/18.37 ! [V_a1_2,V_a3_2,V_a2_2] :
% 18.25/18.37 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 18.25/18.37 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_WT_OLocal,axiom,
% 18.25/18.37 ! [V_a_2,V_Y_2,V_c_2] :
% 18.25/18.37 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 18.25/18.37 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evaln_Oequations_I6_J,axiom,
% 18.25/18.37 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 18.25/18.37 ( 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)
% 18.25/18.37 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.37 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) )
% 18.25/18.37 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.37 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evaln_Oequations_I5_J,axiom,
% 18.25/18.37 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 18.25/18.37 ( 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)
% 18.25/18.37 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.37 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) )
% 18.25/18.37 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.37 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I41_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_com_Osimps_I40_J,axiom,
% 18.25/18.37 ! [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) ).
% 18.25/18.37
% 18.25/18.37 fof(fact_evalc_Oequations_I5_J,axiom,
% 18.25/18.37 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 18.25/18.37 ( 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))
% 18.25/18.37 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.37 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 18.25/18.37 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evalc_Oequations_I6_J,axiom,
% 18.25/18.38 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 18.25/18.38 ( 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))
% 18.25/18.38 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 18.25/18.38 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_WT_Oequations_I5_J,axiom,
% 18.25/18.38 ! [V_a2_2,V_a1_2,V_a3_2] :
% 18.25/18.38 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 18.25/18.38 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 18.25/18.38 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_WT_OIf,axiom,
% 18.25/18.38 ! [V_b_2,V_c1_2,V_c0_2] :
% 18.25/18.38 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 18.25/18.38 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 18.25/18.38 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I55_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I54_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evaln_Oequations_I4_J,axiom,
% 18.25/18.38 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 18.25/18.38 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
% 18.25/18.38 <=> ? [B_s1] :
% 18.25/18.38 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1)
% 18.25/18.38 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I22_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I23_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I43_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I42_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evalc_Oequations_I4_J,axiom,
% 18.25/18.38 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 18.25/18.38 <=> ? [B_s1] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I10_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I11_J,axiom,
% 18.25/18.38 ! [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 ).
% 18.25/18.38
% 18.25/18.38 fof(fact_WT_Oequations_I4_J,axiom,
% 18.25/18.38 ! [V_a2_2,V_a1_2] :
% 18.25/18.38 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 18.25/18.38 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 18.25/18.38 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_WT_OSemi,axiom,
% 18.25/18.38 ! [V_c1,V_c0] :
% 18.25/18.38 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 18.25/18.38 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 18.25/18.38 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I26_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I27_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I49_J,axiom,
% 18.25/18.38 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I48_J,axiom,
% 18.25/18.38 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I57_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I56_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I14_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I15_J,axiom,
% 18.25/18.38 ! [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 ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I24_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I25_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I50_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I51_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I12_J,axiom,
% 18.25/18.38 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I13_J,axiom,
% 18.25/18.38 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__self2__is__0,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__self1__is__0,axiom,
% 18.25/18.38 ! [V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__self1,axiom,
% 18.25/18.38 ! [V_b,V_c,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__self2,axiom,
% 18.25/18.38 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__by__1,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__le__nonneg__dividend,axiom,
% 18.25/18.38 ! [V_k,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 18.25/18.38 ! [V_y,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_neg__mod__bound,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_pos__mod__bound,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__eq__0__iff,axiom,
% 18.25/18.38 ! [V_d_2,V_m_2] :
% 18.25/18.38 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zminus2__not__zero,axiom,
% 18.25/18.38 ! [V_l,V_k] :
% 18.25/18.38 ( 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)
% 18.25/18.38 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zminus1__not__zero,axiom,
% 18.25/18.38 ! [V_l,V_k] :
% 18.25/18.38 ( 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)
% 18.25/18.38 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__neg__neg__trivial,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 18.25/18.38 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_neg__mod__conj,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 & 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_neg__mod__sign,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__pos__pos__trivial,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 18.25/18.38 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_pos__mod__conj,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 & 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_pos__mod__sign,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__pos__neg__trivial,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__zmod,axiom,
% 18.25/18.38 ! [V_k_2,V_n_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 18.25/18.38 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 18.25/18.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 18.25/18.38 => ! [B_i,B_j] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 18.25/18.38 & 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) )
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 18.25/18.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ! [B_i,B_j] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 & 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) )
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmult2__lemma__aux3,axiom,
% 18.25/18.38 ! [V_q,V_b,V_r,V_c] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmult2__lemma__aux4,axiom,
% 18.25/18.38 ! [V_q,V_b,V_r,V_c] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmult2__lemma__aux1,axiom,
% 18.25/18.38 ! [V_q,V_r,V_b,V_c] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_z3mod__def,axiom,
% 18.25/18.38 ! [V_k,V_l] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 18.25/18.38 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__pos__lemma,axiom,
% 18.25/18.38 ! [V_n_2,V_Pa_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 18.25/18.38 <=> ! [B_i,B_j] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 18.25/18.38 & 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) )
% 18.25/18.38 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__neg__lemma,axiom,
% 18.25/18.38 ! [V_n_2,V_Pa_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 18.25/18.38 <=> ! [B_i,B_j] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 & 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) )
% 18.25/18.38 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zmult2__eq,axiom,
% 18.25/18.38 ! [V_b,V_a,V_c] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__zdiv,axiom,
% 18.25/18.38 ! [V_k_2,V_n_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 18.25/18.38 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 18.25/18.38 => ! [B_i] :
% 18.25/18.38 ( ? [B_j] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 18.25/18.38 & 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) )
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 18.25/18.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ! [B_i] :
% 18.25/18.38 ( ? [B_j] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 & 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) )
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_divmod__int__rel__div__eq,axiom,
% 18.25/18.38 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 18.25/18.38 ( 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)
% 18.25/18.38 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 18.25/18.38 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osize_I14_J,axiom,
% 18.25/18.38 ! [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))) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osize_I6_J,axiom,
% 18.25/18.38 ! [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))) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evaln_OWhileFalse,axiom,
% 18.25/18.38 ! [V_n_2,V_c_2,V_s_2,V_b_2] :
% 18.25/18.38 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.38 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evaln_OWhileTrue,axiom,
% 18.25/18.38 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 18.25/18.38 => ( c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2)
% 18.25/18.38 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2)
% 18.25/18.38 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evalc_OWhileTrue,axiom,
% 18.25/18.38 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evalc_OWhileFalse,axiom,
% 18.25/18.38 ! [V_c_2,V_s_2,V_b_2] :
% 18.25/18.38 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_WTs__elim__cases_I6_J,axiom,
% 18.25/18.38 ! [V_c_2,V_b_2] :
% 18.25/18.38 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
% 18.25/18.38 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I5_J,axiom,
% 18.25/18.38 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 18.25/18.38 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 18.25/18.38 <=> ( V_fun_2 = V_fun_H_2
% 18.25/18.38 & V_com_2 = V_com_H_2 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zero,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__less,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__less__eq__dividend,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__distrib2,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__distrib,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zminus__zminus,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zminus2,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__by__0,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__0,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__by__1,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evaln_Oequations_I7_J,axiom,
% 18.25/18.38 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 18.25/18.38 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
% 18.25/18.38 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.38 => ? [B_s1] :
% 18.25/18.38 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 18.25/18.38 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evaln_Oequations_I8_J,axiom,
% 18.25/18.38 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 18.25/18.38 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
% 18.25/18.38 <=> ( ( V_a6_2 = V_a2_2
% 18.25/18.38 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 18.25/18.38 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.38 & ? [B_s1] :
% 18.25/18.38 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 18.25/18.38 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evalc_Oequations_I8_J,axiom,
% 18.25/18.38 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 18.25/18.38 <=> ( ( V_a5_2 = V_a2_2
% 18.25/18.38 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 18.25/18.38 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.38 & ? [B_s1] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_evalc_Oequations_I7_J,axiom,
% 18.25/18.38 ! [V_a2_2,V_a3_2,V_a1_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 18.25/18.38 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 18.25/18.38 => ? [B_s1] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_While,axiom,
% 18.25/18.38 ! [V_b_2,V_c_2] :
% 18.25/18.38 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 18.25/18.38 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_WT_Oequations_I6_J,axiom,
% 18.25/18.38 ! [V_a1_2,V_a2_2] :
% 18.25/18.38 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 18.25/18.38 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I58_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I59_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I52_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I53_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I29_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I28_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I61_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I60_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I38_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I39_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I47_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I46_J,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I17_J,axiom,
% 18.25/18.38 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 18.25/18.38
% 18.25/18.38 fof(fact_com_Osimps_I16_J,axiom,
% 18.25/18.38 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__1,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__Suc,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 18.25/18.38 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.25/18.38 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 18.25/18.38 ! [V_y,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__less__divisor,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 18.25/18.38 ! [V_a_2,V_b_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 18.25/18.38 ! [V_a_2,V_b_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__neg__pos__less0,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__self,axiom,
% 18.25/18.38 ! [V_a] :
% 18.25/18.38 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__eq__0__iff,axiom,
% 18.25/18.38 ! [V_d_2,V_m_2] :
% 18.25/18.38 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_DIVISION__BY__ZERO,axiom,
% 18.25/18.38 ! [V_a] :
% 18.25/18.38 ( 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)
% 18.25/18.38 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zdiv__trivial,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__self3,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zadd1__eq,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__int,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__mult1,axiom,
% 18.25/18.38 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__mult2,axiom,
% 18.25/18.38 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__self1__is__id,axiom,
% 18.25/18.38 ! [V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__self2__is__id,axiom,
% 18.25/18.38 ! [V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__mult1__if,axiom,
% 18.25/18.38 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__self,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__div__trivial,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__eq__0__iff,axiom,
% 18.25/18.38 ! [V_k_2,V_i_2] :
% 18.25/18.38 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 18.25/18.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 18.25/18.38 ! [V_a_2,V_b_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 18.25/18.38 ! [V_i_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__mono2,axiom,
% 18.25/18.38 ! [V_b,V_b_H,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__nonneg__neg__le0,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__pos__pos__trivial,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 18.25/18.38 ! [V_a_2,V_b_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__nonpos__pos__le0,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__mono2__neg,axiom,
% 18.25/18.38 ! [V_b,V_b_H,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__neg__neg__trivial,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__mono1,axiom,
% 18.25/18.38 ! [V_b,V_a_H,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__mono1__neg,axiom,
% 18.25/18.38 ! [V_b,V_a_H,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__le__divisor,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_int__div__less__self,axiom,
% 18.25/18.38 ! [V_k,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zmult2__eq,axiom,
% 18.25/18.38 ! [V_b,V_a,V_c] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult__self4,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zmod__equality2,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zmod__equality,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zmult1__eq,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zdiv__equality,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__self1,axiom,
% 18.25/18.38 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__self2,axiom,
% 18.25/18.38 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__add__self1,axiom,
% 18.25/18.38 ! [V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__add__self2,axiom,
% 18.25/18.38 ! [V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__div__equality2,axiom,
% 18.25/18.38 ! [V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__div__equality,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mod__equality2,axiom,
% 18.25/18.38 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mod__equality,axiom,
% 18.25/18.38 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__lemma,axiom,
% 18.25/18.38 ! [V_q,V_b,V_r,V_c] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__mod,axiom,
% 18.25/18.38 ! [V_k_2,V_n_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 18.25/18.38 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 18.25/18.38 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => ! [B_i,B_j] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 18.25/18.38 => ( 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)
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Suc__times__mod__eq,axiom,
% 18.25/18.38 ! [V_m,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 18.25/18.38 ! [V_y,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__mod__distrib,axiom,
% 18.25/18.38 ! [V_y,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_z3div__def,axiom,
% 18.25/18.38 ! [V_k,V_l] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 18.25/18.38 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zminus1__eq__if,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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)) )
% 18.25/18.38 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__zminus2__eq__if,axiom,
% 18.25/18.38 ! [V_a,V_b] :
% 18.25/18.38 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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)) )
% 18.25/18.38 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__div__decomp,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Osemiring__div(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__div_H,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 18.25/18.38 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 18.25/18.38 | ? [B_q] :
% 18.25/18.38 ( 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))
% 18.25/18.38 & 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))))
% 18.25/18.38 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__div__lemma,axiom,
% 18.25/18.38 ! [V_m_2,V_q_2,V_n_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 18.25/18.38 => ( ( 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))
% 18.25/18.38 & 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)))) )
% 18.25/18.38 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 18.25/18.38 ! [V_y,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_incr__mult__lemma,axiom,
% 18.25/18.38 ! [V_k_2,V_Pa_2,V_d_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 18.25/18.38 => ( ! [B_x] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 18.25/18.38 => ! [B_x] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Divides_Omod__div__equality_H,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mult__div__cancel,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mod__equality_H,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_minus__apply,axiom,
% 18.25/18.38 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 18.25/18.38 ( class_Groups_Ominus(T_b)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_of__int__diff,axiom,
% 18.25/18.38 ! [V_z,V_w,T_a] :
% 18.25/18.38 ( class_Rings_Oring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__commute,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__eq__diff__eq,axiom,
% 18.25/18.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oab__group__add(T_b)
% 18.25/18.38 => ( 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)
% 18.25/18.38 => ( V_a_2 = V_b_2
% 18.25/18.38 <=> V_c_2 = V_d_2 ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_of__nat__diff,axiom,
% 18.25/18.38 ! [V_m,V_n,T_a] :
% 18.25/18.38 ( class_Rings_Oring__1(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiff__int,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__eq__diff__less__eq,axiom,
% 18.25/18.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.38 => ( 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)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_right__minus__eq,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_b)
% 18.25/18.38 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.38 <=> V_a_2 = V_b_2 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_eq__iff__diff__eq__0,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oab__group__add(T_b)
% 18.25/18.38 => ( V_a_2 = V_b_2
% 18.25/18.38 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__self,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__0__right,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__eq__diff__less,axiom,
% 18.25/18.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.38 => ( 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)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__add__cancel,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__diff__cancel,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_minus__diff__eq,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oab__group__add(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__add1__eq,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__diff__right__eq,axiom,
% 18.25/18.38 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Oring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__diff__left__eq,axiom,
% 18.25/18.38 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Oring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__diff__eq,axiom,
% 18.25/18.38 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Oring__div(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__diff__cong,axiom,
% 18.25/18.38 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 18.25/18.38 ( class_Divides_Oring__div(T_a)
% 18.25/18.38 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 18.25/18.38 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 18.25/18.38 => 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) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__le__mono,axiom,
% 18.25/18.38 ! [V_k,V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__le__dividend,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult2__eq,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diffs0__imp__equal,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => V_m = V_n ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__self__eq__0,axiom,
% 18.25/18.38 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_minus__nat_Odiff__0,axiom,
% 18.25/18.38 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__0__eq__0,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__Suc__Suc,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Suc__diff__diff,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__imp__diff__less,axiom,
% 18.25/18.38 ! [V_n,V_k,V_j] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__less__mono2,axiom,
% 18.25/18.38 ! [V_l,V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__geq,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__if,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__add__inverse2,axiom,
% 18.25/18.38 ! [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 ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__add__inverse,axiom,
% 18.25/18.38 ! [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 ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__diff__left,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__cancel,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__cancel2,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__diff__iff,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Nat_Odiff__diff__eq,axiom,
% 18.25/18.38 ! [V_n,V_m,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_eq__diff__iff,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 18.25/18.38 => ( 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)
% 18.25/18.38 <=> V_m_2 = V_n_2 ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__diff__cancel,axiom,
% 18.25/18.38 ! [V_n,V_i] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__le__mono,axiom,
% 18.25/18.38 ! [V_l,V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__le__mono2,axiom,
% 18.25/18.38 ! [V_l,V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__le__self,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__mod__geq,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiff__zmult__distrib2,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiff__zmult__distrib,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__mult__distrib,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__mult__distrib2,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiff__zmod__right,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiff__zmod__left,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__geq,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__if,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__diff__distrib,axiom,
% 18.25/18.38 ! [V_z,V_z_H] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiff__int__split,axiom,
% 18.25/18.38 ! [V_y_2,V_x_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 18.25/18.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 18.25/18.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__div__geq,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__iff__diff__le__0,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 18.25/18.38 <=> 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__iff__diff__less__0,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 18.25/18.38 <=> 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_eq__add__iff1,axiom,
% 18.25/18.38 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oring(T_b)
% 18.25/18.38 => ( 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)
% 18.25/18.38 <=> 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 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_eq__add__iff2,axiom,
% 18.25/18.38 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oring(T_b)
% 18.25/18.38 => ( 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)
% 18.25/18.38 <=> 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__0,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__minus__eq__add,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_ab__diff__minus,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oab__group__add(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__def,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ogroup__add(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 18.25/18.38 ! [V_y,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__ring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__1,axiom,
% 18.25/18.38 ! [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 ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__less,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__mult__div__cancel__disj,axiom,
% 18.25/18.38 ! [V_n,V_m,V_k] :
% 18.25/18.38 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult1__eq,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__mult2__eq,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__bin__lemma,axiom,
% 18.25/18.38 ! [V_l_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 18.25/18.38 <=> 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__less,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zero__less__diff,axiom,
% 18.25/18.38 ! [V_m_2,V_n_2] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zdiv__int,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__less__Suc,axiom,
% 18.25/18.38 ! [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))) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__add__0,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__is__0__eq_H,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__is__0__eq,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2] :
% 18.25/18.38 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__diff__conv,axiom,
% 18.25/18.38 ! [V_k_2,V_j_2,V_i_2] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__diff__inverse,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Suc__diff__le,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__less__mono,axiom,
% 18.25/18.38 ! [V_c,V_b,V_a] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__diff__iff,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__add__assoc2,axiom,
% 18.25/18.38 ! [V_i,V_j,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__diff__assoc2,axiom,
% 18.25/18.38 ! [V_i,V_j,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__add__assoc,axiom,
% 18.25/18.38 ! [V_i,V_j,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__imp__diff__is__add,axiom,
% 18.25/18.38 ! [V_k_2,V_j_2,V_i_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 18.25/18.38 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 18.25/18.38 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__add__diff__inverse2,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__diff__conv2,axiom,
% 18.25/18.38 ! [V_i_2,V_j_2,V_k_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__diff__assoc,axiom,
% 18.25/18.38 ! [V_i,V_j,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__add__diff__inverse,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__add__diff,axiom,
% 18.25/18.38 ! [V_m,V_n,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__diff__conv,axiom,
% 18.25/18.38 ! [V_i_2,V_k_2,V_j_2] :
% 18.25/18.38 ( 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))
% 18.25/18.38 <=> 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__diff__right,axiom,
% 18.25/18.38 ! [V_i,V_j,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Ints__diff,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oring__1(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__int__def__symmetric,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__int__def,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__Suc__1,axiom,
% 18.25/18.38 ! [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 ).
% 18.25/18.38
% 18.25/18.38 fof(fact_tsub__eq,axiom,
% 18.25/18.38 ! [V_x,V_y] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 18.25/18.38 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__add__iff2,axiom,
% 18.25/18.38 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oordered__ring(T_b)
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__add__iff1,axiom,
% 18.25/18.38 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oordered__ring(T_b)
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__add__iff2,axiom,
% 18.25/18.38 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oordered__ring(T_b)
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__add__iff1,axiom,
% 18.25/18.38 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oordered__ring(T_b)
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__le__mono2,axiom,
% 18.25/18.38 ! [V_k,V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__mult__div__cancel1,axiom,
% 18.25/18.38 ! [V_n,V_m,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__self1__is__m,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__mult__self__is__m,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__less__dividend,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__Suc__less,axiom,
% 18.25/18.38 ! [V_i,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Suc__pred,axiom,
% 18.25/18.38 ! [V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__diff__split,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 18.25/18.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 18.25/18.38 & ! [B_d] :
% 18.25/18.38 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__diff__split__asm,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 18.25/18.38 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 18.25/18.38 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 18.25/18.38 | ? [B_d] :
% 18.25/18.38 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 18.25/18.38 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zle__diff1__eq,axiom,
% 18.25/18.38 ! [V_z_2,V_w_2] :
% 18.25/18.38 ( 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))))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__Suc__diff__eq2,axiom,
% 18.25/18.38 ! [V_m,V_j,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__Suc__diff__eq1,axiom,
% 18.25/18.38 ! [V_m,V_j,V_k] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__eq__add__iff2,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 18.25/18.38 => ( 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)
% 18.25/18.38 <=> 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__diff__add__eq2,axiom,
% 18.25/18.38 ! [V_n,V_m,V_u,V_j,V_i] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__le__add__iff2,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__eq__add__iff1,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 18.25/18.38 => ( 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)
% 18.25/18.38 <=> 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 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__diff__add__eq1,axiom,
% 18.25/18.38 ! [V_n,V_m,V_u,V_i,V_j] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__le__add__iff1,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zminus2__eq__if,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zminus1__eq__if,axiom,
% 18.25/18.38 ! [V_b,V_a] :
% 18.25/18.38 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmod__zdiv__equality_H,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zmult__div__cancel,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_tsub__def,axiom,
% 18.25/18.38 ! [V_x,V_y] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 18.25/18.38 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 18.25/18.38 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_split__div,axiom,
% 18.25/18.38 ! [V_k_2,V_n_2,V_Pa_2] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 18.25/18.38 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 18.25/18.38 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => ! [B_i,B_j] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 18.25/18.38 => ( 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)
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__div__distrib,axiom,
% 18.25/18.38 ! [V_y,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 18.25/18.38 ! [V_y,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Suc__diff__1,axiom,
% 18.25/18.38 ! [V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Suc__pred_H,axiom,
% 18.25/18.38 ! [V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__less__add__iff2,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__less__add__iff1,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__eq__if,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 18.25/18.38 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mult__eq__if,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.25/18.38 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_int__power__div__base,axiom,
% 18.25/18.38 ! [V_k,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 18.25/18.38 => 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)))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_decr__mult__lemma,axiom,
% 18.25/18.38 ! [V_k_2,V_Pa_2,V_d_2] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 18.25/18.38 => ( ! [B_x] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 18.25/18.38 => ! [B_x] :
% 18.25/18.38 ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_incr__lemma,axiom,
% 18.25/18.38 ! [V_x,V_z,V_d] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 18.25/18.38 => 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)))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_decr__lemma,axiom,
% 18.25/18.38 ! [V_z,V_x,V_d] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__mod__eq__lemma,axiom,
% 18.25/18.38 ! [V_y,V_n,V_x] :
% 18.25/18.38 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 18.25/18.38 => ? [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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__induct__0,axiom,
% 18.25/18.38 ! [V_i_2,V_Pa_2,V_p_2] :
% 18.25/18.38 ( ! [B_i] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 18.25/18.38 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 18.25/18.38 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 18.25/18.38 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_expand__Suc,axiom,
% 18.25/18.38 ! [V_v] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_divmod__nat__step,axiom,
% 18.25/18.38 ! [V_m,V_n] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_DiffE,axiom,
% 18.25/18.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_DiffI,axiom,
% 18.25/18.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_of__int__power,axiom,
% 18.25/18.38 ! [V_n,V_z,T_a] :
% 18.25/18.38 ( class_Rings_Oring__1(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_of__int__number__of__eq,axiom,
% 18.25/18.38 ! [V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__idempotent,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_eq__number__of,axiom,
% 18.25/18.38 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.38 & class_Int_Oring__char__0(T_b) )
% 18.25/18.38 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 18.25/18.38 <=> V_x_2 = V_y_2 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_number__of__reorient,axiom,
% 18.25/18.38 ! [V_x_2,V_w_2,T_b] :
% 18.25/18.38 ( class_Int_Onumber(T_b)
% 18.25/18.38 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 18.25/18.38 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_divmod__nat__zero,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zero__le__zpower__abs,axiom,
% 18.25/18.38 ! [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))) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_of__nat__number__of__eq,axiom,
% 18.25/18.38 ! [V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__le__D1,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__ge__self,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__zero,axiom,
% 18.25/18.38 ! [T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__eq__0,axiom,
% 18.25/18.38 ! [V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.25/18.38 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__add__abs,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__mult__self,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__mult,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__minus__commute,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__one,axiom,
% 18.25/18.38 ! [T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__minus__cancel,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 18.25/18.38 ! [V_q,V_y,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__of__nat,axiom,
% 18.25/18.38 ! [V_n,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_DiffD2,axiom,
% 18.25/18.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_DiffD1,axiom,
% 18.25/18.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Diff__iff,axiom,
% 18.25/18.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.25/18.38 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__int__eq,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 18.25/18.38 ! [V_q,V_p,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_double__diff,axiom,
% 18.25/18.38 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.25/18.38 => 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 ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Diff__mono,axiom,
% 18.25/18.38 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Diff__subset,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zpower__zpower,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 18.25/18.38 ! [V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zpower__zmod,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_of__nat__number__of__lemma,axiom,
% 18.25/18.38 ! [V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => ( ( 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)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ 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)))
% 18.25/18.38 => 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) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_number__of__eq,axiom,
% 18.25/18.38 ! [V_k,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_divmod__nat__base,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__number__of,axiom,
% 18.25/18.38 ! [V_x,T_a] :
% 18.25/18.38 ( ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 & class_Rings_Olinordered__idom(T_a) )
% 18.25/18.38 => ( ( 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)))
% 18.25/18.38 => 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)) )
% 18.25/18.38 & ( ~ 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)))
% 18.25/18.38 => 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) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zero__less__zpower__abs__iff,axiom,
% 18.25/18.38 ! [V_n_2,V_x_2] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.38 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_divmod__nat__div__mod,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__ge__zero,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__le__zero__iff,axiom,
% 18.25/18.38 ! [V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__of__nonneg,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__of__pos,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zero__less__abs__iff,axiom,
% 18.25/18.38 ! [V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__not__less__zero,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ~ 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__triangle__ineq,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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)))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__mult__less,axiom,
% 18.25/18.38 ! [V_d,V_b,V_c,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__triangle__ineq3,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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)))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__triangle__ineq2,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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)))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__triangle__ineq2__sym,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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)))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__le__D2,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__leI,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__le__iff,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.25/18.38 => ( 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))
% 18.25/18.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 18.25/18.38 & 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)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__ge__minus__self,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__less__iff,axiom,
% 18.25/18.38 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 18.25/18.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 18.25/18.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__number__of__eq__not__less,axiom,
% 18.25/18.38 ! [V_w_2,V_v_2,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber(T_b)
% 18.25/18.38 & class_Orderings_Olinorder(T_b) )
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> ~ 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_right__distrib__number__of,axiom,
% 18.25/18.38 ! [V_c,V_b,V_v,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber(T_b)
% 18.25/18.38 & class_Rings_Osemiring(T_b) )
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_left__distrib__number__of,axiom,
% 18.25/18.38 ! [V_v,V_b,V_a,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber(T_b)
% 18.25/18.38 & class_Rings_Osemiring(T_b) )
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 18.25/18.38 ! [V_q,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 18.25/18.38 ! [V_q,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 18.25/18.38 ! [V_q,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_right__diff__distrib__number__of,axiom,
% 18.25/18.38 ! [V_c,V_b,V_v,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber(T_b)
% 18.25/18.38 & class_Rings_Oring(T_b) )
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_left__diff__distrib__number__of,axiom,
% 18.25/18.38 ! [V_v,V_b,V_a,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber(T_b)
% 18.25/18.38 & class_Rings_Oring(T_b) )
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_le__number__of,axiom,
% 18.25/18.38 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.38 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 18.25/18.38 ! [V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 18.25/18.38 ! [V_q,V_p,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__number__of,axiom,
% 18.25/18.38 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.38 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.38 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__number__of__left,axiom,
% 18.25/18.38 ! [V_z,V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__number__of__eq,axiom,
% 18.25/18.38 ! [V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_number__of__add,axiom,
% 18.25/18.38 ! [V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 18.25/18.38 ! [V_n,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mult__number__of__left,axiom,
% 18.25/18.38 ! [V_z,V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_arith__simps_I32_J,axiom,
% 18.25/18.38 ! [V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_number__of__mult,axiom,
% 18.25/18.38 ! [V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__zmult__eq__1,axiom,
% 18.25/18.38 ! [V_n,V_m] :
% 18.25/18.38 ( 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)
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_number__of__diff,axiom,
% 18.25/18.38 ! [V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zpower__zadd__distrib,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_number__of__minus,axiom,
% 18.25/18.38 ! [V_w,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_arith__simps_I30_J,axiom,
% 18.25/18.38 ! [V_w,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mult__sgn__abs,axiom,
% 18.25/18.38 ! [V_x,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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 ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__sgn,axiom,
% 18.25/18.38 ! [V_k,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Ints__power,axiom,
% 18.25/18.38 ! [V_n_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Oring__1(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Ints__number__of,axiom,
% 18.25/18.38 ! [V_w_2,T_b] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_b)
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__eq__mult,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Oordered__ring__abs(T_a)
% 18.25/18.38 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 18.25/18.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__mult__pos,axiom,
% 18.25/18.38 ! [V_y,V_x,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__triangle__ineq4,axiom,
% 18.25/18.38 ! [V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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)))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__diff__triangle__ineq,axiom,
% 18.25/18.38 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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))))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__of__nonpos,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__minus__le__zero,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__if,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oabs__if(T_a)
% 18.25/18.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__of__neg,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zabs__less__one__iff,axiom,
% 18.25/18.38 ! [V_z_2] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__number__of__diff1,axiom,
% 18.25/18.38 ! [V_c,V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zabs__def,axiom,
% 18.25/18.38 ! [V_i] :
% 18.25/18.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.38 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_minus__number__of__mult,axiom,
% 18.25/18.38 ! [V_z,V_w,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__abs__mult__distrib,axiom,
% 18.25/18.38 ! [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))) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_diff__number__of__eq,axiom,
% 18.25/18.38 ! [V_w,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_add__number__of__diff2,axiom,
% 18.25/18.38 ! [V_w,V_c,V_v,T_a] :
% 18.25/18.38 ( class_Int_Onumber__ring(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__strict__mono,axiom,
% 18.25/18.38 ! [V_n,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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))) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_one__less__power,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__le__imp__le__exp,axiom,
% 18.25/18.38 ! [V_n,V_m,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__increasing__iff,axiom,
% 18.25/18.38 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__decreasing,axiom,
% 18.25/18.38 ! [V_a,V_N,V_n,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 18.25/18.38 => 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))) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__strict__decreasing,axiom,
% 18.25/18.38 ! [V_a,V_N,V_n,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 18.25/18.38 => 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))) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__Suc__less__one,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Diff__idemp,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_number__of__is__id,axiom,
% 18.25/18.38 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__eq__number__of__int__code,axiom,
% 18.25/18.38 ! [V_l_2,V_k_2] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_less__number__of__int__code,axiom,
% 18.25/18.38 ! [V_l_2,V_k_2] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_plus__numeral__code_I9_J,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_times__numeral__code_I5_J,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_minus__numeral__code_I5_J,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 18.25/18.38 ! [V_m_2,V_x_2] :
% 18.25/18.38 ( 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))
% 18.25/18.38 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__Suc__0,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__power__less__imp__less,axiom,
% 18.25/18.38 ! [V_n,V_m,V_i] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__zero__less__power__iff,axiom,
% 18.25/18.38 ! [V_n_2,V_x_2] :
% 18.25/18.38 ( 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)))
% 18.25/18.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 18.25/18.38 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_int__number__of__def,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__one__le__power,axiom,
% 18.25/18.38 ! [V_n,V_i] :
% 18.25/18.38 ( 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))
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__number__of,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__number__of__def,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zpower__int,axiom,
% 18.25/18.38 ! [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)) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_int__power,axiom,
% 18.25/18.38 ! [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) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__nat__number__of__number__of,axiom,
% 18.25/18.38 ! [V_w,V_v] :
% 18.25/18.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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)) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__nat__number__of,axiom,
% 18.25/18.38 ! [V_n,V_v] :
% 18.25/18.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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)) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_minus__numeral__code_I6_J,axiom,
% 18.25/18.38 ! [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))) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_neg__imp__number__of__eq__0,axiom,
% 18.25/18.38 ! [V_v] :
% 18.25/18.38 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__eq__if,axiom,
% 18.25/18.38 ! [V_p,V_m] :
% 18.25/18.38 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 18.25/18.38 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => 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)))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_int__eq__iff__number__of,axiom,
% 18.25/18.38 ! [V_v_2,V_m_2] :
% 18.25/18.38 ( 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)
% 18.25/18.38 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 18.25/18.38 & 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__power__eq,axiom,
% 18.25/18.38 ! [V_n,V_z] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 18.25/18.38 ! [V_n,V_x] :
% 18.25/18.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_eq__nat__number__of,axiom,
% 18.25/18.38 ! [V_v_H_2,V_v_2] :
% 18.25/18.38 ( 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)
% 18.25/18.38 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 18.25/18.38 => 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))) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 18.25/18.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 18.25/18.38 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 18.25/18.38 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_nat__number__of__add__left,axiom,
% 18.25/18.38 ! [V_k,V_v_H,V_v] :
% 18.25/18.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 18.25/18.38 => 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) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_int__nat__number__of,axiom,
% 18.25/18.38 ! [V_v] :
% 18.25/18.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_mod__nat__number__of,axiom,
% 18.25/18.38 ! [V_v_H,V_v] :
% 18.25/18.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 18.25/18.38 => 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))) ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_div__nat__number__of,axiom,
% 18.25/18.38 ! [V_v_H,V_v] :
% 18.25/18.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_field__power__not__zero,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 18.25/18.38 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__commutes,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__mult__distrib,axiom,
% 18.25/18.38 ! [V_n,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Ocomm__monoid__mult(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__one,axiom,
% 18.25/18.38 ! [V_n,T_a] :
% 18.25/18.38 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_of__nat__power,axiom,
% 18.25/18.38 ! [V_n,V_m,T_a] :
% 18.25/18.38 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__mult,axiom,
% 18.25/18.38 ! [V_n,V_m,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_one__div__nat__number__of,axiom,
% 18.25/18.38 ! [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))) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__abs,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__one__right,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_one__mod__nat__number__of,axiom,
% 18.25/18.38 ! [V_v_H] :
% 18.25/18.38 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 18.25/18.38 => 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)) )
% 18.25/18.38 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zero__le__power,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__mono,axiom,
% 18.25/18.38 ! [V_n,V_b,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zero__less__power,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__eq__0__iff,axiom,
% 18.25/18.38 ! [V_n_2,V_a_2,T_b] :
% 18.25/18.38 ( ( class_Power_Opower(T_b)
% 18.25/18.38 & class_Rings_Omult__zero(T_b)
% 18.25/18.38 & class_Rings_Ono__zero__divisors(T_b)
% 18.25/18.38 & class_Rings_Ozero__neq__one(T_b) )
% 18.25/18.38 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.38 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.38 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_one__le__power,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => 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))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__0__Suc,axiom,
% 18.25/18.38 ! [V_n,T_a] :
% 18.25/18.38 ( ( class_Power_Opower(T_a)
% 18.25/18.38 & class_Rings_Osemiring__0(T_a) )
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__inject__exp,axiom,
% 18.25/18.38 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 18.25/18.38 => ( 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)
% 18.25/18.38 <=> V_m_2 = V_n_2 ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__Suc2,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__Suc,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Power_Opower(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__0,axiom,
% 18.25/18.38 ! [V_a,T_a] :
% 18.25/18.38 ( class_Power_Opower(T_a)
% 18.25/18.38 => 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) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__add,axiom,
% 18.25/18.38 ! [V_n,V_m,V_a,T_a] :
% 18.25/18.38 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_abs__power__minus,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__less__imp__less__base,axiom,
% 18.25/18.38 ! [V_b,V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( 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)))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__inject__base,axiom,
% 18.25/18.38 ! [V_b,V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( 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))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.38 => V_a = V_b ) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__le__imp__le__base,axiom,
% 18.25/18.38 ! [V_b,V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( 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))))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__gt1__lemma,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => 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)))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__less__power__Suc,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => 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)))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__0__left,axiom,
% 18.25/18.38 ! [V_n,T_a] :
% 18.25/18.38 ( ( class_Power_Opower(T_a)
% 18.25/18.38 & class_Rings_Osemiring__0(T_a) )
% 18.25/18.38 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => 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) )
% 18.25/18.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.38 => 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) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__gt1,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => 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)))) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__strict__increasing,axiom,
% 18.25/18.38 ! [V_a,V_N,V_n,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__less__imp__less__exp,axiom,
% 18.25/18.38 ! [V_n,V_m,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__strict__increasing__iff,axiom,
% 18.25/18.38 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_b)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 18.25/18.38 => ( 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)))
% 18.25/18.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_zero__le__power__abs,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.38 => 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))) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__increasing,axiom,
% 18.25/18.38 ! [V_a,V_N,V_n,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__minus,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Oring__1(T_a)
% 18.25/18.38 => 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)) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__Suc__less,axiom,
% 18.25/18.38 ! [V_n,V_a,T_a] :
% 18.25/18.38 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 18.25/18.38 => 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))) ) ) ) ).
% 18.25/18.38
% 18.25/18.38 fof(fact_power__eq__imp__eq__base,axiom,
% 18.25/18.39 ! [V_b,V_n,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.39 => ( 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)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.39 => V_a = V_b ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_in__rel__def,axiom,
% 18.25/18.39 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 18.25/18.39 ! [V_a,V_r,V_q,V_c,V_b] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 18.25/18.39 => 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 18.25/18.39 ! [V_c,V_r,V_q,V_b,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__nat__number__of__add,axiom,
% 18.25/18.39 ! [V_n,V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 18.25/18.39 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__nat__number__of,axiom,
% 18.25/18.39 ! [V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.39 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__power__power,axiom,
% 18.25/18.39 ! [T_b] :
% 18.25/18.39 ( class_Power_Opower(T_b)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__rel__unique,axiom,
% 18.25/18.39 ! [V_qr_H,V_qr,V_n,V_m] :
% 18.25/18.39 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 18.25/18.39 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 18.25/18.39 => V_qr = V_qr_H ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__eq,axiom,
% 18.25/18.39 ! [V_qr,V_n,V_m] :
% 18.25/18.39 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 18.25/18.39 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 18.25/18.39 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power_Opower_Opower__0,axiom,
% 18.25/18.39 ! [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 ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power_Opower_Opower__Suc,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__eq,axiom,
% 18.25/18.39 ! [V_r,V_q,V_n,V_m] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_succ__def,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__eq,axiom,
% 18.25/18.39 ! [V_r,V_q,V_n,V_m] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of__succ,axiom,
% 18.25/18.39 ! [V_k,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__rel,axiom,
% 18.25/18.39 ! [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)))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_in__measure,axiom,
% 18.25/18.39 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zmult2__lemma,axiom,
% 18.25/18.39 ! [V_c,V_r,V_q,V_b,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mlex__leq,axiom,
% 18.25/18.39 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 18.25/18.39 => ( 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))
% 18.25/18.39 => 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))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mlex__less,axiom,
% 18.25/18.39 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pdivmod__def,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zmult1__lemma,axiom,
% 18.25/18.39 ! [V_a,V_r,V_q,V_c,V_b] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_in__lex__prod,axiom,
% 18.25/18.39 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> ( 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))
% 18.25/18.39 | ( V_a_2 = V_a_H_2
% 18.25/18.39 & 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__rel__0,axiom,
% 18.25/18.39 ! [V_b] :
% 18.25/18.39 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_self__remainder,axiom,
% 18.25/18.39 ! [V_r,V_q,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_unique__quotient,axiom,
% 18.25/18.39 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => V_q = V_q_H ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_unique__remainder,axiom,
% 18.25/18.39 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => V_r = V_r_H ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_self__quotient,axiom,
% 18.25/18.39 ! [V_r,V_q,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__rel__mod,axiom,
% 18.25/18.39 ! [V_r,V_q,V_b,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__rel__div,axiom,
% 18.25/18.39 ! [V_r,V_q,V_b,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__rel__div__mod,axiom,
% 18.25/18.39 ! [V_a,V_b] :
% 18.25/18.39 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zadd1__lemma,axiom,
% 18.25/18.39 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zminus1__lemma,axiom,
% 18.25/18.39 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__relI,axiom,
% 18.25/18.39 ! [V_r,V_q,V_b,V_a] :
% 18.25/18.39 ( 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)
% 18.25/18.39 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 18.25/18.39 => 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))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_same__fstI,axiom,
% 18.25/18.39 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 18.25/18.39 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg__div__mod,axiom,
% 18.25/18.39 ! [V_l,V_k] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg__div__mod,axiom,
% 18.25/18.39 ! [V_l,V_k] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__mod__div,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pdivmod__posDivAlg,axiom,
% 18.25/18.39 ! [V_k,V_l] :
% 18.25/18.39 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pair__lessI2,axiom,
% 18.25/18.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zmod__minus1,axiom,
% 18.25/18.39 ! [V_b] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I24_J,axiom,
% 18.25/18.39 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I7_J,axiom,
% 18.25/18.39 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_bin__less__0__simps_I2_J,axiom,
% 18.25/18.39 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Int_OMin__def,axiom,
% 18.25/18.39 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__Min,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__number__of__Min,axiom,
% 18.25/18.39 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg__minus1,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I2_J,axiom,
% 18.25/18.39 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__minus1__right,axiom,
% 18.25/18.39 ! [V_z,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__minus1,axiom,
% 18.25/18.39 ! [V_z,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of__Min,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_arith__simps_I31_J,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_abs__minus__one,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_a) )
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg__0,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zmod__minus1__right,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 18.25/18.39 ! [V_n,V_m] :
% 18.25/18.39 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 18.25/18.39 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 18.25/18.39 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zmult__eq__1__iff,axiom,
% 18.25/18.39 ! [V_n_2,V_m_2] :
% 18.25/18.39 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 18.25/18.39 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 18.25/18.39 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 18.25/18.39 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 18.25/18.39 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_of__int__m1,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zdiv__minus1__right,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_abs__power__minus__one,axiom,
% 18.25/18.39 ! [V_n,T_a] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_a) )
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__eq__minus1,axiom,
% 18.25/18.39 ! [V_b] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pair__lessI1,axiom,
% 18.25/18.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg__correct,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__correct,axiom,
% 18.25/18.39 ! [V_a,V_b] :
% 18.25/18.39 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg__correct,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__pos__neg__trivial,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__def,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.39 => 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))) ) ) ) ) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => 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))) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pair__leqI2,axiom,
% 18.25/18.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pair__leqI1,axiom,
% 18.25/18.39 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_intrel__iff,axiom,
% 18.25/18.39 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 18.25/18.39 ( 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))
% 18.25/18.39 <=> 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__pos__pos__1__number__of,axiom,
% 18.25/18.39 ! [V_w] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__pos__pos__1__number__of,axiom,
% 18.25/18.39 ! [V_w] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__int__def,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__int__def,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__pos__neg,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__pos__neg,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__neg__neg,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negateSnd__eq,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__neg__neg,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__int__rel__neg,axiom,
% 18.25/18.39 ! [V_qr,V_b,V_a] :
% 18.25/18.39 ( 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))
% 18.25/18.39 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__neg__pos,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__pos__neg__1__number__of,axiom,
% 18.25/18.39 ! [V_w] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__neg__pos,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__pos__neg__1__number__of,axiom,
% 18.25/18.39 ! [V_w] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__pos__pos,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__pos__pos,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_prod__size__simp,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_exI__realizer,axiom,
% 18.25/18.39 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 18.25/18.39 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_conjI__realizer,axiom,
% 18.25/18.39 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
% 18.25/18.39 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 18.25/18.39 => ( hBOOL(hAPP(V_Qa_2,V_q_2))
% 18.25/18.39 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 18.25/18.39 & hBOOL(hAPP(V_Qa_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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pair__collapse,axiom,
% 18.25/18.39 ! [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 ).
% 18.25/18.39
% 18.25/18.39 fof(fact_surjective__pairing,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_prod__eqI,axiom,
% 18.25/18.39 ! [V_q,V_p,T_b,T_a] :
% 18.25/18.39 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 18.25/18.39 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 18.25/18.39 => V_p = V_q ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__nat__def,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__nat__def,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divmod__nat__rel__def,axiom,
% 18.25/18.39 ! [V_qr_2,V_n_2,V_m_2] :
% 18.25/18.39 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 18.25/18.39 <=> ( 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))
% 18.25/18.39 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.39 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.25/18.39 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 & 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)) ) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 & 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))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_split__paired__All,axiom,
% 18.25/18.39 ! [T_c,T_b,V_Pa_2] :
% 18.25/18.39 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 18.25/18.39 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Pair__eq,axiom,
% 18.25/18.39 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 18.25/18.39 ( 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)
% 18.25/18.39 <=> ( V_a_2 = V_a_H_2
% 18.25/18.39 & V_b_2 = V_b_H_2 ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Pair__inject,axiom,
% 18.25/18.39 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 18.25/18.39 ( 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)
% 18.25/18.39 => ~ ( V_a = V_a_H
% 18.25/18.39 => V_b != V_b_H ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_fst__conv,axiom,
% 18.25/18.39 ! [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 ).
% 18.25/18.39
% 18.25/18.39 fof(fact_fst__eqD,axiom,
% 18.25/18.39 ! [V_a,V_y,V_x,T_b,T_a] :
% 18.25/18.39 ( 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
% 18.25/18.39 => V_x = V_a ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_snd__conv,axiom,
% 18.25/18.39 ! [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 ).
% 18.25/18.39
% 18.25/18.39 fof(fact_snd__eqD,axiom,
% 18.25/18.39 ! [V_a,V_y,V_x,T_a,T_b] :
% 18.25/18.39 ( 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
% 18.25/18.39 => V_y = V_a ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Pair__fst__snd__eq,axiom,
% 18.25/18.39 ! [T_c,T_b,V_t_2,V_s_2] :
% 18.25/18.39 ( V_s_2 = V_t_2
% 18.25/18.39 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 18.25/18.39 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_prod_Orecs,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_int__val__lemma,axiom,
% 18.25/18.39 ! [V_k_2,V_f_2,V_n_2] :
% 18.25/18.39 ( ! [B_i] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 18.25/18.39 => 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))) )
% 18.25/18.39 => ( 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))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 18.25/18.39 => ? [B_i] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 18.25/18.39 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat0__intermed__int__val,axiom,
% 18.25/18.39 ! [V_k_2,V_f_2,V_n_2] :
% 18.25/18.39 ( ! [B_i] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 18.25/18.39 => 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))) )
% 18.25/18.39 => ( 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))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 18.25/18.39 => ? [B_i] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 18.25/18.39 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__number__of__add__1,axiom,
% 18.25/18.39 ! [V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__1__add__number__of,axiom,
% 18.25/18.39 ! [V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__number__of__eq,axiom,
% 18.25/18.39 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 18.25/18.39 <=> 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_iszero__Numeral0,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Pls__def,axiom,
% 18.25/18.39 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I19_J,axiom,
% 18.25/18.39 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I2_J,axiom,
% 18.25/18.39 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Pls__right,axiom,
% 18.25/18.39 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Pls,axiom,
% 18.25/18.39 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__Pls,axiom,
% 18.25/18.39 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I1_J,axiom,
% 18.25/18.39 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus__Pls,axiom,
% 18.25/18.39 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I40_J,axiom,
% 18.25/18.39 c_Int_OMin != c_Int_OPls ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I37_J,axiom,
% 18.25/18.39 c_Int_OPls != c_Int_OMin ).
% 18.25/18.39
% 18.25/18.39 fof(fact_iszero__def,axiom,
% 18.25/18.39 ! [V_z_2,T_b] :
% 18.25/18.39 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.39 => ( c_Int_Oiszero(T_b,V_z_2)
% 18.25/18.39 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_iszero__0,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.39 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_not__iszero__1,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.39 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of__Pls,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_semiring__norm_I112_J,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__numeral__0__right,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__numeral__0,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_bin__less__0__simps_I1_J,axiom,
% 18.25/18.39 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_semiring__norm_I113_J,axiom,
% 18.25/18.39 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__number__of__Pls,axiom,
% 18.25/18.39 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__is__num__zero,axiom,
% 18.25/18.39 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I23_J,axiom,
% 18.25/18.39 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I20_J,axiom,
% 18.25/18.39 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I3_J,axiom,
% 18.25/18.39 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I6_J,axiom,
% 18.25/18.39 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__number__of__Pls__Min,axiom,
% 18.25/18.39 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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_not__neg__number__of__Pls,axiom,
% 18.25/18.39 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__special_I1_J,axiom,
% 18.25/18.39 ! [V_y_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 18.25/18.39 <=> 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__special_I3_J,axiom,
% 18.25/18.39 ! [V_x_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 <=> 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_succ__Min,axiom,
% 18.25/18.39 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__0__number__of,axiom,
% 18.25/18.39 ! [V_v_2] :
% 18.25/18.39 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__number__of__0,axiom,
% 18.25/18.39 ! [V_v_2] :
% 18.25/18.39 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of2,axiom,
% 18.25/18.39 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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__nat__number__of,axiom,
% 18.25/18.39 ! [V_v_H_2,V_v_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__nat__number__of,axiom,
% 18.25/18.39 ! [V_v_H_2,V_v_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nonzero__number__of__Min,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__special_I1_J,axiom,
% 18.25/18.39 ! [V_y_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__special_I3_J,axiom,
% 18.25/18.39 ! [V_x_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__special_I3_J,axiom,
% 18.25/18.39 ! [V_x_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__special_I1_J,axiom,
% 18.25/18.39 ! [V_y_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__0__number__of,axiom,
% 18.25/18.39 ! [V_v_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__nat__number__of,axiom,
% 18.25/18.39 ! [V_v_H,V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 18.25/18.39 => 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)) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Nats__number__of,axiom,
% 18.25/18.39 ! [V_w_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 18.25/18.39 => 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))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__nat__number__of,axiom,
% 18.25/18.39 ! [V_v_H,V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__number__of__mult__left,axiom,
% 18.25/18.39 ! [V_k,V_v_H,V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__number__of__diff__1,axiom,
% 18.25/18.39 ! [V_v] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__diff__number__of,axiom,
% 18.25/18.39 ! [V_m,V_v] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__special_I4_J,axiom,
% 18.25/18.39 ! [V_x_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 18.25/18.39 <=> 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))))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__special_I2_J,axiom,
% 18.25/18.39 ! [V_y_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 18.25/18.39 <=> 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__special_I1_J,axiom,
% 18.25/18.39 ! [V_w,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__special_I2_J,axiom,
% 18.25/18.39 ! [V_v,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus__Bit1,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I51_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 18.25/18.39 <=> V_k_2 = V_l_2 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__eq__int__code_I16_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I34_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I17_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__int__code_I16_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I46_J,axiom,
% 18.25/18.39 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I39_J,axiom,
% 18.25/18.39 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I47_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 18.25/18.39 <=> V_k_2 = c_Int_OMin ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I43_J,axiom,
% 18.25/18.39 ! [V_l_2] :
% 18.25/18.39 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 18.25/18.39 <=> c_Int_OMin = V_l_2 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Bit1__Min,axiom,
% 18.25/18.39 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 18.25/18.39
% 18.25/18.39 fof(fact_succ__pred,axiom,
% 18.25/18.39 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 18.25/18.39
% 18.25/18.39 fof(fact_bin__less__0__simps_I4_J,axiom,
% 18.25/18.39 ! [V_w_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I22_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I12_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Bit1__def,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I30_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I26_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I9_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I13_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__number__of__Bit1,axiom,
% 18.25/18.39 ! [V_w_2] :
% 18.25/18.39 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 18.25/18.39 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_iszero__number__of__Bit1,axiom,
% 18.25/18.39 ! [V_w,T_a] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 & class_Int_Oring__char__0(T_a) )
% 18.25/18.39 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_succ__Pls,axiom,
% 18.25/18.39 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__iff__pred__less,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__Pls,axiom,
% 18.25/18.39 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__def,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Min__right,axiom,
% 18.25/18.39 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Min,axiom,
% 18.25/18.39 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of__Bit1,axiom,
% 18.25/18.39 ! [V_w,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__numeral__1,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__numeral__1__right,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_semiring__norm_I110_J,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_numeral__1__eq__1,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I29_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I5_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_one__is__num__one,axiom,
% 18.25/18.39 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__numeral__1__eq__1,axiom,
% 18.25/18.39 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Numeral1__eq1__nat,axiom,
% 18.25/18.39 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I4_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus__Min,axiom,
% 18.25/18.39 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_not__iszero__Numeral1,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_numeral__3__eq__3,axiom,
% 18.25/18.39 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)))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_numeral__1__eq__Suc__0,axiom,
% 18.25/18.39 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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power3__eq__cube,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 18.25/18.39 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))))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc3__eq__add__3,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 18.25/18.39 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)))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 18.25/18.39 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)))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__special_I2_J,axiom,
% 18.25/18.39 ! [V_y_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__special_I4_J,axiom,
% 18.25/18.39 ! [V_x_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__special_I4_J,axiom,
% 18.25/18.39 ! [V_x_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__special_I2_J,axiom,
% 18.25/18.39 ! [V_y_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Rings_Olinordered__idom(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__special_I3_J,axiom,
% 18.25/18.39 ! [V_v,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__special_I2_J,axiom,
% 18.25/18.39 ! [V_w,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 18.25/18.39 ! [V_m,V_n] :
% 18.25/18.39 ( 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))
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of__pred,axiom,
% 18.25/18.39 ! [V_w,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__Suc__eq__div__add3,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__div__eq__add3__div,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__number__of__pred__iff__0,axiom,
% 18.25/18.39 ! [V_v_2] :
% 18.25/18.39 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 18.25/18.39 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zmod__number__of__Bit1,axiom,
% 18.25/18.39 ! [V_v,V_w] :
% 18.25/18.39 ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__zmod__mult__2,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__zdiv__mult__2,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pos__zdiv__mult__2,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pos__zmod__mult__2,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_of__nat__double,axiom,
% 18.25/18.39 ! [V_x,T_a] :
% 18.25/18.39 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 18.25/18.39 => 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))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I48_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 18.25/18.39 <=> V_k_2 = V_l_2 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I31_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__eq__int__code_I13_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__int__code_I13_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I14_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Bit0__Pls,axiom,
% 18.25/18.39 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I38_J,axiom,
% 18.25/18.39 ! [V_l_2] :
% 18.25/18.39 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 18.25/18.39 <=> c_Int_OPls = V_l_2 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I44_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 18.25/18.39 <=> V_k_2 = c_Int_OPls ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I49_J,axiom,
% 18.25/18.39 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I50_J,axiom,
% 18.25/18.39 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Bit0__Bit0,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Bit0__def,axiom,
% 18.25/18.39 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__Bit0,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I7_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus__Bit0,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I42_J,axiom,
% 18.25/18.39 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I45_J,axiom,
% 18.25/18.39 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 18.25/18.39
% 18.25/18.39 fof(fact_bin__less__0__simps_I3_J,axiom,
% 18.25/18.39 ! [V_w_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I21_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I27_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I32_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__eq__int__code_I14_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I10_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I4_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__int__code_I15_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I16_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Bit0__Bit1,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Bit1__Bit0,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I3_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I10_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I9_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I28_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I8_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zdiv__number__of__Bit0,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__number__of__Bit0,axiom,
% 18.25/18.39 ! [V_w_2] :
% 18.25/18.39 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 18.25/18.39 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__Bit1,axiom,
% 18.25/18.39 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__Bit0,axiom,
% 18.25/18.39 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__Min,axiom,
% 18.25/18.39 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_iszero__number__of__Bit0,axiom,
% 18.25/18.39 ! [V_w_2,T_b] :
% 18.25/18.39 ( ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 & class_Int_Oring__char__0(T_b) )
% 18.25/18.39 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 18.25/18.39 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_succ__Bit1,axiom,
% 18.25/18.39 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_succ__Bit0,axiom,
% 18.25/18.39 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of__Bit0,axiom,
% 18.25/18.39 ! [V_w,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I15_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__int__code_I14_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I33_J,axiom,
% 18.25/18.39 ! [V_l_2,V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__eq__int__code_I15_J,axiom,
% 18.25/18.39 ! [V_k2_2,V_k1_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__Bit1,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I25_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rel__simps_I11_J,axiom,
% 18.25/18.39 ! [V_k_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I6_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I5_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__bin__simps_I8_J,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__Bit1__Bit1,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_double__number__of__Bit0,axiom,
% 18.25/18.39 ! [V_w,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_number__of1,axiom,
% 18.25/18.39 ! [V_n] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( 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))))
% 18.25/18.39 & 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__2,axiom,
% 18.25/18.39 ! [V_z,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__2__right,axiom,
% 18.25/18.39 ! [V_z,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_one__add__one__is__two,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__eq__power2,axiom,
% 18.25/18.39 ! [V_a_2,T_b] :
% 18.25/18.39 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 18.25/18.39 => ( 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)
% 18.25/18.39 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__power2,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_semiring__norm_I115_J,axiom,
% 18.25/18.39 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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_numeral__2__eq__2,axiom,
% 18.25/18.39 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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 18.25/18.39 ! [V_x,T_a] :
% 18.25/18.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__eq__square,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 18.25/18.39 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))))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__2__eq__Suc,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__2__eq__Suc_H,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_one__power2,axiom,
% 18.25/18.39 ! [T_a] :
% 18.25/18.39 ( class_Rings_Osemiring__1(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__minus,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Oring__1(T_a)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__mult__2__right,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__mult__2,axiom,
% 18.25/18.39 ! [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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__even__eq,axiom,
% 18.25/18.39 ! [V_n,V_a,T_a] :
% 18.25/18.39 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 18.25/18.39 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)))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 18.25/18.39 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)))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_abs__power2,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__abs,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__1__add__1,axiom,
% 18.25/18.39 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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod2__Suc__Suc,axiom,
% 18.25/18.39 ! [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)))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div2__Suc__Suc,axiom,
% 18.25/18.39 ! [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))))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zmod__number__of__Bit0,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__self__div__2,axiom,
% 18.25/18.39 ! [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 ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__eq__imp__eq,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.39 => ( 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))))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => V_x = V_y ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__le__imp__le,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.39 => ( 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))))))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__le__power2,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => 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)))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__less__power2,axiom,
% 18.25/18.39 ! [V_a_2,T_b] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.39 => ( 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))))))
% 18.25/18.39 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__less__0,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => ~ 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_sum__power2__eq__zero__iff,axiom,
% 18.25/18.39 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.39 => ( 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)
% 18.25/18.39 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__eq__square__number__of,axiom,
% 18.25/18.39 ! [V_w,T_b] :
% 18.25/18.39 ( ( class_Groups_Omonoid__mult(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__2__cases,axiom,
% 18.25/18.39 ! [V_n] :
% 18.25/18.39 ( 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)))))
% 18.25/18.39 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.39 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__2,axiom,
% 18.25/18.39 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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__eq__1__iff,axiom,
% 18.25/18.39 ! [V_a_2,T_b] :
% 18.25/18.39 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 18.25/18.39 => ( 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)
% 18.25/18.39 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 18.25/18.39 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 18.25/18.39 ! [V_n,V_x,T_a] :
% 18.25/18.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__minus__even,axiom,
% 18.25/18.39 ! [V_n,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Oring__1(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__less__imp__less,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__semidom(T_a)
% 18.25/18.39 => ( 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))))))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_sum__power2__le__zero__iff,axiom,
% 18.25/18.39 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_sum__power2__ge__zero,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => 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))))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_not__sum__power2__lt__zero,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => ~ 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_sum__power2__gt__zero__iff,axiom,
% 18.25/18.39 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_b)
% 18.25/18.39 => ( 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)))))))
% 18.25/18.39 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__sum,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__le__even__power_H,axiom,
% 18.25/18.39 ! [V_n,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__odd__eq,axiom,
% 18.25/18.39 ! [V_n,V_a,T_a] :
% 18.25/18.39 ( class_Groups_Omonoid__mult(T_a)
% 18.25/18.39 => 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 18.25/18.39 ! [V_n,V_x,T_a] :
% 18.25/18.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__minus1__even,axiom,
% 18.25/18.39 ! [V_n,T_a] :
% 18.25/18.39 ( class_Rings_Oring__1(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zdiv__number__of__Bit1,axiom,
% 18.25/18.39 ! [V_v,V_w] :
% 18.25/18.39 ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mod2__gr__0,axiom,
% 18.25/18.39 ! [V_m_2] :
% 18.25/18.39 ( 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))))))
% 18.25/18.39 <=> 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__2__gt__zero,axiom,
% 18.25/18.39 ! [V_n] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 18.25/18.39 => 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)))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power2__diff,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 18.25/18.39 ! [V_n,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => ( 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)))))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_odd__power__less__zero,axiom,
% 18.25/18.39 ! [V_n,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Olinordered__idom(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => 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))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__minus1__odd,axiom,
% 18.25/18.39 ! [V_n,T_a] :
% 18.25/18.39 ( class_Rings_Oring__1(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__m1__even,axiom,
% 18.25/18.39 ! [V_n,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__m1__odd,axiom,
% 18.25/18.39 ! [V_n,T_a] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 18.25/18.39 ! [V_n] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.25/18.39 => 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)))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 18.25/18.39 ! [V_w] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( ( 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))))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ 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))))
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg__eqn,axiom,
% 18.25/18.39 ! [V_a,V_b] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg__eqn__number__of,axiom,
% 18.25/18.39 ! [V_w,V_v] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( ( 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))))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ 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))))
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg_Osimps,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( ( ( 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)))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ ( 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)))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 18.25/18.39 ! [V_w] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg_Osimps,axiom,
% 18.25/18.39 ! [V_b,V_a] :
% 18.25/18.39 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg__eqn,axiom,
% 18.25/18.39 ! [V_a,V_b] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg__eqn__number__of,axiom,
% 18.25/18.39 ! [V_w,V_v] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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)))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_negDivAlg_Opsimps,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( ( ( 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)))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ ( 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)))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_int__of__code,axiom,
% 18.25/18.39 ! [V_k] :
% 18.25/18.39 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.25/18.39 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 18.25/18.39 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.25/18.39 => ( ( 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)
% 18.25/18.39 => 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)))))) )
% 18.25/18.39 & ( 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)
% 18.25/18.39 => 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)) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_posDivAlg_Opsimps,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 18.25/18.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_one__code__numeral__code,axiom,
% 18.25/18.39 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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_adjust__eq,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_half__gt__zero__iff,axiom,
% 18.25/18.39 ! [V_r_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber__ring(T_b) )
% 18.25/18.39 => ( 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))))))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_fun__Compl__def,axiom,
% 18.25/18.39 ! [V_x_2,V_A_2,T_c,T_b] :
% 18.25/18.39 ( class_Groups_Ouminus(T_b)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__equals__eq,axiom,
% 18.25/18.39 ! [V_S_2,V_R_2,T_b] :
% 18.25/18.39 ( 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)
% 18.25/18.39 <=> V_R_2 = V_S_2 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__equals__eq2,axiom,
% 18.25/18.39 ! [V_S_2,V_R_2,T_c,T_b] :
% 18.25/18.39 ( 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)
% 18.25/18.39 <=> V_R_2 = V_S_2 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__subset__eq2,axiom,
% 18.25/18.39 ! [V_S_2,V_R_2,T_c,T_b] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pred__subset__eq,axiom,
% 18.25/18.39 ! [V_S_2,V_R_2,T_b] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_accp_Osimps,axiom,
% 18.25/18.39 ! [V_a_2,V_r_2,T_b] :
% 18.25/18.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 18.25/18.39 <=> ! [B_x] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 18.25/18.39 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_accp_Oequations,axiom,
% 18.25/18.39 ! [V_a_2,V_r_2,T_b] :
% 18.25/18.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 18.25/18.39 <=> ! [B_x] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 18.25/18.39 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_accp__downward,axiom,
% 18.25/18.39 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 18.25/18.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 18.25/18.39 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_code__numeral__zero__minus__one,axiom,
% 18.25/18.39 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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_fun__diff__def,axiom,
% 18.25/18.39 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 18.25/18.39 ( class_Groups_Ominus(T_b)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__zero,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__zero__left,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__divide__distrib,axiom,
% 18.25/18.39 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_times__divide__eq__right,axiom,
% 18.25/18.39 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__divide__distrib,axiom,
% 18.25/18.39 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__1,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus__divide__left,axiom,
% 18.25/18.39 ! [V_b,V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__divide,axiom,
% 18.25/18.39 ! [V_n,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__eq__Suc__le__raw,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__number__of__Bit0,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_accp__subset,axiom,
% 18.25/18.39 ! [V_R2_2,V_R1_2,T_b] :
% 18.25/18.39 ( 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))
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__number__of__even,axiom,
% 18.25/18.39 ! [V_w_2,V_z_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zpower__number__of__even,axiom,
% 18.25/18.39 ! [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))) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__divide__imp,axiom,
% 18.25/18.39 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 18.25/18.39 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__eq__imp,axiom,
% 18.25/18.39 ! [V_a,V_b,V_c,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 18.25/18.39 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nonzero__divide__eq__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_b)
% 18.25/18.39 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 18.25/18.39 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nonzero__eq__divide__eq,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_b)
% 18.25/18.39 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 18.25/18.39 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__self__if,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 18.25/18.39 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 18.25/18.39 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__self,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_right__inverse__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_b_2,T_b] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_b)
% 18.25/18.39 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 18.25/18.39 <=> V_a_2 = V_b_2 ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nonzero__minus__divide__divide,axiom,
% 18.25/18.39 ! [V_a,V_b,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nonzero__minus__divide__right,axiom,
% 18.25/18.39 ! [V_a,V_b,T_a] :
% 18.25/18.39 ( class_Rings_Odivision__ring(T_a)
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nonzero__power__divide,axiom,
% 18.25/18.39 ! [V_n,V_a,V_b,T_a] :
% 18.25/18.39 ( class_Fields_Ofield(T_a)
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__one__over,axiom,
% 18.25/18.39 ! [V_n,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__number__of__even__number__of,axiom,
% 18.25/18.39 ! [V_w_2,V_v_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => 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))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__nat__eq__if,axiom,
% 18.25/18.39 ! [V_z_2,V_z_H_2] :
% 18.25/18.39 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 18.25/18.39 ! [V_n_2,T_b] :
% 18.25/18.39 ( class_Rings_Osemiring__1(T_b)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__divide__eq__number__of1,axiom,
% 18.25/18.39 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => 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 )
% 18.25/18.39 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__divide__eq__number__of,axiom,
% 18.25/18.39 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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)
% 18.25/18.39 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => 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 )
% 18.25/18.39 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__eq__eq__number__of,axiom,
% 18.25/18.39 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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)
% 18.25/18.39 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__eq__eq__number__of1,axiom,
% 18.25/18.39 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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
% 18.25/18.39 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__number__of__Suc,axiom,
% 18.25/18.39 ! [V_n_2,V_v_2] :
% 18.25/18.39 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 18.25/18.39 <=> 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_Suc__eq__number__of,axiom,
% 18.25/18.39 ! [V_v_2,V_n_2] :
% 18.25/18.39 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 18.25/18.39 <=> 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__Numeral0,axiom,
% 18.25/18.39 ! [V_x,T_a] :
% 18.25/18.39 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 & class_Int_Onumber__ring(T_a) )
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__numeral__1,axiom,
% 18.25/18.39 ! [V_a,T_a] :
% 18.25/18.39 ( ( class_Fields_Ofield(T_a)
% 18.25/18.39 & class_Int_Onumber__ring(T_a) )
% 18.25/18.39 => 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 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__Numeral1,axiom,
% 18.25/18.39 ! [V_x,T_a] :
% 18.25/18.39 ( ( class_Fields_Ofield(T_a)
% 18.25/18.39 & class_Int_Onumber__ring(T_a) )
% 18.25/18.39 => 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 ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__minus1,axiom,
% 18.25/18.39 ! [V_x,T_a] :
% 18.25/18.39 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 & class_Int_Onumber__ring(T_a) )
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nat__number__of__Bit1,axiom,
% 18.25/18.39 ! [V_w_2] :
% 18.25/18.39 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 18.25/18.39 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 18.25/18.39 => 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)))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__Suc__number__of,axiom,
% 18.25/18.39 ! [V_v_2,V_n_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__number__of__Suc,axiom,
% 18.25/18.39 ! [V_n_2,V_v_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__Suc__number__of,axiom,
% 18.25/18.39 ! [V_v_2,V_n_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> 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))))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__number__of__Suc,axiom,
% 18.25/18.39 ! [V_n_2,V_v_2] :
% 18.25/18.39 ( 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)))
% 18.25/18.39 <=> 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)))) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__code__numeral__code,axiom,
% 18.25/18.39 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) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__number__of__odd,axiom,
% 18.25/18.39 ! [V_z_2,V_w_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__less__eq__number__of1,axiom,
% 18.25/18.39 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> ( ( 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)))
% 18.25/18.39 => 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)))) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__less__eq__number__of,axiom,
% 18.25/18.39 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__divide__eq__number__of,axiom,
% 18.25/18.39 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__divide__eq__number__of1,axiom,
% 18.25/18.39 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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))))
% 18.25/18.39 <=> ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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)))) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zpower__number__of__odd,axiom,
% 18.25/18.39 ! [V_z_2,V_w_2] :
% 18.25/18.39 ( ( 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)))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__diff,axiom,
% 18.25/18.39 ! [V_m,V_n,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Ofield(T_a)
% 18.25/18.39 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.25/18.39 => 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus1__divide,axiom,
% 18.25/18.39 ! [V_x,T_a] :
% 18.25/18.39 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 & class_Int_Onumber__ring(T_a) )
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_power__number__of__odd__number__of,axiom,
% 18.25/18.39 ! [V_v_2,V_w_2,T_b] :
% 18.25/18.39 ( class_Int_Onumber__ring(T_b)
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => 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) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__divide__eq__number__of1,axiom,
% 18.25/18.39 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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))))
% 18.25/18.39 <=> ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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)))) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__divide__eq__number__of,axiom,
% 18.25/18.39 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__le__eq__number__of,axiom,
% 18.25/18.39 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__le__eq__number__of1,axiom,
% 18.25/18.39 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 & class_Int_Onumber(T_b) )
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> ( ( 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)))
% 18.25/18.39 => 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)))) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => ( ( 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)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ 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)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_diff__nat__number__of,axiom,
% 18.25/18.39 ! [V_v_2,V_v_H_2] :
% 18.25/18.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 18.25/18.39 => 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) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_half__gt__zero,axiom,
% 18.25/18.39 ! [V_r,T_a] :
% 18.25/18.39 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 18.25/18.39 & class_Int_Onumber__ring(T_a) )
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 18.25/18.39 => 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)))))) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_div__mod__code__numeral__def,axiom,
% 18.25/18.39 ! [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)) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_le__divide__eq,axiom,
% 18.25/18.39 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__le__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pos__le__divide__eq,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pos__divide__le__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__imp__div__pos__le,axiom,
% 18.25/18.39 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_predicate2D,axiom,
% 18.25/18.39 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 18.25/18.39 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_rev__predicate2D,axiom,
% 18.25/18.39 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 18.25/18.39 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 18.25/18.39 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_times__divide__times__eq,axiom,
% 18.25/18.39 ! [V_w,V_z,V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus__divide__divide,axiom,
% 18.25/18.39 ! [V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 => 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) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_minus__divide__right,axiom,
% 18.25/18.39 ! [V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_abs__divide,axiom,
% 18.25/18.39 ! [V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 18.25/18.39 => 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)) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__right__mono__neg,axiom,
% 18.25/18.39 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__right__mono,axiom,
% 18.25/18.39 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__le__0__iff,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 18.25/18.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__le__divide__iff,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 18.25/18.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_zero__less__divide__iff,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 18.25/18.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__less__0__iff,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 18.25/18.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__pos__pos,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__pos__neg,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__neg__pos,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__neg__neg,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__strict__right__mono,axiom,
% 18.25/18.39 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__strict__right__mono__neg,axiom,
% 18.25/18.39 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_frac__eq__eq,axiom,
% 18.25/18.39 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 18.25/18.39 ( class_Fields_Ofield(T_b)
% 18.25/18.39 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => ( 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)
% 18.25/18.39 <=> 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) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__divide__mult__cancel__left,axiom,
% 18.25/18.39 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__divide__mult__cancel__right,axiom,
% 18.25/18.39 ! [V_b,V_a,V_c,T_a] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.39 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__eq__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_b)
% 18.25/18.39 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 18.25/18.39 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 18.25/18.39 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_eq__divide__eq,axiom,
% 18.25/18.39 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( class_Fields_Ofield__inverse__zero(T_b)
% 18.25/18.39 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 18.25/18.39 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 18.25/18.39 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.25/18.39 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_nonzero__abs__divide,axiom,
% 18.25/18.39 ! [V_a,V_b,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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)) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__nonneg__pos,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__nonneg__neg,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_frac__less2,axiom,
% 18.25/18.39 ! [V_z,V_w,V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 18.25/18.39 => 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))) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_frac__less,axiom,
% 18.25/18.39 ! [V_z,V_w,V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 18.25/18.39 => 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))) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_frac__le,axiom,
% 18.25/18.39 ! [V_z,V_w,V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 18.25/18.39 => 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))) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__nonpos__pos,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__nonpos__neg,axiom,
% 18.25/18.39 ! [V_y,V_x,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_less__divide__eq,axiom,
% 18.25/18.39 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__less__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => 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))) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => 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)) )
% 18.25/18.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pos__less__divide__eq,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_pos__divide__less__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__imp__div__pos__less,axiom,
% 18.25/18.39 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_mult__imp__less__div__pos,axiom,
% 18.25/18.39 ! [V_x,V_z,V_y,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.39 => ( 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))
% 18.25/18.39 => 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__less__divide__eq,axiom,
% 18.25/18.39 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 <=> 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))) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_neg__divide__less__eq,axiom,
% 18.25/18.39 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.39 => ( 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))
% 18.25/18.39 <=> 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__strict__left__mono,axiom,
% 18.25/18.39 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => 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))) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__strict__left__mono__neg,axiom,
% 18.25/18.39 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.39 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.39 => ( 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)))
% 18.25/18.39 => 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))) ) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_add__frac__eq,axiom,
% 18.25/18.39 ! [V_w,V_x,V_z,V_y,T_a] :
% 18.25/18.39 ( class_Fields_Ofield(T_a)
% 18.25/18.39 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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)) ) ) ) ).
% 18.25/18.39
% 18.25/18.39 fof(fact_divide__add__eq__iff,axiom,
% 18.25/18.39 ! [V_y,V_x,V_z,T_a] :
% 18.25/18.39 ( class_Fields_Ofield(T_a)
% 18.25/18.39 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.39 => 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) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_add__frac__num,axiom,
% 18.25/18.40 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.40 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.40 => 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) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_add__divide__eq__iff,axiom,
% 18.25/18.40 ! [V_y,V_x,V_z,T_a] :
% 18.25/18.40 ( class_Fields_Ofield(T_a)
% 18.25/18.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.40 => 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) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_add__num__frac,axiom,
% 18.25/18.40 ! [V_x,V_z,V_y,T_a] :
% 18.25/18.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 18.25/18.40 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.40 => 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) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_diff__divide__eq__iff,axiom,
% 18.25/18.40 ! [V_y,V_x,V_z,T_a] :
% 18.25/18.40 ( class_Fields_Ofield(T_a)
% 18.25/18.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.40 => 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) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_divide__diff__eq__iff,axiom,
% 18.25/18.40 ! [V_y,V_x,V_z,T_a] :
% 18.25/18.40 ( class_Fields_Ofield(T_a)
% 18.25/18.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.40 => 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) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_diff__frac__eq,axiom,
% 18.25/18.40 ! [V_w,V_x,V_z,V_y,T_a] :
% 18.25/18.40 ( class_Fields_Ofield(T_a)
% 18.25/18.40 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 18.25/18.40 => 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)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_gt__half__sum,axiom,
% 18.25/18.40 ! [V_b,V_a,T_a] :
% 18.25/18.40 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_less__half__sum,axiom,
% 18.25/18.40 ! [V_b,V_a,T_a] :
% 18.25/18.40 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 18.25/18.40 => 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))))) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_abs__div__pos,axiom,
% 18.25/18.40 ! [V_x,V_y,T_a] :
% 18.25/18.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_divide__left__mono__neg,axiom,
% 18.25/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 18.25/18.40 => ( 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)))
% 18.25/18.40 => 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))) ) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_divide__left__mono,axiom,
% 18.25/18.40 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.40 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 18.25/18.40 => ( 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)))
% 18.25/18.40 => 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))) ) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_neg__divide__le__eq,axiom,
% 18.25/18.40 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 18.25/18.40 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.40 => ( 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))
% 18.25/18.40 <=> 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)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_neg__le__divide__eq,axiom,
% 18.25/18.40 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.25/18.40 ( class_Fields_Olinordered__field(T_b)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 18.25/18.40 => ( 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)))
% 18.25/18.40 <=> 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))) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_mult__imp__le__div__pos,axiom,
% 18.25/18.40 ! [V_x,V_z,V_y,T_a] :
% 18.25/18.40 ( class_Fields_Olinordered__field(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 18.25/18.40 => ( 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))
% 18.25/18.40 => 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))) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_of__int__num,axiom,
% 18.25/18.40 ! [V_k_2,T_b] :
% 18.25/18.40 ( class_Rings_Oring__1(T_b)
% 18.25/18.40 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 18.25/18.40 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.40 => 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))) )
% 18.25/18.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.40 => 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))))) ) ) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_negDivAlg_Opinduct,axiom,
% 18.25/18.40 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => ( ! [B_a,B_b] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => ( ( ~ ( 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)))
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 18.25/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 18.25/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_posDivAlg_Opinduct,axiom,
% 18.25/18.40 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => ( ! [B_a,B_b] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 18.25/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 18.25/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 18.25/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__case__add__eq__if,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_adjust__def,axiom,
% 18.25/18.40 ! [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))))))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_split__weak__cong,axiom,
% 18.25/18.40 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 18.25/18.40 ( V_p_2 = V_q_2
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_split__twice,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_prod_Osimps_I2_J,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_split__conv,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_split__eta,axiom,
% 18.25/18.40 ! [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 ).
% 18.25/18.40
% 18.25/18.40 fof(fact_fst__def,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_snd__def,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__case__0,axiom,
% 18.25/18.40 ! [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 ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__case__Suc,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_prod__case__beta,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_split__comp__eq,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_split__beta,axiom,
% 18.25/18.40 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_split__def,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 18.25/18.40 ! [V_n_2,V_m_2] :
% 18.25/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 18.25/18.40 <=> 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_diff__Suc,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_divmod__int__rel__def,axiom,
% 18.25/18.40 ! [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))))))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__case__number__of,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_divmod__int__pdivmod,axiom,
% 18.25/18.40 ! [V_l_2,V_k_2] :
% 18.25/18.40 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => 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)) )
% 18.25/18.40 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => 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) )
% 18.25/18.40 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => 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)))) ) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_divmod__int__code,axiom,
% 18.25/18.40 ! [V_l_2,V_k_2] :
% 18.25/18.40 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => 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)) )
% 18.25/18.40 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => 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) )
% 18.25/18.40 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 => 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)))) ) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__of__aux__code,axiom,
% 18.25/18.40 ! [V_n,V_i] :
% 18.25/18.40 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.25/18.40 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 18.25/18.40 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__rec__add__eq__if,axiom,
% 18.25/18.40 ! [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))))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_MGT__def,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_mem__splitI,axiom,
% 18.25/18.40 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 18.25/18.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 18.25/18.40 => 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)))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_splitI,axiom,
% 18.25/18.40 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 18.25/18.40 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 18.25/18.40 => 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))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_prod__caseI,axiom,
% 18.25/18.40 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 18.25/18.40 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 18.25/18.40 => 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))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_splitD,axiom,
% 18.25/18.40 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_splitD_H,axiom,
% 18.25/18.40 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 18.25/18.40 ( 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))
% 18.25/18.40 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_apsnd__conv,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_fst__apsnd,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_snd__apsnd,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_apsnd__eq__conv,axiom,
% 18.25/18.40 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 18.25/18.40 ( 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)
% 18.25/18.40 <=> 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__rec__0,axiom,
% 18.25/18.40 ! [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 ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__rec__Suc,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_negateSnd__def,axiom,
% 18.25/18.40 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_divmod__nat__if,axiom,
% 18.25/18.40 ! [V_m_2,V_n_2] :
% 18.25/18.40 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 18.25/18.40 => 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) )
% 18.25/18.40 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__rec__number__of,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__number__of__Suc,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__Suc__number__of,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osize_I1_J,axiom,
% 18.25/18.40 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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__Suc__number__of,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__number__of__Suc,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Odistrib__inf__le,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Odistrib__sup__le,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_le__maxI1,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_le__maxI2,axiom,
% 18.25/18.40 ! [V_x,V_y,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__iff__sup,axiom,
% 18.25/18.40 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.40 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__sup__iff,axiom,
% 18.25/18.40 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 18.25/18.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__supI1,axiom,
% 18.25/18.40 ! [V_b,V_a,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 18.25/18.40 => 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))) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__supI2,axiom,
% 18.25/18.40 ! [V_a,V_b,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 18.25/18.40 => 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))) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__absorb2,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__absorb1,axiom,
% 18.25/18.40 ! [V_x,V_y,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__supI,axiom,
% 18.25/18.40 ! [V_b,V_x,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 18.25/18.40 => 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)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__least,axiom,
% 18.25/18.40 ! [V_z,V_x,V_y,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 18.25/18.40 => 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)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__mono,axiom,
% 18.25/18.40 ! [V_d,V_b,V_c,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 18.25/18.40 => 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))) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__supE,axiom,
% 18.25/18.40 ! [V_x,V_b,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( 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))
% 18.25/18.40 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 18.25/18.40 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_le__max__iff__disj,axiom,
% 18.25/18.40 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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)))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__le1,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__le2,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__iff__inf,axiom,
% 18.25/18.40 ! [V_y_2,V_x_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.40 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__inf__iff,axiom,
% 18.25/18.40 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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)))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.25/18.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__infI1,axiom,
% 18.25/18.40 ! [V_b,V_x,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__infI2,axiom,
% 18.25/18.40 ! [V_a,V_x,V_b,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__absorb1,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__absorb2,axiom,
% 18.25/18.40 ! [V_x,V_y,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__infI,axiom,
% 18.25/18.40 ! [V_b,V_a,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 18.25/18.40 => 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))) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__greatest,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 18.25/18.40 => 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))) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__mono,axiom,
% 18.25/18.40 ! [V_d,V_b,V_c,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 18.25/18.40 => 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))) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Ole__infE,axiom,
% 18.25/18.40 ! [V_b,V_a,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( 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)))
% 18.25/18.40 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 18.25/18.40 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__le__iff__disj,axiom,
% 18.25/18.40 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oless__supI1,axiom,
% 18.25/18.40 ! [V_b,V_a,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 18.25/18.40 => 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))) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oless__supI2,axiom,
% 18.25/18.40 ! [V_a,V_b,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 18.25/18.40 => 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))) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_less__max__iff__disj,axiom,
% 18.25/18.40 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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)))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__less__iff__conj,axiom,
% 18.25/18.40 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 18.25/18.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oless__infI1,axiom,
% 18.25/18.40 ! [V_b,V_x,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oless__infI2,axiom,
% 18.25/18.40 ! [V_a,V_x,V_b,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__less__iff__conj,axiom,
% 18.25/18.40 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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)))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 18.25/18.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__less__iff__disj,axiom,
% 18.25/18.40 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => ( 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))
% 18.25/18.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 18.25/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__add__distrib__left,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__add__distrib__left,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup_Oidem,axiom,
% 18.25/18.40 ! [V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf_Oidem,axiom,
% 18.25/18.40 ! [V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup_Ocommute,axiom,
% 18.25/18.40 ! [V_b,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__commute,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf_Ocommute,axiom,
% 18.25/18.40 ! [V_b,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__commute,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__inf__absorb,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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 ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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 ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 18.25/18.40 ! [V_b,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__left__idem,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 18.25/18.40 ! [V_b,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__left__idem,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 18.25/18.40 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__left__commute,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 18.25/18.40 ! [V_c,V_a,V_b,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__left__commute,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup_Oassoc,axiom,
% 18.25/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__assoc,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf_Oassoc,axiom,
% 18.25/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__assoc,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 18.25/18.40 ! [V_x,V_z,V_y,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 18.25/18.40 ! [V_x,V_z,V_y,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_minus__min__eq__max,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Groups_Olinordered__ab__group__add(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_minus__max__eq__min,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Groups_Olinordered__ab__group__add(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__Suc__Suc,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__Suc__Suc,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__0L,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__0R,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__0L,axiom,
% 18.25/18.40 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__0R,axiom,
% 18.25/18.40 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__diff__distrib__left,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Groups_Oordered__ab__group__add(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__diff__distrib__left,axiom,
% 18.25/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.25/18.40 ( class_Groups_Oordered__ab__group__add(T_a)
% 18.25/18.40 => 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__diff,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__number__of,axiom,
% 18.25/18.40 ! [V_v,V_u,T_b] :
% 18.25/18.40 ( ( class_Int_Onumber(T_b)
% 18.25/18.40 & class_Orderings_Oord(T_b) )
% 18.25/18.40 => ( ( 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)))
% 18.25/18.40 => 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) )
% 18.25/18.40 & ( ~ 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)))
% 18.25/18.40 => 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) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__number__of,axiom,
% 18.25/18.40 ! [V_v,V_u,T_b] :
% 18.25/18.40 ( ( class_Int_Onumber(T_b)
% 18.25/18.40 & class_Orderings_Oord(T_b) )
% 18.25/18.40 => ( ( 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)))
% 18.25/18.40 => 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) )
% 18.25/18.40 & ( ~ 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)))
% 18.25/18.40 => 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) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__minus__add__max,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__Suc1,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__Suc2,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__Suc2,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__Suc1,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_max__ord__max,axiom,
% 18.25/18.40 ! [T_b] :
% 18.25/18.40 ( class_Orderings_Oord(T_b)
% 18.25/18.40 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_min__ord__min,axiom,
% 18.25/18.40 ! [T_b] :
% 18.25/18.40 ( class_Orderings_Oord(T_b)
% 18.25/18.40 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osize_I2_J,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_apsnd__apfst,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_apfst__apsnd,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Oinject,axiom,
% 18.25/18.40 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 18.25/18.40 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 18.25/18.40 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_apfst__conv,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_fst__apfst,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_apfst__eq__conv,axiom,
% 18.25/18.40 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 18.25/18.40 ( 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)
% 18.25/18.40 <=> 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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_snd__apfst,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_apsnd__apfst__commute,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 18.25/18.40 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Suc__code__numeral__minus__one,axiom,
% 18.25/18.40 ! [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 ).
% 18.25/18.40
% 18.25/18.40 fof(fact_dual__min,axiom,
% 18.25/18.40 ! [T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_dual__max,axiom,
% 18.25/18.40 ! [T_b] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_b)
% 18.25/18.40 => 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) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osize_I4_J,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osize_I3_J,axiom,
% 18.25/18.40 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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_field__le__mult__one__interval,axiom,
% 18.25/18.40 ! [V_y,V_x,T_a] :
% 18.25/18.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 18.25/18.40 => ( ! [B_z] :
% 18.25/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 18.25/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 18.25/18.40 => 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)) ) )
% 18.25/18.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Min_Oidem,axiom,
% 18.25/18.40 ! [V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Max_Oidem,axiom,
% 18.25/18.40 ! [V_x,T_a] :
% 18.25/18.40 ( class_Orderings_Olinorder(T_a)
% 18.25/18.40 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_OFrac__def,axiom,
% 18.25/18.40 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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 18.25/18.40 ! [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) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_norm__frac_Osimps,axiom,
% 18.25/18.40 ! [V_a_2,V_b_2] :
% 18.25/18.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.40 => 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)) )
% 18.25/18.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.40 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 18.25/18.40 => 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)) )
% 18.25/18.40 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 18.25/18.40 => 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))) ) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_accp__acc__eq,axiom,
% 18.25/18.40 ! [V_x_2,V_r_2,T_b] :
% 18.25/18.40 ( 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))
% 18.25/18.40 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 18.25/18.40 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 18.25/18.40 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 18.25/18.40 ! [V_y,V_x] :
% 18.25/18.40 ( c_Nat__Transfer_Ois__nat(V_x)
% 18.25/18.40 => ( c_Nat__Transfer_Ois__nat(V_y)
% 18.25/18.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 18.25/18.40 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 18.25/18.40 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 18.25/18.40 ! [V_y,V_x] :
% 18.25/18.40 ( c_Nat__Transfer_Ois__nat(V_x)
% 18.25/18.40 => ( c_Nat__Transfer_Ois__nat(V_y)
% 18.25/18.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 18.25/18.40 ! [V_y,V_x] :
% 18.25/18.40 ( c_Nat__Transfer_Ois__nat(V_x)
% 18.25/18.40 => ( c_Nat__Transfer_Ois__nat(V_y)
% 18.25/18.40 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 18.25/18.40 ! [V_y,V_x] :
% 18.25/18.40 ( c_Nat__Transfer_Ois__nat(V_x)
% 18.25/18.40 => ( c_Nat__Transfer_Ois__nat(V_y)
% 18.25/18.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 18.25/18.40 ! [V_n,V_x] :
% 18.25/18.40 ( c_Nat__Transfer_Ois__nat(V_x)
% 18.25/18.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 18.25/18.40 ! [V_y,V_x] :
% 18.25/18.40 ( c_Nat__Transfer_Ois__nat(V_x)
% 18.25/18.40 => ( c_Nat__Transfer_Ois__nat(V_y)
% 18.25/18.40 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_is__nat__def,axiom,
% 18.25/18.40 ! [V_x_2] :
% 18.25/18.40 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 18.25/18.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_acc__subset,axiom,
% 18.25/18.40 ! [V_R2_2,V_R1_2,T_b] :
% 18.25/18.40 ( 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))
% 18.25/18.40 => 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))) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_acc_Osimps,axiom,
% 18.25/18.40 ! [V_r_2,V_a_2,T_b] :
% 18.25/18.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 18.25/18.40 <=> ! [B_x] :
% 18.25/18.40 ( 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))
% 18.25/18.40 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_acc__downward,axiom,
% 18.25/18.40 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 18.25/18.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 18.25/18.40 => ( 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))
% 18.25/18.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 18.25/18.40 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 18.25/18.40 ! [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 ).
% 18.25/18.40
% 18.25/18.40 fof(fact_norm__frac_Opsimps,axiom,
% 18.25/18.40 ! [V_b_2,V_a_2] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.40 => 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)) )
% 18.25/18.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.25/18.40 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 18.25/18.40 => 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)) )
% 18.25/18.40 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.25/18.40 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 18.25/18.40 => 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))) ) ) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_Orefl_H__def,axiom,
% 18.25/18.40 ! [V_r_2,T_b] :
% 18.25/18.40 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 18.25/18.40 <=> ! [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)) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 18.25/18.40 ! [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)))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 18.25/18.40 ! [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)) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__gcd_Osimps,axiom,
% 18.25/18.40 ! [V_x,V_y] :
% 18.25/18.40 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.40 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 18.25/18.40 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.40 => 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)) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_Oone__frac__def,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 18.25/18.40 ! [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))) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_nat__gcd_Opsimps,axiom,
% 18.25/18.40 ! [V_y_2,V_x_2] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.40 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 18.25/18.40 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.25/18.40 => 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)) ) ) ) ).
% 18.25/18.40
% 18.25/18.40 fof(fact_norm__frac_Opinduct,axiom,
% 18.25/18.40 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 18.25/18.40 ( 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)))
% 18.25/18.40 => ( ! [B_a,B_b] :
% 18.25/18.40 ( 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)))
% 18.55/18.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 18.55/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Ofrac__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__gcd_Opinduct,axiom,
% 18.55/18.40 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( ! [B_x,B_y] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_mem__splitE,axiom,
% 18.55/18.40 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ~ ! [B_x,B_y] :
% 18.55/18.40 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 18.55/18.40 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_mem__splitI2,axiom,
% 18.55/18.40 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 18.55/18.40 ( ! [B_a,B_b] :
% 18.55/18.40 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_acc_OaccI,axiom,
% 18.55/18.40 ! [V_r_2,V_x_2,T_b] :
% 18.55/18.40 ( ! [B_y] :
% 18.55/18.40 ( 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))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_not__acc__down,axiom,
% 18.55/18.40 ! [V_R_2,V_x_2,T_b] :
% 18.55/18.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 18.55/18.40 => ~ ! [B_z] :
% 18.55/18.40 ( 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))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_scomp__unfold,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__intermed__int__val,axiom,
% 18.55/18.40 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 18.55/18.40 ( ! [B_i] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 18.55/18.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 18.55/18.40 => 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))) )
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 18.55/18.40 => ? [B_i] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 18.55/18.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 18.55/18.40 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_log_Osimps,axiom,
% 18.55/18.40 ! [V_i,V_b] :
% 18.55/18.40 ( ( ( 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)))
% 18.55/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 18.55/18.40 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 18.55/18.40 & ( ~ ( 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)))
% 18.55/18.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_internal__split__def,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_scomp__scomp,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_scomp__Pair,axiom,
% 18.55/18.40 ! [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 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Pair__scomp,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_scomp__apply,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_scomp__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_internal__split__conv,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Oof__frac__def,axiom,
% 18.55/18.40 ! [V_q,T_a,T_b] :
% 18.55/18.40 ( ( class_Rings_Oinverse(T_b)
% 18.55/18.40 & class_Rings_Oring__1(T_b) )
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_minus__shift__def,axiom,
% 18.55/18.40 ! [V_r,V_l,V_k] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 18.55/18.40 => 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) )
% 18.55/18.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 18.55/18.40 => 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) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Oless__frac__def,axiom,
% 18.55/18.40 ! [V_r_2,V_q_2,T_b] :
% 18.55/18.40 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 18.55/18.40 ! [V_r_2,V_q_2,T_b] :
% 18.55/18.40 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_iterate_Osimps,axiom,
% 18.55/18.40 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 18.55/18.40 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.40 => 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) )
% 18.55/18.40 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.40 => 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)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_inc__shift__def,axiom,
% 18.55/18.40 ! [V_k,V_v] :
% 18.55/18.40 ( ( V_v = V_k
% 18.55/18.40 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 18.55/18.40 & ( V_v != V_k
% 18.55/18.40 => 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)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_range,axiom,
% 18.55/18.40 ! [V_s,V_k] :
% 18.55/18.40 ( 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))
% 18.55/18.40 => 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)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__morphism__int__nat,axiom,
% 18.55/18.40 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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_field__le__epsilon,axiom,
% 18.55/18.40 ! [V_y,V_x,T_a] :
% 18.55/18.40 ( class_Fields_Olinordered__field(T_a)
% 18.55/18.40 => ( ! [B_e] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 18.55/18.40 => 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))) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_subtract__code__numeral__def,axiom,
% 18.55/18.40 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_minus__code__numeral__code,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pair__imageI,axiom,
% 18.55/18.40 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.40 ( 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))
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_image__eqI,axiom,
% 18.55/18.40 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 18.55/18.40 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_subset__image__iff,axiom,
% 18.55/18.40 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> ? [B_AA] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 18.55/18.40 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_image__mono,axiom,
% 18.55/18.40 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_image__image,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_rev__image__eqI,axiom,
% 18.55/18.40 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.40 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_imageI,axiom,
% 18.55/18.40 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_image__iff,axiom,
% 18.55/18.40 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 18.55/18.40 <=> ? [B_x] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.40 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_image__diff__subset,axiom,
% 18.55/18.40 ! [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)))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_image__ident,axiom,
% 18.55/18.40 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pair__box_Osize_I1_J,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_The__split,axiom,
% 18.55/18.40 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Random_Osimps,axiom,
% 18.55/18.40 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 18.55/18.40 ( ( 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)))
% 18.55/18.40 => 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)) )
% 18.55/18.40 & ( ~ 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)))
% 18.55/18.40 => 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))))))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 18.55/18.40 ! [V_B_2,V_A_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 18.55/18.40 ! [V_B_2,V_A_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 18.55/18.40 ! [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 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 18.55/18.40 ! [V_A_2,V_x_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 18.55/18.40 ! [V_B_2,V_A_2] :
% 18.55/18.40 ( V_A_2 = V_B_2
% 18.55/18.40 <=> 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) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pair__box_Oinject,axiom,
% 18.55/18.40 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.40 ( 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)
% 18.55/18.40 <=> ( V_a_2 = V_a_H_2
% 18.55/18.40 & V_b_2 = V_b_H_2 ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_split__paired__The,axiom,
% 18.55/18.40 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_The__split__eq,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_divmod__nat__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 18.55/18.40 ! [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 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Random__Sequence_Oempty__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Random__Sequence_Osingle__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pair__box_Osize_I2_J,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pair__box_Osimps_I2_J,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pair__box_Orecs,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 18.55/18.40 ! [V_B_2,V_A_2] :
% 18.55/18.40 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.40 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.40 <=> 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 18.55/18.40 ! [V_B_2,V_A_2] :
% 18.55/18.40 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.40 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.40 <=> 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 18.55/18.40 ! [V_A_2,V_x_2] :
% 18.55/18.40 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 18.55/18.40 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 18.55/18.40 <=> 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 18.55/18.40 ! [V_A_2] :
% 18.55/18.40 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.40 => 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 ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_the__eq__trivial,axiom,
% 18.55/18.40 ! [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 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__set__def,axiom,
% 18.55/18.40 ! [V_S_2] :
% 18.55/18.40 ( c_Nat__Transfer_Onat__set(V_S_2)
% 18.55/18.40 <=> ! [B_x] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 18.55/18.40 ! [V_B_2,V_A_2] :
% 18.55/18.40 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.40 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.40 => ( V_A_2 = V_B_2
% 18.55/18.40 <=> 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) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 18.55/18.40 ! [V_x_2,V_A_2] :
% 18.55/18.40 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 18.55/18.40 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 18.55/18.40 ! [V_x_2,V_A_2] :
% 18.55/18.40 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_the__sym__eq__trivial,axiom,
% 18.55/18.40 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_exE__realizer,axiom,
% 18.55/18.40 ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 18.55/18.40 => ( ! [B_x,B_y] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 18.55/18.40 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 18.55/18.40 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_code__numeral__not__eq__zero,axiom,
% 18.55/18.40 ! [V_i_2] :
% 18.55/18.40 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 18.55/18.40 <=> 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)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_beyond__def,axiom,
% 18.55/18.40 ! [V_l,V_k] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 18.55/18.40 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 18.55/18.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 18.55/18.40 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_curry__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_curryI,axiom,
% 18.55/18.40 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 18.55/18.40 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 18.55/18.40 ! [V_m_2,V_n_2] :
% 18.55/18.40 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 18.55/18.40 <=> V_n_2 = V_m_2 ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 18.55/18.40 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_times__code__numeral__code,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_beyond__zero,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_curryE,axiom,
% 18.55/18.40 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 18.55/18.40 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_curryD,axiom,
% 18.55/18.40 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 18.55/18.40 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_zero__code__numeral__def,axiom,
% 18.55/18.40 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_curry__conv,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_one__code__numeral__def,axiom,
% 18.55/18.40 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_less__code__numeral__code,axiom,
% 18.55/18.40 ! [V_m_2,V_n_2] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_curry__split,axiom,
% 18.55/18.40 ! [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 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_split__curry,axiom,
% 18.55/18.40 ! [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 ).
% 18.55/18.40
% 18.55/18.40 fof(fact_plus__code__numeral__code,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_less__eq__code__numeral__code,axiom,
% 18.55/18.40 ! [V_m_2,V_n_2] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_subtract__code__numeral__code,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_code__numeral__decr,axiom,
% 18.55/18.40 ! [V_k] :
% 18.55/18.40 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pos__not__random__dseq__def,axiom,
% 18.55/18.40 ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_mod__code__numeral__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_times__code__numeral__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 18.55/18.40 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 18.55/18.40 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.40 => 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) )
% 18.55/18.40 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.40 => 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)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_code__numeral_Onat__of__inject,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2] :
% 18.55/18.40 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 18.55/18.40 <=> V_x_2 = V_y_2 ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 18.55/18.40 ! [V_l_2,V_k_2] :
% 18.55/18.40 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 18.55/18.40 <=> V_k_2 = V_l_2 ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__of__inverse,axiom,
% 18.55/18.40 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 18.55/18.40
% 18.55/18.40 fof(fact_of__nat__nat__of,axiom,
% 18.55/18.40 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__of__of__nat,axiom,
% 18.55/18.40 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 18.55/18.40
% 18.55/18.40 fof(fact_less__code__numeral__def,axiom,
% 18.55/18.40 ! [V_m_2,V_n_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__of__number,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_less__eq__code__numeral__def,axiom,
% 18.55/18.40 ! [V_m_2,V_n_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__of__code,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__of__aux__def,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_Suc__code__numeral__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_minus__code__numeral__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_plus__code__numeral__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_div__code__numeral__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 18.55/18.40 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 18.55/18.40 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 18.55/18.40 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.40 => 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) )
% 18.55/18.40 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.40 => 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)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_less__than__iff,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pair__less__def,axiom,
% 18.55/18.40 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pos__empty__def,axiom,
% 18.55/18.40 ! [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) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_pos__bind__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_mlex__prod__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_in__inv__image,axiom,
% 18.55/18.40 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> 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)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_neg__bind__def,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_rp__inv__image__def,axiom,
% 18.55/18.40 ! [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))) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_measure__def,axiom,
% 18.55/18.40 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_power__dvd__imp__le,axiom,
% 18.55/18.40 ! [V_n,V_m,V_i] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oorder__refl,axiom,
% 18.55/18.40 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__0__right,axiom,
% 18.55/18.40 ! [V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__1__left,axiom,
% 18.55/18.40 ! [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)) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__add,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 18.55/18.40 => 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__reduce,axiom,
% 18.55/18.40 ! [V_n_2,V_k_2] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__diff__nat,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__if__abs__eq,axiom,
% 18.55/18.40 ! [V_k,V_l,T_a] :
% 18.55/18.40 ( class_Rings_Olinordered__idom(T_a)
% 18.55/18.40 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_abs__dvd__iff,axiom,
% 18.55/18.40 ! [V_k_2,V_m_2,T_b] :
% 18.55/18.40 ( class_Rings_Olinordered__idom(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__abs__iff,axiom,
% 18.55/18.40 ! [V_k_2,V_m_2,T_b] :
% 18.55/18.40 ( class_Rings_Olinordered__idom(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__diff,axiom,
% 18.55/18.40 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__ring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 18.55/18.40 => 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_one__dvd,axiom,
% 18.55/18.40 ! [V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_minus__dvd__iff,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.40 ( class_Rings_Ocomm__ring__1(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__minus__iff,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.40 ( class_Rings_Ocomm__ring__1(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mod__imp__dvd,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mod,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_mod__mod__cancel,axiom,
% 18.55/18.40 ! [V_a,V_b,V_c,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 18.55/18.40 => 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) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mod__iff,axiom,
% 18.55/18.40 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 18.55/18.40 => ( 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)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__refl,axiom,
% 18.55/18.40 ! [V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__trans,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oeq__iff,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2] :
% 18.55/18.40 ( V_x_2 = V_y_2
% 18.55/18.40 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Ole__less,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 18.55/18.40 | V_x_2 = V_y_2 ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__le,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 18.55/18.40 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 & V_x_2 != V_y_2 ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oneq__le__trans,axiom,
% 18.55/18.40 ! [V_b,V_a] :
% 18.55/18.40 ( V_a != V_b
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oeq__refl,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( V_x = V_y
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oantisym__conv,axiom,
% 18.55/18.40 ! [V_x_2,V_y_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 | V_x = V_y ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Ole__neq__trans,axiom,
% 18.55/18.40 ! [V_b,V_a] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 18.55/18.40 => ( V_a != V_b
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a] :
% 18.55/18.40 ( V_a = V_b
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 18.55/18.40 => ( V_b = V_c
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__antisym,axiom,
% 18.55/18.40 ! [V_n,V_m] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 18.55/18.40 => V_m = V_n ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oantisym,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 18.55/18.40 => V_x = V_y ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oorder__trans,axiom,
% 18.55/18.40 ! [V_z,V_y,V_x] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a] :
% 18.55/18.40 ( V_a = V_b
% 18.55/18.40 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Ole__less__trans,axiom,
% 18.55/18.40 ! [V_z,V_y,V_x] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__imp__neq,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => V_x != V_y ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__not__sym,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__imp__le,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__imp__not__less,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => V_x != V_y ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => V_y != V_x ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 18.55/18.40 => ( V_b = V_c
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__le__trans,axiom,
% 18.55/18.40 ! [V_z,V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__asym_H,axiom,
% 18.55/18.40 ! [V_b,V_a] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 18.55/18.40 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__trans,axiom,
% 18.55/18.40 ! [V_z,V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Oless__asym,axiom,
% 18.55/18.40 ! [V_y,V_x] :
% 18.55/18.40 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 18.55/18.40 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__0__left,axiom,
% 18.55/18.40 ! [V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 18.55/18.40 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_div__dvd__div,axiom,
% 18.55/18.40 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 18.55/18.40 => ( 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)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__power__same,axiom,
% 18.55/18.40 ! [V_n,V_y,V_x,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__dvd__1__iff__1,axiom,
% 18.55/18.40 ! [V_m_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 18.55/18.40 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__triv__left,axiom,
% 18.55/18.40 ! [V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__triv__right,axiom,
% 18.55/18.40 ! [V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult2,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult,axiom,
% 18.55/18.40 ! [V_b,V_c,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_mult__dvd__mono,axiom,
% 18.55/18.40 ! [V_d,V_c,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 18.55/18.40 => 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvdI,axiom,
% 18.55/18.40 ! [V_k,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Odvd(T_a)
% 18.55/18.40 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__left,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( 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))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__right,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( 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))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__cancel__left,axiom,
% 18.55/18.40 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 18.55/18.40 ( class_Rings_Oidom(T_b)
% 18.55/18.40 => ( 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)))
% 18.55/18.40 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.55/18.40 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__cancel__right,axiom,
% 18.55/18.40 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 18.55/18.40 ( class_Rings_Oidom(T_b)
% 18.55/18.40 => ( 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)))
% 18.55/18.40 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 18.55/18.40 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__imp__mod__0,axiom,
% 18.55/18.40 ! [V_b,V_a,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__eq__mod__eq__0,axiom,
% 18.55/18.40 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 18.55/18.40 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_div__add,axiom,
% 18.55/18.40 ! [V_y,V_x,V_z,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 18.55/18.40 => 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)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__div__cancel,axiom,
% 18.55/18.40 ! [V_b,V_a,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => 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 ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_div__mult__swap,axiom,
% 18.55/18.40 ! [V_a,V_b,V_c,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 18.55/18.40 => 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) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__div__mult__self,axiom,
% 18.55/18.40 ! [V_b,V_a,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => 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 ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__div__mult,axiom,
% 18.55/18.40 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 18.55/18.40 => 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) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_div__mult__div__if__dvd,axiom,
% 18.55/18.40 ! [V_w,V_z,V_x,V_y,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 18.55/18.40 => 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)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__div__neg,axiom,
% 18.55/18.40 ! [V_x,V_y,T_a] :
% 18.55/18.40 ( class_Divides_Oring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 18.55/18.40 => 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)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__neg__div,axiom,
% 18.55/18.40 ! [V_x,V_y,T_a] :
% 18.55/18.40 ( class_Divides_Oring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 18.55/18.40 => 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)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_le__imp__power__dvd,axiom,
% 18.55/18.40 ! [V_a,V_n,V_m,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__power__le,axiom,
% 18.55/18.40 ! [V_m,V_n,V_y,V_x,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.55/18.40 => 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_power__le__dvd,axiom,
% 18.55/18.40 ! [V_m,V_b,V_n,V_a,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( 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))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 18.55/18.40 => 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)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_div__power,axiom,
% 18.55/18.40 ! [V_n,V_x,V_y,T_a] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_a)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 18.55/18.40 => 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)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__1__iff__1,axiom,
% 18.55/18.40 ! [V_m_2] :
% 18.55/18.40 ( 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))))
% 18.55/18.40 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__dvd__not__less,axiom,
% 18.55/18.40 ! [V_n,V_m] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 18.55/18.40 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 18.55/18.40 ! [V_n_2,V_m_2,V_k_2] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.40 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__diffD,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__diffD1,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_unity__coeff__ex,axiom,
% 18.55/18.40 ! [V_l_2,V_Pa_2,T_b] :
% 18.55/18.40 ( ( class_Rings_Odvd(T_b)
% 18.55/18.40 & class_Rings_Osemiring__0(T_b) )
% 18.55/18.40 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 18.55/18.40 <=> ? [B_x] :
% 18.55/18.40 ( 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))))
% 18.55/18.40 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_inf__period_I4_J,axiom,
% 18.55/18.40 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 18.55/18.40 ( ( class_Rings_Ocomm__ring(T_b)
% 18.55/18.40 & class_Rings_Odvd(T_b) )
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 18.55/18.40 => ! [B_x,B_k] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_inf__period_I3_J,axiom,
% 18.55/18.40 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 18.55/18.40 ( ( class_Rings_Ocomm__ring(T_b)
% 18.55/18.40 & class_Rings_Odvd(T_b) )
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 18.55/18.40 => ! [B_x,B_k] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 <=> 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.40 ( ( class_Divides_Osemiring__div(T_b)
% 18.55/18.40 & class_Int_Onumber(T_b) )
% 18.55/18.40 => ( 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)))
% 18.55/18.40 <=> 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) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__div__div__eq__mult,axiom,
% 18.55/18.40 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_b)
% 18.55/18.40 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.55/18.40 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 18.55/18.40 => ( 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)
% 18.55/18.40 <=> 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) ) ) ) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__div__eq__mult,axiom,
% 18.55/18.40 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.40 ( class_Divides_Osemiring__div(T_b)
% 18.55/18.40 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 18.55/18.40 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 18.55/18.40 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__imp__le,axiom,
% 18.55/18.40 ! [V_n,V_k] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__mult__dvd__cancel1,axiom,
% 18.55/18.40 ! [V_n_2,V_m_2,V_k_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 18.55/18.40 => ( 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)))
% 18.55/18.40 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__cancel,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__power,axiom,
% 18.55/18.40 ! [V_x,V_n,T_a] :
% 18.55/18.40 ( class_Rings_Ocomm__semiring__1(T_a)
% 18.55/18.40 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 18.55/18.40 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__cancel2,axiom,
% 18.55/18.40 ! [V_n_2,V_m_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 18.55/18.40 => ( 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))
% 18.55/18.40 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd__mult__cancel1,axiom,
% 18.55/18.40 ! [V_n_2,V_m_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 18.55/18.40 => ( 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))
% 18.55/18.40 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_irrefl__def,axiom,
% 18.55/18.40 ! [V_r_2,T_b] :
% 18.55/18.40 ( c_Relation_Oirrefl(T_b,V_r_2)
% 18.55/18.40 <=> ! [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)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_Ostrict__monoD,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 18.55/18.40 ( class_Orderings_Oorder(T_b)
% 18.55/18.40 => ( 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)
% 18.55/18.40 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_dvd_OmonoD,axiom,
% 18.55/18.40 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 18.55/18.40 ( class_Orderings_Oorder(T_b)
% 18.55/18.40 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.40 => 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))) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_rp__inv__image__rp,axiom,
% 18.55/18.40 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 18.55/18.40 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 18.55/18.40 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_nat__dvd__iff,axiom,
% 18.55/18.40 ! [V_m_2,V_z_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
% 18.55/18.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 18.55/18.40 => 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))) )
% 18.55/18.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 18.55/18.40 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_zdvd__zdiffD,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 18.55/18.40 ! [V_t_2,V_d_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 18.55/18.40 <=> 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)) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 18.55/18.40 ! [V_t_2,V_d_2] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 18.55/18.40 <=> 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))) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_zdvd__zmod__imp__zdvd,axiom,
% 18.55/18.40 ! [V_n,V_m,V_k] :
% 18.55/18.40 ( 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)))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 18.55/18.40 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_zdvd__zmod,axiom,
% 18.55/18.40 ! [V_n,V_m,V_f] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
% 18.55/18.40 => 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))) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_zdvd__antisym__abs,axiom,
% 18.55/18.40 ! [V_b,V_a] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
% 18.55/18.40 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
% 18.55/18.40 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ).
% 18.55/18.40
% 18.55/18.40 fof(fact_zdvd__antisym__nonneg,axiom,
% 18.55/18.40 ! [V_n,V_m] :
% 18.55/18.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 18.55/18.41 => V_m = V_n ) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__not__zless,axiom,
% 18.55/18.41 ! [V_n,V_m] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
% 18.55/18.41 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__mult__cancel,axiom,
% 18.55/18.41 ! [V_n,V_m,V_k] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__mono,axiom,
% 18.55/18.41 ! [V_t_2,V_m_2,V_k_2] :
% 18.55/18.41 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
% 18.55/18.41 <=> 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__reduce,axiom,
% 18.55/18.41 ! [V_m_2,V_n_2,V_k_2] :
% 18.55/18.41 ( 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))))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__period,axiom,
% 18.55/18.41 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 <=> 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_transfer__int__nat__relations_I4_J,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__int,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__mult__div__cancel,axiom,
% 18.55/18.41 ! [V_m,V_n] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 18.55/18.41 => 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 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zmod__eq__dvd__iff,axiom,
% 18.55/18.41 ! [V_y_2,V_n_2,V_x_2] :
% 18.55/18.41 ( 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)
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd1__eq,axiom,
% 18.55/18.41 ! [V_x_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 18.55/18.41 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_abs__div,axiom,
% 18.55/18.41 ! [V_x,V_y] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_Ostrict__mono__mono,axiom,
% 18.55/18.41 ! [V_f_2,T_b] :
% 18.55/18.41 ( class_Orderings_Oorder(T_b)
% 18.55/18.41 => ( 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)
% 18.55/18.41 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__imp__le,axiom,
% 18.55/18.41 ! [V_n,V_z] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd__imp__le__int,axiom,
% 18.55/18.41 ! [V_d,V_i] :
% 18.55/18.41 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_transfer__nat__int__relations_I4_J,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_zdvd__mult__cancel1,axiom,
% 18.55/18.41 ! [V_n_2,V_m_2] :
% 18.55/18.41 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 18.55/18.41 => ( 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))
% 18.55/18.41 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_int__dvd__iff,axiom,
% 18.55/18.41 ! [V_z_2,V_m_2] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd__int__iff,axiom,
% 18.55/18.41 ! [V_m_2,V_z_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_Ostrict__monoI,axiom,
% 18.55/18.41 ! [V_f_2,T_b] :
% 18.55/18.41 ( class_Orderings_Oorder(T_b)
% 18.55/18.41 => ( ! [B_x,B_y] :
% 18.55/18.41 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) )
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 18.55/18.41 => 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) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OmonoI,axiom,
% 18.55/18.41 ! [V_f_2,T_b] :
% 18.55/18.41 ( class_Orderings_Oorder(T_b)
% 18.55/18.41 => ( ! [B_x,B_y] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 18.55/18.41 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_total__on__def,axiom,
% 18.55/18.41 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.41 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 18.55/18.41 <=> ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.41 => ! [B_xa] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 18.55/18.41 => ( B_x != B_xa
% 18.55/18.41 => ( 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))
% 18.55/18.41 | 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)) ) ) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_inv__image__def,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_CollectI,axiom,
% 18.55/18.41 ! [T_b,V_a_2,V_Pa_2] :
% 18.55/18.41 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__def,axiom,
% 18.55/18.41 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_CollectE,axiom,
% 18.55/18.41 ! [V_Pa_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_CollectD,axiom,
% 18.55/18.41 ! [V_Pa_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_mem__Collect__eq,axiom,
% 18.55/18.41 ! [V_Pa_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.41 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__mem__eq,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__neg__eq,axiom,
% 18.55/18.41 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_set__diff__eq,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Compl__eq,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nitpick_Oprod__def,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_int__ge__less__than2__def,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_int__ge__less__than__def,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__def,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__converse,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__inv__image,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_total__on__converse,axiom,
% 18.55/18.41 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.41 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 18.55/18.41 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 18.55/18.41 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 18.55/18.41 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__iff,axiom,
% 18.55/18.41 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converseI,axiom,
% 18.55/18.41 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converseD,axiom,
% 18.55/18.41 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 18.55/18.41 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converseE,axiom,
% 18.55/18.41 ! [V_r_2,V_yx_2,T_c,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => ~ ! [B_x,B_y] :
% 18.55/18.41 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 18.55/18.41 => ~ 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_RangeI,axiom,
% 18.55/18.41 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Id__on__eqI,axiom,
% 18.55/18.41 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 18.55/18.41 ( V_a_2 = V_b_2
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Id__on__iff,axiom,
% 18.55/18.41 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( V_x_2 = V_y_2
% 18.55/18.41 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__Id__on,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__Id__on,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Id__on__def_H,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__Diff__subset,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_snd__eq__Range,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__iff,axiom,
% 18.55/18.41 ! [V_r_2,T_c,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 18.55/18.41 <=> ? [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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_RangeP__Range__eq,axiom,
% 18.55/18.41 ! [V_x_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Id__onE,axiom,
% 18.55/18.41 ! [V_A_2,V_c_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 18.55/18.41 => ~ ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.41 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_RangeE,axiom,
% 18.55/18.41 ! [V_r_2,T_c,V_b_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 18.55/18.41 => ~ ! [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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_transfer__nat__int__set__cong,axiom,
% 18.55/18.41 ! [V_P_H_2,V_Pa_2] :
% 18.55/18.41 ( ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 18.55/18.41 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.55/18.41 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 18.55/18.41 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_RangeP_Ointros,axiom,
% 18.55/18.41 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 18.55/18.41 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_RangeP_Oequations,axiom,
% 18.55/18.41 ! [V_a2_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 18.55/18.41 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__Collect__split,axiom,
% 18.55/18.41 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_irrefl__diff__Id,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OlessThan__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_i_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OgreaterThan__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_i_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_IdI,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Id__def,axiom,
% 18.55/18.41 ! [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))))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__Id,axiom,
% 18.55/18.41 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OlessThan__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OgreaterThan__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_pair__in__Id__conv,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> V_a_2 = V_b_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_total__on__diff__Id,axiom,
% 18.55/18.41 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeast__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_i_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatMost__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_i_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OatMost__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OatLeast__iff,axiom,
% 18.55/18.41 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 18.55/18.41 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 18.55/18.41 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 18.55/18.41 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 18.55/18.41 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 18.55/18.41 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 18.55/18.41 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 18.55/18.41 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 18.55/18.41 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 18.55/18.41 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) )
% 18.55/18.41 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 18.55/18.41 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__comp__def,axiom,
% 18.55/18.41 ! [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))))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__Collect__split,axiom,
% 18.55/18.41 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__less__Suc2,axiom,
% 18.55/18.41 ! [V_i_2,V_M_2] :
% 18.55/18.41 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 18.55/18.41 => 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))))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__less,axiom,
% 18.55/18.41 ! [V_i_2,V_M_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__compI,axiom,
% 18.55/18.41 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_DomainI,axiom,
% 18.55/18.41 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_O__assoc,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__comp__mono,axiom,
% 18.55/18.41 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__rel__comp,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_R__O__Id,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Id__O__R,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__Id__on,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__mono,axiom,
% 18.55/18.41 ! [V_s_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__converse,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__converse,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__def,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_fst__eq__Domain,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__iff,axiom,
% 18.55/18.41 ! [V_r_2,T_c,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 18.55/18.41 <=> ? [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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__Diff__subset,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__less__Suc,axiom,
% 18.55/18.41 ! [V_i_2,V_M_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 18.55/18.41 => 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))))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_DomainP__Domain__eq,axiom,
% 18.55/18.41 ! [V_x_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_DomainE,axiom,
% 18.55/18.41 ! [V_r_2,T_c,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 18.55/18.41 => ~ ! [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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_pred__comp__rel__comp__eq,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_reduction__pairI,axiom,
% 18.55/18.41 ! [V_S_2,V_R_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_R_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__less__than,axiom,
% 18.55/18.41 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_pred__comp_Ointros,axiom,
% 18.55/18.41 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_DomainP_Ointros,axiom,
% 18.55/18.41 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 18.55/18.41 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__inv__image,axiom,
% 18.55/18.41 ! [V_f_2,T_c,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__lex__prod,axiom,
% 18.55/18.41 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 18.55/18.41 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 18.55/18.41 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__measure,axiom,
% 18.55/18.41 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__comp__self,axiom,
% 18.55/18.41 ! [V_R_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_R_2)
% 18.55/18.41 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__subset,axiom,
% 18.55/18.41 ! [V_p_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_pred__comp_Oequations,axiom,
% 18.55/18.41 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
% 18.55/18.41 <=> ? [B_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 18.55/18.41 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__less,axiom,
% 18.55/18.41 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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__pair__less,axiom,
% 18.55/18.41 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__mlex,axiom,
% 18.55/18.41 ! [V_f_2,V_R_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_R_2)
% 18.55/18.41 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__irrefl,axiom,
% 18.55/18.41 ! [V_a_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => ~ 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__asym,axiom,
% 18.55/18.41 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ~ 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__not__sym,axiom,
% 18.55/18.41 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ~ 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__not__refl,axiom,
% 18.55/18.41 ! [V_a_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => ~ 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__int__ge__less__than,axiom,
% 18.55/18.41 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__int__ge__less__than2,axiom,
% 18.55/18.41 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__acc__iff,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_acc__wfD,axiom,
% 18.55/18.41 ! [V_x_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_DomainP_Oequations,axiom,
% 18.55/18.41 ! [V_a1_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 18.55/18.41 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf,axiom,
% 18.55/18.41 ! [T_b] :
% 18.55/18.41 ( class_Orderings_Owellorder(T_b)
% 18.55/18.41 => 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_reduction__pair__def,axiom,
% 18.55/18.41 ! [V_Pa_2,T_b] :
% 18.55/18.41 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 18.55/18.41 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 <=> ~ ? [B_f] :
% 18.55/18.41 ! [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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__if__measure,axiom,
% 18.55/18.41 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 18.55/18.41 ( ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.55/18.41 => 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))) )
% 18.55/18.41 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wfP__def,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wfP__wf__eq,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wfP__empty,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_accp__wfPD,axiom,
% 18.55/18.41 ! [V_x_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 18.55/18.41 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wfP__accp__iff,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 18.55/18.41 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wfP__subset,axiom,
% 18.55/18.41 ! [V_p_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__in__rel,axiom,
% 18.55/18.41 ! [V_R_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_R_2)
% 18.55/18.41 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_pred__nat__def,axiom,
% 18.55/18.41 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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_reduction__pair__lemma,axiom,
% 18.55/18.41 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 18.55/18.41 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 18.55/18.41 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 18.55/18.41 => 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)) ) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wfP__acyclicP,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__same__fst,axiom,
% 18.55/18.41 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 18.55/18.41 ( ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.55/18.41 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 18.55/18.41 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup1E,axiom,
% 18.55/18.41 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 18.55/18.41 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup1CI,axiom,
% 18.55/18.41 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 18.55/18.41 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 18.55/18.41 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_UnCI,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 18.55/18.41 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_UnE,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__comp__distrib2,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__comp__distrib,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__Un__eq,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__Diff__cancel,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__Diff__cancel2,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__Diff,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__Un,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__max,axiom,
% 18.55/18.41 ! [T_b] :
% 18.55/18.41 ( ( class_Lattices_Osemilattice__sup(T_b)
% 18.55/18.41 & class_Orderings_Olinorder(T_b) )
% 18.55/18.41 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__fun__def,axiom,
% 18.55/18.41 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.41 ( class_Lattices_Olattice(T_b)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup_Oidem,axiom,
% 18.55/18.41 ! [V_a,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__idem,axiom,
% 18.55/18.41 ! [V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup_Ocommute,axiom,
% 18.55/18.41 ! [V_b,V_a,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_inf__sup__aci_I5_J,axiom,
% 18.55/18.41 ! [V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Olattice(T_a)
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__commute,axiom,
% 18.55/18.41 ! [V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup_Oleft__idem,axiom,
% 18.55/18.41 ! [V_b,V_a,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_inf__sup__aci_I8_J,axiom,
% 18.55/18.41 ! [V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Olattice(T_a)
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__left__idem,axiom,
% 18.55/18.41 ! [V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup_Oleft__commute,axiom,
% 18.55/18.41 ! [V_c,V_a,V_b,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_inf__sup__aci_I7_J,axiom,
% 18.55/18.41 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Olattice(T_a)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__left__commute,axiom,
% 18.55/18.41 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup_Oassoc,axiom,
% 18.55/18.41 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_inf__sup__aci_I6_J,axiom,
% 18.55/18.41 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Olattice(T_a)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__assoc,axiom,
% 18.55/18.41 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__apply,axiom,
% 18.55/18.41 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.41 ( class_Lattices_Olattice(T_b)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__absorb,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__commute,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__left__absorb,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__left__commute,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__assoc,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bex__Un,axiom,
% 18.55/18.41 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( ? [B_x] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.55/18.41 <=> ( ? [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.41 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.55/18.41 | ? [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 18.55/18.41 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ball__Un,axiom,
% 18.55/18.41 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( ! [B_x] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.55/18.41 <=> ( ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.55/18.41 & ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup1I1,axiom,
% 18.55/18.41 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 18.55/18.41 ( hBOOL(hAPP(V_A_2,V_x_2))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup1I2,axiom,
% 18.55/18.41 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 18.55/18.41 ( hBOOL(hAPP(V_B_2,V_x_2))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Sup__fin_Oidem,axiom,
% 18.55/18.41 ! [V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Olattice(T_a)
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__mono,axiom,
% 18.55/18.41 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__least,axiom,
% 18.55/18.41 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__absorb2,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__absorb1,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__Un__eq,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__upper2,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__upper1,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_inf__sup__ord_I3_J,axiom,
% 18.55/18.41 ! [V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Olattice(T_a)
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__ge1,axiom,
% 18.55/18.41 ! [V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_inf__sup__ord_I4_J,axiom,
% 18.55/18.41 ! [V_x,V_y,T_a] :
% 18.55/18.41 ( class_Lattices_Olattice(T_a)
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__ge2,axiom,
% 18.55/18.41 ! [V_x,V_y,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_le__iff__sup,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_b)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.55/18.41 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_le__sup__iff,axiom,
% 18.55/18.41 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_b)
% 18.55/18.41 => ( 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))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_le__supI1,axiom,
% 18.55/18.41 ! [V_b,V_a,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_le__supI2,axiom,
% 18.55/18.41 ! [V_a,V_b,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__absorb2,axiom,
% 18.55/18.41 ! [V_y,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__absorb1,axiom,
% 18.55/18.41 ! [V_x,V_y,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_le__supI,axiom,
% 18.55/18.41 ! [V_b,V_x,V_a,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__least,axiom,
% 18.55/18.41 ! [V_z,V_x,V_y,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__mono,axiom,
% 18.55/18.41 ! [V_d,V_b,V_c,V_a,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 18.55/18.41 => 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))) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_le__supE,axiom,
% 18.55/18.41 ! [V_x,V_b,V_a,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 18.55/18.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_less__supI1,axiom,
% 18.55/18.41 ! [V_b,V_a,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_less__supI2,axiom,
% 18.55/18.41 ! [V_a,V_b,V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Osemilattice__sup(T_a)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_image__Un,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_UnI2,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_UnI1,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__iff,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.41 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__Un__eq,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__Un__eq,axiom,
% 18.55/18.41 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__disj__eq,axiom,
% 18.55/18.41 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__acyclic,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_acyclic__subset,axiom,
% 18.55/18.41 ! [V_r_2,V_s_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_acyclic__converse,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 18.55/18.41 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Diff__subset__conv,axiom,
% 18.55/18.41 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Diff__partition,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => 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 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Compl__Diff__eq,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__union__merge,axiom,
% 18.55/18.41 ! [V_S_2,V_R_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__def,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__imp__eq,axiom,
% 18.55/18.41 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_pair__leq__def,axiom,
% 18.55/18.41 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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__union__compatible,axiom,
% 18.55/18.41 ! [V_S_2,V_R_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_R_2)
% 18.55/18.41 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__pred__nat,axiom,
% 18.55/18.41 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Eps__split,axiom,
% 18.55/18.41 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Field__def,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__no__infinite__down__chainE,axiom,
% 18.55/18.41 ! [V_f_2,V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => ~ ! [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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_IdE,axiom,
% 18.55/18.41 ! [V_p_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 18.55/18.41 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__nat__def,axiom,
% 18.55/18.41 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2] :
% 18.55/18.41 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.41 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_someI__ex,axiom,
% 18.55/18.41 ! [T_b,V_Pa_2] :
% 18.55/18.41 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_some__eq__ex,axiom,
% 18.55/18.41 ! [T_b,V_Pa_2] :
% 18.55/18.41 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 18.55/18.41 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_some__eq__trivial,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_some__sym__eq__trivial,axiom,
% 18.55/18.41 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_someI,axiom,
% 18.55/18.41 ! [T_b,V_x_2,V_Pa_2] :
% 18.55/18.41 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_tfl__some,axiom,
% 18.55/18.41 ! [T_b,B_P] :
% 18.55/18.41 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 18.55/18.41 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_exE__some,axiom,
% 18.55/18.41 ! [T_b,V_c_2,V_Pa_2] :
% 18.55/18.41 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 18.55/18.41 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 18.55/18.41 => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Field__converse,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2] :
% 18.55/18.41 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.41 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__Un__eq2,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_mono__Field,axiom,
% 18.55/18.41 ! [V_s_2,V_r_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Field__Un,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Eps__split__eq,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_split__paired__Eps,axiom,
% 18.55/18.41 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_reflcl__set__eq,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_hoare__derivs_OBody,axiom,
% 18.55/18.41 ! [V_Procsa_2,V_Qa_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.41 ( 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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_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_Pa_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_Qa_2)),V_Procsa_2))
% 18.55/18.41 => 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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_less__eq,axiom,
% 18.55/18.41 ! [V_n_2,V_m_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__eq__minimal,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 <=> ! [B_Q] :
% 18.55/18.41 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 18.55/18.41 => ? [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 18.55/18.41 & ! [B_y] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup2E,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup2CI,axiom,
% 18.55/18.41 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 18.55/18.41 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl_Or__into__trancl,axiom,
% 18.55/18.41 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup2I1,axiom,
% 18.55/18.41 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup2I2,axiom,
% 18.55/18.41 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__trancl,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__mono,axiom,
% 18.55/18.41 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__domain,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__converse,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_r__r__into__trancl,axiom,
% 18.55/18.41 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__into__trancl2,axiom,
% 18.55/18.41 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 18.55/18.41 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__trans,axiom,
% 18.55/18.41 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_cut,axiom,
% 18.55/18.41 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 18.55/18.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 18.55/18.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_thin,axiom,
% 18.55/18.41 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 18.55/18.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_weaken,axiom,
% 18.55/18.41 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
% 18.55/18.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_asm,axiom,
% 18.55/18.41 ! [V_Ga_2,V_ts_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2))
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_r__into__trancl_H,axiom,
% 18.55/18.41 ! [V_r_2,V_p_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__range,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__unfold,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__converseI,axiom,
% 18.55/18.41 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.41 ( 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))))
% 18.55/18.41 => 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__converseD,axiom,
% 18.55/18.41 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.41 ( 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))))
% 18.55/18.41 => 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__converse__trancl,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 18.55/18.41 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_less__than__def,axiom,
% 18.55/18.41 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_acyclic__def,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 18.55/18.41 <=> ! [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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Body1,axiom,
% 18.55/18.41 ! [V_pn_2,V_Procsa_2,V_Qa_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.41 ( 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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_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_Pa_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_Qa_2)),V_Procsa_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procsa_2))
% 18.55/18.41 => 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_Pa_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Qa_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_acyclicI,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( ! [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)))
% 18.55/18.41 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__compE,axiom,
% 18.55/18.41 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => ~ ! [B_x,B_y,B_z] :
% 18.55/18.41 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ~ 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_acyclicP__converse,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_emptyE,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insertE,axiom,
% 18.55/18.41 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 18.55/18.41 => ( V_a_2 != V_b_2
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insertCI,axiom,
% 18.55/18.41 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 18.55/18.41 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 18.55/18.41 => V_a_2 = V_b_2 )
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty__subsetI,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__empty__left,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__empty__right,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__is__Un,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__insert__right,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__empty,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Un__insert__left,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Field__insert,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_image__is__empty,axiom,
% 18.55/18.41 ! [V_A_2,V_f_2,T_b,T_c] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_image__empty,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty__is__image,axiom,
% 18.55/18.41 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.41 ( 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)
% 18.55/18.41 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_derivs__insertD,axiom,
% 18.55/18.41 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 18.55/18.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))
% 18.55/18.41 => ( 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))))
% 18.55/18.41 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_hoare__derivs_Oinsert,axiom,
% 18.55/18.41 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 18.55/18.41 ( 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))))
% 18.55/18.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_image__insert,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_image__constant__conv,axiom,
% 18.55/18.41 ! [V_c_2,T_c,T_b,V_A_2] :
% 18.55/18.41 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 => 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)) )
% 18.55/18.41 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_image__constant,axiom,
% 18.55/18.41 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Id__on__empty,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__empty,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__empty__iff,axiom,
% 18.55/18.41 ! [V_r_2,T_b,T_c] :
% 18.55/18.41 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Range__insert,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_all__not__in__conv,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.41 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_ex__in__conv,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.41 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty__iff,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_equals0D,axiom,
% 18.55/18.41 ! [V_a_2,T_b,V_A_2] :
% 18.55/18.41 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insertI1,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__iff,axiom,
% 18.55/18.41 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 18.55/18.41 <=> ( V_a_2 = V_b_2
% 18.55/18.41 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__ident,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 18.55/18.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 18.55/18.41 => ( 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)
% 18.55/18.41 <=> V_A_2 = V_B_2 ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insertI2,axiom,
% 18.55/18.41 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__absorb,axiom,
% 18.55/18.41 ! [V_A_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.41 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_singleton__iff,axiom,
% 18.55/18.41 ! [V_a_2,V_b_2,T_b] :
% 18.55/18.41 ( 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)))))
% 18.55/18.41 <=> V_b_2 = V_a_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_singletonE,axiom,
% 18.55/18.41 ! [V_a_2,V_b_2,T_b] :
% 18.55/18.41 ( 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)))))
% 18.55/18.41 => V_b_2 = V_a_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__singletonD,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( 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)))))
% 18.55/18.41 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 | 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__insertI,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__insertI2,axiom,
% 18.55/18.41 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__mono,axiom,
% 18.55/18.41 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bot__apply,axiom,
% 18.55/18.41 ! [V_x_2,T_c,T_b] :
% 18.55/18.41 ( class_Orderings_Obot(T_b)
% 18.55/18.41 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversepD,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversep_Ointros,axiom,
% 18.55/18.41 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversep_Oequations,axiom,
% 18.55/18.41 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversep__iff,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversep__conversep,axiom,
% 18.55/18.41 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversep__eq,axiom,
% 18.55/18.41 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 18.55/18.41
% 18.55/18.41 fof(fact_singleton__inject,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => V_a_2 = V_b_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__code,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 18.55/18.41 <=> ( V_y_2 = V_x_2
% 18.55/18.41 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_doubleton__eq__iff,axiom,
% 18.55/18.41 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.41 ( 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))))
% 18.55/18.41 <=> ( ( V_a_2 = V_c_2
% 18.55/18.41 & V_b_2 = V_d_2 )
% 18.55/18.41 | ( V_a_2 = V_d_2
% 18.55/18.41 & V_b_2 = V_c_2 ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__commute,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__absorb2,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__not__empty,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty__not__insert,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bot__fun__def,axiom,
% 18.55/18.41 ! [V_x_2,T_c,T_b] :
% 18.55/18.41 ( class_Orderings_Obot(T_b)
% 18.55/18.41 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversep__noteq,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
% 18.55/18.41 <=> V_x_2 != V_y_2 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__empty,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( 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))))
% 18.55/18.41 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Diff__cancel,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Diff__empty,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty__Diff,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Diff__insert,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Diff__insert2,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__Diff__single,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Diff__insert__absorb,axiom,
% 18.55/18.41 ! [V_A_2,V_x_2,T_b] :
% 18.55/18.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__Diff,axiom,
% 18.55/18.41 ! [V_A_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.41 => 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 ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__empty,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__empty__iff,axiom,
% 18.55/18.41 ! [V_r_2,T_c,T_b] :
% 18.55/18.41 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Domain__insert,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__empty__eq,axiom,
% 18.55/18.41 ! [V_Pa_2,T_b] :
% 18.55/18.41 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty__Collect__eq,axiom,
% 18.55/18.41 ! [V_Pa_2,T_b] :
% 18.55/18.41 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 18.55/18.41 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__conv__if,axiom,
% 18.55/18.41 ! [T_b,V_a_2,V_Pa_2] :
% 18.55/18.41 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 18.55/18.41 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 18.55/18.41 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Collect__conv__if2,axiom,
% 18.55/18.41 ! [T_b,V_a_2,V_Pa_2] :
% 18.55/18.41 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 18.55/18.41 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 18.55/18.41 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_singleton__conv,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_singleton__conv2,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_not__psubset__empty,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Field__empty,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_diff__single__insert,axiom,
% 18.55/18.41 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__insert__iff,axiom,
% 18.55/18.41 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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)) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__Collect,axiom,
% 18.55/18.41 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bot__empty__eq,axiom,
% 18.55/18.41 ! [V_x_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_empty__def,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bot__least,axiom,
% 18.55/18.41 ! [V_x,T_a] :
% 18.55/18.41 ( class_Orderings_Obot(T_a)
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__eq__bot__iff,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.41 ( class_Lattices_Obounded__lattice__bot(T_b)
% 18.55/18.41 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 18.55/18.41 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 18.55/18.41 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__bot__right,axiom,
% 18.55/18.41 ! [V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Obounded__lattice__bot(T_a)
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_sup__bot__left,axiom,
% 18.55/18.41 ! [V_x,T_a] :
% 18.55/18.41 ( class_Lattices_Obounded__lattice__bot(T_a)
% 18.55/18.41 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Comp,axiom,
% 18.55/18.41 ! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.41 => ( 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_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_hoare__derivs_OSkip,axiom,
% 18.55/18.41 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_total__on__empty,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__join,axiom,
% 18.55/18.41 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_LoopF,axiom,
% 18.55/18.41 ! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_converse__pred__comp,axiom,
% 18.55/18.41 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__subset,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 18.55/18.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__insert,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 18.55/18.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__image,axiom,
% 18.55/18.41 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_psubset__insert__iff,axiom,
% 18.55/18.41 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 18.55/18.41 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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)) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__Diff__if,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 18.55/18.41 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 18.55/18.41 => 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) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__Diff1,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 18.55/18.41 => 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) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_subset__Compl__self__eq,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__compr,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__compr__raw,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Ass,axiom,
% 18.55/18.41 ! [V_a_2,V_X_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_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_Pa_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_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_insert__def,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_set__empty__eq,axiom,
% 18.55/18.41 ! [V_xo_2,T_b] :
% 18.55/18.41 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_BodyN,axiom,
% 18.55/18.41 ! [V_Ga_2,V_Qa_2,V_pn_2,V_Pa_2,T_b] :
% 18.55/18.41 ( 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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_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_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_weak__Body,axiom,
% 18.55/18.41 ! [V_Qa_2,V_pn_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_conversep__converse__eq,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
% 18.55/18.41 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_the__elem__def,axiom,
% 18.55/18.41 ! [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))))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card_Oempty,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_the__elem__eq,axiom,
% 18.55/18.41 ! [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 ).
% 18.55/18.41
% 18.55/18.41 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 18.55/18.41 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => ( 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)
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__empty,axiom,
% 18.55/18.41 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 18.55/18.41 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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_trancl__empty,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 18.55/18.41 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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bot__empty__eq2,axiom,
% 18.55/18.41 ! [V_y_2,V_x_2,T_c,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_less__by__empty,axiom,
% 18.55/18.41 ! [V_B_2,T_b,V_A_2] :
% 18.55/18.41 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__comp__empty1,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rel__comp__empty2,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2] :
% 18.55/18.41 ( V_a_2 = V_b_2
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 18.55/18.41 ! [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))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 18.55/18.41 ! [V_c_2,V_b_2,V_a_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( V_a_2 = V_b_2
% 18.55/18.41 & V_b_2 = V_c_2 ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 18.55/18.41 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2] :
% 18.55/18.41 ( 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)
% 18.55/18.41 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 18.55/18.41 ! [V_l_2,V_k_2] :
% 18.55/18.41 ( 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)
% 18.55/18.41 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 18.55/18.41 ! [V_l_2,V_k_2] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 18.55/18.41 ! [V_k_2,V_l_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 18.55/18.41 ! [V_a_2,V_b_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 18.55/18.41 ! [V_k_2,V_l_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bot__nat__def,axiom,
% 18.55/18.41 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__no__loop,axiom,
% 18.55/18.41 ! [V_R_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_union__comp__emptyL,axiom,
% 18.55/18.41 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_union__comp__emptyR,axiom,
% 18.55/18.41 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 18.55/18.41 ! [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) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 18.55/18.41 ! [V_a_2,V_b_2] :
% 18.55/18.41 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 18.55/18.41 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2] :
% 18.55/18.41 ( 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))
% 18.55/18.41 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 18.55/18.41 ! [V_b_2,V_a_2] :
% 18.55/18.41 ( 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)
% 18.55/18.41 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 18.55/18.41 ! [V_A_2] :
% 18.55/18.41 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wmin__insertI,axiom,
% 18.55/18.41 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wmax__insertI,axiom,
% 18.55/18.41 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_smin__insertI,axiom,
% 18.55/18.41 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_smax__insertI,axiom,
% 18.55/18.41 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => ( 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))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_bot2E,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wmin__emptyI,axiom,
% 18.55/18.41 ! [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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_smin__emptyI,axiom,
% 18.55/18.41 ! [V_X_2] :
% 18.55/18.41 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 18.55/18.41 => 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)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_max__rpair__set,axiom,
% 18.55/18.41 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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_min__rpair__set,axiom,
% 18.55/18.41 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)) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_min__ext__compat,axiom,
% 18.55/18.41 ! [V_S_2,V_R_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_min__weak__def,axiom,
% 18.55/18.41 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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_flat__lub__def,axiom,
% 18.55/18.41 ! [V_b_2,V_A_2,T_b] :
% 18.55/18.41 ( ( 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)))))
% 18.55/18.41 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 18.55/18.41 & ( ~ 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)))))
% 18.55/18.41 => 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)))))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_max__ext__compat,axiom,
% 18.55/18.41 ! [V_S_2,V_R_2,T_b] :
% 18.55/18.41 ( 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))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_max__ext__wf,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_min__ext__wf,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_max__strict__def,axiom,
% 18.55/18.41 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_max__ext__additive,axiom,
% 18.55/18.41 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_min__strict__def,axiom,
% 18.55/18.41 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_max__weak__def,axiom,
% 18.55/18.41 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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_max__extp__max__ext__eq,axiom,
% 18.55/18.41 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 18.55/18.41 ( 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)
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__Diff__singleton__if,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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)) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__Diff__singleton,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card_Oremove,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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)))))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite_OemptyI,axiom,
% 18.55/18.41 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite_OinsertI,axiom,
% 18.55/18.41 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__imageI,axiom,
% 18.55/18.41 ! [V_h_2,T_c,V_F_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Diff,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Collect__conjI,axiom,
% 18.55/18.41 ! [V_Qa_2,V_Pa_2,T_b] :
% 18.55/18.41 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.41 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) )
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Collect__subsets,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Collect__less__nat,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Collect__le__nat,axiom,
% 18.55/18.41 ! [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)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite_Oequations_I1_J,axiom,
% 18.55/18.41 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__insert,axiom,
% 18.55/18.41 ! [V_A_2,V_a_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 18.55/18.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 18.55/18.41 ! [V_N_2] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 18.55/18.41 <=> ? [B_m] :
% 18.55/18.41 ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__UnI,axiom,
% 18.55/18.41 ! [V_Ga_2,V_F_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Un,axiom,
% 18.55/18.41 ! [V_Ga_2,V_F_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.41 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__subset,axiom,
% 18.55/18.41 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_rev__finite__subset,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Diff2,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__code,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( class_Finite__Set_Ofinite(T_b)
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( class_Finite__Set_Ofinite(T_b)
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 18.55/18.41 ! [V_A_2] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__nat__set__iff__bounded,axiom,
% 18.55/18.41 ! [V_N_2] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 18.55/18.41 <=> ? [B_m] :
% 18.55/18.41 ! [B_x] :
% 18.55/18.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Range,axiom,
% 18.55/18.41 ! [V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__converse,axiom,
% 18.55/18.41 ! [V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 18.55/18.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Domain,axiom,
% 18.55/18.41 ! [V_r_2,T_c,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Field,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__trancl,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 18.55/18.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Collect__disjI,axiom,
% 18.55/18.41 ! [V_Qa_2,V_Pa_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2))))
% 18.55/18.41 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.41 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 18.55/18.41 ! [V_A_2] :
% 18.55/18.41 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 18.55/18.41 <=> 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__surj,axiom,
% 18.55/18.41 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Diff__insert,axiom,
% 18.55/18.41 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 18.55/18.41 ( 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))))
% 18.55/18.41 <=> 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__infinite,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__acyclic__wf,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 18.55/18.41 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 18.55/18.41 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 18.55/18.41 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.41 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__Collect__bounded__ex,axiom,
% 18.55/18.41 ! [V_Qa_2,T_c,V_Pa_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2)))))
% 18.55/18.41 <=> ! [B_y] :
% 18.55/18.41 ( hBOOL(hAPP(V_Pa_2,B_y))
% 18.55/18.41 => 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_Qa_2),B_y)))) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__image__set,axiom,
% 18.55/18.41 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__M__bounded__by__nat,axiom,
% 18.55/18.41 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__eq__0__iff,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.41 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__ge__0__finite,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__insert__le,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__mono,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__seteq,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 => V_A_2 = V_B_2 ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__image__le,axiom,
% 18.55/18.41 ! [V_f_2,T_c,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_psubset__card__mono,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => 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))) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_finite__acyclic__wf__converse,axiom,
% 18.55/18.41 ! [V_r_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 18.55/18.41 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 18.55/18.41 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_nat__seg__image__imp__finite,axiom,
% 18.55/18.41 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__insert__if,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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) )
% 18.55/18.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__insert__disjoint,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__gt__0__iff,axiom,
% 18.55/18.41 ! [V_A_2,T_b] :
% 18.55/18.41 ( 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)))
% 18.55/18.41 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.41 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__Diff__subset,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.41 => 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)) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_diff__card__le__card__Diff,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => 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)))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__psubset,axiom,
% 18.55/18.41 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.41 => ( 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)))
% 18.55/18.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__insert,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => 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)))))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card__Diff1__le,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.41 => 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))) ) ).
% 18.55/18.41
% 18.55/18.41 fof(fact_card_Oinsert,axiom,
% 18.55/18.41 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_wmax__emptyI,axiom,
% 18.55/18.42 ! [V_X_2] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_smax__emptyI,axiom,
% 18.55/18.42 ! [V_Y_2] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 18.55/18.42 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Suc__Diff1,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Diff2__less,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Diff1__less,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Diff__insert,axiom,
% 18.55/18.42 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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)))))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_in__finite__psubset,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__pointwise,axiom,
% 18.55/18.42 ! [V_Qa_2,V_Pa_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 18.55/18.42 => ( ! [B_p] :
% 18.55/18.42 ( 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))))
% 18.55/18.42 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_Pa_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Qa_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
% 18.55/18.42 => ( 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))
% 18.55/18.42 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_Pa_2)),V_c0_2)),V_Qa_2)),V_U_2)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__image__simple_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 18.55/18.42 => 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)))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__one_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__image__simple_Oempty,axiom,
% 18.55/18.42 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.42 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__one_Osingleton,axiom,
% 18.55/18.42 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__image__simple_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_wf__finite__psubset,axiom,
% 18.55/18.42 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__one_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => 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)))))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__one_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__psubset__def,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Nitpick_Owf_H__def,axiom,
% 18.55/18.42 ! [V_r_2,T_b] :
% 18.55/18.42 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 18.55/18.42 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 18.55/18.42 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 18.55/18.42 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__le__Sup,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 18.55/18.42 ! [V_x_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 18.55/18.42 ! [V_x_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 18.55/18.42 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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 ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 18.55/18.42 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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 ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => 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 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => 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 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( ! [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))))))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( ! [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))))))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__insert,axiom,
% 18.55/18.42 ! [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)))))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Suc__eq,axiom,
% 18.55/18.42 ! [V_k_2,V_A_2,T_b] :
% 18.55/18.42 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 18.55/18.42 <=> ? [B_b,B_B] :
% 18.55/18.42 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 18.55/18.42 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 18.55/18.42 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 18.55/18.42 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.42 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_r__into__rtrancl,axiom,
% 18.55/18.42 ! [V_r_2,V_p_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__into__rtrancl,axiom,
% 18.55/18.42 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__rtrancl__absorb,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__trancl__absorb,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__idemp,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__converse,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__Un__rtrancl,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_r__comp__rtrancl__eq,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__idemp__self__comp,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__mono,axiom,
% 18.55/18.42 ! [V_s_2,V_r_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__subset,axiom,
% 18.55/18.42 ! [V_S_2,V_R_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__subset__rtrancl,axiom,
% 18.55/18.42 ! [V_s_2,V_r_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__trans,axiom,
% 18.55/18.42 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 18.55/18.42 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 18.55/18.42 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_in__rtrancl__UnI,axiom,
% 18.55/18.42 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 18.55/18.42 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 18.55/18.42 => 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)))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__unfold__left,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__unfold__right,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__Un__subset,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__empty,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__reflcl,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__reflcl__absorb,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__r__diff__Id,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__eq__or__trancl,axiom,
% 18.55/18.42 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 <=> ( V_x_2 = V_y_2
% 18.55/18.42 | ( V_x_2 != V_y_2
% 18.55/18.42 & 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__into__trancl2,axiom,
% 18.55/18.42 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtranclD,axiom,
% 18.55/18.42 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ( V_a_2 = V_b_2
% 18.55/18.42 | ( V_a_2 != V_b_2
% 18.55/18.42 & 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__into__trancl1,axiom,
% 18.55/18.42 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__rtrancl__trancl,axiom,
% 18.55/18.42 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__trancl__trancl,axiom,
% 18.55/18.42 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__converseI,axiom,
% 18.55/18.42 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => 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)))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__converseD,axiom,
% 18.55/18.42 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.42 ( 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))))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__reflcl,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_reflcl__trancl,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__unfold,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Not__Domain__rtrancl,axiom,
% 18.55/18.42 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 18.55/18.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_acc__downwards__aux,axiom,
% 18.55/18.42 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_acc__downwards,axiom,
% 18.55/18.42 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_wf__insert,axiom,
% 18.55/18.42 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.42 & ~ 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_acyclic__insert,axiom,
% 18.55/18.42 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 18.55/18.42 & ~ 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_pred__nat__trancl__eq__le,axiom,
% 18.55/18.42 ! [V_n_2,V_m_2] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__greaterThanLessThan__int,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_sup__Inf2__distrib,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_sup__Inf1__distrib,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__greaterThanLessThan__int,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Osingleton,axiom,
% 18.55/18.42 ! [V_x_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_greaterThanLessThan__empty,axiom,
% 18.55/18.42 ! [V_k_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Oorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.42 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_sup__Inf__absorb,axiom,
% 18.55/18.42 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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 ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_add__Max__commute,axiom,
% 18.55/18.42 ! [V_k_2,V_N_2,T_b] :
% 18.55/18.42 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_add__Min__commute,axiom,
% 18.55/18.42 ! [V_k_2,V_N_2,T_b] :
% 18.55/18.42 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ivl__disj__un_I4_J,axiom,
% 18.55/18.42 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__greaterThanAtMost,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__greaterThanLessThan,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__greaterThanAtMost__int,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_minus__Max__eq__Min,axiom,
% 18.55/18.42 ! [V_S_2,T_b] :
% 18.55/18.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_minus__Min__eq__Max,axiom,
% 18.55/18.42 ! [V_S_2,T_b] :
% 18.55/18.42 ( class_Groups_Olinordered__ab__group__add(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Osingleton,axiom,
% 18.55/18.42 ! [V_x_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Osingleton,axiom,
% 18.55/18.42 ! [V_x_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_greaterThanAtMost__empty,axiom,
% 18.55/18.42 ! [V_k_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Oorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 18.55/18.42 ! [V_l_2,V_k_2,T_b] :
% 18.55/18.42 ( class_Orderings_Oorder(T_b)
% 18.55/18.42 => ( 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)
% 18.55/18.42 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 18.55/18.42 ! [V_l_2,V_k_2,T_b] :
% 18.55/18.42 ( class_Orderings_Oorder(T_b)
% 18.55/18.42 => ( 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))
% 18.55/18.42 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ivl__disj__un_I20_J,axiom,
% 18.55/18.42 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__greaterThanAtMost,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max__ge,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min__le,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max__in,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min__in,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Oin__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Oin__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__greaterThanLessThan,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max__mono,axiom,
% 18.55/18.42 ! [V_N_2,V_M_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 18.55/18.42 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => 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))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min__antimono,axiom,
% 18.55/18.42 ! [V_N_2,V_M_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 18.55/18.42 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => 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))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min__insert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max__insert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__greaterThanAtMost__int,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Osubset__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Osubset__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min__Un,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max__Un,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ivl__disj__un_I16_J,axiom,
% 18.55/18.42 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Oclosed,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( ! [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))))))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Oclosed,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( ! [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))))))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Osingleton,axiom,
% 18.55/18.42 ! [V_x_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Oin__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Osubset__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Ounion__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__le__Sup,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => 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 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Oclosed,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( ! [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))))))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 18.55/18.42 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 18.55/18.42 | ? [B_x,B_y] :
% 18.55/18.42 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 18.55/18.42 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 18.55/18.42 & 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Plus__conv__if,axiom,
% 18.55/18.42 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.42 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 18.55/18.42 => 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)) )
% 18.55/18.42 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__Plus__iff,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__Plus,axiom,
% 18.55/18.42 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__PlusD_I1_J,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__PlusD_I2_J,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Plus,axiom,
% 18.55/18.42 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Plus__eq__empty__conv,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__one_Oclosed,axiom,
% 18.55/18.42 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( ! [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))))))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__image,axiom,
% 18.55/18.42 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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)))))) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__triv,axiom,
% 18.55/18.42 ! [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 ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__def,axiom,
% 18.55/18.42 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 18.55/18.42 ( ( V_x_2 = V_a_2
% 18.55/18.42 => 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 )
% 18.55/18.42 & ( V_x_2 != V_a_2
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__idem,axiom,
% 18.55/18.42 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 18.55/18.42 ( hAPP(V_f_2,V_x_2) = V_y_2
% 18.55/18.42 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__other,axiom,
% 18.55/18.42 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 18.55/18.42 ( V_z_2 != V_x_2
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__twist,axiom,
% 18.55/18.42 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 18.55/18.42 ( V_a_2 != V_c_2
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__apply,axiom,
% 18.55/18.42 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 18.55/18.42 ( ( V_z_2 = V_x_2
% 18.55/18.42 => 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 )
% 18.55/18.42 & ( V_z_2 != V_x_2
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__same,axiom,
% 18.55/18.42 ! [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 ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__upd,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__idem__iff,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 18.55/18.42 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_map__upd__nonempty,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_image__map__upd,axiom,
% 18.55/18.42 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__gen__delta,axiom,
% 18.55/18.42 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.42 => 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)))) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__timesf,axiom,
% 18.55/18.42 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_of__nat__setprod,axiom,
% 18.55/18.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 18.55/18.42 & class_Rings_Osemiring__1(T_b) )
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_int__setprod,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_of__int__setprod,axiom,
% 18.55/18.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 18.55/18.42 & class_Rings_Oring__1(T_b) )
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__1,axiom,
% 18.55/18.42 ! [V_A_2,T_c,T_b] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_abs__setprod,axiom,
% 18.55/18.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( class_Fields_Olinordered__field(T_b)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 18.55/18.42 ! [V_A_2,V_f_2,T_b] :
% 18.55/18.42 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.42 & class_Groups_Ocomm__monoid__mult(T_b) )
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__zero__iff,axiom,
% 18.55/18.42 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 18.55/18.42 & class_Rings_Ono__zero__divisors(T_c) )
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( 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)
% 18.55/18.42 <=> ? [B_x] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.42 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__zero,axiom,
% 18.55/18.42 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Rings_Ocomm__semiring__1(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ? [B_x] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.42 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Oempty,axiom,
% 18.55/18.42 ! [V_g_2,T_c,T_b] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__empty,axiom,
% 18.55/18.42 ! [V_f_2,T_c,T_b] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_b)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Oinfinite,axiom,
% 18.55/18.42 ! [V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__infinite,axiom,
% 18.55/18.42 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__eq__1__iff,axiom,
% 18.55/18.42 ! [V_f_2,V_F_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.42 => ( 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)
% 18.55/18.42 <=> ! [B_x] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 18.55/18.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 18.55/18.42 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.42 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.42 & class_Groups_Ocomm__monoid__mult(T_b) )
% 18.55/18.42 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Odistrib,axiom,
% 18.55/18.42 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__dividef,axiom,
% 18.55/18.42 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Fields_Ofield__inverse__zero(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_dvd__setprod,axiom,
% 18.55/18.42 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Rings_Ocomm__semiring__1(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__pos__nat__iff,axiom,
% 18.55/18.42 ! [V_f_2,V_S_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( 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)))
% 18.55/18.42 <=> ! [B_x] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__dvd__setprod__subset,axiom,
% 18.55/18.42 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 18.55/18.42 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 & class_Rings_Odvd(T_c) )
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__delta,axiom,
% 18.55/18.42 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.42 => 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) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__delta_H,axiom,
% 18.55/18.42 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.42 => 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) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__constant,axiom,
% 18.55/18.42 ! [V_y_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Oinsert,axiom,
% 18.55/18.42 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__insert,axiom,
% 18.55/18.42 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_map__upd__Some__unfold,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 18.55/18.42 ( 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)
% 18.55/18.42 <=> ( ( V_x_2 = V_a_2
% 18.55/18.42 & V_b_2 = V_y_2 )
% 18.55/18.42 | ( V_x_2 != V_a_2
% 18.55/18.42 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_map__upd__triv,axiom,
% 18.55/18.42 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 18.55/18.42 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_map__upd__eqD1,axiom,
% 18.55/18.42 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => V_x_2 = V_y_2 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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)))))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_empty__upd__none,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Oremove,axiom,
% 18.55/18.42 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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)))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__diff1,axiom,
% 18.55/18.42 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Fields_Ofield(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 18.55/18.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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)) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ran__map__upd,axiom,
% 18.55/18.42 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 18.55/18.42 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__None__restrict,axiom,
% 18.55/18.42 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 18.55/18.42 => 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))))) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ran__def,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__in,axiom,
% 18.55/18.42 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__map__empty,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__out,axiom,
% 18.55/18.42 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__map__insert,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__map__def,axiom,
% 18.55/18.42 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__map__to__empty,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ranI,axiom,
% 18.55/18.42 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 18.55/18.42 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__restrict,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ran__empty,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__fun__upd,axiom,
% 18.55/18.42 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 18.55/18.42 => 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) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fun__upd__restrict__conv,axiom,
% 18.55/18.42 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__complement__singleton__eq,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__upd__same,axiom,
% 18.55/18.42 ! [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))))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 18.55/18.42 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.42 ( ! [B_x] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.42 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 18.55/18.42 ! [V_N_2,V_h_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( ! [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))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 18.55/18.42 ! [V_N_2,V_h_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( ! [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))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Ohom__commute,axiom,
% 18.55/18.42 ! [V_N_2,V_h_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( ! [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))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Ohom__commute,axiom,
% 18.55/18.42 ! [V_N_2,V_h_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( ! [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))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Ohom__commute,axiom,
% 18.55/18.42 ! [V_N_2,V_h_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( ! [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))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__mono__one__left,axiom,
% 18.55/18.42 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 18.55/18.42 => ( ! [B_x] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__mono__one__right,axiom,
% 18.55/18.42 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 18.55/18.42 => ( ! [B_x] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_irrefl__tranclI,axiom,
% 18.55/18.42 ! [V_x_2,V_r_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ~ 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf1I,axiom,
% 18.55/18.42 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 18.55/18.42 ( hBOOL(hAPP(V_A_2,V_x_2))
% 18.55/18.42 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf1E,axiom,
% 18.55/18.42 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 18.55/18.42 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_IntE,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.42 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_IntI,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__Int,axiom,
% 18.55/18.42 ! [V_Ga_2,V_F_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.42 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_restrict__restrict,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_disjoint__iff__not__equal,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> ! [B_x] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.42 => ! [B_xa] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 18.55/18.42 => B_x != B_xa ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__empty__right,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__empty__left,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__bot__right,axiom,
% 18.55/18.42 ! [V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Obounded__lattice__bot(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__bot__left,axiom,
% 18.55/18.42 ! [V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Obounded__lattice__bot(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Collect__conj__eq,axiom,
% 18.55/18.42 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_wf__Int2,axiom,
% 18.55/18.42 ! [V_r_H_2,V_r_2,T_b] :
% 18.55/18.42 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_wf__Int1,axiom,
% 18.55/18.42 ! [V_r_H_2,V_r_2,T_b] :
% 18.55/18.42 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__Int__eq,axiom,
% 18.55/18.42 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_IntD2,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_IntD1,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__iff,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.42 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__Int__distrib,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__Diff,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__Int__distrib2,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__Int2,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_converse__Int,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__min,axiom,
% 18.55/18.42 ! [T_b] :
% 18.55/18.42 ( ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.42 & class_Orderings_Olinorder(T_b) )
% 18.55/18.42 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__fun__def,axiom,
% 18.55/18.42 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf_Oidem,axiom,
% 18.55/18.42 ! [V_a,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__idem,axiom,
% 18.55/18.42 ! [V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf_Ocommute,axiom,
% 18.55/18.42 ! [V_b,V_a,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__aci_I1_J,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__commute,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf_Oleft__idem,axiom,
% 18.55/18.42 ! [V_b,V_a,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__aci_I4_J,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__left__idem,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf_Oleft__commute,axiom,
% 18.55/18.42 ! [V_c,V_a,V_b,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__aci_I3_J,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__left__commute,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf_Oassoc,axiom,
% 18.55/18.42 ! [V_c,V_b,V_a,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__aci_I2_J,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__assoc,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__apply,axiom,
% 18.55/18.42 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__absorb,axiom,
% 18.55/18.42 ! [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 ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__commute,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__left__absorb,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__left__commute,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__assoc,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf1D1,axiom,
% 18.55/18.42 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf1D2,axiom,
% 18.55/18.42 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Oidem,axiom,
% 18.55/18.42 ! [V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_less__infI1,axiom,
% 18.55/18.42 ! [V_b,V_x,V_a,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_less__infI2,axiom,
% 18.55/18.42 ! [V_a,V_x,V_b,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__absorb,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_sup__inf__absorb,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__distrib1,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_sup__inf__distrib1,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__distrib2,axiom,
% 18.55/18.42 ! [V_x,V_z,V_y,T_a] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_sup__inf__distrib2,axiom,
% 18.55/18.42 ! [V_x,V_z,V_y,T_a] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__Un__distrib,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Un__Int__distrib,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__Un__distrib2,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Un__Int__distrib2,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Un__Int__crazy,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Domain__Int__subset,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__mono,axiom,
% 18.55/18.42 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__greatest,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__absorb1,axiom,
% 18.55/18.42 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__absorb2,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__lower2,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__lower1,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__ord_I1_J,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__le1,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__sup__ord_I2_J,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__le2,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_le__iff__inf,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.55/18.42 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_le__inf__iff,axiom,
% 18.55/18.42 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.42 => ( 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)))
% 18.55/18.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.55/18.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_le__infI1,axiom,
% 18.55/18.42 ! [V_b,V_x,V_a,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_le__infI2,axiom,
% 18.55/18.42 ! [V_a,V_x,V_b,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__absorb1,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.55/18.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__absorb2,axiom,
% 18.55/18.42 ! [V_x,V_y,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 18.55/18.42 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_le__infI,axiom,
% 18.55/18.42 ! [V_b,V_a,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__greatest,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__mono,axiom,
% 18.55/18.42 ! [V_d,V_b,V_c,V_a,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_le__infE,axiom,
% 18.55/18.42 ! [V_b,V_a,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Osemilattice__inf(T_a)
% 18.55/18.42 => ( 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)))
% 18.55/18.42 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 18.55/18.42 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Range__Int__subset,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_insert__inter__insert,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_distrib__inf__le,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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)))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_distrib__sup__le,axiom,
% 18.55/18.42 ! [V_z,V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Olattice(T_a)
% 18.55/18.42 => 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)))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__compl__bot,axiom,
% 18.55/18.42 ! [V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_compl__inf__bot,axiom,
% 18.55/18.42 ! [V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_diff__eq,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_compl__sup,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_compl__inf,axiom,
% 18.55/18.42 ! [V_y,V_x,T_a] :
% 18.55/18.42 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__insert__left__if1,axiom,
% 18.55/18.42 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__insert__right__if1,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__insert__left__if0,axiom,
% 18.55/18.42 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 18.55/18.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__insert__right__if0,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 18.55/18.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__insert__left,axiom,
% 18.55/18.42 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 18.55/18.42 => 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)) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__insert__right,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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)) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_image__Int__subset,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__triv,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__disjoint,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Un__Int__assoc__eq,axiom,
% 18.55/18.42 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Un__Diff__Int,axiom,
% 18.55/18.42 ! [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 ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__Un,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__Int,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Compl__disjoint2,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Compl__disjoint,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Compl__Un,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Compl__Int,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__eq,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Diff__Compl,axiom,
% 18.55/18.42 ! [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ivl__disj__int_I14_J,axiom,
% 18.55/18.42 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Oorder(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__Collect,axiom,
% 18.55/18.42 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))
% 18.55/18.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__def,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Oin__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__Sup__absorb,axiom,
% 18.55/18.42 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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 ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_disjoint__eq__subset__Compl,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__greaterThanAtMost,axiom,
% 18.55/18.42 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Int__greaterThanLessThan,axiom,
% 18.55/18.42 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_trancl__Int__subset,axiom,
% 18.55/18.42 ! [V_s_2,V_r_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ivl__disj__int_I10_J,axiom,
% 18.55/18.42 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Oorder(T_b)
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_if__image__distrib,axiom,
% 18.55/18.42 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Osubset__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.42 => 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) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Ounion__idem,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__Un__Int,axiom,
% 18.55/18.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Ounion__inter,axiom,
% 18.55/18.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Un__Int,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Diff__subset__Int,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__one_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__one_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_rtrancl__Int__subset,axiom,
% 18.55/18.42 ! [V_r_2,V_s_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Oinsert,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => 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 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__Un__disjoint,axiom,
% 18.55/18.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Un__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Sup__fin_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Min_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Max_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_wf__Un,axiom,
% 18.55/18.42 ! [V_s_2,V_r_2,T_b] :
% 18.55/18.42 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.42 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Oremove,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.42 => ( ( 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))
% 18.55/18.42 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 18.55/18.42 & ( 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))
% 18.55/18.42 => 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)))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__Sup2__distrib,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))))) ) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__Sup1__distrib,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Odistrib__lattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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))))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card_Ounion__inter__neutral,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( ( ? [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)))
% 18.55/18.42 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__Un,axiom,
% 18.55/18.42 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Fields_Ofield(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( ! [B_x] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 18.55/18.42 => 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))) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Oclosed,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => ( ! [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))))))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_converse__meet,axiom,
% 18.55/18.42 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__nat__def,axiom,
% 18.55/18.42 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2] :
% 18.55/18.42 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.42 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2] :
% 18.55/18.42 ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.42 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.42 => 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))) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf__Int__eq2,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 18.55/18.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( ! [B_x] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod__Un__one,axiom,
% 18.55/18.42 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 18.55/18.42 => ( ! [B_x] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fold__Un__disjoint,axiom,
% 18.55/18.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => ( 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))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf2I,axiom,
% 18.55/18.42 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf2E,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 18.55/18.42 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf2D1,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_inf2D2,axiom,
% 18.55/18.42 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fold__image__empty,axiom,
% 18.55/18.42 ! [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 ).
% 18.55/18.42
% 18.55/18.42 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 18.55/18.42 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fold__image__distrib,axiom,
% 18.55/18.42 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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)) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fold__image__insert,axiom,
% 18.55/18.42 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Oab__semigroup__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.42 => 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)) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_Oeq__fold,axiom,
% 18.55/18.42 ! [V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_setprod_OF__eq,axiom,
% 18.55/18.42 ! [V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fold__image__Un__Int,axiom,
% 18.55/18.42 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.42 => 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))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_image__eq__fold__image,axiom,
% 18.55/18.42 ! [V_f_2,T_c,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card_Oeq__fold__g,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__def,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_comm__monoid__big_OF__eq,axiom,
% 18.55/18.42 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 18.55/18.42 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => 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) )
% 18.55/18.42 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_fold__image__Un__one,axiom,
% 18.55/18.42 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 18.55/18.42 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 18.55/18.42 => ( ! [B_x] :
% 18.55/18.42 ( 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)))
% 18.55/18.42 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Inf__fin_Ohom__commute,axiom,
% 18.55/18.42 ! [V_N_2,V_h_2,T_b] :
% 18.55/18.42 ( class_Lattices_Olattice(T_b)
% 18.55/18.42 => ( ! [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))
% 18.55/18.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.42 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.42 => 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)) ) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 18.55/18.42 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 18.55/18.42 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.42 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_sequence__trans,axiom,
% 18.55/18.42 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 18.55/18.42 ( ! [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)))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_card__Pow,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => 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)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_escape,axiom,
% 18.55/18.42 ! [V_Qa_2,V_c_2,V_Ga_2,T_b,V_Pa_2] :
% 18.55/18.42 ( ! [B_Z,B_s] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 18.55/18.42 => 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_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
% 18.55/18.42 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_PowI,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__empty,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__not__empty,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__bottom,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_PowD,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 18.55/18.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__iff,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 18.55/18.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__top,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__mono,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Un__Pow__subset,axiom,
% 18.55/18.42 ! [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)))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Cantors__paradox,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ~ ? [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) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_image__Pow__surj,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 18.55/18.42 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 18.55/18.42 => 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) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__insert,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__Int__eq,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_image__Pow__mono,axiom,
% 18.55/18.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 => 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))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__def,axiom,
% 18.55/18.42 ! [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)) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__Pow__iff,axiom,
% 18.55/18.42 ! [V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 18.55/18.42 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Pow__Compl,axiom,
% 18.55/18.42 ! [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))))) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_Powp__Pow__eq,axiom,
% 18.55/18.42 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.42 ( 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))
% 18.55/18.42 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__empty__induct,axiom,
% 18.55/18.42 ! [V_Pa_2,V_A_2,T_b] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.42 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 18.55/18.42 => ( ! [B_a,B_A] :
% 18.55/18.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 18.55/18.42 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 18.55/18.42 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 18.55/18.42 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_ivl__disj__un_I19_J,axiom,
% 18.55/18.42 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.42 ( class_Orderings_Olinorder(T_b)
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 18.55/18.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 18.55/18.42 => 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) ) ) ) ).
% 18.55/18.42
% 18.55/18.42 fof(fact_finite__atLeastAtMost,axiom,
% 18.55/18.42 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__atLeastAtMost__int,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__add__atLeastAtMost,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__Suc__atLeastAtMost,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 18.55/18.43 ! [V_n_2,V_m_2] :
% 18.55/18.43 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 18.55/18.43 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2] :
% 18.55/18.43 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 18.55/18.43 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastatMost__empty__iff,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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))
% 18.55/18.43 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastatMost__empty__iff2,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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)
% 18.55/18.43 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastatMost__empty,axiom,
% 18.55/18.43 ! [V_a_2,V_b_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastatMost__subset__iff,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 18.55/18.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastAtMost__singleton_H,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( V_a_2 = V_b_2
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 18.55/18.43 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> ( V_a_2 = V_b_2
% 18.55/18.43 & V_b_2 = V_c_2 ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastAtMost__singleton,axiom,
% 18.55/18.43 ! [V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__uminus__atLeastAtMost,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 18.55/18.43 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__atLeastAtMost,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastAtMostSuc__conv,axiom,
% 18.55/18.43 ! [V_n_2,V_m_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Powp__mono,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__atLeastAtMost,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastatMost__psubset__iff,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 18.55/18.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 18.55/18.43 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 18.55/18.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I22_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I16_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I13_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I12_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_simp__from__to,axiom,
% 18.55/18.43 ! [V_i_2,V_j_2] :
% 18.55/18.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__atLeastAtMost__int,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I5_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I8_J,axiom,
% 18.55/18.43 ! [V_B_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 18.55/18.43 => 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))) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I6_J,axiom,
% 18.55/18.43 ! [V_A_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 18.55/18.43 => 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I3_J,axiom,
% 18.55/18.43 ! [V_B_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xa] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 18.55/18.43 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 18.55/18.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ex__nat__less,axiom,
% 18.55/18.43 ! [V_Pa_2,V_n_2] :
% 18.55/18.43 ( ? [B_m] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 18.55/18.43 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_all__nat__less,axiom,
% 18.55/18.43 ! [V_Pa_2,V_n_2] :
% 18.55/18.43 ( ! [B_m] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I4_J,axiom,
% 18.55/18.43 ! [V_A_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( B_x != V_t_2
% 18.55/18.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I3_J,axiom,
% 18.55/18.43 ! [V_A_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xa] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 18.55/18.43 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 18.55/18.43 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I5_J,axiom,
% 18.55/18.43 ! [V_A_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 18.55/18.43 => 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I7_J,axiom,
% 18.55/18.43 ! [V_B_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 18.55/18.43 => 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))) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I4_J,axiom,
% 18.55/18.43 ! [V_B_2,V_t_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( B_x != V_t_2
% 18.55/18.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I6_J,axiom,
% 18.55/18.43 ! [V_t_2,V_B_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I8_J,axiom,
% 18.55/18.43 ! [V_t_2,V_A_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_wf__lenlex,axiom,
% 18.55/18.43 ! [V_r_2,T_b] :
% 18.55/18.43 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.43 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_periodic__finite__ex,axiom,
% 18.55/18.43 ! [V_Pa_2,V_d_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 18.55/18.43 => ( ! [B_x,B_k] :
% 18.55/18.43 ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.55/18.43 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 18.55/18.43 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I5_J,axiom,
% 18.55/18.43 ! [V_t_2,V_B_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_wf__lex,axiom,
% 18.55/18.43 ! [V_r_2,T_b] :
% 18.55/18.43 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.43 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I7_J,axiom,
% 18.55/18.43 ! [V_t_2,V_A_2,V_D_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 18.55/18.43 ! [V_x_2,V_y_2,V_c_2] :
% 18.55/18.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 18.55/18.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.43 => 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))) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 18.55/18.43 => 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__atLeastLessThan,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__eq__iff,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 18.55/18.43 => ( 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)
% 18.55/18.43 <=> ( V_a_2 = V_c_2
% 18.55/18.43 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( 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)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 18.55/18.43 => V_a_2 = V_c_2 ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( 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)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 18.55/18.43 => V_b_2 = V_d_2 ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_all__nat__less__eq,axiom,
% 18.55/18.43 ! [V_Pa_2,V_n_2] :
% 18.55/18.43 ( ! [B_m] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ex__nat__less__eq,axiom,
% 18.55/18.43 ! [V_Pa_2,V_n_2] :
% 18.55/18.43 ( ? [B_m] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 18.55/18.43 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan0,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__atLeastLessThan,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__Suc__atLeastLessThan,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__empty,axiom,
% 18.55/18.43 ! [V_a_2,V_b_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__empty__iff,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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))
% 18.55/18.43 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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)
% 18.55/18.43 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__subset__iff,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 18.55/18.43 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I17_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__diff,axiom,
% 18.55/18.43 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I11_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__add__atLeastLessThan,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__singleton,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I21_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThan__add__Un,axiom,
% 18.55/18.43 ! [V_k_2,V_j_2,V_i_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I15_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__atLeastLessThan,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_subset__card__intvl__is__intvl,axiom,
% 18.55/18.43 ! [V_k_2,V_A_2] :
% 18.55/18.43 ( 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)))))
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I9_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__uminus__atLeastLessThan,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThanSuc,axiom,
% 18.55/18.43 ! [V_n_2,V_m_2] :
% 18.55/18.43 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I15_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I6_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I3_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I18_J,axiom,
% 18.55/18.43 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_wf__lexn,axiom,
% 18.55/18.43 ! [V_n_2,V_r_2,T_b] :
% 18.55/18.43 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.43 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I9_J,axiom,
% 18.55/18.43 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I9_J,axiom,
% 18.55/18.43 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__atLeastLessThan__int,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lexn_Osimps_I1_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__add__int__atLeastLessThan,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__atLeastLessThan__int,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_aset_I10_J,axiom,
% 18.55/18.43 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( ~ 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)))
% 18.55/18.43 => ~ 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_bset_I10_J,axiom,
% 18.55/18.43 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 18.55/18.43 => ! [B_x] :
% 18.55/18.43 ( ! [B_xa] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ! [B_xb] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 18.55/18.43 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 18.55/18.43 => ( ~ 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)))
% 18.55/18.43 => ~ 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__atMost,axiom,
% 18.55/18.43 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atMost__eq__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 18.55/18.43 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeast0AtMost,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__atMost,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atMost__Suc,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atMost__iff,axiom,
% 18.55/18.43 ! [V_k_2,V_i_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oord(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atMost__subset__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atMost__0,axiom,
% 18.55/18.43 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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__atLeastAtMostR1,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__atLeastAtMostL1,axiom,
% 18.55/18.43 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I9_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I3_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I1_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 18.55/18.43 ! [V_u_2] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I7_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.43 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__lessThan,axiom,
% 18.55/18.43 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__eq__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 18.55/18.43 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_folding__one__idem_Oidem,axiom,
% 18.55/18.43 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 18.55/18.43 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 18.55/18.43 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__lessThan,axiom,
% 18.55/18.43 ! [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 ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeast0LessThan,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__0,axiom,
% 18.55/18.43 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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__Suc,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__Suc__atMost,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__iff,axiom,
% 18.55/18.43 ! [V_k_2,V_i_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oord(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__subset__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__strict__subset__iff,axiom,
% 18.55/18.43 ! [V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_folding__one__idem_Oin__idem,axiom,
% 18.55/18.43 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.43 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_single__Diff__lessThan,axiom,
% 18.55/18.43 ! [V_k_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I8_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I4_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I2_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I2_J,axiom,
% 18.55/18.43 ! [V_u_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 18.55/18.43 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.43 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I10_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.43 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.43 => 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) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_arith__series__int,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_arith__series__nat,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_arith__series__general,axiom,
% 18.55/18.43 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Rings_Ocomm__semiring__1(T_b)
% 18.55/18.43 => 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)))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__abs,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__abs__ge__zero,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__eq__0__iff,axiom,
% 18.55/18.43 ! [V_f_2,V_F_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.43 => ( 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)
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 18.55/18.43 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__negf,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Oab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__0,axiom,
% 18.55/18.43 ! [V_A_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__commute,axiom,
% 18.55/18.43 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_of__int__setsum,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Rings_Oring__1(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_int__setsum,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_of__nat__setsum,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Rings_Osemiring__1(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__product,axiom,
% 18.55/18.43 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Rings_Osemiring__0(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__left__distrib,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Rings_Osemiring__0(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__right__distrib,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 18.55/18.43 ( class_Rings_Osemiring__0(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__addf,axiom,
% 18.55/18.43 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__subtractf,axiom,
% 18.55/18.43 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Oab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_abs__setsum__abs,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__divide__distrib,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Fields_Ofield(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__infinite,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Oinfinite,axiom,
% 18.55/18.43 ! [V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__empty,axiom,
% 18.55/18.43 ! [V_f_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Oempty,axiom,
% 18.55/18.43 ! [V_g_2,T_c,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Odistrib,axiom,
% 18.55/18.43 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__eq__setsum,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 18.55/18.43 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 18.55/18.43 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 18.55/18.43 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 18.55/18.43 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__eq__Suc0__iff,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.43 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 18.55/18.43 & ! [B_xa] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 18.55/18.43 => ( B_x != B_xa
% 18.55/18.43 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__eq__1__iff,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( 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)
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.43 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 18.55/18.43 & ! [B_xa] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 18.55/18.43 => ( B_x != B_xa
% 18.55/18.43 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__add__nat__ivl,axiom,
% 18.55/18.43 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__diff__nat__ivl,axiom,
% 18.55/18.43 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Groups_Oab__group__add(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 18.55/18.43 ! [V_k_2,V_f_2] :
% 18.55/18.43 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__delta_H,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.43 => 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) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.43 => 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) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__delta,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.43 => 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) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 18.55/18.43 => 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) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__setsum__restrict,axiom,
% 18.55/18.43 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_d)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__constant,axiom,
% 18.55/18.43 ! [V_A_2,V_y_2,T_c,T_b] :
% 18.55/18.43 ( class_Rings_Osemiring__1(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__lessThan__Suc,axiom,
% 18.55/18.43 ! [V_n_2,V_f_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__atMost__Suc,axiom,
% 18.55/18.43 ! [V_n_2,V_f_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Oinsert,axiom,
% 18.55/18.43 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__insert,axiom,
% 18.55/18.43 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__Un__Int,axiom,
% 18.55/18.43 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__diff,axiom,
% 18.55/18.43 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Oab__group__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Oeq__fold,axiom,
% 18.55/18.43 ! [V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_OF__eq,axiom,
% 18.55/18.43 ! [V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__diff__nat,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 18.55/18.43 ! [V_k_2,V_f_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__head__upt__Suc,axiom,
% 18.55/18.43 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__head__Suc,axiom,
% 18.55/18.43 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__restrict__set_H,axiom,
% 18.55/18.43 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__restrict__set,axiom,
% 18.55/18.43 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__image__gen,axiom,
% 18.55/18.43 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Oinsert__remove,axiom,
% 18.55/18.43 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => 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)))))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__Un__disjoint,axiom,
% 18.55/18.43 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__Un,axiom,
% 18.55/18.43 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Oab__group__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__diff1__nat,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__Un__nat,axiom,
% 18.55/18.43 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__op__ivl__Suc,axiom,
% 18.55/18.43 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 18.55/18.43 => 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) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__cl__ivl__Suc,axiom,
% 18.55/18.43 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 18.55/18.43 => 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) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__head,axiom,
% 18.55/18.43 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__ub__add__nat,axiom,
% 18.55/18.43 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 => ( 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))))
% 18.55/18.43 => 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)))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__cases,axiom,
% 18.55/18.43 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Oremove,axiom,
% 18.55/18.43 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => 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)))))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__diff1_H,axiom,
% 18.55/18.43 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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)))))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__diff1,axiom,
% 18.55/18.43 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Oab__group__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__diff1__ring,axiom,
% 18.55/18.43 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Rings_Oring(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_geometric__sum,axiom,
% 18.55/18.43 ! [V_n_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Fields_Ofield(T_b)
% 18.55/18.43 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_gauss__sum,axiom,
% 18.55/18.43 ! [V_n_2,T_b] :
% 18.55/18.43 ( class_Rings_Ocomm__semiring__1(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__natinterval__difff,axiom,
% 18.55/18.43 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 18.55/18.43 ( class_Groups_Oab__group__add(T_b)
% 18.55/18.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => 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)))) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.43 ( ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.43 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__mono2,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.43 => ( ! [B_b] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 18.55/18.43 => 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))) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__multicount,axiom,
% 18.55/18.43 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 18.55/18.43 => 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 )
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_b] :
% 18.55/18.43 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 & class_Groups_Ocomm__monoid__mult(T_b) )
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.43 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 & class_Groups_Ocomm__monoid__mult(T_b) )
% 18.55/18.43 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__bounded,axiom,
% 18.55/18.43 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 18.55/18.43 & class_Rings_Osemiring__1(T_c) )
% 18.55/18.43 => ( ! [B_i] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 18.55/18.43 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 18.55/18.43 => 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__Un__zero,axiom,
% 18.55/18.43 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 18.55/18.43 => 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__mono3,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 18.55/18.43 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 18.55/18.43 => 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))) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__multicount__gen,axiom,
% 18.55/18.43 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 18.55/18.43 => 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) )
% 18.55/18.43 => 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) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__nonneg__leq__bound,axiom,
% 18.55/18.43 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 18.55/18.43 => ( ! [B_i] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 18.55/18.43 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__nonneg__0,axiom,
% 18.55/18.43 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 18.55/18.43 => ( ! [B_i] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 18.55/18.43 => ( 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)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 18.55/18.43 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_sum__diff__distrib,axiom,
% 18.55/18.43 ! [V_n_2,V_Pa_2,V_Qa_2] :
% 18.55/18.43 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x)))
% 18.55/18.43 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Qa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__mono__zero__left,axiom,
% 18.55/18.43 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 18.55/18.43 => 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) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__mono__zero__right,axiom,
% 18.55/18.43 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 18.55/18.43 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 18.55/18.43 => 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) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__subset__induct,axiom,
% 18.55/18.43 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.43 => ( ! [B_a,B_F] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 18.55/18.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 18.55/18.43 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_setsum__strict__mono,axiom,
% 18.55/18.43 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.43 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 18.55/18.43 => 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))) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__intrel__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2] :
% 18.55/18.43 ( 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))))
% 18.55/18.43 <=> 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atMost__Int__atLeast,axiom,
% 18.55/18.43 ! [V_n_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 18.55/18.43 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 18.55/18.43 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.43 & class_Groups_Ocomm__monoid__mult(T_b) )
% 18.55/18.43 => ( V_A_2 = V_B_2
% 18.55/18.43 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 18.55/18.43 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 18.55/18.43 => 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) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeast__eq__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 18.55/18.43 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__Id,axiom,
% 18.55/18.43 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__Un,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__empty,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__Int__subset,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__closed__trancl,axiom,
% 18.55/18.43 ! [V_X_2,V_r_2,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__mono,axiom,
% 18.55/18.43 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Un__Image,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__Id__on,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeast__iff,axiom,
% 18.55/18.43 ! [V_k_2,V_i_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oord(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeast__subset__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_rev__ImageI,axiom,
% 18.55/18.43 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__iff,axiom,
% 18.55/18.43 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.43 & 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_wfE__pf,axiom,
% 18.55/18.43 ! [V_A_2,V_R_2,T_b] :
% 18.55/18.43 ( c_Wellfounded_Owf(T_b,V_R_2)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__subset__eq,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 <=> 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))))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Compl__lessThan,axiom,
% 18.55/18.43 ! [V_k_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Compl__atLeast,axiom,
% 18.55/18.43 ! [V_k_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I14_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I8_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__atLeastAtMostR2,axiom,
% 18.55/18.43 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__atLeastAtMostL2,axiom,
% 18.55/18.43 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I6_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__uminus__atMost,axiom,
% 18.55/18.43 ! [V_x_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__uminus__atLeast,axiom,
% 18.55/18.43 ! [V_x_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeast__Suc,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__singleton__iff,axiom,
% 18.55/18.43 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 18.55/18.43 ( 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))))))
% 18.55/18.43 <=> 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__singleton,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_of__int,axiom,
% 18.55/18.43 ! [V_j_2,V_i_2,T_b] :
% 18.55/18.43 ( class_Rings_Oring__1(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_One__int__def,axiom,
% 18.55/18.43 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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_mult,axiom,
% 18.55/18.43 ! [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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_minus,axiom,
% 18.55/18.43 ! [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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Zero__int__def,axiom,
% 18.55/18.43 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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_int__def,axiom,
% 18.55/18.43 ! [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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_add,axiom,
% 18.55/18.43 ! [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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_nat,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_less,axiom,
% 18.55/18.43 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 18.55/18.43 ( 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)))))))
% 18.55/18.43 <=> 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_le,axiom,
% 18.55/18.43 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 18.55/18.43 ( 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)))))))
% 18.55/18.43 <=> 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_eq__Abs__Integ,axiom,
% 18.55/18.43 ! [V_z_2] :
% 18.55/18.43 ~ ! [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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_greaterThan__Suc,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I12_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_greaterThan__eq__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 18.55/18.43 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_greaterThan__iff,axiom,
% 18.55/18.43 ! [V_k_2,V_i_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oord(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_greaterThan__subset__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Compl__greaterThan,axiom,
% 18.55/18.43 ! [V_k_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Compl__atMost,axiom,
% 18.55/18.43 ! [V_k_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_atLeast__Suc__greaterThan,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I7_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I11_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__uminus__greaterThan,axiom,
% 18.55/18.43 ! [V_x_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__uminus__lessThan,axiom,
% 18.55/18.43 ! [V_x_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__int_I5_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Oorder(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I1_J,axiom,
% 18.55/18.43 ! [V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ivl__disj__un_I13_J,axiom,
% 18.55/18.43 ! [V_u_2,V_l_2,T_b] :
% 18.55/18.43 ( class_Orderings_Olinorder(T_b)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ImageE,axiom,
% 18.55/18.43 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 18.55/18.43 => ~ ! [B_x] :
% 18.55/18.43 ( 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))
% 18.55/18.43 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__conv__nat__seg__image,axiom,
% 18.55/18.43 ! [V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 <=> ? [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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__eq__singleton__conv,axiom,
% 18.55/18.43 ! [V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 <=> ? [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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__dom__body,axiom,
% 18.55/18.43 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_domIff,axiom,
% 18.55/18.43 ! [V_m_2,T_c,V_a_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 18.55/18.43 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_domI,axiom,
% 18.55/18.43 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 18.55/18.43 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_insert__dom,axiom,
% 18.55/18.43 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 18.55/18.43 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__restrict,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__eq__empty__conv,axiom,
% 18.55/18.43 ! [V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__empty,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__def,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__minus,axiom,
% 18.55/18.43 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 18.55/18.43 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__if,axiom,
% 18.55/18.43 ! [V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__fun__upd,axiom,
% 18.55/18.43 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 18.55/18.43 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 18.55/18.43 => 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)))) )
% 18.55/18.43 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_dom__override__on,axiom,
% 18.55/18.43 ! [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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__class__nondisjoint,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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)))))))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_subset__equiv__class,axiom,
% 18.55/18.43 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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))))))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__comp__eq,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => 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 ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_comp__equivI,axiom,
% 18.55/18.43 ! [V_A_2,V_r_2,T_b] :
% 18.55/18.43 ( 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
% 18.55/18.43 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 18.55/18.43 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_override__on__apply__notin,axiom,
% 18.55/18.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_override__on__apply__in,axiom,
% 18.55/18.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_override__on__emptyset,axiom,
% 18.55/18.43 ! [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 ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__class__self,axiom,
% 18.55/18.43 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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)))))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_override__on__def,axiom,
% 18.55/18.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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) )
% 18.55/18.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__class__eq,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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))
% 18.55/18.43 => 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)))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_eq__equiv__class,axiom,
% 18.55/18.43 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 18.55/18.43 ( 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))))
% 18.55/18.43 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_eq__equiv__class__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 18.55/18.43 => ( 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))))
% 18.55/18.43 <=> 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__class__eq__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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))
% 18.55/18.43 <=> ( 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))))
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__class__subset,axiom,
% 18.55/18.43 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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))
% 18.55/18.43 => 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)))))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_eq__equiv__class__iff2,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 18.55/18.43 => ( 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)
% 18.55/18.43 <=> 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_singleton__quotient,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__eqI,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__empty,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__is__empty2,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( 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)
% 18.55/18.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__is__empty,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__disj,axiom,
% 18.55/18.43 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => ( V_X_2 = V_Y_2
% 18.55/18.43 | 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotientI,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__eq__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 18.55/18.43 => ( V_X_2 = V_Y_2
% 18.55/18.43 <=> 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)) ) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotientE,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ~ ! [B_x] :
% 18.55/18.43 ( 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))))
% 18.55/18.43 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_equiv__imp__dvd__card,axiom,
% 18.55/18.43 ! [V_k_2,V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.43 => ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__quotient__disjoint,axiom,
% 18.55/18.43 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( 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)
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__empty,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__uminus,axiom,
% 18.55/18.43 ! [V_A_2,T_b] :
% 18.55/18.43 ( class_Groups_Oordered__ab__group__add(T_b)
% 18.55/18.43 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__diff,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__strict__subset,axiom,
% 18.55/18.43 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__id2,axiom,
% 18.55/18.43 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__def,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.43 => ! [B_xa] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 18.55/18.43 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 18.55/18.43 => B_x = B_xa ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__onD,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 18.55/18.43 => V_x_2 = V_y_2 ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__iff,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 18.55/18.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 18.55/18.43 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__contraD,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( V_x_2 != V_y_2
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 18.55/18.43 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_subset__inj__on,axiom,
% 18.55/18.43 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.43 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__Int,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 => ( 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)
% 18.55/18.43 <=> V_A_2 = V_B_2 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__image,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__imageD,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 18.55/18.43 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 18.55/18.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__iff__surj,axiom,
% 18.55/18.43 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 18.55/18.43 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => ( ? [B_f] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 18.55/18.43 & 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)) )
% 18.55/18.43 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__surj__inj,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( 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)))
% 18.55/18.43 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_endo__inj__surj,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 18.55/18.43 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__image__Int,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_eq__card__imp__inj__on,axiom,
% 18.55/18.43 ! [V_f_2,T_c,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( 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)
% 18.55/18.43 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__iff__eq__card,axiom,
% 18.55/18.43 ! [V_f_2,T_c,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 <=> 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__image__set__diff,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_pigeonhole,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__fun__updI,axiom,
% 18.55/18.43 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__bij__eq,axiom,
% 18.55/18.43 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.43 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__insert,axiom,
% 18.55/18.43 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 18.55/18.43 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 & ~ 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))))))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__Un,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.43 & 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__iff__card__le,axiom,
% 18.55/18.43 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.43 => ( ? [B_f] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 18.55/18.43 & 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)) )
% 18.55/18.43 <=> 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_card__inj__on__le,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__diff1,axiom,
% 18.55/18.43 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 18.55/18.43 ( 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)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_the__inv__into__into,axiom,
% 18.55/18.43 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.43 => 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)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_quotient__def,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_fold__graph__permute__diff,axiom,
% 18.55/18.43 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 18.55/18.43 ( class_Groups_Oab__semigroup__mult(T_b)
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 18.55/18.43 => 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)) ) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SUP1__I,axiom,
% 18.55/18.43 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__add__nat,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__Some,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__Suc,axiom,
% 18.55/18.43 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_finite__UN,axiom,
% 18.55/18.43 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_fold__graph__imp__finite,axiom,
% 18.55/18.43 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 18.55/18.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_fold__graph_OemptyI,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_empty__fold__graphE,axiom,
% 18.55/18.43 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 => V_x_2 = V_z_2 ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SUP1__iff,axiom,
% 18.55/18.43 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.43 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__UN,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_swap__inj__on,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_fold__graph_OinsertI,axiom,
% 18.55/18.43 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 18.55/18.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Image__eq__UN,axiom,
% 18.55/18.43 ! [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))))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_the__inv__into__f__eq,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_the__inv__into__f__f,axiom,
% 18.55/18.43 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => 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 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_inj__on__the__inv__into,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_the__inv__into__onto,axiom,
% 18.55/18.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => 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 ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_fold__graph__insert__swap,axiom,
% 18.55/18.43 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 18.55/18.43 ( class_Groups_Oab__semigroup__mult(T_b)
% 18.55/18.43 => ( 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))
% 18.55/18.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 18.55/18.43 => 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))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_the__inv__into__def,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Diff1__fold__graph,axiom,
% 18.55/18.43 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_f__the__inv__into__f,axiom,
% 18.55/18.43 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.43 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 18.55/18.43 => 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 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__I,axiom,
% 18.55/18.43 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__Pow__subset,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__eq__UN,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_converse__UNION,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_rel__comp__UNION__distrib,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_rel__comp__UNION__distrib2,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_ball__UN,axiom,
% 18.55/18.43 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.43 ( ! [B_x] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.43 => ! [B_xa] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 18.55/18.43 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__le__add__shift,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Id__on__def,axiom,
% 18.55/18.43 ! [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)))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SUP__commute,axiom,
% 18.55/18.43 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 18.55/18.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I9_J,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I9_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__UN__flatten,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__le__eq__Un0,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SUP__le__iff,axiom,
% 18.55/18.43 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 18.55/18.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.43 => ( 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))
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_less__SUP__iff,axiom,
% 18.55/18.43 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 18.55/18.43 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.43 & class_Orderings_Olinorder(T_b) )
% 18.55/18.43 => ( 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)))
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__iff,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 18.55/18.43 ( 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)))
% 18.55/18.43 <=> ? [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.43 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SUP__const,axiom,
% 18.55/18.43 ! [V_M_2,T_b,V_A_2,T_c] :
% 18.55/18.43 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UNION__empty__conv_I2_J,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( 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))
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.43 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__constant,axiom,
% 18.55/18.43 ! [V_c_2,T_c,T_b,V_A_2] :
% 18.55/18.43 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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 ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__empty2,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UNION__empty__conv_I1_J,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.43 ( 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)
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.43 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__subset__iff,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 18.55/18.43 ( 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))
% 18.55/18.43 <=> ! [B_x] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I10_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_image__UN,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I10_J,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__Un,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__Un__distrib,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I5_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I4_J,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I5_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__UN__distrib,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I4_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_Int__UN__distrib2,axiom,
% 18.55/18.43 ! [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))) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SUPR__apply,axiom,
% 18.55/18.43 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 18.55/18.43 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I6_J,axiom,
% 18.55/18.43 ! [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) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I6_J,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_SUP__subset,axiom,
% 18.55/18.43 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.43 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_le__SUPI,axiom,
% 18.55/18.43 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 18.55/18.43 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 18.55/18.43 => 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))) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__insert__distrib,axiom,
% 18.55/18.43 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 18.55/18.43 => 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)) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__upper,axiom,
% 18.55/18.43 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.43 => 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))) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__absorb,axiom,
% 18.55/18.43 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 18.55/18.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 18.55/18.43 => 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) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I1_J,axiom,
% 18.55/18.43 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 18.55/18.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__singleton,axiom,
% 18.55/18.43 ! [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 ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I1_J,axiom,
% 18.55/18.43 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 18.55/18.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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))) )
% 18.55/18.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I2_J,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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 )
% 18.55/18.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__extend__simps_I3_J,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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 )
% 18.55/18.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I2_J,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__simps_I3_J,axiom,
% 18.55/18.43 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.43 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) )
% 18.55/18.43 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.43 => 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)) ) ) ).
% 18.55/18.43
% 18.55/18.43 fof(fact_UN__insert,axiom,
% 18.55/18.43 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_minus__int__def,axiom,
% 18.55/18.44 ! [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))))))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__equiv__class2,axiom,
% 18.55/18.44 ! [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] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 18.55/18.44 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 18.55/18.44 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 18.55/18.44 => 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) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__equiv__class,axiom,
% 18.55/18.44 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SUP2__I,axiom,
% 18.55/18.44 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Rep__Integ__inject,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2] :
% 18.55/18.44 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 18.55/18.44 <=> V_x_2 = V_y_2 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Rep__Integ__inverse,axiom,
% 18.55/18.44 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_congruent2__implies__congruent,axiom,
% 18.55/18.44 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 18.55/18.44 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_congruent2D,axiom,
% 18.55/18.44 ! [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] :
% 18.55/18.44 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 18.55/18.44 => ( 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))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_congruentD,axiom,
% 18.55/18.44 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 18.55/18.44 => ( 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))
% 18.55/18.44 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_congruent2__implies__congruent__UN,axiom,
% 18.55/18.44 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 18.55/18.44 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 18.55/18.44 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_nat__def,axiom,
% 18.55/18.44 ! [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)))))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__equiv__class__inject,axiom,
% 18.55/18.44 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 18.55/18.44 => ( 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)
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => ! [B_y] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 18.55/18.44 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 18.55/18.44 => 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)) ) ) )
% 18.55/18.44 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__equiv__class__type2,axiom,
% 18.55/18.44 ! [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] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 18.55/18.44 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 18.55/18.44 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ( ! [B_x1] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 18.55/18.44 => ! [B_x2] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 18.55/18.44 => 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)) ) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__equiv__class__type,axiom,
% 18.55/18.44 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SUP2__iff,axiom,
% 18.55/18.44 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> ? [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1Set_Ointros,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_ran__restrictD,axiom,
% 18.55/18.44 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => ? [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.44 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_compl__unique,axiom,
% 18.55/18.44 ! [V_y,V_x,T_a] :
% 18.55/18.44 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 18.55/18.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 18.55/18.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UNIV__I,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__lessThan__UNIV,axiom,
% 18.55/18.44 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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__atMost__UNIV,axiom,
% 18.55/18.44 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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__atLeast__UNIV,axiom,
% 18.55/18.44 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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_injD,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 18.55/18.44 => V_x_2 = V_y_2 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__eq,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 18.55/18.44 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__int,axiom,
% 18.55/18.44 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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_equiv__intrel,axiom,
% 18.55/18.44 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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__UNIV,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Finite__Set_Ofinite(T_b)
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_infinite__UNIV__nat,axiom,
% 18.55/18.44 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__option__UNIV,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__Plus__UNIV__iff,axiom,
% 18.55/18.44 ! [T_c,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__fun__UNIVD2,axiom,
% 18.55/18.44 ! [T_c,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__Prod__UNIV,axiom,
% 18.55/18.44 ! [T_c,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 18.55/18.44 => 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)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_infinite__UNIV__int,axiom,
% 18.55/18.44 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_range__composition,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UNIV__option__conv,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UNIV__not__empty,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inf__top__left,axiom,
% 18.55/18.44 ! [V_x,T_a] :
% 18.55/18.44 ( class_Lattices_Obounded__lattice__top(T_a)
% 18.55/18.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inf__top__right,axiom,
% 18.55/18.44 ! [V_x,T_a] :
% 18.55/18.44 ( class_Lattices_Obounded__lattice__top(T_a)
% 18.55/18.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inf__eq__top__iff,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,T_b] :
% 18.55/18.44 ( class_Lattices_Obounded__lattice__top(T_b)
% 18.55/18.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 18.55/18.44 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 18.55/18.44 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Int__UNIV__left,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Int__UNIV__right,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_sup__top__left,axiom,
% 18.55/18.44 ! [V_x,T_a] :
% 18.55/18.44 ( class_Lattices_Obounded__lattice__top(T_a)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_sup__top__right,axiom,
% 18.55/18.44 ! [V_x,T_a] :
% 18.55/18.44 ( class_Lattices_Obounded__lattice__top(T_a)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_subset__UNIV,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Un__UNIV__right,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Un__UNIV__left,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_top__greatest,axiom,
% 18.55/18.44 ! [V_x,T_a] :
% 18.55/18.44 ( class_Orderings_Otop(T_a)
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UNIV__Plus__UNIV,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UNIV__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_top__apply,axiom,
% 18.55/18.44 ! [V_x_2,T_c,T_b] :
% 18.55/18.44 ( class_Orderings_Otop(T_b)
% 18.55/18.44 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_card__UNIV__unit,axiom,
% 18.55/18.44 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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Pow__UNIV,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1Set__nonempty,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 18.55/18.44 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_empty__fold1SetE,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rangeI,axiom,
% 18.55/18.44 ! [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))))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_range__eqI,axiom,
% 18.55/18.44 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 18.55/18.44 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 18.55/18.44 => 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))))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Diff__UNIV,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__image__eq__iff,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( 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)
% 18.55/18.44 <=> V_A_2 = V_B_2 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Compl__UNIV__eq,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Compl__empty__eq,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__compl,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 18.55/18.44 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Compl__partition2,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Compl__partition,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Domain__rtrancl,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Range__rtrancl,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Domain__Id,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 18.55/18.44 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 18.55/18.44 <=> V_x_2 = V_y_2 ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Range__Id,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__Collect__not,axiom,
% 18.55/18.44 ! [V_Pa_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))))
% 18.55/18.44 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SUP__UN__eq,axiom,
% 18.55/18.44 ! [V_x_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__range__imageI,axiom,
% 18.55/18.44 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 18.55/18.44 ( 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)))))
% 18.55/18.44 => 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))))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_nat__of,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_the__inv__f__f,axiom,
% 18.55/18.44 ! [V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__fun__UNIVD1,axiom,
% 18.55/18.44 ! [T_c,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__of__nat,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Nat_Osemiring__char__0(T_b)
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_dom__const,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_atLeast__0,axiom,
% 18.55/18.44 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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__fun,axiom,
% 18.55/18.44 ! [T_d,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_compl__bot__eq,axiom,
% 18.55/18.44 ! [T_a] :
% 18.55/18.44 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_compl__top__eq,axiom,
% 18.55/18.44 ! [T_a] :
% 18.55/18.44 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.44 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_sup__compl__top,axiom,
% 18.55/18.44 ! [V_x,T_a] :
% 18.55/18.44 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_compl__sup__top,axiom,
% 18.55/18.44 ! [V_x,T_a] :
% 18.55/18.44 ( class_Lattices_Oboolean__algebra(T_a)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__graph,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__image__mem__iff,axiom,
% 18.55/18.44 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_range__ex1__eq,axiom,
% 18.55/18.44 ! [V_b_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( 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)))))
% 18.55/18.44 <=> ? [B_x] :
% 18.55/18.44 ( V_b_2 = hAPP(V_f_2,B_x)
% 18.55/18.44 & ! [B_y] :
% 18.55/18.44 ( V_b_2 = hAPP(V_f_2,B_y)
% 18.55/18.44 => B_y = B_x ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__UNIV__inj__surj,axiom,
% 18.55/18.44 ! [V_f_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__UNIV__surj__inj,axiom,
% 18.55/18.44 ! [V_f_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__image__subset__iff,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_image__Int,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_image__set__diff,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_surj__Compl__image__subset,axiom,
% 18.55/18.44 ! [V_A_2,V_f_2,T_b,T_c] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => 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)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_lex__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_of__nat__inverse,axiom,
% 18.55/18.44 ! [V_y_2] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 18.55/18.44 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1Set__sing,axiom,
% 18.55/18.44 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> V_a_2 = V_b_2 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__range__updI,axiom,
% 18.55/18.44 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( 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)))))
% 18.55/18.44 => 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))))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__UN__finite__eq,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__singleton,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__UNIV__card__ge__0,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 => 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))))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_card__UNIV__bool,axiom,
% 18.55/18.44 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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__image__Compl__subset,axiom,
% 18.55/18.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_greaterThan__0,axiom,
% 18.55/18.44 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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SUP__UN__eq2,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__finite2__subset,axiom,
% 18.55/18.44 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 18.55/18.44 ( ! [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)))
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__finite2__eq,axiom,
% 18.55/18.44 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 18.55/18.44 ( ! [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)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__finite__subset,axiom,
% 18.55/18.44 ! [V_C_2,V_A_2,T_b] :
% 18.55/18.44 ( ! [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))
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_top1I,axiom,
% 18.55/18.44 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Integ__def,axiom,
% 18.55/18.44 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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_iso__tuple__UNIV__I,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Rep__Integ,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_equivp__equiv,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 18.55/18.44 <=> 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition__Integ,axiom,
% 18.55/18.44 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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_equivp__transp,axiom,
% 18.55/18.44 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_equivp__symp,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_equivp__reflp,axiom,
% 18.55/18.44 ! [V_x_2,V_R_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 18.55/18.44 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_equivp__def,axiom,
% 18.55/18.44 ! [V_R_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 18.55/18.44 <=> ! [B_x,B_y] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 18.55/18.44 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_identity__equivp,axiom,
% 18.55/18.44 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition_OAbs__image,axiom,
% 18.55/18.44 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 18.55/18.44 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition_ORep__range,axiom,
% 18.55/18.44 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 18.55/18.44 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 18.55/18.44 => 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 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition_ORep__inject,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 18.55/18.44 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 18.55/18.44 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 18.55/18.44 <=> V_x_2 = V_y_2 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition_ORep__inverse,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 18.55/18.44 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 18.55/18.44 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition__code__numeral,axiom,
% 18.55/18.44 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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition_ORep,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 18.55/18.44 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition_OAbs__inverse,axiom,
% 18.55/18.44 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 18.55/18.44 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 18.55/18.44 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_type__definition_OAbs__inject,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 18.55/18.44 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 18.55/18.44 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 18.55/18.44 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__vimage__singleton,axiom,
% 18.55/18.44 ! [V_a_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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))))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 18.55/18.44 ! [V_R_2,V_p_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 18.55/18.44 => 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)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimageI,axiom,
% 18.55/18.44 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 18.55/18.44 ( hAPP(V_f_2,V_a_2) = V_b_2
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__Diff,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_image__vimage__subset,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_wf__exp,axiom,
% 18.55/18.44 ! [V_R_2,V_n_2,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_funpow__mult,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__commute,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__1,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_funpow__swap1,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__code,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 18.55/18.44 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__ident,axiom,
% 18.55/18.44 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__Compl,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__Collect__eq,axiom,
% 18.55/18.44 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__Un,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__mono,axiom,
% 18.55/18.44 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__Int,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__empty,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__UN,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__UNIV,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_surj__image__vimage__eq,axiom,
% 18.55/18.44 ! [V_A_2,V_f_2,T_b,T_c] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => 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 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__eq,axiom,
% 18.55/18.44 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 18.55/18.44 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimageD,axiom,
% 18.55/18.44 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimageI2,axiom,
% 18.55/18.44 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__imp__rtrancl,axiom,
% 18.55/18.44 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rtrancl__power,axiom,
% 18.55/18.44 ! [V_R_2,V_p_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 18.55/18.44 <=> ? [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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_relpow_Osimps_I2_J,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__add,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_relpow_Osimps_I1_J,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__singleton__eq,axiom,
% 18.55/18.44 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 18.55/18.44 ( 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))))))
% 18.55/18.44 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__insert,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__vimageD,axiom,
% 18.55/18.44 ! [V_F_2,V_h_2,T_c,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__subsetD,axiom,
% 18.55/18.44 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_image__vimage__eq,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__vimageI,axiom,
% 18.55/18.44 ! [V_h_2,T_c,V_F_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__vimage__image__eq,axiom,
% 18.55/18.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__0__E,axiom,
% 18.55/18.44 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => V_x_2 = V_y_2 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__0__I,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__const,axiom,
% 18.55/18.44 ! [T_c,V_A_2,V_c_2,T_b] :
% 18.55/18.44 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.44 => 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)) )
% 18.55/18.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__Suc__I,axiom,
% 18.55/18.44 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__Suc__I2,axiom,
% 18.55/18.44 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__eq__UN,axiom,
% 18.55/18.44 ! [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))))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__subsetI,axiom,
% 18.55/18.44 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__if,axiom,
% 18.55/18.44 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 18.55/18.44 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 18.55/18.44 => 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)) )
% 18.55/18.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 18.55/18.44 => 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 ) ) )
% 18.55/18.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 18.55/18.44 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 18.55/18.44 => 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) )
% 18.55/18.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_trancl__power,axiom,
% 18.55/18.44 ! [V_R_2,V_p_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 18.55/18.44 <=> ? [B_n] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 18.55/18.44 & 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_funpow__code__def,axiom,
% 18.55/18.44 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__E,axiom,
% 18.55/18.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.44 => V_x_2 != V_z_2 )
% 18.55/18.44 => ~ ! [B_y,B_m] :
% 18.55/18.44 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ~ 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__E2,axiom,
% 18.55/18.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.44 => V_x_2 != V_z_2 )
% 18.55/18.44 => ~ ! [B_y,B_m] :
% 18.55/18.44 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 18.55/18.44 => ( 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))
% 18.55/18.44 => ~ 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))) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 18.55/18.44 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.44 & class_Groups_Ocomm__monoid__mult(T_b) )
% 18.55/18.44 => ( V_A_2 = V_B_2
% 18.55/18.44 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 18.55/18.44 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 18.55/18.44 => 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) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_max__extp_Oequations,axiom,
% 18.55/18.44 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 18.55/18.44 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 18.55/18.44 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 18.55/18.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 18.55/18.44 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 & ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 18.55/18.44 => ? [B_xa] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 18.55/18.44 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_max__ext_Ointros,axiom,
% 18.55/18.44 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 18.55/18.44 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 18.55/18.44 => ? [B_xa] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 18.55/18.44 & 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)) ) )
% 18.55/18.44 => 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))) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_conseq2,axiom,
% 18.55/18.44 ! [V_Qa_2,V_Q_H_2,V_c_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.44 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.44 => ( ! [B_Z,B_s] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 18.55/18.44 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) )
% 18.55/18.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_conseq1,axiom,
% 18.55/18.44 ! [V_Pa_2,V_Qa_2,V_c_2,V_P_H_2,V_Ga_2,T_b] :
% 18.55/18.44 ( 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_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.44 => ( ! [B_Z,B_s] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 18.55/18.44 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 18.55/18.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_insert__fold1SetE,axiom,
% 18.55/18.44 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ~ ! [B_a,B_A] :
% 18.55/18.44 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1Set_Oequations,axiom,
% 18.55/18.44 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> ? [B_a,B_A] :
% 18.55/18.44 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 18.55/18.44 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 18.55/18.44 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_image__split__eq__Sigma,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__Un,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Groups_Oab__semigroup__mult(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => 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)) ) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SigmaI,axiom,
% 18.55/18.44 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__comp__subset__Sigma,axiom,
% 18.55/18.44 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => ( 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))))
% 18.55/18.44 => 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)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_swap__product,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__singleton,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__singleton__def,axiom,
% 18.55/18.44 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 18.55/18.44 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 18.55/18.44 => 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 ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__cartesian__product,axiom,
% 18.55/18.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.44 => 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)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_trancl__subset__Sigma,axiom,
% 18.55/18.44 ! [V_A_2,V_r_2,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => 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)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__empty1,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Times__empty,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__empty2,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__cartesian__product,axiom,
% 18.55/18.44 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__Un__distrib2,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Times__Un__distrib1,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__Un__distrib1,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod__cartesian__product,axiom,
% 18.55/18.44 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_b)
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_card__cartesian__product,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Compl__Times__UNIV2,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Compl__Times__UNIV1,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Times__eq__cancel2,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 18.55/18.44 => ( 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))
% 18.55/18.44 <=> V_A_2 = V_B_2 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_equiv__type,axiom,
% 18.55/18.44 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.44 => 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)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__Int__distrib1,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Times__Int__distrib1,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__Int__distrib2,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Id__on__subset__Times,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__Diff__distrib1,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Times__Diff__distrib1,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__Diff__distrib2,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UNIV__Times__UNIV,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SigmaE2,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SigmaD2,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SigmaD1,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_mem__Sigma__iff,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__one_Oeq__fold,axiom,
% 18.55/18.44 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_card__cartesian__product__singleton,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Times__subset__cancel2,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 18.55/18.44 => ( 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))))
% 18.55/18.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Image__subset,axiom,
% 18.55/18.44 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__cartesian__productD2,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__cartesian__productD1,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Collect__split,axiom,
% 18.55/18.44 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SetCompr__Sigma__eq,axiom,
% 18.55/18.44 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Qa_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fst__image__times,axiom,
% 18.55/18.44 ! [V_A_2,T_c,T_b,V_B_2] :
% 18.55/18.44 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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)) )
% 18.55/18.44 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_snd__image__times,axiom,
% 18.55/18.44 ! [V_B_2,T_c,T_b,V_A_2] :
% 18.55/18.44 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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)) )
% 18.55/18.44 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_trancl__subset__Field2,axiom,
% 18.55/18.44 ! [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))))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sup__fin_OF__eq,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Olattice(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Inf__fin_OF__eq,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Olattice(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Min_OF__eq,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Max_OF__eq,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_insert__times__insert,axiom,
% 18.55/18.44 ! [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)))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__equiv__class,axiom,
% 18.55/18.44 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( 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))))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__Times__distrib,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__def,axiom,
% 18.55/18.44 ! [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))))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__belowI,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__quotient,axiom,
% 18.55/18.44 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( 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))))
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_below__fold1__iff,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Ofold1__belowI,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__insert__idem,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__below__iff,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( 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))
% 18.55/18.44 <=> ? [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__Un2,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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)) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__strict__below__iff,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( 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))
% 18.55/18.44 <=> ? [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_strict__below__fold1__iff,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_trancl__subset__Sigma__aux,axiom,
% 18.55/18.44 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ( 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))))
% 18.55/18.44 => ( V_a_2 = V_b_2
% 18.55/18.44 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__insert,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Groups_Oab__semigroup__mult(T_b)
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__antimono,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => 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))) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_semilattice__big_OF__eq,axiom,
% 18.55/18.44 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.44 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 18.55/18.44 ( class_Rings_Osemiring__0(T_d)
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => 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))))))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_image__id,axiom,
% 18.55/18.44 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_surj__id,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__id,axiom,
% 18.55/18.44 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__on__id,axiom,
% 18.55/18.44 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_id__apply,axiom,
% 18.55/18.44 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 18.55/18.44
% 18.55/18.44 fof(fact_id__def,axiom,
% 18.55/18.44 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_apfst__id,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_apsnd__id,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_of__int__eq__id,axiom,
% 18.55/18.44 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_funpow_Osimps_I1_J,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_split__Pair,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__reindex__id,axiom,
% 18.55/18.44 ! [V_B_2,V_f_2,T_b,T_c] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod__reindex__id,axiom,
% 18.55/18.44 ! [V_B_2,V_f_2,T_b,T_c] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 18.55/18.44 ! [V_A_2,V_I_2,T_c,T_b] :
% 18.55/18.44 ? [B_f] :
% 18.55/18.44 ( 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))
% 18.55/18.44 & 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod__Sigma,axiom,
% 18.55/18.44 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_d)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__Sigma,axiom,
% 18.55/18.44 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__add(T_d)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__image__Sigma,axiom,
% 18.55/18.44 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_d)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_card__SigmaI,axiom,
% 18.55/18.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__in,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( class_Groups_Oab__semigroup__mult(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => ( ! [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))))))
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__SigmaI,axiom,
% 18.55/18.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_a] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_hom__fold1__commute,axiom,
% 18.55/18.44 ! [V_N_2,V_h_2,T_b] :
% 18.55/18.44 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 18.55/18.44 => ( ! [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))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.44 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SigmaE,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ~ ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => ! [B_y] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 18.55/18.44 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__surj,axiom,
% 18.55/18.44 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__imageI,axiom,
% 18.55/18.44 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__simp,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__ident,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fst__map__pair,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_snd__prod__fun,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair_Oidentity,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_apsnd__def,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_apfst__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair_Oid,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__surj__on,axiom,
% 18.55/18.44 ! [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] :
% 18.55/18.44 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 18.55/18.44 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_wf__map__pair__image,axiom,
% 18.55/18.44 ! [V_f_2,T_c,V_r_2,T_b] :
% 18.55/18.44 ( c_Wellfounded_Owf(T_b,V_r_2)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__inj__on,axiom,
% 18.55/18.44 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_prod__fun__imageE,axiom,
% 18.55/18.44 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ~ ! [B_x,B_y] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ~ 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__def,axiom,
% 18.55/18.44 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 <=> ( 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))))
% 18.55/18.44 & ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__Id__on,axiom,
% 18.55/18.44 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__converse,axiom,
% 18.55/18.44 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 18.55/18.44 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__rtrancl,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__empty,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__Un,axiom,
% 18.55/18.44 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__Id,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__Int,axiom,
% 18.55/18.44 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__onD,axiom,
% 18.55/18.44 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__onD1,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( 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))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__onD2,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 => ( 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))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__comp__subset,axiom,
% 18.55/18.44 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__reflcl,axiom,
% 18.55/18.44 ! [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))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_reflp__def,axiom,
% 18.55/18.44 ! [V_r_2,T_b] :
% 18.55/18.44 ( c_Predicate_Oreflp(T_b,V_r_2)
% 18.55/18.44 <=> 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__onI,axiom,
% 18.55/18.44 ! [V_A_2,V_r_2,T_b] :
% 18.55/18.44 ( 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))))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => 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)) )
% 18.55/18.44 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_reflpE,axiom,
% 18.55/18.44 ! [V_x_2,V_r_2,T_b] :
% 18.55/18.44 ( c_Predicate_Oreflp(T_b,V_r_2)
% 18.55/18.44 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod__pos__nat,axiom,
% 18.55/18.44 ! [V_f_2,V_S_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 18.55/18.44 => 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))) )
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 18.55/18.44 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 18.55/18.44 => ( ! [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))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 18.55/18.44 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Rep__Integ__induct,axiom,
% 18.55/18.44 ! [V_Pa_2,V_y_2] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 18.55/18.44 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 18.55/18.44 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Rep__Integ__cases,axiom,
% 18.55/18.44 ! [V_y_2] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 18.55/18.44 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => hAPP(V_g_2,B_x) = V_z_2 )
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem__remove,axiom,
% 18.55/18.44 ! [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))))) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem__insert,axiom,
% 18.55/18.44 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 18.55/18.44 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 18.55/18.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 18.55/18.44 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem__inf,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.44 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem__sup,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__sup(T_b)
% 18.55/18.44 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Image__Int__eq,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 18.55/18.44 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_pigeonhole__infinite,axiom,
% 18.55/18.44 ! [V_f_2,T_c,V_A_2,T_b] :
% 18.55/18.44 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 18.55/18.44 => ? [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 & ~ 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)))))) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valued__Id__on,axiom,
% 18.55/18.44 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valued__rel__pow,axiom,
% 18.55/18.44 ! [V_n_2,V_R_2,T_b] :
% 18.55/18.44 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valued__subset,axiom,
% 18.55/18.44 ! [V_s_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 18.55/18.44 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valued__rel__comp,axiom,
% 18.55/18.44 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 18.55/18.44 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 18.55/18.44 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valued__Id,axiom,
% 18.55/18.44 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valuedD,axiom,
% 18.55/18.44 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 18.55/18.44 => ( 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))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => V_y_2 = V_z_2 ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valued__def,axiom,
% 18.55/18.44 ! [V_r_2,T_c,T_b] :
% 18.55/18.44 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 18.55/18.44 <=> ! [B_x,B_y] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ! [B_z] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => B_y = B_z ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_single__valued__confluent,axiom,
% 18.55/18.44 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 18.55/18.44 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 => ( 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)))
% 18.55/18.44 | 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))) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_refl__on__def_H,axiom,
% 18.55/18.44 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.44 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.44 <=> ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 18.55/18.44 => 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)) )
% 18.55/18.44 & ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Abs__Integ__induct,axiom,
% 18.55/18.44 ! [V_x_2,V_Pa_2] :
% 18.55/18.44 ( ! [B_y] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 18.55/18.44 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 18.55/18.44 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Powp__def,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 18.55/18.44 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_ball__empty,axiom,
% 18.55/18.44 ! [V_Pa_2,T_b,B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_congruent__def,axiom,
% 18.55/18.44 ! [V_f_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Abs__Integ__cases,axiom,
% 18.55/18.44 ! [V_x_2] :
% 18.55/18.44 ~ ! [B_y] :
% 18.55/18.44 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 18.55/18.44 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__UN__I,axiom,
% 18.55/18.44 ! [V_B_2,T_c,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_a] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_triples__valid__Suc,axiom,
% 18.55/18.44 ! [V_n_2,V_ts_2,T_b] :
% 18.55/18.44 ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2))
% 18.55/18.44 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 18.55/18.44 => ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2))
% 18.55/18.44 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__on__diff__nat,axiom,
% 18.55/18.44 ! [V_k_2,V_N_2] :
% 18.55/18.44 ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_wfP__SUP,axiom,
% 18.55/18.44 ! [T_b,V_r_2,T_c] :
% 18.55/18.44 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 18.55/18.44 => ( ! [B_i,B_j] :
% 18.55/18.44 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 18.55/18.44 => 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)) )
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_hoare__valids__def,axiom,
% 18.55/18.44 ! [V_ts_2,V_Ga_2,T_b] :
% 18.55/18.44 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2)
% 18.55/18.44 <=> ! [B_n] :
% 18.55/18.44 ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
% 18.55/18.44 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 18.55/18.44 => ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2))
% 18.55/18.44 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__map__freshness,axiom,
% 18.55/18.44 ! [V_f_2,T_c,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 18.55/18.44 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 18.55/18.44 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__Times,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__SucD,axiom,
% 18.55/18.44 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 18.55/18.44 ( 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)
% 18.55/18.44 => ? [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 & 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 18.55/18.44 ! [V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair_Ocompositionality,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair__compose,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_map__pair_Ocomp,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__on__imageI,axiom,
% 18.55/18.44 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 18.55/18.44 ( 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)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_comp__inj__on,axiom,
% 18.55/18.44 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.44 => ( 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))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_comp__inj__on__iff,axiom,
% 18.55/18.44 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.44 => ( 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))
% 18.55/18.44 <=> 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__comp,axiom,
% 18.55/18.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_inj__on__imageI2,axiom,
% 18.55/18.44 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 18.55/18.44 ( 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)
% 18.55/18.44 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_id__o,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__id,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__eq__id__dest,axiom,
% 18.55/18.44 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 18.55/18.44 ( 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)
% 18.55/18.44 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_vimage__compose,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_apfst__compose,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_apsnd__compose,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__assoc,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__apply,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__eq__dest,axiom,
% 18.55/18.44 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 18.55/18.44 ( 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)
% 18.55/18.44 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__eq__elim,axiom,
% 18.55/18.44 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 18.55/18.44 ( 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)
% 18.55/18.44 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_comp__cong,axiom,
% 18.55/18.44 ! [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] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__upd__comp,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_o__eq__dest__lhs,axiom,
% 18.55/18.44 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 18.55/18.44 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 18.55/18.44 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_K__record__comp,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_funpow__add,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_comp__funpow,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_funpow_Osimps_I2_J,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_comp__surj,axiom,
% 18.55/18.44 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_image__compose,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__reindex,axiom,
% 18.55/18.44 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__add(T_d)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod__reindex,axiom,
% 18.55/18.44 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_d)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod__reindex__cong,axiom,
% 18.55/18.44 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_d)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.44 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 18.55/18.44 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 18.55/18.44 => 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) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum_Oreindex,axiom,
% 18.55/18.44 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod_Oreindex,axiom,
% 18.55/18.44 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_the__inv__into__comp,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 18.55/18.44 => ( 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))))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__image__reindex,axiom,
% 18.55/18.44 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Oab__semigroup__mult(T_d)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Nitpick_Onum__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Nitpick_Odenom__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fst__comp__map__pair,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_snd__comp__map__pair,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_UN__o,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_split__comp,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_number__of__code__numeral__def,axiom,
% 18.55/18.44 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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_int__of__def,axiom,
% 18.55/18.44 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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Loop__sound__lemma,axiom,
% 18.55/18.44 ! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.44 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.44 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_hoare__derivs_OIf,axiom,
% 18.55/18.44 ! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.44 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.44 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_peek__and__def,axiom,
% 18.55/18.44 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
% 18.55/18.44 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2))
% 18.55/18.44 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Loop,axiom,
% 18.55/18.44 ! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 18.55/18.44 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_c_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 18.55/18.44 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Oremove,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__image_Oreindex,axiom,
% 18.55/18.44 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.44 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 18.55/18.44 ! [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] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ocommute__comp,axiom,
% 18.55/18.44 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ocommute__left__comp,axiom,
% 18.55/18.44 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__image_Odistrib,axiom,
% 18.55/18.44 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ocommute__comp_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 18.55/18.44 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 18.55/18.44 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Oempty,axiom,
% 18.55/18.44 ! [V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__image_Oeq__fold,axiom,
% 18.55/18.44 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Oinsert,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ounion__inter,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Oinsert__remove,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Ounion,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => ( 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))
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__reindex__nonzero,axiom,
% 18.55/18.44 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__add(T_d)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 18.55/18.44 => ! [B_y] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 18.55/18.44 => ( B_x != B_y
% 18.55/18.44 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 18.55/18.44 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Random__Sequence_Omap__def,axiom,
% 18.55/18.44 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__idem_Ounion__idem,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 18.55/18.44 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__idem_Oidem__comp,axiom,
% 18.55/18.44 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__idem_Oinsert__idem,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_strong__setprod__reindex__cong,axiom,
% 18.55/18.44 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_d)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.44 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => 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) )
% 18.55/18.44 => 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) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_pos__map__def,axiom,
% 18.55/18.44 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_pos__single__def,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_neg__map__def,axiom,
% 18.55/18.44 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_New__DSequence_Opos__single__def,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_neg__single__def,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 18.55/18.44 ! [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) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_wfI__pf,axiom,
% 18.55/18.44 ! [V_R_2,T_b] :
% 18.55/18.44 ( ! [B_A] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 18.55/18.44 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rtrancl__Un__separatorE,axiom,
% 18.55/18.44 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 18.55/18.44 => ! [B_y] :
% 18.55/18.44 ( 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_Qa_2))
% 18.55/18.44 => B_x = B_y ) )
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 18.55/18.44 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 18.55/18.44 => ! [B_y] :
% 18.55/18.44 ( 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_Qa_2))
% 18.55/18.44 => B_y = B_x ) )
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__Suc__E,axiom,
% 18.55/18.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ~ ! [B_y] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ~ 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__Suc__E2,axiom,
% 18.55/18.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ~ ! [B_y] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ~ 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_rel__pow__Suc__D2,axiom,
% 18.55/18.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ? [B_y] :
% 18.55/18.44 ( 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))
% 18.55/18.44 & 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sigma__mono,axiom,
% 18.55/18.44 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => 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))) )
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_tranclD2,axiom,
% 18.55/18.44 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ? [B_z] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 & 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_tranclD,axiom,
% 18.55/18.44 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ? [B_z] :
% 18.55/18.44 ( 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))
% 18.55/18.44 & 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__image__1,axiom,
% 18.55/18.44 ! [V_f_2,V_S_2,T_b,T_c] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__mult(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 18.55/18.44 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_card_Oneutral,axiom,
% 18.55/18.44 ! [V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.55/18.44 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_max__ext_Osimps,axiom,
% 18.55/18.44 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 18.55/18.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 18.55/18.44 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 & ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 18.55/18.44 => ? [B_xa] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 18.55/18.44 & 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__image__cong,axiom,
% 18.55/18.44 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 18.55/18.44 ( class_Groups_Oab__semigroup__mult(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setprod__dvd__setprod__subset2,axiom,
% 18.55/18.44 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 18.55/18.44 ( class_Rings_Ocomm__semiring__1(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 18.55/18.44 => 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))) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Max__eqI,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_y] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Min__eqI,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ! [B_y] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__reindex__cong,axiom,
% 18.55/18.44 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 18.55/18.44 ( class_Groups_Ocomm__monoid__add(T_d)
% 18.55/18.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 18.55/18.44 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 18.55/18.44 => ( ! [B_a] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 18.55/18.44 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 18.55/18.44 => 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) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_setsum__ivl__cong,axiom,
% 18.55/18.44 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 18.55/18.44 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.44 & class_Orderings_Oord(T_b) )
% 18.55/18.44 => ( V_a_2 = V_c_2
% 18.55/18.44 => ( V_b_2 = V_d_2
% 18.55/18.44 => ( ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 18.55/18.44 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 18.55/18.44 => 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding_Oeq__fold,axiom,
% 18.55/18.44 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__empty,axiom,
% 18.55/18.44 ! [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 ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__image__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__def,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_union__fold__insert,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__sup__insert,axiom,
% 18.55/18.44 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__sup(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__inf__insert,axiom,
% 18.55/18.44 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Ofold__inf__insert,axiom,
% 18.55/18.44 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Ofold__sup__insert,axiom,
% 18.55/18.44 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 18.55/18.44 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 18.55/18.44 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_sup__SUPR__fold__sup,axiom,
% 18.55/18.44 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.44 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_sup__le__fold__sup,axiom,
% 18.55/18.44 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__sup(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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))) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold__inf__le__inf,axiom,
% 18.55/18.44 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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))) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 18.55/18.44 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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))) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 18.55/18.44 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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))) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__eq__fold__idem,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Olattice(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Olattice(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_minus__fold__remove,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_folding__one_Oeq__fold_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_SUPR__fold__sup,axiom,
% 18.55/18.44 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.44 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fold1__eq__fold,axiom,
% 18.55/18.44 ! [V_a_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Groups_Oab__semigroup__mult(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Olattice(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Lattices_Olattice(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Min_Oeq__fold_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_Max_Oeq__fold_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 18.55/18.44 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.44 ( class_Orderings_Olinorder(T_b)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 18.55/18.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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)))))) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 18.55/18.44 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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)))))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 18.55/18.44 => V_y_2 = V_x_2 ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 18.55/18.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 18.55/18.44 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm,axiom,
% 18.55/18.44 ! [T_b] :
% 18.55/18.44 ( class_Groups_Oab__semigroup__mult(T_b)
% 18.55/18.44 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 18.55/18.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 18.55/18.44 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 18.55/18.44 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 18.55/18.44 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 18.55/18.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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)) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 18.55/18.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.44 => 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) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 18.55/18.44 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.44 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => ? [B_y_H] :
% 18.55/18.44 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 18.55/18.44 & 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)) ) ) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INFI__fold__inf,axiom,
% 18.55/18.44 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.44 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.44 => 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) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INF1__E,axiom,
% 18.55/18.44 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 18.55/18.44 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INF1__D,axiom,
% 18.55/18.44 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__D,axiom,
% 18.55/18.44 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__E,axiom,
% 18.55/18.44 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 18.55/18.44 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INF2__E,axiom,
% 18.55/18.44 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 18.55/18.44 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INF2__D,axiom,
% 18.55/18.44 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_finite__INT,axiom,
% 18.55/18.44 ! [V_A_2,T_c,V_I_2,T_b] :
% 18.55/18.44 ( ? [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 18.55/18.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__absorb,axiom,
% 18.55/18.44 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 18.55/18.44 => 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) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__iff,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 18.55/18.44 ( 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)))
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__lower,axiom,
% 18.55/18.44 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 18.55/18.44 => 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__insert__distrib,axiom,
% 18.55/18.44 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 18.55/18.44 => 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)) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INF__INT__eq2,axiom,
% 18.55/18.44 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INF__INT__eq,axiom,
% 18.55/18.44 ! [V_x_2,V_r_2,T_c,T_b] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> 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))) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.44 ( 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)
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.44 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 18.55/18.44 ! [V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.44 ( 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))
% 18.55/18.44 <=> ! [B_x] :
% 18.55/18.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.44 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__constant,axiom,
% 18.55/18.44 ! [V_c_2,T_c,T_b,V_A_2] :
% 18.55/18.44 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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)) )
% 18.55/18.44 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.44 => 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 ) ) ).
% 18.55/18.44
% 18.55/18.44 fof(fact_INT__empty,axiom,
% 18.55/18.44 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__insert,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I5_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I5_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Image__INT__subset,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Pow__INT__eq,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INF__less__iff,axiom,
% 18.55/18.45 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 18.55/18.45 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 & class_Orderings_Olinorder(T_b) )
% 18.55/18.45 => ( 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))
% 18.55/18.45 <=> ? [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INF__commute,axiom,
% 18.55/18.45 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INFI__apply,axiom,
% 18.55/18.45 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Un__INT__distrib2,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I6_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Un__INT__distrib,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I7_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I6_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I7_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_le__INF__iff,axiom,
% 18.55/18.45 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( 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)))
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__subset__iff,axiom,
% 18.55/18.45 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__Int__distrib,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I2_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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 )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I1_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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 )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INF__const,axiom,
% 18.55/18.45 ! [V_M_2,T_b,V_A_2,T_c] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_converse__INTER,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__Un,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I9_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I9_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_UN__extend__simps_I7_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_UN__simps_I7_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Compl__UN,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Compl__INT,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I10_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I10_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Collect__ball__eq,axiom,
% 18.55/18.45 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INFI__bool__eq,axiom,
% 18.55/18.45 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_vimage__INT,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INF__subset,axiom,
% 18.55/18.45 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INTER__def,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I1_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I2_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I3_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I3_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I4_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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 )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INF__leI,axiom,
% 18.55/18.45 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__greaterThan__UNIV,axiom,
% 18.55/18.45 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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I4_J,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 18.55/18.45 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Image__INT__eq,axiom,
% 18.55/18.45 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 18.55/18.45 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 18.55/18.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inf__INFI__fold__inf,axiom,
% 18.55/18.45 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__fold__inf,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__fold__sup,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__Inter,axiom,
% 18.55/18.45 ! [V_M_2,T_b] :
% 18.55/18.45 ( ? [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 18.55/18.45 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 18.55/18.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_UnionI,axiom,
% 18.55/18.45 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_InterD,axiom,
% 18.55/18.45 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_InterE,axiom,
% 18.55/18.45 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__extend__simps_I8_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INT__simps_I8_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Un__Inter,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INF1__iff,axiom,
% 18.55/18.45 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INF2__iff,axiom,
% 18.55/18.45 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_INTER__eq__Inter__image,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__image__eq,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__eq,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_vimage__Union,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__Inf,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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)))))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__Sup,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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))))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__UnionD,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 18.55/18.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Field__Union,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sigma__Union,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_image__Union,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Int__Union2,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Int__Union,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Domain__Union,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_UN__simps_I8_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_UN__extend__simps_I8_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Range__Union,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__mono,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__quotient,axiom,
% 18.55/18.45 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.45 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__insert,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__empty,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__lower,axiom,
% 18.55/18.45 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__disjoint,axiom,
% 18.55/18.45 ! [V_A_2,V_C_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__le__iff,axiom,
% 18.55/18.45 ! [V_b_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( 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))
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_le__Inf__iff,axiom,
% 18.55/18.45 ! [V_A_2,V_b_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( 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)))
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_less__Sup__iff,axiom,
% 18.55/18.45 ! [V_S_2,V_a_2,T_b] :
% 18.55/18.45 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 & class_Orderings_Olinorder(T_b) )
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 18.55/18.45 <=> ? [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 18.55/18.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__less__iff,axiom,
% 18.55/18.45 ! [V_a_2,V_S_2,T_b] :
% 18.55/18.45 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 & class_Orderings_Olinorder(T_b) )
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 18.55/18.45 <=> ? [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 18.55/18.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__Pow__eq,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__upper,axiom,
% 18.55/18.45 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_subset__Pow__Union,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__empty,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__anti__mono,axiom,
% 18.55/18.45 ! [V_A_2,V_B_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__UNIV,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__Un__distrib,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__insert,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__image__eq,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_UNION__eq__Union__image,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__upper,axiom,
% 18.55/18.45 ! [V_A_2,V_x_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__UNIV,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__lower,axiom,
% 18.55/18.45 ! [V_A_2,V_x_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__Un__distrib,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__empty,axiom,
% 18.55/18.45 ! [T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__singleton,axiom,
% 18.55/18.45 ! [V_a_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__insert,axiom,
% 18.55/18.45 ! [V_A_2,V_a_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Int__Inter__image,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__singleton,axiom,
% 18.55/18.45 ! [V_a_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__UNIV,axiom,
% 18.55/18.45 ! [T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__empty,axiom,
% 18.55/18.45 ! [T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__UNIV,axiom,
% 18.55/18.45 ! [T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__insert,axiom,
% 18.55/18.45 ! [V_A_2,V_a_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Un__eq__Union,axiom,
% 18.55/18.45 ! [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))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Un__Union__image,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__Int__subset,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Int__eq__Inter,axiom,
% 18.55/18.45 ! [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))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__Un__subset,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__binary,axiom,
% 18.55/18.45 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__binary,axiom,
% 18.55/18.45 ! [V_b_2,V_a_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sup__Sup__fold__sup,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Sup__fin__Sup,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inf__Inf__fold__inf,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inf__fin__Inf,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_image__INT,axiom,
% 18.55/18.45 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 18.55/18.45 => 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)) )
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 18.55/18.45 => 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_card__partition,axiom,
% 18.55/18.45 ! [V_k_2,V_C_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 18.55/18.45 => ( ! [B_c] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 18.55/18.45 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 18.55/18.45 => ( ! [B_c1] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 18.55/18.45 => ! [B_c2] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 18.55/18.45 => ( B_c1 != B_c2
% 18.55/18.45 => 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)) ) ) )
% 18.55/18.45 => 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)) ) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__def,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Union__def,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__Union,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 18.55/18.45 => ( ! [B_M] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 18.55/18.45 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insert__partition,axiom,
% 18.55/18.45 ! [V_F_2,V_x_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ! [B_xa] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( B_x != B_xa
% 18.55/18.45 => 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)) ) ) )
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__on__Inter,axiom,
% 18.55/18.45 ! [V_f_2,T_c,T_b,V_S_2] :
% 18.55/18.45 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 18.55/18.45 => ( ! [B_A] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 18.55/18.45 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Inter__subset,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.45 ( ! [B_X] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 18.55/18.45 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__on__INTER,axiom,
% 18.55/18.45 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 18.55/18.45 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 => ( ! [B_i] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 18.55/18.45 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 18.55/18.45 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.45 => ( 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))
% 18.55/18.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.45 => ~ ! [B_y] :
% 18.55/18.45 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 18.55/18.45 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 18.55/18.45 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 18.55/18.45 => 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 18.55/18.45 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 18.55/18.45 => 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_InterI,axiom,
% 18.55/18.45 ! [V_A_2,V_C_2,T_b] :
% 18.55/18.45 ( ! [B_X] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inf__le__fold__inf,axiom,
% 18.55/18.45 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Lattices_Osemilattice__inf(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 18.55/18.45 => 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_fold__sup__le__sup,axiom,
% 18.55/18.45 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Lattices_Osemilattice__sup(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 18.55/18.45 => 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 18.55/18.45 => 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 18.55/18.45 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.45 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 18.55/18.45 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 18.55/18.45 => 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) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 18.55/18.45 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 18.55/18.45 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 18.55/18.45 => 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) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Int__Collect__mono,axiom,
% 18.55/18.45 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 18.55/18.45 => hBOOL(hAPP(V_Qa_2,B_x)) ) )
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Qa_2)))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_UnionE,axiom,
% 18.55/18.45 ! [V_C_2,V_A_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ~ ! [B_X] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 18.55/18.45 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__upd__left,axiom,
% 18.55/18.45 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_setprod__pos,axiom,
% 18.55/18.45 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.45 ( class_Rings_Olinordered__semidom(T_c)
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__upd,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_dom__map__add,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__SomeD,axiom,
% 18.55/18.45 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 18.55/18.45 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.45 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__Some__iff,axiom,
% 18.55/18.45 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 18.55/18.45 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.45 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__empty,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_empty__map__add,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__def,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__None,axiom,
% 18.55/18.45 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 18.55/18.45 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.45 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.45 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__find__right,axiom,
% 18.55/18.45 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 18.55/18.45 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__assoc,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 18.55/18.45 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 18.55/18.45 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 18.55/18.45 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__on__map__add__dom,axiom,
% 18.55/18.45 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 <=> 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__comm,axiom,
% 18.55/18.45 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__range__map__of__map__add,axiom,
% 18.55/18.45 ! [V_l_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( 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)))))
% 18.55/18.45 => 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))))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_setprod__nonneg,axiom,
% 18.55/18.45 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.45 ( class_Rings_Olinordered__semidom(T_c)
% 18.55/18.45 => ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__dom__map__of,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__range__map__of,axiom,
% 18.55/18.45 ! [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))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__map__of__foldr,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_full__small__int__def,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_small_H_Osimps,axiom,
% 18.55/18.45 ! [V_f_2,V_i_2,V_d_2] :
% 18.55/18.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 18.55/18.45 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_small_H_Opsimps,axiom,
% 18.55/18.45 ! [V_i_2,V_d_2,V_f_2] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 18.55/18.45 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 18.55/18.45 => 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_small__int__def,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_small__prod__def,axiom,
% 18.55/18.45 ! [V_d_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( ( class_Smallcheck_Osmall(T_c)
% 18.55/18.45 & class_Smallcheck_Osmall(T_b) )
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_small_H_Opinduct,axiom,
% 18.55/18.45 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => ( ! [B_f,B_d,B_i] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 18.55/18.45 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 18.55/18.45 => hBOOL(hAPP(hAPP(hAPP(V_Pa_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)))) ) )
% 18.55/18.45 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) )
% 18.55/18.45 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_body__def,axiom,
% 18.55/18.45 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__mapk__SomeI,axiom,
% 18.55/18.45 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.45 => ( 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)
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__def,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__mapI,axiom,
% 18.55/18.45 ! [V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__Some__iff,axiom,
% 18.55/18.45 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ? [B_k_H] :
% 18.55/18.45 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 18.55/18.45 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__simps_I2_J,axiom,
% 18.55/18.45 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 18.55/18.45 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__simps_I1_J,axiom,
% 18.55/18.45 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 18.55/18.45 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__map,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_List_Omap_Ocompositionality,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__map,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_List_Omap_Ocomp,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__injective,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 18.55/18.45 => V_xs_2 = V_ys_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__mapD,axiom,
% 18.55/18.45 ! [V_f_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__map__eq__map,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 18.55/18.45 => ( 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)
% 18.55/18.45 <=> V_xs_2 = V_ys_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__map,axiom,
% 18.55/18.45 ! [V_f_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_List_Omap_Oid,axiom,
% 18.55/18.45 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_List_Omap_Oidentity,axiom,
% 18.55/18.45 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__ident,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_foldr__map,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__empty_I1_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__empty_I2_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__comp__None__iff,axiom,
% 18.55/18.45 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 18.55/18.45 | ? [B_k_H] :
% 18.55/18.45 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 18.55/18.45 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__map,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__map__keys,axiom,
% 18.55/18.45 ! [V_m_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__set,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__eq__conv,axiom,
% 18.55/18.45 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 18.55/18.45 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__map,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_dom__option__map,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_infinite__UNIV__listI,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Option_Omap_Oid,axiom,
% 18.55/18.45 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Option_Omap_Oidentity,axiom,
% 18.55/18.45 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Option_Omap_Ocomp,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Option_Omap_Ocompositionality,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_option__map__comp,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_option__map__o__empty,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_option__map__None,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_option__map__is__None,axiom,
% 18.55/18.45 ! [V_opt_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.45 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_option__map__Some,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_option__map__eq__Some,axiom,
% 18.55/18.45 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ? [B_z] :
% 18.55/18.45 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 18.55/18.45 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_option__map__o__map__upd,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__on__map__eq__map,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( 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)
% 18.55/18.45 <=> V_xs_2 = V_ys_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__inj__on,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => V_xs_2 = V_ys_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__fun__upd,axiom,
% 18.55/18.45 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_inj__on__mapI,axiom,
% 18.55/18.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__eq__dom,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 18.55/18.45 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__SomeD,axiom,
% 18.55/18.45 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__is__SomeD,axiom,
% 18.55/18.45 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_dom__map__of__conv__image__fst,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__eq__None__iff,axiom,
% 18.55/18.45 ! [V_x_2,V_xys_2,T_b,T_c] :
% 18.55/18.45 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 18.55/18.45 <=> ~ 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Option_Omap__def,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_WT__bodies__def,axiom,
% 18.55/18.45 ( c_Com_OWT__bodies
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__map__restrict,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_ran__distinct,axiom,
% 18.55/18.45 ! [V_al_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__map__of__compr,axiom,
% 18.55/18.45 ! [V_xs_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__map,axiom,
% 18.55/18.45 ! [V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 18.55/18.45 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 18.55/18.45 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__inject__set,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 18.55/18.45 <=> 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) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__is__SomeI,axiom,
% 18.55/18.45 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__eq__Some__iff,axiom,
% 18.55/18.45 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( 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)
% 18.55/18.45 <=> 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Some__eq__map__of__iff,axiom,
% 18.55/18.45 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( 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)
% 18.55/18.45 <=> 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_greaterThanLessThan__upto,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_weak__map__of__SomeI,axiom,
% 18.55/18.45 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ? [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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_atLeastAtMost__upto,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__upto,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__upto,axiom,
% 18.55/18.45 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_atLeastLessThan__upto,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_greaterThanAtMost__upto,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nat__list__def,axiom,
% 18.55/18.45 ! [V_l_2] :
% 18.55/18.45 ( c_List_Onat__list(V_l_2)
% 18.55/18.45 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__remove1__eq,axiom,
% 18.55/18.45 ! [V_x_2,V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__remove1__subset,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_remove1__idem,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_notin__set__remove1,axiom,
% 18.55/18.45 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => ~ 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_in__set__remove1,axiom,
% 18.55/18.45 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 18.55/18.45 ( V_a_2 != V_b_2
% 18.55/18.45 => ( 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))))
% 18.55/18.45 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_remove1__commute,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__remove1,axiom,
% 18.55/18.45 ! [V_x,V_xs,T_a] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sorted__list__of__set__remove,axiom,
% 18.55/18.45 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__zip__map,axiom,
% 18.55/18.45 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__zipI2,axiom,
% 18.55/18.45 ! [V_xs,T_b,V_ys,T_a] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__zipI1,axiom,
% 18.55/18.45 ! [V_ys,T_b,V_xs,T_a] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__same__conv__map,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__map__fst__snd,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__zip__map2,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__zip__map,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__same,axiom,
% 18.55/18.45 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 & V_a_2 = V_b_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__zip__leftD,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__zip__rightD,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_in__set__zipE,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__map2,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__map1,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__map__map,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sorted__list__of__set__insert,axiom,
% 18.55/18.45 ! [V_x_2,V_A_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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)))))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__zip__upd,axiom,
% 18.55/18.45 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( 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)
% 18.55/18.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 18.55/18.45 => ( 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))
% 18.55/18.45 => 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)) ) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__zip,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__insort,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_c)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_fun__left__comm__insort,axiom,
% 18.55/18.45 ! [T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_neq__if__length__neq,axiom,
% 18.55/18.45 ! [V_ys,V_xs,T_a] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => V_xs != V_ys ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__insort,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_c)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__key__left__comm,axiom,
% 18.55/18.45 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__left__comm,axiom,
% 18.55/18.45 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexn__length,axiom,
% 18.55/18.45 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 18.55/18.45 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__map,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__eq__imp__length__eq,axiom,
% 18.55/18.45 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_remove1__insort,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_card__length,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_card__distinct,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__card,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__zip__inject,axiom,
% 18.55/18.45 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( 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)
% 18.55/18.45 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 18.55/18.45 => ( 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))
% 18.55/18.45 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__fst__zip,axiom,
% 18.55/18.45 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__snd__zip,axiom,
% 18.55/18.45 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__insort,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_c)
% 18.55/18.45 => ( 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)))
% 18.55/18.45 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__pos__if__in__set,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__eq__conv,axiom,
% 18.55/18.45 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 18.55/18.45 <=> ( 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
% 18.55/18.45 & 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 ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lenlex__conv,axiom,
% 18.55/18.45 ! [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)))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lenlex__def,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__lists__length__eq,axiom,
% 18.55/18.45 ! [V_n_2,V_A_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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))))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__eq__iff__zip__eq,axiom,
% 18.55/18.45 ! [T_b,V_ys_2,V_xs_2] :
% 18.55/18.45 ( V_xs_2 = V_ys_2
% 18.55/18.45 <=> ( 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)
% 18.55/18.45 & ! [B_x] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__zip__is__None,axiom,
% 18.55/18.45 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( 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)
% 18.55/18.45 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__zip__is__Some,axiom,
% 18.55/18.45 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 <=> ? [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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__remove1,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_dom__map__of__zip,axiom,
% 18.55/18.45 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_finite__lists__length__le,axiom,
% 18.55/18.45 ! [V_n_2,V_A_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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))))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Nitpick_Ocard_H__def,axiom,
% 18.55/18.45 ! [V_A_2,T_b] :
% 18.55/18.45 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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)))) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__iff__zip,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( 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)
% 18.55/18.45 & ! [B_x] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__rtrancl__refl,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__eq__len,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__rtrancl__trans,axiom,
% 18.55/18.45 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => ( 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))))
% 18.55/18.45 => 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)))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__mono,axiom,
% 18.55/18.45 ! [V_s_2,V_r_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrelp__listrel__eq,axiom,
% 18.55/18.45 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexn_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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)))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_impossible__Cons,axiom,
% 18.55/18.45 ! [V_x,V_ys,V_xs,T_a] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__ConsD,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => ( V_y_2 = V_x_2
% 18.55/18.45 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__Cons__Cons,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__subset__Cons,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_foldr_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_not__Cons__self,axiom,
% 18.55/18.45 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_not__Cons__self2,axiom,
% 18.55/18.45 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list_Oinject,axiom,
% 18.55/18.45 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ( V_a_2 = V_a_H_2
% 18.55/18.45 & V_list_2 = V_list_H_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrelp_Oequations_I2_J,axiom,
% 18.55/18.45 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 18.55/18.45 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrelp_OCons,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 18.55/18.45 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_remove1_Osimps_I2_J,axiom,
% 18.55/18.45 ! [V_xs,T_a,V_y,V_x] :
% 18.55/18.45 ( ( V_x = V_y
% 18.55/18.45 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 18.55/18.45 & ( V_x != V_y
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__key_Osimps_I2_J,axiom,
% 18.55/18.45 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( ( 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)))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( ~ 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)))
% 18.55/18.45 => 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct_Osimps_I2_J,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 18.55/18.45 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__Cons__code_I2_J,axiom,
% 18.55/18.45 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 18.55/18.45 ( ( V_l = V_k
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( V_l != V_k
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list_Osize_I4_J,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel_OCons,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Cons__in__lex,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( ( 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))
% 18.55/18.45 & 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) )
% 18.55/18.45 | ( V_x_2 = V_y_2
% 18.55/18.45 & 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__Cons,axiom,
% 18.55/18.45 ! [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))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__Cons__def,axiom,
% 18.55/18.45 ! [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)))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__Cons2,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ~ ! [B_x,B_xs] :
% 18.55/18.45 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 18.55/18.45 => ( 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))
% 18.55/18.45 => ~ 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__Cons1,axiom,
% 18.55/18.45 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ~ ! [B_y,B_ys] :
% 18.55/18.45 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 18.55/18.45 => ( 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))
% 18.55/18.45 => ~ 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__sublist,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_pick_Osimps,axiom,
% 18.55/18.45 ! [V_xs,V_x,T_a,V_i] :
% 18.55/18.45 ( ( 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)))
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( ~ 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)))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__sublistI,axiom,
% 18.55/18.45 ! [V_I_2,V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_in__set__sublistD,axiom,
% 18.55/18.45 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_notin__set__sublistI,axiom,
% 18.55/18.45 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => ~ 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__sublist__subset,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_select__weight__cons__zero,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_pick__member,axiom,
% 18.55/18.45 ! [V_xs_2,T_b,V_i_2] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__simps_I2_J,axiom,
% 18.55/18.45 ! [V_xs,V_x,T_a] :
% 18.55/18.45 ( class_Groups_Omonoid__add(T_a)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__addf,axiom,
% 18.55/18.45 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__const__mult,axiom,
% 18.55/18.45 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 18.55/18.45 ( class_Rings_Osemiring__0(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__mult__const,axiom,
% 18.55/18.45 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( class_Rings_Osemiring__0(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__0,axiom,
% 18.55/18.45 ! [V_xs_2,T_c,T_b] :
% 18.55/18.45 ( class_Groups_Omonoid__add(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__subtractf,axiom,
% 18.55/18.45 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( class_Groups_Oab__group__add(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__abs,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_uminus__listsum__map,axiom,
% 18.55/18.45 ! [V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( class_Groups_Oab__group__add(T_b)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_select__weight__def,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 18.55/18.45 ! [V_f_2,V_xs_2,T_b,T_c] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.45 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 18.55/18.45 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 18.55/18.45 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__triv,axiom,
% 18.55/18.45 ! [V_xs_2,V_r_2,T_c,T_b] :
% 18.55/18.45 ( class_Rings_Osemiring__1(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__map__remove1,axiom,
% 18.55/18.45 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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)))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_select__weight__member,axiom,
% 18.55/18.45 ! [V_s_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 18.55/18.45 ! [V_f_2,V_A_2,T_b,T_c] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_c)
% 18.55/18.45 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => 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))))) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.45 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__insert__insort__key,axiom,
% 18.55/18.45 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( ~ 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))))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 18.55/18.45 ! [V_ns_2] :
% 18.55/18.45 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 <=> ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 18.55/18.45 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__insort__insert,axiom,
% 18.55/18.45 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_c)
% 18.55/18.45 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__insert__triv,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__insort__insert,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__insert__key__triv,axiom,
% 18.55/18.45 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( 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))))
% 18.55/18.45 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__insert__insort,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexord__cons__cons,axiom,
% 18.55/18.45 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( 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))
% 18.55/18.45 | ( V_a_2 = V_b_2
% 18.55/18.45 & 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__zip,axiom,
% 18.55/18.45 ! [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)))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__zip,axiom,
% 18.55/18.45 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__map,axiom,
% 18.55/18.45 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_elem__le__listsum__nat,axiom,
% 18.55/18.45 ! [V_ns,V_k] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth_Osimps,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__Cons__Suc,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__Cons__0,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_all__set__conv__all__nth,axiom,
% 18.55/18.45 ! [V_Pa_2,V_xs_2,T_b] :
% 18.55/18.45 ( ! [B_x] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.55/18.45 <=> ! [B_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__eq__iff__nth__eq,axiom,
% 18.55/18.45 ! [T_b,V_ys_2,V_xs_2] :
% 18.55/18.45 ( V_xs_2 = V_ys_2
% 18.55/18.45 <=> ( 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)
% 18.55/18.45 & ! [B_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__conv__nth,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 <=> ! [B_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ! [B_j] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( B_i != B_j
% 18.55/18.45 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__eq__iff__index__eq,axiom,
% 18.55/18.45 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => ( 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)
% 18.55/18.45 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__mem,axiom,
% 18.55/18.45 ! [V_xs_2,T_b,V_n_2] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_in__set__conv__nth,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 <=> ? [B_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__Cons_H,axiom,
% 18.55/18.45 ! [V_xs,V_x,T_a,V_n] :
% 18.55/18.45 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 18.55/18.45 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__conv__nth,axiom,
% 18.55/18.45 ! [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))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__Cons__number__of,axiom,
% 18.55/18.45 ! [V_xs,V_x,T_a,V_v] :
% 18.55/18.45 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => 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 )
% 18.55/18.45 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__setsum__nth,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__sublist,axiom,
% 18.55/18.45 ! [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))))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexord__lex,axiom,
% 18.55/18.45 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( 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)))
% 18.55/18.45 & 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__iff__nth,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( 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)
% 18.55/18.45 & ! [B_n] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_pick__same,axiom,
% 18.55/18.45 ! [V_xs_2,T_b,V_l_2] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_select__def,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexord__take__index__conv,axiom,
% 18.55/18.45 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( ( 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)))
% 18.55/18.45 & 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 )
% 18.55/18.45 | ? [B_i] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 18.55/18.45 & 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_in__set__takeD,axiom,
% 18.55/18.45 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__take,axiom,
% 18.55/18.45 ! [V_xs,T_a,V_n,V_i] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__take__subset,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__all,axiom,
% 18.55/18.45 ! [V_n,V_xs,T_a] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__take,axiom,
% 18.55/18.45 ! [V_i,V_xs,T_a] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__take,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__zip,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__take,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__Suc__Cons,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sublist__upt__eq__take,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__map,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__take__subset__set__take,axiom,
% 18.55/18.45 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__update__nat,axiom,
% 18.55/18.45 ! [V_n,V_ns,V_k] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_select__weigth__select,axiom,
% 18.55/18.45 ! [T_b,V_xs_2] :
% 18.55/18.45 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__Nil2,axiom,
% 18.55/18.45 ! [V_r_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__Nil1,axiom,
% 18.55/18.45 ! [V_r_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__id,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__list__update__neq,axiom,
% 18.55/18.45 ! [V_x,V_xs,T_a,V_j,V_i] :
% 18.55/18.45 ( V_i != V_j
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__beyond,axiom,
% 18.55/18.45 ! [V_x,V_i,V_xs,T_a] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__Nil,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__eq__Nil,axiom,
% 18.55/18.45 ! [V_xs_2,V_n_2,T_b] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.45 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__0,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__list__update,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__0__conv,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list_Osize_I3_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__Cons,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Nil__is__map__conv,axiom,
% 18.55/18.45 ! [V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.45 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map_Osimps_I1_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__update,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__is__Nil__conv,axiom,
% 18.55/18.45 ! [V_xs_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__update,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_update__zip,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sublist__nil,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sublist__empty,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__key_Osimps_I1_J,axiom,
% 18.55/18.45 ! [V_x_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_c)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__code_I3_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list_Osimps_I3_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__code_I2_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sorted__list__of__set__empty,axiom,
% 18.55/18.45 ! [T_b] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_b)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip_Osimps_I1_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__Nil,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_upto__empty,axiom,
% 18.55/18.45 ! [V_i,V_j] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 18.55/18.45 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_foldr_Osimps_I1_J,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of_Osimps_I1_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__Cons__code_I1_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__nonempty,axiom,
% 18.55/18.45 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update_Osimps_I1_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__code_I1_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__overwrite,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__swap,axiom,
% 18.55/18.45 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 18.55/18.45 ( V_i != V_i_H
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_remove1_Osimps_I1_J,axiom,
% 18.55/18.45 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct_Osimps_I1_J,axiom,
% 18.55/18.45 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_insort__not__Nil,axiom,
% 18.55/18.45 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 18.55/18.45 ( class_Orderings_Olinorder(T_c)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrelp_ONil,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrelp_Oequations_I1_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__empty2,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__empty,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__simps_I1_J,axiom,
% 18.55/18.45 ! [T_a] :
% 18.55/18.45 ( class_Groups_Omonoid__add(T_a)
% 18.55/18.45 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__greater__0__conv,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__update__subsetI,axiom,
% 18.55/18.45 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__1__Cons,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__update__subset__insert,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__list__update,axiom,
% 18.55/18.45 ! [V_x,V_j,V_xs,T_a,V_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( ( V_i = V_j
% 18.55/18.45 => 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 )
% 18.55/18.45 & ( V_i != V_j
% 18.55/18.45 => 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) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__same__conv,axiom,
% 18.55/18.45 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 18.55/18.45 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__list__update__eq,axiom,
% 18.55/18.45 ! [V_x,V_xs,T_a,V_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel_ONil,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexord__Nil__right,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Nil__notin__lex,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Nil2__notin__lex,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__update__memI,axiom,
% 18.55/18.45 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_upto_Osimps,axiom,
% 18.55/18.45 ! [V_j,V_i] :
% 18.55/18.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 18.55/18.45 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sublist__singleton,axiom,
% 18.55/18.45 ! [V_x_2,T_b,V_A_2] :
% 18.55/18.45 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__Cons_H,axiom,
% 18.55/18.45 ! [V_xs,V_x,T_a,V_n] :
% 18.55/18.45 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_upto__rec__number__of,axiom,
% 18.55/18.45 ! [V_n,V_m] :
% 18.55/18.45 ( ( 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)))
% 18.55/18.45 => 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))) )
% 18.55/18.45 & ( ~ 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)))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_select,axiom,
% 18.55/18.45 ! [V_s_2,T_b,V_xs_2] :
% 18.55/18.45 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__Nil,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__Cons__sing__Nil,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__Cons__number__of,axiom,
% 18.55/18.45 ! [V_xs,V_x,T_a,V_v] :
% 18.55/18.45 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__list__update,axiom,
% 18.55/18.45 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 => ( ~ 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))))))
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_upto_Opsimps,axiom,
% 18.55/18.45 ! [V_j_2,V_i_2] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 18.55/18.45 => 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)) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 18.55/18.45 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_anamorph_Osimps,axiom,
% 18.55/18.45 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 18.55/18.45 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listset_Osimps_I1_J,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__Cons1,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list_Osimps_I5_J,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list_Osimps_I4_J,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listset_Osimps_I2_J,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__Cons,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_upto_Opinduct,axiom,
% 18.55/18.45 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( ! [B_i,B_j] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 18.55/18.45 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 18.55/18.45 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 18.55/18.45 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upd__upds__conv__if,axiom,
% 18.55/18.45 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 18.55/18.45 ( ( 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))))
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( ~ 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))))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upds__Nil1,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upds__Nil2,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upds__apply__nontin,axiom,
% 18.55/18.45 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__add__upds,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upds__Cons,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upds__list__update2__drop,axiom,
% 18.55/18.45 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => ( 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)))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upds__twist,axiom,
% 18.55/18.45 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 18.55/18.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_restrict__map__upds,axiom,
% 18.55/18.45 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( 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))
% 18.55/18.45 => 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) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_dom__map__upds,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__upds__append1,axiom,
% 18.55/18.45 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sublist__Cons,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append1__eq__conv,axiom,
% 18.55/18.45 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( V_xs_2 = V_ys_2
% 18.55/18.45 & V_x_2 = V_y_2 ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Cons__eq__append__conv,axiom,
% 18.55/18.45 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 18.55/18.45 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 18.55/18.45 | ? [B_ys_H] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 18.55/18.45 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__eq__Cons__conv,axiom,
% 18.55/18.45 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 18.55/18.45 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 18.55/18.45 | ? [B_ys_H] :
% 18.55/18.45 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 18.55/18.45 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_fun__upds__append__drop,axiom,
% 18.55/18.45 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_fun__upds__append2__drop,axiom,
% 18.55/18.45 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__length,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__append__length,axiom,
% 18.55/18.45 ! [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 ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Cons__eq__appendI,axiom,
% 18.55/18.45 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 18.55/18.45 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 18.55/18.45 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__Cons,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__append,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__append1,axiom,
% 18.55/18.45 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_remove1__append,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__append,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_zip__append,axiom,
% 18.55/18.45 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 18.55/18.45 ( 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)
% 18.55/18.45 => ( 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)
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__append,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_foldr__append,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_map__of__append,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__assoc,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__eq__append__conv2,axiom,
% 18.55/18.45 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2)
% 18.55/18.45 <=> ? [B_us] :
% 18.55/18.45 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 18.55/18.45 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 18.55/18.45 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 18.55/18.45 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_same__append__eq,axiom,
% 18.55/18.45 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> V_ys_2 = V_zs_2 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__same__eq,axiom,
% 18.55/18.45 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 18.55/18.45 ( 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)
% 18.55/18.45 <=> V_ys_2 = V_zs_2 ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__eq__appendI,axiom,
% 18.55/18.45 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 18.55/18.45 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 18.55/18.45 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__append,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listsum__append,axiom,
% 18.55/18.45 ! [V_ys,V_xs,T_a] :
% 18.55/18.45 ( class_Groups_Omonoid__add(T_a)
% 18.55/18.45 => 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)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__append__length__plus,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_eq__Nil__appendI,axiom,
% 18.55/18.45 ! [T_a,V_ys,V_xs] :
% 18.55/18.45 ( V_xs = V_ys
% 18.55/18.45 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__self__conv2,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__self__conv,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 18.55/18.45 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__is__Nil__conv,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 18.55/18.45 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 18.55/18.45 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_self__append__conv2,axiom,
% 18.55/18.45 ! [V_xs_2,T_b,V_ys_2] :
% 18.55/18.45 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_self__append__conv,axiom,
% 18.55/18.45 ! [V_ys_2,T_b,V_xs_2] :
% 18.55/18.45 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 18.55/18.45 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__Nil2,axiom,
% 18.55/18.45 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Nil__is__append__conv,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 18.55/18.45 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 18.55/18.45 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__Nil,axiom,
% 18.55/18.45 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexord__append__leftI,axiom,
% 18.55/18.45 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__append,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 18.55/18.45 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.45 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 18.55/18.45 & 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_nth__append,axiom,
% 18.55/18.45 ! [V_ys,V_xs,T_a,V_n] :
% 18.55/18.45 ( ( 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)))
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( ~ 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)))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_list__update__append,axiom,
% 18.55/18.45 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 18.55/18.45 ( ( 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)))
% 18.55/18.45 => 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) )
% 18.55/18.45 & ( ~ 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)))
% 18.55/18.45 => 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)) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_sublist__append,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexord__append__left__rightI,axiom,
% 18.55/18.45 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__Suc__conv__app__nth,axiom,
% 18.55/18.45 ! [V_xs,T_a,V_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 18.55/18.45 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( ( 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)))
% 18.55/18.45 & V_x_2 = V_y_2 )
% 18.55/18.45 | ( V_xs_2 = V_ys_2
% 18.55/18.45 & 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)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_lexord__append__leftD,axiom,
% 18.55/18.45 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( ! [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))
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Cons__acc__listrel1I,axiom,
% 18.55/18.45 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 18.55/18.45 => ( 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))))
% 18.55/18.45 => 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)))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1__converse,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1__mono,axiom,
% 18.55/18.45 ! [V_s_2,V_r_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 18.55/18.45 ! [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)))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 18.55/18.45 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1I2,axiom,
% 18.55/18.45 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 18.55/18.45 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1__eq__len,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_not__Nil__listrel1,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_not__listrel1__Nil,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_append__listrel1I,axiom,
% 18.55/18.45 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( ( ( 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)))
% 18.55/18.45 & V_us_2 = V_vs_2 )
% 18.55/18.45 | ( V_xs_2 = V_ys_2
% 18.55/18.45 & 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))) ) )
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_in__listrel1__converse,axiom,
% 18.55/18.45 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 <=> 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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)))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1I1,axiom,
% 18.55/18.45 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_Cons__listrel1__Cons,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ( ( 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))
% 18.55/18.45 & V_xs_2 = V_ys_2 )
% 18.55/18.45 | ( V_x_2 = V_y_2
% 18.55/18.45 & 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1__subset__listrel,axiom,
% 18.55/18.45 ! [V_r_H_2,V_r_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 18.55/18.45 => 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))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1I,axiom,
% 18.55/18.45 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => ( 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))
% 18.55/18.45 => ( 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))
% 18.55/18.45 => 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))) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 18.55/18.45 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ( 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))))
% 18.55/18.45 => 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)))) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1__iff__update,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 <=> ? [B_y,B_n] :
% 18.55/18.45 ( 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))
% 18.55/18.45 & 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)))
% 18.55/18.45 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_listrel1E,axiom,
% 18.55/18.45 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => ~ ! [B_x,B_y] :
% 18.55/18.45 ( 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))
% 18.55/18.45 => ! [B_us,B_vs] :
% 18.55/18.45 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 18.55/18.45 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_rotate1__def,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_upd__conv__take__nth__drop,axiom,
% 18.55/18.45 ! [V_a,V_xs,T_a,V_i] :
% 18.55/18.45 ( 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)))
% 18.55/18.45 => 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))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_drop__append,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_drop__Nil,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_rotate1__is__Nil__conv,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_drop__take,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_take__drop,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_in__set__dropD,axiom,
% 18.55/18.45 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 18.55/18.45 ( 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))))
% 18.55/18.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__rotate1,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_set__drop__subset,axiom,
% 18.55/18.45 ! [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))) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct1__rotate,axiom,
% 18.55/18.45 ! [V_xs_2,T_b] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 18.55/18.45 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_distinct__drop,axiom,
% 18.55/18.45 ! [V_i,V_xs,T_a] :
% 18.55/18.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.45 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_drop__drop,axiom,
% 18.55/18.45 ! [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) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_drop__0,axiom,
% 18.55/18.45 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 18.55/18.45
% 18.55/18.45 fof(fact_drop__zip,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_drop__map,axiom,
% 18.55/18.45 ! [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)) ).
% 18.55/18.45
% 18.55/18.45 fof(fact_length__rotate1,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__drop,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__1__Cons,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__Suc__Cons,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__via__drop,axiom,
% 18.55/18.46 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 18.55/18.46 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 18.55/18.46 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__all,axiom,
% 18.55/18.46 ! [V_n,V_xs,T_a] :
% 18.55/18.46 ( 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))
% 18.55/18.46 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__eq__Nil,axiom,
% 18.55/18.46 ! [V_xs_2,V_n_2,T_b] :
% 18.55/18.46 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.46 <=> 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__drop__subset__set__drop,axiom,
% 18.55/18.46 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 18.55/18.46 => 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)))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_append__take__drop__id,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_append__eq__conv__conj,axiom,
% 18.55/18.46 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 18.55/18.46 <=> ( 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)
% 18.55/18.46 & 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__Cons,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__Cons_H,axiom,
% 18.55/18.46 ! [V_xs,V_x,T_a,V_n] :
% 18.55/18.46 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.46 => 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) )
% 18.55/18.46 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__drop,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_i,V_n] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_append__eq__append__conv__if,axiom,
% 18.55/18.46 ! [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] :
% 18.55/18.46 ( 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)
% 18.55/18.46 <=> ( ( 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)))
% 18.55/18.46 => ( 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)
% 18.55/18.46 & 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) ) )
% 18.55/18.46 & ( ~ 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)))
% 18.55/18.46 => ( 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
% 18.55/18.46 & 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 ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__drop_H,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_i] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__simps,axiom,
% 18.55/18.46 ! [V_xs,V_x,T_b,T_a] :
% 18.55/18.46 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 18.55/18.46 & 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__Cons__number__of,axiom,
% 18.55/18.46 ! [V_xs,V_x,T_a,V_v] :
% 18.55/18.46 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.46 => 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) )
% 18.55/18.46 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_take__add,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_j,V_i] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate1__length01,axiom,
% 18.55/18.46 ! [V_xs,T_a] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_zip__append1,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_zip__append2,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_id__take__nth__drop,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_i] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_take__hd__drop,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_n] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__drop__conv__nth,axiom,
% 18.55/18.46 ! [V_n,T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__append2,axiom,
% 18.55/18.46 ! [V_ys,T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__append,axiom,
% 18.55/18.46 ! [V_ys,T_a,V_xs] :
% 18.55/18.46 ( ( V_xs = c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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) )
% 18.55/18.46 & ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd_Osimps,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__map,axiom,
% 18.55/18.46 ! [V_f_2,T_c,T_b,V_xs_2] :
% 18.55/18.46 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__in__set,axiom,
% 18.55/18.46 ! [T_b,V_xs_2] :
% 18.55/18.46 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__conv__nth,axiom,
% 18.55/18.46 ! [T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate1__hd__tl,axiom,
% 18.55/18.46 ! [T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__rotate__conv__nth,axiom,
% 18.55/18.46 ! [V_n,T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__Suc,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__tl,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_tl__drop,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_tl_Osimps_I1_J,axiom,
% 18.55/18.46 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__is__Nil__conv,axiom,
% 18.55/18.46 ! [V_xs_2,V_n_2,T_b] :
% 18.55/18.46 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.46 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_take__tl,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__rotate,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__rotate,axiom,
% 18.55/18.46 ! [V_xs_2,V_n_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 18.55/18.46 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__tl,axiom,
% 18.55/18.46 ! [V_xs,T_a] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.46 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__rotate,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__map,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__tl,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__rotate,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__conv__mod,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_tl_Osimps_I2_J,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_tl__append2,axiom,
% 18.55/18.46 ! [V_ys,T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__def,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__Suc,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate1__rotate__swap,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_tl__append,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate0,axiom,
% 18.55/18.46 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__add,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__id,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_n] :
% 18.55/18.46 ( 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)
% 18.55/18.46 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__length01,axiom,
% 18.55/18.46 ! [V_n,V_xs,T_a] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__tl,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_tl__take,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_take__Suc,axiom,
% 18.55/18.46 ! [V_n,T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__drop__take,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_fold1__set,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 18.55/18.46 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 => 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)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_list_Osize_I2_J,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__append,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__Cons,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_list__size__map,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__map,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldr__conv__foldl,axiom,
% 18.55/18.46 ! [V_a_2,V_xs_2,T_b] :
% 18.55/18.46 ( class_Groups_Oab__semigroup__add(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__absorb0,axiom,
% 18.55/18.46 ! [V_zs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Groups_Omonoid__add(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__assoc,axiom,
% 18.55/18.46 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Groups_Osemigroup__add(T_b)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_start__le__sum,axiom,
% 18.55/18.46 ! [V_ns_2,V_n_2,V_m_2] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__Nil,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_listsum__foldl,axiom,
% 18.55/18.46 ! [T_b] :
% 18.55/18.46 ( class_Groups_Omonoid__add(T_b)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__foldr1,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( class_Groups_Omonoid__add(T_b)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__foldr1__lemma,axiom,
% 18.55/18.46 ! [V_xs_2,V_a_2,T_b] :
% 18.55/18.46 ( class_Groups_Omonoid__add(T_b)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sum__eq__0__conv,axiom,
% 18.55/18.46 ! [V_ns_2,V_m_2] :
% 18.55/18.46 ( 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)
% 18.55/18.46 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.46 & ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 18.55/18.46 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_list_Osize_I1_J,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 18.55/18.46 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Sup__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Inf__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Sup__fin__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Lattices_Olattice(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Inf__fin__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Lattices_Olattice(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Min__fin__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Max__fin__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_SUPR__set__fold,axiom,
% 18.55/18.46 ! [V_f_2,V_xs_2,T_c,T_b] :
% 18.55/18.46 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_INFI__set__fold,axiom,
% 18.55/18.46 ! [V_f_2,V_xs_2,T_c,T_b] :
% 18.55/18.46 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_list__size__estimation,axiom,
% 18.55/18.46 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 18.55/18.46 => 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))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_list__size__estimation_H,axiom,
% 18.55/18.46 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 18.55/18.46 => 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))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__upds__fold__map__upd,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_elem__le__sum,axiom,
% 18.55/18.46 ! [V_ns_2,V_n_2] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_list__size__conv__listsum,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_listrel__subset,axiom,
% 18.55/18.46 ! [V_A_2,V_r_2,T_b] :
% 18.55/18.46 ( 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))))
% 18.55/18.46 => 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))))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists__accI,axiom,
% 18.55/18.46 ! [V_r_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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))))
% 18.55/18.46 => 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)))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists_ONil,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_equiv__listrel,axiom,
% 18.55/18.46 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.46 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_listrel__refl__on,axiom,
% 18.55/18.46 ! [V_r_2,V_A_2,T_b] :
% 18.55/18.46 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists__UNIV,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists__mono,axiom,
% 18.55/18.46 ! [V_B_2,V_A_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_append__in__lists__conv,axiom,
% 18.55/18.46 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 18.55/18.46 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Cons__in__lists__iff,axiom,
% 18.55/18.46 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 18.55/18.46 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_in__lists__conv__set,axiom,
% 18.55/18.46 ! [V_A_2,V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists__eq__set,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists__empty,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists__accD,axiom,
% 18.55/18.46 ! [V_r_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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))))
% 18.55/18.46 => 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)))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lexord__append__rightI,axiom,
% 18.55/18.46 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 18.55/18.46 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lexord__Nil__left,axiom,
% 18.55/18.46 ! [V_r_2,V_y_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__list__update,axiom,
% 18.55/18.46 ! [V_x,V_k,T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => ( ( 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))
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 18.55/18.46 & ( 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))
% 18.55/18.46 => 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) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_listsum__mono,axiom,
% 18.55/18.46 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 18.55/18.46 ( ( class_Groups_Omonoid__add(T_c)
% 18.55/18.46 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 18.55/18.46 => ( ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 18.55/18.46 => 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)))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last_Osimps,axiom,
% 18.55/18.46 ! [V_x,T_a,V_xs] :
% 18.55/18.46 ( ( V_xs = c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 18.55/18.46 & ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__ConsR,axiom,
% 18.55/18.46 ! [V_x,T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__ConsL,axiom,
% 18.55/18.46 ! [V_x,T_a,V_xs] :
% 18.55/18.46 ( V_xs = c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__append,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_ys] :
% 18.55/18.46 ( ( V_ys = c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 18.55/18.46 & ( V_ys != c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__appendR,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_ys] :
% 18.55/18.46 ( V_ys != c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__appendL,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_ys] :
% 18.55/18.46 ( V_ys = c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__map,axiom,
% 18.55/18.46 ! [V_f_2,T_c,T_b,V_xs_2] :
% 18.55/18.46 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__in__set,axiom,
% 18.55/18.46 ! [T_b,V_as_2] :
% 18.55/18.46 ( V_as_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__snoc,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__drop,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_n] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__conv__nth,axiom,
% 18.55/18.46 ! [T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lexord__linear,axiom,
% 18.55/18.46 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 18.55/18.46 ( ! [B_a,B_b] :
% 18.55/18.46 ( 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))
% 18.55/18.46 | B_a = B_b
% 18.55/18.46 | 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)) )
% 18.55/18.46 => ( 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)))
% 18.55/18.46 | V_x_2 = V_y_2
% 18.55/18.46 | 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))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lexord__irreflexive,axiom,
% 18.55/18.46 ! [V_y_2,V_r_2,T_b] :
% 18.55/18.46 ( ! [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))
% 18.55/18.46 => ~ 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_lists_Osimps,axiom,
% 18.55/18.46 ! [V_A_2,V_a_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 18.55/18.46 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 18.55/18.46 | ? [B_a,B_l] :
% 18.55/18.46 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 18.55/18.46 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 18.55/18.46 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_list__size__pointwise,axiom,
% 18.55/18.46 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 18.55/18.46 ( ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast__take,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_n] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__take__lemma,axiom,
% 18.55/18.46 ! [V_ys,V_xs,T_a,V_k] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => ( ! [B_i] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 18.55/18.46 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 18.55/18.46 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__butlast,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast__append,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_ys] :
% 18.55/18.46 ( ( V_ys = c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 18.55/18.46 & ( V_ys != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast_Osimps_I2_J,axiom,
% 18.55/18.46 ! [V_x,T_a,V_xs] :
% 18.55/18.46 ( ( V_xs = c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 18.55/18.46 & ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_in__set__butlastD,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__butlast,axiom,
% 18.55/18.46 ! [T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast_Osimps_I1_J,axiom,
% 18.55/18.46 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast__drop,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__butlast,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_in__set__butlast__appendI,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 18.55/18.46 => 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))))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast__snoc,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_take__butlast,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_n] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__butlast,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast__conv__take,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_butlast__list__update,axiom,
% 18.55/18.46 ! [V_x,V_xs,T_a,V_k] :
% 18.55/18.46 ( ( 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))
% 18.55/18.46 => 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) )
% 18.55/18.46 & ( 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))
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_append__butlast__last__id,axiom,
% 18.55/18.46 ! [T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => 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 ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_snoc__eq__iff__butlast,axiom,
% 18.55/18.46 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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
% 18.55/18.46 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 18.55/18.46 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__aux__max,axiom,
% 18.55/18.46 ! [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)))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_partition__set,axiom,
% 18.55/18.46 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__filter__le,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__is__subset,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter_Osimps_I1_J,axiom,
% 18.55/18.46 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__empty__conv,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__id__conv,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__insort__triv,axiom,
% 18.55/18.46 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_c)
% 18.55/18.46 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__filter,axiom,
% 18.55/18.46 ! [V_Pa_2,V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__remove1,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2),V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remove1__filter__not,axiom,
% 18.55/18.46 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__filter,axiom,
% 18.55/18.46 ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2)),V_Pa_2)),V_xs_2) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_partition__filter1,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sum__length__filter__compl,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter_Osimps_I2_J,axiom,
% 18.55/18.46 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 18.55/18.46 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) )
% 18.55/18.46 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__append,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_partition__filter__conv,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__map,axiom,
% 18.55/18.46 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_partition__filter2,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__filter,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__filter__map,axiom,
% 18.55/18.46 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__filter__less,axiom,
% 18.55/18.46 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__minus__filter__out,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_partition__P,axiom,
% 18.55/18.46 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 18.55/18.46 => ( ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 18.55/18.46 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 18.55/18.46 & ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 18.55/18.46 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_partition_Osimps_I1_J,axiom,
% 18.55/18.46 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__in__sublist,axiom,
% 18.55/18.46 ! [V_s_2,V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_partition_Osimps_I2_J,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__filter__conv__card,axiom,
% 18.55/18.46 ! [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))))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__filter__def,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__max__length,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__of__filter__in,axiom,
% 18.55/18.46 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 18.55/18.46 ( 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)
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2))
% 18.55/18.46 => 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_Pa_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__filter__simps_I1_J,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__map__map,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose_Osimps_I2_J,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__empty,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 18.55/18.46 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__filter__simps_I2_J,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose_Osimps_I1_J,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sublist__shift__lemma__Suc,axiom,
% 18.55/18.46 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_select__weigth__drop__zero,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_pick__drop__zero,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__transpose,axiom,
% 18.55/18.46 ! [V_xs_2,T_b,V_i_2] :
% 18.55/18.46 ( 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))))
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__transpose,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__filter__map__filter,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_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_Pa_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_Pa_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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_insort__key__remove1,axiom,
% 18.55/18.46 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_c)
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 18.55/18.46 => ( 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
% 18.55/18.46 => 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 ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sublist__def,axiom,
% 18.55/18.46 ! [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))))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted_ONil,axiom,
% 18.55/18.46 ! [T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__single,axiom,
% 18.55/18.46 ! [V_x,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__same,axiom,
% 18.55/18.46 ! [V_xs_2,V_g_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__filter,axiom,
% 18.55/18.46 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__map__same,axiom,
% 18.55/18.46 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__upt,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__butlast,axiom,
% 18.55/18.46 ! [V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__append,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 18.55/18.46 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 18.55/18.46 & ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ! [B_xa] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__Suc,axiom,
% 18.55/18.46 ! [V_j,V_i] :
% 18.55/18.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => 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))) )
% 18.55/18.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__Suc__append,axiom,
% 18.55/18.46 ! [V_j,V_i] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__add__eq__append,axiom,
% 18.55/18.46 ! [V_k,V_j,V_i] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__many__eq,axiom,
% 18.55/18.46 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( 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)))
% 18.55/18.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 18.55/18.46 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__many,axiom,
% 18.55/18.46 ! [V_zs,V_y,V_x,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 18.55/18.46 => 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))) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_take__upt,axiom,
% 18.55/18.46 ! [V_n,V_m,V_i] :
% 18.55/18.46 ( 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))
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__eq__Nil__conv,axiom,
% 18.55/18.46 ! [V_j_2,V_i_2] :
% 18.55/18.46 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 18.55/18.46 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__conv__Nil,axiom,
% 18.55/18.46 ! [V_i,V_j] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 18.55/18.46 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__Cons,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 18.55/18.46 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 & ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_drop__upt,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__drop,axiom,
% 18.55/18.46 ! [V_n,V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__upt,axiom,
% 18.55/18.46 ! [V_j,V_i] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__0,axiom,
% 18.55/18.46 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted_Oequations_I1_J,axiom,
% 18.55/18.46 ! [T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__take,axiom,
% 18.55/18.46 ! [V_n,V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__upt,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_atLeastLessThan__upt,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__distinct__set__unique,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 18.55/18.46 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 18.55/18.46 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 18.55/18.46 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__insort,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( 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))
% 18.55/18.46 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__upt,axiom,
% 18.55/18.46 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__remove1,axiom,
% 18.55/18.46 ! [V_a,V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__upt,axiom,
% 18.55/18.46 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__upto,axiom,
% 18.55/18.46 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__list__of__set__range,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__insort__insert,axiom,
% 18.55/18.46 ! [V_x_2,V_xs_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 => 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)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__conv__Cons,axiom,
% 18.55/18.46 ! [V_j,V_i] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__rec,axiom,
% 18.55/18.46 ! [V_j,V_i] :
% 18.55/18.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => 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)) )
% 18.55/18.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__tl,axiom,
% 18.55/18.46 ! [V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__insort__key,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( 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)))
% 18.55/18.46 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__map__remove1,axiom,
% 18.55/18.46 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 18.55/18.46 => 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))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__Suc__upt,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__insort__insert__key,axiom,
% 18.55/18.46 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 18.55/18.46 => 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))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__rec__number__of,axiom,
% 18.55/18.46 ! [V_n,V_m] :
% 18.55/18.46 ( ( 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)))
% 18.55/18.46 => 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))) )
% 18.55/18.46 & ( ~ 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)))
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_upt__eq__Cons__conv,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 18.55/18.46 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 18.55/18.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 18.55/18.46 & V_i_2 = V_x_2
% 18.55/18.46 & 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 ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__upt,axiom,
% 18.55/18.46 ! [V_j,V_i] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__insort,axiom,
% 18.55/18.46 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 18.55/18.46 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__nth,axiom,
% 18.55/18.46 ! [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 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_atLeastAtMost__upt,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_atLeast__upt,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 18.55/18.46 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 18.55/18.46 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 18.55/18.46 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 18.55/18.46 ( class_Groups_Ocomm__monoid__add(T_b)
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__upt,axiom,
% 18.55/18.46 ! [V_j,V_k,V_i] :
% 18.55/18.46 ( 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))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_greaterThanAtMost__upt,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted_Oequations_I2_J,axiom,
% 18.55/18.46 ! [V_a1_2,V_a2_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 18.55/18.46 <=> ( ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 18.55/18.46 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_greaterThanLessThan__upt,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__map__upt,axiom,
% 18.55/18.46 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__list__of__set,axiom,
% 18.55/18.46 ! [V_A_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 18.55/18.46 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 18.55/18.46 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 18.55/18.46 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_atMost__upto,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_insort__remove1,axiom,
% 18.55/18.46 ! [V_xs_2,V_a_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 => 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 ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__nth__mono,axiom,
% 18.55/18.46 ! [V_j,V_i,V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => 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))) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__equals__nth__mono,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 <=> ! [B_j] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => ! [B_i] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 18.55/18.46 => 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))) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__sorted__distinct__set__unique,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_c)
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 18.55/18.46 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 18.55/18.46 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 18.55/18.46 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 18.55/18.46 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sublist__shift__lemma,axiom,
% 18.55/18.46 ! [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))))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__rectangle,axiom,
% 18.55/18.46 ! [V_n_2,T_b,V_xs_2] :
% 18.55/18.46 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 18.55/18.46 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 18.55/18.46 => ( ! [B_i] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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 )
% 18.55/18.46 => 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)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose_Opsimps_I2_J,axiom,
% 18.55/18.46 ! [V_xss_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose_Opsimps_I1_J,axiom,
% 18.55/18.46 ! [T_b] :
% 18.55/18.46 ( 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))))
% 18.55/18.46 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__column,axiom,
% 18.55/18.46 ! [V_i_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__aux__filter__head,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_inj__on__rev,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__concat,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__concat,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev_Osimps_I1_J,axiom,
% 18.55/18.46 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat_Osimps_I1_J,axiom,
% 18.55/18.46 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Nil__is__rev__conv,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 18.55/18.46 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__is__Nil__conv,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.46 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_Nil__eq__concat__conv,axiom,
% 18.55/18.46 ! [V_xss_2,T_b] :
% 18.55/18.46 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 18.55/18.46 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat__eq__Nil__conv,axiom,
% 18.55/18.46 ! [V_xss_2,T_b] :
% 18.55/18.46 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 18.55/18.46 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__singleton__conv,axiom,
% 18.55/18.46 ! [V_x_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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))
% 18.55/18.46 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_singleton__rev__conv,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( 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)
% 18.55/18.46 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat_Osimps_I2_J,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__eq__Cons__iff,axiom,
% 18.55/18.46 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 18.55/18.46 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 18.55/18.46 <=> 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev_Osimps_I2_J,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__concat,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__map,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__concat,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__foldl__cons,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat__conv__foldl,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__conv__concat,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__append,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat__append,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__rev,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 18.55/18.46 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__concat,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__rev,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_listsum__rev,axiom,
% 18.55/18.46 ! [V_xs,T_a] :
% 18.55/18.46 ( class_Groups_Ocomm__monoid__add(T_a)
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__is__rev__conv,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 18.55/18.46 <=> V_xs_2 = V_ys_2 ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__swap,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 18.55/18.46 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__rev__ident,axiom,
% 18.55/18.46 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldr__foldl,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldl__foldr,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__rev,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_zip__rev,axiom,
% 18.55/18.46 ! [V_ys,T_b,V_xs,T_a] :
% 18.55/18.46 ( 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)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__filter,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_last__rev,axiom,
% 18.55/18.46 ! [T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__rev,axiom,
% 18.55/18.46 ! [T_a,V_xs] :
% 18.55/18.46 ( V_xs != c_List_Olist_ONil(T_a)
% 18.55/18.46 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__transpose,axiom,
% 18.55/18.46 ! [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)))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__take,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__drop,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rotate__rev,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose_Osimps_I3_J,axiom,
% 18.55/18.46 ! [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))))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__nth,axiom,
% 18.55/18.46 ! [V_xs,T_a,V_n] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat__injective,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 18.55/18.46 => ( 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)
% 18.55/18.46 => ( ! [B_x] :
% 18.55/18.46 ( 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))))
% 18.55/18.46 => 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)) )
% 18.55/18.46 => V_xs_2 = V_ys_2 ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat__eq__concat__iff,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,T_b] :
% 18.55/18.46 ( ! [B_x] :
% 18.55/18.46 ( 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))))
% 18.55/18.46 => 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)) )
% 18.55/18.46 => ( 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)
% 18.55/18.46 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 18.55/18.46 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_rev__update,axiom,
% 18.55/18.46 ! [V_y,V_xs,T_a,V_k] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_concat__map__singleton,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__rev__nth__mono,axiom,
% 18.55/18.46 ! [V_j,V_i,V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => 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))) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_foldr__max__sorted,axiom,
% 18.55/18.46 ! [V_y_2,V_xs_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 18.55/18.46 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 18.55/18.46 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 18.55/18.46 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 => 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) ) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose_Opsimps_I3_J,axiom,
% 18.55/18.46 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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))))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__transpose__sorted,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 18.55/18.46 => 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) )
% 18.55/18.46 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 18.55/18.46 => 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))) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__column__length,axiom,
% 18.55/18.46 ! [V_i_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => 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)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__aux__filter__tail,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__nth__transpose__sorted,axiom,
% 18.55/18.46 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => ( 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))))
% 18.55/18.46 => ( 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))))
% 18.55/18.46 => 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) ) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transpose__transpose,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( 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)))
% 18.55/18.46 => 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) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 18.55/18.46 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__map,axiom,
% 18.55/18.46 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_return__list__def,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_zip__takeWhile__snd,axiom,
% 18.55/18.46 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_zip__takeWhile__fst,axiom,
% 18.55/18.46 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__takeWhileD,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__eq__all__conv,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__takeWhile__le,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__eq__take,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__takeWhile,axiom,
% 18.55/18.46 ! [V_Pa_2,V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__tail,axiom,
% 18.55/18.46 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 18.55/18.46 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 18.55/18.46 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) )
% 18.55/18.46 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__takeWhile,axiom,
% 18.55/18.46 ! [V_Pa_2,V_xs_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 18.55/18.46 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__append1,axiom,
% 18.55/18.46 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_nth__length__takeWhile,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 18.55/18.46 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__nth,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 18.55/18.46 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_map__upds__def,axiom,
% 18.55/18.46 ! [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)))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__not__last,axiom,
% 18.55/18.46 ! [T_b,V_xs_2] :
% 18.55/18.46 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 18.55/18.46 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 18.55/18.46 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( 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)))
% 18.55/18.46 => 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) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 18.55/18.46 ! [V_l] :
% 18.55/18.46 ( c_List_Onat__list(V_l)
% 18.55/18.46 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__remdups__concat,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__remdups,axiom,
% 18.55/18.46 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__remdups__leq,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups__map__remdups,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_embed__list__def,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_set__remdups,axiom,
% 18.55/18.46 ! [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) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups_Osimps_I1_J,axiom,
% 18.55/18.46 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups__eq__nil__right__iff,axiom,
% 18.55/18.46 ! [V_x_2,T_b] :
% 18.55/18.46 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 18.55/18.46 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups__eq__nil__iff,axiom,
% 18.55/18.46 ! [V_x_2,T_b] :
% 18.55/18.46 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 18.55/18.46 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__remdups,axiom,
% 18.55/18.46 ! [V_l,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remove1__remdups,axiom,
% 18.55/18.46 ! [V_x,V_xs,T_a] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__remdups__id,axiom,
% 18.55/18.46 ! [V_xs,T_a] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.46 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups__id__iff__distinct,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 18.55/18.46 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__remdups__eq,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( 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)
% 18.55/18.46 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups__remdups,axiom,
% 18.55/18.46 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups__filter,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_remdups_Osimps_I2_J,axiom,
% 18.55/18.46 ! [V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => 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) )
% 18.55/18.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => 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)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__remdups__card__conv,axiom,
% 18.55/18.46 ! [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)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 18.55/18.46 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 18.55/18.46 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 18.55/18.46 => 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)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 18.55/18.46 ! [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))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__neq__rev,axiom,
% 18.55/18.46 ! [V_x_2,V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => 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))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile__neq__rev,axiom,
% 18.55/18.46 ! [V_x_2,V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => 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))) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile__map,axiom,
% 18.55/18.46 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_takeWhile__dropWhile__id,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__dropWhile__le,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__dropWhile,axiom,
% 18.55/18.46 ! [V_Pa_2,V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 18.55/18.46 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 18.55/18.46 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) )
% 18.55/18.46 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__dropWhile,axiom,
% 18.55/18.46 ! [V_Pa_2,V_xs_2,T_b] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_b)
% 18.55/18.46 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 18.55/18.46 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_hd__dropWhile,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 18.55/18.46 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 18.55/18.46 <=> ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile__append1,axiom,
% 18.55/18.46 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 18.55/18.46 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 18.55/18.46 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
% 18.55/18.46 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 18.55/18.46 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 18.55/18.46 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile__eq__drop,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_dropWhile__nth,axiom,
% 18.55/18.46 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 18.55/18.46 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_listsum__map__filter,axiom,
% 18.55/18.46 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
% 18.55/18.46 ( class_Groups_Omonoid__add(T_c)
% 18.55/18.46 => ( ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 18.55/18.46 => ( ~ hBOOL(hAPP(V_Pa_2,B_x))
% 18.55/18.46 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 18.55/18.46 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sorted__nth__monoI,axiom,
% 18.55/18.46 ! [V_xs,T_a] :
% 18.55/18.46 ( class_Orderings_Olinorder(T_a)
% 18.55/18.46 => ( ! [B_i,B_j] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 18.55/18.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 18.55/18.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
% 18.55/18.46 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_n__lists_Osimps_I2_J,axiom,
% 18.55/18.46 ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sublists__powset,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__n__lists,axiom,
% 18.55/18.46 ! [V_n,V_xs,T_a] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 18.55/18.46 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_distinct__set__sublists,axiom,
% 18.55/18.46 ! [V_xs_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 18.55/18.46 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__n__lists,axiom,
% 18.55/18.46 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_length__n__lists__elem,axiom,
% 18.55/18.46 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
% 18.55/18.46 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 18.55/18.46
% 18.55/18.46 fof(fact_sublists_Osimps_I1_J,axiom,
% 18.55/18.46 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ).
% 18.55/18.46
% 18.55/18.46 %----Arity declarations (201)
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 18.55/18.46 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Obounded__lattice(T_1)
% 18.55/18.46 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 18.55/18.46 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Obounded__lattice(T_1)
% 18.55/18.46 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Obounded__lattice(T_1)
% 18.55/18.46 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Olattice(T_1)
% 18.55/18.46 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Olattice(T_1)
% 18.55/18.46 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Odistrib__lattice(T_1)
% 18.55/18.46 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Oboolean__algebra(T_1)
% 18.55/18.46 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Orderings_Opreorder,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Orderings_Opreorder(T_1)
% 18.55/18.46 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 18.55/18.46 ! [T_1,T_2] :
% 18.55/18.46 ( ( class_Finite__Set_Ofinite(T_2)
% 18.55/18.46 & class_Finite__Set_Ofinite(T_1) )
% 18.55/18.46 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Lattices_Olattice,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Lattices_Olattice(T_1)
% 18.55/18.46 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Orderings_Oorder,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Orderings_Oorder(T_1)
% 18.55/18.46 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Orderings_Otop,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Orderings_Otop(T_1)
% 18.55/18.46 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Orderings_Oord,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Orderings_Oord(T_1)
% 18.55/18.46 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Orderings_Obot,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Orderings_Obot(T_1)
% 18.55/18.46 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Groups_Ouminus,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Groups_Ouminus(T_1)
% 18.55/18.46 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_fun__Groups_Ominus,axiom,
% 18.55/18.46 ! [T_2,T_1] :
% 18.55/18.46 ( class_Groups_Ominus(T_1)
% 18.55/18.46 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 18.55/18.46 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 18.55/18.46 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 18.55/18.46 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 18.55/18.46 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 18.55/18.46 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 18.55/18.46 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 18.55/18.46 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 18.55/18.46 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 18.55/18.46 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 18.55/18.46 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 18.55/18.46 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 18.55/18.46 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 18.55/18.46 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 18.55/18.46 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 18.55/18.46 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 18.55/18.46 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 18.55/18.46 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 18.55/18.46 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 18.55/18.46 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 18.55/18.46 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 18.55/18.46 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 18.55/18.46 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 18.55/18.46 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 18.55/18.46 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 18.55/18.46 class_Orderings_Opreorder(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 18.55/18.46 class_Orderings_Olinorder(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 18.55/18.46 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 18.55/18.46 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 18.55/18.46 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 18.55/18.46 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 18.55/18.46 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 18.55/18.46 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 18.55/18.46 class_Lattices_Olattice(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 18.55/18.46 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 18.55/18.46 class_Divides_Oring__div(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 18.55/18.46 class_Rings_Omult__zero(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 18.55/18.46 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 18.55/18.46 class_Orderings_Oorder(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 18.55/18.46 class_Int_Oring__char__0(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 18.55/18.46 class_Int_Onumber__ring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 18.55/18.46 class_Rings_Osemiring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 18.55/18.46 class_Orderings_Oord(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 18.55/18.46 class_Groups_Ouminus(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 18.55/18.46 class_Groups_Osgn__if(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 18.55/18.46 class_Groups_Oabs__if(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 18.55/18.46 class_Rings_Oring__1(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 18.55/18.46 class_Groups_Ominus(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Power_Opower,axiom,
% 18.55/18.46 class_Power_Opower(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 18.55/18.46 class_Groups_Ozero(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oring,axiom,
% 18.55/18.46 class_Rings_Oring(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 18.55/18.46 class_Rings_Oidom(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Int_Onumber,axiom,
% 18.55/18.46 class_Int_Onumber(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Groups_Oone,axiom,
% 18.55/18.46 class_Groups_Oone(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 18.55/18.46 class_Rings_Odvd(tc_Int_Oint) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 18.55/18.46 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 18.55/18.46 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 18.55/18.46 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 18.55/18.46 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 18.55/18.46 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 18.55/18.46 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 18.55/18.46 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 18.55/18.46 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 18.55/18.46 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 18.55/18.46 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 18.55/18.46 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 18.55/18.46 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 18.55/18.46 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 18.55/18.46 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 18.55/18.46 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 18.55/18.46 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 18.55/18.46 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 18.55/18.46 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 18.55/18.46 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 18.55/18.46 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 18.55/18.46 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 18.55/18.46 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 18.55/18.46 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 18.55/18.46 class_Lattices_Olattice(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 18.55/18.46 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 18.55/18.46 class_Orderings_Oorder(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 18.55/18.46 class_Rings_Osemiring(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 18.55/18.46 class_Orderings_Oord(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 18.55/18.46 class_Orderings_Obot(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 18.55/18.46 class_Groups_Ominus(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Power_Opower,axiom,
% 18.55/18.46 class_Power_Opower(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 18.55/18.46 class_Groups_Ozero(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 18.55/18.46 class_Int_Onumber(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 18.55/18.46 class_Groups_Oone(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 18.55/18.46 class_Rings_Odvd(tc_Nat_Onat) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 18.55/18.46 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 18.55/18.46 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 18.55/18.46 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 18.55/18.46 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 18.55/18.46 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 18.55/18.46 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 18.55/18.46 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 18.55/18.46 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 18.55/18.46 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 18.55/18.46 class_Lattices_Olattice(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 18.55/18.46 class_Orderings_Oorder(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 18.55/18.46 class_Orderings_Otop(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 18.55/18.46 class_Orderings_Oord(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 18.55/18.46 class_Orderings_Obot(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 18.55/18.46 class_Groups_Ouminus(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 18.55/18.46 class_Groups_Ominus(tc_HOL_Obool) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 18.55/18.46 ! [T_1,T_2] :
% 18.55/18.46 ( ( class_Finite__Set_Ofinite(T_2)
% 18.55/18.46 & class_Finite__Set_Ofinite(T_1) )
% 18.55/18.46 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 18.55/18.46 ! [T_1] :
% 18.55/18.46 ( class_Finite__Set_Ofinite(T_1)
% 18.55/18.46 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 18.55/18.46 ! [T_1,T_2] :
% 18.55/18.46 ( ( class_Finite__Set_Ofinite(T_2)
% 18.55/18.46 & class_Finite__Set_Ofinite(T_1) )
% 18.55/18.46 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_prod__Smallcheck_Osmall,axiom,
% 18.55/18.46 ! [T_1,T_2] :
% 18.55/18.46 ( ( class_Smallcheck_Osmall(T_2)
% 18.55/18.46 & class_Smallcheck_Osmall(T_1) )
% 18.55/18.46 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 18.55/18.46 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 18.55/18.46 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 18.55/18.46 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 18.55/18.46 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 18.55/18.46 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 18.55/18.46 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 18.55/18.46 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 18.55/18.46 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 18.55/18.46 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 18.55/18.46 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 18.55/18.46 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 18.55/18.46 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 18.55/18.46 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 18.55/18.46 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 18.55/18.46 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 18.55/18.46 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 18.55/18.46 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 18.55/18.46 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 18.55/18.46 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 18.55/18.46 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 18.55/18.46 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 18.55/18.46 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 18.55/18.46 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 18.55/18.46 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 18.55/18.46 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 18.55/18.46 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 18.55/18.46 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 18.55/18.46 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 18.55/18.46 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 18.55/18.46 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 18.55/18.46 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 18.55/18.46 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 18.55/18.46 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 18.55/18.46
% 18.55/18.46 %----Helper facts (20)
% 18.55/18.46 fof(help_c__COMBI__1,axiom,
% 18.55/18.46 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__COMBK__1,axiom,
% 18.55/18.46 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__COMBB__1,axiom,
% 18.55/18.46 ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__COMBC__1,axiom,
% 18.55/18.46 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__COMBS__1,axiom,
% 18.55/18.46 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fequal__1,axiom,
% 18.55/18.46 ! [V_y_2,V_x_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 18.55/18.46 | V_x_2 = V_y_2 ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fequal__2,axiom,
% 18.55/18.46 ! [V_y_2,V_x_2] :
% 18.55/18.46 ( V_x_2 != V_y_2
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fFalse__1,axiom,
% 18.55/18.46 ~ hBOOL(c_fFalse) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fTrue__1,axiom,
% 18.55/18.46 hBOOL(c_fTrue) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fNot__1,axiom,
% 18.55/18.46 ! [V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 18.55/18.46 | ~ hBOOL(V_Pa_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fNot__2,axiom,
% 18.55/18.46 ! [V_Pa_2] :
% 18.55/18.46 ( ~ ~ hBOOL(V_Pa_2)
% 18.55/18.46 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fconj__1,axiom,
% 18.55/18.46 ! [V_Qa_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(V_Pa_2)
% 18.55/18.46 | ~ hBOOL(V_Qa_2)
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fconj__2,axiom,
% 18.55/18.46 ! [V_Qa_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 18.55/18.46 | hBOOL(V_Pa_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fconj__3,axiom,
% 18.55/18.46 ! [V_Qa_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 18.55/18.46 | hBOOL(V_Qa_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fdisj__1,axiom,
% 18.55/18.46 ! [V_Qa_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(V_Pa_2)
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fdisj__2,axiom,
% 18.55/18.46 ! [V_Pa_2,V_Qa_2] :
% 18.55/18.46 ( ~ hBOOL(V_Qa_2)
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fdisj__3,axiom,
% 18.55/18.46 ! [V_Qa_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
% 18.55/18.46 | hBOOL(V_Pa_2)
% 18.55/18.46 | hBOOL(V_Qa_2) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fimplies__1,axiom,
% 18.55/18.46 ! [V_Qa_2,V_Pa_2] :
% 18.55/18.46 ( hBOOL(V_Pa_2)
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fimplies__2,axiom,
% 18.55/18.46 ! [V_Pa_2,V_Qa_2] :
% 18.55/18.46 ( ~ hBOOL(V_Qa_2)
% 18.55/18.46 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 18.55/18.46
% 18.55/18.46 fof(help_c__fimplies__3,axiom,
% 18.55/18.46 ! [V_Qa_2,V_Pa_2] :
% 18.55/18.46 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
% 18.55/18.46 | ~ hBOOL(V_Pa_2)
% 18.55/18.46 | hBOOL(V_Qa_2) ) ).
% 18.55/18.46
% 18.55/18.46 %----Conjectures (5)
% 18.55/18.46 fof(conj_0,hypothesis,
% 18.55/18.46 hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)) ).
% 18.55/18.46
% 18.55/18.46 fof(conj_1,hypothesis,
% 18.55/18.46 ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 18.55/18.46 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,B_x) ) ).
% 18.55/18.46
% 18.55/18.46 fof(conj_2,hypothesis,
% 18.55/18.46 ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
% 18.55/18.46 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Com_Ocom_OBODY,B_x)),v_Q(B_x))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(conj_3,hypothesis,
% 18.55/18.46 ! [B_x] :
% 18.55/18.46 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
% 18.55/18.46 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ) ).
% 18.55/18.46
% 18.55/18.46 fof(conj_4,conjecture,
% 18.55/18.46 c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))) ).
% 18.55/18.46
% 18.55/18.46 %------------------------------------------------------------------------------
% 18.55/18.46 %-------------------------------------------
% 18.55/18.46 % Proof found
% 18.55/18.46 % SZS status Theorem for theBenchmark
% 18.55/18.46 % SZS output start Proof
% 18.55/18.47 %ClaNum:9991(EqnAxiom:2751)
% 18.55/18.47 %VarNum:77871(SingletonVarNum:23349)
% 18.55/18.47 %MaxLitNum:8
% 18.55/18.47 %MaxfuncDepth:13
% 18.55/18.47 %SharedTerms:1033
% 18.55/18.47 %goalClause: 4399
% 18.55/18.47 %singleGoalClaCount:1
% 18.55/18.47 [2755]P1(a176)
% 18.55/18.47 [2756]P2(a838)
% 18.55/18.47 [2757]P2(a1)
% 18.55/18.47 [2758]P2(a101)
% 18.55/18.47 [2759]P3(a838)
% 18.55/18.47 [2760]P3(a1)
% 18.55/18.47 [2761]P3(a101)
% 18.55/18.47 [2762]P84(a838)
% 18.55/18.47 [2763]P84(a1)
% 18.55/18.47 [2764]P84(a101)
% 18.55/18.47 [2765]P85(a838)
% 18.55/18.47 [2766]P85(a832)
% 18.55/18.47 [2767]P85(a1)
% 18.55/18.47 [2768]P85(a101)
% 18.55/18.47 [2769]P102(a838)
% 18.55/18.47 [2770]P102(a832)
% 18.55/18.47 [2771]P102(a1)
% 18.55/18.47 [2772]P102(a101)
% 18.55/18.47 [2773]P86(a838)
% 18.55/18.47 [2774]P86(a1)
% 18.55/18.47 [2775]P86(a101)
% 18.55/18.47 [2776]P87(a838)
% 18.55/18.47 [2777]P87(a1)
% 18.55/18.47 [2778]P87(a101)
% 18.55/18.47 [2779]P101(a838)
% 18.55/18.47 [2780]P101(a832)
% 18.55/18.47 [2781]P101(a1)
% 18.55/18.47 [2782]P101(a101)
% 18.55/18.47 [2783]P103(a1)
% 18.55/18.47 [2784]P119(a1)
% 18.55/18.47 [2785]P88(a1)
% 18.55/18.47 [2786]P4(a838)
% 18.55/18.47 [2787]P4(a1)
% 18.55/18.47 [2788]P4(a101)
% 18.55/18.47 [2789]P120(a838)
% 18.55/18.47 [2790]P120(a1)
% 18.55/18.47 [2791]P120(a101)
% 18.55/18.47 [2792]P132(a1)
% 18.55/18.47 [2793]P121(a838)
% 18.55/18.47 [2794]P121(a1)
% 18.55/18.47 [2795]P121(a101)
% 18.55/18.47 [2796]P117(a1)
% 18.55/18.47 [2797]P104(a838)
% 18.55/18.47 [2798]P104(a1)
% 18.55/18.47 [2799]P104(a101)
% 18.55/18.47 [2800]P122(a838)
% 18.55/18.47 [2801]P122(a1)
% 18.55/18.47 [2802]P122(a101)
% 18.55/18.47 [2803]P118(a1)
% 18.55/18.47 [2804]P105(a838)
% 18.55/18.47 [2805]P105(a1)
% 18.55/18.47 [2806]P105(a101)
% 18.55/18.47 [2807]P63(a1)
% 18.55/18.47 [2808]P69(a1)
% 18.55/18.47 [2809]P70(a1)
% 18.55/18.47 [2810]P112(a1)
% 18.55/18.47 [2811]P126(a1)
% 18.55/18.47 [2812]P127(a838)
% 18.55/18.47 [2813]P127(a1)
% 18.55/18.47 [2814]P127(a101)
% 18.55/18.47 [2815]P128(a1)
% 18.55/18.47 [2816]P130(a838)
% 18.55/18.47 [2817]P130(a1)
% 18.55/18.47 [2818]P130(a101)
% 18.55/18.47 [2819]P129(a838)
% 18.55/18.47 [2820]P129(a1)
% 18.55/18.47 [2821]P129(a101)
% 18.55/18.47 [2822]P123(a838)
% 18.55/18.47 [2823]P123(a1)
% 18.55/18.47 [2824]P123(a101)
% 18.55/18.47 [2825]P91(a832)
% 18.55/18.47 [2826]P64(a838)
% 18.55/18.47 [2827]P64(a1)
% 18.55/18.47 [2828]P64(a101)
% 18.55/18.47 [2829]P65(a838)
% 18.55/18.47 [2830]P65(a1)
% 18.55/18.47 [2831]P65(a101)
% 18.55/18.47 [2832]P5(a838)
% 18.55/18.47 [2833]P5(a1)
% 18.55/18.47 [2834]P5(a101)
% 18.55/18.47 [2835]P71(a838)
% 18.55/18.47 [2836]P71(a1)
% 18.55/18.47 [2837]P71(a101)
% 18.55/18.47 [2838]P76(a838)
% 18.55/18.47 [2839]P76(a1)
% 18.55/18.47 [2840]P76(a101)
% 18.55/18.47 [2841]P77(a838)
% 18.55/18.47 [2842]P77(a1)
% 18.55/18.47 [2843]P77(a101)
% 18.55/18.47 [2844]P136(a838)
% 18.55/18.47 [2845]P136(a1)
% 18.55/18.47 [2846]P72(a838)
% 18.55/18.47 [2847]P72(a1)
% 18.55/18.47 [2848]P72(a101)
% 18.55/18.47 [2849]P67(a838)
% 18.55/18.47 [2850]P67(a1)
% 18.55/18.47 [2851]P67(a101)
% 18.55/18.47 [2852]P79(a838)
% 18.55/18.47 [2853]P79(a1)
% 18.55/18.47 [2854]P79(a101)
% 18.55/18.47 [2855]P134(a838)
% 18.55/18.47 [2856]P134(a1)
% 18.55/18.47 [2857]P134(a101)
% 18.55/18.47 [2858]P106(a838)
% 18.55/18.47 [2859]P106(a1)
% 18.55/18.47 [2860]P106(a101)
% 18.55/18.47 [2861]P137(a838)
% 18.55/18.47 [2862]P137(a1)
% 18.55/18.47 [2863]P137(a101)
% 18.55/18.47 [2864]P68(a838)
% 18.55/18.47 [2865]P68(a1)
% 18.55/18.47 [2866]P68(a101)
% 18.55/18.47 [2867]P75(a838)
% 18.55/18.47 [2868]P75(a1)
% 18.55/18.47 [2869]P75(a101)
% 18.55/18.47 [2870]P6(a1)
% 18.55/18.47 [2871]P124(a1)
% 18.55/18.47 [2872]P125(a1)
% 18.55/18.47 [2873]P80(a838)
% 18.55/18.47 [2874]P80(a1)
% 18.55/18.47 [2875]P80(a101)
% 18.55/18.47 [2876]P107(a1)
% 18.55/18.47 [2877]P133(a1)
% 18.55/18.47 [2878]P81(a832)
% 18.55/18.47 [2879]P81(a1)
% 18.55/18.47 [2880]P82(a1)
% 18.55/18.47 [2881]P7(a838)
% 18.55/18.47 [2882]P7(a1)
% 18.55/18.47 [2883]P7(a101)
% 18.55/18.47 [2884]P8(a1)
% 18.55/18.47 [2885]P73(a838)
% 18.55/18.47 [2886]P73(a832)
% 18.55/18.47 [2887]P73(a1)
% 18.55/18.47 [2888]P73(a101)
% 18.55/18.47 [2889]P89(a1)
% 18.55/18.47 [2890]P78(a1)
% 18.55/18.47 [2891]P90(a838)
% 18.55/18.47 [2892]P90(a1)
% 18.55/18.47 [2893]P90(a101)
% 18.55/18.47 [2894]P131(a1)
% 18.55/18.47 [2895]P66(a1)
% 18.55/18.47 [2896]P108(a838)
% 18.55/18.47 [2897]P108(a1)
% 18.55/18.47 [2898]P108(a101)
% 18.55/18.47 [2899]P135(a838)
% 18.55/18.47 [2900]P135(a1)
% 18.55/18.47 [2901]P135(a101)
% 18.55/18.47 [2902]P113(a838)
% 18.55/18.47 [2903]P113(a1)
% 18.55/18.47 [2904]P113(a101)
% 18.55/18.47 [2905]P111(a1)
% 18.55/18.47 [2906]P109(a838)
% 18.55/18.47 [2907]P93(a838)
% 18.55/18.47 [2908]P93(a832)
% 18.55/18.47 [2909]P93(a1)
% 18.55/18.47 [2910]P94(a838)
% 18.55/18.47 [2911]P94(a832)
% 18.55/18.47 [2912]P94(a1)
% 18.55/18.47 [2913]P100(a838)
% 18.55/18.47 [2914]P100(a832)
% 18.55/18.47 [2915]P95(a832)
% 18.55/18.47 [2916]P58(a832)
% 18.55/18.47 [2917]P58(a841)
% 18.55/18.47 [2918]P97(a838)
% 18.55/18.47 [2919]P97(a832)
% 18.55/18.47 [2920]P97(a1)
% 18.55/18.47 [2921]P74(a838)
% 18.55/18.47 [2922]P74(a1)
% 18.55/18.47 [2923]P74(a101)
% 18.55/18.47 [2924]P99(a838)
% 18.55/18.47 [2925]P99(a832)
% 18.55/18.47 [2926]P99(a1)
% 18.55/18.47 [2927]P9(a832)
% 18.55/18.47 [2928]P98(a832)
% 18.55/18.47 [2929]P110(a832)
% 18.55/18.47 [2930]P138(a1)
% 18.55/18.47 [2931]P138(a841)
% 18.55/18.47 [2932]P83(a838)
% 18.55/18.47 [2933]P83(a1)
% 18.55/18.47 [2934]P83(a101)
% 18.55/18.47 [2935]P96(a832)
% 18.55/18.47 [2947]P36(a838,a236)
% 18.55/18.47 [2948]P36(a838,a315)
% 18.55/18.47 [4287]~E(a99,a85)
% 18.55/18.47 [4288]~E(a99,a85)
% 18.55/18.47 [4289]~P1(a177)
% 18.55/18.47 [2752]E(f2(a1),a85)
% 18.55/18.47 [2753]E(f3(a101),a4)
% 18.55/18.47 [2754]E(f102(a101),a5)
% 18.55/18.47 [2936]E(f34(a25),f2(a838))
% 18.55/18.47 [2937]E(f86(a177),f2(a838))
% 18.55/18.47 [2938]E(f86(a176),f2(a838))
% 18.55/18.47 [2939]E(f178(a838),f103(a838))
% 18.55/18.47 [2940]E(f179(a838),f2(a838))
% 18.55/18.47 [2941]E(f235(a838),f104(a838))
% 18.55/18.47 [2942]E(f105(a1),f37(a1))
% 18.55/18.47 [2943]P10(f2(a1))
% 18.55/18.47 [2944]P10(f80(a1))
% 18.55/18.47 [2984]P1(f324(a26,a25))
% 18.55/18.47 [2985]P1(f324(a26,a25))
% 18.55/18.47 [2994]P36(f844(a838,a838),a38)
% 18.55/18.47 [3023]E(f165(a834,a833,a29),a30)
% 18.55/18.47 [3339]E(f318(a838,a838,a236,a236),a38)
% 18.55/18.47 [4290]~E(f80(a1),f2(a1))
% 18.55/18.47 [2945]E(f113(f2(a838)),f2(a838))
% 18.55/18.47 [2946]E(f6(f2(a101)),f2(a838))
% 18.55/18.47 [2950]E(f324(f81(a1),a85),a85)
% 18.55/18.47 [2953]E(f324(a107,f2(a1)),f2(a838))
% 18.55/18.47 [2954]E(f324(a5,f2(a838)),f2(a101))
% 18.55/18.47 [2955]E(f324(a114,f2(a838)),f80(a838))
% 18.55/18.47 [2956]E(f324(a107,f80(a1)),f80(a838))
% 18.55/18.47 [2957]E(f324(a5,f80(a838)),f80(a101))
% 18.55/18.47 [2958]E(f324(f106(a838),a85),f2(a838))
% 18.55/18.47 [2959]E(f324(f106(a1),a85),f2(a1))
% 18.55/18.47 [2960]E(f324(f106(a101),a85),f2(a101))
% 18.55/18.47 [2961]E(f324(a107,f2(a1)),f2(a838))
% 18.55/18.47 [2962]E(f324(f180(a833),a25),f2(a838))
% 18.55/18.47 [2963]E(f324(f106(a838),a85),f2(a838))
% 18.55/18.47 [2969]E(f324(f81(a1),f80(a1)),a99)
% 18.55/18.47 [2974]E(f324(f102(a1),f2(a838)),f2(a1))
% 18.55/18.47 [2975]E(f324(f102(a1),f80(a838)),f80(a1))
% 18.55/18.47 [2976]E(f324(f180(a838),f2(a838)),f2(a838))
% 18.55/18.47 [2977]E(f324(f180(a101),f2(a101)),f2(a838))
% 18.55/18.47 [2978]E(f324(f102(a1),f2(a838)),f2(a1))
% 18.55/18.47 [2979]E(f324(f102(a1),f80(a838)),f80(a1))
% 18.55/18.47 [2980]E(f324(f81(a1),f2(a1)),f2(a1))
% 18.55/18.47 [2990]E(f324(a107,f80(a1)),f324(a114,f2(a838)))
% 18.55/18.47 [2992]E(f316(f844(a838,a838),a38),a39)
% 18.55/18.47 [2993]E(f317(f844(a838,a838),a38),a40)
% 18.55/18.47 [3014]E(f324(f258(a838),f2(a838)),f179(f845(a838,a832)))
% 18.55/18.47 [3015]E(f324(f259(a838),f2(a838)),f238(f845(a838,a832)))
% 18.55/18.47 [3025]P38(f179(f845(a1,a832)))
% 18.55/18.47 [3062]E(f324(f324(f3(a101),f2(a101)),f80(a101)),f2(a101))
% 18.55/18.47 [3104]E(f324(f324(f141(a1,a838),a107),f115(a1)),f115(a838))
% 18.55/18.47 [3136]P1(f324(f324(f232(a1),a99),f2(a1)))
% 18.55/18.47 [3161]P1(f324(f324(f232(a1),f2(a1)),f80(a1)))
% 18.55/18.47 [3162]P1(f324(f324(f231(a1),f2(a1)),f2(a1)))
% 18.55/18.47 [3163]P1(f324(f324(f231(a1),f2(a1)),f80(a1)))
% 18.55/18.47 [3330]P1(f324(f64(a834),f168(a834,a833,a30)))
% 18.55/18.47 [3372]E(f324(f324(f282(a838,a838,a838),a315),f301(a838,a315)),a236)
% 18.55/18.47 [3409]P40(a1,a838,a107,f324(f231(a1),f2(a1)))
% 18.55/18.47 [3412]E(f324(f324(f45(a838,f845(a838,a832)),f238(f845(a838,a832))),f294(a838)),f238(f845(a838,a832)))
% 18.55/18.47 [3413]E(f324(f324(f45(a838,f845(a838,a832)),f238(f845(a838,a832))),f258(a838)),f238(f845(a838,a832)))
% 18.55/18.47 [3414]E(f324(f324(f45(a838,f845(a838,a832)),f238(f845(a838,a832))),f259(a838)),f238(f845(a838,a832)))
% 18.55/18.47 [3415]E(f324(f324(f46(a838,f845(a838,a832)),f238(f845(a838,a832))),f297(a838)),f179(f845(a838,a832)))
% 18.55/18.47 [3431]P29(a838,a1,f102(a1),f238(f845(a838,a832)))
% 18.55/18.47 [3442]P40(a838,a1,f102(a1),f324(f18(a832,a838),a176))
% 18.55/18.47 [3576]E(f324(f75(a838,a101,a1,a5),a107),f106(a101))
% 18.55/18.47 [3794]P54(a101,a838,a22,a5,f238(f845(a838,a832)))
% 18.55/18.47 [3802]P54(a1,f845(f844(a838,a838),a832),a110,a91,a100)
% 18.55/18.47 [4068]E(f253(a1,a1,a1,a1,f37(a1),f81(a1)),a57)
% 18.55/18.47 [4321]~E(f324(f106(a1),a99),f324(f106(a1),a85))
% 18.55/18.47 [4322]~P1(f324(a185,f2(a1)))
% 18.55/18.47 [4323]~P1(f324(a185,f80(a1)))
% 18.55/18.47 [4375]~P1(f324(f324(f232(a1),a85),f2(a1)))
% 18.55/18.47 [4399]~P31(a830,f324(a114,a851),f324(f324(f324(f93(a830),f849(a846)),f324(a27,a846)),f852(a846)))
% 18.55/18.47 [3006]E(f324(f324(f82(a1),a85),a99),a99)
% 18.55/18.47 [3007]E(f324(f324(f82(a1),a85),a85),a85)
% 18.55/18.47 [3008]E(f324(f324(f3(a1),a99),a99),a85)
% 18.55/18.47 [3022]E(f324(f102(a1),f324(a114,f2(a838))),f80(a1))
% 18.55/18.47 [3086]E(f324(f41(a841),f238(f845(a841,a832))),f80(a838))
% 18.55/18.47 [3109]P1(f324(a185,f324(f106(a1),a99)))
% 18.55/18.47 [3110]P1(f324(f324(f326(a834),a846),a847))
% 18.55/18.47 [3111]P1(f324(f324(f232(a1),a99),a85))
% 18.55/18.47 [3112]P1(f324(f324(f231(a1),a99),a99))
% 18.55/18.47 [3113]P1(f324(f324(f231(a1),a99),a85))
% 18.55/18.47 [3114]P1(f324(f324(f231(a1),a85),a85))
% 18.55/18.47 [3173]E(f324(f324(f303(a838),f2(a838)),f179(f845(a838,a832))),f324(f294(a838),f2(a838)))
% 18.55/18.47 [3228]P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),a85)))
% 18.55/18.47 [3239]E(f324(f304(a838,a838,a114),f238(f845(a838,a832))),f324(f297(a838),f2(a838)))
% 18.55/18.47 [3244]E(f324(f304(a1,a838,a107),f179(f845(a1,a832))),f179(f845(a838,a832)))
% 18.55/18.47 [3253]E(f324(f304(a838,a1,f102(a1)),f179(f845(a838,a832))),f179(f845(a1,a832)))
% 18.55/18.47 [3277]P12(f844(a838,a838),f238(f845(f844(a838,a838),a832)),a111)
% 18.55/18.47 [3583]E(f324(f75(a838,a1,a101,f102(a1)),a22),a23)
% 18.55/18.47 [3643]P36(a838,f324(f257(f844(a838,a838)),f324(f252(a838,a838,a832),f232(a838))))
% 18.55/18.47 [4366]~P1(f324(a185,f324(f106(a1),a85)))
% 18.55/18.47 [4367]~P1(f324(f324(f232(a1),a99),a99))
% 18.55/18.47 [4368]~P1(f324(f324(f232(a1),a85),a99))
% 18.55/18.47 [4369]~P1(f324(f324(f232(a1),a85),a85))
% 18.55/18.47 [4370]~P1(f324(f324(f231(a1),a85),a99))
% 18.55/18.47 [4385]~P1(f324(f64(a838),f238(f845(a838,a832))))
% 18.55/18.47 [4386]~P1(f324(f64(a1),f238(f845(a1,a832))))
% 18.55/18.47 [4233]E(f324(f252(a1,a1,a832),f324(f324(f10(f845(a1,a832),f845(a1,a832),a1),f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f232(a1),f2(a1))))),f324(f324(f9(a1,a1,f845(a1,a832)),f324(f324(f10(f845(a1,f845(a1,a832)),f845(a1,f845(a1,a832)),a1),f9(a1,a1,a832)),f324(f324(f10(f845(a1,a1),f845(a1,f845(a1,a832)),a1),f324(f10(a1,f845(a1,a832),a1),a321)),a211))),f80(a1)))),a207)
% 18.55/18.47 [3280]E(f324(f324(f3(a1),f324(f324(f82(a1),a99),a99)),a99),a99)
% 18.55/18.47 [3312]E(f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99),f324(f81(a1),a99))
% 18.55/18.47 [3354]E(f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99),f324(f324(f3(a1),a85),a99))
% 18.55/18.47 [3507]E(f324(f324(f63(f844(a838,a838)),f238(f845(f844(a838,a838),a832))),a111),a100)
% 18.55/18.47 [3536]E(f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f80(a838))
% 18.55/18.47 [3537]E(f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f80(a1))
% 18.55/18.47 [3538]E(f324(f106(a101),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f80(a101))
% 18.55/18.47 [3539]E(f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f80(a838))
% 18.55/18.47 [3543]E(f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(a114,f2(a838)))
% 18.55/18.47 [3932]E(f324(f324(f103(f845(f844(f844(a838,a838),f844(a838,a838)),a832)),a38),f301(f844(a838,a838),f179(f845(f844(f844(a838,a838),f844(a838,a838)),a832)))),a72)
% 18.55/18.47 [3999]E(f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),f2(a838)),f2(a838))),f179(f845(f844(a838,a838),a832))))),f2(a1))
% 18.55/18.47 [4000]E(f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),f80(a838)),f2(a838))),f179(f845(f844(a838,a838),a832))))),f80(a1))
% 18.55/18.47 [4014]E(f324(f257(f844(a838,a838)),f324(f252(a838,a838,a832),f324(f324(f10(a838,f845(a838,a832),a838),f324(f9(a838,a838,a832),a321)),a114))),a315)
% 18.55/18.47 [3984]E(f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),f324(a114,f324(a114,f2(a838))))
% 18.55/18.47 [3985]E(f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),f324(a114,f324(a114,f2(a838))))
% 18.55/18.47 [3988]E(f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),f324(f324(f82(a838),f80(a838)),f80(a838)))
% 18.55/18.47 [3989]E(f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),f324(f41(a832),f238(f845(a832,a832))))
% 18.55/18.47 [4053]P10(f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))
% 18.55/18.47 [4124]P30(f845(f844(a838,a838),a832),f324(f324(f247(f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832),f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832)),a39),a73))
% 18.55/18.47 [4125]P30(f845(f844(a838,a838),a832),f324(f324(f247(f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832),f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832)),a40),a71))
% 18.55/18.47 [4163]E(f324(f324(f103(f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832)),f316(f844(a838,a838),a72)),f324(f324(f303(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),f179(f845(f844(a838,a838),a832))),f179(f845(f844(a838,a838),a832)))),f179(f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832)))),a73)
% 18.55/18.47 [4164]E(f324(f324(f103(f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832)),f317(f844(a838,a838),a72)),f324(f324(f303(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),f179(f845(f844(a838,a838),a832))),f179(f845(f844(a838,a838),a832)))),f179(f845(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a832)))),a71)
% 18.55/18.47 [4055]E(f324(a107,f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(a114,f324(a114,f2(a838))))
% 18.55/18.47 [4100]E(f324(a107,f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))
% 18.55/18.47 [4101]E(f324(f102(a1),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))
% 18.55/18.47 [4135]P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.47 [4136]E(f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99)),f324(a114,f324(a114,f324(a114,f2(a838)))))
% 18.55/18.47 [4177]P10(f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99)))
% 18.55/18.47 [4203]E(f324(a107,f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99)))
% 18.55/18.47 [4204]E(f324(f102(a1),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99)))
% 18.55/18.47 [4219]P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))))
% 18.55/18.47 [2949]P11(x29491,a321)
% 18.55/18.47 [3340]P29(a838,a838,a114,x33401)
% 18.55/18.47 [2964]P36(a1,f108(x29641))
% 18.55/18.47 [2965]P36(a1,f109(x29651))
% 18.55/18.47 [2968]P37(x29681,f182(x29681))
% 18.55/18.47 [3011]P36(f845(x30111,a832),f300(x30111))
% 18.55/18.47 [3037]E(f239(x30371,x30371,a321),a321)
% 18.55/18.47 [3053]E(f51(a1,x30531,x30531),f2(a1))
% 18.55/18.47 [3106]P19(x31061,f845(x31061,a832),f303(x31061))
% 18.55/18.47 [4291]~E(f324(a27,x42911),a25)
% 18.55/18.47 [4292]~E(f324(a27,x42921),a25)
% 18.55/18.47 [4293]~E(f324(a114,x42931),x42931)
% 18.55/18.47 [4294]~E(f324(a114,x42941),x42941)
% 18.55/18.47 [4301]~E(f324(a114,x43011),f2(a838))
% 18.55/18.47 [4302]~E(f324(a114,x43021),f2(a838))
% 18.55/18.47 [4303]~E(f324(a114,x43031),f2(a838))
% 18.55/18.47 [4304]~E(f324(a114,x43041),f2(a838))
% 18.55/18.47 [4305]~E(f324(a114,x43051),f2(a838))
% 18.55/18.47 [4306]~E(f324(a114,x43061),f2(a838))
% 18.55/18.47 [2951]E(f324(f180(a838),x29511),x29511)
% 18.55/18.47 [2952]E(f324(f106(a1),x29521),x29521)
% 18.55/18.47 [2966]E(f324(a91,f325(x29661)),x29661)
% 18.55/18.47 [2967]E(f237(x29671,f2(a101)),f2(a101))
% 18.55/18.47 [2981]E(f116(x29811,f115(x29811)),f115(x29811))
% 18.55/18.47 [2982]E(f140(x29821,f115(x29821)),f115(x29821))
% 18.55/18.47 [2986]E(f34(f324(a27,x29861)),f2(a838))
% 18.55/18.47 [2987]E(f324(f153(x29871),f115(x29871)),f115(x29871))
% 18.55/18.47 [2988]E(f324(f156(x29881),f115(x29881)),f115(x29881))
% 18.55/18.47 [2989]E(f324(f154(x29891),f115(x29891)),f115(x29891))
% 18.55/18.47 [2995]E(f324(f106(a1),x29951),f324(f105(a1),x29951))
% 18.55/18.47 [2996]E(f324(a5,f324(a22,x29961)),x29961)
% 18.55/18.47 [2997]E(f324(a5,f324(a22,x29971)),x29971)
% 18.55/18.47 [2998]E(f324(a22,f324(a5,x29981)),x29981)
% 18.55/18.47 [2999]E(f324(a91,f324(a110,x29991)),x29991)
% 18.55/18.47 [3000]P10(f324(f102(a1),x30001))
% 18.55/18.47 [3004]E(f324(f180(f842(x30041)),f182(x30041)),f2(a838))
% 18.55/18.47 [3005]E(f324(f180(f839(x30051)),f115(x30051)),f2(a838))
% 18.55/18.47 [3010]E(f324(f180(a833),f324(a27,x30101)),f2(a838))
% 18.55/18.47 [3020]E(f225(x30201,f182(x30201)),f179(f845(x30201,a832)))
% 18.55/18.47 [3028]E(f324(f324(f83(a838),x30281),f80(a838)),x30281)
% 18.55/18.47 [3029]E(f324(f324(f83(a1),x30291),f80(a1)),x30291)
% 18.55/18.47 [3030]E(f324(f324(f82(a838),x30301),f2(a838)),x30301)
% 18.55/18.47 [3031]E(f324(f324(f82(a1),x30311),f2(a1)),x30311)
% 18.55/18.47 [3032]E(f324(f324(f3(a838),x30321),f2(a838)),x30321)
% 18.55/18.47 [3033]E(f324(f324(f178(a838),x30331),f2(a838)),x30331)
% 18.55/18.47 [3034]E(f324(f324(f83(a838),x30341),f2(a838)),f2(a838))
% 18.55/18.47 [3035]E(f324(f324(f42(a1),x30351),f2(a1)),f2(a1))
% 18.55/18.47 [3036]E(f324(f324(f235(a838),x30361),f2(a838)),f2(a838))
% 18.55/18.47 [3043]E(f324(f157(x30431),f115(x30431)),f179(f845(x30431,a832)))
% 18.55/18.47 [3048]P1(f324(f127(x30481),f115(x30481)))
% 18.55/18.47 [3054]E(f324(f141(x30541,x30541),f7(x30541)),f37(f839(x30541)))
% 18.55/18.47 [3055]E(f324(f141(x30551,x30551),f37(x30551)),f37(f839(x30551)))
% 18.55/18.47 [3056]E(f324(f195(x30561,x30561),f7(x30561)),f37(f842(x30561)))
% 18.55/18.47 [3057]E(f324(f195(x30571,x30571),f37(x30571)),f37(f842(x30571)))
% 18.55/18.47 [3058]E(f51(a1,x30581,f2(a1)),x30581)
% 18.55/18.47 [3059]E(f324(f231(a838),f324(a114,x30591)),f324(f232(a838),x30591))
% 18.55/18.47 [3060]E(f324(f258(a838),f324(a114,x30601)),f324(f294(a838),x30601))
% 18.55/18.47 [3061]E(f324(f259(a838),f324(a114,x30611)),f324(f297(a838),x30611))
% 18.55/18.47 [3063]E(f51(a1,f2(a1),x30631),f2(a1))
% 18.55/18.47 [3070]E(f324(f324(f82(a838),x30701),f80(a838)),f324(a114,x30701))
% 18.55/18.47 [3080]E(f324(f295(a838,x30801),f2(a838)),f179(f845(a838,a832)))
% 18.55/18.47 [3092]E(f296(a838,f2(a838),x30921),f324(f294(a838),x30921))
% 18.55/18.47 [3139]E(f324(f324(f3(a838),f324(a114,x31391)),f80(a838)),x31391)
% 18.55/18.47 [3152]E(f53(f2(a1),x31521),f324(f324(f247(a1,a1),f2(a1)),f2(a1)))
% 18.55/18.47 [3156]E(f324(f324(f82(a838),f324(a22,x31561)),f2(a838)),f324(a22,x31561))
% 18.55/18.47 [3202]P1(f324(f324(f232(a838),x32021),f324(a114,x32021)))
% 18.55/18.47 [3214]P1(f324(f324(f232(a838),f2(a838)),f324(a114,x32141)))
% 18.55/18.47 [3226]E(f324(f324(f172(f839(x32261),f839(x32261)),f2(a838)),f153(x32261)),f37(f839(x32261)))
% 18.55/18.47 [3494]E(f324(f324(f3(a101),f324(a5,f324(a114,f324(a22,x34941)))),f80(a101)),x34941)
% 18.55/18.47 [3565]P1(f324(f324(f231(a1),f324(f81(a1),f324(f102(a1),x35651))),f2(a1)))
% 18.55/18.47 [3717]P1(f324(f324(f232(a1),f324(f81(a1),f324(f102(a1),f324(a114,x37171)))),f2(a1)))
% 18.55/18.47 [4329]~E(f238(f845(x43291,a832)),f179(f845(x43291,a832)))
% 18.55/18.47 [4376]~P1(f324(f324(f232(a838),x43761),f2(a838)))
% 18.55/18.47 [4377]~P1(f324(f324(f232(a838),x43771),f2(a838)))
% 18.55/18.47 [4378]~P1(f324(f324(f232(a838),x43781),f2(a838)))
% 18.55/18.47 [4394]~P1(f324(f324(f232(a1),f324(f102(a1),x43941)),f2(a1)))
% 18.55/18.47 [3009]E(f163(x30091,f115(f839(x30091))),f115(f839(x30091)))
% 18.55/18.47 [3012]E(f324(f324(f83(a1),a85),x30121),a85)
% 18.55/18.47 [3013]E(f324(f324(f82(a1),a85),x30131),x30131)
% 18.55/18.47 [3016]E(f324(a107,f324(f102(a1),x30161)),x30161)
% 18.55/18.47 [3017]E(f324(f324(f82(a1),x30171),a85),x30171)
% 18.55/18.47 [3018]E(f324(f324(f3(a1),x30181),a85),x30181)
% 18.55/18.47 [3021]E(f324(f324(f3(a838),x30211),x30211),f2(a838))
% 18.55/18.47 [3026]E(f324(f81(a1),f324(f81(a1),x30261)),x30261)
% 18.55/18.47 [3027]E(f324(f41(a838),f324(f258(a838),x30271)),x30271)
% 18.55/18.47 [3038]E(f324(f324(f83(a838),f80(a838)),x30381),x30381)
% 18.55/18.47 [3039]E(f324(f324(f83(a1),f80(a1)),x30391),x30391)
% 18.55/18.47 [3040]E(f324(f324(f82(a838),f2(a838)),x30401),x30401)
% 18.55/18.47 [3041]E(f324(f324(f82(a1),f2(a1)),x30411),x30411)
% 18.55/18.47 [3042]E(f324(f324(f178(a838),f2(a838)),x30421),x30421)
% 18.55/18.47 [3049]E(f324(f324(f83(a838),f2(a838)),x30491),f2(a838))
% 18.55/18.47 [3050]E(f324(f324(f42(a1),f2(a1)),x30501),f2(a1))
% 18.55/18.47 [3051]E(f324(f324(f3(a838),f2(a838)),x30511),f2(a838))
% 18.55/18.47 [3052]E(f324(f324(f235(a838),f2(a838)),x30521),f2(a838))
% 18.55/18.47 [3068]E(f324(f295(a838,f2(a838)),x30681),f324(f258(a838),x30681))
% 18.55/18.47 [3069]E(f324(f324(f83(a1),a99),x30691),f324(f81(a1),x30691))
% 18.55/18.47 [3071]E(f324(a107,f324(f106(a1),x30711)),f324(f106(a838),x30711))
% 18.55/18.47 [3072]E(f324(a107,f324(f106(a1),x30721)),f324(f106(a838),x30721))
% 18.55/18.47 [3073]E(f324(a22,f324(f106(a101),x30731)),f324(f106(a838),x30731))
% 18.55/18.47 [3074]E(f324(f41(a838),f324(f294(a838),x30741)),f324(a114,x30741))
% 18.55/18.47 [3084]E(f324(f324(f82(a838),f80(a838)),x30841),f324(a114,x30841))
% 18.55/18.47 [3088]E(f324(f105(a1),f324(f102(a1),x30881)),f324(f102(a1),x30881))
% 18.55/18.47 [3089]E(f324(f77(a1),f324(f102(a1),x30891)),f324(f102(a1),x30891))
% 18.55/18.47 [3094]E(f324(f41(x30941),f179(f845(x30941,a832))),f2(a838))
% 18.55/18.47 [3096]E(f324(f324(f42(a838),x30961),f324(a114,f2(a838))),x30961)
% 18.55/18.47 [3107]E(f51(a838,x31071,f324(a114,f2(a838))),f2(a838))
% 18.55/18.47 [3108]E(f51(a1,x31081,f324(f106(a1),a99)),f2(a1))
% 18.55/18.47 [3116]E(f324(f324(f82(a1),a99),x31161),f324(f324(f82(a1),x31161),a99))
% 18.55/18.47 [3123]E(f324(f324(f42(a1),x31231),f324(f106(a1),a99)),f324(f81(a1),x31231))
% 18.55/18.47 [3127]E(f129(a838,f324(f295(a838,x31271),f2(a838))),f115(a838))
% 18.55/18.47 [3128]E(f324(f324(f3(a1),x31281),f80(a1)),f324(f324(f82(a1),x31281),a99))
% 18.55/18.47 [3129]E(f324(f324(f82(a1),x31291),f80(a1)),f324(f324(f3(a1),x31291),a99))
% 18.55/18.47 [3131]P1(f324(f324(f186(a25),x31311),x31311))
% 18.55/18.47 [3132]P1(f324(f324(f186(a25),x31321),x31321))
% 18.55/18.47 [3133]P1(f324(f324(f231(a838),x31331),x31331))
% 18.55/18.47 [3134]P1(f324(f324(f231(a1),x31341),x31341))
% 18.55/18.47 [3135]P1(f324(f324(f280(a838),x31351),x31351))
% 18.55/18.47 [3140]E(f324(f81(a1),f324(f106(a1),x31401)),f324(f106(a1),f324(f81(a1),x31401)))
% 18.55/18.47 [3141]P1(f324(f64(a838),f324(f294(a838),x31411)))
% 18.55/18.47 [3142]P1(f324(f64(a838),f324(f258(a838),x31421)))
% 18.55/18.47 [3150]E(f147(x31501,f238(f845(x31501,a832))),f238(f845(f839(x31501),a832)))
% 18.55/18.47 [3154]P1(f324(f324(f231(a838),f2(a838)),x31541))
% 18.55/18.47 [3155]P1(f324(f324(f231(a838),f2(a838)),x31551))
% 18.55/18.47 [3166]E(f324(f324(f82(a838),f113(x31661)),f324(a114,f2(a838))),f113(f324(a114,x31661)))
% 18.55/18.47 [3167]E(f324(f257(x31671),f324(f18(a832,x31671),a177)),f179(f845(x31671,a832)))
% 18.55/18.47 [3168]E(f324(f257(x31681),f324(f18(a832,x31681),a176)),f238(f845(x31681,a832)))
% 18.55/18.47 [3172]E(f324(f324(f303(a838),x31721),f324(f258(a838),x31721)),f324(f258(a838),f324(a114,x31721)))
% 18.55/18.47 [3183]E(f324(f324(f82(a1),f80(a1)),f324(f102(a1),x31831)),f324(f102(a1),f324(a114,x31831)))
% 18.55/18.47 [3186]E(f324(f324(f139(f839(x31861)),f115(x31861)),f115(f839(x31861))),f60(x31861,f115(x31861)))
% 18.55/18.47 [3205]E(f179(f845(f844(x32051,x32051),a832)),f261(x32051,f179(f845(x32051,a832))))
% 18.55/18.47 [3206]E(f324(f302(x32061),f238(f845(x32061,a832))),f238(f845(f845(x32061,a832),a832)))
% 18.55/18.47 [3207]E(f324(f81(f845(x32071,a832)),f179(f845(x32071,a832))),f238(f845(x32071,a832)))
% 18.55/18.47 [3208]E(f324(f81(f845(x32081,a832)),f238(f845(x32081,a832))),f179(f845(x32081,a832)))
% 18.55/18.47 [3209]P1(f324(f64(x32091),f179(f845(x32091,a832))))
% 18.55/18.47 [3210]P1(f324(f64(x32101),f179(f845(x32101,a832))))
% 18.55/18.47 [3212]E(f324(f295(a838,x32121),f324(a114,x32121)),f324(f324(f303(a838),x32121),f179(f845(a838,a832))))
% 18.55/18.47 [3213]E(f87(f844(a838,a838),f54(x32131,f2(a838))),f324(f324(f247(a838,a838),f2(a838)),x32131))
% 18.55/18.47 [3227]E(f324(f324(f303(a838),f324(a114,x32271)),f324(f294(a838),x32271)),f324(f294(a838),f324(a114,x32271)))
% 18.55/18.47 [3230]P36(x32301,f179(f845(f844(x32301,x32301),a832)))
% 18.55/18.47 [3232]P1(f324(f324(f231(a1),f2(a1)),f324(f102(a1),x32321)))
% 18.55/18.47 [3233]P1(f324(f324(f231(a1),f2(a1)),f324(f102(a1),x32331)))
% 18.55/18.47 [3241]E(f324(f324(f82(a838),f324(f180(a838),x32411)),f324(a114,f2(a838))),f324(f180(a838),f324(a114,x32411)))
% 18.55/18.47 [3292]E(f324(f304(x32921,x32921,f37(x32921)),f238(f845(x32921,a832))),f238(f845(x32921,a832)))
% 18.55/18.47 [3347]P38(f324(f304(a838,a1,f102(a1)),x33471))
% 18.55/18.47 [3387]P47(x33871,f179(f845(x33871,a832)),f179(f845(f844(x33871,x33871),a832)))
% 18.55/18.47 [3406]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f3(a1),x34061),f80(a1))),f56(f324(f106(a1),a99),x34061))
% 18.55/18.47 [3407]P1(f324(f324(f326(a838),f324(a22,x34071)),f238(f845(a838,a832))))
% 18.55/18.47 [3454]P57(x34541,f324(f18(f845(x34541,a832),x34541),f324(f18(a832,x34541),a177)))
% 18.55/18.47 [3464]E(f283(a838,f280(a838),x34641,x34641),f324(f324(f303(a838),x34641),f179(f845(a838,a832))))
% 18.55/18.47 [3637]E(f324(f131(f839(x36371),f839(x36371),f125(x36371),f115(x36371)),f115(f839(x36371))),f115(x36371))
% 18.55/18.47 [3655]P1(f324(f324(f326(f845(f844(a838,a838),a832)),f325(x36551)),a100))
% 18.55/18.47 [3681]P1(f324(f324(f326(f845(f844(a838,a838),a832)),f324(a110,x36811)),a100))
% 18.55/18.47 [3812]P29(x38121,f845(x38121,a832),f324(f324(f9(x38121,f845(x38121,a832),f845(x38121,a832)),f303(x38121)),f179(f845(x38121,a832))),f238(f845(x38121,a832)))
% 18.55/18.47 [4324]~E(f324(f324(f82(a1),x43241),x43241),a99)
% 18.55/18.47 [4325]~E(f324(f324(f82(a1),x43251),x43251),a99)
% 18.55/18.47 [4364]~E(f324(a5,f324(a114,f324(a22,x43641))),f2(a101))
% 18.55/18.47 [4365]~E(f324(a5,f324(a114,f324(a22,x43651))),f2(a101))
% 18.55/18.47 [4371]~P1(f324(a185,f324(f102(a1),x43711)))
% 18.55/18.47 [4373]~P1(f324(f324(f232(a838),x43731),x43731))
% 18.55/18.47 [4374]~P1(f324(f324(f232(a838),x43741),x43741))
% 18.55/18.47 [4387]~P1(f324(f324(f231(a838),f324(a114,x43871)),x43871))
% 18.55/18.47 [3157]E(f324(a107,f324(f81(a1),f324(f102(a1),x31571))),f2(a838))
% 18.55/18.47 [3160]E(f324(f324(f82(a1),f324(f81(a1),x31601)),x31601),f2(a1))
% 18.55/18.47 [3165]E(f324(f41(a1),f324(f295(a1,f2(a1)),x31651)),f324(a107,x31651))
% 18.55/18.47 [3176]E(f324(f324(f240(a838),f324(a114,f2(a838))),x31761),f324(a114,f2(a838)))
% 18.55/18.47 [3274]E(f324(f277(x32741),f179(f845(f844(x32741,x32741),a832))),f179(f845(x32741,a832)))
% 18.55/18.47 [3276]P1(f324(f64(a1),f324(f295(a1,f2(a1)),x32761)))
% 18.55/18.47 [3282]E(f44(f845(x32821,a832),f179(f845(f845(x32821,a832),a832))),f238(f845(x32821,a832)))
% 18.55/18.47 [3283]E(f44(f845(x32831,a832),f238(f845(f845(x32831,a832),a832))),f179(f845(x32831,a832)))
% 18.55/18.47 [3284]E(f43(f845(x32841,a832),f179(f845(f845(x32841,a832),a832))),f179(f845(x32841,a832)))
% 18.55/18.47 [3285]E(f43(f845(x32851,a832),f238(f845(f845(x32851,a832),a832))),f238(f845(x32851,a832)))
% 18.55/18.47 [3290]P1(f324(f324(f280(a838),f324(a114,f2(a838))),x32901))
% 18.55/18.47 [3328]E(f324(f324(f303(f839(x33281)),f115(x33281)),f179(f845(f839(x33281),a832))),f148(x33281,f115(f845(x33281,a832))))
% 18.55/18.47 [3329]E(f324(f324(f303(f839(x33291)),f115(x33291)),f179(f845(f839(x33291),a832))),f147(x33291,f179(f845(x33291,a832))))
% 18.55/18.47 [3360]E(f324(f324(f82(a1),f324(f81(a1),x33601)),f324(f81(a1),x33601)),f324(f81(a1),f324(f324(f82(a1),x33601),x33601)))
% 18.55/18.47 [3371]E(f324(f324(f82(a838),f6(x33711)),f324(a114,f2(a838))),f6(f324(a5,f324(a114,f324(a22,x33711)))))
% 18.55/18.47 [3398]E(f324(f41(a1),f324(f304(a838,a1,f102(a1)),x33981)),f324(f41(a838),x33981))
% 18.55/18.47 [3399]P1(f324(f324(f231(a838),x33991),f324(f324(f83(a838),x33991),x33991)))
% 18.55/18.47 [3435]E(f324(f304(a1,a838,a107),f296(a1,f2(a1),f324(f102(a1),x34351))),f324(f294(a838),x34351))
% 18.55/18.47 [3449]E(f324(f324(f42(a838),f324(a114,f2(a838))),f324(f106(a838),x34491)),f324(a107,f324(f324(f42(a1),f80(a1)),f324(f106(a1),x34491))))
% 18.55/18.47 [3451]E(f324(f157(a838),f129(a838,f324(f295(a838,f2(a838)),f324(a114,x34511)))),f324(f294(a838),x34511))
% 18.55/18.47 [3452]E(f324(f324(f82(a838),f324(f180(a101),x34521)),f324(a114,f2(a838))),f324(f180(a101),f324(a5,f324(a114,f324(a22,x34521)))))
% 18.55/18.47 [3469]E(f324(f304(a1,a838,a107),f324(f304(a838,a1,f102(a1)),x34691)),x34691)
% 18.55/18.47 [3499]E(f324(f324(f303(a838),f2(a838)),f324(f304(a838,a838,a114),f324(f258(a838),x34991))),f324(f258(a838),f324(a114,x34991)))
% 18.55/18.47 [3506]P52(x35061,x35061,f301(x35061,f179(f845(f844(x35061,x35061),a832))))
% 18.55/18.47 [3512]P1(f324(a185,f324(f81(a1),f324(f102(a1),f324(a114,x35121)))))
% 18.55/18.47 [3523]E(f324(f324(f3(f845(a838,a832)),f324(f259(a838),x35231)),f324(f324(f303(a838),x35231),f179(f845(a838,a832)))),f324(f259(a838),f324(a114,x35231)))
% 18.55/18.47 [3540]E(f324(f324(f82(a1),f324(f324(f3(a1),a85),x35401)),f324(f324(f3(a1),a85),x35401)),f324(f324(f3(a1),a85),f324(f324(f82(a1),x35401),x35401)))
% 18.55/18.47 [3544]P47(x35441,f238(f845(x35441,a832)),f301(x35441,f179(f845(f844(x35441,x35441),a832))))
% 18.55/18.47 [3555]E(f324(f324(f303(f845(x35551,a832)),f179(f845(x35551,a832))),f179(f845(f845(x35551,a832),a832))),f324(f302(x35551),f179(f845(x35551,a832))))
% 18.55/18.47 [3584]E(f324(f324(f3(f845(a838,a832)),f324(f297(a838),x35841)),f324(f324(f303(a838),f324(a114,x35841)),f179(f845(a838,a832)))),f324(f297(a838),f324(a114,x35841)))
% 18.55/18.47 [3593]E(f324(f324(f303(f842(x35931)),f182(x35931)),f324(f304(x35931,f842(x35931),f226(x35931)),f238(f845(x35931,a832)))),f238(f845(f842(x35931),a832)))
% 18.55/18.47 [3693]E(f324(f106(a838),f324(f324(f82(a1),x36931),x36931)),f324(f324(f88(a838,a838),f324(f106(a838),x36931)),f324(f324(f20(a838,a838,a838),f82(a838)),f7(a838))))
% 18.55/18.47 [4077]P19(x40771,f845(x40771,a832),f324(f324(f10(f845(x40771,a832),f845(f845(x40771,a832),f845(x40771,a832)),x40771),f324(f9(f845(x40771,a832),f845(x40771,a832),f845(x40771,a832)),f3(f845(x40771,a832)))),f324(f324(f9(x40771,f845(x40771,a832),f845(x40771,a832)),f303(x40771)),f179(f845(x40771,a832)))))
% 18.55/18.47 [4162]E(f324(f257(f844(a1,a1)),f324(f252(a1,a1,a832),f324(f324(f10(f845(a1,a832),f845(a1,a832),a1),f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),x41621)))),f232(a1)))),f108(x41621))
% 18.55/18.47 [4195]E(f324(f257(f844(a1,a1)),f324(f252(a1,a1,a832),f324(f324(f20(a1,f845(a1,a832),f845(a1,a832)),f324(f324(f10(f845(a832,a832),f845(f845(a1,a832),f845(a1,a832)),a1),f10(a832,a832,a1)),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),x41951)))),f232(a1)))),f109(x41951))
% 18.55/18.47 [4248]E(f324(f257(f844(f845(x42481,a832),f845(x42481,a832))),f324(f252(f845(x42481,a832),f845(x42481,a832),a832),f324(f324(f9(f845(x42481,a832),f845(f845(x42481,a832),a832),f845(f845(x42481,a832),a832)),f324(f324(f10(f845(f845(x42481,a832),f845(a832,a832)),f845(f845(f845(x42481,a832),a832),f845(f845(x42481,a832),a832)),f845(x42481,a832)),f20(f845(x42481,a832),a832,a832)),f324(f324(f10(f845(f845(x42481,a832),a832),f845(f845(x42481,a832),f845(a832,a832)),f845(x42481,a832)),f324(f10(a832,f845(a832,a832),f845(x42481,a832)),a322)),f232(f845(x42481,a832))))),f64(x42481)))),f300(x42481))
% 18.55/18.47 [4391]~P1(f324(f64(f839(x43911)),f238(f845(f839(x43911),a832))))
% 18.55/18.47 [4405]~P1(f324(f324(f231(a1),f2(a1)),f324(f81(a1),f324(f102(a1),f324(a114,x44051)))))
% 18.55/18.47 [3306]E(f324(f324(f3(a1),f324(f324(f82(a1),x33061),a99)),a99),x33061)
% 18.55/18.47 [3322]E(f324(f157(a838),f129(a838,f324(f295(a838,f2(a838)),x33221))),f324(f258(a838),x33221))
% 18.55/18.47 [3514]E(f324(f260(x35141,x35141),f301(x35141,f179(f845(f844(x35141,x35141),a832)))),f238(f845(x35141,a832)))
% 18.55/18.47 [3515]E(f324(f262(x35151,x35151),f301(x35151,f179(f845(f844(x35151,x35151),a832)))),f238(f845(x35151,a832)))
% 18.55/18.47 [3561]E(f324(f324(f82(a1),f324(f324(f82(a1),f80(a1)),x35611)),x35611),f324(f324(f3(a1),f324(f324(f82(a1),x35611),x35611)),a99))
% 18.55/18.47 [3611]E(f324(f279(x36111,x36111),f301(x36111,f179(f845(f844(x36111,x36111),a832)))),f301(x36111,f179(f845(f844(x36111,x36111),a832))))
% 18.55/18.47 [3658]P1(f324(f324(f231(a838),x36581),f324(f324(f83(a838),x36581),f324(f324(f83(a838),x36581),x36581))))
% 18.55/18.47 [3747]E(f324(f324(f282(x37471,x37471,x37471),f179(f845(f844(x37471,x37471),a832))),f301(x37471,f179(f845(f844(x37471,x37471),a832)))),f179(f845(f844(x37471,x37471),a832)))
% 18.55/18.47 [3936]P1(f324(f64(a838),f324(f257(a838),f324(f324(f9(a838,a838,a832),f232(a838)),x39361))))
% 18.55/18.47 [3937]P1(f324(f64(a838),f324(f257(a838),f324(f324(f9(a838,a838,a832),f231(a838)),x39371))))
% 18.55/18.47 [4214]E(f324(f257(f844(x42141,x42141)),f324(f324(f10(f845(x42141,a832),a832,f844(x42141,x42141)),f89(x42141)),f324(f324(f9(f844(x42141,x42141),f845(x42141,f844(x42141,x42141)),f845(x42141,a832)),f324(f324(f10(f845(f844(x42141,x42141),a832),f845(f845(x42141,f844(x42141,x42141)),f845(x42141,a832)),f844(x42141,x42141)),f10(f844(x42141,x42141),a832,x42141)),a321)),f324(f324(f20(x42141,x42141,f844(x42141,x42141)),f247(x42141,x42141)),f7(x42141))))),f301(x42141,f179(f845(f844(x42141,x42141),a832))))
% 18.55/18.47 [4392]~E(f324(f324(f3(a1),f324(f324(f82(a1),x43921),x43921)),a99),a85)
% 18.55/18.47 [4393]~E(f324(f324(f3(a1),f324(f324(f82(a1),x43931),x43931)),a99),a85)
% 18.55/18.47 [4395]~E(f324(f324(f82(a1),f324(f324(f82(a1),f80(a1)),x43951)),x43951),f2(a1))
% 18.55/18.47 [3705]E(f324(f324(f82(a1),f324(f324(f3(a1),a99),x37051)),f324(f324(f3(a1),a99),x37051)),f324(f324(f3(a1),a99),f324(f324(f3(a1),f324(f324(f82(a1),x37051),x37051)),a99)))
% 18.55/18.47 [3820]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),a99),x38201)),f324(f324(f3(a1),a99),x38201))),a99),f324(f324(f3(a1),a99),f324(f324(f82(a1),x38201),x38201)))
% 18.55/18.47 [3857]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f82(a1),x38571),a99)),f324(f324(f82(a1),x38571),a99))),a99),f324(f324(f82(a1),f324(f324(f82(a1),x38571),x38571)),a99))
% 18.55/18.47 [3896]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),a99),x38961)),f324(f324(f3(a1),a99),x38961))),a99),f324(f324(f3(a1),a85),f324(f324(f3(a1),f324(f324(f82(a1),x38961),x38961)),a99)))
% 18.55/18.47 [3995]E(f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x39951),f2(a838))),f179(f845(f844(a838,a838),a832))))),f324(f102(a1),x39951))
% 18.55/18.47 [4005]E(f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),f329(x40051)),f512(x40051))),f179(f845(f844(a838,a838),a832))))),x40051)
% 18.55/18.47 [4036]E(f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x40361)),f324(f304(a838,a1,f102(a1)),f324(f257(a838),f324(f324(f10(a1,a832,a838),x40361),f102(a1)))))
% 18.55/18.47 [4085]P38(f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x40851)))
% 18.55/18.47 [4104]P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x41041),f179(f845(f844(a838,a838),a832)))),a73))
% 18.55/18.47 [4110]E(f324(f304(a1,a838,a107),f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),f324(f324(f10(a838,a832,a1),x41101),a107)))),f324(f257(a838),x41101))
% 18.55/18.47 [4262]E(f306(a838,f324(f324(f45(f844(a838,a838),f845(a838,a832)),f324(a110,x42621)),f324(f252(a838,a838,f845(a838,a832)),f324(f324(f9(a838,f845(a838,a832),f845(a838,f845(a838,a832))),f324(f324(f10(f845(a838,f845(f845(a838,a832),f845(a838,a832))),f845(f845(a838,a832),f845(a838,f845(a838,a832))),a838),f9(a838,f845(a838,a832),f845(a838,a832))),f324(f324(f10(f845(a838,a838),f845(a838,f845(f845(a838,a832),f845(a838,a832))),a838),f324(f10(a838,f845(f845(a838,a832),f845(a838,a832)),a838),f303(a838))),f3(a838)))),f179(f845(a838,a832)))))),f324(a107,x42621))
% 18.55/18.47 [3748]E(f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),x37481),x37481)),a99)),a99),f324(f324(f82(a1),x37481),x37481))
% 18.55/18.47 [3795]E(f324(f324(f3(a1),f324(f324(f3(a1),f324(f324(f82(a1),x37951),x37951)),a99)),a99),f324(f324(f82(a1),f324(f324(f3(a1),x37951),a99)),f324(f324(f3(a1),x37951),a99)))
% 18.55/18.47 [4012]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f82(a1),f324(f81(a1),x40121)),a99)),f324(f324(f82(a1),f324(f81(a1),x40121)),a99))),a99),f324(f81(a1),f324(f324(f3(a1),f324(f324(f82(a1),x40121),x40121)),a99)))
% 18.55/18.47 [4056]E(f324(f324(f82(a838),x40561),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(a114,f324(a114,x40561)))
% 18.55/18.47 [4057]E(f324(f324(f83(a838),x40571),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f82(a838),x40571),x40571))
% 18.55/18.47 [4058]E(f324(f324(f42(a838),f324(f324(f82(a838),x40581),x40581)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x40581)
% 18.55/18.47 [4138]E(f51(a838,f324(a114,f324(a114,x41381)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f51(a838,x41381,f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.47 [4279]E(f324(a91,f324(f324(f45(f844(a838,a838),f845(f844(a838,a838),a832)),f324(a110,x42791)),f324(f252(a838,a838,f845(f844(a838,a838),a832)),f324(f324(f10(f845(a838,f845(f844(a838,a838),a832)),f845(a838,f845(f844(a838,a838),a832)),a838),f324(f10(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832),a838),f278(f844(a838,a838),f844(a838,a838),a111))),f324(f324(f9(a838,f845(f844(a838,a838),a832),f845(a838,f845(f844(a838,a838),a832))),f324(f324(f10(f845(a838,f845(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f845(f845(f844(a838,a838),a832),f845(a838,f845(f844(a838,a838),a832))),a838),f9(a838,f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f10(f845(a838,f844(a838,a838)),f845(a838,f845(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),a838),f324(f10(f844(a838,a838),f845(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),a838),f303(f844(a838,a838)))),f324(f9(a838,a838,f844(a838,a838)),f247(a838,a838))))),f179(f845(f844(a838,a838),a832))))))),f324(f81(a1),x42791))
% 18.55/18.47 [4133]E(f324(f324(f82(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x41331),f324(a114,f324(a114,x41331)))
% 18.55/18.47 [4134]E(f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x41341),f324(f324(f82(a838),x41341),x41341))
% 18.55/18.47 [4167]E(f324(f324(f42(a838),f324(a114,f324(a114,x41671))),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(a114,f324(f324(f42(a838),x41671),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.55/18.47 [4220]E(f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42201),f324(a114,f324(a114,f324(a114,x42201))))
% 18.55/18.47 [4286]E(f324(f252(a1,a1,f844(a1,a1)),f324(f324(f20(a1,f845(a1,f844(a1,a1)),f845(a1,f844(a1,a1))),f324(f324(f10(f845(a1,f845(f844(a1,a1),f844(a1,a1))),f845(f845(a1,f844(a1,a1)),f845(a1,f844(a1,a1))),a1),f20(a1,f844(a1,a1),f844(a1,a1))),f324(f324(f10(f845(a1,f844(a1,a1)),f845(a1,f845(f844(a1,a1),f844(a1,a1))),a1),f324(f20(a1,f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),f324(f324(f10(a832,f845(f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),a1),f98(f844(a1,a1))),f324(f324(f10(a1,a832,a1),f324(f231(a1),f2(a1))),f324(f324(f9(a1,a1,a1),f3(a1)),x42861))))),f324(f324(f9(a1,f845(a1,a1),f845(a1,f844(a1,a1))),f324(f324(f10(f845(a1,f844(a1,a1)),f845(f845(a1,a1),f845(a1,f844(a1,a1))),a1),f10(a1,f844(a1,a1),a1)),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f324(f324(f9(a1,a1,a1),f324(f324(f10(a1,f845(a1,a1),a1),f82(a1)),f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f80(a1))))),f324(f324(f9(a1,a1,a1),f3(a1)),x42861))))),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))),f49(x42861))
% 18.55/18.47 [3349]P39(a25,x33491,x33492,x33491)
% 18.55/18.47 [3350]P39(a25,x33501,x33502,x33501)
% 18.55/18.47 [3003]P18(a1,f162(x30031,x30032))
% 18.55/18.47 [3102]P47(x31021,x31022,f261(x31021,x31022))
% 18.55/18.47 [3103]P52(x31031,x31031,f261(x31031,x31032))
% 18.55/18.47 [3374]P29(x33741,x33741,f7(x33741),x33742)
% 18.55/18.47 [3375]P29(x33751,x33751,f37(x33751),x33752)
% 18.55/18.47 [3381]P34(x33811,x33812,f115(x33811),f115(x33811))
% 18.55/18.47 [3382]P34(x33821,x33822,f115(x33821),f115(x33821))
% 18.55/18.47 [3383]P29(x33831,f842(x33831),f226(x33831),x33832)
% 18.55/18.47 [3392]P29(f839(x33921),f839(x33921),f154(x33921),x33922)
% 18.55/18.47 [4295]~E(f28(x42951,x42952),a25)
% 18.55/18.47 [4296]~E(f36(x42961,x42962),a25)
% 18.55/18.47 [4297]~E(f35(x42971,x42972),a25)
% 18.55/18.47 [4298]~E(f28(x42981,x42982),a25)
% 18.55/18.47 [4299]~E(f36(x42991,x42992),a25)
% 18.55/18.47 [4300]~E(f35(x43001,x43002),a25)
% 18.55/18.47 [2970]E(f324(f7(x29701),x29702),x29702)
% 18.55/18.47 [2971]E(f324(f257(x29711),x29712),x29712)
% 18.55/18.47 [2972]E(f324(f37(x29721),x29722),x29722)
% 18.55/18.47 [2973]E(f324(f37(x29731),x29732),x29732)
% 18.55/18.47 [2983]E(f324(f183(x29831),x29832),f117(x29831))
% 18.55/18.47 [2991]E(f34(f28(x29911,x29912)),f2(a838))
% 18.55/18.47 [3001]E(f87(x30011,f324(a321,x30012)),x30012)
% 18.55/18.47 [3002]E(f92(x30021,f324(a321,x30022)),x30022)
% 18.55/18.47 [3019]E(f324(f180(a833),f28(x30191,x30192)),f2(a838))
% 18.55/18.47 [3024]E(f324(f126(x30241,x30242),f115(x30241)),f115(x30241))
% 18.55/18.47 [3044]E(f301(x30441,f301(x30441,x30442)),f301(x30441,x30442))
% 18.55/18.47 [3045]E(f140(x30451,f140(x30451,x30452)),f140(x30451,x30452))
% 18.55/18.47 [3066]E(f324(f324(f125(x30661),x30662),f115(x30661)),x30662)
% 18.55/18.47 [3075]E(f324(f324(f158(x30751),x30752),f115(x30751)),f115(x30751))
% 18.55/18.47 [3076]E(f324(f324(f128(x30761),x30762),f115(x30761)),f115(x30761))
% 18.55/18.47 [3078]E(f227(x30781,x30782,f182(x30781)),f2(a838))
% 18.55/18.47 [3079]E(f142(x30791,x30792,f115(x30791)),f2(a838))
% 18.55/18.47 [3081]E(f155(x30811,x30812,f115(x30811)),f115(x30811))
% 18.55/18.47 [3082]E(f161(x30821,x30822,f115(x30821)),f115(x30821))
% 18.55/18.47 [3083]E(f159(x30831,f115(x30831),x30832),f115(x30831))
% 18.55/18.47 [3087]E(f324(f157(x30871),f140(x30871,x30872)),f324(f157(x30871),x30872))
% 18.55/18.47 [3090]E(f324(f260(x30901,x30901),f261(x30901,x30902)),x30902)
% 18.55/18.47 [3091]E(f324(f262(x30911,x30911),f261(x30911,x30912)),x30912)
% 18.55/18.47 [3099]P1(f324(a26,f28(x30991,x30992)))
% 18.55/18.47 [3100]P1(f324(a26,f28(x31001,x31002)))
% 18.55/18.47 [3101]E(f324(f279(x31011,x31011),f261(x31011,x31012)),f261(x31011,x31012))
% 18.55/18.47 [3115]E(f301(f839(x31151),f144(x31151,x31152)),f145(x31151,f301(x31151,x31152)))
% 18.55/18.47 [3117]P1(f324(f127(a1),f162(x31171,x31172)))
% 18.55/18.47 [3125]E(f324(f260(x31251,x31251),f301(x31251,x31252)),f238(f845(x31251,a832)))
% 18.55/18.47 [3126]E(f324(f262(x31261,x31261),f301(x31261,x31262)),f238(f845(x31261,a832)))
% 18.55/18.47 [3130]P1(f324(f127(x31301),f140(x31301,x31302)))
% 18.55/18.47 [3137]E(f324(f157(a1),f162(x31371,x31372)),f296(a1,x31371,x31372))
% 18.55/18.47 [3138]E(f324(f157(a1),f162(x31381,x31382)),f296(a1,x31381,x31382))
% 18.55/18.47 [3153]P53(x31531,f179(f845(x31531,a832)),x31532)
% 18.55/18.47 [3158]E(f324(f251(a1,a1),f52(x31581,x31582)),f51(a1,x31581,x31582))
% 18.55/18.47 [3159]E(f324(f295(a838,x31591),f324(a114,x31592)),f296(a838,x31591,x31592))
% 18.55/18.47 [3188]E(f296(a838,f324(a114,x31881),x31882),f298(a838,x31881,x31882))
% 18.55/18.47 [3191]P47(x31911,f238(f845(x31911,a832)),f301(x31911,x31912))
% 18.55/18.47 [3252]E(f324(f324(f3(a838),x32521),f324(a114,x32522)),f324(f41(a838),f299(a838,x32522,x32521)))
% 18.55/18.47 [3307]E(f152(x33071,x33072,f115(x33071)),f324(f324(f247(f839(x33071),f839(x33071)),f115(x33071)),f115(x33071)))
% 18.55/18.47 [3326]E(f324(f252(x33261,x33262,f844(x33261,x33262)),f247(x33261,x33262)),f37(f844(x33261,x33262)))
% 18.55/18.47 [3331]P1(f324(f324(f326(f839(x33311)),f115(x33311)),f147(x33311,x33312)))
% 18.55/18.47 [3332]E(f324(f180(f839(x33321)),f116(x33321,x33322)),f324(f324(f3(a838),f324(f180(f839(x33321)),x33322)),f80(a838)))
% 18.55/18.47 [3341]P1(f324(f64(a838),f299(a838,x33411,x33412)))
% 18.55/18.47 [3342]P1(f324(f64(a838),f298(a838,x33421,x33422)))
% 18.55/18.47 [3343]P1(f324(f64(a838),f296(a838,x33431,x33432)))
% 18.55/18.47 [3344]P1(f324(f64(a1),f299(a1,x33441,x33442)))
% 18.55/18.47 [3345]P1(f324(f64(a1),f298(a1,x33451,x33452)))
% 18.55/18.47 [3346]P1(f324(f64(a1),f296(a1,x33461,x33462)))
% 18.55/18.47 [3448]E(f324(f304(a838,a838,a114),f296(a838,x34481,x34482)),f296(a838,f324(a114,x34481),f324(a114,x34482)))
% 18.55/18.47 [3466]E(f324(f324(f282(x34661,x34661,x34661),f301(x34661,x34662)),f301(x34661,x34662)),f301(x34661,x34662))
% 18.55/18.47 [3497]E(f324(f324(f247(a1,a1),f324(f324(f42(a1),x34971),x34972)),f51(a1,x34971,x34972)),f52(x34971,x34972))
% 18.55/18.47 [3498]E(f324(f324(f247(a101,a101),f324(f324(f42(a101),x34981),x34982)),f51(a101,x34981,x34982)),f24(x34981,x34982))
% 18.55/18.47 [3527]E(f324(f324(f247(a838,a838),f324(f324(f42(a838),x35271),x35272)),f51(a838,x35271,x35272)),f87(f844(a838,a838),f54(x35271,x35272)))
% 18.55/18.47 [3580]P1(f324(f324(f232(a838),f324(f324(f3(a838),x35801),x35802)),f324(a114,x35801)))
% 18.55/18.47 [3669]E(f324(f324(f128(x36691),f324(f180(f839(x36691)),f161(x36691,x36692,f115(x36691)))),f115(x36691)),f115(x36691))
% 18.55/18.47 [3680]E(f324(f324(f82(a1),f324(f324(f83(a1),x36801),f324(f324(f42(a1),x36802),x36801))),f51(a1,x36802,x36801)),x36802)
% 18.55/18.47 [3684]E(f324(f324(f45(a838,f845(f844(f839(x36841),f839(x36841)),a832)),f238(f845(a838,a832))),f132(x36841,x36842)),f134(x36841,x36842))
% 18.55/18.47 [3911]P1(f324(f324(f326(f844(f839(x39111),f839(x39111))),f324(f324(f247(f839(x39111),f839(x39111)),f115(x39111)),f115(x39111))),f145(x39111,x39112)))
% 18.55/18.47 [4069]E(f253(x40691,x40691,x40692,x40692,f37(x40691),f37(x40692)),f37(f844(x40691,x40692)))
% 18.55/18.47 [4070]E(f253(x40701,x40701,x40702,x40702,f7(x40701),f7(x40702)),f37(f844(x40701,x40702)))
% 18.55/18.47 [4071]E(f253(x40711,x40711,x40712,x40712,f37(x40711),f37(x40712)),f37(f844(x40711,x40712)))
% 18.55/18.47 [4072]E(f253(x40721,x40721,x40722,x40722,f37(x40721),f37(x40722)),f37(f844(x40721,x40722)))
% 18.55/18.47 [4307]~E(f324(f226(x43071),x43072),f182(x43071))
% 18.55/18.47 [4308]~E(f324(f226(x43081),x43082),f182(x43081))
% 18.55/18.47 [4326]~P37(x43261,f324(f226(x43261),x43262))
% 18.55/18.47 [3064]E(f324(f230(x30641),f324(f226(x30641),x30642)),x30642)
% 18.55/18.47 [3065]E(f324(f154(x30651),f324(f154(x30651),x30652)),x30652)
% 18.55/18.47 [3067]E(f324(f324(f128(x30671),f2(a838)),x30672),x30672)
% 18.55/18.47 [3077]E(f324(f324(f158(x30771),f2(a838)),x30772),f115(x30771))
% 18.55/18.47 [3085]E(f324(f324(f125(x30851),f115(x30851)),x30852),x30852)
% 18.55/18.47 [3093]E(f324(f180(f842(x30931)),f324(f226(x30931),x30932)),f2(a838))
% 18.55/18.47 [3095]E(f43(f845(x30951,a832),f324(f302(x30951),x30952)),x30952)
% 18.55/18.47 [3097]E(f324(f157(x30971),f324(f153(x30971),x30972)),f324(f157(x30971),x30972))
% 18.55/18.47 [3098]E(f324(f157(x30981),f324(f154(x30981),x30982)),f324(f157(x30981),x30982))
% 18.55/18.47 [3105]E(f324(f324(f3(a101),x31051),x31052),f324(f324(a4,x31051),x31052))
% 18.55/18.47 [3119]E(f324(f324(f83(a838),x31191),x31192),f324(f324(f83(a838),x31192),x31191))
% 18.55/18.47 [3120]E(f324(f324(f83(a1),x31201),x31202),f324(f324(f83(a1),x31202),x31201))
% 18.55/18.47 [3121]E(f324(f324(f82(a838),x31211),x31212),f324(f324(f82(a838),x31212),x31211))
% 18.55/18.47 [3122]E(f324(f324(f82(a1),x31221),x31222),f324(f324(f82(a1),x31222),x31221))
% 18.55/18.47 [3145]E(f324(f324(f172(x31451,x31451),f2(a838)),x31452),f37(x31451))
% 18.55/18.47 [3146]E(f324(f180(f839(x31461)),f324(f153(x31461),x31462)),f324(f180(f839(x31461)),x31462))
% 18.55/18.47 [3147]E(f324(f180(f839(x31471)),f324(f154(x31471),x31472)),f324(f180(f839(x31471)),x31472))
% 18.55/18.47 [3148]E(f159(x31481,x31482,f179(f845(a838,a832))),f115(x31481))
% 18.55/18.47 [3149]E(f324(f324(f141(x31491,x31491),f7(x31491)),x31492),x31492)
% 18.55/18.47 [3151]E(f324(f246(a1,a1),f52(x31511,x31512)),f324(f324(f42(a1),x31511),x31512))
% 18.55/18.47 [3169]E(f324(f180(f839(x31691)),f140(x31691,x31692)),f324(f41(x31691),f324(f157(x31691),x31692)))
% 18.55/18.47 [3170]E(f34(f35(x31701,x31702)),f324(f324(f82(a838),f34(x31702)),f324(a114,f2(a838))))
% 18.55/18.47 [3171]E(f324(f277(x31711),f324(f279(x31711,x31711),x31712)),f324(f277(x31711),x31712))
% 18.55/18.47 [3175]P1(f324(f64(x31751),f324(f157(x31751),x31752)))
% 18.55/18.47 [3181]E(f324(f324(f82(a1),x31811),f324(f81(a1),x31812)),f324(f324(f3(a1),x31811),x31812))
% 18.55/18.47 [3182]E(f324(f324(f82(a1),x31821),f324(f81(a1),x31822)),f324(f324(f3(a1),x31821),x31822))
% 18.55/18.47 [3189]P28(x31891,x31892,f179(f845(f837(x31891),a832)))
% 18.55/18.47 [3190]P28(x31901,x31902,f179(f845(f837(x31901),a832)))
% 18.55/18.47 [3192]E(f324(f304(x31921,x31921,f7(x31921)),x31922),x31922)
% 18.55/18.47 [3193]E(f324(f304(x31931,x31931,f37(x31931)),x31932),x31932)
% 18.55/18.47 [3194]E(f324(f305(x31941,x31941,f7(x31941)),x31942),x31942)
% 18.55/18.47 [3195]E(f324(f305(x31951,x31951,f37(x31951)),x31952),x31952)
% 18.55/18.47 [3196]P1(f324(f238(f845(x31961,a832)),x31962))
% 18.55/18.47 [3198]E(f324(f41(a838),f324(f295(a838,x31981),x31982)),f324(f324(f3(a838),x31982),x31981))
% 18.55/18.47 [3199]E(f324(f295(a838,f324(a114,x31991)),x31992),f299(a838,x31991,x31992))
% 18.55/18.47 [3211]E(f324(f324(f303(x32111),x32112),f179(f845(x32111,a832))),f324(f257(x32111),f324(a321,x32112)))
% 18.55/18.47 [3215]E(f324(f324(f303(x32151),x32152),f179(f845(x32151,a832))),f225(x32151,f324(f226(x32151),x32152)))
% 18.55/18.47 [3217]E(f301(x32171,f324(f279(x32171,x32171),x32172)),f324(f279(x32171,x32171),f301(x32171,x32172)))
% 18.55/18.47 [3222]E(f324(f324(f82(a838),f324(a114,x32221)),x32222),f324(f324(f82(a838),x32221),f324(a114,x32222)))
% 18.55/18.47 [3223]E(f324(f324(f3(a838),f324(a114,x32231)),f324(a114,x32232)),f324(f324(f3(a838),x32231),x32232))
% 18.55/18.47 [3229]E(f324(f41(a838),f298(a838,x32291,x32292)),f324(f324(f3(a838),x32292),x32291))
% 18.55/18.47 [3238]P36(x32381,f324(f324(f281(a838,x32381),a236),x32382))
% 18.55/18.47 [3240]P18(a838,f129(a838,f324(f295(a838,x32401),x32402)))
% 18.55/18.47 [3242]P1(f324(f64(a838),f324(f295(a838,x32421),x32422)))
% 18.55/18.47 [3243]P1(f324(f64(a1),f324(f295(a1,x32431),x32432)))
% 18.55/18.47 [3245]E(f324(f279(f839(x32451),f839(x32451)),f144(x32451,x32452)),f144(x32451,f324(f279(x32451,x32451),x32452)))
% 18.55/18.47 [3246]E(f324(f180(a833),f35(x32461,x32462)),f324(f324(f82(a838),f324(f180(a833),x32462)),f324(a114,f2(a838))))
% 18.55/18.47 [3248]E(f324(f295(a1,x32481),f324(f324(f82(a1),x32482),f80(a1))),f296(a1,x32481,x32482))
% 18.55/18.47 [3251]E(f324(f324(f42(a1),f324(f81(a1),x32511)),f324(f81(a1),x32512)),f324(f324(f42(a1),x32511),x32512))
% 18.55/18.47 [3259]E(f170(x32591,x32592,f324(f18(f842(x32592),x32591),f182(x32592))),f179(f845(x32592,a832)))
% 18.55/18.47 [3260]E(f168(x32601,x32602,f324(f18(f842(x32602),x32601),f182(x32602))),f179(f845(x32601,a832)))
% 18.55/18.47 [3261]E(f324(f324(f172(f844(x32611,x32611),a832),f80(a838)),x32612),x32612)
% 18.55/18.47 [3263]E(f324(f324(f3(f845(x32631,a832)),x32632),f179(f845(x32631,a832))),x32632)
% 18.55/18.47 [3264]E(f324(f324(f103(f845(x32641,a832)),x32642),f179(f845(x32641,a832))),x32642)
% 18.55/18.47 [3265]E(f324(f324(f104(f845(x32651,a832)),x32652),f238(f845(x32651,a832))),x32652)
% 18.55/18.47 [3266]E(f324(f246(a838,a838),f87(f844(a838,a838),f54(x32661,x32662))),f324(f324(f42(a838),x32661),x32662))
% 18.55/18.47 [3272]E(f307(x32721,f324(a23,x32722),f324(f81(a1),f324(a23,x32722))),f324(f324(f310(a1),x32721),x32722))
% 18.55/18.47 [3273]E(f296(a1,f324(f324(f82(a1),x32731),f80(a1)),x32732),f298(a1,x32731,x32732))
% 18.55/18.47 [3278]E(f324(f251(a838,a838),f87(f844(a838,a838),f54(x32781,x32782))),f51(a838,x32781,x32782))
% 18.55/18.47 [3286]E(f308(x32861,f324(a23,x32862),f324(f81(a1),f324(a23,x32862))),f309(a1,x32861,x32862))
% 18.55/18.47 [3288]P1(f324(f324(f326(x32881),x32882),f238(f845(x32881,a832))))
% 18.55/18.47 [3289]P1(f324(f324(f326(x32891),x32892),f238(f845(x32891,a832))))
% 18.55/18.47 [3293]E(f324(f324(f3(a838),f324(a114,x32931)),x32932),f324(f41(a838),f296(a838,x32932,x32931)))
% 18.55/18.47 [3318]E(f324(f324(f3(f845(x33181,a832)),x33182),f238(f845(x33181,a832))),f179(f845(x33181,a832)))
% 18.55/18.47 [3319]E(f324(f324(f103(f845(x33191,a832)),x33192),f238(f845(x33191,a832))),f238(f845(x33191,a832)))
% 18.55/18.47 [3320]E(f324(f324(f104(f845(x33201,a832)),x33202),f179(f845(x33201,a832))),f179(f845(x33201,a832)))
% 18.55/18.47 [3333]E(f51(a1,f324(f102(a1),x33331),f324(f102(a1),x33332)),f324(f102(a1),f51(a838,x33331,x33332)))
% 18.55/18.47 [3334]E(f51(a1,f324(f102(a1),x33341),f324(f102(a1),x33342)),f324(f102(a1),f51(a838,x33341,x33342)))
% 18.55/18.47 [3335]E(f51(a1,f324(f81(a1),x33351),f324(f81(a1),x33352)),f324(f81(a1),f51(a1,x33351,x33352)))
% 18.55/18.47 [3348]E(f324(f180(f839(x33481)),f324(f156(x33481),x33482)),f324(f324(f3(a838),f324(f180(f839(x33481)),x33482)),f80(a838)))
% 18.55/18.47 [3376]E(f324(f324(f42(a1),f51(a1,x33761,x33762)),x33762),f2(a1))
% 18.55/18.47 [3385]E(f324(a5,f51(a838,f324(a22,x33851),f324(a22,x33852))),f51(a101,x33851,x33852))
% 18.55/18.47 [3417]E(f324(a5,f324(f324(f83(a838),f324(a22,x34171)),f324(a22,x34172))),f324(f324(f83(a101),x34171),x34172))
% 18.55/18.47 [3418]E(f324(a5,f324(f324(f82(a838),f324(a22,x34181)),f324(a22,x34182))),f324(f324(f82(a101),x34181),x34182))
% 18.55/18.47 [3419]E(f324(a5,f324(f324(f42(a838),f324(a22,x34191)),f324(a22,x34192))),f324(f324(f42(a101),x34191),x34192))
% 18.55/18.47 [3420]E(f324(a5,f324(f324(f3(a838),f324(a22,x34201)),f324(a22,x34202))),f324(f324(f3(a101),x34201),x34202))
% 18.55/18.47 [3429]E(f324(f304(a838,a838,a114),f324(f295(a838,x34291),x34292)),f324(f295(a838,f324(a114,x34291)),f324(a114,x34292)))
% 18.55/18.47 [3453]P1(f324(f54(x34531,x34532),f87(f844(a838,a838),f54(x34531,x34532))))
% 18.55/18.47 [3471]E(f324(f324(f82(a838),f324(f324(f82(a838),f34(x34711)),f34(x34712))),f324(a114,f2(a838))),f34(f36(x34711,x34712)))
% 18.55/18.47 [3472]E(f51(a838,f324(a114,f51(a838,x34721,x34722)),x34722),f51(a838,f324(a114,x34721),x34722))
% 18.55/18.47 [3486]E(f324(f324(f46(f845(x34861,a832),f845(x34861,a832)),x34862),f7(f845(x34861,a832))),f44(f845(x34861,a832),x34862))
% 18.55/18.47 [3487]E(f324(f324(f45(f845(x34871,a832),f845(x34871,a832)),x34872),f7(f845(x34871,a832))),f43(f845(x34871,a832),x34872))
% 18.55/18.47 [3488]E(f324(f304(f839(x34881),f845(x34881,a832),f157(x34881)),f324(f157(f839(x34881)),f60(x34881,x34882))),f324(f302(x34881),f324(f157(x34881),x34882)))
% 18.55/18.47 [3491]P1(f324(f324(f326(f845(x34911,a832)),x34912),f324(f302(x34911),x34912)))
% 18.55/18.47 [3496]E(f51(a1,f324(f81(a1),f51(a1,x34961,x34962)),x34962),f51(a1,f324(f81(a1),x34961),x34962))
% 18.55/18.48 [3508]P1(f324(f324(f231(f845(x35081,a832)),x35082),f238(f845(x35081,a832))))
% 18.55/18.48 [3510]E(f324(f324(f282(x35101,x35101,x35101),f301(x35101,x35102)),f301(x35101,f301(x35101,x35102))),f301(x35101,x35102))
% 18.55/18.48 [3511]E(f324(f324(f103(f845(x35111,a832)),f324(f262(x35111,x35111),x35112)),f324(f260(x35111,x35111),x35112)),f324(f277(x35111),x35112))
% 18.55/18.48 [3533]E(f312(x35331,x35332,f238(f845(x35331,a832)),f238(f845(x35332,a832))),f238(f845(f848(x35331,x35332),a832)))
% 18.55/18.48 [3585]P1(f324(f324(f231(a838),f51(a838,x35851,x35852)),x35851))
% 18.55/18.48 [3609]P1(f324(f324(f231(a1),f324(f81(a1),f324(f102(a1),x36091))),f324(f102(a1),x36092)))
% 18.55/18.48 [3634]P1(f324(f324(f326(f845(x36341,a832)),f179(f845(x36341,a832))),f324(f302(x36341),x36342)))
% 18.55/18.48 [3639]E(f301(x36391,f324(f324(f282(x36391,x36391,x36391),x36392),f301(x36391,x36392))),f301(x36391,x36392))
% 18.55/18.48 [3641]E(f324(f324(f282(x36411,x36411,x36411),f301(x36411,x36412)),x36412),f324(f324(f282(x36411,x36411,x36411),x36412),f301(x36411,x36412)))
% 18.55/18.48 [3642]E(f324(f324(f282(x36421,x36421,x36421),f301(x36421,x36422)),x36422),f324(f324(f282(x36421,x36421,x36421),x36422),f301(x36421,x36422)))
% 18.55/18.48 [3644]E(f324(a107,f324(f324(f82(a1),f324(f324(f3(a1),x36441),x36442)),f80(a1))),f324(f41(a1),f296(a1,x36442,x36441)))
% 18.55/18.48 [3659]E(f324(f260(x36591,x36591),f324(f324(f282(x36591,x36591,x36591),x36592),f301(x36591,x36592))),f324(f260(x36591,x36591),x36592))
% 18.55/18.48 [3660]E(f324(f262(x36601,x36601),f324(f324(f282(x36601,x36601,x36601),x36602),f301(x36601,x36602))),f324(f262(x36601,x36601),x36602))
% 18.55/18.48 [3676]E(f324(f324(f82(a838),f324(f324(f82(a838),f324(f180(a833),x36761)),f324(f180(a833),x36762))),f324(a114,f2(a838))),f324(f180(a833),f36(x36761,x36762)))
% 18.55/18.48 [3688]P29(a838,a838,f324(f324(f9(a838,a838,a838),f82(a838)),x36881),x36882)
% 18.55/18.48 [3690]P18(a838,f324(f154(a838),f324(f324(f141(f839(x36901),a838),f180(f839(x36901))),f163(x36901,x36902))))
% 18.55/18.48 [3737]P1(f324(f324(f232(a1),f324(f81(a1),f324(f102(a1),f324(a114,x37371)))),f324(f102(a1),x37372)))
% 18.55/18.48 [3777]E(f324(f131(f839(x37771),x37771,f324(f9(x37771,f839(x37771),f839(x37771)),f139(x37771)),f115(x37771)),x37772),f324(f154(x37771),x37772))
% 18.55/18.48 [3827]P1(f324(f324(f231(f845(f844(f839(x38271),f839(x38271)),a832)),f145(x38271,x38272)),f301(f839(x38271),f144(x38271,x38272))))
% 18.55/18.48 [3861]P1(f324(f54(x38611,x38612),f324(f324(f247(a838,a838),f324(f324(f42(a838),x38611),x38612)),f51(a838,x38611,x38612))))
% 18.55/18.48 [3872]P1(f324(f324(f231(f845(f844(f839(x38721),f839(x38721)),a832)),f144(x38721,f301(x38721,x38722))),f301(f839(x38721),f144(x38721,x38722))))
% 18.55/18.48 [4096]E(f324(f324(f254(f844(a101,a101),a101,f844(a101,a101),f844(x40961,f844(a101,a101))),f265(f324(f151(a101),f324(f324(f141(f844(a101,x40961),a101),f246(a101,x40961)),x40962)))),f324(f324(f10(x40961,f845(f844(a101,a101),f844(x40961,f844(a101,a101))),a101),f247(x40961,f844(a101,a101))),f266(x40961,x40962))),f264(x40961,x40962))
% 18.55/18.48 [4244]E(f51(a838,f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42441),f324(f106(a838),x42442)),f51(a838,f324(a114,f324(a114,f324(a114,x42441))),f324(f106(a838),x42442)))
% 18.55/18.48 [4258]E(f324(f324(f42(a838),f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42581)),f324(f106(a838),x42582)),f324(f324(f42(a838),f324(a114,f324(a114,f324(a114,x42581)))),f324(f106(a838),x42582)))
% 18.55/18.48 [4278]E(f324(f252(f845(f844(x42781,x42781),a832),f845(f844(x42781,x42781),a832),f845(f845(x42782,x42781),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832)))),f324(f324(f9(f845(f844(x42781,x42781),a832),f845(f845(f844(x42781,x42781),a832),f845(f845(x42782,x42781),f845(f844(x42782,x42782),a832))),f845(f845(f844(x42781,x42781),a832),f845(f845(x42782,x42781),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832))))),f324(f324(f10(f845(f845(f845(x42782,x42781),f845(f844(x42782,x42782),a832)),f845(f845(x42782,x42781),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832)))),f845(f845(f845(f844(x42781,x42781),a832),f845(f845(x42782,x42781),f845(f844(x42782,x42782),a832))),f845(f845(f844(x42781,x42781),a832),f845(f845(x42782,x42781),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832))))),f845(f844(x42781,x42781),a832)),f10(f845(f845(x42782,x42781),f845(f844(x42782,x42782),a832)),f845(f845(x42782,x42781),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832))),f845(f844(x42781,x42781),a832))),f324(f324(f10(f845(f845(x42782,x42781),f845(f845(f844(x42782,x42782),a832),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832)))),f845(f845(f845(x42782,x42781),f845(f844(x42782,x42782),a832)),f845(f845(x42782,x42781),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832)))),f845(f844(x42781,x42781),a832)),f20(f845(x42782,x42781),f845(f844(x42782,x42782),a832),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832)))),f324(f324(f10(f845(f845(x42782,x42781),f845(f844(x42782,x42782),a832)),f845(f845(x42782,x42781),f845(f845(f844(x42782,x42782),a832),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832)))),f845(f844(x42781,x42781),a832)),f324(f10(f845(f844(x42782,x42782),a832),f845(f845(f844(x42782,x42782),a832),f844(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832))),f845(x42782,x42781)),f247(f845(f844(x42782,x42782),a832),f845(f844(x42782,x42782),a832)))),f281(x42781,x42782))))),f281(x42781,x42782))),f76(x42781,x42782))
% 18.55/18.48 [4372]~E(f324(f302(x43721),x43722),f179(f845(f845(x43721,a832),a832)))
% 18.55/18.48 [4389]~P1(f324(f324(f326(x43891),x43892),f179(f845(x43891,a832))))
% 18.55/18.48 [4390]~P1(f324(f324(f326(x43901),x43902),f179(f845(x43901,a832))))
% 18.55/18.48 [4400]~P1(f324(f324(f232(f845(x44001,a832)),x44002),f179(f845(x44001,a832))))
% 18.55/18.48 [3201]E(f324(f324(f3(a838),x32011),f324(f324(f82(a838),x32011),x32012)),f2(a838))
% 18.55/18.48 [3203]E(f324(f324(f103(f845(x32031,a832)),x32032),x32032),x32032)
% 18.55/18.48 [3204]E(f324(f324(f104(f845(x32041,a832)),x32042),x32042),x32042)
% 18.55/18.48 [3231]E(f324(f324(f3(f845(x32311,a832)),x32312),x32312),f179(f845(x32311,a832)))
% 18.55/18.48 [3234]E(f324(f132(x32341,x32342),f2(a838)),f179(f845(f844(f839(x32341),f839(x32341)),a832)))
% 18.55/18.48 [3235]E(f324(f324(f82(a838),x32351),f324(a114,x32352)),f324(a114,f324(f324(f82(a838),x32351),x32352)))
% 18.55/18.48 [3247]E(f187(f324(f102(a1),x32471),f324(f102(a1),x32472)),f324(f102(a1),f324(f324(f3(a838),x32471),x32472)))
% 18.55/18.48 [3250]E(f324(f324(f42(a1),f324(f81(a1),x32501)),x32502),f324(f324(f42(a1),x32501),f324(f81(a1),x32502)))
% 18.55/18.48 [3254]E(f324(f41(a1),f324(f295(a1,x32541),x32542)),f324(a107,f324(f324(f3(a1),x32542),x32541)))
% 18.55/18.48 [3257]E(f324(f324(f82(a838),f324(a114,x32571)),x32572),f324(a114,f324(f324(f82(a838),x32571),x32572)))
% 18.55/18.48 [3262]E(f324(f81(f845(x32621,a832)),f324(f81(f845(x32621,a832)),x32622)),x32622)
% 18.55/18.48 [3275]E(f163(x32751,f324(f324(f139(f839(x32751)),f115(x32751)),x32752)),f163(x32751,x32752))
% 18.55/18.48 [3279]E(f324(f324(f82(a838),x32791),f324(f324(f83(a838),x32791),x32792)),f324(f324(f83(a838),x32791),f324(a114,x32792)))
% 18.55/18.48 [3287]E(f324(f324(a4,f324(a5,x32871)),f324(a5,x32872)),f324(a5,f324(f324(f3(a838),x32871),x32872)))
% 18.55/18.48 [3297]E(f324(f324(f240(a1),f324(f102(a1),x32971)),x32972),f324(f102(a1),f324(f324(f240(a838),x32971),x32972)))
% 18.55/18.48 [3298]E(f324(f324(f83(a1),f324(f81(a1),x32981)),x32982),f324(f81(a1),f324(f324(f83(a1),x32981),x32982)))
% 18.55/18.48 [3299]E(f324(f324(f240(a1),f324(f102(a1),x32991)),x32992),f324(f102(a1),f324(f324(f240(a838),x32991),x32992)))
% 18.55/18.48 [3300]E(f324(f324(f240(a1),f324(f102(a1),x33001)),x33002),f324(f102(a1),f324(f324(f240(a838),x33001),x33002)))
% 18.55/18.48 [3301]E(f324(f324(f83(a101),f324(a5,x33011)),f324(a5,x33012)),f324(a5,f324(f324(f83(a838),x33011),x33012)))
% 18.55/18.48 [3302]E(f324(f324(f82(a101),f324(a5,x33021)),f324(a5,x33022)),f324(a5,f324(f324(f82(a838),x33021),x33022)))
% 18.55/18.48 [3303]E(f324(f324(f235(a838),f324(a114,x33031)),f324(a114,x33032)),f324(a114,f324(f324(f235(a838),x33031),x33032)))
% 18.55/18.48 [3304]E(f324(f324(f178(a838),f324(a114,x33041)),f324(a114,x33042)),f324(a114,f324(f324(f178(a838),x33041),x33042)))
% 18.55/18.48 [3309]E(f324(f157(a838),f129(a838,f324(f295(a838,x33091),x33092))),f324(f295(a838,x33091),x33092))
% 18.55/18.48 [3310]E(f324(f157(a838),f129(a838,f324(f295(a838,x33101),x33102))),f324(f295(a838,x33101),x33102))
% 18.55/18.48 [3311]E(f306(x33111,f324(f324(f303(x33111),x33112),f179(f845(x33111,a832)))),x33112)
% 18.55/18.48 [3316]E(f324(f260(x33161,x33162),f179(f845(f844(x33161,x33162),a832))),f179(f845(x33162,a832)))
% 18.55/18.48 [3317]E(f324(f262(x33171,x33172),f179(f845(f844(x33171,x33172),a832))),f179(f845(x33171,a832)))
% 18.55/18.48 [3321]E(f324(a107,f324(f324(f3(a1),x33211),x33212)),f324(f41(a1),f298(a1,x33212,x33211)))
% 18.55/18.48 [3325]E(f324(f324(f82(a838),x33251),f324(f324(f83(a838),x33252),x33251)),f324(f324(f83(a838),f324(a114,x33252)),x33251))
% 18.55/18.48 [3327]E(f324(f324(f63(x33271),f179(f845(x33271,a832))),x33272),f179(f845(f845(x33271,a832),a832)))
% 18.55/18.48 [3336]E(f324(f180(f839(a838)),f129(a838,f324(f295(a838,x33361),x33362))),f324(f324(f3(a838),x33362),x33361))
% 18.55/18.48 [3355]E(f324(f324(f103(f845(x33551,a832)),f179(f845(x33551,a832))),x33552),x33552)
% 18.55/18.48 [3356]E(f324(f324(f104(f845(x33561,a832)),f238(f845(x33561,a832))),x33562),x33562)
% 18.55/18.48 [3357]E(f324(f324(f83(a1),f324(f102(a1),x33571)),f324(f102(a1),x33572)),f324(f102(a1),f324(f324(f83(a838),x33571),x33572)))
% 18.55/18.48 [3358]E(f324(f324(f42(a1),f324(f102(a1),x33581)),f324(f102(a1),x33582)),f324(f102(a1),f324(f324(f42(a838),x33581),x33582)))
% 18.55/18.48 [3359]E(f324(f324(f82(a1),f324(f81(a1),x33591)),f324(f81(a1),x33592)),f324(f81(a1),f324(f324(f82(a1),x33591),x33592)))
% 18.55/18.48 [3361]E(f324(f324(f83(a1),f324(f102(a1),x33611)),f324(f102(a1),x33612)),f324(f102(a1),f324(f324(f83(a838),x33611),x33612)))
% 18.55/18.48 [3362]E(f324(f324(f83(a1),f324(f102(a1),x33621)),f324(f102(a1),x33622)),f324(f102(a1),f324(f324(f83(a838),x33621),x33622)))
% 18.55/18.48 [3363]E(f324(f324(f83(a1),f324(f106(a1),x33631)),f324(f106(a1),x33632)),f324(f106(a1),f324(f324(f83(a1),x33631),x33632)))
% 18.55/18.48 [3364]E(f324(f324(f82(a1),f324(f102(a1),x33641)),f324(f102(a1),x33642)),f324(f102(a1),f324(f324(f82(a838),x33641),x33642)))
% 18.55/18.48 [3365]E(f324(f324(f82(a1),f324(f102(a1),x33651)),f324(f102(a1),x33652)),f324(f102(a1),f324(f324(f82(a838),x33651),x33652)))
% 18.55/18.48 [3366]E(f324(f324(f82(a1),f324(f106(a1),x33661)),f324(f106(a1),x33662)),f324(f106(a1),f324(f324(f82(a1),x33661),x33662)))
% 18.55/18.48 [3367]E(f324(f324(f42(a1),f324(f102(a1),x33671)),f324(f102(a1),x33672)),f324(f102(a1),f324(f324(f42(a838),x33671),x33672)))
% 18.55/18.48 [3386]E(f324(f324(f8(x33861,a838),f324(f18(a838,x33861),f80(a838))),x33862),f324(f41(x33861),x33862))
% 18.55/18.48 [3393]E(f324(f81(a1),f51(a1,f324(f81(a1),x33931),x33932)),f51(a1,x33931,f324(f81(a1),x33932)))
% 18.55/18.48 [3395]E(f324(f157(a1),f162(x33951,f324(f324(f3(a1),x33952),f80(a1)))),f324(f295(a1,x33951),x33952))
% 18.55/18.48 [3400]P1(f324(f324(f231(a838),x34001),f324(f324(f82(a838),x34002),x34001)))
% 18.55/18.48 [3401]P1(f324(f324(f231(a838),x34011),f324(f324(f82(a838),x34011),x34012)))
% 18.55/18.48 [3403]E(f324(f324(f3(f845(x34031,a832)),f179(f845(x34031,a832))),x34032),f179(f845(x34031,a832)))
% 18.55/18.48 [3404]E(f324(f324(f103(f845(x34041,a832)),f238(f845(x34041,a832))),x34042),f238(f845(x34041,a832)))
% 18.55/18.48 [3405]E(f324(f324(f104(f845(x34051,a832)),f179(f845(x34051,a832))),x34052),f179(f845(x34051,a832)))
% 18.55/18.48 [3410]E(f324(f324(f247(a1,a1),x34101),f324(f81(a1),x34102)),f324(a57,f324(f324(f247(a1,a1),x34101),x34102)))
% 18.55/18.48 [3411]E(f324(f295(a1,f324(f324(f82(a1),x34111),f80(a1))),x34112),f299(a1,x34111,x34112))
% 18.55/18.48 [3421]E(f324(f324(f83(a838),x34211),f324(f324(f42(a838),x34212),x34211)),f324(f324(f3(a838),x34212),f51(a838,x34212,x34211)))
% 18.55/18.48 [3422]E(f324(f324(f83(a1),x34221),f324(f324(f42(a1),x34222),x34221)),f324(f324(f3(a1),x34222),f51(a1,x34222,x34221)))
% 18.55/18.48 [3426]E(f324(f157(a1),f162(f324(f324(f82(a1),x34261),f80(a1)),x34262)),f298(a1,x34261,x34262))
% 18.55/18.48 [3430]P1(f324(f324(f231(f845(x34301,a832)),x34302),x34302))
% 18.55/18.48 [3433]E(f324(f324(f103(f845(x34331,a832)),x34332),f324(f81(f845(x34331,a832)),x34332)),f238(f845(x34331,a832)))
% 18.55/18.48 [3434]E(f324(f324(f104(f845(x34341,a832)),x34342),f324(f81(f845(x34341,a832)),x34342)),f179(f845(x34341,a832)))
% 18.55/18.48 [3440]E(f324(f324(f3(a838),f324(f324(f3(a838),x34401),f80(a838))),x34402),f324(f324(f3(a838),x34401),f324(a114,x34402)))
% 18.55/18.48 [3445]E(f324(f324(f3(f845(x34451,a832)),f238(f845(x34451,a832))),x34452),f324(f81(f845(x34451,a832)),x34452))
% 18.55/18.48 [3446]E(f324(f324(f3(a1),f324(f106(a1),x34461)),f324(f106(a1),x34462)),f324(f106(a1),f324(f324(f82(a1),x34461),f324(f81(a1),x34462))))
% 18.55/18.48 [3458]E(f324(f157(a838),f129(a838,f324(f295(a838,x34581),f324(a114,x34582)))),f296(a838,x34581,x34582))
% 18.55/18.48 [3489]E(f324(f324(f172(f844(x34891,x34891),a832),f2(a838)),x34892),f301(x34891,f179(f845(f844(x34891,x34891),a832))))
% 18.55/18.48 [3493]P1(f324(f127(a838),f129(a838,f324(f295(a838,x34931),x34932))))
% 18.55/18.48 [3509]E(f324(f304(a1,a838,a107),f296(a1,f324(f102(a1),x35091),f324(f102(a1),x35092))),f296(a838,x35091,x35092))
% 18.55/18.48 [3519]E(f174(a838,f2(a838),f7(a838),f324(f324(f3(a838),x35191),x35192)),f324(f324(f3(a838),x35191),f324(a114,x35192)))
% 18.55/18.48 [3520]E(f324(a107,f324(f324(f3(a1),x35201),f324(f324(f82(a1),x35202),f80(a1)))),f324(f41(a1),f299(a1,x35202,x35201)))
% 18.55/18.48 [3556]E(f324(f324(f141(a838,a838),a114),f129(a838,f324(f295(a838,x35561),x35562))),f129(a838,f324(f295(a838,f324(a114,x35561)),f324(a114,x35562))))
% 18.55/18.48 [3563]E(f324(f157(a1),f162(f324(f324(f82(a1),x35631),f80(a1)),f324(f324(f3(a1),x35632),f80(a1)))),f299(a1,x35631,x35632))
% 18.55/18.48 [3577]P1(f324(f324(f231(f845(x35771,a832)),f179(f845(x35771,a832))),x35772))
% 18.55/18.48 [3581]E(f87(x35811,f324(f324(f9(x35811,x35811,a832),a321),x35812)),x35812)
% 18.55/18.48 [3582]E(f92(x35821,f324(f324(f9(x35821,x35821,a832),a321),x35822)),x35822)
% 18.55/18.48 [3586]E(f324(f157(a838),f129(a838,f324(f295(a838,f324(a114,x35861)),f324(a114,x35862)))),f298(a838,x35861,x35862))
% 18.55/18.48 [3612]E(f324(f324(f249(x36121,x36122),f238(f845(x36121,a832))),f324(f18(f845(x36122,a832),x36121),f238(f845(x36122,a832)))),f238(f845(f844(x36121,x36122),a832)))
% 18.55/18.48 [3646]E(f324(f257(x36461),f324(f324(f10(a832,a832,x36461),a320),x36462)),f324(f81(f845(x36461,a832)),f324(f257(x36461),x36462)))
% 18.55/18.48 [3649]E(f324(f257(x36491),f324(f324(f9(x36491,x36491,a832),a321),x36492)),f324(f324(f303(x36491),x36492),f179(f845(x36491,a832))))
% 18.55/18.48 [3656]E(f324(f324(f82(a1),f324(f324(f82(a1),x36561),x36561)),f324(f324(f82(a1),x36562),x36562)),f324(f324(f82(a1),f324(f324(f82(a1),x36561),x36562)),f324(f324(f82(a1),x36561),x36562)))
% 18.55/18.48 [3657]E(f324(f324(f3(a1),f324(f324(f82(a1),x36571),x36571)),f324(f324(f82(a1),x36572),x36572)),f324(f324(f82(a1),f324(f324(f3(a1),x36571),x36572)),f324(f324(f3(a1),x36571),x36572)))
% 18.55/18.48 [3673]P1(f324(f324(f231(a838),f324(f41(x36731),f324(f157(x36731),x36732))),f324(f180(f839(x36731)),x36732)))
% 18.55/18.48 [3674]P1(f324(f324(f231(a838),f324(f180(f839(x36741)),f140(x36741,x36742))),f324(f180(f839(x36741)),x36742)))
% 18.55/18.48 [3685]E(f324(f257(x36851),f324(f324(f9(x36851,f845(x36851,a832),a832),f326(x36851)),x36852)),x36852)
% 18.55/18.48 [3701]E(f324(f324(f158(x37011),f324(f324(f3(a838),f324(f180(f839(x37011)),x37012)),f80(a838))),x37012),f116(x37011,x37012))
% 18.55/18.48 [3724]E(f174(a838,f2(a838),f324(f324(f10(a838,a838,a838),a114),f324(f235(a838),x37241)),x37242),f324(f324(f235(a838),f324(a114,x37241)),x37242))
% 18.55/18.48 [3728]E(f43(f845(x37281,a832),f324(f304(f845(f844(x37281,x37281),a832),f845(x37281,a832),f277(x37281)),x37282)),f324(f277(x37281),f43(f845(f844(x37281,x37281),a832),x37282)))
% 18.55/18.48 [3729]E(f174(a838,f324(a114,x37291),f324(f324(f10(a838,a838,a838),a114),f324(f178(a838),x37291)),x37292),f324(f324(f178(a838),f324(a114,x37291)),x37292))
% 18.55/18.48 [3731]E(f324(f324(f247(a1,a1),f324(f324(f42(a1),f324(f77(a1),x37311)),f324(f77(a1),x37312))),f51(a1,f324(f77(a1),x37311),f324(f77(a1),x37312))),f59(x37311,x37312))
% 18.55/18.48 [3751]P1(f324(f324(f231(f845(f845(x37511,a832),a832)),x37512),f324(f302(x37511),f43(f845(x37511,a832),x37512))))
% 18.55/18.48 [3782]E(f324(f324(f45(x37821,f845(x37821,a832)),x37822),f324(f324(f9(x37821,f845(x37821,a832),f845(x37821,a832)),f303(x37821)),f179(f845(x37821,a832)))),x37822)
% 18.55/18.48 [3783]E(f324(f324(f282(x37831,x37831,x37831),f324(f279(x37831,x37831),x37832)),f301(x37831,f324(f279(x37831,x37831),x37832))),f324(f279(x37831,x37831),f324(f324(f282(x37831,x37831,x37831),x37832),f301(x37831,x37832))))
% 18.55/18.48 [3852]E(f324(f157(x38521),f324(f131(f839(x38521),f839(x38521),f125(x38521),f115(x38521)),x38522)),f324(f324(f45(f839(x38521),f845(x38521,a832)),f324(f157(f839(x38521)),x38522)),f157(x38521)))
% 18.55/18.48 [3884]E(f324(f324(f103(f845(f844(x38841,x38841),a832)),f301(x38841,f179(f845(f844(x38841,x38841),a832)))),f324(f324(f282(x38841,x38841,x38841),f301(x38841,x38842)),x38842)),f301(x38841,x38842))
% 18.55/18.48 [3921]E(f324(f324(f166(x39211,x39211),x39212),x39212),f324(f324(f141(x39211,f844(x39211,x39211)),f324(f324(f20(x39211,x39211,f844(x39211,x39211)),f247(x39211,x39211)),f7(x39211))),x39212))
% 18.55/18.48 [4032]E(f324(f131(a838,f839(x40321),f324(f9(f839(x40321),a838,a838),f324(f324(f10(a838,f845(a838,a838),f839(x40321)),f178(a838)),f180(f839(x40321)))),f2(a838)),f324(f154(f839(x40321)),x40322)),f324(f180(f839(f839(x40321))),f163(x40321,x40322)))
% 18.55/18.48 [4109]E(f324(f324(f281(f844(a838,f839(x41091)),f839(x41091)),f318(a838,f839(x41091),a236,f134(x41091,x41092))),f324(f324(f20(f839(x41091),f839(x41091),f844(a838,f839(x41091))),f324(f324(f10(a838,f845(f839(x41091),f844(a838,f839(x41091))),f839(x41091)),f247(a838,f839(x41091))),f180(f839(x41091)))),f7(f839(x41091)))),f135(x41091,x41092))
% 18.55/18.48 [4235]E(f324(f257(x42351),f324(f324(f10(f845(f845(x42351,a832),a832),a832,x42351),f90(f845(x42351,a832))),f324(f324(f10(f845(f845(x42351,a832),a832),f845(f845(x42351,a832),a832),x42351),f324(f20(f845(x42351,a832),a832,a832),f324(f324(f10(a832,f845(a832,a832),f845(x42351,a832)),a327),f324(f324(f9(f845(x42351,a832),f845(f845(x42351,a832),a832),a832),f326(f845(x42351,a832))),x42352)))),f326(x42351)))),f44(f845(x42351,a832),x42352))
% 18.55/18.48 [4401]~P1(f324(f324(f232(a1),f324(f102(a1),x44011)),f324(f81(a1),f324(f102(a1),x44012))))
% 18.55/18.48 [3323]E(f324(f324(f3(a838),f324(f324(f82(a838),x33231),x33232)),x33232),x33231)
% 18.55/18.48 [3324]E(f324(f324(f3(a838),f324(f324(f82(a838),x33241),x33242)),x33241),x33242)
% 18.55/18.48 [3394]E(f324(f324(f82(a838),f324(f324(f3(a838),x33941),x33942)),x33942),f324(f324(f178(a838),x33941),x33942))
% 18.55/18.48 [3495]E(f324(f324(f83(a838),f324(f324(f42(a838),x34951),x34952)),x34952),f324(f324(f3(a838),x34951),f51(a838,x34951,x34952)))
% 18.55/18.48 [3524]E(f324(f157(a838),f129(a838,f324(f295(a838,f324(a114,x35241)),x35242))),f299(a838,x35241,x35242))
% 18.55/18.48 [3532]E(f324(f102(a1),f210(f324(a107,f324(f77(a1),x35321)),f324(a107,f324(f77(a1),x35322)))),f324(f324(a211,x35321),x35322))
% 18.55/18.48 [3534]E(f324(f324(f103(f845(x35341,a832)),f324(f81(f845(x35341,a832)),x35342)),x35342),f238(f845(x35341,a832)))
% 18.55/18.48 [3535]E(f324(f324(f104(f845(x35351,a832)),f324(f81(f845(x35351,a832)),x35352)),x35352),f179(f845(x35351,a832)))
% 18.55/18.48 [3552]P1(f324(f324(f231(a838),f324(f324(f42(a838),x35521),x35522)),x35521))
% 18.55/18.48 [3553]P1(f324(f324(f231(a838),f324(f324(f3(a838),x35531),x35532)),x35531))
% 18.55/18.48 [3578]P1(f324(f324(f232(a838),x35781),f324(a114,f324(f324(f82(a838),x35782),x35781))))
% 18.55/18.48 [3579]P1(f324(f324(f232(a838),x35791),f324(a114,f324(f324(f82(a838),x35791),x35792))))
% 18.55/18.48 [3598]E(f324(f324(f83(a838),f324(a107,f324(f77(a1),x35981))),f324(a107,f324(f77(a1),x35982))),f324(a107,f324(f77(a1),f324(f324(f83(a1),x35981),x35982))))
% 18.55/18.48 [3605]E(f324(f324(f82(a1),f324(f324(f83(a1),x36051),x36052)),f324(f324(f83(a1),x36051),x36052)),f324(f324(f83(a1),f324(f324(f82(a1),x36051),x36051)),x36052))
% 18.55/18.48 [3608]P1(f324(f324(f231(a1),f2(a1)),f324(f324(f240(a1),f324(f77(a1),x36081)),x36082)))
% 18.55/18.48 [3679]E(f324(f278(f839(x36791),f839(x36791),f145(x36791,x36792)),f324(f324(f303(f839(x36791)),f115(x36791)),f179(f845(f839(x36791),a832)))),f324(f324(f303(f839(x36791)),f115(x36791)),f179(f845(f839(x36791),a832))))
% 18.55/18.48 [3697]E(f324(f324(f103(f845(f844(x36971,x36971),a832)),f301(x36971,x36972)),f301(x36971,f179(f845(f844(x36971,x36971),a832)))),f301(x36971,x36972))
% 18.55/18.48 [3713]E(f324(f324(f42(a1),f324(f106(a1),f324(f324(f82(a1),x37131),x37131))),f324(f106(a1),f324(f324(f82(a1),x37132),x37132))),f324(f324(f42(a1),f324(f106(a1),x37131)),f324(f106(a1),x37132)))
% 18.55/18.48 [3772]E(f324(f324(f240(a1),x37721),f324(f106(a838),f324(f324(f82(a1),x37722),x37722))),f324(f324(f88(a1,a1),f324(f324(f240(a1),x37721),f324(f106(a838),x37722))),f324(f324(f20(a1,a1,a1),f83(a1)),f7(a1))))
% 18.55/18.48 [3778]E(f324(f257(f845(x37781,a832)),f324(f324(f9(f845(x37781,a832),f845(x37781,a832),a832),f231(f845(x37781,a832))),x37782)),f324(f302(x37781),x37782))
% 18.55/18.48 [3792]E(f324(f324(f141(a1,a838),a107),f324(f324(f125(a1),f324(f324(f141(a838,a1),f102(a1)),x37921)),f324(f324(f141(a838,a1),f102(a1)),x37922))),f324(f324(f125(a838),x37921),x37922))
% 18.55/18.48 [3826]E(f324(f304(a1,a1,f324(f324(f9(a1,a1,a1),f82(a1)),x38261)),f324(f295(a1,f2(a1)),f324(f324(f3(a1),x38262),x38261))),f324(f295(a1,x38261),x38262))
% 18.55/18.48 [3829]P48(x38291,f324(f324(f3(f845(f844(x38291,x38291),a832)),x38292),f301(x38291,f179(f845(f844(x38291,x38291),a832)))))
% 18.55/18.48 [3849]E(f324(f180(f839(x38491)),f324(f131(f839(x38491),f839(x38491),f125(x38491),f115(x38491)),x38492)),f324(f151(a838),f324(f324(f141(f839(x38491),a838),f180(f839(x38491))),x38492)))
% 18.55/18.48 [3855]P47(x38551,f238(f845(x38551,a832)),f324(f324(f103(f845(f844(x38551,x38551),a832)),x38552),f301(x38551,f179(f845(f844(x38551,x38551),a832)))))
% 18.55/18.48 [3895]P1(f324(f324(f326(f844(x38951,x38951)),f324(f324(f247(x38951,x38951),x38952),x38952)),f301(x38951,f179(f845(f844(x38951,x38951),a832)))))
% 18.55/18.48 [3901]E(f174(a838,f2(a838),f324(f324(f10(a838,a838,a838),a114),f324(f324(f9(a838,a838,a838),f235(a838)),x39011)),x39012),f324(f324(f235(a838),x39012),f324(a114,x39011)))
% 18.55/18.48 [3904]E(f174(a838,f324(a114,x39041),f324(f324(f10(a838,a838,a838),a114),f324(f324(f9(a838,a838,a838),f178(a838)),x39041)),x39042),f324(f324(f178(a838),x39042),f324(a114,x39041)))
% 18.55/18.48 [3907]E(f324(f304(x39071,f839(x39071),f324(f324(f9(x39071,f839(x39071),f839(x39071)),f139(x39071)),f115(x39071))),x39072),f160(x39071,x39072,f324(f324(f303(f839(x39071)),f115(x39071)),f179(f845(f839(x39071),a832)))))
% 18.55/18.48 [3908]E(f324(f324(f103(f845(f844(x39081,x39081),a832)),f324(f324(f282(x39081,x39081,x39081),x39082),f301(x39081,x39082))),f301(x39081,f179(f845(f844(x39081,x39081),a832)))),f301(x39081,x39082))
% 18.55/18.48 [3916]P1(f324(f324(f231(f845(f844(x39161,x39161),a832)),f261(x39161,x39162)),f324(f324(f249(x39161,x39161),x39162),f324(f18(f845(x39161,a832),x39161),x39162))))
% 18.55/18.48 [3919]E(f324(f304(a1,a838,a107),f324(f324(f103(f845(a1,a832)),f324(f304(a838,a1,f102(a1)),x39191)),f324(f304(a838,a1,f102(a1)),x39192))),f324(f324(f103(f845(a838,a832)),x39191),x39192))
% 18.55/18.48 [3920]E(f324(f304(a1,a838,a107),f324(f324(f104(f845(a1,a832)),f324(f304(a838,a1,f102(a1)),x39201)),f324(f304(a838,a1,f102(a1)),x39202))),f324(f324(f104(f845(a838,a832)),x39201),x39202))
% 18.55/18.48 [3924]E(f324(f257(x39241),f324(f324(f10(a832,a832,x39241),a320),f324(f324(f9(x39241,f845(x39241,a832),a832),f326(x39241)),x39242))),f324(f81(f845(x39241,a832)),x39242))
% 18.55/18.48 [3951]E(f324(f131(f839(x39511),f839(x39511),f125(x39511),f115(x39511)),f324(f324(f141(f839(x39511),f839(x39511)),f154(x39511)),f324(f154(f839(x39511)),x39512))),f324(f154(x39511),f324(f131(f839(x39511),f839(x39511),f125(x39511),f115(x39511)),x39512)))
% 18.55/18.48 [3978]E(f324(f324(f45(a838,f845(f844(x39781,x39781),a832)),f238(f845(a838,a832))),f324(f324(f9(a838,f845(f844(x39781,x39781),a832),f845(f844(x39781,x39781),a832)),f172(f844(x39781,x39781),a832)),x39782)),f301(x39781,x39782))
% 18.55/18.48 [3996]E(f87(x39961,f324(f324(f10(f845(x39961,a832),a832,x39961),f324(a321,x39962)),f324(f324(f9(x39961,f845(x39961,a832),f845(x39961,a832)),f303(x39961)),f179(f845(x39961,a832))))),f306(x39961,x39962))
% 18.55/18.48 [4004]E(f324(f180(f839(x40041)),f140(x40041,f324(f131(f839(x40041),f839(x40041),f125(x40041),f115(x40041)),x40042))),f324(f41(x40041),f324(f324(f45(f839(x40041),f845(x40041,a832)),f324(f157(f839(x40041)),x40042)),f157(x40041))))
% 18.55/18.48 [4019]E(f324(f324(f103(f845(f844(x40191,x40191),a832)),x40192),f324(f324(f282(x40191,x40191,x40191),f324(f324(f282(x40191,x40191,x40191),x40192),f301(x40191,x40192))),x40192)),f324(f324(f282(x40191,x40191,x40191),x40192),f301(x40191,x40192)))
% 18.55/18.48 [4041]P1(f324(f324(f231(f845(f844(x40411,x40411),a832)),f324(f324(f282(x40411,x40411,x40411),x40412),f301(x40411,x40412))),f324(f324(f249(x40411,x40411),f324(f277(x40411),x40412)),f324(f18(f845(x40411,a832),x40411),f324(f277(x40411),x40412)))))
% 18.55/18.48 [4086]E(f324(f257(f839(x40861)),f324(f324(f9(f839(x40861),f845(x40861,a832),a832),f324(f324(f10(f845(x40861,a832),f845(f845(x40861,a832),a832),f839(x40861)),f231(f845(x40861,a832))),f157(x40861))),x40862)),f147(x40861,x40862))
% 18.55/18.48 [4097]E(f324(f143(f839(x40971),x40971,f115(x40971),f324(f324(f10(f839(x40971),f845(f839(x40971),f839(x40971)),x40971),f324(f9(f839(x40971),f839(x40971),f839(x40971)),f125(x40971))),f324(f324(f9(x40971,f839(x40971),f839(x40971)),f139(x40971)),f115(x40971)))),x40972),f324(f153(x40971),x40972))
% 18.55/18.48 [4137]P29(f845(x41371,x41372),f845(f844(x41371,x41372),a832),f324(f324(f10(f845(f844(x41371,x41372),a832),f845(f844(x41371,x41372),a832),f845(x41371,x41372)),f257(f844(x41371,x41372))),f324(f324(f10(f845(x41371,f845(x41372,a832)),f845(f844(x41371,x41372),a832),f845(x41371,x41372)),f252(x41371,x41372,a832)),f324(f10(x41372,f845(x41372,a832),x41371),f324(f9(x41372,x41372,a832),a321)))),f238(f845(f845(x41371,x41372),a832)))
% 18.55/18.48 [4142]E(f51(a1,f324(f106(a1),f324(f324(f82(a1),x41421),x41421)),f324(f106(a1),f324(f324(f82(a1),x41422),x41422))),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f51(a1,f324(f106(a1),x41421),f324(f106(a1),x41422))))
% 18.55/18.48 [4184]E(f324(f324(f45(x41841,f845(f844(x41841,x41841),a832)),x41842),f324(f324(f9(x41841,f845(f844(x41841,x41841),a832),f845(f844(x41841,x41841),a832)),f324(f324(f10(f844(x41841,x41841),f845(f845(f844(x41841,x41841),a832),f845(f844(x41841,x41841),a832)),x41841),f303(f844(x41841,x41841))),f324(f324(f20(x41841,x41841,f844(x41841,x41841)),f247(x41841,x41841)),f7(x41841)))),f179(f845(f844(x41841,x41841),a832)))),f261(x41841,x41842))
% 18.55/18.48 [4192]E(f197(x41921,f324(f324(f247(a1,a1),f324(f81(a1),f324(f324(f75(f844(a1,a1),a1,x41921,f246(a1,a1)),f206(x41921)),x41922))),f324(f324(f75(f844(a1,a1),a1,x41921,f251(a1,a1)),f206(x41921)),x41922))),f220(x41921,x41922))
% 18.55/18.48 [4273]E(f324(f257(f845(x42731,a832)),f324(f324(f10(f845(f845(x42731,a832),a832),a832,f845(x42731,a832)),f89(f845(x42731,a832))),f324(f324(f9(f845(x42731,a832),f845(f845(x42731,a832),a832),f845(f845(x42731,a832),a832)),f324(f324(f10(f845(f845(x42731,a832),f845(a832,a832)),f845(f845(f845(x42731,a832),a832),f845(f845(x42731,a832),a832)),f845(x42731,a832)),f20(f845(x42731,a832),a832,a832)),f324(f324(f10(f845(f845(x42731,a832),a832),f845(f845(x42731,a832),f845(a832,a832)),f845(x42731,a832)),f324(f10(a832,f845(a832,a832),f845(x42731,a832)),a322)),f324(f324(f9(f845(x42731,a832),f845(f845(x42731,a832),f845(x42731,a832)),f845(f845(x42731,a832),a832)),f324(f324(f10(f845(f845(x42731,a832),a832),f845(f845(f845(x42731,a832),f845(x42731,a832)),f845(f845(x42731,a832),a832)),f845(x42731,a832)),f10(f845(x42731,a832),a832,f845(x42731,a832))),a321)),f81(f845(x42731,a832)))))),f324(f324(f10(f845(f845(x42731,a832),a832),a832,f845(x42731,a832)),f324(f326(f845(x42731,a832)),x42732)),f302(x42731))))),f324(f302(x42731),f324(f81(f845(x42731,a832)),x42732)))
% 18.55/18.48 [4396]~E(f324(f324(f82(a1),x43961),x43961),f324(f324(f3(a1),f324(f324(f82(a1),x43962),x43962)),a99))
% 18.55/18.48 [4397]~E(f324(f324(f82(a1),x43971),x43971),f324(f324(f3(a1),f324(f324(f82(a1),x43972),x43972)),a99))
% 18.55/18.48 [4403]~P1(f324(f324(f232(a838),f324(f324(f82(a838),x44031),x44032)),x44032))
% 18.55/18.48 [4404]~P1(f324(f324(f232(a838),f324(f324(f82(a838),x44041),x44042)),x44041))
% 18.55/18.48 [3613]E(f324(f324(f3(a838),x36131),f324(f324(f83(a838),f324(f324(f42(a838),x36131),x36132)),x36132)),f51(a838,x36131,x36132))
% 18.55/18.48 [3614]E(f324(f324(f3(a1),x36141),f324(f324(f83(a1),f324(f324(f42(a1),x36141),x36142)),x36142)),f51(a1,x36141,x36142))
% 18.55/18.48 [3647]E(f324(f324(f141(a838,x36471),f324(f149(x36471),x36472)),f129(a838,f324(f295(a838,f2(a838)),f324(f180(f839(x36471)),x36472)))),x36472)
% 18.55/18.48 [3709]E(f324(f278(x37091,x37091,f301(x37091,f179(f845(f844(x37091,x37091),a832)))),x37092),x37092)
% 18.55/18.48 [3832]E(f301(x38321,f324(f324(f3(f845(f844(x38321,x38321),a832)),x38322),f301(x38321,f179(f845(f844(x38321,x38321),a832))))),f301(x38321,x38322))
% 18.55/18.48 [3833]E(f301(x38331,f324(f324(f103(f845(f844(x38331,x38331),a832)),x38332),f301(x38331,f179(f845(f844(x38331,x38331),a832))))),f301(x38331,x38332))
% 18.55/18.48 [3888]E(f324(f324(f3(a1),f324(f324(f3(a1),f324(f324(f82(a1),x38881),x38881)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x38882),x38882)),a99)),f324(f324(f82(a1),f324(f324(f3(a1),x38881),x38882)),f324(f324(f3(a1),x38881),x38882)))
% 18.55/18.48 [3929]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f82(a1),x39291),x39292)),f324(f324(f82(a1),x39291),x39292))),a99),f324(f324(f82(a1),f324(f324(f82(a1),x39291),x39291)),f324(f324(f3(a1),f324(f324(f82(a1),x39292),x39292)),a99)))
% 18.55/18.48 [3955]E(f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),x39551),x39551)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x39552),x39552)),a99)),f324(f324(f82(a1),f324(f324(f82(a1),x39551),f324(f324(f3(a1),x39552),a99))),f324(f324(f82(a1),x39551),f324(f324(f3(a1),x39552),a99))))
% 18.55/18.48 [3966]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f82(a1),x39661),x39662)),f324(f324(f82(a1),x39661),x39662))),a99),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),x39661),x39661)),a99)),f324(f324(f82(a1),x39662),x39662)))
% 18.55/18.48 [3967]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),x39671),x39672)),f324(f324(f3(a1),x39671),x39672))),a99),f324(f324(f3(a1),f324(f324(f3(a1),f324(f324(f82(a1),x39671),x39671)),a99)),f324(f324(f82(a1),x39672),x39672)))
% 18.55/18.48 [4016]E(f324(f102(a1),f324(f324(f42(a838),f324(f324(f83(a838),f324(a107,f324(f77(a1),x40161))),f324(a107,f324(f77(a1),x40162)))),f210(f324(a107,f324(f77(a1),x40161)),f324(a107,f324(f77(a1),x40162))))),f212(x40161,x40162))
% 18.55/18.48 [4062]E(f324(f324(f254(f844(a101,a101),a101,f844(a101,a101),f844(x40621,f844(a101,a101))),f265(f324(a5,f324(f180(f839(x40621)),x40622)))),f324(f324(f10(x40621,f845(f844(a101,a101),f844(x40621,f844(a101,a101))),a101),f247(x40621,f844(a101,a101))),f324(f324(f10(a838,x40621,a101),f324(f149(x40621),x40622)),a22))),f271(x40621,x40622))
% 18.55/18.48 [4143]E(f324(f131(a838,f839(x41431),f324(f9(f839(x41431),a838,a838),f324(f324(f10(a838,f845(a838,a838),f839(x41431)),f178(a838)),f180(f839(x41431)))),f2(a838)),f324(f154(f839(x41431)),f163(x41431,x41432))),f324(f180(f839(f839(x41431))),f324(f126(f839(x41431),f324(f324(f10(a832,a832,f839(x41431)),a320),f324(f324(f9(f839(x41431),f839(x41431),a832),a321),f115(x41431)))),x41432)))
% 18.55/18.48 [4149]E(f324(f324(f45(a838,f845(x41491,a832)),f238(f845(a838,a832))),f324(f324(f9(a838,f845(a838,f845(x41491,a832)),f845(x41491,a832)),f324(f324(f10(f845(a838,a832),f845(f845(a838,f845(x41491,a832)),f845(x41491,a832)),a838),f45(a838,f845(x41491,a832))),f295(a838,f2(a838)))),x41492)),f324(f324(f45(a838,f845(x41491,a832)),f238(f845(a838,a832))),x41492))
% 18.55/18.48 [4168]P1(f324(f64(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),x41681)),f324(f324(f9(a838,a838,a832),f232(a838)),x41682)))))
% 18.55/18.48 [4283]E(f324(f257(f844(f839(x42831),f839(x42831))),f324(f252(f839(x42831),f839(x42831),a832),f324(f324(f20(f839(x42831),f845(f839(x42831),a832),f845(f839(x42831),a832)),f324(f324(f10(f845(f839(x42831),f845(a832,a832)),f845(f845(f839(x42831),a832),f845(f839(x42831),a832)),f839(x42831)),f20(f839(x42831),a832,a832)),f324(f324(f10(f845(f839(x42831),a832),f845(f839(x42831),f845(a832,a832)),f839(x42831)),f324(f10(a832,f845(a832,a832),f839(x42831)),a323)),f324(f324(f9(f839(x42831),f845(f839(x42831),a838),f845(f839(x42831),a832)),f324(f324(f10(f845(a838,a832),f845(f845(f839(x42831),a838),f845(f839(x42831),a832)),f839(x42831)),f10(a838,a832,f839(x42831))),f324(f324(f10(a838,f845(a838,a832),f839(x42831)),f232(a838)),f180(f839(x42831))))),f180(f839(x42831)))))),f324(f324(f20(f839(x42831),f845(f839(x42831),a832),f845(f839(x42831),a832)),f324(f324(f10(f845(f839(x42831),f845(a832,a832)),f845(f845(f839(x42831),a832),f845(f839(x42831),a832)),f839(x42831)),f20(f839(x42831),a832,a832)),f324(f324(f10(f845(f839(x42831),a832),f845(f839(x42831),f845(a832,a832)),f839(x42831)),f324(f10(a832,f845(a832,a832),f839(x42831)),a322)),f324(f324(f9(f839(x42831),f845(f839(x42831),a838),f845(f839(x42831),a832)),f324(f324(f10(f845(a838,a832),f845(f845(f839(x42831),a838),f845(f839(x42831),a832)),f839(x42831)),f10(a838,a832,f839(x42831))),f324(f324(f10(a838,f845(a838,a832),f839(x42831)),a321),f180(f839(x42831))))),f180(f839(x42831)))))),f324(f324(f9(f839(x42831),f845(f844(f839(x42831),f839(x42831)),a832),f845(f839(x42831),a832)),f324(f324(f10(f845(f839(x42831),f845(f845(f844(f839(x42831),f839(x42831)),a832),a832)),f845(f845(f844(f839(x42831),f839(x42831)),a832),f845(f839(x42831),a832)),f839(x42831)),f9(f839(x42831),f845(f844(f839(x42831),f839(x42831)),a832),a832)),f324(f324(f10(f845(f839(x42831),f844(f839(x42831),f839(x42831))),f845(f839(x42831),f845(f845(f844(f839(x42831),f839(x42831)),a832),a832)),f839(x42831)),f324(f10(f844(f839(x42831),f839(x42831)),f845(f845(f844(f839(x42831),f839(x42831)),a832),a832),f839(x42831)),f326(f844(f839(x42831),f839(x42831))))),f247(f839(x42831),f839(x42831))))),f134(x42831,x42832)))))),f135(x42831,x42832))
% 18.55/18.48 [3958]E(f324(f324(f82(a1),f324(f324(f82(a1),f324(f324(f83(a1),x39581),x39582)),f324(f324(f83(a1),x39581),x39582))),x39582),f324(f324(f83(a1),f324(f324(f3(a1),f324(f324(f82(a1),x39581),x39581)),a99)),x39582))
% 18.55/18.48 [4060]E(f324(a107,f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x40601),x40602)),f179(f845(f844(a838,a838),a832)))))),f324(f324(f3(a838),x40601),x40602))
% 18.55/18.48 [4066]E(f324(f324(f282(x40661,x40661,x40661),f324(f324(f103(f845(f844(x40661,x40661),a832)),x40662),f301(x40661,f179(f845(f844(x40661,x40661),a832))))),f301(x40661,f324(f324(f103(f845(f844(x40661,x40661),a832)),x40662),f301(x40661,f179(f845(f844(x40661,x40661),a832)))))),f301(x40661,x40662))
% 18.55/18.48 [4102]E(f266(x41021,f324(f126(f844(a101,x41021),f324(f252(a101,x41021,a832),f324(f324(f10(a832,f845(x41021,a832),a101),f18(a832,x41021)),f324(f232(a101),f2(a101))))),x41022)),f266(x41021,x41022))
% 18.55/18.48 [4103]E(f264(x41031,f324(f126(f844(a101,x41031),f324(f252(a101,x41031,a832),f324(f324(f10(a832,f845(x41031,a832),a101),f18(a832,x41031)),f324(f232(a101),f2(a101))))),x41032)),f264(x41031,x41032))
% 18.55/18.48 [4105]E(f324(f81(a1),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x41051),x41052)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x41052),x41051)),f179(f845(f844(a838,a838),a832))))))
% 18.55/18.48 [4181]E(f324(f324(f88(a1,a838),f324(f106(a1),f324(f324(f82(a1),x41811),a99))),f324(f324(f20(a1,a838,a838),f324(f324(f9(a1,a838,f845(a838,a838)),f324(f324(f10(a832,f845(a838,f845(a838,a838)),a1),f98(a838)),a185)),f2(a838))),f324(f324(f10(a838,a838,a1),a114),f324(f324(f10(a838,a838,a1),f324(f235(a838),x41812)),a107)))),f324(f324(f235(a838),f324(a114,x41812)),f324(f106(a838),x41811)))
% 18.55/18.48 [4182]E(f324(f324(f88(a1,a838),f324(f106(a1),f324(f324(f82(a1),x41821),a99))),f324(f324(f20(a1,a838,a838),f324(f324(f9(a1,a838,f845(a838,a838)),f324(f324(f10(a832,f845(a838,f845(a838,a838)),a1),f98(a838)),a185)),f324(a114,x41822))),f324(f324(f10(a838,a838,a1),a114),f324(f324(f10(a838,a838,a1),f324(f178(a838),x41822)),a107)))),f324(f324(f178(a838),f324(a114,x41822)),f324(f106(a838),x41821)))
% 18.55/18.48 [4202]E(f324(f131(f839(x42021),f839(x42021),f125(x42021),f115(x42021)),f324(f324(f141(f839(x42021),f839(x42021)),f143(f839(x42021),x42021,f115(x42021),f324(f324(f10(f839(x42021),f845(f839(x42021),f839(x42021)),x42021),f18(f839(x42021),f839(x42021))),f324(f324(f9(x42021,f839(x42021),f839(x42021)),f139(x42021)),f115(x42021))))),x42022)),f324(f324(f141(f839(x42021),x42021),f130(x42021)),f324(f126(f839(x42021),f324(f324(f10(a832,a832,f839(x42021)),a320),f324(f324(f9(f839(x42021),f839(x42021),a832),a321),f115(x42021)))),x42022)))
% 18.55/18.48 [4263]E(f324(f252(a1,a1,a832),f324(f324(f9(a1,f845(a1,a832),f845(a1,a832)),f324(f324(f10(f845(a1,f845(a832,a832)),f845(f845(a1,a832),f845(a1,a832)),a1),f20(a1,a832,a832)),f324(f324(f10(f845(a1,a832),f845(a1,f845(a832,a832)),a1),f324(f10(a832,f845(a832,a832),a1),a322)),f324(f324(f10(f845(a1,a1),f845(a1,a832),a1),f324(f10(a1,a832,a1),f324(a321,x42631))),f324(f324(f10(a1,f845(a1,a1),a1),f82(a1)),f324(f83(a1),x42632)))))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),f324(a327,f324(f324(f232(a1),f2(a1)),x42632))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),f324(f324(f9(a1,a1,a832),f232(a1)),x42632))))),f324(f324(f10(a832,a832,a1),f324(a327,f324(a320,f324(f324(f232(a1),f2(a1)),x42632)))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f232(a1),x42632))),f324(f324(f9(a1,a1,a832),f231(a1)),f2(a1))))))),f55(x42631,x42632))
% 18.55/18.48 [4265]E(f324(f257(x42651),f324(f324(f10(f845(a838,a832),a832,x42651),f89(a838)),f324(f324(f9(x42651,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),x42651),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),x42651),f324(f10(a832,f845(a832,a832),a838),a322)),f324(f324(f9(x42651,f845(a838,x42651),f845(a838,a832)),f324(f324(f10(f845(x42651,a832),f845(f845(a838,x42651),f845(a838,a832)),x42651),f10(x42651,a832,a838)),a321)),f324(f149(x42651),x42652))))),f324(f324(f9(a838,a838,a832),f232(a838)),f324(f180(f839(x42651)),x42652))))),f324(f157(x42651),x42652))
% 18.55/18.48 [4076]E(f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),x40761),a99)),x40762)),f324(f324(f3(a1),f324(f324(f82(a1),x40761),a99)),x40762))),a99),f324(f324(f3(a1),f324(f324(f82(a1),x40761),x40761)),f324(f324(f3(a1),f324(f324(f82(a1),x40762),x40762)),a99)))
% 18.55/18.48 [4197]E(f324(f131(f839(f839(x41971)),f839(f839(x41971)),f125(f839(x41971)),f115(f839(x41971))),f324(f324(f141(f839(x41971),f839(f839(x41971))),f143(f839(f839(x41971)),x41971,f115(f839(x41971)),f324(f18(f845(f839(x41971),f839(f839(x41971))),x41971),f324(f324(f9(f839(x41971),f839(f839(x41971)),f839(f839(x41971))),f139(f839(x41971))),f115(f839(x41971)))))),x41972)),f324(f324(f141(f839(x41971),f839(x41971)),f156(x41971)),f324(f126(f839(x41971),f324(f324(f10(a832,a832,f839(x41971)),a320),f324(f324(f9(f839(x41971),f839(x41971),a832),a321),f115(x41971)))),x41972)))
% 18.55/18.48 [4207]E(f324(f324(f88(a1,a838),f324(f106(a1),f324(f324(f82(a1),x42071),a99))),f324(f324(f20(a1,a838,a838),f324(f324(f9(a1,a838,f845(a838,a838)),f324(f324(f10(a832,f845(a838,f845(a838,a838)),a1),f98(a838)),a185)),f2(a838))),f324(f324(f10(a838,a838,a1),a114),f324(f324(f9(a1,a838,a838),f324(f324(f10(a838,f845(a838,a838),a1),f235(a838)),a107)),x42072)))),f324(f324(f235(a838),f324(f106(a838),x42071)),f324(a114,x42072)))
% 18.55/18.48 [4208]E(f324(f324(f88(a1,a838),f324(f106(a1),f324(f324(f82(a1),x42081),a99))),f324(f324(f20(a1,a838,a838),f324(f324(f9(a1,a838,f845(a838,a838)),f324(f324(f10(a832,f845(a838,f845(a838,a838)),a1),f98(a838)),a185)),f324(a114,x42082))),f324(f324(f10(a838,a838,a1),a114),f324(f324(f9(a1,a838,a838),f324(f324(f10(a838,f845(a838,a838),a1),f178(a838)),a107)),x42082)))),f324(f324(f178(a838),f324(f106(a838),x42081)),f324(a114,x42082)))
% 18.55/18.48 [4196]E(f324(f252(x41961,x41961,a832),f324(f324(f20(x41961,a832,f845(x41961,a832)),f324(f324(f10(f845(x41961,f845(a832,a832)),f845(a832,f845(x41961,a832)),x41961),f9(x41961,a832,a832)),f324(f324(f10(f845(x41961,a832),f845(x41961,f845(a832,a832)),x41961),f324(f10(a832,f845(a832,a832),x41961),a322)),a321))),x41962)),f261(x41961,x41962))
% 18.55/18.48 [4241]E(f324(f324(f42(a838),x42411),f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42412)),f324(f324(f42(a838),x42411),f324(a114,f324(a114,f324(a114,x42412)))))
% 18.55/18.48 [4242]E(f51(a838,x42421,f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42422)),f51(a838,x42421,f324(a114,f324(a114,f324(a114,x42422)))))
% 18.55/18.48 [4243]E(f51(a838,f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42431),x42432),f51(a838,f324(a114,f324(a114,f324(a114,x42431))),x42432))
% 18.55/18.48 [4256]E(f123(f324(x42561,f324(f324(f83(a101),f324(f106(a101),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42562))),f324(f194(x42561),x42562))
% 18.55/18.48 [4257]E(f324(f324(f42(a838),f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),x42571)),x42572),f324(f324(f42(a838),f324(a114,f324(a114,f324(a114,x42571)))),x42572))
% 18.55/18.48 [4309]~E(f28(x43091,x43092),f324(a27,x43093))
% 18.55/18.48 [4310]~E(f36(x43101,x43102),f324(a27,x43103))
% 18.55/18.48 [4311]~E(f35(x43111,x43112),f324(a27,x43113))
% 18.55/18.48 [4312]~E(f324(a27,x43121),f28(x43122,x43123))
% 18.55/18.48 [4313]~E(f324(a27,x43131),f36(x43132,x43133))
% 18.55/18.48 [4314]~E(f324(a27,x43141),f35(x43142,x43143))
% 18.55/18.48 [4330]~E(f31(x43301,x43302,x43303),a25)
% 18.55/18.48 [4331]~E(f33(x43311,x43312,x43313),a25)
% 18.55/18.48 [4332]~E(f32(x43321,x43322,x43323),a25)
% 18.55/18.48 [4333]~E(f31(x43331,x43332,x43333),a25)
% 18.55/18.48 [4334]~E(f33(x43341,x43342,x43343),a25)
% 18.55/18.48 [4335]~E(f32(x43351,x43352,x43353),a25)
% 18.55/18.48 [3046]E(f324(f193(x30461,x30462),x30463),f120(x30461,x30462))
% 18.55/18.48 [3047]E(f324(f184(x30471,x30472),x30473),f121(x30471,x30472))
% 18.55/18.48 [3143]E(f324(f324(f141(x31431,x31432),x31433),f115(x31431)),f115(x31432))
% 18.55/18.48 [3144]E(f324(f324(f195(x31441,x31442),x31443),f182(x31441)),f182(x31442))
% 18.55/18.48 [3164]E(f34(f31(x31641,x31642,x31643)),f2(a838))
% 18.55/18.48 [3184]E(f324(f173(x31841,x31842,x31843),f2(a838)),x31842)
% 18.55/18.48 [3185]E(f324(f180(a833),f31(x31851,x31852,x31853)),f2(a838))
% 18.55/18.48 [3187]E(f324(f324(f166(x31871,x31872),x31873),f115(x31872)),f115(f844(x31871,x31872)))
% 18.55/18.48 [3221]E(f87(x32211,f65(x32211,x32212,x32213)),f324(f66(x32211,x32212),x32213))
% 18.55/18.48 [3225]E(f239(x32251,x32252,f239(x32252,x32251,x32253)),x32253)
% 18.55/18.48 [3291]E(f324(f246(f839(x32911),f839(x32911)),f152(x32911,x32912,x32913)),f324(f126(x32911,x32912),x32913))
% 18.55/18.48 [3368]E(f174(x33681,x33682,x33683,f2(a838)),x33682)
% 18.55/18.48 [3369]E(f19(x33691,x33692,x33693,f2(a101)),x33692)
% 18.55/18.48 [3370]E(f21(x33701,x33702,x33703,f2(a101)),x33702)
% 18.55/18.48 [3377]E(f150(x33771,x33772,x33773,f115(x33771)),f115(x33772))
% 18.55/18.48 [3384]E(f324(f324(f149(x33841),f324(f324(f139(x33841),x33842),x33843)),f2(a838)),x33842)
% 18.55/18.48 [3432]P29(x34321,x34322,x34323,f179(f845(x34321,a832)))
% 18.55/18.48 [3528]E(f263(x35281,x35282,x35283),f324(f247(f845(a101,f845(a832,f842(f840(x35281)))),f844(a101,a101)),f47(x35281)))
% 18.55/18.48 [3588]E(f324(f75(x35881,x35882,x35881,x35883),f37(x35881)),x35883)
% 18.55/18.48 [3763]P1(f324(f324(f326(f844(x37631,x37631)),f324(f324(f247(x37631,x37631),x37632),x37632)),f301(x37631,x37633)))
% 18.55/18.48 [4407]~P1(f324(f324(f326(f844(f839(x44071),f839(x44071))),f324(f324(f247(f839(x44071),f839(x44071)),x44072),f115(x44071))),f134(x44071,x44073)))
% 18.55/18.48 [4408]~P1(f324(f324(f326(f844(f839(x44081),f839(x44081))),f324(f324(f247(f839(x44081),f839(x44081)),x44082),f115(x44081))),f136(x44081,x44083)))
% 18.55/18.48 [4409]~P1(f324(f324(f326(f844(f839(x44091),f839(x44091))),f324(f324(f247(f839(x44091),f839(x44091)),x44092),f115(x44091))),f144(x44091,x44093)))
% 18.55/18.48 [4410]~P1(f324(f324(f326(f844(f839(x44101),f839(x44101))),f324(f324(f247(f839(x44101),f839(x44101)),f115(x44101)),x44102)),f134(x44101,x44103)))
% 18.55/18.48 [4411]~P1(f324(f324(f326(f844(f839(x44111),f839(x44111))),f324(f324(f247(f839(x44111),f839(x44111)),f115(x44111)),x44112)),f144(x44111,x44113)))
% 18.55/18.48 [3118]E(f324(f324(f196(x31181),x31182),x31183),f197(x31181,f209(x31182,x31183)))
% 18.55/18.48 [3174]E(f324(f279(x31741,x31742),f324(f279(x31742,x31741),x31743)),x31743)
% 18.55/18.48 [3197]E(f324(f324(f166(x31971,x31972),f115(x31971)),x31973),f115(f844(x31971,x31972)))
% 18.55/18.48 [3200]E(f159(x32001,x32002,f324(f258(a838),x32003)),f324(f324(f158(x32001),x32003),x32002))
% 18.55/18.48 [3216]E(f324(f262(x32161,x32162),f324(f279(x32162,x32161),x32163)),f324(f260(x32162,x32161),x32163))
% 18.55/18.48 [3218]E(f140(x32181,f324(f126(x32181,x32182),x32183)),f324(f126(x32181,x32182),f140(x32181,x32183)))
% 18.55/18.48 [3219]E(f324(f260(x32191,x32192),f324(f279(x32192,x32191),x32193)),f324(f262(x32192,x32191),x32193))
% 18.55/18.48 [3220]E(f324(f262(x32201,x32202),f324(f279(x32202,x32201),x32203)),f324(f260(x32202,x32201),x32203))
% 18.55/18.48 [3236]E(f324(f126(x32361,x32362),f324(f154(x32361),x32363)),f324(f154(x32361),f324(f126(x32361,x32362),x32363)))
% 18.55/18.48 [3249]E(f324(f324(f128(x32491),x32492),f324(f156(x32491),x32493)),f324(f324(f128(x32491),f324(a114,x32492)),x32493))
% 18.55/18.48 [3267]E(f34(f32(x32671,x32672,x32673)),f324(f324(f82(a838),f34(x32673)),f324(a114,f2(a838))))
% 18.55/18.48 [3268]E(f324(f304(x32681,x32682,x32683),f179(f845(x32681,a832))),f179(f845(x32682,a832)))
% 18.55/18.48 [3269]E(f324(f278(x32691,x32692,x32693),f179(f845(x32691,a832))),f179(f845(x32692,a832)))
% 18.55/18.48 [3270]E(f324(f305(x32701,x32702,x32703),f179(f845(x32702,a832))),f179(f845(x32701,a832)))
% 18.55/18.48 [3271]E(f324(f305(x32711,x32712,x32713),f238(f845(x32712,a832))),f238(f845(x32711,a832)))
% 18.55/18.48 [3308]E(f227(x33081,x33082,f324(f226(x33081),x33083)),f324(f324(f82(a838),f324(x33082,x33083)),f324(a114,f2(a838))))
% 18.55/18.48 [3388]E(f324(f180(a833),f32(x33881,x33882,x33883)),f324(f324(f82(a838),f324(f180(a833),x33883)),f324(a114,f2(a838))))
% 18.55/18.48 [3389]E(f324(f304(f844(x33891,x33892),x33892,f251(x33891,x33892)),x33893),f324(f260(x33891,x33892),x33893))
% 18.55/18.48 [3390]E(f324(f304(f844(x33901,x33902),x33901,f246(x33901,x33902)),x33903),f324(f262(x33901,x33902),x33903))
% 18.55/18.48 [3456]E(f324(f324(f247(x34561,x34562),f324(f246(x34561,x34562),x34563)),f324(f251(x34561,x34562),x34563)),x34563)
% 18.55/18.48 [3457]E(f324(f324(f247(x34571,x34572),f324(f246(x34571,x34572),x34573)),f324(f251(x34571,x34572),x34573)),x34573)
% 18.55/18.48 [3465]E(f324(f324(f252(x34651,x34652,x34651),f18(x34651,x34652)),x34653),f324(f246(x34651,x34652),x34653))
% 18.55/18.48 [3484]E(f169(x34841,x34842,x34843,f324(f18(f842(x34842),x34841),f182(x34842))),x34843)
% 18.55/18.48 [3485]E(f169(x34851,x34852,f324(f18(f842(x34852),x34851),f182(x34852)),x34853),x34853)
% 18.55/18.48 [3541]E(f34(f33(x35411,x35412,x35413)),f324(f324(f82(a838),f324(f324(f82(a838),f34(x35412)),f34(x35413))),f324(a114,f2(a838))))
% 18.55/18.48 [3592]E(f324(f75(x35921,x35921,x35922,f37(x35921)),x35923),x35923)
% 18.55/18.48 [3677]P1(f324(f64(x36771),f168(x36771,x36772,f165(x36771,x36772,x36773))))
% 18.55/18.48 [3699]P1(f324(f324(f186(f28(x36991,x36992)),x36993),f324(f324(f324(a188,x36993),x36991),f324(x36992,x36993))))
% 18.55/18.48 [3700]P1(f324(f324(f186(f28(x37001,x37002)),x37003),f324(f324(f324(a188,x37003),x37001),f324(x37002,x37003))))
% 18.55/18.48 [3702]E(f324(f180(a833),f33(x37021,x37022,x37023)),f324(f324(f82(a838),f324(f324(f82(a838),f324(f180(a833),x37022)),f324(f180(a833),x37023))),f324(a114,f2(a838))))
% 18.55/18.48 [3773]P1(f324(f324(f231(f845(x37731,a832)),f324(f157(x37731),f324(f126(x37731,x37732),x37733))),f324(f157(x37731),x37733)))
% 18.55/18.48 [3817]P1(f324(f324(f231(f845(x38171,a832)),f324(f157(x38171),f324(f324(f158(x38171),x38172),x38173))),f324(f157(x38171),x38173)))
% 18.55/18.48 [3818]P1(f324(f324(f231(f845(x38181,a832)),f324(f157(x38181),f324(f324(f128(x38181),x38182),x38183))),f324(f157(x38181),x38183)))
% 18.55/18.48 [3822]P1(f324(f324(f231(f845(x38221,a832)),f324(f157(x38221),f155(x38221,x38222,x38223))),f324(f157(x38221),x38223)))
% 18.55/18.48 [3823]P1(f324(f324(f231(f845(x38231,a832)),f324(f157(x38231),f159(x38231,x38232,x38233))),f324(f157(x38231),x38232)))
% 18.55/18.48 [3847]P29(f844(x38471,x38472),f844(x38472,x38471),f324(f252(x38471,x38472,f844(x38472,x38471)),f324(f9(x38472,x38471,f844(x38472,x38471)),f247(x38472,x38471))),x38473)
% 18.55/18.48 [3860]E(f324(f324(f324(f172(f839(x38601),f839(x38601)),f51(a838,x38602,f324(f180(f839(x38601)),x38603))),f153(x38601)),x38603),f324(f324(f324(f172(f839(x38601),f839(x38601)),x38602),f153(x38601)),x38603))
% 18.55/18.48 [3902]E(f324(f75(f839(x39021),f839(x39021),f839(x39021),f324(f324(f172(f839(x39021),f839(x39021)),x39022),f153(x39021))),f324(f324(f172(f839(x39021),f839(x39021)),x39023),f153(x39021))),f324(f324(f172(f839(x39021),f839(x39021)),f324(f324(f82(a838),x39022),x39023)),f153(x39021)))
% 18.55/18.48 [3905]P1(f324(f324(f326(f844(f839(x39051),f839(x39051))),f324(f324(f247(f839(x39051),f839(x39051)),x39052),x39052)),f145(x39051,f301(x39051,x39053))))
% 18.55/18.48 [4045]E(f87(f844(x40451,x40452),f324(f324(f20(f844(x40451,x40452),x40452,a832),f324(f324(f10(x40451,f845(x40452,a832),f844(x40451,x40452)),x40453),f246(x40451,x40452))),f251(x40451,x40452))),f87(f844(x40451,x40452),f324(f252(x40451,x40452,a832),x40453)))
% 18.55/18.48 [4046]E(f92(f844(x40461,x40462),f324(f324(f20(f844(x40461,x40462),x40462,a832),f324(f324(f10(x40461,f845(x40462,a832),f844(x40461,x40462)),x40463),f246(x40461,x40462))),f251(x40461,x40462))),f92(f844(x40461,x40462),f324(f252(x40461,x40462,a832),x40463)))
% 18.55/18.48 [4083]E(f324(f324(f281(f844(a838,x40831),x40831),f318(a838,x40831,a236,x40832)),f324(f324(f20(x40831,x40831,f844(a838,x40831)),f324(f324(f10(a838,f845(x40831,f844(a838,x40831)),x40831),f247(a838,x40831)),x40833)),f7(x40831))),f319(x40831,x40833,x40832))
% 18.55/18.48 [4145]E(f324(f253(x41451,x41451,x41452,x41452,f7(x41451),f7(x41452)),x41453),x41453)
% 18.55/18.48 [4218]E(f324(f131(f839(f839(x42181)),f839(f839(x42181)),f125(f839(x42181)),f115(f839(x42181))),f324(f324(f141(f839(x42181),f839(f839(x42181))),f324(f324(f9(f839(x42181),f839(x42181),f839(f839(x42181))),f324(f324(f10(f845(x42181,f839(x42181)),f845(f839(x42181),f839(f839(x42181))),f839(x42181)),f141(x42181,f839(x42181))),f324(f9(x42181,f839(x42181),f839(x42181)),f139(x42181)))),x42182)),f61(x42181,x42183,x42182))),f61(x42181,f324(a114,x42183),x42182))
% 18.55/18.48 [4282]E(f324(f324(f88(a1,x42821),f212(f324(f324(f75(f844(a1,a1),a1,x42821,f251(a1,a1)),f206(x42821)),x42822),f324(f324(f75(f844(a1,a1),a1,x42821,f251(a1,a1)),f206(x42821)),x42823))),f324(f324(f20(a1,a1,x42821),f324(f324(f10(a1,f845(a1,x42821),a1),f196(x42821)),f324(f324(f20(a1,a1,a1),f324(f324(f10(a1,f845(a1,a1),a1),f82(a1)),f324(f324(f10(a1,a1,a1),f324(f83(a1),f324(f324(f75(f844(a1,a1),a1,x42821,f246(a1,a1)),f206(x42821)),x42822))),f324(f324(f9(a1,a1,a1),f42(a1)),f324(f324(f75(f844(a1,a1),a1,x42821,f251(a1,a1)),f206(x42821)),x42822))))),f324(f324(f10(a1,a1,a1),f324(f83(a1),f324(f324(f75(f844(a1,a1),a1,x42821,f246(a1,a1)),f206(x42821)),x42823))),f324(f324(f9(a1,a1,a1),f42(a1)),f324(f324(f75(f844(a1,a1),a1,x42821,f251(a1,a1)),f206(x42821)),x42823)))))),f7(a1))),f223(x42821,x42822,x42823))
% 18.55/18.48 [4327]~E(f324(f324(f139(x43271),x43272),x43273),x43273)
% 18.55/18.48 [4328]~E(f324(f324(f139(x43281),x43282),x43283),x43283)
% 18.55/18.48 [4336]~E(f324(f324(f139(x43361),x43362),x43363),f115(x43361))
% 18.55/18.48 [4337]~E(f324(f324(f139(x43371),x43372),x43373),f115(x43371))
% 18.55/18.48 [4362]~E(f324(f324(f303(x43621),x43622),x43623),f179(f845(x43621,a832)))
% 18.55/18.48 [4363]~E(f324(f324(f303(x43631),x43632),x43633),f179(f845(x43631,a832)))
% 18.55/18.48 [4388]~E(f324(f304(x43881,f845(x43881,a832),x43882),x43883),f324(f302(x43881),x43883))
% 18.55/18.48 [3177]E(f324(f324(f146(x31771,f115(x31771)),x31772),x31773),f115(x31771))
% 18.55/18.48 [3178]E(f324(f324(f146(x31781,f115(x31781)),x31782),x31783),f115(x31781))
% 18.55/18.48 [3179]E(f324(f130(x31791),f324(f324(f139(x31791),x31792),x31793)),x31792)
% 18.55/18.48 [3180]E(f324(f156(x31801),f324(f324(f139(x31801),x31802),x31803)),x31803)
% 18.55/18.48 [3224]E(f324(f324(f128(x32241),f80(a838)),f324(f324(f139(x32241),x32242),x32243)),x32243)
% 18.55/18.48 [3255]E(f116(x32551,f324(f324(f128(x32551),x32552),x32553)),f324(f324(f128(x32551),x32552),f116(x32551,x32553)))
% 18.55/18.48 [3256]E(f116(x32561,f324(f324(f128(x32561),x32562),x32563)),f324(f324(f128(x32561),x32562),f116(x32561,x32563)))
% 18.55/18.48 [3258]E(f324(f324(f146(x32581,x32582),x32583),f324(f324(f149(x32581),x32582),x32583)),x32582)
% 18.55/18.48 [3281]E(f324(f324(f303(x32811),x32812),f324(f324(f303(x32811),x32812),x32813)),f324(f324(f303(x32811),x32812),x32813))
% 18.55/18.48 [3294]E(f324(f324(f303(x32941),x32942),f324(f157(x32941),x32943)),f324(f157(x32941),f324(f324(f139(x32941),x32942),x32943)))
% 18.55/18.48 [3295]E(f324(f324(f128(x32951),x32952),f324(f156(x32951),x32953)),f324(f156(x32951),f324(f324(f128(x32951),x32952),x32953)))
% 18.55/18.48 [3296]E(f324(f324(f128(x32961),x32962),f324(f156(x32961),x32963)),f324(f156(x32961),f324(f324(f128(x32961),x32962),x32963)))
% 18.55/18.48 [3305]E(f324(f324(f158(x33051),f80(a838)),f324(f324(f139(x33051),x33052),x33053)),f324(f324(f139(x33051),x33052),f115(x33051)))
% 18.55/18.48 [3337]E(f324(f165(x33371,x33372,f115(f844(x33371,x33372))),x33373),f182(x33372))
% 18.55/18.48 [3338]E(f324(f165(x33381,x33382,f115(f844(x33381,x33382))),x33383),f182(x33382))
% 18.55/18.48 [3353]E(f324(f66(x33531,x33532),f324(f324(f303(x33531),x33533),f179(f845(x33531,a832)))),x33533)
% 18.55/18.48 [3396]E(f324(f324(f82(a838),x33961),f324(f324(f82(a838),x33962),x33963)),f324(f324(f82(a838),x33962),f324(f324(f82(a838),x33961),x33963)))
% 18.55/18.48 [3397]E(f324(f324(f82(a1),x33971),f324(f324(f82(a1),x33972),x33973)),f324(f324(f82(a1),x33972),f324(f324(f82(a1),x33971),x33973)))
% 18.55/18.48 [3402]E(f324(f324(f249(x34021,x34022),f179(f845(x34021,a832))),x34023),f179(f845(f844(x34021,x34022),a832)))
% 18.55/18.48 [3424]E(f324(f324(f103(f845(x34241,a832)),x34242),x34243),f324(f324(f103(f845(x34241,a832)),x34243),x34242))
% 18.55/18.48 [3425]E(f324(f324(f104(f845(x34251,a832)),x34252),x34253),f324(f324(f104(f845(x34251,a832)),x34253),x34252))
% 18.55/18.48 [3427]E(f324(f324(f125(x34271),x34272),f324(f324(f139(x34271),x34273),f115(x34271))),f324(f153(x34271),f324(f324(f139(x34271),x34273),x34272)))
% 18.55/18.48 [3428]E(f324(f324(f125(x34281),f324(f154(x34281),x34282)),f324(f154(x34281),x34283)),f324(f154(x34281),f324(f324(f125(x34281),x34283),x34282)))
% 18.55/18.48 [3436]E(f324(f156(x34361),f324(f324(f158(x34361),f324(a114,x34362)),x34363)),f324(f324(f158(x34361),x34362),f324(f156(x34361),x34363)))
% 18.55/18.48 [3443]P1(f324(f324(f326(x34431),x34432),f324(f324(f303(x34431),x34432),x34433)))
% 18.55/18.48 [3447]E(f324(f324(f46(x34471,f845(x34472,a832)),f179(f845(x34471,a832))),x34473),f238(f845(x34472,a832)))
% 18.55/18.48 [3450]E(f324(f278(x34501,x34501,f261(x34501,x34502)),x34503),f324(f324(f104(f845(x34501,a832)),x34502),x34503))
% 18.55/18.48 [3463]E(f324(f180(f839(x34631)),f324(f324(f139(x34631),x34632),x34633)),f324(f324(f82(a838),f324(f180(f839(x34631)),x34633)),f324(a114,f2(a838))))
% 18.55/18.48 [3467]E(f133(x34671,f324(f324(f125(x34671),x34672),f324(f324(f139(x34671),x34673),f115(x34671)))),x34673)
% 18.55/18.48 [3468]E(f116(x34681,f324(f324(f125(x34681),x34682),f324(f324(f139(x34681),x34683),f115(x34681)))),x34682)
% 18.55/18.48 [3473]E(f324(f324(f125(x34731),f324(f324(f158(x34731),x34732),x34733)),f324(f324(f128(x34731),x34732),x34733)),x34733)
% 18.55/18.48 [3482]E(f324(f324(f3(a838),f324(f324(f82(a838),x34821),x34822)),f324(f324(f82(a838),x34823),x34822)),f324(f324(f3(a838),x34821),x34823))
% 18.55/18.48 [3483]E(f324(f324(f3(a838),f324(f324(f82(a838),x34831),x34832)),f324(f324(f82(a838),x34831),x34833)),f324(f324(f3(a838),x34832),x34833))
% 18.55/18.48 [3490]E(f324(f324(f125(x34901),f324(f154(x34901),x34902)),f324(f324(f139(x34901),x34903),f115(x34901))),f324(f154(x34901),f324(f324(f139(x34901),x34903),x34902)))
% 18.55/18.48 [3492]E(f324(f324(f82(a838),f324(f180(f839(x34921)),x34922)),f324(f180(f839(x34921)),x34923)),f324(f180(f839(x34921)),f324(f324(f125(x34921),x34922),x34923)))
% 18.55/18.48 [3502]E(f324(f324(f103(f845(x35021,a832)),f324(f157(x35021),x35022)),f324(f157(x35021),x35023)),f324(f157(x35021),f324(f324(f125(x35021),x35022),x35023)))
% 18.55/18.48 [3503]E(f51(a838,f324(f324(f83(a838),x35031),x35032),f324(f324(f83(a838),x35031),x35033)),f324(f324(f83(a838),x35031),f51(a838,x35032,x35033)))
% 18.55/18.48 [3516]E(f324(f324(f158(x35161),f324(f324(f3(a838),x35162),f80(a838))),f324(f156(x35161),x35163)),f324(f156(x35161),f324(f324(f158(x35161),x35162),x35163)))
% 18.55/18.48 [3521]E(f324(f324(f104(f845(x35211,a832)),x35212),f324(f81(f845(x35211,a832)),x35213)),f324(f324(f3(f845(x35211,a832)),x35212),x35213))
% 18.55/18.48 [3522]E(f324(f324(f3(f845(x35221,a832)),x35222),f324(f81(f845(x35221,a832)),x35223)),f324(f324(f104(f845(x35221,a832)),x35222),x35223))
% 18.55/18.48 [3545]E(f324(f324(f249(x35451,x35452),x35453),f324(f18(f845(x35452,a832),x35451),f179(f845(x35452,a832)))),f179(f845(f844(x35451,x35452),a832)))
% 18.55/18.48 [3547]E(f324(f324(f82(a838),f324(f324(f83(a838),x35471),x35472)),f324(f324(f83(a838),x35471),x35473)),f324(f324(f83(a838),x35471),f324(f324(f82(a838),x35472),x35473)))
% 18.55/18.48 [3548]E(f324(f324(f3(a838),f324(f324(f83(a838),x35481),x35482)),f324(f324(f83(a838),x35481),x35483)),f324(f324(f83(a838),x35481),f324(f324(f3(a838),x35482),x35483)))
% 18.55/18.48 [3549]E(f324(f324(f82(a1),f324(f324(f83(a1),x35491),x35492)),f324(f324(f83(a1),x35491),x35493)),f324(f324(f83(a1),x35491),f324(f324(f82(a1),x35492),x35493)))
% 18.55/18.48 [3550]E(f324(f324(f3(a1),f324(f324(f83(a1),x35501),x35502)),f324(f324(f83(a1),x35501),x35503)),f324(f324(f83(a1),x35501),f324(f324(f3(a1),x35502),x35503)))
% 18.55/18.48 [3551]E(f324(f324(f83(a1),f324(f324(f240(a1),x35511),x35512)),f324(f324(f240(a1),x35511),x35513)),f324(f324(f240(a1),x35511),f324(f324(f82(a838),x35512),x35513)))
% 18.55/18.48 [3564]E(f324(f324(f45(x35641,f845(x35642,a832)),x35643),f324(f18(f845(x35642,a832),x35641),f179(f845(x35642,a832)))),f179(f845(x35642,a832)))
% 18.55/18.48 [3566]E(f51(a838,f324(f324(f83(a838),x35661),x35662),f324(f324(f83(a838),x35663),x35662)),f324(f324(f83(a838),f51(a838,x35661,x35663)),x35662))
% 18.55/18.48 [3570]E(f51(a1,f324(f324(f83(a1),x35701),f51(a1,x35702,x35703)),x35703),f51(a1,f324(f324(f83(a1),x35701),x35702),x35703))
% 18.55/18.48 [3571]E(f51(a1,f324(f324(f83(a1),x35711),f51(a1,x35712,x35713)),x35713),f51(a1,f324(f324(f83(a1),x35711),x35712),x35713))
% 18.55/18.48 [3572]E(f51(a1,f324(f324(f3(a1),x35721),f51(a1,x35722,x35723)),x35723),f51(a1,f324(f324(f3(a1),x35721),x35722),x35723))
% 18.55/18.48 [3573]P1(f324(f324(f231(f845(x35731,a832)),x35732),f324(f324(f303(x35731),x35733),x35732)))
% 18.55/18.48 [3597]E(f324(f304(f844(x35971,x35972),x35971,f246(x35971,x35972)),f324(f157(f844(x35971,x35972)),x35973)),f168(x35971,x35972,f165(x35971,x35972,x35973)))
% 18.55/18.48 [3652]E(f324(f324(f46(f845(x36521,a832),f845(x36521,a832)),x36522),f324(f103(f845(x36521,a832)),x36523)),f324(f324(f103(f845(x36521,a832)),x36523),f44(f845(x36521,a832),x36522)))
% 18.55/18.48 [3653]E(f324(f324(f45(f845(x36531,a832),f845(x36531,a832)),x36532),f324(f104(f845(x36531,a832)),x36533)),f324(f324(f104(f845(x36531,a832)),x36533),f43(f845(x36531,a832),x36532)))
% 18.55/18.48 [3663]E(f324(f157(x36631),f324(f324(f324(f172(f839(x36631),f839(x36631)),x36632),f153(x36631)),x36633)),f324(f157(x36631),x36633))
% 18.55/18.48 [3667]E(f324(f324(f158(x36671),f324(f180(f839(x36671)),f161(x36671,x36672,x36673))),x36673),f161(x36671,x36672,x36673))
% 18.55/18.48 [3668]E(f168(x36681,x36682,f324(f324(f10(x36682,f842(x36682),x36681),f226(x36682)),x36683)),f238(f845(x36681,a832)))
% 18.55/18.48 [3672]E(f324(f180(f839(x36721)),f324(f324(f324(f172(f839(x36721),f839(x36721)),x36722),f153(x36721)),x36723)),f324(f180(f839(x36721)),x36723))
% 18.55/18.48 [3675]E(f324(f324(f252(x36751,x36752,x36752),f324(f18(f845(x36752,x36752),x36751),f7(x36752))),x36753),f324(f251(x36751,x36752),x36753))
% 18.55/18.48 [3682]E(f51(a1,f324(f324(f3(a1),f51(a1,x36821,x36822)),x36823),x36822),f51(a1,f324(f324(f3(a1),x36821),x36823),x36822))
% 18.55/18.48 [3683]E(f51(a1,f324(f324(f240(a1),f51(a1,x36831,x36832)),x36833),x36832),f51(a1,f324(f324(f240(a1),x36831),x36833),x36832))
% 18.55/18.48 [3686]E(f324(f324(f45(f845(f844(x36861,x36862),a832),f845(x36862,a832)),x36863),f260(x36861,x36862)),f324(f260(x36861,x36862),f43(f845(f844(x36861,x36862),a832),x36863)))
% 18.55/18.48 [3687]E(f324(f324(f45(f845(f844(x36871,x36872),a832),f845(x36871,a832)),x36873),f262(x36871,x36872)),f324(f262(x36871,x36872),f43(f845(f844(x36871,x36872),a832),x36873)))
% 18.55/18.48 [3715]E(f324(f75(x37151,x37151,x37151,x37152),f324(f324(f172(x37151,x37151),x37153),x37152)),f324(f324(f172(x37151,x37151),f324(a114,x37153)),x37152))
% 18.55/18.48 [3725]E(f228(f842(x37251),x37252,f182(x37251),f324(f324(f10(x37251,f842(x37251),x37252),f226(x37251)),x37253)),f324(f195(x37252,x37251),x37253))
% 18.55/18.48 [3732]E(f324(f324(f128(x37321),f324(f324(f3(a838),f324(f180(f839(x37321)),x37322)),x37323)),f324(f154(x37321),x37322)),f324(f154(x37321),f324(f324(f158(x37321),x37323),x37322)))
% 18.55/18.48 [3733]E(f324(f324(f158(x37331),f324(f324(f3(a838),f324(f180(f839(x37331)),x37332)),x37333)),f324(f154(x37331),x37332)),f324(f154(x37331),f324(f324(f128(x37331),x37333),x37332)))
% 18.55/18.48 [3736]E(f324(f324(f82(a838),f324(f151(a838),f324(f324(f141(x37361,a838),x37362),x37363))),f324(f180(f839(x37361)),x37363)),f142(x37361,x37362,x37363))
% 18.55/18.48 [3745]E(f324(f324(f324(f172(f839(x37451),f839(x37451)),x37452),f153(x37451)),f324(f153(x37451),x37453)),f324(f153(x37451),f324(f324(f324(f172(f839(x37451),f839(x37451)),x37452),f153(x37451)),x37453)))
% 18.55/18.48 [3752]E(f324(f153(x37521),f324(f324(f324(f172(f839(x37521),f839(x37521)),x37522),f153(x37521)),x37523)),f324(f324(f324(f172(f839(x37521),f839(x37521)),f324(a114,x37522)),f153(x37521)),x37523))
% 18.55/18.48 [3764]P1(f324(f324(f231(a838),f324(f180(f839(x37641)),f324(f126(x37641,x37642),x37643))),f324(f180(f839(x37641)),x37643)))
% 18.55/18.48 [3781]E(f324(f324(f103(f845(f845(x37811,a832),a832)),f324(f302(x37811),x37812)),f324(f304(f845(x37811,a832),f845(x37811,a832),f324(f303(x37811),x37813)),f324(f302(x37811),x37812))),f324(f302(x37811),f324(f324(f303(x37811),x37813),x37812)))
% 18.55/18.48 [3797]P28(x37971,x37972,f324(f324(f303(f837(x37971)),f324(f324(f324(f93(x37971),x37973),a25),x37973)),f179(f845(f837(x37971),a832))))
% 18.55/18.48 [3798]P28(x37981,x37982,f324(f324(f303(f837(x37981)),f324(f324(f324(f93(x37981),x37983),a25),x37983)),f179(f845(f837(x37981),a832))))
% 18.55/18.48 [3814]P1(f324(f324(f231(a838),f324(f180(f839(x38141)),f161(x38141,x38142,x38143))),f324(f180(f839(x38141)),x38143)))
% 18.55/18.48 [3821]E(f324(f262(x38211,x38212),f324(f257(f844(x38211,x38212)),f324(f252(x38211,x38212,a832),x38213))),f324(f257(x38211),f324(f324(f10(f845(x38212,a832),a832,x38211),f89(x38212)),x38213)))
% 18.55/18.48 [3834]E(f324(f304(a838,a838,f324(f324(f9(a838,a838,a838),f82(a838)),x38341)),f296(a838,x38342,x38343)),f296(a838,f324(f324(f82(a838),x38342),x38341),f324(f324(f82(a838),x38343),x38341)))
% 18.55/18.48 [3850]E(f324(f304(a838,a838,f324(f324(f9(a838,a838,a838),f82(a838)),x38501)),f324(f295(a838,x38502),x38503)),f324(f295(a838,f324(f324(f82(a838),x38502),x38501)),f324(f324(f82(a838),x38503),x38501)))
% 18.55/18.48 [3869]E(f324(f324(f166(x38691,x38692),f324(f324(f141(f844(x38691,x38692),x38691),f246(x38691,x38692)),x38693)),f324(f324(f141(f844(x38691,x38692),x38692),f251(x38691,x38692)),x38693)),x38693)
% 18.55/18.48 [3874]E(f324(f324(f82(a838),f324(f324(f83(a838),x38741),f51(a838,f324(f324(f42(a838),x38742),x38741),x38743))),f51(a838,x38742,x38741)),f51(a838,x38742,f324(f324(f83(a838),x38741),x38743)))
% 18.55/18.48 [3885]P1(f324(f64(f842(x38851)),f324(f304(x38852,f842(x38851),f165(x38852,x38851,x38853)),f238(f845(x38852,a832)))))
% 18.55/18.48 [3889]E(f324(f324(f125(x38891),x38892),f324(f131(f839(x38891),f839(x38891),f125(x38891),f115(x38891)),x38893)),f324(f131(f839(x38891),f839(x38891),f125(x38891),x38892),x38893))
% 18.55/18.48 [3909]P1(f324(f324(f326(f844(x39091,x39091)),f324(f324(f247(x39091,x39091),x39092),x39092)),f324(f324(f172(f844(x39091,x39091),a832),f2(a838)),x39093)))
% 18.55/18.48 [3915]E(f324(f257(x39151),f324(f324(f10(f845(x39152,a832),a832,x39151),f89(x39152)),f324(f9(x39152,x39151,a832),x39153))),f324(f260(x39152,x39151),f324(f257(f844(x39152,x39151)),f324(f252(x39152,x39151,a832),x39153))))
% 18.55/18.48 [3933]E(f324(f324(f103(f845(x39331,a832)),f324(f324(f45(a838,f845(x39331,a832)),f296(a838,f80(a838),x39332)),x39333)),f324(x39333,f2(a838))),f324(f324(f45(a838,f845(x39331,a832)),f324(f294(a838),x39332)),x39333))
% 18.55/18.48 [3948]E(f324(f131(f839(x39481),f839(x39481),f125(x39481),f115(x39481)),f324(f324(f141(f839(x39481),f839(x39481)),f126(x39481,x39482)),x39483)),f324(f126(x39481,x39482),f324(f131(f839(x39481),f839(x39481),f125(x39481),f115(x39481)),x39483)))
% 18.55/18.48 [3953]E(f324(f251(f839(x39531),f839(x39531)),f152(x39531,x39532,x39533)),f324(f126(x39531,f324(f75(a832,a832,x39531,a320),x39532)),x39533))
% 18.55/18.48 [3998]E(f324(f324(f82(a1),f324(f324(f82(a1),f324(f324(f83(a1),x39981),f324(f324(f42(a1),x39982),x39981))),f51(a1,x39982,x39981))),x39983),f324(f324(f82(a1),x39982),x39983))
% 18.55/18.48 [4033]E(f324(f324(f82(a1),f324(f324(f82(a1),f324(f324(f83(a1),f324(f324(f42(a1),x40331),x40332)),x40332)),f51(a1,x40331,x40332))),x40333),f324(f324(f82(a1),x40331),x40333))
% 18.55/18.48 [4063]E(f87(f844(x40631,x40632),f324(f252(x40631,x40632,a832),f324(f324(f10(f845(x40632,f844(x40631,x40632)),f845(x40632,a832),x40631),f324(f10(f844(x40631,x40632),a832,x40632),x40633)),f247(x40631,x40632)))),f87(f844(x40631,x40632),x40633))
% 18.55/18.48 [4064]E(f92(f844(x40641,x40642),f324(f252(x40641,x40642,a832),f324(f324(f10(f845(x40642,f844(x40641,x40642)),f845(x40642,a832),x40641),f324(f10(f844(x40641,x40642),a832,x40642),x40643)),f247(x40641,x40642)))),f92(f844(x40641,x40642),x40643))
% 18.55/18.48 [4093]P1(f324(f324(f231(f845(x40931,a832)),f43(f845(x40931,a832),f324(f324(f104(f845(f845(x40931,a832),a832)),x40932),x40933))),f324(f324(f104(f845(x40931,a832)),f43(f845(x40931,a832),x40932)),f43(f845(x40931,a832),x40933))))
% 18.55/18.48 [4094]E(f324(f154(x40941),f324(f324(f324(f172(f839(x40941),f839(x40941)),f324(f324(f3(a838),f324(f180(f839(x40941)),x40942)),f51(a838,x40943,f324(f180(f839(x40941)),x40942)))),f153(x40941)),x40942)),f324(f324(f324(f172(f839(x40941),f839(x40941)),x40943),f153(x40941)),f324(f154(x40941),x40942)))
% 18.55/18.48 [4106]E(f324(f257(x41061),f324(f324(f10(a832,a832,x41061),a320),f324(f324(f9(x41061,f842(x41062),a832),f324(f324(f10(f842(x41062),f845(f842(x41062),a832),x41061),a321),x41063)),f182(x41062)))),f168(x41061,x41062,x41063))
% 18.55/18.48 [4130]P1(f324(f324(f231(a838),f324(f180(f839(x41301)),f324(f324(f128(x41301),f324(f180(f839(x41301)),f161(x41301,x41302,x41303))),x41303))),f324(f180(f839(x41301)),x41303)))
% 18.55/18.48 [4170]E(f324(f257(x41701),f324(f324(f10(f845(x41702,a832),a832,x41701),f89(x41702)),f324(f324(f10(f842(x41701),f845(x41702,a832),x41701),f324(f9(x41702,f842(x41701),a832),f324(f324(f10(f842(x41701),f845(f842(x41701),a832),x41702),a321),x41703))),f226(x41701)))),f170(x41702,x41701,x41703))
% 18.55/18.48 [4402]~P1(f324(f65(x44021,x44022,f179(f845(x44021,a832))),x44023))
% 18.55/18.48 [3437]E(f324(f180(f839(x34371)),f324(f324(f158(x34371),x34372),x34373)),f324(f324(f235(a838),f324(f180(f839(x34371)),x34373)),x34372))
% 18.55/18.48 [3438]E(f324(f180(f839(x34381)),f324(f324(f128(x34381),x34382),x34383)),f324(f324(f3(a838),f324(f180(f839(x34381)),x34383)),x34382))
% 18.55/18.48 [3462]E(f324(f180(f839(f839(x34621))),f61(x34621,x34622,x34623)),f324(f324(f240(a838),f324(f180(f839(x34621)),x34623)),x34622))
% 18.55/18.48 [3475]E(f324(f324(f42(a838),f324(f324(f42(a838),x34751),x34752)),x34753),f324(f324(f42(a838),x34751),f324(f324(f83(a838),x34752),x34753)))
% 18.55/18.48 [3476]E(f324(f324(f83(a838),f324(f324(f83(a838),x34761),x34762)),x34763),f324(f324(f83(a838),x34761),f324(f324(f83(a838),x34762),x34763)))
% 18.55/18.48 [3477]E(f324(f324(f83(a1),f324(f324(f83(a1),x34771),x34772)),x34773),f324(f324(f83(a1),x34771),f324(f324(f83(a1),x34772),x34773)))
% 18.55/18.48 [3478]E(f324(f324(f82(a838),f324(f324(f82(a838),x34781),x34782)),x34783),f324(f324(f82(a838),x34781),f324(f324(f82(a838),x34782),x34783)))
% 18.55/18.48 [3479]E(f324(f324(f82(a1),f324(f324(f82(a1),x34791),x34792)),x34793),f324(f324(f82(a1),x34791),f324(f324(f82(a1),x34792),x34793)))
% 18.55/18.48 [3480]E(f324(f324(f3(a838),f324(f324(f3(a838),x34801),x34802)),x34803),f324(f324(f3(a838),x34801),f324(f324(f82(a838),x34802),x34803)))
% 18.55/18.48 [3481]E(f324(f324(f240(a1),f324(f324(f240(a1),x34811),x34812)),x34813),f324(f324(f240(a1),x34811),f324(f324(f83(a838),x34812),x34813)))
% 18.55/18.48 [3500]E(f148(x35001,f324(f324(f139(f845(x35001,a832)),x35002),x35003)),f160(x35001,x35002,f148(x35001,x35003)))
% 18.55/18.48 [3546]E(f324(f324(f3(a838),f324(f324(f3(a838),x35461),x35462)),x35463),f324(f324(f3(a838),f324(f324(f3(a838),x35461),x35463)),x35462))
% 18.55/18.48 [3554]E(f324(f324(f104(f845(x35541,a832)),x35542),f324(f324(f3(f845(x35541,a832)),x35543),x35542)),f179(f845(x35541,a832)))
% 18.55/18.48 [3599]E(f44(f845(x35991,a832),f324(f324(f303(f845(x35991,a832)),x35992),x35993)),f324(f324(f104(f845(x35991,a832)),x35992),f44(f845(x35991,a832),x35993)))
% 18.55/18.48 [3600]E(f43(f845(x36001,a832),f324(f324(f303(f845(x36001,a832)),x36002),x36003)),f324(f324(f103(f845(x36001,a832)),x36002),f43(f845(x36001,a832),x36003)))
% 18.55/18.48 [3602]E(f324(f324(f82(a838),f324(f324(f83(a838),x36021),x36022)),f324(f324(f83(a838),x36023),x36022)),f324(f324(f83(a838),f324(f324(f82(a838),x36021),x36023)),x36022))
% 18.55/18.48 [3603]E(f324(f324(f3(a838),f324(f324(f83(a838),x36031),x36032)),f324(f324(f83(a838),x36033),x36032)),f324(f324(f83(a838),f324(f324(f3(a838),x36031),x36033)),x36032))
% 18.55/18.48 [3604]E(f324(f324(f82(a1),f324(f324(f83(a1),x36041),x36042)),f324(f324(f83(a1),x36043),x36042)),f324(f324(f83(a1),f324(f324(f82(a1),x36041),x36043)),x36042))
% 18.55/18.48 [3606]E(f324(f324(f3(a1),f324(f324(f83(a1),x36061),x36062)),f324(f324(f83(a1),x36063),x36062)),f324(f324(f83(a1),f324(f324(f3(a1),x36061),x36063)),x36062))
% 18.55/18.48 [3607]E(f324(f324(f235(a838),f324(f324(f3(a838),x36071),x36072)),f324(f324(f3(a838),x36073),x36072)),f324(f324(f3(a838),f324(f324(f235(a838),x36071),x36073)),x36072))
% 18.55/18.48 [3631]E(f324(f324(f103(f845(x36311,a832)),x36312),f324(f324(f3(f845(x36311,a832)),x36313),x36312)),f324(f324(f103(f845(x36311,a832)),x36312),x36313))
% 18.55/18.48 [3632]E(f324(f324(f103(f845(x36321,a832)),x36322),f324(f324(f103(f845(x36321,a832)),x36322),x36323)),f324(f324(f103(f845(x36321,a832)),x36322),x36323))
% 18.55/18.48 [3633]E(f324(f324(f104(f845(x36331,a832)),x36332),f324(f324(f104(f845(x36331,a832)),x36332),x36333)),f324(f324(f104(f845(x36331,a832)),x36332),x36333))
% 18.55/18.48 [3645]E(f324(f324(f282(x36451,x36452,x36452),x36453),f301(x36452,f179(f845(f844(x36452,x36452),a832)))),x36453)
% 18.55/18.48 [3648]E(f324(f324(f103(f845(x36481,a832)),f324(f324(f303(x36481),x36482),f179(f845(x36481,a832)))),x36483),f324(f324(f303(x36481),x36482),x36483))
% 18.55/18.48 [3666]E(f324(f324(f3(a838),f324(f324(f3(a838),f324(a114,x36661)),x36662)),f324(a114,x36663)),f324(f324(f3(a838),f324(f324(f3(a838),x36661),x36662)),x36663))
% 18.55/18.48 [3695]E(f324(f324(f104(f845(f845(x36951,a832),a832)),f324(f302(x36951),x36952)),f324(f302(x36951),x36953)),f324(f302(x36951),f324(f324(f104(f845(x36951,a832)),x36952),x36953)))
% 18.55/18.48 [3698]E(f324(f324(f103(f845(x36981,a832)),f324(f81(f845(x36981,a832)),x36982)),x36983),f324(f81(f845(x36981,a832)),f324(f324(f3(f845(x36981,a832)),x36982),x36983)))
% 18.55/18.48 [3711]E(f324(f324(f303(x37111),x37112),f324(f324(f3(f845(x37111,a832)),x37113),f324(f324(f303(x37111),x37112),f179(f845(x37111,a832))))),f324(f324(f303(x37111),x37112),x37113))
% 18.55/18.48 [3722]P1(f324(f324(f231(f845(x37221,a832)),x37222),f324(f324(f103(f845(x37221,a832)),x37223),x37222)))
% 18.55/18.48 [3723]P1(f324(f324(f231(f845(x37231,a832)),x37232),f324(f324(f103(f845(x37231,a832)),x37232),x37233)))
% 18.55/18.48 [3726]E(f324(f324(f104(f845(x37261,a832)),f324(f81(f845(x37261,a832)),x37262)),f324(f81(f845(x37261,a832)),x37263)),f324(f81(f845(x37261,a832)),f324(f324(f103(f845(x37261,a832)),x37262),x37263)))
% 18.55/18.48 [3727]E(f324(f324(f103(f845(x37271,a832)),f324(f81(f845(x37271,a832)),x37272)),f324(f81(f845(x37271,a832)),x37273)),f324(f81(f845(x37271,a832)),f324(f324(f104(f845(x37271,a832)),x37272),x37273)))
% 18.55/18.48 [3740]P1(f324(f324(f231(f845(x37401,a832)),f324(f157(x37401),x37402)),f324(f157(x37401),f324(f324(f139(x37401),x37403),x37402))))
% 18.55/18.48 [3749]E(f324(f324(f103(f845(x37491,a832)),f324(f324(f3(f845(x37491,a832)),x37492),x37493)),f324(f324(f104(f845(x37491,a832)),x37492),x37493)),x37492)
% 18.55/18.48 [3800]E(f324(f324(f11(x38001,a1),f324(f324(f10(a838,a1,x38001),f102(a1)),x38002)),x38003),f324(f102(a1),f324(f324(f11(x38001,a838),x38002),x38003)))
% 18.55/18.48 [3801]E(f324(f324(f8(x38011,a1),f324(f324(f10(a838,a1,x38011),f102(a1)),x38012)),x38013),f324(f102(a1),f324(f324(f8(x38011,a838),x38012),x38013)))
% 18.55/18.48 [3853]E(f324(f324(f125(x38531),f161(x38531,x38532,x38533)),f324(f324(f128(x38531),f324(f180(f839(x38531)),f161(x38531,x38532,x38533))),x38533)),x38533)
% 18.55/18.48 [3858]E(f324(f81(f845(f844(x38581,x38582),a832)),f324(f324(f249(x38581,x38582),x38583),f324(f18(f845(x38582,a832),x38581),f238(f845(x38582,a832))))),f324(f324(f249(x38581,x38582),f324(f81(f845(x38581,a832)),x38583)),f324(f18(f845(x38582,a832),x38581),f238(f845(x38582,a832)))))
% 18.55/18.48 [3859]E(f324(f81(f845(f844(x38591,x38592),a832)),f324(f324(f249(x38591,x38592),f238(f845(x38591,a832))),f324(f18(f845(x38592,a832),x38591),x38593))),f324(f324(f249(x38591,x38592),f238(f845(x38591,a832))),f324(f18(f845(x38592,a832),x38591),f324(f81(f845(x38592,a832)),x38593))))
% 18.55/18.48 [3910]E(f324(f324(f45(f845(x39101,a832),f845(x39101,a832)),x39102),f324(f324(f9(f845(x39101,a832),f845(x39101,a832),f845(x39101,a832)),f104(f845(x39101,a832))),x39103)),f324(f324(f104(f845(x39101,a832)),f43(f845(x39101,a832),x39102)),x39103))
% 18.55/18.48 [3917]E(f324(f131(f839(x39171),f839(x39171),f125(x39171),f115(x39171)),f324(f324(f139(f839(x39171)),x39172),x39173)),f324(f324(f125(x39171),x39172),f324(f131(f839(x39171),f839(x39171),f125(x39171),f115(x39171)),x39173)))
% 18.55/18.48 [3939]E(f324(f324(f303(f845(x39391,a832)),f324(f278(x39391,x39391,x39392),f324(f324(f303(x39391),x39393),f179(f845(x39391,a832))))),f179(f845(f845(x39391,a832),a832))),f324(f324(f63(x39391),f324(f324(f303(x39391),x39393),f179(f845(x39391,a832)))),x39392))
% 18.55/18.48 [3949]E(f324(f324(f82(a838),f324(f324(f83(a838),x39491),f324(f324(f42(a838),x39492),x39493))),f324(f324(f42(a838),f324(f324(f83(a838),x39491),f51(a838,x39492,x39493))),x39493)),f324(f324(f42(a838),f324(f324(f83(a838),x39491),x39492)),x39493))
% 18.55/18.48 [3950]E(f324(f324(f82(a1),f324(f324(f83(a1),x39501),f324(f324(f42(a1),x39502),x39503))),f324(f324(f42(a1),f324(f324(f83(a1),x39501),f51(a1,x39502,x39503))),x39503)),f324(f324(f42(a1),f324(f324(f83(a1),x39501),x39502)),x39503))
% 18.55/18.48 [4031]E(f324(f324(f125(x40311),f324(f131(f839(x40311),f839(x40311),f125(x40311),f115(x40311)),x40312)),f324(f131(f839(x40311),f839(x40311),f125(x40311),f115(x40311)),x40313)),f324(f131(f839(x40311),f839(x40311),f125(x40311),f115(x40311)),f324(f324(f125(f839(x40311)),x40312),x40313)))
% 18.55/18.48 [4034]E(f324(f324(f247(f839(x40341),f839(x40341)),f324(f126(x40341,x40342),x40343)),f324(f126(x40341,f324(f75(a832,a832,x40341,a320),x40342)),x40343)),f152(x40341,x40342,x40343))
% 18.55/18.48 [4037]E(f324(f324(f82(a838),f324(f324(f82(a838),f324(f324(f42(a838),x40371),x40372)),f324(f324(f42(a838),x40373),x40372))),f324(f324(f42(a838),f324(f324(f82(a838),f51(a838,x40371,x40372)),f51(a838,x40373,x40372))),x40372)),f324(f324(f42(a838),f324(f324(f82(a838),x40371),x40373)),x40372))
% 18.55/18.48 [4038]E(f324(f324(f82(a1),f324(f324(f82(a1),f324(f324(f42(a1),x40381),x40382)),f324(f324(f42(a1),x40383),x40382))),f324(f324(f42(a1),f324(f324(f82(a1),f51(a1,x40381,x40382)),f51(a1,x40383,x40382))),x40382)),f324(f324(f42(a1),f324(f324(f82(a1),x40381),x40383)),x40382))
% 18.55/18.48 [4107]E(f324(f257(x41071),f324(f324(f20(x41071,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41071),a323),f324(f324(f9(x41071,x41071,a832),a321),x41072))),f324(f324(f9(x41071,f845(x41071,a832),a832),f326(x41071)),x41073))),f324(f324(f303(x41071),x41072),x41073))
% 18.55/18.48 [4108]E(f324(f257(x41081),f324(f324(f20(x41081,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41081),a323),f324(f324(f9(x41081,x41081,a832),a321),x41082))),f324(f324(f9(x41081,f845(x41081,a832),a832),f326(x41081)),x41083))),f324(f324(f303(x41081),x41082),x41083))
% 18.55/18.48 [4131]E(f324(f257(x41311),f324(f324(f20(x41311,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41311),a323),f324(f324(f9(x41311,f845(x41311,a832),a832),f326(x41311)),x41312))),f324(f324(f9(x41311,f845(x41311,a832),a832),f326(x41311)),x41313))),f324(f324(f103(f845(x41311,a832)),x41312),x41313))
% 18.55/18.48 [4132]E(f324(f257(x41321),f324(f324(f20(x41321,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41321),a322),f324(f324(f9(x41321,f845(x41321,a832),a832),f326(x41321)),x41322))),f324(f324(f9(x41321,f845(x41321,a832),a832),f326(x41321)),x41323))),f324(f324(f104(f845(x41321,a832)),x41322),x41323))
% 18.55/18.48 [4221]E(f324(f324(f45(x42211,f845(f845(x42211,a832),a832)),x42212),f324(f324(f9(x42211,f845(f845(x42211,a832),a832),f845(f845(x42211,a832),a832)),f324(f324(f10(f845(x42211,a832),f845(f845(f845(x42211,a832),a832),f845(f845(x42211,a832),a832)),x42211),f303(f845(x42211,a832))),f324(f324(f10(f845(x42211,a832),f845(x42211,a832),x42211),f278(x42211,x42211,x42213)),f324(f324(f9(x42211,f845(x42211,a832),f845(x42211,a832)),f303(x42211)),f179(f845(x42211,a832)))))),f179(f845(f845(x42211,a832),a832)))),f324(f324(f63(x42211),x42212),x42213))
% 18.55/18.48 [4223]E(f324(f324(f196(x42231),f324(f324(f83(a1),f324(f324(f75(f844(a1,a1),a1,x42231,f246(a1,a1)),f206(x42231)),x42232)),f324(f324(f75(f844(a1,a1),a1,x42231,f246(a1,a1)),f206(x42231)),x42233))),f324(f324(f83(a1),f324(f324(f75(f844(a1,a1),a1,x42231,f251(a1,a1)),f206(x42231)),x42232)),f324(f324(f75(f844(a1,a1),a1,x42231,f251(a1,a1)),f206(x42231)),x42233))),f221(x42231,x42232,x42233))
% 18.55/18.48 [3620]E(f51(a838,f324(f324(f82(a838),f324(f324(f83(a838),x36201),x36202)),x36203),x36202),f51(a838,x36203,x36202))
% 18.55/18.48 [3665]E(f129(a838,f324(f295(a838,f324(f324(f82(a838),x36651),x36652)),x36653)),f324(f324(f128(a838),x36652),f129(a838,f324(f295(a838,x36651),x36653))))
% 18.55/18.48 [3710]E(f324(f324(f82(a1),f324(f102(a1),x37101)),f324(f324(f82(a1),f324(f102(a1),x37102)),x37103)),f324(f324(f82(a1),f324(f102(a1),f324(f324(f82(a838),x37101),x37102))),x37103))
% 18.55/18.48 [3718]E(f324(f324(f3(f845(x37181,a832)),f324(f324(f3(f845(x37181,a832)),x37182),x37183)),x37183),f324(f324(f3(f845(x37181,a832)),x37182),x37183))
% 18.55/18.48 [3719]E(f324(f324(f103(f845(x37191,a832)),f324(f324(f3(f845(x37191,a832)),x37192),x37193)),x37193),f324(f324(f103(f845(x37191,a832)),x37192),x37193))
% 18.55/18.48 [3741]E(f324(f324(f282(x37411,x37411,x37412),f301(x37411,f179(f845(f844(x37411,x37411),a832)))),x37413),x37413)
% 18.55/18.48 [3746]E(f324(f324(f103(f845(x37461,a832)),f324(f277(x37461),x37462)),f324(f277(x37461),x37463)),f324(f277(x37461),f324(f324(f103(f845(f844(x37461,x37461),a832)),x37462),x37463)))
% 18.55/18.48 [3755]E(f264(x37551,f324(f324(f139(f844(a101,x37551)),f324(f324(f247(a101,x37551),f2(a101)),x37552)),x37553)),f264(x37551,x37553))
% 18.55/18.48 [3758]E(f324(f324(f104(f845(x37581,a832)),f44(f845(x37581,a832),x37582)),f44(f845(x37581,a832),x37583)),f44(f845(x37581,a832),f324(f324(f103(f845(f845(x37581,a832),a832)),x37582),x37583)))
% 18.55/18.48 [3759]E(f324(f324(f103(f845(x37591,a832)),f43(f845(x37591,a832),x37592)),f43(f845(x37591,a832),x37593)),f43(f845(x37591,a832),f324(f324(f103(f845(f845(x37591,a832),a832)),x37592),x37593)))
% 18.55/18.48 [3793]E(f324(f324(f282(x37931,x37931,x37931),f324(f324(f172(f844(x37931,x37931),a832),x37932),x37933)),x37933),f324(f324(f172(f844(x37931,x37931),a832),f324(a114,x37932)),x37933))
% 18.55/18.48 [3843]P1(f324(f324(f231(f845(x38431,a832)),f324(f324(f3(f845(x38431,a832)),x38432),x38433)),x38432))
% 18.55/18.48 [3844]P1(f324(f324(f231(f845(x38441,a832)),f324(f324(f104(f845(x38441,a832)),x38442),x38443)),x38443))
% 18.55/18.48 [3845]P1(f324(f324(f231(f845(x38451,a832)),f324(f324(f104(f845(x38451,a832)),x38452),x38453)),x38452))
% 18.55/18.48 [3871]E(f301(x38711,f324(f324(f103(f845(f844(x38711,x38711),a832)),f301(x38711,x38712)),f301(x38711,x38713))),f301(x38711,f324(f324(f103(f845(f844(x38711,x38711),a832)),x38712),x38713)))
% 18.55/18.48 [3875]E(f43(f845(x38751,a832),f324(f324(f303(f845(x38751,a832)),x38752),f324(f324(f303(f845(x38751,a832)),x38753),f179(f845(f845(x38751,a832),a832))))),f324(f324(f103(f845(x38751,a832)),x38752),x38753))
% 18.55/18.48 [3876]E(f44(f845(x38761,a832),f324(f324(f303(f845(x38761,a832)),x38762),f324(f324(f303(f845(x38761,a832)),x38763),f179(f845(f845(x38761,a832),a832))))),f324(f324(f104(f845(x38761,a832)),x38762),x38763))
% 18.55/18.48 [3882]E(f324(f324(f282(x38821,x38821,x38821),f324(f324(f172(f844(x38821,x38821),a832),x38822),x38823)),x38823),f324(f324(f282(x38821,x38821,x38821),x38823),f324(f324(f172(f844(x38821,x38821),a832),x38822),x38823)))
% 18.55/18.48 [3954]E(f324(f324(f103(f845(x39541,a832)),f324(f257(x39541),f324(f324(f9(x39541,x39541,a832),a321),x39542))),x39543),f324(f324(f303(x39541),x39542),x39543))
% 18.55/18.48 [3956]E(f324(a107,f324(f324(f11(x39561,a1),f324(f324(f10(a838,a1,x39561),f102(a1)),x39562)),x39563)),f324(f324(f11(x39561,a838),x39562),x39563))
% 18.55/18.48 [3957]E(f324(a107,f324(f324(f8(x39571,a1),f324(f324(f10(a838,a1,x39571),f102(a1)),x39572)),x39573)),f324(f324(f8(x39571,a838),x39572),x39573))
% 18.55/18.48 [4028]E(f324(f143(f839(x40281),x40281,f324(f156(x40281),x40282),f324(f18(f845(f839(x40281),f839(x40281)),x40281),f324(f324(f9(f839(x40281),f839(x40281),f839(x40281)),f125(x40281)),x40282))),x40283),f324(f156(x40281),f324(f324(f125(x40281),x40283),x40282)))
% 18.55/18.48 [4059]P1(f324(f324(f231(f845(f845(x40591,a832),a832)),f324(f324(f103(f845(f845(x40591,a832),a832)),f324(f302(x40591),x40592)),f324(f302(x40591),x40593))),f324(f302(x40591),f324(f324(f103(f845(x40591,a832)),x40592),x40593))))
% 18.55/18.48 [4150]E(f324(f257(x41501),f324(f324(f20(x41501,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41501),a322),f324(f324(f9(x41501,f845(x41501,a832),a832),f326(x41501)),x41502))),f324(f324(f10(a832,a832,x41501),a320),f324(f324(f9(x41501,f845(x41501,a832),a832),f326(x41501)),x41503)))),f324(f324(f3(f845(x41501,a832)),x41502),x41503))
% 18.55/18.48 [4171]E(f324(f41(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,a838,a832),f232(a838)),f324(f180(f839(x41711)),x41712)))),f324(f324(f10(x41711,a832,a838),x41713),f324(f149(x41711),x41712))))),f324(f180(f839(x41711)),f324(f126(x41711,x41713),x41712)))
% 18.55/18.48 [4173]E(f324(f180(f839(x41731)),f159(x41731,x41732,x41733)),f324(f41(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,a838,a832),f232(a838)),f324(f180(f839(x41731)),x41732)))),f324(f324(f9(a838,f845(a838,a832),a832),f326(a838)),x41733)))))
% 18.55/18.48 [4268]E(f324(f324(f104(f845(f844(f839(x42681),f839(x42681)),a832)),f324(f304(f844(f844(x42681,f839(x42681)),f844(x42681,f839(x42681))),f844(f839(x42681),f839(x42681)),f253(f844(x42681,f839(x42681)),f839(x42681),f844(x42681,f839(x42681)),f839(x42681),f324(f252(x42681,f839(x42681),f839(x42681)),f139(x42681)),f324(f252(x42681,f839(x42681),f839(x42681)),f139(x42681)))),f318(x42681,f839(x42681),x42682,f324(f132(x42681,x42682),x42683)))),f324(f257(f844(f839(x42681),f839(x42681))),f324(f252(f839(x42681),f839(x42681),a832),f324(f324(f9(f839(x42681),f845(f839(x42681),a832),f845(f839(x42681),a832)),f324(f324(f10(f845(a832,a832),f845(f845(f839(x42681),a832),f845(f839(x42681),a832)),f839(x42681)),f10(a832,a832,f839(x42681))),f324(f324(f10(a832,f845(a832,a832),f839(x42681)),a322),f324(f324(f9(f839(x42681),a838,a832),f324(f324(f10(a838,f845(a838,a832),f839(x42681)),a321),f180(f839(x42681)))),f324(a114,x42683))))),f324(f324(f9(f839(x42681),a838,a832),f324(f324(f10(a838,f845(a838,a832),f839(x42681)),a321),f180(f839(x42681)))),f324(a114,x42683)))))),f324(f132(x42681,x42682),f324(a114,x42683)))
% 18.55/18.48 [3760]E(f51(a838,f324(a114,f324(f324(f82(a838),f324(f324(f83(a838),x37601),x37602)),x37603)),x37602),f51(a838,f324(a114,x37603),x37602))
% 18.55/18.48 [4017]E(f324(f257(x40171),f324(f324(f20(x40171,a832,a832),f324(f324(f10(a832,f845(a832,a832),x40171),a322),x40172)),x40173)),f324(f324(f104(f845(x40171,a832)),f324(f257(x40171),x40172)),f324(f257(x40171),x40173)))
% 18.55/18.48 [4018]E(f324(f257(x40181),f324(f324(f20(x40181,a832,a832),f324(f324(f10(a832,f845(a832,a832),x40181),a323),x40182)),x40183)),f324(f324(f103(f845(x40181,a832)),f324(f257(x40181),x40182)),f324(f257(x40181),x40183)))
% 18.55/18.48 [4020]E(f324(f324(f125(x40201),f324(f324(f128(x40201),f51(a838,x40202,f324(f180(f839(x40201)),x40203))),x40203)),f324(f324(f158(x40201),f51(a838,x40202,f324(f180(f839(x40201)),x40203))),x40203)),f324(f324(f324(f172(f839(x40201),f839(x40201)),x40202),f153(x40201)),x40203))
% 18.55/18.48 [4025]E(f324(f257(x40251),f324(f324(f20(x40251,a832,a832),f324(f324(f10(a832,f845(a832,a832),x40251),a327),x40252)),x40253)),f324(f324(f103(f845(x40251,a832)),f324(f81(f845(x40251,a832)),f324(f257(x40251),x40252))),f324(f257(x40251),x40253)))
% 18.55/18.48 [4040]E(f324(f324(f82(a838),f324(f180(f839(x40401)),f324(f126(x40401,x40402),x40403))),f324(f180(f839(x40401)),f324(f126(x40401,f324(f324(f10(a832,a832,x40401),a320),x40402)),x40403))),f324(f180(f839(x40401)),x40403))
% 18.55/18.48 [4067]P1(f324(f324(f231(f845(x40671,a832)),f324(f324(f103(f845(x40671,a832)),f44(f845(x40671,a832),x40672)),f44(f845(x40671,a832),x40673))),f44(f845(x40671,a832),f324(f324(f104(f845(f845(x40671,a832),a832)),x40672),x40673))))
% 18.55/18.48 [4081]E(f324(f157(x40811),f324(f126(x40811,f324(f324(f10(a832,a832,x40811),a320),f324(f324(f9(x40811,x40811,a832),a321),x40812))),x40813)),f324(f324(f3(f845(x40811,a832)),f324(f157(x40811),x40813)),f324(f324(f303(x40811),x40812),f179(f845(x40811,a832)))))
% 18.55/18.48 [4090]P1(f324(f324(f231(f845(f844(x40901,x40901),a832)),f324(f324(f103(f845(f844(x40901,x40901),a832)),f301(x40901,x40902)),f301(x40901,x40903))),f301(x40901,f324(f324(f103(f845(f844(x40901,x40901),a832)),x40902),x40903))))
% 18.55/18.48 [4113]E(f324(f324(f83(a838),f324(a114,f324(a114,f2(a838)))),f324(f324(f8(a838,a838),f324(f324(f10(a838,a838,a838),f324(f82(a838),x41131)),f324(f324(f9(a838,a838,a838),f83(a838)),x41132))),f324(f258(a838),x41133))),f324(f324(f83(a838),x41133),f324(f324(f82(a838),x41131),f324(f324(f82(a838),x41131),f324(f324(f83(a838),f324(f324(f3(a838),x41133),f80(a838))),x41132)))))
% 18.55/18.48 [4123]E(f324(f257(x41231),f324(f324(f20(x41231,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41231),a322),f324(f324(f9(x41231,f845(x41231,a832),a832),f326(x41231)),f324(f157(x41231),x41232)))),x41233)),f324(f157(x41231),f324(f126(x41231,x41233),x41232)))
% 18.55/18.48 [4267]E(f324(f257(x42671),f324(f324(f10(f845(a838,a832),a832,x42671),f89(a838)),f324(f324(f9(x42671,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),x42671),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),x42671),f324(f10(a832,f845(a832,a832),a838),a322)),f324(f324(f9(x42671,f845(a838,x42671),f845(a838,a832)),f324(f324(f10(f845(x42671,a832),f845(f845(a838,x42671),f845(a838,a832)),x42671),f10(x42671,a832,a838)),a321)),f324(f149(x42671),x42672))))),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,a838,a832),f232(a838)),f324(f180(f839(x42671)),x42672)))),f324(f324(f9(a838,f845(a838,a832),a832),f326(a838)),x42673))))),f324(f157(x42671),f159(x42671,x42672,x42673)))
% 18.55/18.48 [4161]E(f324(f257(x41611),f324(f324(f20(x41611,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41611),a327),f324(f324(f10(a832,a832,x41611),a320),f324(f324(f9(x41611,x41611,a832),a321),x41612)))),x41613)),f324(f324(f303(x41611),x41612),f324(f257(x41611),x41613)))
% 18.55/18.48 [4193]E(f324(f324(f141(f844(x41931,a838),x41931),f246(x41931,a838)),f324(f126(f844(x41931,a838),f324(f324(f9(f844(x41931,a838),f845(a838,a832),a832),f324(f324(f10(a838,f845(f845(a838,a832),a832),f844(x41931,a838)),f326(a838)),f251(x41931,a838))),x41932)),f324(f324(f166(x41931,a838),x41933),f129(a838,f324(f295(a838,f2(a838)),f324(f180(f839(x41931)),x41933)))))),f159(x41931,x41933,x41932))
% 18.55/18.48 [4222]E(f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f8(a838,a1),f324(f324(f10(a1,a1,a838),f324(f82(a1),x42221)),f324(f324(f9(a838,a1,a1),f324(f324(f10(a1,f845(a1,a1),a838),f83(a1)),f102(a1))),x42222))),f324(f258(a838),x42223))),f324(f324(f83(a1),f324(f102(a1),x42223)),f324(f324(f82(a1),x42221),f324(f324(f82(a1),x42221),f324(f324(f83(a1),f324(f102(a1),f324(f324(f3(a838),x42223),f80(a838)))),x42222)))))
% 18.55/18.48 [4261]E(f324(f257(f844(x42611,x42612)),f324(f252(x42611,x42612,a832),f324(f324(f9(x42611,f845(f844(x42612,x42611),a832),f845(x42612,a832)),f324(f324(f10(f845(x42612,f845(f845(f844(x42612,x42611),a832),a832)),f845(f845(f844(x42612,x42611),a832),f845(x42612,a832)),x42611),f9(x42612,f845(f844(x42612,x42611),a832),a832)),f324(f324(f10(f845(x42612,f844(x42612,x42611)),f845(x42612,f845(f845(f844(x42612,x42611),a832),a832)),x42611),f324(f10(f844(x42612,x42611),f845(f845(f844(x42612,x42611),a832),a832),x42612),f326(f844(x42612,x42611)))),f324(f9(x42612,x42611,f844(x42612,x42611)),f247(x42612,x42611))))),x42613))),f324(f279(x42612,x42611),x42613))
% 18.55/18.48 [4284]E(f324(f257(f839(x42841)),f324(f324(f10(f845(x42841,a832),a832,f839(x42841)),f89(x42841)),f324(f324(f10(f845(x42841,f845(f839(x42841),a832)),f845(x42841,a832),f839(x42841)),f324(f10(f845(f839(x42841),a832),a832,x42841),f89(f839(x42841)))),f324(f324(f9(f839(x42841),f845(x42841,f845(f839(x42841),a832)),f845(x42841,f845(f839(x42841),a832))),f324(f324(f10(f845(x42841,f845(f845(f839(x42841),a832),f845(f839(x42841),a832))),f845(f845(x42841,f845(f839(x42841),a832)),f845(x42841,f845(f839(x42841),a832))),f839(x42841)),f20(x42841,f845(f839(x42841),a832),f845(f839(x42841),a832))),f324(f324(f10(f845(x42841,f845(f839(x42841),f845(a832,a832))),f845(x42841,f845(f845(f839(x42841),a832),f845(f839(x42841),a832))),f839(x42841)),f324(f10(f845(f839(x42841),f845(a832,a832)),f845(f845(f839(x42841),a832),f845(f839(x42841),a832)),x42841),f20(f839(x42841),a832,a832))),f324(f324(f10(f845(x42841,f845(f839(x42841),a832)),f845(x42841,f845(f839(x42841),f845(a832,a832))),f839(x42841)),f324(f10(f845(f839(x42841),a832),f845(f839(x42841),f845(a832,a832)),x42841),f324(f10(a832,f845(a832,a832),f839(x42841)),a322))),f324(f324(f9(f839(x42841),f845(x42841,f845(f839(x42841),f839(x42841))),f845(x42841,f845(f839(x42841),a832))),f324(f324(f10(f845(f845(f839(x42841),f839(x42841)),f845(f839(x42841),a832)),f845(f845(x42841,f845(f839(x42841),f839(x42841))),f845(x42841,f845(f839(x42841),a832))),f839(x42841)),f10(f845(f839(x42841),f839(x42841)),f845(f839(x42841),a832),x42841)),f324(f324(f10(f845(f839(x42841),a832),f845(f845(f839(x42841),f839(x42841)),f845(f839(x42841),a832)),f839(x42841)),f10(f839(x42841),a832,f839(x42841))),a321))),f139(x42841)))))),f324(f324(f9(x42841,f845(f839(x42841),a832),f845(f839(x42841),a832)),f324(f324(f10(f845(a832,a832),f845(f845(f839(x42841),a832),f845(f839(x42841),a832)),x42841),f10(a832,a832,f839(x42841))),f324(f324(f10(a832,f845(a832,a832),x42841),a322),f324(f324(f9(x42841,f845(x42841,a832),a832),f326(x42841)),x42842)))),f324(f324(f9(f839(x42841),f845(f839(x42841),a832),a832),f326(f839(x42841))),x42843)))))),f160(x42841,x42842,x42843))
% 18.55/18.48 [4281]E(f324(f324(f88(a1,f844(a1,a1)),f324(f324(f3(a1),x42811),x42812)),f324(f324(f9(a1,f844(a1,a1),f844(a1,a1)),f324(f324(f20(a1,f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),f324(f324(f10(a832,f845(f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),a1),f98(f844(a1,a1))),f324(f231(a1),f2(a1)))),f324(f247(a1,a1),f324(f324(f82(a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x42813)),f80(a1))))),f324(f324(f247(a1,a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x42813)),x42811))),f324(f49(x42812),f324(f324(f247(a1,a1),x42813),x42811)))
% 18.55/18.48 [4315]~E(f36(x43151,x43152),f28(x43153,x43154))
% 18.55/18.48 [4316]~E(f36(x43161,x43162),f28(x43163,x43164))
% 18.55/18.48 [4317]~E(f35(x43171,x43172),f28(x43173,x43174))
% 18.55/18.48 [4318]~E(f35(x43181,x43182),f36(x43183,x43184))
% 18.55/18.48 [4319]~E(f35(x43191,x43192),f28(x43193,x43194))
% 18.55/18.48 [4320]~E(f35(x43201,x43202),f36(x43203,x43204))
% 18.55/18.48 [4338]~E(f324(a27,x43381),f31(x43382,x43383,x43384))
% 18.55/18.48 [4339]~E(f324(a27,x43391),f33(x43392,x43393,x43394))
% 18.55/18.48 [4340]~E(f324(a27,x43401),f32(x43402,x43403,x43404))
% 18.55/18.48 [4341]~E(f31(x43411,x43412,x43413),f324(a27,x43414))
% 18.55/18.48 [4342]~E(f33(x43421,x43422,x43423),f324(a27,x43424))
% 18.55/18.48 [4343]~E(f32(x43431,x43432,x43433),f324(a27,x43434))
% 18.55/18.48 [3315]E(f324(f324(f324(f74(x33151,x33152),x33153),x33154),f324(x33153,x33154)),x33153)
% 18.55/18.48 [3378]E(f324(f324(f241(x33781,x33782,x33783),x33784),f2(a838)),x33782)
% 18.55/18.48 [3416]E(f174(x34161,x34162,x34163,f324(a114,x34164)),f324(x34163,x34164))
% 18.55/18.48 [3455]E(f155(x34551,x34552,f155(x34551,x34553,x34554)),f155(x34551,x34553,f155(x34551,x34552,x34554)))
% 18.55/18.48 [3574]P39(f28(x35741,x35742),x35743,x35744,f324(f324(f324(a188,x35743),x35741),f324(x35742,x35743)))
% 18.55/18.48 [3575]P39(f28(x35751,x35752),x35753,x35754,f324(f324(f324(a188,x35753),x35751),f324(x35752,x35753)))
% 18.55/18.48 [3587]E(f324(f228(x35871,x35872,x35873,x35874),f182(x35872)),x35873)
% 18.55/18.48 [3589]E(f324(f143(x35891,x35892,x35893,x35894),f115(x35892)),x35893)
% 18.55/18.48 [3590]E(f324(f131(x35901,x35902,x35903,x35904),f115(x35902)),x35904)
% 18.55/18.48 [3627]E(f324(f180(f843(x36271,x36272)),f214(x36271,x36272,x36273,x36274)),f2(a838))
% 18.55/18.48 [3650]E(f324(f252(x36501,x36502,x36503),f250(x36501,x36502,x36503,x36504)),x36504)
% 18.55/18.48 [3707]E(f324(f228(f842(x37071),x37072,f182(x37071),f324(f18(f842(x37071),x37072),f182(x37071))),f324(x37073,x37074)),f182(x37071))
% 18.55/18.48 [3750]E(f324(f324(f103(f845(x37501,a832)),f168(x37501,x37502,x37503)),f168(x37501,x37502,x37504)),f168(x37501,x37502,f169(x37501,x37502,x37504,x37503)))
% 18.55/18.48 [3779]E(f324(f324(f254(x37791,x37792,x37793,f844(x37792,x37793)),x37794),f247(x37792,x37793)),x37794)
% 18.55/18.48 [3788]E(f229(x37881,x37882,x37883,x37884,f182(x37882)),x37883)
% 18.55/18.48 [4073]P41(x40731,x40732,x40733,x40734,f179(f845(x40731,a832)),x40734)
% 18.55/18.48 [4074]P41(x40741,x40742,x40743,x40744,f179(f845(x40741,a832)),x40744)
% 18.55/18.48 [3124]E(f324(f324(f18(x31241,x31242),x31243),x31244),x31243)
% 18.55/18.48 [3237]E(f324(f324(f195(x32371,x32372),x32373),f324(f226(x32371),x32374)),f324(f226(x32372),f324(x32373,x32374)))
% 18.55/18.48 [3408]E(f155(x34081,x34082,f324(f126(x34081,x34083),x34084)),f324(f126(x34081,x34083),f155(x34081,x34082,x34084)))
% 18.55/18.48 [3439]E(f324(f324(f67(x34391,x34392,x34393),x34394),f179(f845(x34391,a832))),x34394)
% 18.55/18.48 [3461]E(f324(f324(f149(x34611),f324(f324(f139(x34611),x34612),x34613)),f324(a114,x34614)),f324(f324(f149(x34611),x34613),x34614))
% 18.55/18.48 [3501]P31(x35011,f2(a838),f324(f324(f324(f93(x35011),x35012),f324(a27,x35013)),x35014))
% 18.55/18.48 [3526]E(f324(f324(x35261,x35262),f324(f173(x35263,x35264,x35261),x35262)),f324(f173(x35263,x35264,x35261),f324(a114,x35262)))
% 18.55/18.48 [3567]E(f250(x35671,x35672,x35673,f324(f252(x35671,x35672,x35673),x35674)),x35674)
% 18.55/18.48 [3625]E(f324(f324(f146(x36251,f324(f324(f139(x36251),x36252),x36253)),f2(a838)),x36254),f324(f324(f139(x36251),x36254),x36253))
% 18.55/18.48 [3635]E(f324(f324(f45(f845(x36351,a832),f845(x36352,a832)),x36353),f304(x36351,x36352,x36354)),f324(f304(x36351,x36352,x36354),f43(f845(x36351,a832),x36353)))
% 18.55/18.48 [3636]E(f324(f324(f45(f845(x36361,a832),f845(x36362,a832)),x36363),f305(x36362,x36361,x36364)),f324(f305(x36362,x36361,x36364),f43(f845(x36361,a832),x36363)))
% 18.55/18.48 [3735]E(f168(x37351,x37352,f171(x37351,x37352,x37353,x37354)),f324(f324(f104(f845(x37351,a832)),f168(x37351,x37352,x37353)),x37354))
% 18.55/18.48 [3754]E(f324(f131(x37541,x37542,f324(f9(x37542,x37541,x37541),x37543),x37544),f324(f154(x37542),f115(x37542))),x37544)
% 18.55/18.48 [3799]E(f78(x37991,x37992,x37993,x37994,f179(f845(x37991,a832))),x37993)
% 18.55/18.48 [3846]E(f324(f324(f324(f324(f74(x38461,f842(x38462)),f324(f18(f842(x38462),x38461),f182(x38462))),x38463),f182(x38462)),x38464),f182(x38462))
% 18.55/18.48 [4001]E(f324(f252(x40011,x40012,x40013),f324(f324(f10(f845(x40012,f844(x40011,x40012)),f845(x40012,x40013),x40011),f324(f10(f844(x40011,x40012),x40013,x40012),x40014)),f247(x40011,x40012))),x40014)
% 18.55/18.48 [3313]E(f324(f251(x33131,x33132),f324(f324(f247(x33131,x33132),x33133),x33134)),x33134)
% 18.55/18.48 [3314]E(f324(f246(x33141,x33142),f324(f324(f247(x33141,x33142),x33143),x33144)),x33143)
% 18.55/18.48 [3351]E(f324(f180(f839(x33511)),f324(f324(f141(x33512,x33511),x33513),x33514)),f324(f180(f839(x33512)),x33514))
% 18.55/18.48 [3352]E(f324(f180(f839(x33521)),f324(f324(f146(x33521,x33522),x33523),x33524)),f324(f180(f839(x33521)),x33522))
% 18.55/18.48 [3373]E(f324(f324(f128(x33731),f324(a114,x33732)),f324(f324(f139(x33731),x33733),x33734)),f324(f324(f128(x33731),x33732),x33734))
% 18.55/18.48 [3441]E(f324(f324(f303(x34411),x34412),f324(f324(f303(x34411),x34413),x34414)),f324(f324(f303(x34411),x34413),f324(f324(f303(x34411),x34412),x34414)))
% 18.55/18.48 [3444]E(f324(f324(f141(x34441,x34442),x34443),f116(x34441,x34444)),f116(x34442,f324(f324(f141(x34441,x34442),x34443),x34444)))
% 18.55/18.48 [3459]E(f324(f154(x34591),f324(f324(f141(x34592,x34591),x34593),x34594)),f324(f324(f141(x34592,x34591),x34593),f324(f154(x34592),x34594)))
% 18.55/18.48 [3460]E(f324(f324(f141(x34601,x34602),x34603),f324(f156(x34601),x34604)),f324(f156(x34602),f324(f324(f141(x34601,x34602),x34603),x34604)))
% 18.55/18.48 [3470]E(f324(f324(f158(x34701),f324(a114,x34702)),f324(f324(f139(x34701),x34703),x34704)),f324(f324(f139(x34701),x34703),f324(f324(f158(x34701),x34702),x34704)))
% 18.55/18.48 [3474]E(f324(f157(x34741),f324(f324(f141(x34742,x34741),x34743),x34744)),f324(f304(x34742,x34741,x34743),f324(f157(x34742),x34744)))
% 18.55/18.48 [3525]E(f19(x35251,x35252,x35253,f324(a5,f324(a114,f324(a22,x35254)))),f324(x35253,x35254))
% 18.55/18.48 [3529]E(f324(f324(f125(x35291),f324(f126(x35291,x35292),x35293)),f324(f126(x35291,x35292),x35294)),f324(f126(x35291,x35292),f324(f324(f125(x35291),x35293),x35294)))
% 18.55/18.48 [3542]E(f140(x35421,f324(f324(f141(x35422,x35421),x35423),f140(x35422,x35424))),f140(x35421,f324(f324(f141(x35422,x35421),x35423),x35424)))
% 18.55/18.48 [3557]E(f324(f279(x35571,x35571),f324(f324(f281(x35572,x35571),x35573),x35574)),f324(f324(f281(x35572,x35571),f324(f279(x35572,x35572),x35573)),x35574))
% 18.55/18.48 [3568]E(f324(f324(f282(x35681,x35682,x35683),x35684),f179(f845(f844(x35682,x35683),a832))),f179(f845(f844(x35681,x35683),a832)))
% 18.55/18.48 [3569]E(f324(f324(f158(x35691),f324(f324(f3(a838),x35692),x35693)),f324(f324(f128(x35691),x35693),x35694)),f324(f324(f128(x35691),x35693),f324(f324(f158(x35691),x35692),x35694)))
% 18.55/18.48 [3591]E(f324(f324(f324(f274(x35911),x35912),x35913),x35914),f324(f247(f845(a101,f845(a832,f842(f840(x35911)))),f844(a101,a101)),f324(f48(x35911),x35912)))
% 18.55/18.48 [3615]E(f43(f845(x36151,a832),f324(f304(x36152,f845(x36151,a832),x36153),x36154)),f324(f324(f45(x36152,f845(x36151,a832)),x36154),x36153))
% 18.55/18.48 [3616]E(f44(f845(x36161,a832),f324(f304(x36162,f845(x36161,a832),x36163),x36164)),f324(f324(f46(x36162,f845(x36161,a832)),x36164),x36163))
% 18.55/18.48 [3617]E(f44(f845(x36171,a832),f324(f304(x36172,f845(x36171,a832),x36173),x36174)),f324(f324(f46(x36172,f845(x36171,a832)),x36174),x36173))
% 18.55/18.48 [3618]E(f43(f845(x36181,a832),f324(f304(x36182,f845(x36181,a832),x36183),x36184)),f324(f324(f45(x36182,f845(x36181,a832)),x36184),x36183))
% 18.55/18.48 [3619]E(f324(f180(f839(f844(x36191,x36192))),f324(f324(f166(x36191,x36192),x36193),x36194)),f324(f324(f235(a838),f324(f180(f839(x36191)),x36193)),f324(f180(f839(x36192)),x36194)))
% 18.55/18.48 [3621]E(f324(f305(x36211,x36212,x36213),f324(f81(f845(x36212,a832)),x36214)),f324(f81(f845(x36211,a832)),f324(f305(x36211,x36212,x36213),x36214)))
% 18.55/18.48 [3651]E(f324(f171(x36511,x36512,x36513,f179(f845(x36511,a832))),x36514),f182(x36512))
% 18.55/18.48 [3671]E(f324(f305(x36711,x36712,x36713),f324(f257(x36712),x36714)),f324(f257(x36711),f324(f324(f10(x36712,a832,x36711),x36714),x36713)))
% 18.55/18.48 [3689]E(f324(f324(f149(x36891),f324(f324(f125(x36891),x36892),f324(f324(f139(x36891),x36893),x36894))),f324(f180(f839(x36891)),x36892)),x36893)
% 18.55/18.48 [3694]E(f324(f171(x36941,x36942,f324(f18(f842(x36942),x36941),f182(x36942)),x36943),x36944),f182(x36942))
% 18.55/18.48 [3716]E(f324(f304(x37161,x37162,x37163),f324(f305(x37161,x37162,x37163),x37164)),f324(f324(f104(f845(x37162,a832)),x37164),f324(f304(x37161,x37162,x37163),f238(f845(x37161,a832)))))
% 18.55/18.48 [3734]P1(f324(f324(f326(x37341),f324(x37342,x37343)),f324(f304(x37344,x37341,x37342),f238(f845(x37344,a832)))))
% 18.55/18.48 [3742]E(f21(x37421,x37422,x37423,f324(a5,f324(a114,f324(a22,x37424)))),f324(f324(x37423,x37424),f21(x37421,x37422,x37423,x37424)))
% 18.55/18.48 [3757]E(f142(x37571,x37572,f324(f324(f139(x37571),x37573),x37574)),f324(f324(f82(a838),f324(f324(f82(a838),f324(x37572,x37573)),f142(x37571,x37572,x37574))),f324(a114,f2(a838))))
% 18.55/18.48 [3770]E(f174(f839(x37701),f324(f324(f139(x37701),x37702),x37703),f324(f324(f9(a838,f839(x37701),f839(x37701)),f128(x37701)),x37703),x37704),f324(f324(f128(x37701),x37704),f324(f324(f139(x37701),x37702),x37703)))
% 18.55/18.48 [3771]P29(x37711,f844(x37712,x37711),f328(x37713,x37714,x37712,x37711),f324(f324(f45(x37712,f845(x37711,a832)),x37714),x37713))
% 18.55/18.48 [3780]E(f324(f324(f3(f845(x37801,a832)),f324(f324(f3(f845(x37801,a832)),x37802),x37803)),f324(f324(f303(x37801),x37804),f179(f845(x37801,a832)))),f324(f324(f3(f845(x37801,a832)),x37802),f324(f324(f303(x37801),x37804),x37803)))
% 18.55/18.48 [3791]E(f324(f324(f172(f845(x37911,x37912),f845(x37911,x37912)),x37913),f75(x37912,x37912,x37911,x37914)),f75(x37912,x37912,x37911,f324(f324(f172(x37912,x37912),x37913),x37914)))
% 18.55/18.48 [3870]E(f324(f324(f324(f172(f839(x38701),f839(x38701)),x38702),f153(x38701)),f324(f324(f324(f172(f839(x38701),f839(x38701)),x38703),f153(x38701)),x38704)),f324(f324(f324(f172(f839(x38701),f839(x38701)),f324(f324(f82(a838),x38702),x38703)),f153(x38701)),x38704))
% 18.55/18.48 [3959]P1(f324(f324(f231(f845(x39591,a832)),f324(f157(x39591),f324(f324(f146(x39591,x39592),x39593),x39594))),f324(f324(f303(x39591),x39594),f324(f157(x39591),x39592))))
% 18.55/18.48 [3991]E(f324(f324(f45(f845(x39911,a832),f845(f844(x39911,x39912),a832)),x39913),f324(f324(f9(f845(x39911,a832),f845(x39911,f845(x39912,a832)),f845(f844(x39911,x39912),a832)),f249(x39911,x39912)),x39914)),f324(f324(f249(x39911,x39912),f43(f845(x39911,a832),x39913)),x39914))
% 18.55/18.48 [4027]E(f203(x40271,x40272,x40273,f324(f75(x40272,f845(a101,f845(a101,f845(f844(a101,a101),f845(a101,f840(x40272))))),x40271,f198(x40272)),x40274)),f204(x40271,x40272,x40274,x40273))
% 18.55/18.48 [4043]E(f200(x40431,x40432,x40433,f324(f75(x40432,f845(a101,f845(a101,f845(f844(a101,a101),f845(a101,f840(f842(x40432)))))),x40431,f199(x40432)),x40434)),f201(x40431,x40432,x40434,x40433))
% 18.55/18.48 [4047]P1(f324(f69(x40471,x40472,x40473,x40474,f179(f845(x40471,a832))),x40474))
% 18.55/18.48 [4048]P1(f324(f69(x40481,x40482,x40483,x40484,f179(f845(x40481,a832))),x40484))
% 18.55/18.48 [4092]E(f324(f324(f45(x40921,f845(x40922,a832)),x40923),f324(f324(f9(x40921,f845(x40922,a832),f845(x40922,a832)),f324(f324(f10(x40922,f845(f845(x40922,a832),f845(x40922,a832)),x40921),f303(x40922)),x40924)),f179(f845(x40922,a832)))),f324(f304(x40921,x40922,x40924),x40923))
% 18.55/18.48 [4098]P1(f324(f324(f231(f845(x40981,a832)),f324(f260(x40982,x40981),f324(f324(f104(f845(f844(x40982,x40981),a832)),x40983),x40984))),f324(f324(f104(f845(x40981,a832)),f324(f260(x40982,x40981),x40983)),f324(f260(x40982,x40981),x40984))))
% 18.55/18.48 [4099]P1(f324(f324(f231(f845(x40991,a832)),f324(f262(x40991,x40992),f324(f324(f104(f845(f844(x40991,x40992),a832)),x40993),x40994))),f324(f324(f104(f845(x40991,a832)),f324(f262(x40991,x40992),x40993)),f324(f262(x40991,x40992),x40994))))
% 18.55/18.48 [4159]P1(f324(f324(f231(f845(f844(x41591,x41592),a832)),f324(f304(x41592,f844(x41591,x41592),f328(x41593,x41594,x41591,x41592)),f324(f324(f45(x41591,f845(x41592,a832)),x41594),x41593))),f324(f324(f249(x41591,x41592),x41594),x41593)))
% 18.55/18.48 [4160]E(f272(x41601,x41602,x41603,f324(f75(x41602,f845(a101,f845(a101,f845(f844(a101,a101),f844(f845(a101,f845(a832,f842(f840(x41602)))),f844(a101,a101))))),x41601,f274(x41602)),x41604)),f275(x41601,x41602,x41604,x41603))
% 18.55/18.48 [4199]E(f87(f844(x41991,x41992),f324(f252(x41991,x41992,a832),f324(f324(f9(x41991,f845(x41992,a832),f845(x41992,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x41992,a832),f845(x41992,a832)),x41991),f10(a832,a832,x41992)),f324(f324(f10(a832,f845(a832,a832),x41991),a322),f324(a321,x41993)))),f324(a321,x41994)))),f324(f324(f247(x41991,x41992),x41993),x41994))
% 18.55/18.48 [4200]E(f92(f844(x42001,x42002),f324(f252(x42001,x42002,a832),f324(f324(f9(x42001,f845(x42002,a832),f845(x42002,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x42002,a832),f845(x42002,a832)),x42001),f10(a832,a832,x42002)),f324(f324(f10(a832,f845(a832,a832),x42001),a322),f324(a321,x42003)))),f324(a321,x42004)))),f324(f324(f247(x42001,x42002),x42003),x42004))
% 18.55/18.48 [4271]E(f324(f324(f252(f839(x42711),f839(x42711),f844(f839(x42711),f839(x42711))),f324(f324(f20(f839(x42711),f845(f839(x42711),f844(f839(x42711),f839(x42711))),f845(f839(x42711),f844(f839(x42711),f839(x42711)))),f324(f324(f10(f845(f839(x42711),f845(f844(f839(x42711),f839(x42711)),f844(f839(x42711),f839(x42711)))),f845(f845(f839(x42711),f844(f839(x42711),f839(x42711))),f845(f839(x42711),f844(f839(x42711),f839(x42711)))),f839(x42711)),f20(f839(x42711),f844(f839(x42711),f839(x42711)),f844(f839(x42711),f839(x42711)))),f324(f324(f10(f845(f839(x42711),f844(f839(x42711),f839(x42711))),f845(f839(x42711),f845(f844(f839(x42711),f839(x42711)),f844(f839(x42711),f839(x42711)))),f839(x42711)),f324(f10(f844(f839(x42711),f839(x42711)),f845(f844(f839(x42711),f839(x42711)),f844(f839(x42711),f839(x42711))),f839(x42711)),f324(f98(f844(f839(x42711),f839(x42711))),f324(x42712,x42713)))),f324(f324(f10(f839(x42711),f845(f839(x42711),f844(f839(x42711),f839(x42711))),f839(x42711)),f247(f839(x42711),f839(x42711))),f324(f139(x42711),x42713))))),f324(f324(f9(f839(x42711),f845(f839(x42711),f839(x42711)),f845(f839(x42711),f844(f839(x42711),f839(x42711)))),f324(f324(f10(f845(f839(x42711),f844(f839(x42711),f839(x42711))),f845(f845(f839(x42711),f839(x42711)),f845(f839(x42711),f844(f839(x42711),f839(x42711)))),f839(x42711)),f10(f839(x42711),f844(f839(x42711),f839(x42711)),f839(x42711))),f247(f839(x42711),f839(x42711)))),f324(f139(x42711),x42713)))),f152(x42711,x42712,x42714)),f152(x42711,x42712,f324(f324(f139(x42711),x42713),x42714)))
% 18.55/18.48 [4277]E(f324(f131(f845(x42771,f842(x42772)),f844(x42771,x42772),f324(f9(f844(x42771,x42772),f845(x42771,f842(x42772)),f845(x42771,f842(x42772))),f324(f252(x42771,x42772,f845(f845(x42771,f842(x42772)),f845(x42771,f842(x42772)))),f324(f324(f9(x42771,f845(x42772,f842(x42772)),f845(x42772,f845(f845(x42771,f842(x42772)),f845(x42771,f842(x42772))))),f324(f324(f10(f845(f842(x42772),f845(f845(x42771,f842(x42772)),f845(x42771,f842(x42772)))),f845(f845(x42772,f842(x42772)),f845(x42772,f845(f845(x42771,f842(x42772)),f845(x42771,f842(x42772))))),x42771),f10(f842(x42772),f845(f845(x42771,f842(x42772)),f845(x42771,f842(x42772))),x42772)),f324(f324(f10(f845(f845(x42771,f842(x42772)),f845(f842(x42772),f845(x42771,f842(x42772)))),f845(f842(x42772),f845(f845(x42771,f842(x42772)),f845(x42771,f842(x42772)))),x42771),f9(f845(x42771,f842(x42772)),f842(x42772),f845(x42771,f842(x42772)))),f324(f9(f845(x42771,f842(x42772)),x42771,f845(f842(x42772),f845(x42771,f842(x42772)))),f74(x42771,f842(x42772)))))),f226(x42772)))),x42773),f324(f154(f844(x42771,x42772)),x42774)),f169(x42771,x42772,x42773,f165(x42771,x42772,x42774)))
% 18.55/18.48 [3391]E(f324(f180(f837(x33911)),f324(f324(f324(f93(x33911),x33912),x33913),x33914)),f2(a838))
% 18.55/18.48 [3504]E(f324(f324(f158(x35041),x35042),f324(f324(f158(x35041),x35043),x35044)),f324(f324(f158(x35041),f324(f324(f235(a838),x35042),x35043)),x35044))
% 18.55/18.48 [3505]E(f324(f324(f128(x35051),x35052),f324(f324(f128(x35051),x35053),x35054)),f324(f324(f128(x35051),f324(f324(f82(a838),x35052),x35053)),x35054))
% 18.55/18.48 [3517]E(f324(f324(f125(x35171),f324(f324(f139(x35171),x35172),x35173)),x35174),f324(f324(f139(x35171),x35172),f324(f324(f125(x35171),x35173),x35174)))
% 18.55/18.48 [3518]E(f324(f324(f125(x35181),f324(f324(f125(x35181),x35182),x35183)),x35184),f324(f324(f125(x35181),x35182),f324(f324(f125(x35181),x35183),x35184)))
% 18.55/18.48 [3601]E(f324(f324(f149(x36011),f324(f324(f139(x36011),x36012),x36013)),x36014),f174(x36011,x36012,f324(f149(x36011),x36013),x36014))
% 18.55/18.48 [3610]E(f324(f324(f172(x36101,x36101),x36102),f324(f324(f172(x36101,x36101),x36103),x36104)),f324(f324(f172(x36101,x36101),f324(f324(f83(a838),x36103),x36102)),x36104))
% 18.55/18.48 [3638]E(f324(f324(f103(f845(x36381,a832)),x36382),f324(f324(f303(x36381),x36383),x36384)),f324(f324(f303(x36381),x36383),f324(f324(f103(f845(x36381,a832)),x36382),x36384)))
% 18.55/18.48 [3654]E(f324(f324(f324(f172(x36541,x36541),x36542),x36543),f324(x36543,x36544)),f324(x36543,f324(f324(f324(f172(x36541,x36541),x36542),x36543),x36544)))
% 18.55/18.48 [3661]E(f324(f324(f282(x36611,x36612,x36613),f179(f845(f844(x36611,x36612),a832))),x36614),f179(f845(f844(x36611,x36613),a832)))
% 18.55/18.48 [3678]E(f324(f324(f103(f845(x36781,a832)),f324(f324(f303(x36781),x36782),x36783)),x36784),f324(f324(f303(x36781),x36782),f324(f324(f103(f845(x36781,a832)),x36783),x36784)))
% 18.55/18.48 [3696]E(f324(f41(f844(x36961,x36962)),f324(f324(f249(x36961,x36962),x36963),f324(f18(f845(x36962,a832),x36961),x36964))),f324(f324(f83(a838),f324(f41(x36961),x36963)),f324(f41(x36962),x36964)))
% 18.55/18.48 [3704]E(f324(f324(f104(f845(x37041,a832)),f324(f324(f303(x37041),x37042),x37043)),f324(f324(f303(x37041),x37042),x37044)),f324(f324(f303(x37041),x37042),f324(f324(f104(f845(x37041,a832)),x37043),x37044)))
% 18.55/18.48 [3714]E(f169(x37141,x37142,f165(x37141,x37142,x37143),f165(x37141,x37142,x37144)),f165(x37141,x37142,f324(f324(f125(f844(x37141,x37142)),x37144),x37143)))
% 18.55/18.48 [3720]E(f324(f324(f103(f845(x37201,a832)),x37202),f324(f324(f103(f845(x37201,a832)),x37203),x37204)),f324(f324(f103(f845(x37201,a832)),x37203),f324(f324(f103(f845(x37201,a832)),x37202),x37204)))
% 18.55/18.48 [3721]E(f324(f324(f104(f845(x37211,a832)),x37212),f324(f324(f104(f845(x37211,a832)),x37213),x37214)),f324(f324(f104(f845(x37211,a832)),x37213),f324(f324(f104(f845(x37211,a832)),x37212),x37214)))
% 18.55/18.48 [3730]E(f67(x37301,x37302,f324(f324(f10(x37302,f845(x37302,x37302),x37301),x37303),x37304)),f324(f68(x37302,x37301,x37303),x37304))
% 18.55/18.48 [3739]E(f163(x37391,f324(f324(f141(f839(x37392),f839(x37391)),f324(f141(x37392,x37391),x37393)),x37394)),f324(f324(f141(f839(x37392),f839(x37391)),f324(f141(x37392,x37391),x37393)),f163(x37392,x37394)))
% 18.55/18.48 [3756]E(f171(x37561,x37562,x37563,f324(f81(f845(x37561,a832)),f324(f324(f303(x37561),x37564),f179(f845(x37561,a832))))),f324(f324(f324(f74(x37561,f842(x37562)),x37563),x37564),f182(x37562)))
% 18.55/18.48 [3813]E(f324(f75(x38131,x38131,x38131,f324(f324(f172(x38131,x38131),x38132),x38133)),f324(f324(f172(x38131,x38131),x38134),x38133)),f324(f324(f172(x38131,x38131),f324(f324(f82(a838),x38132),x38134)),x38133))
% 18.55/18.48 [3828]E(f324(f324(f324(f74(x38281,f842(x38282)),f165(x38281,x38282,x38283)),f324(f246(x38281,x38282),x38284)),f324(f226(x38282),f324(f251(x38281,x38282),x38284))),f165(x38281,x38282,f324(f324(f139(f844(x38281,x38282)),x38284),x38283)))
% 18.55/18.48 [3835]E(f169(x38351,x38352,x38353,f165(x38351,x38352,f324(f154(f844(x38351,x38352)),f324(f324(f166(x38351,x38352),x38354),f115(x38352))))),x38353)
% 18.55/18.48 [3838]E(f324(f324(f104(f845(x38381,a832)),f324(f324(f3(f845(x38381,a832)),x38382),x38383)),f324(f324(f3(f845(x38381,a832)),x38382),x38384)),f324(f324(f3(f845(x38381,a832)),x38382),f324(f324(f103(f845(x38381,a832)),x38383),x38384)))
% 18.55/18.48 [3839]E(f324(f324(f103(f845(x38391,a832)),f324(f324(f3(f845(x38391,a832)),x38392),x38393)),f324(f324(f3(f845(x38391,a832)),x38392),x38394)),f324(f324(f3(f845(x38391,a832)),x38392),f324(f324(f104(f845(x38391,a832)),x38393),x38394)))
% 18.55/18.48 [3840]E(f324(f324(f104(f845(x38401,a832)),f324(f324(f103(f845(x38401,a832)),x38402),x38403)),f324(f324(f103(f845(x38401,a832)),x38402),x38404)),f324(f324(f103(f845(x38401,a832)),x38402),f324(f324(f104(f845(x38401,a832)),x38403),x38404)))
% 18.55/18.48 [3841]E(f324(f324(f3(f845(x38411,a832)),f324(f324(f104(f845(x38411,a832)),x38412),x38413)),f324(f324(f104(f845(x38411,a832)),x38412),x38414)),f324(f324(f104(f845(x38411,a832)),x38412),f324(f324(f3(f845(x38411,a832)),x38413),x38414)))
% 18.55/18.48 [3842]E(f324(f324(f103(f845(x38421,a832)),f324(f324(f104(f845(x38421,a832)),x38422),x38423)),f324(f324(f104(f845(x38421,a832)),x38422),x38424)),f324(f324(f104(f845(x38421,a832)),x38422),f324(f324(f103(f845(x38421,a832)),x38423),x38424)))
% 18.55/18.48 [3848]E(f324(f41(f844(x38481,x38482)),f324(f324(f249(x38481,x38482),f324(f324(f303(x38481),x38483),f179(f845(x38481,a832)))),f324(f18(f845(x38482,a832),x38481),x38484))),f324(f41(x38482),x38484))
% 18.55/18.48 [3886]E(f324(f324(f46(x38861,f845(x38862,a832)),x38863),f324(f324(f10(f845(x38862,a832),f845(x38862,a832),x38861),f81(f845(x38862,a832))),x38864)),f324(f81(f845(x38862,a832)),f324(f324(f45(x38861,f845(x38862,a832)),x38863),x38864)))
% 18.55/18.48 [3887]E(f324(f324(f45(x38871,f845(x38872,a832)),x38873),f324(f324(f10(f845(x38872,a832),f845(x38872,a832),x38871),f81(f845(x38872,a832))),x38874)),f324(f81(f845(x38872,a832)),f324(f324(f46(x38871,f845(x38872,a832)),x38873),x38874)))
% 18.55/18.48 [3903]E(f324(f324(f282(x39031,x39031,x39031),f324(f324(f172(f844(x39031,x39031),a832),x39032),x39033)),f324(f324(f172(f844(x39031,x39031),a832),x39034),x39033)),f324(f324(f172(f844(x39031,x39031),a832),f324(f324(f82(a838),x39032),x39034)),x39033))
% 18.55/18.48 [3934]E(f324(f324(f46(x39341,f845(f845(x39342,a832),a832)),x39343),f324(f324(f10(f845(x39342,a832),f845(f845(x39342,a832),a832),x39341),f302(x39342)),x39344)),f324(f302(x39342),f324(f324(f46(x39341,f845(x39342,a832)),x39343),x39344)))
% 18.55/18.48 [3962]E(f324(f324(f45(f845(x39621,a832),f845(x39622,a832)),x39623),f324(f324(f9(f845(x39621,a832),f845(x39621,f845(x39622,a832)),f845(x39622,a832)),f45(x39621,f845(x39622,a832))),x39624)),f324(f324(f45(x39621,f845(x39622,a832)),f43(f845(x39621,a832),x39623)),x39624))
% 18.55/18.48 [3963]E(f324(f324(f46(f845(x39631,a832),f845(x39632,a832)),x39633),f324(f324(f9(f845(x39631,a832),f845(x39631,f845(x39632,a832)),f845(x39632,a832)),f46(x39631,f845(x39632,a832))),x39634)),f324(f324(f46(x39631,f845(x39632,a832)),f43(f845(x39631,a832),x39633)),x39634))
% 18.55/18.48 [3964]E(f324(f324(f45(f845(x39641,a832),f845(x39642,a832)),x39643),f324(f324(f9(f845(x39641,a832),f845(x39641,f845(x39642,a832)),f845(x39642,a832)),f45(x39641,f845(x39642,a832))),x39644)),f324(f324(f45(x39641,f845(x39642,a832)),f43(f845(x39641,a832),x39643)),x39644))
% 18.55/18.48 [3965]E(f324(f324(f46(f845(x39651,a832),f845(x39652,a832)),x39653),f324(f324(f9(f845(x39651,a832),f845(x39651,f845(x39652,a832)),f845(x39652,a832)),f46(x39651,f845(x39652,a832))),x39654)),f324(f324(f46(x39651,f845(x39652,a832)),f43(f845(x39651,a832),x39653)),x39654))
% 18.55/18.48 [3970]E(f324(f324(f141(x39701,x39702),x39703),f324(f131(f839(x39701),f839(x39701),f125(x39701),f115(x39701)),x39704)),f324(f131(f839(x39702),f839(x39702),f125(x39702),f115(x39702)),f324(f324(f141(f839(x39701),f839(x39702)),f324(f141(x39701,x39702),x39703)),x39704)))
% 18.55/18.48 [3972]E(f174(f839(x39721),f115(x39721),f324(f324(f10(f839(x39721),f839(x39721),a838),f324(f139(x39721),x39722)),f324(f324(f9(a838,f839(x39721),f839(x39721)),f158(x39721)),x39723)),x39724),f324(f324(f158(x39721),x39724),f324(f324(f139(x39721),x39722),x39723)))
% 18.55/18.48 [4011]P1(f324(f324(f231(f845(x40111,a832)),f324(f304(x40112,x40111,x40113),f324(f305(x40112,x40111,x40113),x40114))),x40114))
% 18.55/18.48 [4013]E(f324(f304(f844(x40131,x40132),f844(x40132,x40131),f324(f252(x40131,x40132,f844(x40132,x40131)),f324(f9(x40132,x40131,f844(x40132,x40131)),f247(x40132,x40131)))),f324(f324(f249(x40131,x40132),x40133),f324(f18(f845(x40132,a832),x40131),x40134))),f324(f324(f249(x40132,x40131),x40134),f324(f18(f845(x40131,a832),x40132),x40133)))
% 18.55/18.48 [4022]E(f324(f324(f45(x40221,f845(x40222,a832)),x40223),f324(f324(f10(f845(x40221,a832),f845(x40222,a832),x40221),f278(x40221,x40222,x40224)),f324(f324(f9(x40221,f845(x40221,a832),f845(x40221,a832)),f303(x40221)),f179(f845(x40221,a832))))),f324(f278(x40221,x40222,x40224),x40223))
% 18.55/18.48 [4023]E(f324(f324(f45(x40231,f845(x40232,a832)),x40233),f324(f324(f10(f845(x40231,a832),f845(x40232,a832),x40231),f305(x40232,x40231,x40234)),f324(f324(f9(x40231,f845(x40231,a832),f845(x40231,a832)),f303(x40231)),f179(f845(x40231,a832))))),f324(f305(x40232,x40231,x40234),x40233))
% 18.55/18.48 [4112]E(f324(f324(f104(f845(x41121,a832)),f324(f324(f104(f845(x41121,a832)),f324(f324(f103(f845(x41121,a832)),x41122),x41123)),f324(f324(f103(f845(x41121,a832)),x41123),x41124))),f324(f324(f103(f845(x41121,a832)),x41124),x41122)),f324(f324(f103(f845(x41121,a832)),f324(f324(f103(f845(x41121,a832)),f324(f324(f104(f845(x41121,a832)),x41122),x41123)),f324(f324(f104(f845(x41121,a832)),x41123),x41124))),f324(f324(f104(f845(x41121,a832)),x41124),x41122)))
% 18.55/18.48 [4172]E(f324(f131(f839(x41721),f839(x41721),f125(x41721),f115(x41721)),f324(f324(f141(x41722,f839(x41721)),f324(f324(f9(x41722,f839(x41721),f839(x41721)),f324(f324(f10(x41721,f845(f839(x41721),f839(x41721)),x41722),f139(x41721)),x41723)),f115(x41721))),x41724)),f324(f324(f141(x41722,x41721),x41723),x41724))
% 18.55/18.48 [4183]E(f324(f324(f88(a1,x41831),f324(f106(a1),f324(f324(f82(a1),x41832),a99))),f324(f324(f20(a1,x41831,x41831),f324(f324(f9(a1,x41831,f845(x41831,x41831)),f324(f324(f10(a832,f845(x41831,f845(x41831,x41831)),a1),f98(x41831)),a185)),x41833)),f324(f324(f10(a838,x41831,a1),x41834),a107))),f174(x41831,x41833,x41834,f324(f106(a838),x41832)))
% 18.55/18.48 [4406]~P1(f324(f324(f179(f845(x44061,f845(x44062,a832))),x44063),x44064))
% 18.55/18.48 [3664]E(f324(f324(f149(x36641),f324(f324(f125(x36641),x36642),x36643)),f324(f324(f82(a838),f324(f180(f839(x36641)),x36642)),x36644)),f324(f324(f149(x36641),x36643),x36644))
% 18.55/18.48 [3670]E(f324(f324(f128(x36701),x36702),f324(f324(f158(x36701),f324(f324(f82(a838),x36703),x36702)),x36704)),f324(f324(f158(x36701),x36703),f324(f324(f128(x36701),x36702),x36704)))
% 18.55/18.48 [3768]E(f324(f324(f103(f845(x37681,a832)),f324(f260(x37682,x37681),x37683)),f324(f260(x37682,x37681),x37684)),f324(f260(x37682,x37681),f324(f324(f103(f845(f844(x37682,x37681),a832)),x37683),x37684)))
% 18.55/18.48 [3769]E(f324(f324(f103(f845(x37691,a832)),f324(f262(x37691,x37692),x37693)),f324(f262(x37691,x37692),x37694)),f324(f262(x37691,x37692),f324(f324(f103(f845(f844(x37691,x37692),a832)),x37693),x37694)))
% 18.55/18.48 [3774]E(f324(f324(f3(f845(x37741,a832)),f324(f324(f104(f845(x37741,a832)),x37742),x37743)),x37744),f324(f324(f104(f845(x37741,a832)),x37742),f324(f324(f3(f845(x37741,a832)),x37743),x37744)))
% 18.55/18.48 [3775]E(f324(f324(f103(f845(x37751,a832)),f324(f324(f103(f845(x37751,a832)),x37752),x37753)),x37754),f324(f324(f103(f845(x37751,a832)),x37752),f324(f324(f103(f845(x37751,a832)),x37753),x37754)))
% 18.55/18.48 [3776]E(f324(f324(f104(f845(x37761,a832)),f324(f324(f104(f845(x37761,a832)),x37762),x37763)),x37764),f324(f324(f104(f845(x37761,a832)),x37762),f324(f324(f104(f845(x37761,a832)),x37763),x37764)))
% 18.55/18.48 [3815]E(f324(f324(f103(f845(f844(x38151,x38152),a832)),f324(f279(x38152,x38151),x38153)),f324(f279(x38152,x38151),x38154)),f324(f279(x38152,x38151),f324(f324(f103(f845(f844(x38152,x38151),a832)),x38153),x38154)))
% 18.55/18.48 [3816]E(f324(f324(f104(f845(f844(x38161,x38162),a832)),f324(f279(x38162,x38161),x38163)),f324(f279(x38162,x38161),x38164)),f324(f279(x38162,x38161),f324(f324(f104(f845(f844(x38162,x38161),a832)),x38163),x38164)))
% 18.55/18.48 [3830]E(f324(f324(f103(f845(x38301,f845(x38302,a832))),f239(x38302,x38301,x38303)),f239(x38302,x38301,x38304)),f239(x38302,x38301,f324(f324(f103(f845(x38302,f845(x38301,a832))),x38303),x38304)))
% 18.55/18.48 [3831]E(f324(f324(f104(f845(x38311,f845(x38312,a832))),f239(x38312,x38311,x38313)),f239(x38312,x38311,x38314)),f239(x38312,x38311,f324(f324(f104(f845(x38312,f845(x38311,a832))),x38313),x38314)))
% 18.55/18.48 [3851]E(f169(x38511,x38512,x38513,f165(x38511,x38512,f324(f154(f844(x38511,x38512)),f324(f324(f166(x38511,x38512),f115(x38511)),x38514)))),x38513)
% 18.55/18.48 [3890]E(f324(f324(f103(f845(x38901,a832)),f324(f324(f3(f845(x38901,a832)),x38902),x38903)),f324(f324(f3(f845(x38901,a832)),x38904),x38903)),f324(f324(f3(f845(x38901,a832)),f324(f324(f103(f845(x38901,a832)),x38902),x38904)),x38903))
% 18.55/18.48 [3891]E(f324(f324(f104(f845(x38911,a832)),f324(f324(f103(f845(x38911,a832)),x38912),x38913)),f324(f324(f103(f845(x38911,a832)),x38914),x38913)),f324(f324(f103(f845(x38911,a832)),f324(f324(f104(f845(x38911,a832)),x38912),x38914)),x38913))
% 18.55/18.48 [3892]E(f324(f324(f3(f845(x38921,a832)),f324(f324(f104(f845(x38921,a832)),x38922),x38923)),f324(f324(f104(f845(x38921,a832)),x38924),x38923)),f324(f324(f104(f845(x38921,a832)),f324(f324(f3(f845(x38921,a832)),x38922),x38924)),x38923))
% 18.55/18.48 [3893]E(f324(f324(f103(f845(x38931,a832)),f324(f324(f104(f845(x38931,a832)),x38932),x38933)),f324(f324(f104(f845(x38931,a832)),x38934),x38933)),f324(f324(f104(f845(x38931,a832)),f324(f324(f103(f845(x38931,a832)),x38932),x38934)),x38933))
% 18.55/18.48 [3894]E(f324(f324(f3(f845(x38941,a832)),f324(f324(f104(f845(x38941,a832)),x38942),x38943)),f324(f324(f104(f845(x38941,a832)),x38944),x38943)),f324(f324(f3(f845(x38941,a832)),f324(f324(f104(f845(x38941,a832)),x38942),x38943)),x38944))
% 18.55/18.48 [3906]E(f324(f324(f3(f845(x39061,a832)),f324(f324(f3(f845(x39061,a832)),x39062),f324(f324(f303(x39061),x39063),f179(f845(x39061,a832))))),x39064),f324(f324(f3(f845(x39061,a832)),x39062),f324(f324(f303(x39061),x39063),x39064)))
% 18.55/18.48 [3961]E(f324(f324(f103(f845(x39611,a832)),f324(f324(f303(x39611),x39612),f324(f324(f303(x39611),x39613),f179(f845(x39611,a832))))),f324(f277(x39611),x39614)),f324(f277(x39611),f324(f324(f303(f844(x39611,x39611)),f324(f324(f247(x39611,x39611),x39612),x39613)),x39614)))
% 18.55/18.48 [3986]E(f324(f324(f45(a838,f845(x39861,a832)),f324(f294(a838),x39862)),f324(f324(f10(a838,f845(x39861,a832),a838),x39863),f324(f324(f9(a838,a838,a838),f82(a838)),x39864))),f324(f324(f45(a838,f845(x39861,a832)),f296(a838,x39864,f324(f324(f82(a838),x39862),x39864))),x39863))
% 18.55/18.48 [3987]E(f160(x39871,f324(f278(x39871,x39871,x39872),f324(f324(f303(x39871),x39873),f179(f845(x39871,a832)))),f324(f278(f839(x39871),f839(x39871),f145(x39871,x39872)),f324(f324(f303(f839(x39871)),x39874),f179(f845(f839(x39871),a832))))),f324(f278(f839(x39871),f839(x39871),f145(x39871,x39872)),f324(f324(f303(f839(x39871)),f324(f324(f139(x39871),x39873),x39874)),f179(f845(f839(x39871),a832)))))
% 18.55/18.48 [4049]E(f165(x40491,x40492,f324(f324(f141(x40491,f844(x40491,x40492)),f324(f324(f20(x40491,x40492,f844(x40491,x40492)),f247(x40491,x40492)),x40493)),x40494)),f171(x40491,x40492,f324(f75(x40492,f842(x40492),x40491,f226(x40492)),x40493),f324(f157(x40491),x40494)))
% 18.55/18.48 [4052]E(f324(f257(x40521),f324(f324(f9(x40521,f845(x40522,a832),a832),f324(f324(f10(x40522,f845(f845(x40522,a832),a832),x40521),f326(x40522)),x40523)),x40524)),f324(f305(x40521,x40522,x40523),x40524))
% 18.55/18.48 [4144]E(f324(f257(x41441),f324(f324(f9(x41441,f845(f844(x41442,x41441),a832),a832),f324(f324(f10(f844(x41442,x41441),f845(f845(f844(x41442,x41441),a832),a832),x41441),f326(f844(x41442,x41441))),f324(f247(x41442,x41441),x41443))),x41444)),f324(f278(x41442,x41441,x41444),f324(f324(f303(x41442),x41443),f179(f845(x41442,a832)))))
% 18.55/18.48 [4158]E(f324(f324(f141(f844(x41581,a838),x41581),f246(x41581,a838)),f324(f126(f844(x41581,a838),f324(f324(f10(a838,a832,f844(x41581,a838)),x41582),f324(f324(f10(a838,a838,f844(x41581,a838)),a114),f251(x41581,a838)))),f324(f324(f166(x41581,a838),x41583),x41584))),f324(f324(f141(f844(x41581,a838),x41581),f246(x41581,a838)),f324(f126(f844(x41581,a838),f324(f324(f10(a838,a832,f844(x41581,a838)),x41582),f251(x41581,a838))),f324(f324(f166(x41581,a838),x41583),f324(f324(f141(a838,a838),a114),x41584)))))
% 18.55/18.48 [4165]P1(f324(f324(f231(f845(f845(x41651,a832),a832)),f324(f324(f45(x41652,f845(f845(x41651,a832),a832)),x41653),f324(f324(f10(f845(x41651,a832),f845(f845(x41651,a832),a832),x41652),f302(x41651)),x41654))),f324(f302(x41651),f324(f324(f45(x41652,f845(x41651,a832)),x41653),x41654))))
% 18.55/18.48 [4206]E(f324(f324(f88(a1,x42061),f324(f106(a1),f324(f324(f82(a1),x42062),a99))),f324(f324(f20(a1,x42061,x42061),f324(f324(f9(a1,x42061,f845(x42061,x42061)),f324(f324(f10(a832,f845(x42061,f845(x42061,x42061)),a1),f98(x42061)),a185)),x42063)),f324(f324(f20(a1,x42061,x42061),f324(f324(f10(a838,f845(x42061,x42061),a1),x42064),a107)),f324(f324(f10(a838,x42061,a1),f173(x42061,x42063,x42064)),a107)))),f324(f173(x42061,x42063,x42064),f324(f106(a838),x42062)))
% 18.55/18.48 [4209]E(f324(f324(f141(x42091,x42092),f324(f75(f842(x42092),x42092,x42091,f230(x42092)),x42093)),f324(f126(x42091,f324(f324(f10(a832,a832,x42091),a320),f324(f324(f9(x42091,f842(x42092),a832),f324(f324(f10(f842(x42092),f845(f842(x42092),a832),x42091),a321),x42093)),f182(x42092)))),x42094)),f150(x42091,x42092,x42093,x42094))
% 18.55/18.48 [4231]E(f324(f257(f844(x42311,x42312)),f324(f252(x42311,x42312,a832),f324(f324(f9(x42311,f845(x42312,a832),f845(x42312,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x42312,a832),f845(x42312,a832)),x42311),f10(a832,a832,x42312)),f324(f324(f10(a832,f845(a832,a832),x42311),a322),f324(f324(f9(x42311,f845(x42311,a832),a832),f326(x42311)),x42313)))),f324(f324(f9(x42312,f845(x42312,a832),a832),f326(x42312)),x42314)))),f222(x42311,x42312,x42313,x42314))
% 18.55/18.48 [4264]E(f324(f324(f45(x42641,f845(f844(x42641,x42642),a832)),x42643),f324(f324(f20(x42641,f845(x42642,f845(f844(x42641,x42642),a832)),f845(f844(x42641,x42642),a832)),f324(f324(f10(f845(x42642,a832),f845(f845(x42642,f845(f844(x42641,x42642),a832)),f845(f844(x42641,x42642),a832)),x42641),f45(x42642,f845(f844(x42641,x42642),a832))),x42644)),f324(f324(f9(x42641,f845(f844(x42641,x42642),a832),f845(x42642,f845(f844(x42641,x42642),a832))),f324(f324(f10(f845(x42642,f845(f845(f844(x42641,x42642),a832),f845(f844(x42641,x42642),a832))),f845(f845(f844(x42641,x42642),a832),f845(x42642,f845(f844(x42641,x42642),a832))),x42641),f9(x42642,f845(f844(x42641,x42642),a832),f845(f844(x42641,x42642),a832))),f324(f324(f10(f845(x42642,f844(x42641,x42642)),f845(x42642,f845(f845(f844(x42641,x42642),a832),f845(f844(x42641,x42642),a832))),x42641),f324(f10(f844(x42641,x42642),f845(f845(f844(x42641,x42642),a832),f845(f844(x42641,x42642),a832)),x42642),f303(f844(x42641,x42642)))),f247(x42641,x42642)))),f179(f845(f844(x42641,x42642),a832))))),f324(f324(f249(x42641,x42642),x42643),x42644))
% 18.55/18.48 [3824]E(f324(f324(f125(x38241),f324(f324(f158(x38241),x38242),x38243)),f324(f324(f158(x38241),f324(f324(f3(a838),x38242),f324(f180(f839(x38241)),x38243))),x38244)),f324(f324(f158(x38241),x38242),f324(f324(f125(x38241),x38243),x38244)))
% 18.55/18.48 [3825]E(f324(f324(f125(x38251),f324(f324(f128(x38251),x38252),x38253)),f324(f324(f128(x38251),f324(f324(f3(a838),x38252),f324(f180(f839(x38251)),x38253))),x38254)),f324(f324(f128(x38251),x38252),f324(f324(f125(x38251),x38253),x38254)))
% 18.55/18.48 [3879]E(f324(f324(f82(a838),f324(f324(f83(a838),x38791),x38792)),f324(f324(f82(a838),f324(f324(f83(a838),x38793),x38792)),x38794)),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f82(a838),x38791),x38793)),x38792)),x38794))
% 18.55/18.48 [4078]P1(f324(f324(f231(f845(x40781,a832)),f324(f324(f3(f845(x40781,a832)),f324(f260(x40782,x40781),x40783)),f324(f260(x40782,x40781),x40784))),f324(f260(x40782,x40781),f324(f324(f3(f845(f844(x40782,x40781),a832)),x40783),x40784))))
% 18.55/18.48 [4079]P1(f324(f324(f231(f845(x40791,a832)),f324(f324(f3(f845(x40791,a832)),f324(f262(x40791,x40792),x40793)),f324(f262(x40791,x40792),x40794))),f324(f262(x40791,x40792),f324(f324(f3(f845(f844(x40791,x40792),a832)),x40793),x40794))))
% 18.55/18.48 [4185]E(f324(f324(f82(a1),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x41851),x41852)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x41853),x41854)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),f324(f324(f82(a838),x41851),x41853)),f324(f324(f82(a838),x41852),x41854))),f179(f845(f844(a838,a838),a832))))))
% 18.55/18.48 [4226]E(f324(f324(f83(a1),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x42261),x42262)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x42263),x42264)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),f324(f324(f82(a838),f324(f324(f83(a838),x42261),x42263)),f324(f324(f83(a838),x42262),x42264))),f324(f324(f82(a838),f324(f324(f83(a838),x42261),x42264)),f324(f324(f83(a838),x42262),x42263)))),f179(f845(f844(a838,a838),a832))))))
% 18.55/18.48 [4246]E(f324(f257(x42461),f324(f324(f10(f845(x42462,a832),a832,x42461),f90(x42462)),f324(f324(f10(f845(x42462,a832),f845(x42462,a832),x42461),f324(f20(x42462,a832,a832),f324(f324(f10(a832,f845(a832,a832),x42462),a327),f324(f324(f9(x42462,f845(x42462,a832),a832),f326(x42462)),x42463)))),f324(f324(f9(x42461,f845(x42462,f845(x42461,a832)),f845(x42462,a832)),f324(f324(f10(f845(f845(x42461,a832),a832),f845(f845(x42462,f845(x42461,a832)),f845(x42462,a832)),x42461),f10(f845(x42461,a832),a832,x42462)),f326(x42461))),x42464)))),f324(f324(f46(x42462,f845(x42461,a832)),x42463),x42464))
% 18.55/18.48 [4280]E(f324(f324(f282(x42801,x42801,x42801),f324(f324(f303(f844(x42801,x42801)),f324(f324(f247(x42801,x42801),x42802),x42803)),x42804)),f301(x42801,f324(f324(f303(f844(x42801,x42801)),f324(f324(f247(x42801,x42801),x42802),x42803)),x42804))),f324(f324(f103(f845(f844(x42801,x42801),a832)),f324(f324(f282(x42801,x42801,x42801),x42804),f301(x42801,x42804))),f324(f257(f844(x42801,x42801)),f324(f252(x42801,x42801,a832),f324(f324(f9(x42801,f845(x42801,a832),f845(x42801,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x42801,a832),f845(x42801,a832)),x42801),f10(a832,a832,x42801)),f324(f324(f10(a832,f845(a832,a832),x42801),a322),f324(f324(f9(x42801,f845(f844(x42801,x42801),a832),a832),f324(f324(f10(f844(x42801,x42801),f845(f845(f844(x42801,x42801),a832),a832),x42801),f326(f844(x42801,x42801))),f324(f324(f9(x42801,x42801,f844(x42801,x42801)),f247(x42801,x42801)),x42802))),f301(x42801,x42804))))),f324(f324(f9(x42801,f845(f844(x42801,x42801),a832),a832),f324(f324(f10(f844(x42801,x42801),f845(f845(f844(x42801,x42801),a832),a832),x42801),f326(f844(x42801,x42801))),f324(f247(x42801,x42801),x42803))),f301(x42801,x42804)))))))
% 18.55/18.48 [4080]E(f324(f126(x40801,f324(f324(f20(x40801,a832,a832),f324(f324(f10(a832,f845(a832,a832),x40801),a322),x40802)),x40803)),x40804),f324(f126(x40801,x40803),f324(f126(x40801,x40802),x40804)))
% 18.55/18.48 [4179]E(f324(f324(f125(x41791),f324(f324(f324(f98(f839(x41791)),f324(f324(f326(a838),f2(a838)),x41792)),f324(f324(f139(x41791),x41793),f115(x41791))),f115(x41791))),f159(x41791,x41794,f324(f257(a838),f324(f324(f9(a838,f845(a838,a832),a832),f324(f324(f10(a838,f845(f845(a838,a832),a832),a838),f326(a838)),a114)),x41792)))),f159(x41791,f324(f324(f139(x41791),x41793),x41794),x41792))
% 18.55/18.48 [4275]E(f324(f257(f844(x42751,x42752)),f324(f324(f10(f845(a838,a832),a832,f844(x42751,x42752)),f89(a838)),f324(f324(f9(f844(x42751,x42752),f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),f844(x42751,x42752)),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),f844(x42751,x42752)),f324(f10(a832,f845(a832,a832),a838),a322)),f324(f324(f9(f844(x42751,x42752),f845(a838,f844(x42751,x42752)),f845(a838,a832)),f324(f324(f10(f845(f844(x42751,x42752),a832),f845(f845(a838,f844(x42751,x42752)),f845(a838,a832)),f844(x42751,x42752)),f10(f844(x42751,x42752),a832,a838)),a321)),f324(f324(f20(a838,x42752,f844(x42751,x42752)),f324(f324(f10(x42751,f845(x42752,f844(x42751,x42752)),a838),f247(x42751,x42752)),f324(f149(x42751),x42753))),f324(f149(x42752),x42754)))))),f324(f324(f9(a838,a838,a832),f232(a838)),f324(f324(f235(a838),f324(f180(f839(x42751)),x42753)),f324(f180(f839(x42752)),x42754)))))),f324(f157(f844(x42751,x42752)),f324(f324(f166(x42751,x42752),x42753),x42754)))
% 18.55/18.48 [4198]E(f324(f257(f844(x41981,x41982)),f324(f252(x41981,x41982,a832),f324(f324(f9(x41981,f845(x41982,a832),f845(x41982,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x41982,a832),f845(x41982,a832)),x41981),f10(a832,a832,x41982)),f324(f324(f10(a832,f845(a832,a832),x41981),a322),x41983))),x41984))),f324(f324(f249(x41981,x41982),f324(f257(x41981),x41983)),f324(f18(f845(x41982,a832),x41981),f324(f257(x41982),x41984))))
% 18.55/18.48 [4201]E(f324(f257(f844(x42011,x42012)),f324(f252(x42011,x42012,a832),f324(f324(f20(x42011,f845(x42012,a832),f845(x42012,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x42012,a832),f845(x42012,a832)),x42011),f10(a832,a832,x42012)),f324(f324(f10(a832,f845(a832,a832),x42011),a322),x42013))),x42014))),f324(f324(f249(x42011,x42012),f324(f257(x42011),x42013)),f324(f324(f10(f845(x42012,a832),f845(x42012,a832),x42011),f257(x42012)),x42014)))
% 18.55/18.48 [4216]E(f324(f257(x42161),f324(f324(f10(f845(x42162,a832),a832,x42161),f90(x42162)),f324(f324(f10(f845(x42162,a832),f845(x42162,a832),x42161),f324(f20(x42162,a832,a832),f324(f324(f10(a832,f845(a832,a832),x42162),a327),f324(f324(f9(x42162,f845(x42162,a832),a832),f326(x42162)),x42163)))),x42164))),f324(f324(f46(x42162,f845(x42161,a832)),x42163),f324(f324(f10(f845(x42161,a832),f845(x42161,a832),x42162),f257(x42161)),f324(f9(x42161,x42162,a832),x42164))))
% 18.55/18.48 [4259]E(f324(f324(f141(f844(x42591,a838),x42591),f246(x42591,a838)),f324(f126(f844(x42591,a838),f324(f324(f9(f844(x42591,a838),f845(a838,a832),a832),f324(f324(f10(a838,f845(f845(a838,a832),a832),f844(x42591,a838)),f326(a838)),f251(x42591,a838))),x42592)),f324(f324(f166(x42591,a838),x42593),f129(a838,f324(f295(a838,x42594),f324(f324(f82(a838),x42594),f324(f180(f839(x42591)),x42593))))))),f324(f324(f141(f844(x42591,a838),x42591),f246(x42591,a838)),f324(f126(f844(x42591,a838),f324(f324(f9(f844(x42591,a838),f845(a838,a832),a832),f324(f324(f10(a838,f845(f845(a838,a832),a832),f844(x42591,a838)),f326(a838)),f324(f324(f9(f844(x42591,a838),a838,a838),f324(f324(f10(a838,f845(a838,a838),f844(x42591,a838)),f82(a838)),f251(x42591,a838))),x42594))),x42592)),f324(f324(f166(x42591,a838),x42593),f129(a838,f324(f295(a838,f2(a838)),f324(f180(f839(x42591)),x42593)))))))
% 18.55/18.48 [4260]E(f324(a114,f324(f324(f178(a838),f324(f180(f839(x42601)),x42602)),f324(f131(a838,f839(x42603),f324(f9(f839(x42603),a838,a838),f324(f324(f10(a838,f845(a838,a838),f839(x42603)),f178(a838)),f324(f324(f9(f839(x42603),a838,a838),f324(f324(f10(a838,f845(a838,a838),f839(x42603)),f3(a838)),f180(f839(x42603)))),f324(a114,f2(a838))))),f2(a838)),f324(f154(f839(x42603)),f324(f126(f839(x42603),f324(f324(f10(a832,a832,f839(x42603)),a320),f324(f324(f9(f839(x42603),f839(x42603),a832),a321),f115(x42603)))),x42604))))),f324(f324(f178(a838),f324(a114,f324(f180(f839(x42601)),x42602))),f324(f131(a838,f839(x42603),f324(f9(f839(x42603),a838,a838),f324(f324(f10(a838,f845(a838,a838),f839(x42603)),f178(a838)),f180(f839(x42603)))),f2(a838)),f324(f154(f839(x42603)),x42604))))
% 18.55/18.48 [4215]E(f324(f324(f125(x42151),f159(x42151,x42152,x42153)),f159(x42151,x42154,f324(f257(a838),f324(f324(f9(a838,f845(a838,a832),a832),f324(f324(f10(a838,f845(f845(a838,a832),a832),a838),f326(a838)),f324(f324(f9(a838,a838,a838),f82(a838)),f324(f180(f839(x42151)),x42152)))),x42153)))),f159(x42151,f324(f324(f125(x42151),x42152),x42154),x42153))
% 18.55/18.48 [4266]E(f324(f324(f139(f839(x42661)),f324(f324(f139(x42661),x42662),f324(f131(f839(x42661),f839(x42661),f125(x42661),f115(x42661)),f324(f324(f141(f839(x42661),f839(x42661)),f143(f839(x42661),x42661,f115(x42661),f324(f324(f10(f839(x42661),f845(f839(x42661),f839(x42661)),x42661),f18(f839(x42661),f839(x42661))),f324(f324(f9(x42661,f839(x42661),f839(x42661)),f139(x42661)),f115(x42661))))),x42663)))),f163(x42661,f324(f324(f139(f839(x42661)),x42664),f324(f131(f839(f839(x42661)),f839(f839(x42661)),f125(f839(x42661)),f115(f839(x42661))),f324(f324(f141(f839(x42661),f839(f839(x42661))),f143(f839(f839(x42661)),x42661,f115(f839(x42661)),f324(f18(f845(f839(x42661),f839(f839(x42661))),x42661),f324(f324(f9(f839(x42661),f839(f839(x42661)),f839(f839(x42661))),f139(f839(x42661))),f115(f839(x42661)))))),x42663))))),f163(x42661,f324(f324(f139(f839(x42661)),f324(f324(f139(x42661),x42662),x42664)),x42663)))
% 18.55/18.48 [4276]E(f324(f257(f844(x42761,x42761)),f324(f252(x42761,x42761,a832),f324(f324(f9(x42761,f845(f844(x42762,x42762),a832),f845(x42761,a832)),f324(f324(f10(f845(x42761,f845(f845(f844(x42762,x42762),a832),a832)),f845(f845(f844(x42762,x42762),a832),f845(x42761,a832)),x42761),f9(x42761,f845(f844(x42762,x42762),a832),a832)),f324(f324(f10(f845(x42761,f844(x42762,x42762)),f845(x42761,f845(f845(f844(x42762,x42762),a832),a832)),x42761),f324(f10(f844(x42762,x42762),f845(f845(f844(x42762,x42762),a832),a832),x42761),f326(f844(x42762,x42762)))),f324(f324(f9(x42761,f845(x42761,x42762),f845(x42761,f844(x42762,x42762))),f324(f324(f10(f845(x42762,f844(x42762,x42762)),f845(f845(x42761,x42762),f845(x42761,f844(x42762,x42762))),x42761),f10(x42762,f844(x42762,x42762),x42761)),f324(f324(f10(x42762,f845(x42762,f844(x42762,x42762)),x42761),f247(x42762,x42762)),x42763))),x42763)))),x42764))),f324(f324(f281(x42762,x42761),x42764),x42763))
% 18.55/18.48 [4344]~E(f28(x43441,x43442),f31(x43443,x43444,x43445))
% 18.55/18.48 [4345]~E(f28(x43451,x43452),f33(x43453,x43454,x43455))
% 18.55/18.48 [4346]~E(f28(x43461,x43462),f32(x43463,x43464,x43465))
% 18.55/18.48 [4347]~E(f36(x43471,x43472),f31(x43473,x43474,x43475))
% 18.55/18.48 [4348]~E(f36(x43481,x43482),f33(x43483,x43484,x43485))
% 18.55/18.48 [4349]~E(f36(x43491,x43492),f32(x43493,x43494,x43495))
% 18.55/18.48 [4350]~E(f35(x43501,x43502),f31(x43503,x43504,x43505))
% 18.55/18.48 [4351]~E(f35(x43511,x43512),f33(x43513,x43514,x43515))
% 18.55/18.48 [4352]~E(f35(x43521,x43522),f32(x43523,x43524,x43525))
% 18.55/18.48 [4353]~E(f31(x43531,x43532,x43533),f28(x43534,x43535))
% 18.55/18.48 [4354]~E(f31(x43541,x43542,x43543),f36(x43544,x43545))
% 18.55/18.48 [4355]~E(f31(x43551,x43552,x43553),f35(x43554,x43555))
% 18.55/18.48 [4356]~E(f33(x43561,x43562,x43563),f28(x43564,x43565))
% 18.55/18.48 [4357]~E(f33(x43571,x43572,x43573),f36(x43574,x43575))
% 18.55/18.48 [4358]~E(f33(x43581,x43582,x43583),f35(x43584,x43585))
% 18.55/18.48 [4359]~E(f32(x43591,x43592,x43593),f28(x43594,x43595))
% 18.55/18.48 [4360]~E(f32(x43601,x43602,x43603),f36(x43604,x43605))
% 18.55/18.48 [4361]~E(f32(x43611,x43612,x43613),f35(x43614,x43615))
% 18.55/18.48 [3766]E(f324(f169(x37661,x37662,x37663,x37664),x37665),f324(f228(f842(x37662),x37662,f324(x37663,x37665),f226(x37662)),f324(x37664,x37665)))
% 18.55/18.48 [3854]E(f169(x38541,x38542,f169(x38541,x38542,x38543,x38544),x38545),f169(x38541,x38542,x38543,f169(x38541,x38542,x38544,x38545)))
% 18.55/18.48 [4026]E(f248(x40261,x40262,x40263,f239(x40262,x40261,x40264),f239(x40263,x40262,x40265)),f239(x40263,x40261,f248(x40263,x40262,x40261,x40265,x40264)))
% 18.55/18.48 [3594]E(f324(f324(f252(x35941,x35942,x35943),x35944),x35945),f324(f324(x35944,f324(f246(x35941,x35942),x35945)),f324(f251(x35941,x35942),x35945)))
% 18.55/18.48 [3595]E(f324(f324(f252(x35951,x35952,x35953),x35954),x35955),f324(f324(x35954,f324(f246(x35951,x35952),x35955)),f324(f251(x35951,x35952),x35955)))
% 18.55/18.48 [3596]E(f324(f324(f252(x35961,x35962,x35963),x35964),x35965),f324(f324(x35964,f324(f246(x35961,x35962),x35965)),f324(f251(x35961,x35962),x35965)))
% 18.55/18.48 [3622]E(f324(f228(x36221,x36222,x36223,x36224),f324(f226(x36222),x36225)),f324(x36224,x36225))
% 18.55/18.48 [3630]E(f324(f324(f324(f68(x36301,x36302,x36303),x36304),x36305),f179(f845(x36302,a832))),x36305)
% 18.55/18.48 [3796]E(f229(x37961,x37962,x37963,x37964,f324(f226(x37962),x37965)),f324(x37964,x37965))
% 18.55/18.48 [3912]E(f324(f75(f842(x39121),f842(x39122),f842(x39123),f324(f195(x39121,x39122),x39124)),f324(f195(x39123,x39121),x39125)),f324(f195(x39123,x39122),f324(f75(x39121,x39122,x39123,x39124),x39125)))
% 18.55/18.48 [3913]E(f324(f75(f839(x39131),f839(x39132),f839(x39133),f324(f141(x39131,x39132),x39134)),f324(f141(x39133,x39131),x39135)),f324(f141(x39133,x39132),f324(f75(x39131,x39132,x39133,x39134),x39135)))
% 18.55/18.48 [3914]E(f324(f75(f839(x39141),f839(x39142),f839(x39143),f324(f141(x39141,x39142),x39144)),f324(f141(x39143,x39141),x39145)),f324(f141(x39143,x39142),f324(f75(x39141,x39142,x39143,x39144),x39145)))
% 18.55/18.48 [3990]E(f87(x39901,f69(x39902,x39901,x39903,x39904,x39905)),f324(f324(f67(x39902,x39901,x39903),x39904),x39905))
% 18.55/18.48 [4024]E(f324(f324(f82(a838),f324(f324(f82(a838),f324(x40241,f324(f246(x40242,x40243),x40244))),f324(x40245,f324(f251(x40242,x40243),x40244)))),f324(a114,f2(a838))),f256(x40242,x40243,x40241,x40245,x40244))
% 18.55/18.48 [4211]E(f150(x42111,x42112,f324(f324(f9(x42111,f842(x42112),f842(x42112)),f324(f324(f20(x42111,f842(x42112),f845(f842(x42112),f842(x42112))),f324(f324(f10(a832,f845(f842(x42112),f845(f842(x42112),f842(x42112))),x42111),f98(f842(x42112))),x42113)),f324(f324(f10(x42112,f842(x42112),x42111),f226(x42112)),x42114))),f182(x42112)),x42115),f324(f324(f141(x42111,x42112),x42114),f324(f126(x42111,x42113),x42115)))
% 18.55/18.48 [4398]~E(f324(f324(f324(f74(x43981,f842(x43982)),x43983),x43984),f324(f226(x43982),x43985)),f324(f18(f842(x43982),x43981),f182(x43982)))
% 18.55/18.48 [3530]E(f324(f324(f158(x35301),x35302),f324(f324(f141(x35303,x35301),x35304),x35305)),f324(f324(f141(x35303,x35301),x35304),f324(f324(f158(x35303),x35302),x35305)))
% 18.55/18.48 [3531]E(f324(f324(f128(x35311),x35312),f324(f324(f141(x35313,x35311),x35314),x35315)),f324(f324(f141(x35313,x35311),x35314),f324(f324(f128(x35313),x35312),x35315)))
% 18.55/18.48 [3562]E(f324(f324(f141(x35621,x35622),x35623),f324(f324(f139(x35621),x35624),x35625)),f324(f324(f139(x35622),f324(x35623,x35624)),f324(f324(f141(x35621,x35622),x35623),x35625)))
% 18.55/18.48 [3626]E(f324(f304(x36261,x36262,x36263),f324(f324(f303(x36261),x36264),x36265)),f324(f324(f303(x36262),f324(x36263,x36264)),f324(f304(x36261,x36262,x36263),x36265)))
% 18.55/18.48 [3691]E(f324(f324(f166(x36911,x36912),f324(f324(f158(x36911),x36913),x36914)),f324(f324(f158(x36912),x36913),x36915)),f324(f324(f158(f844(x36911,x36912)),x36913),f324(f324(f166(x36911,x36912),x36914),x36915)))
% 18.55/18.48 [3692]E(f324(f324(f166(x36921,x36922),f324(f324(f128(x36921),x36923),x36924)),f324(f324(f128(x36922),x36923),x36925)),f324(f324(f128(f844(x36921,x36922)),x36923),f324(f324(f166(x36921,x36922),x36924),x36925)))
% 18.55/18.48 [3703]E(f324(f324(f146(x37031,f324(f324(f139(x37031),x37032),x37033)),f324(a114,x37034)),x37035),f324(f324(f139(x37031),x37032),f324(f324(f146(x37031,x37033),x37034),x37035)))
% 18.55/18.48 [3706]E(f324(f228(f842(x37061),x37062,f182(x37061),x37063),f324(f324(f18(f842(x37062),x37064),f182(x37062)),x37065)),f182(x37061))
% 18.55/18.48 [3708]E(f324(f324(f125(x37081),f324(f324(f141(x37082,x37081),x37083),x37084)),f324(f324(f141(x37082,x37081),x37083),x37085)),f324(f324(f141(x37082,x37081),x37083),f324(f324(f125(x37082),x37084),x37085)))
% 18.55/18.48 [3712]E(f324(f324(x37121,x37122),f324(f324(f241(x37123,x37124,x37121),x37122),x37125)),f324(f324(f241(x37123,x37124,x37121),x37122),f324(a114,x37125)))
% 18.55/18.48 [3753]E(f324(f324(f282(x37531,x37532,x37533),f324(f279(x37532,x37531),x37534)),f324(f279(x37533,x37532),x37535)),f324(f279(x37533,x37531),f324(f324(f282(x37533,x37532,x37531),x37535),x37534)))
% 18.55/18.48 [3784]E(f324(f324(f324(f172(f839(x37841),f839(x37841)),x37842),f153(x37841)),f324(f324(f141(x37843,x37841),x37844),x37845)),f324(f324(f141(x37843,x37841),x37844),f324(f324(f324(f172(f839(x37843),f839(x37843)),x37842),f153(x37843)),x37845)))
% 18.55/18.48 [3785]E(f324(f324(f254(x37851,x37852,x37851,x37853),f324(f247(x37852,x37851),x37854)),x37855),f324(x37855,x37854))
% 18.55/18.48 [3810]E(f142(x38101,x38102,f324(f324(f141(x38103,x38101),x38104),x38105)),f142(x38103,f324(f75(x38101,a838,x38103,x38102),x38104),x38105))
% 18.55/18.48 [3877]E(f324(f324(f75(f842(x38771),f842(x38772),x38773,f324(f195(x38771,x38772),x38774)),f324(f18(f842(x38771),x38773),f182(x38771))),x38775),f182(x38772))
% 18.55/18.48 [3878]E(f161(f844(x38781,x38782),f324(f75(x38782,a832,f844(x38781,x38782),x38783),f251(x38781,x38782)),f324(f324(f166(x38781,x38782),x38784),x38785)),f324(f324(f166(x38781,x38782),x38784),f161(x38782,x38783,x38785)))
% 18.55/18.48 [3883]E(f324(f304(x38831,x38832,f324(f324(f10(x38833,x38832,x38831),x38834),x38835)),f238(f845(x38831,a832))),f324(f304(x38833,x38832,x38834),f324(f304(x38831,x38833,x38835),f238(f845(x38831,a832)))))
% 18.55/18.48 [3897]E(f161(f844(x38971,x38972),f324(f75(x38971,a832,f844(x38971,x38972),x38973),f246(x38971,x38972)),f324(f324(f166(x38971,x38972),x38974),x38975)),f324(f324(f166(x38971,x38972),f161(x38971,x38973,x38974)),x38975))
% 18.55/18.48 [3918]E(f324(f324(f103(f845(x39181,a832)),f324(f305(x39181,x39182,x39183),f324(f324(f303(x39182),x39184),f179(f845(x39182,a832))))),f324(f305(x39181,x39182,x39183),x39185)),f324(f305(x39181,x39182,x39183),f324(f324(f303(x39182),x39184),x39185)))
% 18.55/18.48 [3977]E(f324(f324(f141(x39771,x39772),x39773),f161(x39771,f324(f75(x39772,a832,x39771,x39774),x39773),x39775)),f161(x39772,x39774,f324(f324(f141(x39771,x39772),x39773),x39775)))
% 18.55/18.48 [3982]E(f324(f131(x39821,x39822,f324(f9(x39822,x39821,x39821),f324(f9(x39821,x39822,x39821),x39823)),x39824),f324(f154(x39822),f324(f154(x39822),x39825))),f324(f131(x39821,x39822,x39823,x39824),x39825))
% 18.55/18.48 [3983]E(f324(f324(f324(f74(x39831,f842(x39832)),f171(x39831,x39832,x39833,x39834)),x39835),f324(x39833,x39835)),f171(x39831,x39832,x39833,f324(f324(f303(x39831),x39835),x39834)))
% 18.55/18.48 [4050]E(f324(f228(f839(x40501),x40501,f150(x40502,x40501,x40503,x40504),f324(f324(f9(x40501,f839(x40501),f839(x40501)),f139(x40501)),f150(x40502,x40501,x40503,x40504))),f324(x40503,x40505)),f150(x40502,x40501,x40503,f324(f324(f139(x40502),x40505),x40504)))
% 18.55/18.48 [4088]P1(f324(f324(f231(f845(x40881,a832)),f324(f304(x40882,x40881,x40883),f324(f324(f104(f845(x40882,a832)),x40884),x40885))),f324(f324(f104(f845(x40881,a832)),f324(f304(x40882,x40881,x40883),x40884)),f324(f304(x40882,x40881,x40883),x40885))))
% 18.55/18.48 [4089]P1(f324(f324(f231(f845(x40891,a832)),f324(f278(x40892,x40891,x40893),f324(f324(f104(f845(x40892,a832)),x40894),x40895))),f324(f324(f104(f845(x40891,a832)),f324(f278(x40892,x40891,x40893),x40894)),f324(f278(x40892,x40891,x40893),x40895))))
% 18.55/18.48 [4186]E(f324(f251(x41861,x41862),f324(f253(x41863,x41861,x41862,x41862,x41864,f37(x41862)),x41865)),f324(f251(x41863,x41862),x41865))
% 18.55/18.48 [4187]E(f324(f246(x41871,x41872),f324(f253(x41871,x41871,x41873,x41872,f37(x41871),x41874),x41875)),f324(f246(x41871,x41873),x41875))
% 18.55/18.48 [4190]E(f324(f246(x41901,x41902),f324(f253(x41903,x41901,x41902,x41902,x41904,f37(x41902)),x41905)),f324(x41904,f324(f246(x41903,x41902),x41905)))
% 18.55/18.48 [4191]E(f324(f251(x41911,x41912),f324(f253(x41911,x41911,x41913,x41912,f37(x41911),x41914),x41915)),f324(x41914,f324(f251(x41911,x41913),x41915)))
% 18.55/18.48 [4269]P28(x42691,x42692,f324(f324(f303(f837(x42691)),f324(f324(f324(f93(x42691),f324(f324(f9(x42691,f845(a835,a835),f845(a835,a832)),f324(f324(f10(f845(a835,a832),f845(f845(a835,a835),f845(a835,a832)),x42691),f10(a835,a832,a835)),x42693)),f324(f324(f20(a835,a838,a835),f324(f324(f9(a835,a836,f845(a838,a835)),a188),x42694)),x42695))),f28(x42694,x42695)),x42693)),f179(f845(f837(x42691),a832))))
% 18.55/18.48 [4270]P28(x42701,x42702,f324(f324(f303(f837(x42701)),f324(f324(f324(f93(x42701),f324(f324(f9(x42701,f845(a835,a835),f845(a835,a832)),f324(f324(f10(f845(a835,a832),f845(f845(a835,a835),f845(a835,a832)),x42701),f10(a835,a832,a835)),x42703)),f324(f324(f20(a835,a838,a835),f324(f324(f9(a835,a836,f845(a838,a835)),a188),x42704)),x42705))),f28(x42704,x42705)),x42703)),f179(f845(f837(x42701),a832))))
% 18.55/18.48 [4274]P28(x42741,x42742,f324(f324(f303(f837(x42741)),f324(f324(f324(f93(x42741),f324(f324(f9(x42741,f845(a835,a832),f845(a835,a832)),f324(f324(f10(f845(a835,f845(a832,a832)),f845(f845(a835,a832),f845(a835,a832)),x42741),f20(a835,a832,a832)),f324(f324(f10(f845(a835,a832),f845(a835,f845(a832,a832)),x42741),f324(f10(a832,f845(a832,a832),a835),a322)),x42743))),f324(f324(f10(a832,a832,a835),a320),x42744))),f35(x42744,x42745)),x42743)),f179(f845(f837(x42741),a832))))
% 18.55/18.48 [3379]E(f324(f324(f324(f324(f198(x33791),x33792),x33793),x33794),x33795),f193(x33791,x33792))
% 18.55/18.48 [3380]E(f324(f324(f324(f324(f199(x33801),x33802),x33803),x33804),x33805),f184(x33801,x33802))
% 18.55/18.48 [3423]E(f95(x34231,x34232,f324(f324(f324(f93(x34231),x34233),x34234),x34235)),f2(a838))
% 18.55/18.48 [3513]E(f324(f324(f324(f324(f74(x35131,x35132),x35133),x35134),x35135),x35134),x35135)
% 18.55/18.48 [3743]E(f324(f324(f45(x37431,f845(x37432,a832)),f324(f324(f303(x37431),x37433),x37434)),x37435),f324(f324(f103(f845(x37432,a832)),f324(x37435,x37433)),f324(f324(f45(x37431,f845(x37432,a832)),x37434),x37435)))
% 18.55/18.48 [3744]E(f324(f324(f46(x37441,f845(x37442,a832)),f324(f324(f303(x37441),x37443),x37444)),x37445),f324(f324(f104(f845(x37442,a832)),f324(x37445,x37443)),f324(f324(f46(x37441,f845(x37442,a832)),x37444),x37445)))
% 18.55/18.48 [3803]E(f324(f324(f103(f845(x38031,a832)),f324(f304(x38032,x38031,x38033),x38034)),f324(f304(x38032,x38031,x38033),x38035)),f324(f304(x38032,x38031,x38033),f324(f324(f103(f845(x38032,a832)),x38034),x38035)))
% 18.55/18.48 [3804]E(f324(f324(f103(f845(x38041,a832)),f324(f278(x38042,x38041,x38043),x38044)),f324(f278(x38042,x38041,x38043),x38045)),f324(f278(x38042,x38041,x38043),f324(f324(f103(f845(x38042,a832)),x38044),x38045)))
% 18.55/18.48 [3805]E(f324(f324(f3(f845(x38051,a832)),f324(f305(x38051,x38052,x38053),x38054)),f324(f305(x38051,x38052,x38053),x38055)),f324(f305(x38051,x38052,x38053),f324(f324(f3(f845(x38052,a832)),x38054),x38055)))
% 18.55/18.48 [3806]E(f324(f324(f103(f845(x38061,a832)),f324(f305(x38061,x38062,x38063),x38064)),f324(f305(x38061,x38062,x38063),x38065)),f324(f305(x38061,x38062,x38063),f324(f324(f103(f845(x38062,a832)),x38064),x38065)))
% 18.55/18.48 [3807]E(f324(f324(f104(f845(x38071,a832)),f324(f305(x38071,x38072,x38073),x38074)),f324(f305(x38071,x38072,x38073),x38075)),f324(f305(x38071,x38072,x38073),f324(f324(f104(f845(x38072,a832)),x38074),x38075)))
% 18.55/18.48 [3809]E(f171(x38091,x38092,f171(x38091,x38092,x38093,x38094),x38095),f171(x38091,x38092,x38093,f324(f324(f104(f845(x38091,a832)),x38094),x38095)))
% 18.55/18.48 [3811]E(f118(x38111,x38112,f324(x38113,x38114),f324(f324(f9(x38111,a101,f840(x38112)),x38115),x38114)),f324(f191(x38111,x38112,x38113,x38115),x38114))
% 18.55/18.48 [3873]E(f324(f324(f146(x38731,f324(f324(f125(x38731),x38732),f324(f324(f139(x38731),x38733),x38734))),f324(f180(f839(x38731)),x38732)),x38735),f324(f324(f125(x38731),x38732),f324(f324(f139(x38731),x38735),x38734)))
% 18.55/18.48 [3880]E(f324(f324(f46(x38801,f845(x38802,a832)),x38803),f324(f324(f10(f845(x38802,a832),f845(x38802,a832),x38801),f324(f303(x38802),x38804)),x38805)),f324(f324(f303(x38802),x38804),f324(f324(f46(x38801,f845(x38802,a832)),x38803),x38805)))
% 18.55/18.48 [3881]E(f324(f324(f46(x38811,f845(x38812,a832)),x38813),f324(f324(f10(f845(x38812,a832),f845(x38812,a832),x38811),f324(f303(x38812),x38814)),x38815)),f324(f324(f303(x38812),x38814),f324(f324(f46(x38811,f845(x38812,a832)),x38813),x38815)))
% 18.55/18.48 [3952]E(f171(x39521,x39522,f324(f324(f324(f74(x39521,f842(x39522)),x39523),x39524),f324(f226(x39522),x39525)),f324(f81(f845(x39521,a832)),f324(f324(f303(x39521),x39524),f179(f845(x39521,a832))))),f171(x39521,x39522,x39523,f324(f81(f845(x39521,a832)),f324(f324(f303(x39521),x39524),f179(f845(x39521,a832))))))
% 18.55/18.48 [3992]E(f324(f324(f3(f845(f844(x39921,x39922),a832)),f324(f324(f249(x39921,x39922),x39923),f324(f18(f845(x39922,a832),x39921),x39924))),f324(f324(f249(x39921,x39922),x39925),f324(f18(f845(x39922,a832),x39921),x39924))),f324(f324(f249(x39921,x39922),f324(f324(f3(f845(x39921,a832)),x39923),x39925)),f324(f18(f845(x39922,a832),x39921),x39924)))
% 18.55/18.48 [3993]E(f324(f324(f103(f845(f844(x39931,x39932),a832)),f324(f324(f249(x39931,x39932),x39933),f324(f18(f845(x39932,a832),x39931),x39934))),f324(f324(f249(x39931,x39932),x39935),f324(f18(f845(x39932,a832),x39931),x39934))),f324(f324(f249(x39931,x39932),f324(f324(f103(f845(x39931,a832)),x39933),x39935)),f324(f18(f845(x39932,a832),x39931),x39934)))
% 18.55/18.48 [3994]E(f324(f324(f104(f845(f844(x39941,x39942),a832)),f324(f324(f249(x39941,x39942),x39943),f324(f18(f845(x39942,a832),x39941),x39944))),f324(f324(f249(x39941,x39942),x39945),f324(f18(f845(x39942,a832),x39941),x39944))),f324(f324(f249(x39941,x39942),f324(f324(f104(f845(x39941,a832)),x39943),x39945)),f324(f18(f845(x39942,a832),x39941),x39944)))
% 18.55/18.48 [4035]E(f324(f324(f141(x40351,x40352),x40353),f324(f126(x40351,f324(f75(x40352,a832,x40351,x40354),x40353)),x40355)),f324(f126(x40352,x40354),f324(f324(f141(x40351,x40352),x40353),x40355)))
% 18.55/18.48 [4042]E(f324(f180(f839(x40421)),f324(f126(x40421,x40422),f324(f324(f141(x40423,x40421),x40424),x40425))),f324(f180(f839(x40423)),f324(f126(x40423,f324(f75(x40421,a832,x40423,x40422),x40424)),x40425)))
% 18.55/18.48 [4178]E(f324(f324(f103(f845(x41781,a832)),f324(f324(f3(f845(x41781,a832)),f168(x41781,x41782,x41783)),f324(f257(x41781),f324(f324(f9(x41781,f845(x41781,a832),a832),f326(x41781)),f324(f324(f3(f845(x41781,a832)),x41784),f168(x41781,x41782,x41785)))))),f324(f257(x41781),f324(f324(f9(x41781,f845(x41781,a832),a832),f326(x41781)),f324(f324(f104(f845(x41781,a832)),x41784),f168(x41781,x41782,x41785))))),f168(x41781,x41782,f78(x41781,f842(x41782),x41783,x41785,x41784)))
% 18.55/18.48 [4251]E(f324(f143(f839(f844(x42511,x42512)),x42512,f115(f844(x42511,x42512)),f324(f324(f9(x42512,f845(f839(x42512),f839(f844(x42511,x42512))),f845(f839(x42512),f839(f844(x42511,x42512)))),f324(f324(f10(f845(f839(f844(x42511,x42512)),f839(f844(x42511,x42512))),f845(f845(f839(x42512),f839(f844(x42511,x42512))),f845(f839(x42512),f839(f844(x42511,x42512)))),x42512),f10(f839(f844(x42511,x42512)),f839(f844(x42511,x42512)),f839(x42512))),f324(f324(f10(f844(x42511,x42512),f845(f839(f844(x42511,x42512)),f839(f844(x42511,x42512))),x42512),f139(f844(x42511,x42512))),f324(f247(x42511,x42512),x42513)))),f324(f166(x42511,x42512),x42514))),x42515),f324(f324(f166(x42511,x42512),f324(f324(f139(x42511),x42513),x42514)),x42515))
% 18.55/18.48 [3738]E(f324(f324(f146(x37381,f324(f324(f146(x37381,x37382),x37383),x37384)),x37383),x37385),f324(f324(f146(x37381,x37382),x37383),x37385))
% 18.55/18.48 [3786]E(f324(f260(x37861,x37862),f324(f324(f303(f844(x37861,x37862)),f324(f324(f247(x37861,x37862),x37863),x37864)),x37865)),f324(f324(f303(x37862),x37864),f324(f260(x37861,x37862),x37865)))
% 18.55/18.48 [3787]E(f324(f262(x37871,x37872),f324(f324(f303(f844(x37871,x37872)),f324(f324(f247(x37871,x37872),x37873),x37874)),x37875)),f324(f324(f303(x37871),x37873),f324(f262(x37871,x37872),x37875)))
% 18.55/18.48 [3836]E(f122(x38361,x38362,f324(x38363,x38364),f324(f324(f9(x38361,a101,f840(f842(x38362))),x38365),x38364)),f324(f189(x38361,x38362,x38363,x38365),x38364))
% 18.55/18.48 [3866]E(f324(f324(f3(f845(f844(x38661,x38662),a832)),f324(f324(f249(x38661,x38662),x38663),x38664)),f324(f324(f249(x38661,x38662),x38665),x38664)),f324(f324(f249(x38661,x38662),f324(f324(f3(f845(x38661,a832)),x38663),x38665)),x38664))
% 18.55/18.48 [3867]E(f324(f324(f103(f845(f844(x38671,x38672),a832)),f324(f324(f249(x38671,x38672),x38673),x38674)),f324(f324(f249(x38671,x38672),x38675),x38674)),f324(f324(f249(x38671,x38672),f324(f324(f103(f845(x38671,a832)),x38673),x38675)),x38674))
% 18.55/18.48 [3868]E(f324(f324(f104(f845(f844(x38681,x38682),a832)),f324(f324(f249(x38681,x38682),x38683),x38684)),f324(f324(f249(x38681,x38682),x38685),x38684)),f324(f324(f249(x38681,x38682),f324(f324(f104(f845(x38681,a832)),x38683),x38685)),x38684))
% 18.55/18.48 [3930]E(f324(f324(f103(f845(x39301,a832)),f324(f324(f45(x39302,f845(x39301,a832)),x39303),x39304)),f324(f324(f45(x39302,f845(x39301,a832)),x39305),x39304)),f324(f324(f45(x39302,f845(x39301,a832)),f324(f324(f103(f845(x39302,a832)),x39303),x39305)),x39304))
% 18.55/18.48 [3931]E(f324(f324(f104(f845(x39311,a832)),f324(f324(f46(x39312,f845(x39311,a832)),x39313),x39314)),f324(f324(f46(x39312,f845(x39311,a832)),x39315),x39314)),f324(f324(f46(x39312,f845(x39311,a832)),f324(f324(f103(f845(x39312,a832)),x39313),x39315)),x39314))
% 18.55/18.48 [3940]E(f324(f324(f45(x39401,f845(x39402,a832)),x39403),f324(f324(f10(f845(x39402,a832),f845(x39402,a832),x39401),f324(f3(f845(x39402,a832)),x39404)),x39405)),f324(f324(f3(f845(x39402,a832)),x39404),f324(f324(f46(x39401,f845(x39402,a832)),x39403),x39405)))
% 18.55/18.48 [3941]E(f324(f324(f46(x39411,f845(x39412,a832)),x39413),f324(f324(f10(f845(x39412,a832),f845(x39412,a832),x39411),f324(f103(f845(x39412,a832)),x39414)),x39415)),f324(f324(f103(f845(x39412,a832)),x39414),f324(f324(f46(x39411,f845(x39412,a832)),x39413),x39415)))
% 18.55/18.48 [3942]E(f324(f324(f46(x39421,f845(x39422,a832)),x39423),f324(f324(f10(f845(x39422,a832),f845(x39422,a832),x39421),f324(f103(f845(x39422,a832)),x39424)),x39425)),f324(f324(f103(f845(x39422,a832)),x39424),f324(f324(f46(x39421,f845(x39422,a832)),x39423),x39425)))
% 18.55/18.48 [3943]E(f324(f324(f45(x39431,f845(x39432,a832)),x39433),f324(f324(f10(f845(x39432,a832),f845(x39432,a832),x39431),f324(f104(f845(x39432,a832)),x39434)),x39435)),f324(f324(f104(f845(x39432,a832)),x39434),f324(f324(f45(x39431,f845(x39432,a832)),x39433),x39435)))
% 18.55/18.48 [3944]E(f324(f324(f45(x39441,f845(x39442,a832)),x39443),f324(f324(f10(f845(x39442,a832),f845(x39442,a832),x39441),f324(f104(f845(x39442,a832)),x39444)),x39445)),f324(f324(f104(f845(x39442,a832)),x39444),f324(f324(f45(x39441,f845(x39442,a832)),x39443),x39445)))
% 18.55/18.48 [3945]E(f324(f324(f45(x39451,f845(x39452,a832)),x39453),f324(f324(f10(f845(x39452,a832),f845(x39452,a832),x39451),f324(f3(f845(x39452,a832)),x39454)),x39455)),f324(f324(f3(f845(x39452,a832)),x39454),f324(f324(f46(x39451,f845(x39452,a832)),x39453),x39455)))
% 18.55/18.48 [3946]E(f324(f324(f45(x39461,f845(x39462,a832)),x39463),f324(f324(f10(f845(x39462,a832),f845(x39462,a832),x39461),f324(f104(f845(x39462,a832)),x39464)),x39465)),f324(f324(f104(f845(x39462,a832)),x39464),f324(f324(f45(x39461,f845(x39462,a832)),x39463),x39465)))
% 18.55/18.48 [3947]E(f324(f324(f46(x39471,f845(x39472,a832)),x39473),f324(f324(f10(f845(x39472,a832),f845(x39472,a832),x39471),f324(f103(f845(x39472,a832)),x39474)),x39475)),f324(f324(f103(f845(x39472,a832)),x39474),f324(f324(f46(x39471,f845(x39472,a832)),x39473),x39475)))
% 18.55/18.48 [4002]E(f174(f839(x40021),f324(f324(f139(x40021),x40022),x40023),f324(f324(f10(f839(x40021),f839(x40021),a838),f324(f139(x40021),x40024)),f324(f324(f9(a838,x40021,f839(x40021)),f146(x40021,x40023)),x40022)),x40025),f324(f324(f146(x40021,f324(f324(f139(x40021),x40024),x40023)),x40025),x40022))
% 18.55/18.48 [4006]E(f324(f324(f45(x40061,f845(f844(x40062,x40063),a832)),x40064),f324(f324(f10(f845(f844(x40063,x40062),a832),f845(f844(x40062,x40063),a832),x40061),f279(x40063,x40062)),x40065)),f324(f279(x40063,x40062),f324(f324(f45(x40061,f845(f844(x40063,x40062),a832)),x40064),x40065)))
% 18.55/18.48 [4007]E(f324(f324(f46(x40071,f845(f844(x40072,x40073),a832)),x40074),f324(f324(f10(f845(f844(x40073,x40072),a832),f845(f844(x40072,x40073),a832),x40071),f279(x40073,x40072)),x40075)),f324(f279(x40073,x40072),f324(f324(f46(x40071,f845(f844(x40073,x40072),a832)),x40074),x40075)))
% 18.55/18.48 [4061]E(f168(x40611,x40612,f324(f324(f20(x40611,f842(x40613),f842(x40612)),f324(f324(f10(f845(x40613,x40612),f845(f842(x40613),f842(x40612)),x40611),f195(x40613,x40612)),x40614)),x40615)),f168(x40611,x40613,x40615))
% 18.55/18.48 [4111]P1(f324(f324(f231(f845(x41111,a832)),f324(f324(f3(f845(x41111,a832)),f324(f304(x41112,x41111,x41113),x41114)),f324(f304(x41112,x41111,x41113),x41115))),f324(f304(x41112,x41111,x41113),f324(f324(f3(f845(x41112,a832)),x41114),x41115))))
% 18.55/18.48 [4255]E(f324(f143(f839(f844(x42551,x42552)),x42551,f115(f844(x42551,x42552)),f324(f324(f9(x42551,f845(f839(x42551),f839(f844(x42551,x42552))),f845(f839(x42551),f839(f844(x42551,x42552)))),f324(f324(f10(f845(f839(f844(x42551,x42552)),f839(f844(x42551,x42552))),f845(f845(f839(x42551),f839(f844(x42551,x42552))),f845(f839(x42551),f839(f844(x42551,x42552)))),x42551),f10(f839(f844(x42551,x42552)),f839(f844(x42551,x42552)),f839(x42551))),f324(f324(f10(f844(x42551,x42552),f845(f839(f844(x42551,x42552)),f839(f844(x42551,x42552))),x42551),f139(f844(x42551,x42552))),f324(f324(f9(x42551,x42552,f844(x42551,x42552)),f247(x42551,x42552)),x42553)))),f324(f324(f9(f839(x42551),f839(x42552),f839(f844(x42551,x42552))),f166(x42551,x42552)),x42554))),x42555),f324(f324(f166(x42551,x42552),x42555),f324(f324(f139(x42552),x42553),x42554)))
% 18.55/18.48 [4272]E(f324(f131(f845(x42721,f842(x42722)),f844(x42721,x42722),f324(f324(f10(f845(x42721,f845(x42722,f845(x42721,f842(x42722)))),f845(f844(x42721,x42722),f845(x42721,f842(x42722))),f845(x42721,f842(x42722))),f252(x42721,x42722,f845(x42721,f842(x42722)))),f324(f324(f9(f845(x42721,f842(x42722)),f845(x42722,f842(x42722)),f845(x42721,f845(x42722,f845(x42721,f842(x42722))))),f324(f324(f10(f845(x42721,f845(f845(x42722,f842(x42722)),f845(x42722,f845(x42721,f842(x42722))))),f845(f845(x42722,f842(x42722)),f845(x42721,f845(x42722,f845(x42721,f842(x42722))))),f845(x42721,f842(x42722))),f9(x42721,f845(x42722,f842(x42722)),f845(x42722,f845(x42721,f842(x42722))))),f324(f324(f10(f845(x42721,f845(f842(x42722),f845(x42721,f842(x42722)))),f845(x42721,f845(f845(x42722,f842(x42722)),f845(x42722,f845(x42721,f842(x42722))))),f845(x42721,f842(x42722))),f324(f10(f845(f842(x42722),f845(x42721,f842(x42722))),f845(f845(x42722,f842(x42722)),f845(x42722,f845(x42721,f842(x42722)))),x42721),f10(f842(x42722),f845(x42721,f842(x42722)),x42722))),f74(x42721,f842(x42722))))),f226(x42722))),x42723),f324(f324(f166(x42721,x42722),x42724),x42725)),f169(x42721,x42722,x42723,f165(x42721,x42722,f324(f154(f844(x42721,x42722)),f324(f324(f166(x42721,x42722),x42724),x42725)))))
% 18.55/18.48 [3971]E(f324(f324(f103(f845(x39711,a832)),f324(f278(x39712,x39711,x39713),x39714)),f324(f278(x39712,x39711,x39715),x39714)),f324(f278(x39712,x39711,f324(f324(f103(f845(f844(x39712,x39711),a832)),x39713),x39715)),x39714))
% 18.55/18.48 [4009]E(f324(f324(f125(f844(x40091,x40092)),f324(f324(f166(x40091,x40092),x40093),f324(f324(f158(x40092),f324(f180(f839(x40091)),x40093)),x40094))),f324(f324(f166(x40091,x40092),x40095),f324(f324(f128(x40092),f324(f180(f839(x40091)),x40093)),x40094))),f324(f324(f166(x40091,x40092),f324(f324(f125(x40091),x40093),x40095)),x40094))
% 18.55/18.48 [4039]E(f168(x40391,x40392,f169(x40391,x40392,x40393,f165(x40391,x40392,f324(f154(f844(x40391,x40392)),f324(f324(f166(x40391,x40392),x40394),x40395))))),f324(f324(f103(f845(x40391,a832)),f324(f157(x40391),f324(f324(f158(x40391),f324(f180(f839(x40392)),x40395)),x40394))),f168(x40391,x40392,x40393)))
% 18.55/18.48 [4114]E(f324(f324(f249(x41141,x41142),x41143),f324(f324(f20(x41141,f845(x41142,a832),f845(x41142,a832)),f324(f324(f10(f845(x41142,a832),f845(f845(x41142,a832),f845(x41142,a832)),x41141),f3(f845(x41142,a832))),x41144)),x41145)),f324(f324(f3(f845(f844(x41141,x41142),a832)),f324(f324(f249(x41141,x41142),x41143),x41144)),f324(f324(f249(x41141,x41142),x41143),x41145)))
% 18.55/18.48 [4115]E(f324(f324(f249(x41151,x41152),x41153),f324(f324(f20(x41151,f845(x41152,a832),f845(x41152,a832)),f324(f324(f10(f845(x41152,a832),f845(f845(x41152,a832),f845(x41152,a832)),x41151),f103(f845(x41152,a832))),x41154)),x41155)),f324(f324(f103(f845(f844(x41151,x41152),a832)),f324(f324(f249(x41151,x41152),x41153),x41154)),f324(f324(f249(x41151,x41152),x41153),x41155)))
% 18.55/18.48 [4116]E(f324(f324(f249(x41161,x41162),x41163),f324(f324(f20(x41161,f845(x41162,a832),f845(x41162,a832)),f324(f324(f10(f845(x41162,a832),f845(f845(x41162,a832),f845(x41162,a832)),x41161),f104(f845(x41162,a832))),x41164)),x41165)),f324(f324(f104(f845(f844(x41161,x41162),a832)),f324(f324(f249(x41161,x41162),x41163),x41164)),f324(f324(f249(x41161,x41162),x41163),x41165)))
% 18.55/18.48 [4117]E(f324(f324(f45(x41171,f845(x41172,a832)),x41173),f324(f324(f9(x41171,f845(x41172,a832),f845(x41172,a832)),f324(f324(f10(f845(x41172,a832),f845(f845(x41172,a832),f845(x41172,a832)),x41171),f3(f845(x41172,a832))),x41174)),x41175)),f324(f324(f3(f845(x41172,a832)),f324(f324(f45(x41171,f845(x41172,a832)),x41173),x41174)),x41175))
% 18.55/18.48 [4118]E(f324(f324(f46(x41181,f845(x41182,a832)),x41183),f324(f324(f9(x41181,f845(x41182,a832),f845(x41182,a832)),f324(f324(f10(f845(x41182,a832),f845(f845(x41182,a832),f845(x41182,a832)),x41181),f103(f845(x41182,a832))),x41184)),x41185)),f324(f324(f103(f845(x41182,a832)),f324(f324(f46(x41181,f845(x41182,a832)),x41183),x41184)),x41185))
% 18.55/18.48 [4119]E(f324(f324(f45(x41191,f845(x41192,a832)),x41193),f324(f324(f9(x41191,f845(x41192,a832),f845(x41192,a832)),f324(f324(f10(f845(x41192,a832),f845(f845(x41192,a832),f845(x41192,a832)),x41191),f104(f845(x41192,a832))),x41194)),x41195)),f324(f324(f104(f845(x41192,a832)),f324(f324(f45(x41191,f845(x41192,a832)),x41193),x41194)),x41195))
% 18.55/18.48 [4120]E(f324(f324(f45(x41201,f845(x41202,a832)),x41203),f324(f324(f9(x41201,f845(x41202,a832),f845(x41202,a832)),f324(f324(f10(f845(x41202,a832),f845(f845(x41202,a832),f845(x41202,a832)),x41201),f3(f845(x41202,a832))),x41204)),x41205)),f324(f324(f3(f845(x41202,a832)),f324(f324(f45(x41201,f845(x41202,a832)),x41203),x41204)),x41205))
% 18.55/18.48 [4121]E(f324(f324(f45(x41211,f845(x41212,a832)),x41213),f324(f324(f9(x41211,f845(x41212,a832),f845(x41212,a832)),f324(f324(f10(f845(x41212,a832),f845(f845(x41212,a832),f845(x41212,a832)),x41211),f104(f845(x41212,a832))),x41214)),x41215)),f324(f324(f104(f845(x41212,a832)),f324(f324(f45(x41211,f845(x41212,a832)),x41213),x41214)),x41215))
% 18.55/18.48 [4122]E(f324(f324(f46(x41221,f845(x41222,a832)),x41223),f324(f324(f9(x41221,f845(x41222,a832),f845(x41222,a832)),f324(f324(f10(f845(x41222,a832),f845(f845(x41222,a832),f845(x41222,a832)),x41221),f103(f845(x41222,a832))),x41224)),x41225)),f324(f324(f103(f845(x41222,a832)),f324(f324(f46(x41221,f845(x41222,a832)),x41223),x41224)),x41225))
% 18.55/18.48 [4126]E(f324(f324(f45(x41261,f845(x41262,a832)),x41263),f324(f324(f20(x41261,f845(x41262,a832),f845(x41262,a832)),f324(f324(f10(f845(x41262,a832),f845(f845(x41262,a832),f845(x41262,a832)),x41261),f103(f845(x41262,a832))),x41264)),x41265)),f324(f324(f103(f845(x41262,a832)),f324(f324(f45(x41261,f845(x41262,a832)),x41263),x41264)),f324(f324(f45(x41261,f845(x41262,a832)),x41263),x41265)))
% 18.55/18.48 [4127]E(f324(f324(f46(x41271,f845(x41272,a832)),x41273),f324(f324(f20(x41271,f845(x41272,a832),f845(x41272,a832)),f324(f324(f10(f845(x41272,a832),f845(f845(x41272,a832),f845(x41272,a832)),x41271),f104(f845(x41272,a832))),x41274)),x41275)),f324(f324(f104(f845(x41272,a832)),f324(f324(f46(x41271,f845(x41272,a832)),x41273),x41274)),f324(f324(f46(x41271,f845(x41272,a832)),x41273),x41275)))
% 18.55/18.48 [4140]E(f324(f324(f45(x41401,f845(x41402,a832)),x41403),f324(f324(f20(x41401,f845(x41402,a832),f845(x41402,a832)),f324(f324(f10(f845(x41402,a832),f845(f845(x41402,a832),f845(x41402,a832)),x41401),f103(f845(x41402,a832))),x41404)),x41405)),f324(f324(f103(f845(x41402,a832)),f43(f845(x41402,a832),f324(f304(x41401,f845(x41402,a832),x41404),x41403))),f43(f845(x41402,a832),f324(f304(x41401,f845(x41402,a832),x41405),x41403))))
% 18.55/18.48 [4141]E(f324(f324(f46(x41411,f845(x41412,a832)),x41413),f324(f324(f20(x41411,f845(x41412,a832),f845(x41412,a832)),f324(f324(f10(f845(x41412,a832),f845(f845(x41412,a832),f845(x41412,a832)),x41411),f104(f845(x41412,a832))),x41414)),x41415)),f324(f324(f104(f845(x41412,a832)),f44(f845(x41412,a832),f324(f304(x41411,f845(x41412,a832),x41414),x41413))),f44(f845(x41412,a832),f324(f304(x41411,f845(x41412,a832),x41415),x41413))))
% 18.55/18.48 [4174]E(f324(f324(f128(x41741),f324(f180(f839(x41741)),f161(x41741,x41742,f324(f324(f141(x41743,x41741),x41744),x41745)))),f324(f324(f141(x41743,x41741),x41744),x41745)),f324(f324(f141(x41743,x41741),x41744),f324(f324(f128(x41743),f324(f180(f839(x41743)),f161(x41743,f324(f75(x41741,a832,x41743,x41742),x41744),x41745))),x41745)))
% 18.55/18.48 [4051]E(f324(f324(f125(f844(x40511,x40512)),f324(f324(f166(x40511,x40512),f324(f324(f158(x40511),f324(f180(f839(x40512)),x40513)),x40514)),x40513)),f324(f324(f166(x40511,x40512),f324(f324(f128(x40511),f324(f180(f839(x40512)),x40513)),x40514)),x40515)),f324(f324(f166(x40511,x40512),x40514),f324(f324(f125(x40512),x40513),x40515)))
% 18.55/18.48 [4166]E(f87(x41661,f324(f324(f20(x41661,a832,a832),f324(f324(f10(a832,f845(a832,a832),x41661),a322),f324(f324(f9(x41661,f845(x41661,a832),a832),f326(x41661)),x41662))),f324(f324(f9(x41661,x41663,a832),f324(f324(f10(x41663,f845(x41663,a832),x41661),a321),x41664)),x41665))),f324(f79(x41661,x41663,x41662,x41664),x41665))
% 18.55/18.48 [4217]E(f324(f324(f88(a1,x42171),f324(f106(a1),f324(f324(f82(a1),x42172),a99))),f324(f324(f20(a1,x42171,x42171),f324(f324(f9(a1,x42171,f845(x42171,x42171)),f324(f324(f10(a832,f845(x42171,f845(x42171,x42171)),a1),f98(x42171)),a185)),f174(x42171,x42173,x42174,x42175))),f324(f324(f10(a838,x42171,a1),x42174),f324(f324(f9(a1,a838,a838),f324(f324(f10(a838,f845(a838,a838),a1),f82(a838)),a107)),x42175)))),f174(x42171,x42173,x42174,f324(f324(f82(a838),f324(f106(a838),x42172)),x42175)))
% 18.55/18.48 [4252]E(f165(x42521,x42522,f324(f324(f141(f844(x42521,x42523),f844(x42521,x42522)),f324(f252(x42521,x42523,f844(x42521,x42522)),f324(f324(f9(x42521,f845(x42523,x42522),f845(x42523,f844(x42521,x42522))),f324(f324(f10(f845(x42522,f844(x42521,x42522)),f845(f845(x42523,x42522),f845(x42523,f844(x42521,x42522))),x42521),f10(x42522,f844(x42521,x42522),x42523)),f247(x42521,x42522))),x42524))),x42525)),f324(f75(f842(x42523),f842(x42522),x42521,f324(f195(x42523,x42522),x42524)),f165(x42521,x42523,x42525)))
% 18.55/18.48 [4210]E(f168(x42101,x42102,f324(f324(f20(x42101,f842(x42102),f842(x42102)),f324(f324(f20(x42101,f842(x42102),f845(f842(x42102),f842(x42102))),f324(f324(f10(a832,f845(f842(x42102),f845(f842(x42102),f842(x42102))),x42101),f98(f842(x42102))),x42103)),x42104)),x42105)),f324(f324(f103(f845(x42101,a832)),f324(f324(f104(f845(x42101,a832)),f168(x42101,x42102,x42104)),f324(f257(x42101),x42103))),f324(f324(f104(f845(x42101,a832)),f168(x42101,x42102,x42105)),f324(f257(x42101),f324(f324(f10(a832,a832,x42101),a320),x42103)))))
% 18.55/18.48 [4250]E(f324(f324(f88(a1,x42501),f324(f106(a1),f324(f324(f82(a1),x42502),a99))),f324(f324(f20(a1,x42501,x42501),f324(f324(f9(a1,x42501,f845(x42501,x42501)),f324(f324(f10(a832,f845(x42501,f845(x42501,x42501)),a1),f98(x42501)),a185)),f324(f173(x42501,x42503,x42504),x42505))),f324(f324(f20(a1,x42501,x42501),f324(f324(f10(a838,f845(x42501,x42501),a1),x42504),f324(f324(f9(a1,a838,a838),f324(f324(f10(a838,f845(a838,a838),a1),f82(a838)),a107)),x42505))),f324(f324(f10(a838,x42501,a1),f173(x42501,x42503,x42504)),f324(f324(f9(a1,a838,a838),f324(f324(f10(a838,f845(a838,a838),a1),f82(a838)),a107)),x42505))))),f324(f173(x42501,x42503,x42504),f324(f324(f82(a838),f324(f106(a838),x42502)),x42505)))
% 18.55/18.48 [4285]E(f324(f257(f844(x42851,x42852)),f324(f252(x42851,x42852,a832),f324(f324(f10(f845(x42852,f845(x42853,a832)),f845(x42852,a832),x42851),f324(f10(f845(x42853,a832),a832,x42852),f89(x42853))),f324(f324(f9(x42851,f845(x42852,f845(x42853,a832)),f845(x42852,f845(x42853,a832))),f324(f324(f10(f845(f845(x42853,a832),f845(x42853,a832)),f845(f845(x42852,f845(x42853,a832)),f845(x42852,f845(x42853,a832))),x42851),f10(f845(x42853,a832),f845(x42853,a832),x42852)),f324(f324(f10(f845(x42853,f845(a832,a832)),f845(f845(x42853,a832),f845(x42853,a832)),x42851),f20(x42853,a832,a832)),f324(f324(f10(f845(x42853,a832),f845(x42853,f845(a832,a832)),x42851),f324(f10(a832,f845(a832,a832),x42853),a322)),f324(f324(f9(x42851,f845(f844(x42851,x42853),a832),f845(x42853,a832)),f324(f324(f10(f845(x42853,f845(f845(f844(x42851,x42853),a832),a832)),f845(f845(f844(x42851,x42853),a832),f845(x42853,a832)),x42851),f9(x42853,f845(f844(x42851,x42853),a832),a832)),f324(f324(f10(f845(x42853,f844(x42851,x42853)),f845(x42853,f845(f845(f844(x42851,x42853),a832),a832)),x42851),f324(f10(f844(x42851,x42853),f845(f845(f844(x42851,x42853),a832),a832),x42853),f326(f844(x42851,x42853)))),f247(x42851,x42853)))),x42854))))),f324(f324(f9(x42852,f845(f844(x42853,x42852),a832),f845(x42853,a832)),f324(f324(f10(f845(x42853,f845(f845(f844(x42853,x42852),a832),a832)),f845(f845(f844(x42853,x42852),a832),f845(x42853,a832)),x42852),f9(x42853,f845(f844(x42853,x42852),a832),a832)),f324(f324(f10(f845(x42853,f844(x42853,x42852)),f845(x42853,f845(f845(f844(x42853,x42852),a832),a832)),x42852),f324(f10(f844(x42853,x42852),f845(f845(f844(x42853,x42852),a832),a832),x42853),f326(f844(x42853,x42852)))),f324(f9(x42853,x42852,f844(x42853,x42852)),f247(x42853,x42852))))),x42855))))),f324(f324(f282(x42851,x42853,x42852),x42854),x42855))
% 18.55/18.48 [4379]~E(f33(x43791,x43792,x43793),f31(x43794,x43795,x43796))
% 18.55/18.48 [4380]~E(f33(x43801,x43802,x43803),f31(x43804,x43805,x43806))
% 18.55/18.48 [4381]~E(f32(x43811,x43812,x43813),f31(x43814,x43815,x43816))
% 18.55/18.48 [4382]~E(f32(x43821,x43822,x43823),f33(x43824,x43825,x43826))
% 18.55/18.48 [4383]~E(f32(x43831,x43832,x43833),f31(x43834,x43835,x43836))
% 18.55/18.48 [4384]~E(f32(x43841,x43842,x43843),f33(x43844,x43845,x43846))
% 18.55/18.48 [3898]E(f217(x38981,x38982,x38983,x38984,f214(x38981,x38982,x38985,x38986)),f324(f324(x38984,x38985),x38986))
% 18.55/18.48 [3899]E(f218(x38991,x38992,x38993,x38994,f214(x38991,x38992,x38995,x38996)),f324(f324(x38994,x38995),x38996))
% 18.55/18.48 [4156]E(f324(f75(f844(x41561,x41562),x41562,f844(x41563,x41564),f251(x41561,x41562)),f253(x41563,x41561,x41564,x41562,x41565,x41566)),f324(f75(x41564,x41562,f844(x41563,x41564),x41566),f251(x41563,x41564)))
% 18.55/18.48 [4157]E(f324(f75(f844(x41571,x41572),x41571,f844(x41573,x41574),f246(x41571,x41572)),f253(x41573,x41571,x41574,x41572,x41575,x41576)),f324(f75(x41573,x41571,f844(x41573,x41574),x41575),f246(x41573,x41574)))
% 18.55/18.48 [3761]E(f324(f324(f75(x37611,x37612,x37613,x37614),x37615),x37616),f324(x37614,f324(x37615,x37616)))
% 18.55/18.48 [3762]E(f324(f324(f75(x37621,x37622,x37623,x37624),x37625),x37626),f324(x37624,f324(x37625,x37626)))
% 18.55/18.48 [3960]E(f219(x39601,x39602,x39603,x39604,f214(x39601,x39602,x39605,x39606)),f324(f324(f82(a838),f324(f324(f82(a838),f324(x39603,x39605)),f324(x39604,x39606))),f324(a114,f2(a838))))
% 18.55/18.48 [3558]E(f324(f324(f252(x35581,x35582,x35583),x35584),f324(f324(f247(x35581,x35582),x35585),x35586)),f324(f324(x35584,x35585),x35586))
% 18.55/18.48 [3559]E(f324(f324(f252(x35591,x35592,x35593),x35594),f324(f324(f247(x35591,x35592),x35595),x35596)),f324(f324(x35594,x35595),x35596))
% 18.55/18.48 [3560]E(f324(f324(f252(x35601,x35602,x35603),x35604),f324(f324(f247(x35601,x35602),x35605),x35606)),f324(f324(x35604,x35605),x35606))
% 18.55/18.48 [3623]E(f324(f324(f324(f10(x36231,x36232,x36233),x36234),x36235),x36236),f324(x36234,f324(x36235,x36236)))
% 18.55/18.48 [3624]E(f324(f324(f324(f9(x36241,x36242,x36243),x36244),x36245),x36246),f324(f324(x36244,x36246),x36245))
% 18.55/18.48 [3640]E(f324(f324(f324(f20(x36401,x36402,x36403),x36404),x36405),x36406),f324(f324(x36404,x36406),f324(x36405,x36406)))
% 18.55/18.48 [3662]E(f324(f143(x36621,x36622,x36623,x36624),f324(f324(f139(x36622),x36625),x36626)),f324(f324(x36624,x36625),x36626))
% 18.55/18.48 [3765]E(f324(f324(f139(f844(x37651,x37652)),f324(f324(f247(x37651,x37652),x37653),x37654)),f324(f324(f166(x37651,x37652),x37655),x37656)),f324(f324(f166(x37651,x37652),f324(f324(f139(x37651),x37653),x37655)),f324(f324(f139(x37652),x37654),x37656)))
% 18.55/18.48 [3767]E(f324(f324(f141(x37671,x37672),x37673),f324(f324(f146(x37671,x37674),x37675),x37676)),f324(f324(f146(x37672,f324(f324(f141(x37671,x37672),x37673),x37674)),x37675),f324(x37673,x37676)))
% 18.55/18.48 [3789]E(f324(f324(f250(x37891,x37892,x37893,x37894),x37895),x37896),f324(x37894,f324(f324(f247(x37891,x37892),x37895),x37896)))
% 18.55/18.48 [3790]E(f324(f324(f250(x37901,x37902,x37903,x37904),x37905),x37906),f324(x37904,f324(f324(f247(x37901,x37902),x37905),x37906)))
% 18.55/18.48 [3808]E(f324(f131(x38081,x38082,x38083,x38084),f324(f324(f139(x38082),x38085),x38086)),f324(f131(x38081,x38082,x38083,f324(f324(x38083,x38084),x38085)),x38086))
% 18.55/18.48 [3837]E(f255(x38371,x38372,x38373,x38374,f324(f324(f247(x38371,x38372),x38375),x38376)),f324(f324(x38374,x38375),x38376))
% 18.55/18.48 [3923]E(f324(f324(f45(x39231,f845(x39232,a832)),x39233),f324(f75(x39234,f845(x39232,a832),x39231,x39235),x39236)),f324(f324(f45(x39234,f845(x39232,a832)),f324(f304(x39231,x39234,x39236),x39233)),x39235))
% 18.55/18.48 [3973]E(f324(f324(f141(x39731,x39732),x39733),f324(f324(f141(x39734,x39731),x39735),x39736)),f324(f324(f141(x39734,x39732),f324(f75(x39731,x39732,x39734,x39733),x39735)),x39736))
% 18.55/18.48 [3974]E(f324(f324(f141(x39741,x39742),x39743),f324(f324(f141(x39744,x39741),x39745),x39746)),f324(f324(f141(x39744,x39742),f324(f75(x39741,x39742,x39744,x39743),x39745)),x39746))
% 18.55/18.48 [3975]E(f324(f324(f195(x39751,x39752),x39753),f324(f324(f195(x39754,x39751),x39755),x39756)),f324(f324(f195(x39754,x39752),f324(f75(x39751,x39752,x39754,x39753),x39755)),x39756))
% 18.55/18.48 [3976]E(f324(f324(f195(x39761,x39762),x39763),f324(f324(f195(x39764,x39761),x39765),x39766)),f324(f324(f195(x39764,x39762),f324(f75(x39761,x39762,x39764,x39763),x39765)),x39766))
% 18.55/18.48 [3980]E(f324(f304(x39801,x39802,f324(f75(x39803,x39802,x39801,x39804),x39805)),x39806),f324(f304(x39803,x39802,x39804),f324(f304(x39801,x39803,x39805),x39806)))
% 18.55/18.48 [3981]E(f324(f305(x39811,x39812,f324(f75(x39813,x39812,x39811,x39814),x39815)),x39816),f324(f305(x39811,x39813,x39815),f324(f305(x39813,x39812,x39814),x39816)))
% 18.55/18.48 [4008]E(f169(x40081,x40082,x40083,f324(f324(f324(f74(x40081,f842(x40082)),x40084),x40085),f324(f226(x40082),x40086))),f324(f324(f324(f74(x40081,f842(x40082)),f169(x40081,x40082,x40083,x40084)),x40085),f324(f226(x40082),x40086)))
% 18.55/18.48 [4010]E(f324(f131(x40101,x40102,x40103,f324(f131(x40101,x40102,x40103,x40104),x40105)),x40106),f324(f131(x40101,x40102,x40103,x40104),f324(f324(f125(x40102),x40105),x40106)))
% 18.55/18.48 [4146]E(f324(f253(x41461,x41461,x41462,x41463,f37(x41461),x41464),f324(f324(f247(x41461,x41462),x41465),x41466)),f324(f324(f247(x41461,x41463),x41465),f324(x41464,x41466)))
% 18.55/18.48 [4147]E(f324(f253(x41471,x41472,x41473,x41473,x41474,f37(x41473)),f324(f324(f247(x41471,x41473),x41475),x41476)),f324(f324(f247(x41472,x41473),f324(x41474,x41475)),x41476))
% 18.55/18.48 [4234]E(f324(f324(f141(f844(x42341,x42342),f844(x42341,x42343)),f324(f252(x42341,x42342,f844(x42341,x42343)),f324(f324(f9(x42341,f845(x42342,x42343),f845(x42342,f844(x42341,x42343))),f324(f324(f10(f845(x42343,f844(x42341,x42343)),f845(f845(x42342,x42343),f845(x42342,f844(x42341,x42343))),x42341),f10(x42343,f844(x42341,x42343),x42342)),f247(x42341,x42343))),x42344))),f324(f324(f166(x42341,x42342),x42345),x42346)),f324(f324(f166(x42341,x42343),x42345),f324(f324(f141(x42342,x42343),x42344),x42346)))
% 18.55/18.48 [3628]E(f96(x36281,x36282,x36283,f324(f324(f324(f93(x36281),x36284),x36285),x36286)),f324(f324(f324(x36283,x36284),x36285),x36286))
% 18.55/18.48 [3629]E(f97(x36291,x36292,x36293,f324(f324(f324(f93(x36291),x36294),x36295),x36296)),f324(f324(f324(x36293,x36294),x36295),x36296))
% 18.55/18.48 [3819]E(f324(f324(f75(x38191,x38192,x38193,f324(f18(x38192,x38191),x38194)),x38195),x38196),x38194)
% 18.55/18.48 [3856]E(f324(f304(x38561,x38562,x38563),f324(f304(x38564,x38561,x38565),x38566)),f324(f304(x38564,x38562,f324(f324(f10(x38561,x38562,x38564),x38563),x38565)),x38566))
% 18.55/18.48 [3862]E(f324(f324(f45(x38621,f845(x38622,a832)),f324(f304(x38623,x38621,x38624),x38625)),x38626),f324(f324(f45(x38623,f845(x38622,a832)),x38625),f324(f324(f10(x38621,f845(x38622,a832),x38623),x38626),x38624)))
% 18.55/18.48 [3863]E(f324(f324(f46(x38631,f845(x38632,a832)),f324(f304(x38633,x38631,x38634),x38635)),x38636),f324(f324(f46(x38633,f845(x38632,a832)),x38635),f324(f324(f10(x38631,f845(x38632,a832),x38633),x38636),x38634)))
% 18.55/18.48 [3864]E(f324(f324(f45(x38641,f845(x38642,a832)),x38643),f324(f324(f10(x38644,f845(x38642,a832),x38641),x38645),x38646)),f324(f324(f45(x38644,f845(x38642,a832)),f324(f304(x38641,x38644,x38646),x38643)),x38645))
% 18.55/18.48 [3865]E(f324(f324(f46(x38651,f845(x38652,a832)),x38653),f324(f324(f10(x38654,f845(x38652,a832),x38651),x38655),x38656)),f324(f324(f46(x38654,f845(x38652,a832)),f324(f304(x38651,x38654,x38656),x38653)),x38655))
% 18.55/18.48 [3925]E(f324(f324(f45(x39251,f845(x39252,a832)),x39253),f324(f324(f10(f845(x39254,a832),f845(x39252,a832),x39251),f304(x39254,x39252,x39255)),x39256)),f324(f304(x39254,x39252,x39255),f324(f324(f45(x39251,f845(x39254,a832)),x39253),x39256)))
% 18.55/18.48 [3926]E(f324(f324(f45(x39261,f845(x39262,a832)),x39263),f324(f324(f10(f845(x39264,a832),f845(x39262,a832),x39261),f278(x39264,x39262,x39265)),x39266)),f324(f278(x39264,x39262,x39265),f324(f324(f45(x39261,f845(x39264,a832)),x39263),x39266)))
% 18.55/18.48 [3927]E(f324(f324(f45(x39271,f845(x39272,a832)),x39273),f324(f324(f10(f845(x39274,a832),f845(x39272,a832),x39271),f305(x39272,x39274,x39275)),x39276)),f324(f305(x39272,x39274,x39275),f324(f324(f45(x39271,f845(x39274,a832)),x39273),x39276)))
% 18.55/18.48 [3928]E(f324(f324(f46(x39281,f845(x39282,a832)),x39283),f324(f324(f10(f845(x39284,a832),f845(x39282,a832),x39281),f305(x39282,x39284,x39285)),x39286)),f324(f305(x39282,x39284,x39285),f324(f324(f46(x39281,f845(x39284,a832)),x39283),x39286)))
% 18.55/18.48 [4015]E(f324(f131(x40151,x40152,f324(f9(x40152,x40151,x40151),x40153),x40154),f324(f154(x40152),f324(f324(f139(x40152),x40155),x40156))),f324(f324(x40153,x40155),f324(f131(x40151,x40152,f324(f9(x40152,x40151,x40151),x40153),x40154),f324(f154(x40152),x40156))))
% 18.55/18.48 [4075]E(f324(f324(f20(f844(x40751,x40752),x40752,x40753),f324(f324(f10(x40754,f845(x40752,x40753),f844(x40751,x40752)),x40755),f324(f324(f10(x40751,x40754,f844(x40751,x40752)),x40756),f246(x40751,x40752)))),f251(x40751,x40752)),f324(f252(x40751,x40752,x40753),f324(f324(f10(x40754,f845(x40752,x40753),x40751),x40755),x40756)))
% 18.55/18.48 [4082]E(f324(f131(x40821,x40822,f324(f9(x40822,x40821,x40821),x40823),f324(f131(x40821,x40822,f324(f9(x40822,x40821,x40821),x40823),x40824),f324(f154(x40822),x40825))),f324(f154(x40822),x40826)),f324(f131(x40821,x40822,f324(f9(x40822,x40821,x40821),x40823),x40824),f324(f154(x40822),f324(f324(f125(x40822),x40826),x40825))))
% 18.55/18.48 [4084]E(f324(f324(f141(f844(x40841,x40842),f844(x40843,x40842)),f324(f252(x40841,x40842,f844(x40843,x40842)),f324(f324(f10(x40843,f845(x40842,f844(x40843,x40842)),x40841),f247(x40843,x40842)),x40844))),f324(f324(f166(x40841,x40842),x40845),x40846)),f324(f324(f166(x40843,x40842),f324(f324(f141(x40841,x40843),x40844),x40845)),x40846))
% 18.55/18.48 [4129]P1(f324(f324(f231(f845(x41291,a832)),f324(f278(x41292,x41291,x41293),f324(f324(f46(x41294,f845(x41292,a832)),x41295),x41296))),f324(f324(f46(x41294,f845(x41291,a832)),x41295),f324(f324(f10(f845(x41292,a832),f845(x41291,a832),x41294),f278(x41292,x41291,x41293)),x41296))))
% 18.55/18.48 [3938]E(f324(f324(f166(x39381,x39382),f324(f324(f146(x39381,x39383),x39384),f324(f246(x39381,x39382),x39385))),f324(f324(f146(x39382,x39386),x39384),f324(f251(x39381,x39382),x39385))),f324(f324(f146(f844(x39381,x39382),f324(f324(f166(x39381,x39382),x39383),x39386)),x39384),x39385))
% 18.55/18.48 [3997]E(f324(f324(f103(f845(f844(x39971,x39972),a832)),f324(f324(f282(x39971,x39973,x39972),x39974),x39975)),f324(f324(f282(x39971,x39973,x39972),x39974),x39976)),f324(f324(f282(x39971,x39973,x39972),x39974),f324(f324(f103(f845(f844(x39973,x39972),a832)),x39975),x39976)))
% 18.55/18.48 [4095]E(f324(f324(f303(f844(x40951,x40952)),f324(f324(f247(x40951,x40952),x40953),x40954)),f324(f324(f103(f845(f844(x40951,x40952),a832)),f324(f324(f249(x40951,x40952),x40955),f324(f18(f845(x40952,a832),x40951),f324(f324(f303(x40952),x40954),x40956)))),f324(f324(f249(x40951,x40952),f324(f324(f303(x40951),x40953),x40955)),f324(f18(f845(x40952,a832),x40951),x40956)))),f324(f324(f249(x40951,x40952),f324(f324(f303(x40951),x40953),x40955)),f324(f18(f845(x40952,a832),x40951),f324(f324(f303(x40952),x40954),x40956))))
% 18.55/18.48 [4169]E(f324(f324(f104(f845(x41691,a832)),f324(f305(x41691,x41692,f324(f75(f844(x41692,x41693),x41692,x41691,f246(x41692,x41693)),x41694)),x41695)),f324(f305(x41691,x41693,f324(f75(f844(x41692,x41693),x41693,x41691,f251(x41692,x41693)),x41694)),x41696)),f324(f305(x41691,f844(x41692,x41693),x41694),f324(f324(f249(x41692,x41693),x41695),f324(f18(f845(x41693,a832),x41692),x41696))))
% 18.55/18.48 [3922]E(f324(f324(f324(f74(x39221,x39222),f324(f324(f324(f74(x39221,x39222),x39223),x39224),x39225)),x39224),x39226),f324(f324(f324(f74(x39221,x39222),x39223),x39224),x39226))
% 18.55/18.48 [4021]E(f324(f324(f103(f845(f844(x40211,x40212),a832)),f324(f324(f282(x40211,x40213,x40212),x40214),x40215)),f324(f324(f282(x40211,x40213,x40212),x40216),x40215)),f324(f324(f282(x40211,x40213,x40212),f324(f324(f103(f845(f844(x40211,x40213),a832)),x40214),x40216)),x40215))
% 18.55/18.48 [4044]E(f169(x40441,x40442,f169(x40441,x40442,x40443,x40444),f165(x40441,x40442,f324(f154(f844(x40441,x40442)),f324(f324(f166(x40441,x40442),x40445),x40446)))),f169(x40441,x40442,x40443,f169(x40441,x40442,x40444,f165(x40441,x40442,f324(f154(f844(x40441,x40442)),f324(f324(f166(x40441,x40442),x40445),x40446))))))
% 18.55/18.48 [4151]E(f324(f324(f45(x41511,f845(x41512,a832)),x41513),f324(f324(f9(x41511,f845(x41514,f845(x41512,a832)),f845(x41512,a832)),f324(f324(f10(f845(x41514,a832),f845(f845(x41514,f845(x41512,a832)),f845(x41512,a832)),x41511),f45(x41514,f845(x41512,a832))),x41515)),x41516)),f324(f324(f45(x41514,f845(x41512,a832)),f324(f324(f45(x41511,f845(x41514,a832)),x41513),x41515)),x41516))
% 18.55/18.48 [4152]E(f324(f324(f45(x41521,f845(x41522,a832)),x41523),f324(f324(f9(x41521,f845(x41524,f845(x41522,a832)),f845(x41522,a832)),f324(f324(f10(f845(x41524,a832),f845(f845(x41524,f845(x41522,a832)),f845(x41522,a832)),x41521),f45(x41524,f845(x41522,a832))),x41525)),x41526)),f324(f324(f45(x41524,f845(x41522,a832)),f324(f324(f45(x41521,f845(x41524,a832)),x41523),x41525)),x41526))
% 18.55/18.48 [4153]E(f324(f324(f46(x41531,f845(x41532,a832)),x41533),f324(f324(f9(x41531,f845(x41534,f845(x41532,a832)),f845(x41532,a832)),f324(f324(f10(f845(x41534,a832),f845(f845(x41534,f845(x41532,a832)),f845(x41532,a832)),x41531),f46(x41534,f845(x41532,a832))),x41535)),x41536)),f324(f324(f46(x41534,f845(x41532,a832)),f324(f324(f45(x41531,f845(x41534,a832)),x41533),x41535)),x41536))
% 18.55/18.48 [4154]E(f324(f324(f45(x41541,f845(x41542,a832)),x41543),f324(f324(f9(x41541,f845(x41544,f845(x41542,a832)),f845(x41542,a832)),f324(f324(f10(f845(x41544,a832),f845(f845(x41544,f845(x41542,a832)),f845(x41542,a832)),x41541),f45(x41544,f845(x41542,a832))),x41545)),x41546)),f324(f324(f45(x41544,f845(x41542,a832)),f324(f324(f45(x41541,f845(x41544,a832)),x41543),x41545)),x41546))
% 18.55/18.48 [4155]E(f324(f324(f46(x41551,f845(x41552,a832)),x41553),f324(f324(f9(x41551,f845(x41554,f845(x41552,a832)),f845(x41552,a832)),f324(f324(f10(f845(x41554,a832),f845(f845(x41554,f845(x41552,a832)),f845(x41552,a832)),x41551),f46(x41554,f845(x41552,a832))),x41555)),x41556)),f324(f324(f46(x41554,f845(x41552,a832)),f324(f324(f45(x41551,f845(x41554,a832)),x41553),x41555)),x41556))
% 18.55/18.48 [4205]E(f324(f252(x42051,x42052,f844(x42053,x42054)),f324(f324(f9(x42051,f845(x42052,x42054),f845(x42052,f844(x42053,x42054))),f324(f324(f10(f845(x42054,f844(x42053,x42054)),f845(f845(x42052,x42054),f845(x42052,f844(x42053,x42054))),x42051),f10(x42054,f844(x42053,x42054),x42052)),f324(f324(f10(x42053,f845(x42054,f844(x42053,x42054)),x42051),f247(x42053,x42054)),x42055))),x42056)),f253(x42051,x42053,x42052,x42054,x42055,x42056))
% 18.55/18.48 [4128]E(f324(f324(f324(f74(x41281,f842(x41282)),f171(x41281,x41282,x41283,f324(f324(f3(f845(x41281,a832)),x41284),f324(f324(f303(x41281),x41285),f179(f845(x41281,a832)))))),x41285),x41286),f324(f324(f324(f74(x41281,f842(x41282)),f171(x41281,x41282,x41283,x41284)),x41285),x41286))
% 18.55/18.48 [4229]E(f324(f304(x42291,x42292,f324(f324(f20(x42291,x42292,x42292),f324(f324(f20(x42291,x42292,f845(x42292,x42292)),f324(f324(f10(a832,f845(x42292,f845(x42292,x42292)),x42291),f98(x42292)),x42293)),x42294)),x42295)),x42296),f324(f324(f103(f845(x42292,a832)),f324(f304(x42291,x42292,x42294),f324(f324(f104(f845(x42291,a832)),x42296),f324(f257(x42291),x42293)))),f324(f304(x42291,x42292,x42295),f324(f324(f104(f845(x42291,a832)),x42296),f324(f257(x42291),f324(f324(f10(a832,a832,x42291),a320),x42293))))))
% 18.55/18.48 [4240]E(f324(f304(x42401,f844(x42402,x42403),f324(f324(f20(x42401,x42403,f844(x42402,x42403)),f324(f324(f10(x42402,f845(x42403,f844(x42402,x42403)),x42401),f247(x42402,x42403)),x42404)),x42405)),x42406),f324(f324(f249(x42402,x42403),f324(f304(x42401,x42402,x42404),x42406)),f324(f324(f10(f845(x42401,a832),f845(x42403,a832),x42402),f304(x42401,x42403,x42405)),f324(f324(f9(x42402,f845(x42401,a832),f845(x42401,a832)),f324(f324(f10(f845(x42401,a832),f845(f845(x42401,a832),f845(x42401,a832)),x42402),f104(f845(x42401,a832))),f324(f324(f10(f845(x42402,a832),f845(x42401,a832),x42402),f305(x42401,x42402,x42404)),f324(f324(f9(x42402,f845(x42402,a832),f845(x42402,a832)),f303(x42402)),f179(f845(x42402,a832)))))),x42406))))
% 18.55/18.48 [4188]E(f324(f251(x41881,x41882),f324(f253(x41883,x41881,x41884,x41882,x41885,x41886),x41887)),f324(x41886,f324(f251(x41883,x41884),x41887)))
% 18.55/18.48 [4189]E(f324(f246(x41891,x41892),f324(f253(x41893,x41891,x41894,x41892,x41895,x41896),x41897)),f324(x41895,f324(f246(x41893,x41894),x41897)))
% 18.55/18.48 [3900]E(f324(f324(f166(x39001,x39002),f324(f324(f146(x39001,x39003),x39004),x39005)),f324(f324(f146(x39002,x39006),x39004),x39007)),f324(f324(f146(f844(x39001,x39002),f324(f324(f166(x39001,x39002),x39003),x39006)),x39004),f324(f324(f247(x39001,x39002),x39005),x39007)))
% 18.55/18.48 [3968]E(f324(f324(f324(f254(x39681,x39682,x39683,x39684),x39685),x39686),x39687),f324(f324(f252(x39682,x39683,x39684),x39686),f324(x39685,x39687)))
% 18.55/18.48 [3969]E(f324(f324(f324(f254(x39691,x39692,x39693,x39694),x39695),x39696),x39697),f324(f324(f252(x39692,x39693,x39694),x39696),f324(x39695,x39697)))
% 18.55/18.48 [3979]E(f324(f324(f324(f254(x39791,x39792,x39793,x39794),x39795),x39796),x39797),f324(f324(x39796,f324(f246(x39792,x39793),f324(x39795,x39797))),f324(f251(x39792,x39793),f324(x39795,x39797))))
% 18.55/18.48 [4029]E(f324(f75(x40291,x40292,x40293,x40294),f324(f75(x40295,x40291,x40293,x40296),x40297)),f324(f75(x40295,x40292,x40293,f324(f75(x40291,x40292,x40295,x40294),x40296)),x40297))
% 18.55/18.48 [4091]E(f324(f75(f842(x40911),f842(x40912),x40913,f324(f195(x40911,x40912),x40914)),f324(f324(f324(f74(x40913,f842(x40911)),x40915),x40916),f324(f226(x40911),x40917))),f324(f324(f324(f74(x40913,f842(x40912)),f324(f75(f842(x40911),f842(x40912),x40913,f324(f195(x40911,x40912),x40914)),x40915)),x40916),f324(f226(x40912),f324(x40914,x40917))))
% 18.55/18.48 [4212]E(f324(f253(x42121,x42122,x42123,x42123,x42124,f37(x42123)),f324(f253(x42121,x42121,x42125,x42123,f37(x42121),x42126),x42127)),f324(f324(f247(x42122,x42123),f324(x42124,f324(f246(x42121,x42125),x42127))),f324(x42126,f324(f251(x42121,x42125),x42127))))
% 18.55/18.48 [4213]E(f324(f253(x42131,x42131,x42132,x42133,f37(x42131),x42134),f324(f253(x42135,x42131,x42132,x42132,x42136,f37(x42132)),x42137)),f324(f324(f247(x42131,x42133),f324(x42136,f324(f246(x42135,x42132),x42137))),f324(x42134,f324(f251(x42135,x42132),x42137))))
% 18.55/18.48 [4227]E(f324(f253(x42271,x42272,x42273,x42273,x42274,f37(x42273)),f324(f253(x42275,x42271,x42273,x42273,x42276,f37(x42273)),x42277)),f324(f253(x42275,x42272,x42273,x42273,f324(f75(x42271,x42272,x42275,x42274),x42276),f37(x42273)),x42277))
% 18.55/18.48 [4228]E(f324(f253(x42281,x42281,x42282,x42283,f37(x42281),x42284),f324(f253(x42281,x42281,x42285,x42282,f37(x42281),x42286),x42287)),f324(f253(x42281,x42281,x42285,x42283,f37(x42281),f324(f75(x42282,x42283,x42285,x42284),x42286)),x42287))
% 18.55/18.48 [4237]E(f324(f253(x42371,x42372,x42373,x42373,x42374,f37(x42373)),f324(f253(x42371,x42371,x42375,x42373,f37(x42371),x42376),x42377)),f324(f253(x42372,x42372,x42375,x42373,f37(x42372),x42376),f324(f253(x42371,x42372,x42375,x42375,x42374,f37(x42375)),x42377)))
% 18.55/18.48 [3935]E(f324(f324(f282(x39351,x39352,x39353),f324(f324(f282(x39351,x39354,x39352),x39355),x39356)),x39357),f324(f324(f282(x39351,x39354,x39353),x39355),f324(f324(f282(x39354,x39352,x39353),x39356),x39357)))
% 18.55/18.48 [4003]E(f324(f324(f252(x40031,x40032,x40033),f324(f75(x40034,f845(x40032,x40033),x40031,x40035),x40036)),x40037),f324(f324(x40035,f324(x40036,f324(f246(x40031,x40032),x40037))),f324(f251(x40031,x40032),x40037)))
% 18.55/18.48 [4054]E(f324(f75(x40541,x40542,x40543,x40544),f324(f324(f324(f74(x40543,x40541),x40545),x40546),x40547)),f324(f324(f324(f74(x40543,x40542),f324(f75(x40541,x40542,x40543,x40544),x40545)),x40546),f324(x40544,x40547)))
% 18.55/18.48 [4087]E(f324(f131(x40871,x40872,f324(f9(x40872,x40871,x40871),x40873),x40874),f324(f154(x40872),f324(f324(f141(x40875,x40872),x40876),x40877))),f324(f131(x40871,x40875,f324(f9(x40875,x40871,x40871),f324(f75(x40872,f845(x40871,x40871),x40875,x40873),x40876)),x40874),f324(f154(x40875),x40877)))
% 18.55/18.48 [4030]E(f324(f324(f45(x40301,f845(f844(x40302,x40303),a832)),x40304),f324(f324(f10(f845(f844(x40305,x40303),a832),f845(f844(x40302,x40303),a832),x40301),f324(f282(x40302,x40305,x40303),x40306)),x40307)),f324(f324(f282(x40302,x40305,x40303),x40306),f324(f324(f45(x40301,f845(f844(x40305,x40303),a832)),x40304),x40307)))
% 18.55/18.48 [4065]E(f169(x40651,x40652,f324(f324(f324(f74(x40651,f842(x40652)),x40653),x40654),f324(f226(x40652),x40655)),f165(x40651,x40652,f324(f154(f844(x40651,x40652)),f324(f324(f166(x40651,x40652),x40656),x40657)))),f169(x40651,x40652,x40653,f165(x40651,x40652,f324(f154(f844(x40651,x40652)),f324(f324(f166(x40651,x40652),f324(f324(f139(x40651),x40654),x40656)),f324(f324(f139(x40652),x40655),x40657))))))
% 18.55/18.48 [4175]E(f324(f324(f45(x41751,f845(f844(x41752,x41753),a832)),x41754),f324(f324(f9(x41751,f845(f844(x41755,x41753),a832),f845(f844(x41752,x41753),a832)),f324(f324(f10(f845(f844(x41752,x41755),a832),f845(f845(f844(x41755,x41753),a832),f845(f844(x41752,x41753),a832)),x41751),f282(x41752,x41755,x41753)),x41756)),x41757)),f324(f324(f282(x41752,x41755,x41753),f324(f324(f45(x41751,f845(f844(x41752,x41755),a832)),x41754),x41756)),x41757))
% 18.55/18.48 [4176]E(f324(f131(x41761,x41762,f324(f324(f9(x41761,f845(x41762,x41763),f845(x41762,x41761)),f324(f324(f10(f845(x41763,x41761),f845(f845(x41762,x41763),f845(x41762,x41761)),x41761),f10(x41763,x41761,x41762)),x41764)),x41765),x41766),x41767),f324(f131(x41761,x41763,x41764,x41766),f324(f324(f141(x41762,x41763),x41765),x41767)))
% 18.55/18.48 [4238]E(f324(f324(f46(x42381,f845(x42382,a832)),x42383),f324(f324(f10(f845(x42384,f845(x42382,a832)),f845(x42382,a832),x42381),f324(f46(x42384,f845(x42382,a832)),x42385)),f324(f324(f9(x42381,f845(x42384,f845(x42382,a832)),f845(x42384,f845(x42382,a832))),f324(f324(f10(f845(f845(x42382,a832),f845(x42382,a832)),f845(f845(x42384,f845(x42382,a832)),f845(x42384,f845(x42382,a832))),x42381),f10(f845(x42382,a832),f845(x42382,a832),x42384)),f324(f324(f10(f845(x42382,a832),f845(f845(x42382,a832),f845(x42382,a832)),x42381),f103(f845(x42382,a832))),x42386))),x42387))),f324(f324(f103(f845(x42382,a832)),f324(f324(f46(x42381,f845(x42382,a832)),x42383),x42386)),f324(f324(f46(x42384,f845(x42382,a832)),x42385),x42387)))
% 18.55/18.48 [4239]E(f324(f324(f45(x42391,f845(x42392,a832)),x42393),f324(f324(f10(f845(x42394,f845(x42392,a832)),f845(x42392,a832),x42391),f324(f45(x42394,f845(x42392,a832)),x42395)),f324(f324(f9(x42391,f845(x42394,f845(x42392,a832)),f845(x42394,f845(x42392,a832))),f324(f324(f10(f845(f845(x42392,a832),f845(x42392,a832)),f845(f845(x42394,f845(x42392,a832)),f845(x42394,f845(x42392,a832))),x42391),f10(f845(x42392,a832),f845(x42392,a832),x42394)),f324(f324(f10(f845(x42392,a832),f845(f845(x42392,a832),f845(x42392,a832)),x42391),f104(f845(x42392,a832))),x42396))),x42397))),f324(f324(f104(f845(x42392,a832)),f324(f324(f45(x42391,f845(x42392,a832)),x42393),x42396)),f324(f324(f45(x42394,f845(x42392,a832)),x42395),x42397)))
% 18.55/18.48 [4232]E(f191(x42321,x42322,f324(f324(f324(x42323,x42324),x42325),x42326),f324(f324(f9(x42321,f844(a101,a101),f845(a101,f840(x42322))),f324(f324(f9(x42321,a101,f845(f844(a101,a101),f845(a101,f840(x42322)))),f324(f324(f9(x42321,a101,f845(a101,f845(f844(a101,a101),f845(a101,f840(x42322))))),x42327),x42324)),x42325)),x42326)),f324(f324(f324(f203(x42321,x42322,x42323,x42327),x42324),x42325),x42326))
% 18.55/18.48 [4245]E(f192(x42451,x42452,f324(f324(f324(x42453,x42454),x42455),x42456),f324(f324(f9(x42451,f844(a101,a101),f845(a101,f840(x42452))),f324(f324(f9(x42451,a101,f845(f844(a101,a101),f845(a101,f840(x42452)))),f324(f324(f9(x42451,a101,f845(a101,f845(f844(a101,a101),f845(a101,f840(x42452))))),x42457),x42454)),x42455)),x42456)),f205(x42451,x42452,x42453,x42457,x42454,x42455,x42456))
% 18.55/18.48 [4236]E(f189(x42361,x42362,f324(f324(f324(x42363,x42364),x42365),x42366),f324(f324(f9(x42361,f844(a101,a101),f845(a101,f840(f842(x42362)))),f324(f324(f9(x42361,a101,f845(f844(a101,a101),f845(a101,f840(f842(x42362))))),f324(f324(f9(x42361,a101,f845(a101,f845(f844(a101,a101),f845(a101,f840(f842(x42362)))))),x42367),x42364)),x42365)),x42366)),f324(f324(f324(f200(x42361,x42362,x42363,x42367),x42364),x42365),x42366))
% 18.55/18.48 [4247]E(f190(x42471,x42472,f324(f324(f324(x42473,x42474),x42475),x42476),f324(f324(f9(x42471,f844(a101,a101),f845(a101,f840(f842(x42472)))),f324(f324(f9(x42471,a101,f845(f844(a101,a101),f845(a101,f840(f842(x42472))))),f324(f324(f9(x42471,a101,f845(a101,f845(f844(a101,a101),f845(a101,f840(f842(x42472)))))),x42477),x42474)),x42475)),x42476)),f202(x42471,x42472,x42473,x42477,x42474,x42475,x42476))
% 18.55/18.48 [4148]E(f324(f253(x41481,x41482,x41483,x41484,x41485,x41486),f324(f324(f247(x41481,x41483),x41487),x41488)),f324(f324(f247(x41482,x41484),f324(x41485,x41487)),f324(x41486,x41488)))
% 18.55/18.48 [4249]E(f324(f324(f141(f844(x42491,x42492),f844(x42493,x42494)),f324(f252(x42491,x42492,f844(x42493,x42494)),f324(f324(f9(x42491,f845(x42492,x42494),f845(x42492,f844(x42493,x42494))),f324(f324(f10(f845(x42494,f844(x42493,x42494)),f845(f845(x42492,x42494),f845(x42492,f844(x42493,x42494))),x42491),f10(x42494,f844(x42493,x42494),x42492)),f324(f324(f10(x42493,f845(x42494,f844(x42493,x42494)),x42491),f247(x42493,x42494)),x42495))),x42496))),f324(f324(f166(x42491,x42492),x42497),x42498)),f324(f324(f166(x42493,x42494),f324(f324(f141(x42491,x42493),x42495),x42497)),f324(f324(f141(x42492,x42494),x42496),x42498)))
% 18.55/18.48 [4253]E(f324(f324(f141(f844(x42531,x42532),x42533),f324(f252(x42531,x42532,x42533),f324(f324(f10(f845(x42532,f844(x42531,x42534)),f845(x42532,x42533),x42531),f324(f10(f844(x42531,x42534),x42533,x42532),x42535)),f324(f324(f9(x42531,f845(x42532,x42534),f845(x42532,f844(x42531,x42534))),f324(f324(f10(f845(x42534,f844(x42531,x42534)),f845(f845(x42532,x42534),f845(x42532,f844(x42531,x42534))),x42531),f10(x42534,f844(x42531,x42534),x42532)),f247(x42531,x42534))),x42536)))),f324(f324(f166(x42531,x42532),x42537),x42538)),f324(f324(f141(f844(x42531,x42534),x42533),x42535),f324(f324(f166(x42531,x42534),x42537),f324(f324(f141(x42532,x42534),x42536),x42538))))
% 18.55/18.48 [4180]E(f324(f324(f141(f844(x41801,x41802),x41803),f324(f252(x41801,x41802,x41803),f324(f324(f10(f845(x41802,f844(x41804,x41802)),f845(x41802,x41803),x41801),f324(f10(f844(x41804,x41802),x41803,x41802),x41805)),f324(f324(f10(x41804,f845(x41802,f844(x41804,x41802)),x41801),f247(x41804,x41802)),x41806)))),f324(f324(f166(x41801,x41802),x41807),x41808)),f324(f324(f141(f844(x41804,x41802),x41803),x41805),f324(f324(f166(x41804,x41802),f324(f324(f141(x41801,x41804),x41806),x41807)),x41808)))
% 18.55/18.48 [4139]E(f324(f324(f252(x41391,x41392,x41393),f324(f324(f10(f845(x41392,f844(x41394,x41395)),f845(x41392,x41393),x41391),f324(f10(f844(x41394,x41395),x41393,x41392),f324(f252(x41394,x41395,x41393),x41396))),x41397)),x41398),f324(f324(f252(x41394,x41395,x41393),x41396),f324(f324(f252(x41391,x41392,f844(x41394,x41395)),x41397),x41398)))
% 18.55/18.48 [4254]E(f324(f324(f45(f844(x42541,x42542),f845(f844(x42543,x42544),a832)),f324(f324(f249(x42541,x42542),x42545),f324(f18(f845(x42542,a832),x42541),x42546))),f324(f252(x42541,x42542,f845(f844(x42543,x42544),a832)),f324(f324(f9(x42541,f845(x42542,f845(x42543,f845(x42544,a832))),f845(x42542,f845(f844(x42543,x42544),a832))),f324(f324(f10(f845(f845(x42543,f845(x42544,a832)),f845(f844(x42543,x42544),a832)),f845(f845(x42542,f845(x42543,f845(x42544,a832))),f845(x42542,f845(f844(x42543,x42544),a832))),x42541),f10(f845(x42543,f845(x42544,a832)),f845(f844(x42543,x42544),a832),x42542)),f324(f324(f10(f845(x42543,a832),f845(f845(x42543,f845(x42544,a832)),f845(f844(x42543,x42544),a832)),x42541),f249(x42543,x42544)),x42547))),f324(f324(f10(f845(x42544,a832),f845(x42543,f845(x42544,a832)),x42542),f18(f845(x42544,a832),x42543)),x42548)))),f324(f324(f249(x42543,x42544),f324(f324(f45(x42541,f845(x42543,a832)),x42545),x42547)),f324(f18(f845(x42544,a832),x42543),f324(f324(f45(x42542,f845(x42544,a832)),x42546),x42548))))
% 18.55/18.48 [4194]E(f324(f324(f254(x41941,x41942,x41943,x41944),f324(f324(f254(x41941,x41945,x41946,f844(x41942,x41943)),x41947),x41948)),x41949),f324(f324(f254(x41941,x41945,x41946,x41944),x41947),f324(f324(f9(x41945,f845(x41942,f845(x41943,x41944)),f845(x41946,x41944)),f324(f324(f10(f845(x41946,f844(x41942,x41943)),f845(f845(x41942,f845(x41943,x41944)),f845(x41946,x41944)),x41945),f254(x41946,x41942,x41943,x41944)),x41948)),x41949)))
% 18.55/18.48 [4224]E(f324(f75(f844(x42241,x42242),f844(x42243,x42244),f844(x42245,x42246),f253(x42241,x42243,x42242,x42244,x42247,x42248)),f253(x42245,x42241,x42246,x42242,x42249,x422410)),f253(x42245,x42243,x42246,x42244,f324(f75(x42241,x42243,x42245,x42247),x42249),f324(f75(x42242,x42244,x42246,x42248),x422410)))
% 18.55/18.48 [4225]E(f324(f75(f844(x42251,x42252),f844(x42253,x42254),f844(x42255,x42256),f253(x42251,x42253,x42252,x42254,x42257,x42258)),f253(x42255,x42251,x42256,x42252,x42259,x422510)),f253(x42255,x42253,x42256,x42254,f324(f75(x42251,x42253,x42255,x42257),x42259),f324(f75(x42252,x42254,x42256,x42258),x422510)))
% 18.55/18.48 [4230]E(f324(f253(x42301,x42302,x42303,x42304,x42305,x42306),f324(f253(x42307,x42301,x42308,x42303,x42309,x423010),x423011)),f324(f253(x42307,x42302,x42308,x42304,f324(f75(x42301,x42302,x42307,x42305),x42309),f324(f75(x42303,x42304,x42308,x42306),x423010)),x423011))
% 18.55/18.48 [6292]P13(a500)+P1(f324(f324(f326(f844(a834,a833)),a684),f324(f157(f844(a834,a833)),a29)))
% 18.55/18.48 [8349]P13(a500)+~P1(f324(f324(f252(a834,a833,a832),f324(f18(f845(a833,a832),a834),a26)),a684))
% 18.55/18.48 [4412]~P58(x44121)+P58(f842(x44121))
% 18.55/18.48 [4414]~P137(x44141)+~E(f80(x44141),f2(x44141))
% 18.55/18.48 [4415]~P137(x44151)+~E(f80(x44151),f2(x44151))
% 18.55/18.48 [4417]~E(x44171,f2(a101))+E(f324(a23,x44171),f2(a1))
% 18.55/18.48 [4418]~E(x44181,f2(a1))+E(f84(a1,x44181),f2(a1))
% 18.55/18.48 [4426]~P2(x44261)+P33(x44261,f2(x44261))
% 18.55/18.48 [4427]~P86(x44271)+P18(x44271,f115(x44271))
% 18.55/18.48 [4428]~P86(x44281)+P18(x44281,f115(x44281))
% 18.55/18.48 [4437]P1(x44371)+P1(f324(a320,x44371))
% 18.55/18.48 [4480]~P2(x44801)+~P33(x44801,f80(x44801))
% 18.55/18.48 [4524]~P1(x45241)+~P1(f324(a320,x45241))
% 18.55/18.48 [4547]E(f324(a107,x45471),f2(a838))+~P1(f324(a185,x45471))
% 18.55/18.48 [4608]~P92(x46081)+P19(x46081,x46081,f83(x46081))
% 18.55/18.48 [4609]~P86(x46091)+P19(x46091,x46091,f235(x46091))
% 18.55/18.48 [4610]~P86(x46101)+P19(x46101,x46101,f178(x46101))
% 18.55/18.48 [4611]~P93(x46111)+P19(x46111,x46111,f103(x46111))
% 18.55/18.48 [4612]~P99(x46121)+P19(x46121,x46121,f104(x46121))
% 18.55/18.48 [4613]~P4(x46131)+P20(x46131,x46131,f83(x46131))
% 18.55/18.48 [4422]E(x44221,f2(a838))+E(f324(a114,f612(x44221)),x44221)
% 18.55/18.48 [4423]~E(x44231,f2(a838))+E(f324(f102(a1),x44231),f2(a1))
% 18.55/18.48 [4430]~P89(x44301)+E(f324(f106(x44301),a85),f2(x44301))
% 18.55/18.48 [4431]~P89(x44311)+E(f324(f106(x44311),a85),f2(x44311))
% 18.55/18.48 [4433]~E(f613(x44331),f2(a838))+E(f324(f151(a838),x44331),f2(a838))
% 18.55/18.48 [4434]~P101(x44341)+E(f233(x44341,f231(x44341)),f235(x44341))
% 18.55/18.48 [4435]~P101(x44351)+E(f234(x44351,f231(x44351)),f178(x44351))
% 18.55/18.48 [4436]~P82(x44361)+E(f84(x44361,f2(x44361)),f2(x44361))
% 18.55/18.48 [4445]~P2(x44451)+E(f324(f102(x44451),f2(a838)),f2(x44451))
% 18.55/18.48 [4446]~P2(x44461)+E(f324(f102(x44461),f80(a838)),f80(x44461))
% 18.55/18.48 [4447]~P119(x44471)+E(f324(f105(x44471),f2(a1)),f2(x44471))
% 18.55/18.48 [4448]~P119(x44481)+E(f324(f105(x44481),f80(a1)),f80(x44481))
% 18.55/18.48 [4449]E(x44491,f2(a838))+~E(f324(f102(a1),x44491),f2(a1))
% 18.55/18.48 [4474]~P63(x44741)+E(f324(f81(x44741),f2(x44741)),f2(x44741))
% 18.55/18.48 [4475]~P91(x44751)+E(f324(f81(x44751),f179(x44751)),f238(x44751))
% 18.55/18.48 [4476]~P91(x44761)+E(f324(f81(x44761),f238(x44761)),f179(x44761))
% 18.55/18.48 [4477]~P78(x44771)+E(f324(f77(x44771),f2(x44771)),f2(x44771))
% 18.55/18.48 [4478]~P103(x44781)+E(f324(f77(x44781),f80(x44781)),f80(x44781))
% 18.55/18.48 [4479]~P72(x44791)+E(f324(f151(x44791),f115(x44791)),f2(x44791))
% 18.55/18.48 [4500]~P35(x45001)+P38(f324(f157(a1),x45001))
% 18.55/18.48 [4528]~P89(x45281)+E(f324(f81(x45281),f80(x45281)),f324(f106(x45281),a99))
% 18.55/18.48 [4529]~P89(x45291)+E(f324(f81(x45291),f80(x45291)),f324(f106(x45291),a99))
% 18.55/18.48 [4546]~P89(x45461)+P33(x45461,f324(f106(x45461),a85))
% 18.55/18.48 [4571]P35(x45711)+~P38(f324(f157(a1),x45711))
% 18.55/18.48 [4614]E(f324(f102(a1),f324(a107,x46141)),x46141)+P1(f324(a185,x46141))
% 18.55/18.48 [4681]~P108(x46811)+E(f241(x46811,f80(x46811),f83(x46811)),f240(x46811))
% 18.55/18.48 [4711]~P89(x47111)+~P33(x47111,f324(f106(x47111),a99))
% 18.55/18.48 [4721]E(f324(a30,x47211),f182(a833))+P1(f324(a26,f324(a27,x47211)))
% 18.55/18.48 [4798]~E(x47981,f2(a838))+P1(f324(f324(f231(a838),x47981),f2(a838)))
% 18.55/18.48 [4799]~E(x47991,f80(a838))+P1(f324(f324(f280(a838),x47991),f80(a838)))
% 18.55/18.48 [4851]E(f324(f77(a1),x48511),x48511)+P1(f324(f324(f232(a1),x48511),f2(a1)))
% 18.55/18.48 [4871]~E(f324(a107,x48711),f2(a838))+P1(f324(f324(f231(a1),x48711),f2(a1)))
% 18.55/18.48 [4902]~E(f324(f77(a1),x49021),f80(a1))+P1(f324(f324(f280(a1),x49021),f80(a1)))
% 18.55/18.48 [4932]~P1(f324(a185,x49321))+P1(f324(f324(f232(a1),x49321),f2(a1)))
% 18.55/18.48 [4972]~P2(x49721)+P1(f324(f324(f326(x49721),f2(x49721)),f175(x49721)))
% 18.55/18.48 [4973]~P119(x49731)+P1(f324(f324(f326(x49731),f2(x49731)),f112(x49731)))
% 18.55/18.48 [4974]~P2(x49741)+P1(f324(f324(f326(x49741),f80(x49741)),f175(x49741)))
% 18.55/18.48 [4975]~P119(x49751)+P1(f324(f324(f326(x49751),f80(x49751)),f112(x49751)))
% 18.55/18.48 [4976]~P84(x49761)+P1(f324(f324(f232(x49761),f2(x49761)),f80(x49761)))
% 18.55/18.48 [4977]~P84(x49771)+P1(f324(f324(f231(x49771),f2(x49771)),f80(x49771)))
% 18.55/18.48 [4980]E(f324(f226(a833),f392(x49801)),f324(a30,x49801))+~P1(f324(a26,f324(a27,x49801)))
% 18.55/18.48 [4981]E(f324(f226(a833),f419(x49811)),f324(a30,x49811))+~P1(f324(a26,f324(a27,x49811)))
% 18.55/18.48 [5032]E(x50321,f2(a838))+~P1(f324(f324(f231(a838),x50321),f2(a838)))
% 18.55/18.48 [5033]E(x50331,f80(a838))+~P1(f324(f324(f280(a838),x50331),f80(a838)))
% 18.55/18.48 [5073]E(f324(a107,x50731),f2(a838))+~P1(f324(f324(f231(a1),x50731),f2(a1)))
% 18.55/18.48 [5074]E(f324(a107,x50741),f2(a838))+~P1(f324(f324(f231(a1),x50741),f2(a1)))
% 18.55/18.48 [5102]E(f324(f77(a1),x51021),f80(a1))+~P1(f324(f324(f280(a1),x51021),f80(a1)))
% 18.55/18.48 [5129]P1(f324(a185,x51291))+~P1(f324(f324(f232(a1),x51291),f2(a1)))
% 18.55/18.48 [5134]~P86(x51341)+P20(x51341,f839(x51341),f137(x51341,x51341,f7(x51341)))
% 18.55/18.48 [5152]P38(x51521)+~P1(f324(f324(f231(a1),f2(a1)),f819(x51521)))
% 18.55/18.48 [5158]E(f324(f77(a1),x51581),f324(f81(a1),x51581))+~P1(f324(f324(f232(a1),x51581),f2(a1)))
% 18.55/18.48 [5327]~P84(x53271)+~P1(f324(f324(f232(x53271),f80(x53271)),f2(x53271)))
% 18.55/18.48 [5328]~P84(x53281)+~P1(f324(f324(f231(x53281),f80(x53281)),f2(x53281)))
% 18.55/18.48 [5340]~E(x53401,f2(a1))+P1(f324(f324(f232(a1),f324(f77(a1),x53401)),f80(a1)))
% 18.55/18.48 [5341]~E(x53411,f2(a838))+P1(f324(f324(f231(a1),f324(f102(a1),x53411)),f2(a1)))
% 18.55/18.48 [5459]~P72(x54591)+E(f131(x54591,x54591,f82(x54591),f2(x54591)),f151(x54591))
% 18.55/18.48 [5634]~P87(x56341)+P29(a838,x56341,f102(x56341),f238(f845(a838,a832)))
% 18.55/18.48 [5832]E(x58321,f2(a838))+~P1(f324(f324(f231(a1),f324(f102(a1),x58321)),f2(a1)))
% 18.55/18.48 [5833]E(x58331,f2(a1))+~P1(f324(f324(f232(a1),f324(f77(a1),x58331)),f80(a1)))
% 18.55/18.48 [6664]~P1(f324(f324(f232(a1),x66641),f2(a1)))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x66641),x66641)),f2(a1)))
% 18.55/18.48 [7240]P1(f324(f324(f232(a1),x72401),f2(a1)))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x72401),x72401)),f2(a1)))
% 18.55/18.48 [7811]E(x78111,f324(a5,f2(a838)))+P1(f324(f324(f232(a838),f324(f324(f3(a838),f324(a22,x78111)),f324(a114,f2(a838)))),f324(a22,x78111)))
% 18.55/18.48 [8559]~P1(f324(f324(f232(a1),x85591),f2(a1)))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x85591),x85591)),a99)),f2(a1)))
% 18.55/18.48 [8645]~P1(f324(f324(f232(a1),x86451),f2(a1)))+P1(f324(f324(f232(a1),f324(f324(f82(a1),f324(f324(f82(a1),f80(a1)),x86451)),x86451)),f2(a1)))
% 18.55/18.48 [8930]P1(f324(f324(f232(a1),x89301),f2(a1)))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89301),x89301)),a99)),f2(a1)))
% 18.55/18.48 [8988]P1(f324(f324(f232(a1),x89881),f2(a1)))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),f324(f324(f82(a1),f80(a1)),x89881)),x89881)),f2(a1)))
% 18.55/18.48 [4517]~E(a85,x45171)+E(f324(f324(f82(a1),x45171),x45171),a85)
% 18.55/18.48 [4518]~E(x45181,a85)+E(f324(f324(f82(a1),x45181),x45181),a85)
% 18.55/18.48 [4532]E(x45321,f2(a1))+E(f324(f324(f42(a1),x45321),x45321),f80(a1))
% 18.55/18.48 [4659]E(x46591,a85)+~E(f324(f324(f82(a1),x46591),x46591),a85)
% 18.55/18.48 [4660]E(a85,x46601)+~E(f324(f324(f82(a1),x46601),x46601),a85)
% 18.55/18.48 [4661]~P89(x46611)+E(f324(f105(x46611),f324(f106(a1),a99)),f324(f106(x46611),a99))
% 18.55/18.48 [4671]~P9(x46711)+E(f44(x46711,f179(f845(x46711,a832))),f238(x46711))
% 18.55/18.48 [4672]~P9(x46721)+E(f44(x46721,f238(f845(x46721,a832))),f179(x46721))
% 18.55/18.48 [4673]~P9(x46731)+E(f43(x46731,f179(f845(x46731,a832))),f179(x46731))
% 18.55/18.48 [4674]~P9(x46741)+E(f43(x46741,f238(f845(x46741,a832))),f238(x46741))
% 18.55/18.48 [4675]~P86(x46751)+E(f129(x46751,f179(f845(x46751,a832))),f115(x46751))
% 18.55/18.48 [4810]E(x48101,f2(a838))+P1(f324(f324(f232(a838),f2(a838)),x48101))
% 18.55/18.48 [4811]E(x48111,f2(a838))+P1(f324(f324(f232(a838),f2(a838)),x48111))
% 18.55/18.48 [4831]~P10(x48311)+P1(f324(f324(f231(a1),f2(a1)),x48311))
% 18.55/18.48 [4861]~E(f324(f106(a838),x48611),f2(a838))+P1(f324(f324(f231(a1),x48611),a85))
% 18.55/18.48 [4862]~E(f324(f106(a838),x48621),f2(a838))+P1(f324(f324(f231(a1),x48621),a85))
% 18.55/18.48 [4867]P38(x48671)+P1(f324(f324(f326(a1),f819(x48671)),x48671))
% 18.55/18.48 [4868]E(x48681,f324(a5,f2(a838)))+P1(f324(f324(f231(a101),f80(a101)),x48681))
% 18.55/18.48 [4907]P1(f324(a185,x49071))+P1(f324(f324(f231(a1),f2(a1)),x49071))
% 18.55/18.48 [4954]E(f324(f102(a1),f324(a107,x49541)),f2(a1))+P1(f324(f324(f231(a1),f2(a1)),x49541))
% 18.55/18.48 [5006]~P58(x50061)+P1(f324(f64(x50061),f238(f845(x50061,a832))))
% 18.55/18.48 [5019]E(f324(f102(a1),f324(f106(a838),x50191)),f324(f106(a1),x50191))+P1(f324(a185,f324(f106(a1),x50191)))
% 18.55/18.48 [5022]~E(x50221,f2(a838))+P1(f324(f324(f232(a838),x50221),f324(a114,f2(a838))))
% 18.55/18.48 [5038]E(f324(f106(a838),x50381),f2(a838))+~P1(f324(f324(f231(a1),x50381),a85))
% 18.55/18.48 [5039]E(f324(f106(a838),x50391),f2(a838))+~P1(f324(a185,f324(f106(a1),x50391)))
% 18.55/18.48 [5040]E(f324(f106(a838),x50401),f2(a838))+~P1(f324(f324(f231(a1),x50401),a85))
% 18.55/18.48 [5071]P10(x50711)+~P1(f324(f324(f231(a1),f2(a1)),x50711))
% 18.55/18.48 [5089]~E(x50891,f2(a838))+~P1(f324(f324(f232(a838),f2(a838)),x50891))
% 18.55/18.48 [5112]~E(x51121,f324(a114,f2(a838)))+P1(f324(f324(f280(a838),x51121),f324(a114,f2(a838))))
% 18.55/18.48 [5137]E(f324(a114,f332(x51371)),x51371)+~P1(f324(f324(f232(a838),f2(a838)),x51371))
% 18.55/18.48 [5138]E(f324(a114,f343(x51381)),x51381)+~P1(f324(f324(f232(a838),f2(a838)),x51381))
% 18.55/18.48 [5146]E(f324(a114,f324(f106(a838),x51461)),f80(a838))+~P1(f324(a185,f324(f106(a1),x51461)))
% 18.55/18.48 [5154]E(f324(f102(a1),f453(x51541)),x51541)+~P1(f324(f324(f232(a1),f2(a1)),x51541))
% 18.55/18.48 [5161]~E(x51611,f324(a5,f2(a838)))+~P1(f324(f324(f231(a101),f80(a101)),x51611))
% 18.55/18.48 [5168]E(f324(f102(a1),f324(f106(a838),x51681)),f2(a1))+~P1(f324(a185,f324(f106(a1),x51681)))
% 18.55/18.48 [5192]E(f324(f151(a838),x51921),f2(a838))+P1(f324(f324(f326(a838),f613(x51921)),f324(f157(a838),x51921)))
% 18.55/18.48 [5211]E(f324(f102(a1),f324(a107,x52111)),x52111)+~P1(f324(f324(f231(a1),f2(a1)),x52111))
% 18.55/18.48 [5212]E(f324(f102(a1),f324(a107,x52121)),x52121)+~P1(f324(f324(f231(a1),f2(a1)),x52121))
% 18.55/18.48 [5221]~P1(f324(a185,x52211))+~P1(f324(f324(f231(a1),f2(a1)),x52211))
% 18.55/18.48 [5320]E(f324(f324(f82(a838),f80(a838)),f324(f106(a838),x53201)),f80(a838))+~P1(f324(f324(f232(a1),x53201),a85))
% 18.55/18.48 [5378]E(x53781,f2(a838))+~P1(f324(f324(f232(a838),x53781),f324(a114,f2(a838))))
% 18.55/18.48 [5400]E(x54001,f324(a114,f2(a838)))+~P1(f324(f324(f280(a838),x54001),f324(a114,f2(a838))))
% 18.55/18.48 [5418]E(f324(f324(f82(a838),f324(f106(a838),x54181)),f80(a838)),f80(a838))+~P1(f324(f324(f232(a1),x54181),a85))
% 18.55/18.48 [5419]E(f324(f324(f3(a838),f324(f106(a838),x54191)),f80(a838)),f2(a838))+~P1(f324(f324(f231(a1),x54191),a85))
% 18.55/18.48 [5429]~P38(x54291)+E(f324(f41(a838),f324(f304(a1,a838,a107),x54291)),f324(f41(a1),x54291))
% 18.55/18.48 [5460]~P86(x54601)+E(f234(x54601,f324(f9(x54601,x54601,a832),f231(x54601))),f235(x54601))
% 18.55/18.48 [5461]~P86(x54611)+E(f233(x54611,f324(f9(x54611,x54611,a832),f231(x54611))),f178(x54611))
% 18.55/18.48 [5471]E(f51(a838,f324(a114,f2(a838)),f324(f106(a838),x54711)),f324(a114,f2(a838)))+~P1(f324(a185,f324(f106(a1),x54711)))
% 18.55/18.48 [5479]P1(f324(f324(f232(a1),f2(a1)),x54791))+~P1(f324(f324(f231(a1),f80(a1)),x54791))
% 18.55/18.48 [5480]~P1(f324(f324(f232(a1),f2(a1)),x54801))+P1(f324(f324(f231(a1),f80(a1)),x54801))
% 18.55/18.48 [5489]E(f324(a114,f324(f324(f3(a838),x54891),f80(a838))),x54891)+~P1(f324(f324(f232(a838),f2(a838)),x54891))
% 18.55/18.48 [5490]E(f324(a114,f324(f324(f3(a838),x54901),f80(a838))),x54901)+~P1(f324(f324(f232(a838),f2(a838)),x54901))
% 18.55/18.48 [5548]P1(f324(f324(f232(a838),f2(a838)),f453(x55481)))+~P1(f324(f324(f232(a1),f2(a1)),x55481))
% 18.55/18.48 [5605]E(f51(a1,f324(f106(a1),a99),x56051),f324(f324(f3(a1),x56051),f80(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x56051))
% 18.55/18.48 [5648]~P1(f324(f324(f232(a1),a85),x56481))+P1(f324(f324(f232(a838),f2(a838)),f324(f106(a838),x56481)))
% 18.55/18.48 [5702]P1(f324(f324(f232(a838),f2(a838)),f324(a107,x57021)))+~P1(f324(f324(f232(a1),f2(a1)),x57021))
% 18.55/18.48 [5724]E(f324(a22,f324(a5,x57241)),x57241)+~P1(f324(f324(f326(a838),x57241),f238(f845(a838,a832))))
% 18.55/18.48 [5749]~P1(f324(f324(f232(a838),f2(a838)),x57491))+P1(f324(f324(f232(a1),f2(a1)),f324(f102(a1),x57491)))
% 18.55/18.48 [5785]~P1(f324(f324(f232(a838),f2(a838)),f324(a107,x57851)))+P1(f324(f324(f232(a1),f2(a1)),x57851))
% 18.55/18.48 [5801]~P38(x58011)+E(f324(f304(a838,a1,f102(a1)),f324(f304(a1,a838,a107),x58011)),x58011)
% 18.55/18.48 [5812]P1(f324(f324(f232(a1),a85),x58121))+~P1(f324(f324(f232(a838),f2(a838)),f324(f106(a838),x58121)))
% 18.55/18.48 [5874]P1(f324(f324(f232(a838),f2(a838)),x58741))+~P1(f324(f324(f232(a1),f2(a1)),f324(f102(a1),x58741)))
% 18.55/18.48 [5907]E(f163(x59071,f115(f839(x59071))),f115(f839(x59071)))+~P1(f324(f313(f839(f839(x59071)),f164(x59071)),f115(f839(x59071))))
% 18.55/18.48 [5991]E(f324(f304(a838,a1,f102(a1)),f324(f258(a838),f324(a107,x59911))),f324(f295(a1,f2(a1)),x59911))+~P1(f324(f324(f231(a1),f2(a1)),x59911))
% 18.55/18.48 [6007]~P84(x60071)+P1(f324(f324(f232(x60071),f2(x60071)),f324(f324(f82(x60071),f80(x60071)),f80(x60071))))
% 18.55/18.48 [6059]P1(f324(f324(f232(a838),f324(a114,f2(a838))),f324(a107,x60591)))+~P1(f324(f324(f232(a1),f80(a1)),x60591))
% 18.55/18.48 [6156]E(x61561,f2(a1))+P1(f324(f55(f2(a1),x61561),f324(f324(f247(a1,a1),f2(a1)),f2(a1))))
% 18.55/18.48 [6335]~P1(f324(f324(f232(a838),f324(a114,f2(a838))),f324(a107,x63351)))+P1(f324(f324(f232(a1),f80(a1)),x63351))
% 18.55/18.48 [6386]E(f324(a114,f324(f324(f3(a838),f324(f106(a838),x63861)),f80(a838))),f324(f106(a838),x63861))+~P1(f324(f324(f232(a838),f2(a838)),f324(f106(a838),x63861)))
% 18.55/18.48 [6506]P31(a830,a851,f324(f324(f324(f93(a830),f849(x65061)),f324(a27,x65061)),f852(x65061)))+~P1(f324(f324(f326(a834),x65061),a847))
% 18.55/18.48 [6788]~P109(x67881)+P36(x67881,f324(f257(f844(x67881,x67881)),f324(f252(x67881,x67881,a832),f232(x67881))))
% 18.55/18.48 [7092]P31(a830,a851,f324(f324(f324(f93(a830),f849(x70921)),f324(f230(a833),f324(a30,x70921))),f852(x70921)))+~P1(f324(f324(f326(a834),x70921),a847))
% 18.55/18.48 [5367]E(f324(f106(a838),f324(f324(f3(a1),x53671),a99)),f324(a114,f324(f106(a838),x53671)))+P1(f324(a185,f324(f106(a1),x53671)))
% 18.55/18.48 [5381]~P35(x53811)+E(f324(f324(f141(a838,a1),f102(a1)),f324(f324(f141(a1,a838),a107),x53811)),x53811)
% 18.55/18.48 [5394]P31(a830,a851,x53941)+~P1(f324(f324(f326(f837(a830)),x53941),a850))
% 18.55/18.48 [5496]E(f324(f81(a1),f324(f102(a1),f324(a114,f464(x54961)))),x54961)+~P1(f324(f324(f232(a1),x54961),f2(a1)))
% 18.55/18.48 [5506]E(f324(f324(f82(a838),f80(a838)),f324(f106(a838),x55061)),f324(f106(a838),f324(f324(f3(a1),x55061),a99)))+P1(f324(f324(f232(a1),x55061),a85))
% 18.55/18.48 [5550]E(f324(f324(f42(a1),f324(f106(a1),a99)),x55501),f324(f106(a1),a99))+~P1(f324(f324(f232(a1),f2(a1)),x55501))
% 18.55/18.48 [5644]E(f324(f324(f82(a838),f324(f106(a838),x56441)),f80(a838)),f324(f106(a838),f324(f324(f3(a1),x56441),a99)))+P1(f324(f324(f232(a1),x56441),a85))
% 18.55/18.48 [5645]E(f324(f324(f3(a838),f324(f106(a838),x56451)),f80(a838)),f324(f106(a838),f324(f324(f82(a1),x56451),a99)))+P1(f324(f324(f231(a1),x56451),a85))
% 18.55/18.48 [5688]E(f324(a107,f324(f324(f82(a1),f80(a1)),x56881)),f324(a114,f324(a107,x56881)))+~P1(f324(f324(f231(a1),f2(a1)),x56881))
% 18.55/18.48 [5726]E(f324(a114,f324(f324(f3(a838),x57261),f324(a114,f2(a838)))),x57261)+~P1(f324(f324(f232(a838),f2(a838)),x57261))
% 18.55/18.48 [5936]E(f51(a838,f324(a114,f2(a838)),f324(f106(a838),x59361)),f324(a107,f51(a1,f80(a1),f324(f106(a1),x59361))))+P1(f324(a185,f324(f106(a1),x59361)))
% 18.55/18.48 [5982]~P1(f324(f324(f232(a1),a99),x59821))+P1(f324(f324(f232(a1),a99),f324(f324(f82(a1),x59821),x59821)))
% 18.55/18.48 [5983]~P1(f324(f324(f232(a1),a85),x59831))+P1(f324(f324(f232(a1),a85),f324(f324(f82(a1),x59831),x59831)))
% 18.55/18.48 [5984]~P1(f324(f324(f232(a1),a99),x59841))+P1(f324(f324(f231(a1),a99),f324(f324(f82(a1),x59841),x59841)))
% 18.55/18.48 [5985]~P1(f324(f324(f231(a1),a85),x59851))+P1(f324(f324(f231(a1),a85),f324(f324(f82(a1),x59851),x59851)))
% 18.55/18.48 [6170]~P1(f324(f64(x61701),f238(f845(x61701,a832))))+P1(f324(f64(f842(x61701)),f238(f845(f842(x61701),a832))))
% 18.55/18.48 [6260]~P1(f324(f324(f231(a1),f2(a1)),x62601))+P1(f324(f324(f232(a1),f2(a1)),f324(f324(f82(a1),f80(a1)),x62601)))
% 18.55/18.48 [6266]E(f324(f246(a1,a1),f53(f80(a1),f324(f106(a1),x62661))),f324(f324(f42(a1),f80(a1)),f324(f106(a1),x62661)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x62661)))
% 18.55/18.48 [6291]E(f324(f251(a1,a1),f53(f80(a1),f324(f106(a1),x62911))),f51(a1,f80(a1),f324(f106(a1),x62911)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x62911)))
% 18.55/18.48 [6304]P1(f324(f64(x63041),f238(f845(x63041,a832))))+~P1(f324(f64(f842(x63041)),f238(f845(f842(x63041),a832))))
% 18.55/18.48 [6336]P1(f324(f324(f232(a1),a99),x63361))+~P1(f324(f324(f232(a1),a99),f324(f324(f82(a1),x63361),x63361)))
% 18.55/18.48 [6337]P1(f324(f324(f232(a1),a99),x63371))+~P1(f324(f324(f231(a1),a99),f324(f324(f82(a1),x63371),x63371)))
% 18.55/18.48 [6338]P1(f324(f324(f232(a1),a85),x63381))+~P1(f324(f324(f232(a1),a85),f324(f324(f82(a1),x63381),x63381)))
% 18.55/18.48 [6339]P1(f324(f324(f231(a1),a85),x63391))+~P1(f324(f324(f231(a1),a85),f324(f324(f82(a1),x63391),x63391)))
% 18.55/18.48 [6534]~P1(f324(f64(a838),x65341))+P1(f324(f64(a1),f324(f304(a838,a1,f102(a1)),x65341)))
% 18.55/18.48 [6669]~P1(f324(f64(x66691),f238(f845(x66691,a832))))+P1(f324(f324(f232(a838),f2(a838)),f324(f41(x66691),f238(f845(x66691,a832)))))
% 18.55/18.48 [7285]P1(f324(f64(a838),x72851))+~P1(f324(f64(a1),f324(f304(a838,a1,f102(a1)),x72851)))
% 18.55/18.48 [5295]~E(a99,x52951)+E(f324(f324(f3(a1),f324(f324(f82(a1),x52951),x52951)),a99),a99)
% 18.55/18.48 [5296]~E(x52961,a99)+E(f324(f324(f3(a1),f324(f324(f82(a1),x52961),x52961)),a99),a99)
% 18.55/18.48 [5806]E(x58061,a99)+~E(f324(f324(f3(a1),f324(f324(f82(a1),x58061),x58061)),a99),a99)
% 18.55/18.48 [5807]E(a99,x58071)+~E(f324(f324(f3(a1),f324(f324(f82(a1),x58071),x58071)),a99),a99)
% 18.55/18.48 [6229]~E(f324(f106(a838),x62291),f2(a838))+P1(f324(a185,f324(f106(a1),f324(f324(f82(a1),x62291),a99))))
% 18.55/18.48 [6594]~P1(f324(a185,f324(f106(a1),x65941)))+P1(f324(a185,f324(f106(a1),f324(f324(f82(a1),x65941),x65941))))
% 18.55/18.48 [6595]~P1(f324(f324(f231(a1),x65951),a99))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x65951),x65951)),a99))
% 18.55/18.48 [6596]~P1(f324(f324(f232(a1),x65961),a85))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x65961),x65961)),a85))
% 18.55/18.48 [6597]~P1(f324(f324(f231(a1),x65971),a99))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x65971),x65971)),a99))
% 18.55/18.48 [6598]~P1(f324(f324(f231(a1),x65981),a85))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x65981),x65981)),a85))
% 18.55/18.48 [6930]E(f324(f106(a838),x69301),f2(a838))+~P1(f324(a185,f324(f106(a1),f324(f324(f82(a1),x69301),a99))))
% 18.55/18.48 [7188]~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x71881)))+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),f324(f324(f82(a1),x71881),x71881))))
% 18.55/18.48 [7189]P1(f324(a185,f324(f106(a1),x71891)))+~P1(f324(a185,f324(f106(a1),f324(f324(f82(a1),x71891),x71891))))
% 18.55/18.48 [7190]P1(f324(f324(f232(a1),x71901),a85))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x71901),x71901)),a85))
% 18.55/18.48 [7191]P1(f324(f324(f231(a1),x71911),a99))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x71911),x71911)),a99))
% 18.55/18.48 [7192]P1(f324(f324(f231(a1),x71921),a99))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x71921),x71921)),a99))
% 18.55/18.48 [7193]P1(f324(f324(f231(a1),x71931),a85))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x71931),x71931)),a85))
% 18.55/18.48 [7575]E(f324(a110,f595(x75751)),x75751)+~P1(f324(f324(f326(f845(f844(a838,a838),a832)),x75751),a100))
% 18.55/18.48 [6142]~P89(x61421)+E(f324(f106(x61421),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f80(x61421))
% 18.55/18.48 [6143]~P89(x61431)+E(f324(f106(x61431),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f80(x61431))
% 18.55/18.48 [6648]~P1(f324(a185,f324(f106(a1),x66481)))+E(f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x66481),x66481)),a99)),f2(a838))
% 18.55/18.48 [7757]~P1(f324(f324(f232(a1),f324(f106(a1),x77571)),f2(a1)))+E(f324(f246(a1,a1),f324(a57,f56(f324(f81(a1),f80(a1)),f324(f81(a1),f324(f106(a1),x77571))))),f324(f324(f42(a1),f80(a1)),f324(f106(a1),x77571)))
% 18.55/18.48 [7770]~P1(f324(f324(f232(a1),f324(f106(a1),x77701)),f2(a1)))+E(f324(f251(a1,a1),f324(a57,f56(f324(f81(a1),f80(a1)),f324(f81(a1),f324(f106(a1),x77701))))),f51(a1,f80(a1),f324(f106(a1),x77701)))
% 18.55/18.48 [7817]~P1(f324(f324(f232(a1),a99),x78171))+P1(f324(f324(f232(a1),a99),f324(f324(f3(a1),f324(f324(f82(a1),x78171),x78171)),a99)))
% 18.55/18.48 [7818]~P1(f324(f324(f231(a1),a85),x78181))+P1(f324(f324(f232(a1),a85),f324(f324(f3(a1),f324(f324(f82(a1),x78181),x78181)),a99)))
% 18.55/18.48 [7819]~P1(f324(f324(f231(a1),a99),x78191))+P1(f324(f324(f231(a1),a99),f324(f324(f3(a1),f324(f324(f82(a1),x78191),x78191)),a99)))
% 18.55/18.48 [7820]~P1(f324(f324(f231(a1),a85),x78201))+P1(f324(f324(f231(a1),a85),f324(f324(f3(a1),f324(f324(f82(a1),x78201),x78201)),a99)))
% 18.55/18.48 [8123]~P89(x81231)+~P33(x81231,f324(f106(x81231),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))
% 18.55/18.48 [8304]P1(f324(f324(f232(a1),a99),x83041))+~P1(f324(f324(f232(a1),a99),f324(f324(f3(a1),f324(f324(f82(a1),x83041),x83041)),a99)))
% 18.55/18.48 [8305]P1(f324(f324(f231(a1),a99),x83051))+~P1(f324(f324(f231(a1),a99),f324(f324(f3(a1),f324(f324(f82(a1),x83051),x83051)),a99)))
% 18.55/18.48 [8306]P1(f324(f324(f231(a1),a85),x83061))+~P1(f324(f324(f232(a1),a85),f324(f324(f3(a1),f324(f324(f82(a1),x83061),x83061)),a99)))
% 18.55/18.48 [8307]P1(f324(f324(f231(a1),a85),x83071))+~P1(f324(f324(f231(a1),a85),f324(f324(f3(a1),f324(f324(f82(a1),x83071),x83071)),a99)))
% 18.55/18.48 [8602]E(f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x86021),x86021)),a99)),f324(f324(f88(a838,a838),f324(f106(a838),x86021)),f324(f324(f10(a838,a838,a838),a114),f324(f324(f20(a838,a838,a838),f82(a838)),f7(a838)))))+P1(f324(a185,f324(f106(a1),x86021)))
% 18.55/18.48 [9373]E(x93731,f179(f845(f844(a838,a838),a832)))+P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x93731),f179(f845(f844(a838,a838),a832)))),a39))
% 18.55/18.48 [8535]~P1(f324(a185,f324(f106(a1),x85351)))+P1(f324(a185,f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),x85351),x85351)),a99))))
% 18.55/18.48 [8536]~P1(f324(f324(f232(a1),x85361),a99))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x85361),x85361)),a99)),a99))
% 18.55/18.48 [8537]~P1(f324(f324(f232(a1),x85371),a85))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x85371),x85371)),a99)),a85))
% 18.55/18.48 [8538]~P1(f324(f324(f231(a1),x85381),a99))+P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x85381),x85381)),a99)),a99))
% 18.55/18.48 [8539]~P1(f324(f324(f232(a1),x85391),a85))+P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x85391),x85391)),a99)),a85))
% 18.55/18.48 [8638]~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x86381)))+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),x86381),x86381)),a99))))
% 18.55/18.48 [8771]~P89(x87711)+E(f324(f324(f82(x87711),f80(x87711)),f80(x87711)),f324(f106(x87711),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))
% 18.55/18.48 [8916]P1(f324(a185,f324(f106(a1),x89161)))+~P1(f324(a185,f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89161),x89161)),a99))))
% 18.55/18.48 [8917]P1(f324(f324(f232(a1),x89171),a99))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89171),x89171)),a99)),a99))
% 18.55/18.48 [8918]P1(f324(f324(f232(a1),x89181),a85))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89181),x89181)),a99)),a85))
% 18.55/18.48 [8919]P1(f324(f324(f232(a1),x89191),a85))+~P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89191),x89191)),a99)),a85))
% 18.55/18.48 [8920]P1(f324(f324(f231(a1),x89201),a99))+~P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89201),x89201)),a99)),a99))
% 18.55/18.48 [9423]~P1(f324(f64(f844(a838,a838)),x94231))+P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),f179(f845(f844(a838,a838),a832))),x94231)),a71))
% 18.55/18.48 [9208]~P2(x92081)+E(f324(f324(f240(x92081),f2(x92081)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f2(x92081))
% 18.55/18.48 [9209]~P2(x92091)+E(f324(f324(f240(x92091),f80(x92091)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f80(x92091))
% 18.55/18.48 [9627]~P1(f324(f324(f232(a838),f80(a838)),x96271))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f42(a838),x96271),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.55/18.48 [9633]~P1(f324(f324(f232(a838),f2(a838)),x96331))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f42(a838),f324(f324(f82(a838),x96331),f80(a838))),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.55/18.48 [9674]~E(f51(a838,x96741,f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f80(a838))+P1(f324(f324(f232(a838),f2(a838)),f51(a838,x96741,f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.55/18.48 [9707]E(f51(a838,x97071,f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f80(a838))+~P1(f324(f324(f232(a838),f2(a838)),f51(a838,x97071,f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.55/18.48 [4453]~P36(x44531,x44532)+P55(x44531,x44532)
% 18.55/18.48 [4454]~P42(x44541,x44542)+P55(x44541,x44542)
% 18.55/18.48 [4413]~E(x44131,x44132)+E(f267(x44131,x44132),f80(a101))
% 18.55/18.48 [4416]E(f210(x44161,x44162),x44161)+~E(x44162,f2(a838))
% 18.55/18.48 [4421]P37(x44211,x44212)+~E(x44212,f182(x44211))
% 18.55/18.48 [4424]~E(x44242,f115(x44241))+E(f140(x44241,x44242),f115(x44241))
% 18.55/18.48 [4425]~E(x44252,f115(x44251))+E(f140(x44251,x44252),f115(x44251))
% 18.55/18.48 [4429]~P37(x44292,x44291)+E(x44291,f182(x44292))
% 18.55/18.48 [4443]~E(f140(x44432,x44431),f115(x44432))+E(x44431,f115(x44432))
% 18.55/18.48 [4444]~E(f140(x44442,x44441),f115(x44442))+E(x44441,f115(x44442))
% 18.55/18.48 [4458]~P85(x44582)+P85(f845(x44581,x44582))
% 18.55/18.48 [4459]~P102(x44592)+P102(f845(x44591,x44592))
% 18.55/18.48 [4460]~P101(x44602)+P101(f845(x44601,x44602))
% 18.55/18.48 [4461]~P91(x44612)+P91(f845(x44611,x44612))
% 18.55/18.48 [4462]~P81(x44622)+P81(f845(x44621,x44622))
% 18.55/18.48 [4463]~P73(x44632)+P73(f845(x44631,x44632))
% 18.55/18.48 [4464]~P94(x44642)+P93(f845(x44641,x44642))
% 18.55/18.48 [4465]~P94(x44652)+P94(f845(x44651,x44652))
% 18.55/18.48 [4466]~P100(x44662)+P100(f845(x44661,x44662))
% 18.55/18.48 [4467]~P96(x44672)+P95(f845(x44671,x44672))
% 18.55/18.48 [4468]~P97(x44682)+P97(f845(x44681,x44682))
% 18.55/18.48 [4469]~P94(x44692)+P99(f845(x44691,x44692))
% 18.55/18.48 [4470]~P9(x44702)+P9(f845(x44701,x44702))
% 18.55/18.48 [4471]~P96(x44712)+P98(f845(x44711,x44712))
% 18.55/18.48 [4472]~P110(x44722)+P110(f845(x44721,x44722))
% 18.55/18.48 [4473]~P96(x44732)+P96(f845(x44731,x44732))
% 18.55/18.48 [4485]E(x44851,x44852)+~E(f324(a114,x44851),f324(a114,x44852))
% 18.55/18.48 [4486]E(x44861,x44862)+~E(f324(a114,x44861),f324(a114,x44862))
% 18.55/18.48 [4487]E(x44871,x44872)+~E(f324(a27,x44871),f324(a27,x44872))
% 18.55/18.48 [4488]E(x44881,x44882)+~E(f324(a5,x44881),f324(a5,x44882))
% 18.55/18.48 [4489]E(x44891,x44892)+~E(f324(a22,x44891),f324(a22,x44892))
% 18.55/18.48 [4490]E(x44901,x44902)+~E(f324(a22,x44901),f324(a22,x44902))
% 18.55/18.48 [4491]E(x44911,x44912)+~E(f324(a110,x44911),f324(a110,x44912))
% 18.55/18.48 [4587]~P7(x45871)+E(f51(x45871,x45872,x45872),f2(x45871))
% 18.55/18.48 [4621]~P36(x46211,x46212)+P36(f839(x46211),f135(x46211,x46212))
% 18.55/18.48 [4622]~P36(x46221,x46222)+P36(f839(x46221),f134(x46221,x46222))
% 18.55/18.48 [4716]~P36(x47161,x47162)+P36(f845(x47161,a832),f316(x47161,x47162))
% 18.55/18.48 [4717]~P36(x47171,x47172)+P36(f845(x47171,a832),f317(x47171,x47172))
% 18.55/18.48 [4836]~P10(x48361)+P38(f296(a1,x48361,x48362))
% 18.55/18.48 [4935]~P36(x49351,x49352)+P57(x49351,f70(x49351,x49351,x49352))
% 18.55/18.48 [5423]~P70(x54231)+P29(x54231,x54231,f81(x54231),x54232)
% 18.55/18.48 [4438]~E(x44382,f115(x44381))+E(f324(f154(x44381),x44382),f115(x44381))
% 18.55/18.48 [4439]~E(x44392,f115(x44391))+E(f324(f153(x44391),x44392),f115(x44391))
% 18.55/18.48 [4440]~E(x44402,f115(x44401))+E(f324(f154(x44401),x44402),f115(x44401))
% 18.55/18.48 [4495]E(x44951,f324(a107,x44952))+~E(f324(f102(a1),x44951),x44952)
% 18.55/18.48 [4497]E(x44971,f115(x44972))+~E(f324(f154(x44972),x44971),f115(x44972))
% 18.55/18.48 [4498]E(x44981,f115(x44982))+~E(f324(f153(x44982),x44981),f115(x44982))
% 18.55/18.48 [4499]E(x44991,f115(x44992))+~E(f324(f154(x44992),x44991),f115(x44992))
% 18.55/18.48 [4514]~P89(x45141)+E(f324(f106(x45141),x45142),f324(f105(x45141),x45142))
% 18.55/18.48 [4521]~E(x45212,f182(x45211))+E(f225(x45211,x45212),f179(f845(x45211,a832)))
% 18.55/18.48 [4522]~P58(x45221)+P1(f324(f64(x45221),x45222))
% 18.55/18.48 [4523]~P58(x45231)+P1(f324(f64(x45231),x45232))
% 18.55/18.48 [4530]E(x45301,f182(x45302))+E(f324(f226(x45302),f330(x45302,x45301)),x45301)
% 18.55/18.48 [4531]E(x45311,f182(x45312))+E(f324(f226(x45312),f440(x45312,x45311)),x45311)
% 18.55/18.48 [4533]~E(f709(x45332,x45331),f115(x45331))+E(f163(x45331,x45332),f115(f839(x45331)))
% 18.55/18.48 [4542]~E(x45422,f115(x45421))+E(f324(f157(x45421),x45422),f179(f845(x45421,a832)))
% 18.55/18.48 [4543]~E(x45432,f115(x45431))+E(f179(f845(x45431,a832)),f324(f157(x45431),x45432))
% 18.55/18.48 [4544]E(x45441,x45442)+~E(f324(f102(a1),x45441),f324(f102(a1),x45442))
% 18.55/18.48 [4545]E(x45451,x45452)+~E(f324(f102(a1),x45451),f324(f102(a1),x45452))
% 18.55/18.48 [4548]E(f208(x45481,x45482),f2(a838))+P1(f324(f64(x45481),x45482))
% 18.55/18.48 [4566]~P103(x45661)+E(f84(x45661,f84(x45661,x45662)),f84(x45661,x45662))
% 18.55/18.48 [4578]~P105(x45781)+E(f324(f324(f240(x45781),x45782),f80(a838)),x45782)
% 18.55/18.48 [4579]~P75(x45791)+E(f324(f324(f240(x45791),x45792),f80(a838)),x45792)
% 18.55/18.48 [4581]E(x45811,x45812)+E(f267(x45811,x45812),f324(f324(f82(a101),x45812),f80(a101)))
% 18.55/18.48 [4582]E(f324(f41(x45821),x45822),f2(a838))+P1(f324(f64(x45821),x45822))
% 18.55/18.48 [4583]E(f324(f41(x45831),x45832),f2(a838))+P1(f324(f64(x45831),x45832))
% 18.55/18.48 [4584]E(f324(f41(x45841),x45842),f2(a838))+P1(f324(f64(x45841),x45842))
% 18.55/18.48 [4588]~E(f140(x45881,x45882),x45882)+P1(f324(f127(x45881),x45882))
% 18.55/18.48 [4591]~P105(x45911)+E(f324(f324(f83(x45911),x45912),f80(x45911)),x45912)
% 18.55/18.48 [4592]~P68(x45921)+E(f324(f324(f83(x45921),x45922),f80(x45921)),x45922)
% 18.55/18.48 [4593]~P75(x45931)+E(f324(f324(f83(x45931),x45932),f80(x45931)),x45932)
% 18.55/18.48 [4594]~P105(x45941)+E(f324(f324(f82(x45941),x45942),f2(x45941)),x45942)
% 18.55/18.48 [4595]~P72(x45951)+E(f324(f324(f82(x45951),x45952),f2(x45951)),x45952)
% 18.55/18.48 [4596]~P67(x45961)+E(f324(f324(f82(x45961),x45962),f2(x45961)),x45962)
% 18.55/18.48 [4597]~P7(x45971)+E(f324(f324(f42(x45971),x45972),f80(x45971)),x45972)
% 18.55/18.48 [4598]~P63(x45981)+E(f324(f324(f3(x45981),x45982),f2(x45981)),x45982)
% 18.55/18.48 [4599]~P114(x45991)+E(f324(f324(f284(x45991),x45992),f80(x45991)),x45992)
% 18.55/18.48 [4600]~P95(x46001)+E(f324(f324(f103(x46001),x46002),f179(x46001)),x46002)
% 18.55/18.48 [4601]~P98(x46011)+E(f324(f324(f104(x46011),x46012),f238(x46011)),x46012)
% 18.55/18.48 [4602]~P105(x46021)+E(f324(f324(f240(x46021),x46022),f2(a838)),f80(x46021))
% 18.55/18.48 [4603]~P108(x46031)+E(f324(f324(f240(x46031),x46032),f2(a838)),f80(x46031))
% 18.55/18.48 [4604]~E(x46042,f179(f845(x46041,a832)))+E(f324(f41(x46041),x46042),f2(a838))
% 18.55/18.48 [4615]~P7(x46151)+E(f51(x46151,x46152,f2(x46151)),x46152)
% 18.55/18.48 [4623]~P121(x46231)+E(f324(f324(f83(x46231),x46232),f2(x46231)),f2(x46231))
% 18.55/18.48 [4624]~P105(x46241)+E(f324(f324(f83(x46241),x46242),f2(x46241)),f2(x46241))
% 18.55/18.48 [4625]~P7(x46251)+E(f324(f324(f42(x46251),x46252),f2(x46251)),f2(x46251))
% 18.55/18.48 [4626]~P115(x46261)+E(f324(f324(f284(x46261),x46262),f2(x46261)),f2(x46261))
% 18.55/18.48 [4627]~P98(x46271)+E(f324(f324(f103(x46271),x46272),f238(x46271)),f238(x46271))
% 18.55/18.48 [4628]~P95(x46281)+E(f324(f324(f104(x46281),x46282),f179(x46281)),f179(x46281))
% 18.55/18.48 [4629]E(x46291,f182(x46292))+~E(f225(x46292,x46291),f179(f845(x46292,a832)))
% 18.55/18.48 [4631]~P7(x46311)+E(f51(x46311,x46312,f80(x46311)),f2(x46311))
% 18.55/18.48 [4632]~P7(x46321)+E(f51(x46321,f2(x46321),x46322),f2(x46321))
% 18.55/18.48 [4683]P36(x46831,x46832)+~E(f614(x46832,x46831),f179(f845(x46831,a832)))
% 18.55/18.48 [4684]E(x46841,f115(x46842))+~E(f324(f157(x46842),x46841),f179(f845(x46842,a832)))
% 18.55/18.48 [4685]E(x46851,f115(x46852))+~E(f179(f845(x46852,a832)),f324(f157(x46852),x46851))
% 18.55/18.48 [4688]~E(x46881,x46882)+P1(f324(f324(a321,x46881),x46882))
% 18.55/18.48 [4698]P1(x46981)+P1(f324(f324(a327,x46981),x46982))
% 18.55/18.48 [4699]E(x46991,f115(x46992))+E(f324(f324(f149(x46992),x46991),f2(a838)),f324(f130(x46992),x46991))
% 18.55/18.48 [4701]E(f140(x47011,x47012),x47012)+~P1(f324(f127(x47011),x47012))
% 18.55/18.48 [4702]E(f140(x47021,x47022),x47022)+~P1(f324(f127(x47021),x47022))
% 18.55/18.48 [4707]~P1(x47072)+P1(f324(f324(a327,x47071),x47072))
% 18.55/18.48 [4708]~P1(x47082)+P1(f324(f324(a323,x47081),x47082))
% 18.55/18.48 [4709]~P1(x47091)+P1(f324(f324(a323,x47091),x47092))
% 18.55/18.48 [4719]~E(f710(x47192,x47191),f714(x47192,x47191))+P1(f324(f127(x47191),x47192))
% 18.55/18.48 [4727]E(f324(f257(x47271),x47272),f179(f845(x47271,a832)))+P1(f324(x47272,f331(x47272)))
% 18.55/18.48 [4728]E(f179(f845(x47281,a832)),f324(f257(x47281),x47282))+P1(f324(x47282,f378(x47282)))
% 18.55/18.48 [4792]~P103(x47921)+E(f324(f324(f83(x47921),x47922),f84(x47921,x47922)),f324(f77(x47921),x47922))
% 18.55/18.48 [4803]~E(x48031,f2(a1))+E(f52(x48031,x48032),f324(f324(f247(a1,a1),f2(a1)),f2(a1)))
% 18.55/18.48 [4804]~E(x48041,f2(a1))+E(f52(x48041,x48042),f324(f324(f247(a1,a1),f2(a1)),f2(a1)))
% 18.55/18.48 [4835]~P55(x48351,x48352)+P55(x48351,f324(f279(x48351,x48351),x48352))
% 18.55/18.48 [4852]~E(f324(a30,x48521),f324(f226(a833),x48522))+P1(f324(a26,f324(a27,x48521)))
% 18.55/18.48 [4856]E(x48561,x48562)+~P1(f324(f324(a321,x48561),x48562))
% 18.55/18.48 [4859]~P1(f324(a26,x48592))+P1(f324(a26,f35(x48591,x48592)))
% 18.55/18.48 [4860]~P1(f324(a26,x48602))+P1(f324(a26,f35(x48601,x48602)))
% 18.55/18.48 [4869]P1(x48691)+~P1(f324(f324(a322,x48692),x48691))
% 18.55/18.48 [4870]P1(x48701)+~P1(f324(f324(a322,x48701),x48702))
% 18.55/18.48 [4874]~P110(x48741)+P1(f324(f324(f231(x48741),x48742),f238(x48741)))
% 18.55/18.48 [4875]~P105(x48751)+P1(f324(f324(f280(x48751),x48752),f2(x48751)))
% 18.55/18.48 [4879]E(x48791,x48792)+~E(f324(x48791,f441(x48792,x48791)),f324(x48792,f441(x48792,x48791)))
% 18.55/18.48 [4909]E(x49091,f2(a838))+E(f210(x49091,f51(a838,x49092,x49091)),f210(x49092,x49091))
% 18.55/18.48 [4914]~P86(x49141)+P18(x49141,f324(f324(f139(x49141),x49142),f115(x49141)))
% 18.55/18.48 [4916]E(x49161,f2(a1))+P1(f324(f55(x49162,x49161),f52(x49162,x49161)))
% 18.55/18.48 [4933]~E(x49331,x49332)+P1(f324(f324(f232(a838),x49331),f324(a114,x49332)))
% 18.55/18.48 [4943]~E(x49431,f2(a838))+P1(f324(f324(f232(a838),x49431),f324(a114,x49432)))
% 18.55/18.48 [4953]P1(f324(x49531,x49532))+P1(f324(f324(f231(a1),f2(a1)),f514(x49531)))
% 18.55/18.48 [4989]P1(f324(a26,x49891))+~P1(f324(a26,f35(x49892,x49891)))
% 18.55/18.48 [4990]P1(f324(a26,x49901))+~P1(f324(a26,f35(x49902,x49901)))
% 18.55/18.48 [4991]P1(f324(a26,x49911))+~P1(f324(a26,f36(x49912,x49911)))
% 18.55/18.48 [4992]P1(f324(a26,x49921))+~P1(f324(a26,f36(x49922,x49921)))
% 18.55/18.48 [4993]P1(f324(a26,x49931))+~P1(f324(a26,f36(x49931,x49932)))
% 18.55/18.48 [4994]P1(f324(a26,x49941))+~P1(f324(a26,f36(x49941,x49942)))
% 18.55/18.48 [5023]P55(x50231,x50232)+~P55(x50231,f324(f279(x50231,x50231),x50232))
% 18.55/18.48 [5025]~E(f51(a838,x50252,x50251),f2(a838))+E(f324(f324(f83(a838),x50251),f748(x50251,x50252)),x50252)
% 18.55/18.48 [5026]~E(f51(a1,x50262,x50261),f2(a1))+E(f324(f324(f83(a1),x50261),f631(x50261,x50262)),x50262)
% 18.55/18.48 [5031]~E(x50311,f324(a114,x50312))+P1(f324(f324(f231(a838),x50311),f324(a114,x50312)))
% 18.55/18.48 [5052]~P1(f324(x50521,x50522))+P1(f324(f324(f231(a1),f2(a1)),f513(x50521)))
% 18.55/18.48 [5063]E(f324(f324(f3(a838),f324(a107,x50631)),f324(a107,x50632)),f324(a107,x50631))+~P1(f324(a185,x50632))
% 18.55/18.48 [5091]E(f268(x50911,x50912),f80(a101))+~P1(f324(f324(f231(a101),x50911),f80(a101)))
% 18.55/18.48 [5180]E(f324(f324(f149(x51801),x51802),f710(x51802,x51801)),f324(f324(f149(x51801),x51802),f714(x51802,x51801)))+P1(f324(f127(x51801),x51802))
% 18.55/18.48 [5222]~P1(f324(x52221,f92(x52222,x52221)))+P1(f324(x52221,f365(x52222,x52221)))
% 18.55/18.48 [5285]P57(x52851,x52852)+~P1(f324(f313(x52851,x52852),f344(x52852,x52851)))
% 18.55/18.48 [5430]~E(f324(a114,f51(a838,x54301,x54302)),x54302)+E(f51(a838,f324(a114,x54301),x54302),f2(a838))
% 18.55/18.48 [5486]P36(x54861,x54862)+P1(f324(f324(f326(x54861),f367(x54862,x54861)),f368(x54862,x54861)))
% 18.55/18.48 [5492]~P2(x54921)+P1(f324(f324(f326(x54921),f324(f102(x54921),x54922)),f175(x54921)))
% 18.55/18.48 [5493]~P119(x54931)+P1(f324(f324(f326(x54931),f324(f102(x54931),x54932)),f112(x54931)))
% 18.55/18.48 [5494]~P119(x54941)+P1(f324(f324(f326(x54941),f324(f105(x54941),x54942)),f112(x54941)))
% 18.55/18.48 [5495]~P89(x54951)+P1(f324(f324(f326(x54951),f324(f106(x54951),x54952)),f112(x54951)))
% 18.55/18.48 [5647]E(f324(a114,f51(a838,x56471,x56472)),x56472)+E(f51(a838,f324(a114,x56471),x56472),f324(a114,f51(a838,x56471,x56472)))
% 18.55/18.48 [6072]P36(x60721,x60722)+~P1(f324(f324(f326(x60721),f346(x60722,x60721)),f314(x60721,x60722)))
% 18.55/18.48 [6106]~P84(x61061)+~P1(f324(f324(f232(x61061),f324(f102(x61061),x61062)),f2(x61061)))
% 18.55/18.48 [6107]~P78(x61071)+~P1(f324(f324(f232(x61071),f324(f77(x61071),x61072)),f2(x61071)))
% 18.55/18.48 [6198]P1(f324(f324(f232(a1),x61981),f51(a1,x61982,x61981)))+~P1(f324(f324(f232(a1),x61981),f2(a1)))
% 18.55/18.48 [6199]P1(f324(f324(f232(a1),x61991),f51(a1,x61992,x61991)))+~P1(f324(f324(f232(a1),x61991),f2(a1)))
% 18.55/18.48 [6306]E(f324(f324(f303(a838),f324(a114,x63061)),f296(a838,x63062,x63061)),f296(a838,x63062,f324(a114,x63061)))+~P1(f324(f324(f231(a838),x63062),f324(a114,x63061)))
% 18.55/18.48 [6532]E(f324(f153(x65321),x65322),x65322)+~P1(f324(f324(f231(a838),f324(f180(f839(x65321)),x65322)),f80(a838)))
% 18.55/18.48 [6555]~P78(x65551)+P1(f324(f324(f231(x65551),f324(f81(x65551),f324(f77(x65551),x65552))),f2(x65551)))
% 18.55/18.48 [6591]~P36(x65911,x65912)+P36(x65911,f324(f324(f282(x65911,x65911,x65911),x65912),f301(x65911,x65912)))
% 18.55/18.48 [6824]~P1(f324(f324(f232(a1),x68242),f2(a1)))+P1(f324(f324(f231(a1),f51(a1,x68241,x68242)),f2(a1)))
% 18.55/18.48 [6825]~P1(f324(f324(f232(a1),x68252),f2(a1)))+P1(f324(f324(f231(a1),f51(a1,x68251,x68252)),f2(a1)))
% 18.55/18.48 [7235]~P2(x72351)+E(f181(x72351,f324(f324(f9(x72351,x72351,x72351),f82(x72351)),f80(x72351)),x72352,f2(x72351)),f324(f102(x72351),x72352))
% 18.55/18.48 [7268]~P118(x72681)+~P1(f324(f324(f232(x72681),f324(f324(f83(x72681),x72682),x72682)),f2(x72681)))
% 18.55/18.48 [9801]~P103(x98011)+~P1(f324(f324(f232(x98011),f324(f324(f240(x98011),x98012),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f2(x98011)))
% 18.55/18.48 [4496]~E(x44962,f115(x44961))+E(f324(f180(f839(x44961)),x44962),f2(a838))
% 18.55/18.48 [4534]~E(x45341,f2(a838))+E(f324(f324(f82(a838),x45341),x45342),x45342)
% 18.55/18.48 [4535]~E(x45352,f2(a838))+E(f324(f324(f83(a838),x45351),x45352),f2(a838))
% 18.55/18.48 [4536]~E(x45361,f2(a838))+E(f324(f324(f83(a838),x45361),x45362),f2(a838))
% 18.55/18.48 [4537]~E(x45371,f2(a838))+E(f324(f324(f83(a838),x45371),x45372),f2(a838))
% 18.55/18.48 [4538]~E(x45382,f2(a1))+E(f324(f324(f42(a1),x45381),x45382),f2(a1))
% 18.55/18.48 [4539]~E(x45392,f2(a838))+E(f324(f324(f240(a838),x45391),x45392),f80(a838))
% 18.55/18.48 [4549]E(x45491,f115(x45492))+~E(f324(f180(f839(x45492)),x45491),f2(a838))
% 18.55/18.48 [4550]~P92(x45501)+E(f324(f324(f83(x45501),x45502),x45502),x45502)
% 18.55/18.48 [4551]~P92(x45511)+E(f324(f324(f83(x45511),x45512),x45512),x45512)
% 18.55/18.48 [4552]~P86(x45521)+E(f324(f324(f235(x45521),x45522),x45522),x45522)
% 18.55/18.48 [4553]~P86(x45531)+E(f324(f324(f235(x45531),x45532),x45532),x45532)
% 18.55/18.48 [4554]~P86(x45541)+E(f324(f324(f178(x45541),x45542),x45542),x45542)
% 18.55/18.48 [4555]~P86(x45551)+E(f324(f324(f178(x45551),x45552),x45552),x45552)
% 18.55/18.48 [4556]~P93(x45561)+E(f324(f324(f103(x45561),x45562),x45562),x45562)
% 18.55/18.48 [4557]~P93(x45571)+E(f324(f324(f103(x45571),x45572),x45572),x45572)
% 18.55/18.48 [4558]~P94(x45581)+E(f324(f324(f103(x45581),x45582),x45582),x45582)
% 18.55/18.48 [4559]~P94(x45591)+E(f324(f324(f104(x45591),x45592),x45592),x45592)
% 18.55/18.48 [4560]~P99(x45601)+E(f324(f324(f104(x45601),x45602),x45602),x45602)
% 18.55/18.48 [4561]~P99(x45611)+E(f324(f324(f104(x45611),x45612),x45612),x45612)
% 18.55/18.48 [4577]~P63(x45771)+E(f324(f324(f3(x45771),x45772),x45772),f2(x45771))
% 18.55/18.48 [4589]~P63(x45891)+E(f324(f81(x45891),f324(f81(x45891),x45892)),x45892)
% 18.55/18.48 [4590]~P91(x45901)+E(f324(f81(x45901),f324(f81(x45901),x45902)),x45902)
% 18.55/18.48 [4607]~E(x46072,f2(a838))+E(f324(f324(f240(a838),x46071),x46072),f324(a114,f2(a838)))
% 18.55/18.48 [4640]~P105(x46401)+E(f324(f324(f83(x46401),f80(x46401)),x46402),x46402)
% 18.55/18.48 [4641]~P68(x46411)+E(f324(f324(f83(x46411),f80(x46411)),x46412),x46412)
% 18.55/18.48 [4642]~P75(x46421)+E(f324(f324(f83(x46421),f80(x46421)),x46422),x46422)
% 18.55/18.48 [4643]~P105(x46431)+E(f324(f324(f82(x46431),f2(x46431)),x46432),x46432)
% 18.55/18.48 [4644]~P72(x46441)+E(f324(f324(f82(x46441),f2(x46441)),x46442),x46442)
% 18.55/18.48 [4645]~P67(x46451)+E(f324(f324(f82(x46451),f2(x46451)),x46452),x46452)
% 18.55/18.48 [4646]~P95(x46461)+E(f324(f324(f103(x46461),f179(x46461)),x46462),x46462)
% 18.55/18.48 [4647]~P98(x46471)+E(f324(f324(f104(x46471),f238(x46471)),x46472),x46472)
% 18.55/18.48 [4664]~P121(x46641)+E(f324(f324(f83(x46641),f2(x46641)),x46642),f2(x46641))
% 18.55/18.48 [4665]~P105(x46651)+E(f324(f324(f83(x46651),f2(x46651)),x46652),f2(x46651))
% 18.55/18.48 [4666]~P7(x46661)+E(f324(f324(f42(x46661),f2(x46661)),x46662),f2(x46661))
% 18.55/18.48 [4667]~P75(x46671)+E(f324(f324(f240(x46671),f80(x46671)),x46672),f80(x46671))
% 18.55/18.48 [4668]~P114(x46681)+E(f324(f324(f284(x46681),f2(x46681)),x46682),f2(x46681))
% 18.55/18.48 [4669]~P98(x46691)+E(f324(f324(f103(x46691),f238(x46691)),x46692),f238(x46691))
% 18.55/18.48 [4670]~P95(x46701)+E(f324(f324(f104(x46701),f179(x46701)),x46702),f179(x46701))
% 18.55/18.48 [4678]E(x46781,f115(x46782))+E(f133(x46782,f324(f154(x46782),x46781)),f324(f130(x46782),x46781))
% 18.55/18.48 [4679]E(x46791,f115(x46792))+E(f324(f130(x46792),f324(f154(x46792),x46791)),f133(x46792,x46791))
% 18.55/18.48 [4680]E(x46801,f2(a838))+~E(f324(f324(f82(a838),x46802),x46801),x46802)
% 18.55/18.48 [4686]~P119(x46861)+E(f324(f105(x46861),f324(f102(a1),x46862)),f324(f102(x46861),x46862))
% 18.55/18.48 [4687]~P89(x46871)+E(f324(f105(x46871),f324(f106(a1),x46872)),f324(f106(x46871),x46872))
% 18.55/18.48 [4692]E(x46921,f80(a838))+~E(f324(f324(f83(a838),x46922),x46921),f80(a838))
% 18.55/18.48 [4693]E(x46931,f80(a838))+~E(f324(f324(f83(a838),x46931),x46932),f80(a838))
% 18.55/18.48 [4694]E(x46941,f2(a838))+~E(f324(f324(f82(a838),x46942),x46941),f2(a838))
% 18.55/18.48 [4695]E(x46951,f2(a838))+~E(f324(f324(f82(a838),x46951),x46952),f2(a838))
% 18.55/18.48 [4696]E(x46961,f80(a838))+~E(f324(f324(f83(a838),x46962),x46961),f80(a838))
% 18.55/18.48 [4697]E(x46971,f80(a838))+~E(f324(f324(f83(a838),x46971),x46972),f80(a838))
% 18.55/18.48 [4712]~P103(x47121)+E(f324(f77(x47121),f324(f102(x47121),x47122)),f324(f102(x47121),x47122))
% 18.55/18.48 [4713]~P78(x47131)+E(f324(f77(x47131),f324(f81(x47131),x47132)),f324(f77(x47131),x47132))
% 18.55/18.48 [4714]~P78(x47141)+E(f324(f77(x47141),f324(f77(x47141),x47142)),f324(f77(x47141),x47142))
% 18.55/18.48 [4715]~P67(x47151)+E(f324(f151(x47151),f324(f154(x47151),x47152)),f324(f151(x47151),x47152))
% 18.55/18.48 [4720]~E(x47201,f324(a114,f2(a838)))+E(f324(f324(f240(a838),x47201),x47202),f324(a114,f2(a838)))
% 18.55/18.48 [4730]~P63(x47301)+E(f324(f324(f3(x47301),f2(x47301)),x47302),f324(f81(x47301),x47302))
% 18.55/18.48 [4731]~E(x47312,f2(a838))+E(f129(a838,f324(f295(a838,x47311),x47312)),f115(a838))
% 18.55/18.48 [4740]~P89(x47401)+E(f324(f324(f82(x47401),x47402),f324(f106(x47401),a85)),x47402)
% 18.55/18.48 [4741]E(x47411,f2(a1))+E(f53(f324(f77(a1),x47412),f324(f77(a1),x47411)),f59(x47412,x47411))
% 18.55/18.48 [4751]~E(x47511,x47512)+P1(f324(f324(f231(a838),x47511),x47512))
% 18.55/18.48 [4752]~E(x47521,x47522)+P1(f324(f324(f231(a838),x47521),x47522))
% 18.55/18.48 [4753]~E(x47531,x47532)+P1(f324(f324(f231(a838),x47531),x47532))
% 18.55/18.48 [4754]~E(x47541,x47542)+P1(f324(f324(f280(a838),x47541),x47542))
% 18.55/18.48 [4755]~E(x47551,x47552)+P1(f324(f324(f280(a838),x47551),x47552))
% 18.55/18.48 [4756]~E(x47561,x47562)+P1(f324(f324(f280(a838),x47561),x47562))
% 18.55/18.48 [4757]~E(x47571,x47572)+P1(f324(f324(f280(a838),x47571),x47572))
% 18.55/18.48 [4764]~E(x47641,f2(a101))+E(f324(f324(f82(a838),f324(a22,x47641)),x47642),x47642)
% 18.55/18.48 [4765]~E(f324(f106(a1),x47652),f324(f102(a1),x47651))+E(x47651,f324(a107,f324(f106(a1),x47652)))
% 18.55/18.48 [4774]~P10(x47741)+P10(f324(f324(f240(a1),x47741),x47742))
% 18.55/18.48 [4775]~P63(x47751)+E(f324(f324(f82(x47751),x47752),f324(f81(x47751),x47752)),f2(x47751))
% 18.55/18.48 [4776]~P91(x47761)+E(f324(f324(f103(x47761),x47762),f324(f81(x47761),x47762)),f238(x47761))
% 18.55/18.48 [4777]~P91(x47771)+E(f324(f324(f104(x47771),x47772),f324(f81(x47771),x47772)),f179(x47771))
% 18.55/18.48 [4801]E(x48011,f2(a838))+~E(f324(f81(a1),f324(f102(a1),x48012)),f324(f102(a1),x48011))
% 18.55/18.48 [4802]E(x48021,f2(a838))+~E(f324(f81(a1),f324(f102(a1),x48021)),f324(f102(a1),x48022))
% 18.55/18.48 [4812]E(f187(x48121,x48122),f2(a1))+P1(f324(f324(f231(a1),x48122),x48121))
% 18.55/18.48 [4813]E(f237(x48131,x48132),f2(a101))+P1(f324(f324(f232(a101),x48131),x48132))
% 18.55/18.48 [4814]E(f162(x48141,x48142),f115(a1))+P1(f324(f324(f231(a1),x48141),x48142))
% 18.55/18.48 [4827]E(x48271,f324(a114,f2(a838)))+~E(f324(f324(f83(a838),x48272),x48271),f324(a114,f2(a838)))
% 18.55/18.48 [4828]E(x48281,f324(a114,f2(a838)))+~E(f324(f324(f83(a838),x48281),x48282),f324(a114,f2(a838)))
% 18.55/18.48 [4829]~P102(x48291)+P1(f324(f324(f231(x48291),x48292),x48292))
% 18.55/18.48 [4830]~P105(x48301)+P1(f324(f324(f280(x48301),x48302),x48302))
% 18.55/18.48 [4833]~P89(x48331)+E(f324(f324(f83(x48331),x48332),f324(f106(x48331),a99)),f324(f81(x48331),x48332))
% 18.55/18.48 [4848]~P89(x48481)+E(f324(f81(x48481),f324(f106(x48481),x48482)),f324(f106(x48481),f324(f81(a1),x48482)))
% 18.55/18.48 [4849]~P119(x48491)+E(f324(f81(x48491),f324(f105(x48491),x48492)),f324(f105(x48491),f324(f81(a1),x48492)))
% 18.55/18.48 [4850]~P89(x48501)+E(f324(f81(x48501),f324(f106(x48501),x48502)),f324(f106(x48501),f324(f81(a1),x48502)))
% 18.55/18.48 [4880]~E(x48801,f324(a114,x48802))+P1(f324(f324(f232(a838),f2(a838)),x48801))
% 18.55/18.48 [4897]~P86(x48971)+E(f324(f81(f845(x48971,a832)),f324(f294(x48971),x48972)),f324(f297(x48971),x48972))
% 18.55/18.48 [4898]~P86(x48981)+E(f324(f81(f845(x48981,a832)),f324(f258(x48981),x48982)),f324(f259(x48981),x48982))
% 18.55/18.48 [4899]~P86(x48991)+E(f324(f81(f845(x48991,a832)),f324(f259(x48991),x48992)),f324(f258(x48991),x48992))
% 18.55/18.48 [4900]~P86(x49001)+E(f324(f81(f845(x49001,a832)),f324(f297(x49001),x49002)),f324(f294(x49001),x49002))
% 18.55/18.48 [4908]~E(f324(f102(a1),x49082),x49081)+P1(f324(f324(f231(a1),f2(a1)),x49081))
% 18.55/18.48 [4915]~E(x49152,f2(a1))+E(f59(x49151,x49152),f324(f324(f247(a1,a1),f2(a1)),f324(f77(a1),x49151)))
% 18.55/18.48 [4917]~P100(x49171)+P1(f324(f324(f231(x49171),f179(x49171)),x49172))
% 18.55/18.48 [4918]~P105(x49181)+P1(f324(f324(f280(x49181),f80(x49181)),x49182))
% 18.55/18.48 [4948]E(x49481,x49482)+~E(f324(f324(f82(a1),x49481),x49481),f324(f324(f82(a1),x49482),x49482))
% 18.55/18.48 [4952]~P1(f324(x49521,x49522))+P1(f324(x49521,f324(a107,f513(x49521))))
% 18.55/18.48 [4978]~P103(x49781)+E(f324(f324(f83(x49781),f84(x49781,x49782)),f324(f77(x49781),x49782)),x49782)
% 18.55/18.48 [4979]E(x49791,x49792)+~P1(f324(f324(f186(a25),x49791),x49792))
% 18.55/18.48 [4988]~E(x49882,f2(a838))+E(f87(f844(a838,a838),f54(x49881,x49882)),f324(f324(f247(a838,a838),f2(a838)),x49881))
% 18.55/18.48 [4995]~E(x49951,x49952)+~P1(f324(f324(f232(a838),x49951),x49952))
% 18.55/18.48 [4996]~E(x49961,x49962)+~P1(f324(f324(f232(a838),x49961),x49962))
% 18.55/18.48 [4997]~E(x49971,x49972)+~P1(f324(f324(f232(a838),x49971),x49972))
% 18.55/18.48 [4998]~E(x49981,x49982)+~P1(f324(f324(f232(a838),x49981),x49982))
% 18.55/18.48 [4999]~E(x49991,x49992)+~P1(f324(f324(f232(a838),x49991),x49992))
% 18.55/18.48 [5000]~E(x50001,x50002)+~P1(f324(f324(f232(a1),x50001),x50002))
% 18.55/18.48 [5003]~P2(x50031)+E(f324(f324(f82(x50031),f80(x50031)),f324(f102(x50031),x50032)),f324(f102(x50031),f324(a114,x50032)))
% 18.55/18.48 [5007]~E(x50071,f2(a838))+~P1(f324(f324(f232(a838),x50072),x50071))
% 18.55/18.48 [5020]E(f140(x50201,x50202),x50202)+~E(f324(f180(f839(x50201)),f140(x50201,x50202)),f324(f180(f839(x50201)),x50202))
% 18.55/18.48 [5021]E(f324(f41(x50211),f324(f157(x50211),x50212)),f324(f180(f839(x50211)),x50212))+~P1(f324(f127(x50211),x50212))
% 18.55/18.48 [5030]~P1(f324(x50301,f579(x50301)))+P1(f324(x50301,f324(f102(a1),x50302)))
% 18.55/18.48 [5041]E(f237(x50411,x50412),x50412)+~P1(f324(f324(f232(a101),x50411),x50412))
% 18.55/18.48 [5043]E(f268(x50431,x50432),f80(a101))+~P1(f324(f324(f232(a101),x50432),x50431))
% 18.55/18.48 [5044]E(f162(x50441,x50442),f115(a1))+~P1(f324(f324(f232(a1),x50442),x50441))
% 18.55/18.48 [5047]~P85(x50471)+E(f296(x50471,x50472,x50472),f324(f324(f303(x50471),x50472),f179(f845(x50471,a832))))
% 18.55/18.48 [5066]~E(f324(f324(f3(a838),x50661),x50662),f2(a838))+P1(f324(f324(f231(a838),x50661),x50662))
% 18.55/18.48 [5092]~P102(x50921)+~P1(f324(f324(f232(x50921),x50922),x50922))
% 18.55/18.48 [5094]~E(f51(a1,x50941,x50942),f2(a1))+E(f51(a1,x50941,f324(f81(a1),x50942)),f2(a1))
% 18.55/18.48 [5095]~E(f51(a1,x50951,x50952),f2(a1))+E(f51(a1,x50951,f324(f81(a1),x50952)),f2(a1))
% 18.55/18.48 [5096]~E(f51(a1,x50961,x50962),f2(a1))+E(f51(a1,f324(f81(a1),x50961),x50962),f2(a1))
% 18.55/18.48 [5097]~E(f51(a1,x50971,x50972),f2(a1))+E(f51(a1,f324(f81(a1),x50971),x50972),f2(a1))
% 18.55/18.48 [5104]E(f324(f295(a838,x51041),f324(a114,x51042)),f179(f845(a838,a832)))+P1(f324(f324(f231(a838),x51041),x51042))
% 18.55/18.48 [5121]E(f129(a838,f324(f295(a838,x51211),x51212)),f115(a838))+P1(f324(f324(f232(a838),x51211),x51212))
% 18.55/18.48 [5126]~E(f324(f41(x51261),f324(f157(x51261),x51262)),f324(f180(f839(x51261)),x51262))+P1(f324(f127(x51261),x51262))
% 18.55/18.48 [5130]~P1(f324(f127(x51301),x51302))+P1(f324(f127(x51301),f324(f153(x51301),x51302)))
% 18.55/18.48 [5131]~P1(f324(f127(x51311),x51312))+P1(f324(f127(x51311),f324(f156(x51311),x51312)))
% 18.55/18.48 [5132]~P1(f324(f127(x51321),x51322))+P1(f324(f127(x51321),f324(f154(x51321),x51322)))
% 18.55/18.48 [5140]P1(f324(x51401,x51402))+~P1(f324(x51401,f324(a107,f514(x51401))))
% 18.55/18.48 [5141]P1(f324(f324(f231(a838),x51412),x51411))+P1(f324(f324(f231(a838),x51411),x51412))
% 18.55/18.48 [5142]P1(f324(f324(f231(a1),x51422),x51421))+P1(f324(f324(f231(a1),x51421),x51422))
% 18.55/18.48 [5144]~P78(x51441)+P1(f324(f324(f231(x51441),x51442),f324(f77(x51441),x51442)))
% 18.55/18.48 [5147]P1(f324(x51471,f554(x51471)))+~P1(f324(x51471,f324(f102(a1),x51472)))
% 18.55/18.48 [5171]E(f324(f324(f42(a838),x51711),x51712),f2(a838))+~P1(f324(f324(f232(a838),x51711),x51712))
% 18.55/18.48 [5172]E(f324(f324(f3(a838),x51721),x51722),f2(a838))+~P1(f324(f324(f231(a838),x51721),x51722))
% 18.55/18.48 [5173]E(f324(f324(f3(a838),x51731),x51732),f2(a838))+~P1(f324(f324(f231(a838),x51731),x51732))
% 18.55/18.48 [5189]E(f51(a838,x51891,x51892),x51891)+~P1(f324(f324(f232(a838),x51891),x51892))
% 18.55/18.48 [5190]E(f51(a838,x51901,x51902),x51901)+~P1(f324(f324(f232(a838),x51901),x51902))
% 18.55/18.48 [5197]E(f51(a1,x51971,f324(f81(a1),x51972)),f285(x51971,x51972))+P1(f324(f324(f231(a1),f2(a1)),x51972))
% 18.55/18.48 [5209]E(f324(f324(f3(a1),x52091),x52092),f187(x52091,x52092))+~P1(f324(f324(f231(a1),x52092),x52091))
% 18.55/18.48 [5210]E(f324(f324(f3(a1),x52101),x52102),f187(x52101,x52102))+~P1(f324(f324(f231(a1),x52102),x52101))
% 18.55/18.48 [5228]P1(f324(f324(f231(a1),f2(a1)),f579(x52281)))+P1(f324(x52281,f324(f102(a1),x52282)))
% 18.55/18.48 [5241]~P84(x52411)+P1(f324(f324(f231(x52411),f2(x52411)),f324(f102(x52411),x52412)))
% 18.55/18.48 [5242]~P84(x52421)+P1(f324(f324(f231(x52421),f2(x52421)),f324(f102(x52421),x52422)))
% 18.55/18.48 [5243]~P78(x52431)+P1(f324(f324(f231(x52431),f2(x52431)),f324(f77(x52431),x52432)))
% 18.55/18.48 [5271]E(f324(f324(f82(a838),x52711),f583(x52712,x52711)),x52712)+~P1(f324(f324(f231(a838),x52711),x52712))
% 18.55/18.48 [5283]~E(f324(f106(a1),x52831),f324(f102(a1),x52832))+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x52831)))
% 18.55/18.48 [5286]E(f296(a1,x52861,x52862),f179(f845(a1,a832)))+~P1(f324(f324(f232(a1),x52862),x52861))
% 18.55/18.48 [5289]~P103(x52891)+E(f324(f324(f83(x52891),f324(f77(x52891),x52892)),f324(f77(x52891),x52892)),f324(f324(f83(x52891),x52892),x52892))
% 18.55/18.48 [5294]E(f129(a838,f324(f295(a838,x52941),f324(a114,x52942))),f115(a838))+P1(f324(f324(f231(a838),x52941),x52942))
% 18.55/18.48 [5298]E(f324(f324(f42(a1),x52981),x52982),f286(x52981,x52982))+~P1(f324(f324(f231(a1),f2(a1)),x52982))
% 18.55/18.48 [5318]P1(f324(f127(x53181),x53182))+~P1(f324(f127(x53181),f324(f153(x53181),x53182)))
% 18.55/18.48 [5319]P1(f324(f127(x53191),x53192))+~P1(f324(f127(x53191),f324(f154(x53191),x53192)))
% 18.55/18.48 [5342]P1(f324(f64(a838),x53421))+P1(f324(f324(f326(a838),f380(x53421,x53422)),x53421))
% 18.55/18.48 [5343]P1(f324(f64(a838),x53431))+P1(f324(f324(f326(a838),f382(x53431,x53432)),x53431))
% 18.55/18.48 [5344]P1(f324(f324(f232(a838),x53442),f324(a114,x53441)))+P1(f324(f324(f232(a838),x53441),x53442))
% 18.55/18.48 [5345]E(f51(a1,x53451,x53452),f285(x53451,x53452))+~P1(f324(f324(f231(a1),f2(a1)),x53452))
% 18.55/18.48 [5347]E(f129(a838,f324(f295(a838,x53471),x53472)),f115(a838))+~P1(f324(f324(f231(a838),x53472),x53471))
% 18.55/18.48 [5348]E(f129(a838,f324(f295(a838,x53481),x53482)),f115(a838))+~P1(f324(f324(f231(a838),x53482),x53481))
% 18.55/18.48 [5349]~P70(x53491)+E(f324(f304(x53491,x53491,f81(x53491)),f324(f294(x53491),x53492)),f324(f259(x53491),f324(f81(x53491),x53492)))
% 18.55/18.48 [5350]~P70(x53501)+E(f324(f304(x53501,x53501,f81(x53501)),f324(f258(x53501),x53502)),f324(f297(x53501),f324(f81(x53501),x53502)))
% 18.55/18.48 [5351]~P70(x53511)+E(f324(f304(x53511,x53511,f81(x53511)),f324(f259(x53511),x53512)),f324(f294(x53511),f324(f81(x53511),x53512)))
% 18.55/18.48 [5352]~P70(x53521)+E(f324(f304(x53521,x53521,f81(x53521)),f324(f297(x53521),x53522)),f324(f258(x53521),f324(f81(x53521),x53522)))
% 18.55/18.48 [5363]E(x53631,f179(f845(x53632,a832)))+P1(f324(f324(f326(x53632),f366(x53631,x53632)),x53631))
% 18.55/18.48 [5364]E(x53641,f179(f845(x53642,a832)))+P1(f324(f324(f326(x53642),f377(x53641,x53642)),x53641))
% 18.55/18.48 [5372]~P1(f324(f324(f232(a838),x53721),x53722))+P1(f324(f324(f231(a838),x53721),x53722))
% 18.55/18.48 [5373]~P1(f324(f324(f232(a838),x53731),x53732))+P1(f324(f324(f231(a838),x53731),x53732))
% 18.55/18.48 [5374]~P1(f324(f324(f232(a838),x53741),x53742))+P1(f324(f324(f231(a838),x53741),x53742))
% 18.55/18.48 [5375]~P1(f324(f324(f232(a838),x53751),x53752))+P1(f324(f324(f231(a838),x53751),x53752))
% 18.55/18.48 [5376]~P1(f324(f324(f232(a838),x53761),x53762))+P1(f324(f324(f231(a838),x53761),x53762))
% 18.55/18.48 [5377]~P1(f324(f324(f232(a1),x53771),x53772))+P1(f324(f324(f231(a1),x53771),x53772))
% 18.55/18.48 [5390]E(f53(x53901,x53902),f324(f324(f247(a1,a1),f2(a1)),x53901))+~P1(f324(f324(f232(a1),x53901),x53902))
% 18.55/18.48 [5391]E(f209(f324(f81(a1),x53911),f324(f81(a1),x53912)),f209(x53911,x53912))+~P1(f324(f324(f232(a1),x53912),f2(a1)))
% 18.55/18.48 [5404]E(x54041,x54042)+~E(f324(a5,f324(a114,f324(a22,x54041))),f324(a5,f324(a114,f324(a22,x54042))))
% 18.55/18.48 [5409]E(f53(x54091,x54092),f324(f324(f247(a1,a1),f2(a1)),x54091))+~P1(f324(f324(f231(a1),x54092),f2(a1)))
% 18.55/18.48 [5436]E(f51(a838,f324(f106(a838),x54361),f324(f106(a838),x54362)),f2(a838))+~P1(f324(a185,f324(f106(a1),x54361)))
% 18.55/18.48 [5451]P1(f324(f324(f231(a1),f2(a1)),f554(x54511)))+~P1(f324(x54511,f324(f102(a1),x54512)))
% 18.55/18.48 [5484]P38(f296(a1,x54841,x54842))+~P1(f324(f324(f231(a1),f2(a1)),x54841))
% 18.55/18.48 [5488]~P1(f324(f64(x54881),x54882))+P1(f324(f64(f845(x54881,a832)),f324(f302(x54881),x54882)))
% 18.55/18.48 [5501]E(f324(f324(f82(a1),x55011),f324(f102(a1),f615(x55012,x55011))),x55012)+~P1(f324(f324(f231(a1),x55011),x55012))
% 18.55/18.48 [5509]P1(f324(f324(f231(a838),x55091),x55092))+P1(f324(f324(f231(a838),f324(a114,x55092)),x55091))
% 18.55/18.48 [5554]E(f324(f324(f42(a838),f324(f106(a838),x55541)),f324(f106(a838),x55542)),f2(a838))+~P1(f324(a185,f324(f106(a1),x55541)))
% 18.55/18.48 [5555]E(f324(f324(f83(a838),f324(f106(a838),x55551)),f324(f106(a838),x55552)),f2(a838))+~P1(f324(f324(f232(a1),x55551),a85))
% 18.55/18.48 [5556]P1(f324(f324(f232(a838),x55561),f324(a114,x55562)))+~P1(f324(f324(f232(a838),x55561),x55562))
% 18.55/18.48 [5557]P1(f324(f324(f232(a838),x55571),f324(a114,x55572)))+~P1(f324(f324(f232(a838),x55571),x55572))
% 18.55/18.48 [5558]P1(f324(f324(f232(a838),x55581),f324(a114,x55582)))+~P1(f324(f324(f231(a838),x55581),x55582))
% 18.55/18.48 [5559]P1(f324(f324(f232(a838),x55591),f324(a114,x55592)))+~P1(f324(f324(f231(a838),x55591),x55592))
% 18.55/18.48 [5560]P1(f324(f324(f231(a838),x55601),f324(a114,x55602)))+~P1(f324(f324(f231(a838),x55601),x55602))
% 18.55/18.48 [5561]P1(f324(f324(f231(a838),x55611),f324(a114,x55612)))+~P1(f324(f324(f231(a838),x55611),x55612))
% 18.55/18.48 [5562]~E(x55621,x55622)+P1(f324(f324(f232(a1),x55621),f324(f324(f82(a1),x55622),f80(a1))))
% 18.55/18.48 [5565]E(f51(a1,x55651,x55652),f2(a1))+E(f324(f324(f3(a1),x55652),f51(a1,x55651,x55652)),f51(a1,f324(f81(a1),x55651),x55652))
% 18.55/18.48 [5573]E(x55731,f115(x55732))+P1(f324(f324(f326(x55732),f133(x55732,x55731)),f324(f157(x55732),x55731)))
% 18.55/18.48 [5584]E(f87(f844(a838,a838),f54(x55841,x55842)),f324(f324(f247(a838,a838),f2(a838)),x55841))+~P1(f324(f324(f232(a838),x55841),x55842))
% 18.55/18.48 [5585]E(f87(f844(a838,a838),f54(x55851,x55852)),f324(f324(f247(a838,a838),f2(a838)),x55851))+~P1(f324(f324(f232(a838),x55851),x55852))
% 18.55/18.48 [5625]E(f324(f324(f82(a838),f324(f106(a838),x56251)),f324(f106(a838),x56252)),f324(f106(a838),x56252))+~P1(f324(f324(f232(a1),x56251),a85))
% 18.55/18.48 [5626]E(f324(f324(f3(a838),f324(f106(a838),x56261)),f324(f106(a838),x56262)),f324(f106(a838),x56261))+~P1(f324(f324(f232(a1),x56262),a85))
% 18.55/18.48 [5631]E(f324(a114,f324(f324(f82(a838),x56311),f616(x56312,x56311))),x56312)+~P1(f324(f324(f232(a838),x56311),x56312))
% 18.55/18.48 [5638]~P1(f324(f324(f280(a1),x56381),x56382))+P1(f324(f324(f280(a1),x56381),f324(f81(a1),x56382)))
% 18.55/18.48 [5657]P1(f324(x56571,x56572))+~P1(f324(x56571,f324(a91,f607(x56572,x56571))))
% 18.55/18.48 [5665]~P1(f324(f324(f232(a838),x56651),f324(a114,x56652)))+P1(f324(f324(f231(a838),x56651),x56652))
% 18.55/18.48 [5714]E(f324(f324(f303(a838),x57141),f324(f295(a838,x57142),x57141)),f324(f295(a838,x57142),f324(a114,x57141)))+~P1(f324(f324(f231(a838),x57142),x57141))
% 18.55/18.48 [5719]E(x57191,f115(x57192))+E(f324(f324(f125(x57192),f116(x57192,x57191)),f324(f324(f139(x57192),f133(x57192,x57191)),f115(x57192))),x57191)
% 18.55/18.48 [5729]P1(f324(f64(x57291),x57292))+~P1(f324(f324(f232(a838),f2(a838)),f324(f41(x57291),x57292)))
% 18.55/18.48 [5730]P1(f324(f64(x57301),x57302))+~P1(f324(f324(f232(a838),f2(a838)),f324(f41(x57301),x57302)))
% 18.55/18.48 [5734]~E(x57341,f179(f845(x57342,a832)))+~P1(f324(f324(f232(a838),f2(a838)),f324(f41(x57342),x57341)))
% 18.55/18.48 [5742]~P1(f324(f324(f232(a838),x57421),x57422))+P1(f324(f324(f231(a838),f324(a114,x57421)),x57422))
% 18.55/18.48 [5743]~P1(f324(f324(f232(a838),x57431),x57432))+P1(f324(f324(f231(a838),f324(a114,x57431)),x57432))
% 18.55/18.48 [5744]~P1(f324(f324(f232(a838),x57441),x57442))+P1(f324(f324(f231(a838),f324(a114,x57441)),x57442))
% 18.55/18.48 [5752]E(x57521,f115(x57522))+P1(f324(f324(f326(x57522),f324(f130(x57522),x57521)),f324(f157(x57522),x57521)))
% 18.55/18.48 [5758]~P84(x57581)+P1(f324(f324(f232(x57581),x57582),f324(f324(f82(x57581),x57582),f80(x57581))))
% 18.55/18.48 [5760]~P78(x57601)+P1(f324(f324(f231(x57601),f324(f81(x57601),x57602)),f324(f77(x57601),x57602)))
% 18.55/18.48 [5772]P1(f324(f324(f280(a1),x57721),x57722))+~P1(f324(f324(f280(a1),x57721),f324(f81(a1),x57722)))
% 18.55/18.48 [5773]~E(x57731,x57732)+E(f283(a838,f280(a838),x57731,x57732),f324(f324(f303(a838),x57731),f179(f845(a838,a832))))
% 18.55/18.48 [5793]P1(f324(f64(a838),x57931))+~P1(f324(f324(f232(a838),f382(x57931,x57932)),x57932))
% 18.55/18.48 [5794]P1(f324(f64(a838),x57941))+~P1(f324(f324(f231(a838),f380(x57941,x57942)),x57942))
% 18.55/18.48 [5798]~P1(f324(f64(f844(x57981,x57981)),x57982))+P1(f324(f64(x57981),f324(f277(x57981),x57982)))
% 18.55/18.48 [5848]E(f283(a838,f280(a838),x58481,x58482),f179(f845(a838,a832)))+P1(f324(f324(f280(a838),x58481),x58482))
% 18.55/18.48 [5849]E(f283(a838,f280(a838),x58491,x58492),f179(f845(a838,a832)))+P1(f324(f324(f280(a838),x58491),x58492))
% 18.55/18.48 [5850]E(f162(f324(f106(a1),x58501),f324(f106(a1),x58502)),f115(a1))+P1(f324(f324(f231(a1),f324(f106(a1),x58501)),f324(f106(a1),x58502)))
% 18.55/18.48 [5855]~P1(f324(f324(f232(a838),x58552),f324(a114,x58551)))+~P1(f324(f324(f232(a838),x58551),x58552))
% 18.55/18.48 [5856]~P85(x58561)+E(f324(f324(f104(f845(x58561,a832)),f324(f294(x58561),x58562)),f324(f259(x58561),x58562)),f324(f324(f303(x58561),x58562),f179(f845(x58561,a832))))
% 18.55/18.48 [5858]E(f324(f324(f240(a838),f324(f106(a838),x58581)),f324(f106(a838),x58582)),f324(f324(f240(a838),f2(a838)),f324(f106(a838),x58582)))+~P1(f324(a185,f324(f106(a1),x58581)))
% 18.55/18.48 [5869]P1(f324(f64(x58691),x58692))+~P1(f324(f64(f845(x58691,a832)),f324(f302(x58691),x58692)))
% 18.55/18.48 [5893]P1(f324(f324(f232(a838),f324(a114,x58931)),f324(a114,x58932)))+~P1(f324(f324(f232(a838),x58931),x58932))
% 18.55/18.48 [5894]P1(f324(f324(f232(a838),f324(a114,x58941)),f324(a114,x58942)))+~P1(f324(f324(f232(a838),x58941),x58942))
% 18.55/18.48 [5895]P1(f324(f324(f232(a838),f324(a22,x58951)),f324(a22,x58952)))+~P1(f324(f324(f232(a101),x58951),x58952))
% 18.55/18.48 [5896]P1(f324(f324(f232(a101),f324(a5,x58961)),f324(a5,x58962)))+~P1(f324(f324(f232(a838),x58961),x58962))
% 18.55/18.48 [5897]P1(f324(f324(f231(a838),f324(a114,x58971)),f324(a114,x58972)))+~P1(f324(f324(f231(a838),x58971),x58972))
% 18.55/18.48 [5898]P1(f324(f324(f231(a838),f324(a22,x58981)),f324(a22,x58982)))+~P1(f324(f324(f231(a101),x58981),x58982))
% 18.55/18.48 [5899]P1(f324(f324(f231(a101),f324(a5,x58991)),f324(a5,x58992)))+~P1(f324(f324(f231(a838),x58991),x58992))
% 18.55/18.48 [5902]E(x59021,x59022)+~E(f324(f304(a838,a1,f102(a1)),x59021),f324(f304(a838,a1,f102(a1)),x59022))
% 18.55/18.48 [5918]P1(f324(f324(f232(a838),x59181),x59182))+~P1(f324(f324(f232(a838),f324(a114,x59181)),x59182))
% 18.55/18.48 [5919]P1(f324(f324(f232(a838),x59191),x59192))+~P1(f324(f324(f231(a838),f324(a114,x59191)),x59192))
% 18.55/18.48 [5920]P1(f324(f324(f232(a838),x59201),x59202))+~P1(f324(f324(f231(a838),f324(a114,x59201)),x59202))
% 18.55/18.48 [5921]P1(f324(f324(f232(a838),x59211),x59212))+~P1(f324(f324(f231(a838),f324(a114,x59211)),x59212))
% 18.55/18.48 [5922]P1(f324(f324(f231(a838),x59221),x59222))+~P1(f324(f324(f231(a838),f324(a114,x59221)),x59222))
% 18.55/18.48 [5939]E(f51(a1,x59391,x59392),f2(a1))+E(f324(f324(f3(a1),f51(a1,x59391,x59392)),x59392),f51(a1,x59391,f324(f81(a1),x59392)))
% 18.55/18.48 [6010]E(f324(f41(f845(x60101,a832)),f324(f302(x60101),x60102)),f324(f324(f240(a838),f324(a114,f324(a114,f2(a838)))),f324(f41(x60101),x60102)))+~P1(f324(f64(x60101),x60102))
% 18.55/18.48 [6013]E(x60131,f115(x60132))+E(f324(f324(f149(x60132),x60131),f324(f324(f3(a838),f324(f180(f839(x60132)),x60131)),f80(a838))),f133(x60132,x60131))
% 18.55/18.48 [6038]E(x60381,f115(x60382))+E(f324(f324(f125(x60382),f324(f156(x60382),x60381)),f324(f324(f139(x60382),f324(f130(x60382),x60381)),f115(x60382))),f324(f153(x60382),x60381))
% 18.55/18.48 [6039]~P1(f324(f179(f845(x60391,a832)),x60392))+P1(f324(f324(f326(x60391),x60392),f179(f845(x60391,a832))))
% 18.55/18.48 [6069]~P1(f324(f64(x60691),f43(f845(x60691,a832),x60692)))+P1(f324(f64(f845(x60691,a832)),x60692))
% 18.55/18.48 [6090]P1(f324(f324(f231(a838),f324(f106(a838),x60901)),f324(f106(a838),x60902)))+~P1(f324(f324(f231(a1),x60901),a85))
% 18.55/18.48 [6110]~P1(f324(f324(f232(a1),x61101),x61102))+P1(f324(f324(f232(a1),x61101),f324(f324(f82(a1),x61102),f80(a1))))
% 18.55/18.48 [6111]~P1(f324(f324(f231(a1),x61111),x61112))+P1(f324(f324(f232(a1),x61111),f324(f324(f82(a1),x61112),f80(a1))))
% 18.55/18.48 [6112]~P1(f324(f324(f232(a1),x61121),x61122))+P1(f324(f324(f231(a1),x61121),f324(f324(f3(a1),x61122),f80(a1))))
% 18.55/18.48 [6114]~P1(f324(f324(f232(a838),x61141),x61142))+P1(f324(f324(f232(a1),f324(f102(a1),x61141)),f324(f102(a1),x61142)))
% 18.55/18.48 [6115]~P1(f324(f324(f232(a838),x61151),x61152))+P1(f324(f324(f232(a1),f324(f102(a1),x61151)),f324(f102(a1),x61152)))
% 18.55/18.48 [6116]~P1(f324(f324(f232(a1),x61161),x61162))+P1(f324(f324(f232(a1),f324(f106(a1),x61161)),f324(f106(a1),x61162)))
% 18.55/18.48 [6117]~P1(f324(f324(f231(a1),x61171),x61172))+P1(f324(f324(f231(a838),f324(f106(a838),x61171)),f324(f106(a838),x61172)))
% 18.55/18.48 [6118]~P1(f324(f324(f231(a838),x61181),x61182))+P1(f324(f324(f231(a1),f324(f102(a1),x61181)),f324(f102(a1),x61182)))
% 18.55/18.48 [6119]~P1(f324(f324(f231(a838),x61191),x61192))+P1(f324(f324(f231(a1),f324(f102(a1),x61191)),f324(f102(a1),x61192)))
% 18.55/18.48 [6120]~P1(f324(f324(f231(a1),x61201),x61202))+P1(f324(f324(f231(a1),f324(f106(a1),x61201)),f324(f106(a1),x61202)))
% 18.55/18.48 [6121]~P1(f324(f324(f280(a838),x61211),x61212))+P1(f324(f324(f280(a1),f324(f102(a1),x61211)),f324(f102(a1),x61212)))
% 18.55/18.48 [6122]~P1(f324(f324(f280(a838),x61221),x61222))+P1(f324(f324(f280(a1),f324(f102(a1),x61221)),f324(f102(a1),x61222)))
% 18.55/18.48 [6129]~E(x61292,f179(f845(x61291,a832)))+P1(f324(f324(f231(f845(x61291,a832)),x61292),f179(f845(x61291,a832))))
% 18.55/18.48 [6138]~P1(f324(f324(f231(a838),x61381),x61382))+~P1(f324(f324(f231(a838),f324(a114,x61382)),x61381))
% 18.55/18.48 [6185]~P1(f324(f324(f232(a838),f324(a114,x61851)),f324(a114,x61852)))+P1(f324(f324(f232(a838),x61851),x61852))
% 18.55/18.48 [6186]~P1(f324(f324(f232(a838),f324(a114,x61861)),f324(a114,x61862)))+P1(f324(f324(f232(a838),x61861),x61862))
% 18.55/18.48 [6187]~P1(f324(f324(f232(a101),f324(a5,x61871)),f324(a5,x61872)))+P1(f324(f324(f232(a838),x61871),x61872))
% 18.55/18.48 [6188]~P1(f324(f324(f232(a838),f324(a107,x61881)),f324(a107,x61882)))+P1(f324(f324(f232(a1),x61881),x61882))
% 18.55/18.48 [6189]~P1(f324(f324(f232(a838),f324(a22,x61891)),f324(a22,x61892)))+P1(f324(f324(f232(a101),x61891),x61892))
% 18.55/18.48 [6190]~P1(f324(f324(f231(a838),f324(a114,x61901)),f324(a114,x61902)))+P1(f324(f324(f231(a838),x61901),x61902))
% 18.55/18.48 [6191]~P1(f324(f324(f231(a101),f324(a5,x61911)),f324(a5,x61912)))+P1(f324(f324(f231(a838),x61911),x61912))
% 18.55/18.48 [6192]~P1(f324(f324(f231(a838),f324(a22,x61921)),f324(a22,x61922)))+P1(f324(f324(f231(a101),x61921),x61922))
% 18.55/18.48 [6209]~P1(f324(f324(f280(a838),x62092),x62091))+P1(f324(f324(f326(a838),x62091),f287(a838,f280(a838),x62092)))
% 18.55/18.48 [6210]~P1(f324(f324(f280(a838),x62101),x62102))+P1(f324(f324(f326(a838),x62101),f289(a838,f280(a838),x62102)))
% 18.55/18.48 [6214]~P1(f324(f324(f326(x62141),x62142),f179(f845(x62141,a832))))+P1(f324(f179(f845(x62141,a832)),x62142))
% 18.55/18.48 [6235]~P1(f324(f324(f232(a838),f324(a107,x62352)),f324(a107,x62351)))+P1(f324(f324(f232(a1),f2(a1)),x62351))
% 18.55/18.48 [6246]~E(f51(a1,f324(f106(a1),x62462),f324(f106(a1),x62461)),f2(a1))+P1(f324(f324(f280(a1),f324(f106(a1),x62461)),f324(f106(a1),x62462)))
% 18.55/18.48 [6264]P1(f324(f324(f231(a1),f2(a1)),f51(a1,x62641,x62642)))+~P1(f324(f324(f232(a1),f2(a1)),x62642))
% 18.55/18.48 [6265]P1(f324(f324(f231(a1),f2(a1)),f51(a1,x62651,x62652)))+~P1(f324(f324(f232(a1),f2(a1)),x62652))
% 18.55/18.48 [6433]P36(x64331,x64332)+~E(f324(f324(f282(x64331,x64331,x64331),x64332),x64332),f179(f845(f844(x64331,x64331),a832)))
% 18.55/18.48 [6449]~P36(x64491,x64492)+P36(x64491,f324(f324(f282(x64491,x64491,x64491),x64492),x64492))
% 18.55/18.48 [6461]P1(f324(f324(f232(a1),x64611),x64612))+~P1(f324(f324(f231(a1),x64611),f324(f324(f3(a1),x64612),f80(a1))))
% 18.55/18.48 [6462]P1(f324(f324(f231(a1),x64621),x64622))+~P1(f324(f324(f232(a1),x64621),f324(f324(f82(a1),x64622),f80(a1))))
% 18.55/18.48 [6464]P1(f324(f324(f232(a838),x64641),x64642))+~P1(f324(f324(f232(a1),f324(f102(a1),x64641)),f324(f102(a1),x64642)))
% 18.55/18.48 [6465]P1(f324(f324(f232(a838),x64651),x64652))+~P1(f324(f324(f232(a1),f324(f102(a1),x64651)),f324(f102(a1),x64652)))
% 18.55/18.48 [6466]P1(f324(f324(f232(a1),x64661),x64662))+~P1(f324(f324(f232(a838),f324(f106(a838),x64661)),f324(f106(a838),x64662)))
% 18.55/18.48 [6467]P1(f324(f324(f232(a1),x64671),x64672))+~P1(f324(f324(f232(a1),f324(f106(a1),x64671)),f324(f106(a1),x64672)))
% 18.55/18.48 [6468]P1(f324(f324(f231(a838),x64681),x64682))+~P1(f324(f324(f231(a1),f324(f102(a1),x64681)),f324(f102(a1),x64682)))
% 18.55/18.48 [6469]P1(f324(f324(f231(a838),x64691),x64692))+~P1(f324(f324(f231(a1),f324(f102(a1),x64691)),f324(f102(a1),x64692)))
% 18.55/18.48 [6470]P1(f324(f324(f231(a1),x64701),x64702))+~P1(f324(f324(f231(a1),f324(f106(a1),x64701)),f324(f106(a1),x64702)))
% 18.55/18.48 [6471]P1(f324(f324(f280(a838),x64711),x64712))+~P1(f324(f324(f280(a1),f324(f102(a1),x64711)),f324(f102(a1),x64712)))
% 18.55/18.48 [6472]P1(f324(f324(f280(a838),x64721),x64722))+~P1(f324(f324(f280(a1),f324(f102(a1),x64721)),f324(f102(a1),x64722)))
% 18.55/18.48 [6528]E(f51(a1,f324(f106(a1),x65281),f324(f106(a1),x65282)),f2(a1))+~P1(f324(f324(f280(a1),f324(f106(a1),x65282)),f324(f106(a1),x65281)))
% 18.55/18.48 [6542]~E(f283(a838,f280(a838),x65421,x65422),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x65421),x65422))
% 18.55/18.48 [6543]~E(f283(a838,f280(a838),x65431,x65432),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x65431),x65432))
% 18.55/18.48 [6569]P1(f324(f324(f280(a838),x65691),x65692))+~P1(f324(f324(f326(a838),x65692),f287(a838,f280(a838),x65691)))
% 18.55/18.48 [6570]P1(f324(f324(f280(a838),x65701),x65702))+~P1(f324(f324(f326(a838),x65701),f289(a838,f280(a838),x65702)))
% 18.55/18.48 [6571]~E(f758(x65712,x65711),f115(x65711))+E(f324(f131(f839(x65711),f839(x65711),f125(x65711),f115(x65711)),x65712),f115(x65711))
% 18.55/18.48 [6572]~E(f760(x65722,x65721),f115(x65721))+E(f324(f131(f839(x65721),f839(x65721),f125(x65721),f115(x65721)),x65722),f115(x65721))
% 18.55/18.48 [6579]~P9(x65791)+E(f324(f131(x65791,x65791,f104(x65791),f238(x65791)),x65792),f44(x65791,f324(f157(x65791),x65792)))
% 18.55/18.48 [6580]~P9(x65801)+E(f324(f131(x65801,x65801,f103(x65801),f179(x65801)),x65802),f43(x65801,f324(f157(x65801),x65802)))
% 18.55/18.48 [6592]E(x65921,f2(a101))+E(f324(f324(f82(a838),f324(a22,f324(f324(f3(a101),x65921),f80(a101)))),f324(a114,x65922)),f324(f324(f82(a838),f324(a22,x65921)),x65922))
% 18.55/18.48 [6644]P1(f324(f324(f232(a1),f324(f324(f3(a1),x66441),x66442)),f2(a1)))+~P1(f324(f324(f232(a1),x66441),x66442))
% 18.55/18.48 [6671]~P86(x66711)+E(f324(f324(f103(f845(x66711,a832)),f324(f324(f303(x66711),x66712),f179(f845(x66711,a832)))),f324(f297(x66711),x66712)),f324(f259(x66711),x66712))
% 18.55/18.48 [6756]~P57(x67561,x67562)+P36(x67561,f324(f257(f844(x67561,x67561)),f324(f252(x67561,x67561,a832),x67562)))
% 18.55/18.48 [6757]~P57(x67571,x67572)+P55(x67571,f324(f257(f844(x67571,x67571)),f324(f252(x67571,x67571,a832),x67572)))
% 18.55/18.48 [6758]E(x67581,f179(f845(x67582,a832)))+~P1(f324(f324(f231(f845(x67582,a832)),x67581),f179(f845(x67582,a832))))
% 18.55/18.48 [6843]~P1(f324(f324(f232(a838),f2(a838)),x68432))+P1(f324(f324(f232(a838),f51(a838,x68431,x68432)),x68432))
% 18.55/18.48 [6844]~P1(f324(f324(f232(a1),f2(a1)),x68442))+P1(f324(f324(f232(a1),f51(a1,x68441,x68442)),x68442))
% 18.55/18.48 [6845]~P1(f324(f324(f232(a1),f2(a1)),x68452))+P1(f324(f324(f232(a1),f51(a1,x68451,x68452)),x68452))
% 18.55/18.48 [6846]~P1(f324(f324(f232(a838),f2(a838)),x68462))+P1(f324(f324(f231(a838),f51(a838,x68461,x68462)),x68462))
% 18.55/18.48 [6847]~P1(f324(f324(f231(a1),f2(a1)),x68471))+P1(f324(f324(f231(a1),f51(a1,x68471,x68472)),x68471))
% 18.55/18.48 [6919]~P85(x69191)+E(f324(f324(f3(f845(x69191,a832)),f324(f324(f303(x69191),x69192),f179(f845(x69191,a832)))),f324(f258(x69191),x69192)),f324(f324(f303(x69191),x69192),f179(f845(x69191,a832))))
% 18.55/18.48 [6997]~P49(x69971,x69972)+P47(x69971,f238(f845(x69971,a832)),f324(f257(f844(x69971,x69971)),f324(f252(x69971,x69971,a832),x69972)))
% 18.55/18.48 [6998]P1(f324(x69981,x69982))+P1(f324(f324(f326(f845(f844(a838,a838),a832)),f607(x69982,x69981)),a100))
% 18.55/18.48 [7040]E(f324(f324(f125(a838),f129(a838,f324(f295(a838,x70401),x70402))),f324(f324(f139(a838),x70402),f115(a838))),f129(a838,f324(f295(a838,x70401),f324(a114,x70402))))+~P1(f324(f324(f231(a838),x70401),x70402))
% 18.55/18.48 [7041]E(f324(f324(f125(a838),f129(a838,f324(f295(a838,x70411),x70412))),f324(f324(f139(a838),x70412),f115(a838))),f129(a838,f324(f295(a838,x70411),f324(a114,x70412))))+~P1(f324(f324(f231(a838),x70411),x70412))
% 18.55/18.48 [7197]E(x71971,f2(a838))+~E(f324(f131(a838,a838,f82(a838),x71971),x71972),f2(a838))
% 18.55/18.48 [7226]~P1(f324(f324(f232(a1),f324(f324(f3(a1),x72261),x72262)),f2(a1)))+P1(f324(f324(f232(a1),x72261),x72262))
% 18.55/18.48 [7256]P36(x72561,x72562)+~P36(x72561,f324(f324(f282(x72561,x72561,x72561),x72562),x72562))
% 18.55/18.48 [7288]~P1(f324(f324(f231(a838),f324(a114,x72881)),x72882))+P1(f174(a832,a177,f324(f231(a838),x72881),x72882))
% 18.55/18.48 [7451]P29(a838,a838,f324(f324(f9(a838,a838,a838),f3(a838)),x74511),x74512)+P1(f324(f324(f326(a838),f620(x74511,x74512)),x74512))
% 18.55/18.48 [7509]E(f324(f324(f324(f68(a838,x75091,f82(a838)),f324(f18(a838,x75091),f80(a838))),f2(a838)),x75092),f324(f41(x75091),x75092))+~P1(f324(f64(x75091),x75092))
% 18.55/18.48 [7510]E(f324(f324(f324(f68(a838,x75101,f82(a838)),f324(f18(a838,x75101),f80(a838))),f2(a838)),x75102),f324(f41(x75101),x75102))+~P1(f324(f64(x75101),x75102))
% 18.55/18.48 [7553]P29(a838,a838,f324(f324(f9(a838,a838,a838),f3(a838)),x75531),x75532)+~P1(f324(f324(f231(a838),x75531),f620(x75531,x75532)))
% 18.55/18.48 [7610]P36(x76101,x76102)+P1(f324(f324(f231(f845(x76101,a832)),f614(x76102,x76101)),f324(f278(x76101,x76101,x76102),f614(x76102,x76101))))
% 18.55/18.48 [7615]P57(x76151,x76152)+~P36(x76151,f324(f257(f844(x76151,x76151)),f324(f252(x76151,x76151,a832),x76152)))
% 18.55/18.48 [7687]P1(f324(f324(f231(a838),f324(a114,x76871)),x76872))+~P1(f174(a832,a177,f324(f231(a838),x76871),x76872))
% 18.55/18.48 [7745]P1(f324(f324(f326(f844(a838,a838)),f324(f324(f247(a838,a838),x77451),x77452)),f301(a838,a315)))+~P1(f324(f324(f231(a838),x77451),x77452))
% 18.55/18.48 [7839]P49(x78391,x78392)+~P47(x78391,f238(f845(x78391,a832)),f324(f257(f844(x78391,x78391)),f324(f252(x78391,x78391,a832),x78392)))
% 18.55/18.48 [7903]~P1(f324(f127(x79031),x79032))+P1(f324(f127(f845(x79031,a832)),f324(f324(f141(f839(x79031),f845(x79031,a832)),f157(x79031)),f60(x79031,x79032))))
% 18.55/18.48 [8101]~P36(x81011,f324(f279(x81011,x81011),x81012))+P36(x81011,f324(f279(x81011,x81011),f324(f324(f282(x81011,x81011,x81011),x81012),f301(x81011,x81012))))
% 18.55/18.48 [8220]P1(f324(f64(f844(x82201,x82201)),f324(f324(f282(x82201,x82201,x82201),x82202),f301(x82201,x82202))))+~P1(f324(f64(f844(x82201,x82201)),x82202))
% 18.55/18.48 [8250]E(x82501,f2(a1))+P1(f324(f55(x82502,x82501),f324(f324(f247(a1,a1),f324(f324(f42(a1),x82502),x82501)),f51(a1,x82502,x82501))))
% 18.55/18.48 [8264]~P1(f324(f324(f326(f844(a838,a838)),f324(f324(f247(a838,a838),x82641),x82642)),f301(a838,a315)))+P1(f324(f324(f231(a838),x82641),x82642))
% 18.55/18.48 [8283]~P72(x82831)+E(f324(f131(x82831,x82831,f324(f9(x82831,x82831,x82831),f82(x82831)),f2(x82831)),f324(f154(x82831),x82832)),f324(f131(x82831,x82831,f82(x82831),f2(x82831)),x82832))
% 18.55/18.48 [8544]~P55(x85441,f324(f257(f844(x85441,x85441)),f324(f252(x85441,x85441,a832),x85442)))+P55(x85441,f324(f257(f844(x85441,x85441)),f324(f252(x85441,x85441,a832),f239(x85441,x85441,x85442))))
% 18.55/18.48 [8558]P1(f324(f324(f326(f844(a838,a838)),f324(f324(f247(a838,a838),x85581),x85582)),f324(f324(f282(a838,a838,a838),a315),f301(a838,a315))))+~P1(f324(f324(f232(a838),x85581),x85582))
% 18.55/18.48 [8600]~P1(f324(f64(f844(x86001,x86001)),f324(f324(f282(x86001,x86001,x86001),x86002),f301(x86001,x86002))))+P1(f324(f64(f844(x86001,x86001)),x86002))
% 18.55/18.48 [8650]~P55(x86501,f324(f257(f844(x86501,x86501)),f324(f252(x86501,x86501,a832),f239(x86501,x86501,x86502))))+P55(x86501,f324(f257(f844(x86501,x86501)),f324(f252(x86501,x86501,a832),x86502)))
% 18.55/18.48 [8824]P55(x88241,x88242)+P1(f324(f324(f326(f844(x88241,x88241)),f324(f324(f247(x88241,x88241),f371(x88242,x88241)),f371(x88242,x88241))),f324(f324(f282(x88241,x88241,x88241),x88242),f301(x88241,x88242))))
% 18.55/18.48 [8825]P55(x88251,x88252)+P1(f324(f324(f326(f844(x88251,x88251)),f324(f324(f247(x88251,x88251),f372(x88252,x88251)),f372(x88252,x88251))),f324(f324(f282(x88251,x88251,x88251),x88252),f301(x88251,x88252))))
% 18.55/18.48 [8933]~P1(f324(f324(f326(f844(a838,a838)),f324(f324(f247(a838,a838),x89331),x89332)),f324(f324(f282(a838,a838,a838),a315),f301(a838,a315))))+P1(f324(f324(f232(a838),x89331),x89332))
% 18.55/18.48 [4893]~P89(x48931)+E(f324(f324(f82(x48931),f324(f106(x48931),a85)),x48932),x48932)
% 18.55/18.48 [4923]~P63(x49231)+E(f324(f324(f82(x49231),f324(f81(x49231),x49232)),x49232),f2(x49231))
% 18.55/18.48 [4924]~P6(x49241)+E(f324(f324(f82(x49241),f324(f81(x49241),x49242)),x49242),f2(x49241))
% 18.55/18.48 [4925]~P91(x49251)+E(f324(f324(f103(x49251),f324(f81(x49251),x49252)),x49252),f238(x49251))
% 18.55/18.48 [4926]~P91(x49261)+E(f324(f324(f104(x49261),f324(f81(x49261),x49262)),x49262),f179(x49261))
% 18.55/18.48 [4956]~P89(x49561)+E(f324(f324(f83(x49561),f324(f106(x49561),a99)),x49562),f324(f81(x49561),x49562))
% 18.55/18.48 [5115]~P107(x51151)+E(f324(f324(f83(x51151),f324(f81(x51151),f80(x51151))),x51152),f324(f81(x51151),x51152))
% 18.55/18.48 [5157]E(f324(f77(a1),x51571),f80(a1))+~E(f324(f77(a1),f324(f324(f83(a1),x51571),x51572)),f80(a1))
% 18.55/18.48 [5245]~P89(x52451)+E(f324(f324(f82(x52451),f80(x52451)),f324(f106(x52451),x52452)),f324(f106(x52451),f324(f324(f3(a1),x52452),a99)))
% 18.55/18.48 [5299]~P94(x52991)+E(f12(x52991,f324(f324(f303(x52991),x52992),f179(f845(x52991,a832)))),x52992)
% 18.55/18.48 [5300]~P86(x53001)+E(f16(x53001,f324(f324(f303(x53001),x53002),f179(f845(x53001,a832)))),x53002)
% 18.55/18.48 [5301]~P86(x53011)+E(f17(x53011,f324(f324(f303(x53011),x53012),f179(f845(x53011,a832)))),x53012)
% 18.55/18.48 [5302]~P94(x53021)+E(f15(x53021,f324(f324(f303(x53021),x53022),f179(f845(x53021,a832)))),x53022)
% 18.55/18.48 [5303]~P9(x53031)+E(f44(x53031,f324(f324(f303(x53031),x53032),f179(f845(x53031,a832)))),x53032)
% 18.55/18.48 [5304]~P9(x53041)+E(f43(x53041,f324(f324(f303(x53041),x53042),f179(f845(x53041,a832)))),x53042)
% 18.55/18.48 [5326]E(f324(f324(f82(a838),x53261),f324(f324(f3(a838),x53262),x53261)),x53262)+P1(f324(f324(f232(a838),x53262),x53261))
% 18.55/18.48 [5358]E(x53581,f115(x53582))+P1(f324(f324(f232(a838),f2(a838)),f324(f180(f839(x53582)),x53581)))
% 18.55/18.48 [5481]~P86(x54811)+E(f13(x54811,f178(x54811),f324(f324(f303(x54811),x54812),f179(f845(x54811,a832)))),x54812)
% 18.55/18.48 [5482]~P86(x54821)+E(f14(x54821,f235(x54821),f324(f324(f303(x54821),x54822),f179(f845(x54821,a832)))),x54822)
% 18.55/18.48 [5543]E(f324(f324(f83(a1),x55431),f324(f324(f42(a1),x55432),x55431)),x55432)+~P1(f324(f324(f280(a1),x55431),x55432))
% 18.55/18.48 [5544]E(f324(f324(f82(a838),x55441),f324(f324(f3(a838),x55442),x55441)),x55442)+~P1(f324(f324(f231(a838),x55441),x55442))
% 18.55/18.49 [5545]E(f324(f324(f3(a838),x55451),f324(f324(f3(a838),x55451),x55452)),x55452)+~P1(f324(f324(f231(a838),x55452),x55451))
% 18.55/18.49 [5563]E(f51(a838,f324(f324(f3(a838),x55631),x55632),x55632),f51(a838,x55631,x55632))+P1(f324(f324(f232(a838),x55631),x55632))
% 18.55/18.49 [5564]E(f51(a838,f324(f324(f3(a838),x55641),x55642),x55642),f51(a838,x55641,x55642))+P1(f324(f324(f232(a838),x55641),x55642))
% 18.55/18.49 [5574]E(f324(f81(a1),f324(f324(f42(a1),x55741),f324(f81(a1),x55742))),f286(x55741,x55742))+P1(f324(f324(f231(a1),f2(a1)),x55742))
% 18.55/18.49 [5576]~E(x55762,f2(a838))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f240(a838),x55761),x55762)))
% 18.55/18.49 [5635]~P89(x56351)+E(f324(f324(f82(x56351),f324(f81(x56351),f80(x56351))),f324(f106(x56351),x56352)),f324(f106(x56351),f324(f324(f82(a1),x56352),a99)))
% 18.55/18.49 [5636]E(f324(f324(f240(a838),f324(f106(a838),x56361)),x56362),f324(f324(f240(a838),f2(a838)),x56362))+~P1(f324(a185,f324(f106(a1),x56361)))
% 18.55/18.49 [5736]E(f324(f130(a838),f129(a838,f324(f295(a838,x57361),x57362))),x57361)+~P1(f324(f324(f232(a838),x57361),x57362))
% 18.55/18.49 [5753]E(f324(f324(f83(a838),f324(f106(a838),x57531)),f324(f106(a838),x57532)),f324(f106(a838),f324(f324(f83(a1),x57531),x57532)))+P1(f324(f324(f232(a1),x57531),a85))
% 18.55/18.49 [5759]~P118(x57591)+P1(f324(f324(f231(x57591),f2(x57591)),f324(f324(f83(x57591),x57592),x57592)))
% 18.55/18.49 [5771]E(f324(f324(f3(a838),f324(a114,x57711)),x57712),f324(a114,f324(f324(f3(a838),x57711),x57712)))+~P1(f324(f324(f231(a838),x57712),x57711))
% 18.55/18.49 [5774]E(f51(a838,f324(f324(f3(a838),x57741),x57742),x57742),f51(a838,x57741,x57742))+~P1(f324(f324(f231(a838),x57742),x57741))
% 18.55/18.49 [5827]E(f324(f324(f240(a838),f324(a107,x58271)),x58272),f324(a107,f324(f324(f240(a1),x58271),x58272)))+~P1(f324(f324(f231(a1),f2(a1)),x58271))
% 18.55/18.49 [5828]E(f324(f324(f240(a838),f324(a107,x58281)),x58282),f324(a107,f324(f324(f240(a1),x58281),x58282)))+~P1(f324(f324(f231(a1),f2(a1)),x58281))
% 18.55/18.49 [5844]P1(f324(f127(x58441),x58442))+P1(f324(f324(f232(a838),f710(x58442,x58441)),f324(f180(f839(x58441)),x58442)))
% 18.55/18.49 [5845]P1(f324(f127(x58451),x58452))+P1(f324(f324(f232(a838),f714(x58452,x58451)),f324(f180(f839(x58451)),x58452)))
% 18.55/18.49 [5860]~P1(f324(f324(f280(a1),x58601),x58602))+P1(f324(f324(f280(a1),f324(f81(a1),x58601)),x58602))
% 18.55/18.49 [5863]~E(x58631,f115(x58632))+~P1(f324(f324(f232(a838),f2(a838)),f324(f180(f839(x58632)),x58631)))
% 18.55/18.49 [5876]E(f133(a838,f129(a838,f324(f295(a838,x58761),x58762))),f324(f324(f3(a838),x58762),f80(a838)))+~P1(f324(f324(f232(a838),x58761),x58762))
% 18.55/18.49 [5879]E(f324(f324(f82(a1),x58791),f324(f102(a1),f324(a114,f634(x58792,x58791)))),x58792)+~P1(f324(f324(f232(a1),x58791),x58792))
% 18.55/18.49 [5886]E(x58861,f2(a838))+E(f324(f324(f83(a838),x58862),f324(f324(f240(a838),x58862),f324(f324(f3(a838),x58861),f80(a838)))),f324(f324(f240(a838),x58862),x58861))
% 18.55/18.49 [5912]E(f324(f324(f83(a838),f324(a107,x59121)),f324(a107,x59122)),f324(a107,f324(f324(f83(a1),x59121),x59122)))+~P1(f324(f324(f231(a1),f2(a1)),x59121))
% 18.55/18.49 [5913]E(f324(f324(f42(a838),f324(a107,x59131)),f324(a107,x59132)),f324(a107,f324(f324(f42(a1),x59131),x59132)))+~P1(f324(f324(f231(a1),f2(a1)),x59131))
% 18.55/18.49 [5927]~P105(x59271)+E(f324(f324(f82(x59271),x59272),x59272),f324(f324(f83(x59271),f324(f324(f82(x59271),f80(x59271)),f80(x59271))),x59272))
% 18.55/18.49 [5946]E(f324(f324(f42(a1),f324(f77(a1),x59461)),f324(f77(a1),x59462)),f324(f77(a1),f324(f324(f42(a1),x59461),x59462)))+~P1(f324(f324(f280(a1),x59462),x59461))
% 18.55/18.49 [5947]E(f324(f324(f3(a1),f324(f102(a1),x59471)),f324(f102(a1),x59472)),f324(f102(a1),f324(f324(f3(a838),x59471),x59472)))+~P1(f324(f324(f231(a838),x59472),x59471))
% 18.55/18.49 [5949]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f82(a1),x59491),x59492)),f56(x59491,x59492))+~P1(f324(f324(f231(a1),x59492),f2(a1)))
% 18.55/18.49 [5988]E(f163(x59881,x59882),f115(f839(x59881)))+P1(f324(f324(f326(f839(x59881)),f709(x59882,x59881)),f324(f157(f839(x59881)),x59882)))
% 18.55/18.49 [6053]~P1(f324(f324(f280(a838),x60531),x60532))+P1(f324(f324(f280(a838),x60531),f324(f324(f82(a838),x60532),x60531)))
% 18.55/18.49 [6075]E(f324(f324(f139(a1),x60751),f162(f324(f324(f82(a1),x60751),f80(a1)),x60752)),f162(x60751,x60752))+~P1(f324(f324(f231(a1),x60751),x60752))
% 18.55/18.49 [6113]~P1(f324(f324(f232(a838),x61132),x61131))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f3(a838),x61131),x61132)))
% 18.55/18.49 [6145]~P1(f324(f324(f232(a838),x61451),f324(a107,x61452)))+P1(f324(f324(f232(a1),f324(f102(a1),x61451)),x61452))
% 18.55/18.49 [6146]P1(f324(f324(f280(a1),x61461),x61462))+~P1(f324(f324(f280(a1),f324(f81(a1),x61461)),x61462))
% 18.55/18.49 [6176]~P86(x61761)+E(f324(f324(f103(f845(x61761,a832)),f324(f258(x61761),x61762)),f324(f324(f303(x61761),x61762),f179(f845(x61761,a832)))),f324(f294(x61761),x61762))
% 18.55/18.49 [6177]~P1(f324(f324(f232(a838),f2(a838)),x61772))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f82(a838),x61771),x61772)))
% 18.55/18.49 [6178]~P1(f324(f324(f232(a838),f2(a838)),x61781))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f82(a838),x61781),x61782)))
% 18.55/18.49 [6179]~P1(f324(f324(f232(a838),f2(a838)),x61791))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f240(a838),x61791),x61792)))
% 18.55/18.49 [6180]~P1(f324(f324(f231(a1),f2(a1)),x61801))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f240(a1),x61801),x61802)))
% 18.55/18.49 [6208]~E(f324(x62081,f2(a838)),f2(a838))+E(f324(f324(f8(a838,a838),x62081),f296(a838,f324(a114,f2(a838)),x62082)),f324(f324(f8(a838,a838),x62081),f296(a838,f2(a838),x62082)))
% 18.55/18.49 [6273]~P89(x62731)+E(f324(f324(f83(x62731),f324(f324(f82(x62731),f80(x62731)),f80(x62731))),f324(f106(x62731),x62732)),f324(f106(x62731),f324(f324(f82(a1),x62732),x62732)))
% 18.55/18.49 [6295]E(f324(f324(f303(a1),x62951),f296(a1,f324(f324(f82(a1),x62951),f80(a1)),x62952)),f296(a1,x62951,x62952))+P1(f324(f324(f232(a1),x62952),x62951))
% 18.55/18.49 [6296]P1(f324(f324(f232(a838),x62961),f324(a107,x62962)))+~P1(f324(f324(f232(a1),f324(f102(a1),x62961)),x62962))
% 18.55/18.49 [6398]P1(f324(f324(f280(a838),x63981),x63982))+~P1(f324(f324(f280(a838),x63981),f324(f324(f82(a838),x63982),x63981)))
% 18.55/18.49 [6403]E(f324(a107,f324(f324(f42(a1),f324(f106(a1),x64031)),f324(f106(a1),x64032))),f324(f324(f42(a838),f324(f106(a838),x64031)),f324(f106(a838),x64032)))+P1(f324(a185,f324(f106(a1),x64031)))
% 18.55/18.49 [6404]E(f324(a107,f324(f324(f240(a1),f324(f106(a1),x64041)),f324(f106(a838),x64042))),f324(f324(f240(a838),f324(f106(a838),x64041)),f324(f106(a838),x64042)))+P1(f324(a185,f324(f106(a1),x64041)))
% 18.55/18.49 [6463]P1(f324(f324(f232(a838),x64631),x64632))+~P1(f324(f324(f232(a838),f2(a838)),f324(f324(f3(a838),x64632),x64631)))
% 18.55/18.49 [6507]P1(f324(f324(f232(a838),f2(a838)),x65071))+~P1(f324(f324(f232(a838),f2(a838)),f324(f324(f83(a838),x65072),x65071)))
% 18.55/18.49 [6508]P1(f324(f324(f232(a838),f2(a838)),x65081))+~P1(f324(f324(f232(a838),f2(a838)),f324(f324(f83(a838),x65081),x65082)))
% 18.55/18.49 [6522]E(f129(a838,f324(f295(a838,f324(f106(a838),x65221)),f324(f106(a838),x65222))),f115(a838))+P1(f324(f324(f232(a838),f324(f106(a838),x65221)),f324(f106(a838),x65222)))
% 18.55/18.49 [6524]~P1(f324(f324(f231(a1),x65241),f2(a1)))+E(f324(f324(f83(a838),f324(a107,f324(f81(a1),x65241))),f324(a107,f324(f81(a1),x65242))),f324(a107,f324(f324(f83(a1),x65241),x65242)))
% 18.55/18.49 [6590]~E(x65902,f179(f845(x65901,a832)))+P1(f324(f324(f231(f845(x65901,a832)),x65902),f324(f81(f845(x65901,a832)),x65902)))
% 18.55/18.49 [6653]~P89(x66531)+E(f324(f324(f82(x66531),f324(f324(f82(x66531),f2(x66531)),f324(f106(x66531),x66532))),f324(f106(x66531),x66532)),f324(f106(x66531),f324(f324(f82(a1),x66532),x66532)))
% 18.55/18.49 [6662]~P1(f324(f324(f280(a1),f324(f102(a1),x66621)),x66622))+P1(f324(f324(f280(a838),x66621),f324(a107,f324(f77(a1),x66622))))
% 18.55/18.49 [6712]~P1(f324(f324(f232(a1),x67121),x67122))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x67121),f80(a1))),x67122))
% 18.55/18.49 [6713]~P1(f324(f324(f232(a1),x67131),x67132))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x67131),f80(a1))),x67132))
% 18.55/18.49 [6755]P1(f324(f324(f280(a1),f324(f102(a1),x67551)),x67552))+~P1(f324(f324(f280(a838),x67551),f324(a107,f324(f77(a1),x67552))))
% 18.55/18.49 [6789]E(x67891,f2(a838))+~P1(f324(f324(f231(a1),f324(f102(a1),x67892)),f324(f81(a1),f324(f102(a1),x67891))))
% 18.55/18.49 [6790]E(x67901,f2(a838))+~P1(f324(f324(f231(a1),f324(f102(a1),x67901)),f324(f81(a1),f324(f102(a1),x67902))))
% 18.55/18.49 [6895]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f82(a1),x68951),x68952)),f56(x68951,x68952))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),x68951),x68952)))
% 18.55/18.49 [6932]~P30(x69321,x69322)+P36(x69321,f324(f246(f845(f844(x69321,x69321),a832),f845(f844(x69321,x69321),a832)),x69322))
% 18.55/18.49 [6953]~P1(f324(f324(f231(a838),f324(a114,f2(a838))),x69531))+P1(f324(f324(f231(a838),f324(a114,f2(a838))),f324(f324(f240(a838),x69531),x69532)))
% 18.55/18.49 [7121]~P1(f324(f324(f232(a1),x71211),x71212))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x71211),x71211)),f324(f324(f82(a1),x71212),x71212)))
% 18.55/18.49 [7122]~P1(f324(f324(f232(a1),x71221),x71222))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x71221),x71221)),f324(f324(f82(a1),x71222),x71222)))
% 18.55/18.49 [7133]~P1(f324(f324(f231(a1),x71331),x71332))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x71331),x71331)),f324(f324(f82(a1),x71332),x71332)))
% 18.55/18.49 [7134]~P1(f324(f324(f231(a1),x71341),x71342))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x71341),x71341)),f324(f324(f82(a1),x71342),x71342)))
% 18.55/18.49 [7201]~P1(f324(f324(f232(a838),f2(a838)),x72011))+P1(f324(f324(f232(a838),f324(f324(f3(a838),x72011),f324(a114,x72012))),x72011))
% 18.55/18.49 [7238]P1(f324(f324(f231(a838),f324(a114,f2(a838))),x72381))+~P1(f324(f324(f231(a838),f324(a114,f2(a838))),f324(f324(f83(a838),x72382),x72381)))
% 18.55/18.49 [7239]P1(f324(f324(f231(a838),f324(a114,f2(a838))),x72391))+~P1(f324(f324(f231(a838),f324(a114,f2(a838))),f324(f324(f83(a838),x72391),x72392)))
% 18.55/18.49 [7243]P1(f324(f324(f231(a838),f324(f324(f149(a838),x72431),x72432)),f324(f151(a838),x72431)))+~P1(f324(f324(f232(a838),x72432),f324(f180(f839(a838)),x72431)))
% 18.55/18.49 [7287]P1(f324(f324(f232(a1),x72871),x72872))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x72871),f80(a1))),x72872))
% 18.55/18.49 [7296]~P1(f324(f324(f326(a838),x72961),x72962))+P1(f324(f324(f326(a1),f324(f102(a1),x72961)),f324(f304(a838,a1,f102(a1)),x72962)))
% 18.55/18.49 [7333]P1(f324(f64(x73331),f238(f845(x73331,a832))))+~P1(f324(f64(f845(x73332,x73331)),f238(f845(f845(x73332,x73331),a832))))
% 18.55/18.49 [7334]P1(f324(f64(x73341),f238(f845(x73341,a832))))+~P1(f324(f64(f848(x73342,x73341)),f238(f845(f848(x73342,x73341),a832))))
% 18.55/18.49 [7335]P1(f324(f64(x73351),f238(f845(x73351,a832))))+~P1(f324(f64(f848(x73351,x73352)),f238(f845(f848(x73351,x73352),a832))))
% 18.55/18.49 [7377]E(x73771,f179(f845(x73772,a832)))+~P1(f324(f324(f231(f845(x73772,a832)),x73771),f324(f81(f845(x73772,a832)),x73771)))
% 18.55/18.49 [7520]E(f324(f131(f839(x75201),f839(x75201),f125(x75201),f115(x75201)),x75202),f115(x75201))+P1(f324(f324(f326(f839(x75201)),f758(x75202,x75201)),f324(f157(f839(x75201)),x75202)))
% 18.55/18.49 [7521]E(f324(f131(f839(x75211),f839(x75211),f125(x75211),f115(x75211)),x75212),f115(x75211))+P1(f324(f324(f326(f839(x75211)),f760(x75212,x75211)),f324(f157(f839(x75211)),x75212)))
% 18.55/18.49 [7658]E(f163(x76581,f324(f324(f139(f839(x76581)),f115(x76581)),x76582)),f163(x76581,x76582))+~P1(f324(f313(f839(f839(x76581)),f164(x76581)),f324(f324(f139(f839(x76581)),f115(x76581)),x76582)))
% 18.55/18.49 [7764]P1(f324(f324(f232(a1),x77641),x77642))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x77641),x77641)),f324(f324(f82(a1),x77642),x77642)))
% 18.55/18.49 [7765]P1(f324(f324(f232(a1),x77651),x77652))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x77651),x77651)),f324(f324(f82(a1),x77652),x77652)))
% 18.55/18.49 [7767]P1(f324(f324(f231(a1),x77671),x77672))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x77671),x77671)),f324(f324(f82(a1),x77672),x77672)))
% 18.55/18.49 [7768]P1(f324(f324(f231(a1),x77681),x77682))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x77681),x77681)),f324(f324(f82(a1),x77682),x77682)))
% 18.55/18.49 [7861]~P105(x78611)+E(f324(f324(f83(x78611),f324(f324(f82(x78611),f80(x78611)),f80(x78611))),f324(f324(f8(a838,x78611),f102(x78611)),f296(a838,f80(a838),x78612))),f324(f324(f83(x78611),f324(f102(x78611),x78612)),f324(f324(f82(x78611),f324(f102(x78611),x78612)),f80(x78611))))
% 18.55/18.49 [7902]E(f324(f324(f139(a1),f324(f106(a1),x79021)),f162(f324(f324(f82(a1),f324(f106(a1),x79021)),f80(a1)),f324(f106(a1),x79022))),f162(f324(f106(a1),x79021),f324(f106(a1),x79022)))+~P1(f324(f324(f231(a1),f324(f106(a1),x79021)),f324(f106(a1),x79022)))
% 18.55/18.49 [7918]P1(f324(f324(f326(a838),x79181),x79182))+~P1(f324(f324(f326(a1),f324(f102(a1),x79181)),f324(f304(a838,a1,f102(a1)),x79182)))
% 18.55/18.49 [8072]~P1(f324(f64(x80721),x80722))+E(f324(f304(a838,x80721,f516(x80722,x80721)),f324(f257(a838),f324(f324(f9(a838,a838,a832),f232(a838)),f517(x80722,x80721)))),x80722)
% 18.55/18.49 [8358]P48(x83581,x83582)+P1(f324(f324(f326(f844(x83581,x83581)),f324(f324(f247(x83581,x83581),f828(x83582,x83581)),f828(x83582,x83581))),x83582))
% 18.55/18.49 [8491]~P89(x84911)+E(f324(f324(f3(x84911),f80(x84911)),f324(f106(x84911),x84912)),f324(f106(x84911),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f81(a1),x84912))))
% 18.55/18.49 [8596]~P1(f324(f324(f232(f845(a838,a832)),x85961),x85962))+P1(f324(f324(f232(f845(a1,a832)),f324(f304(a838,a1,f102(a1)),x85961)),f324(f304(a838,a1,f102(a1)),x85962)))
% 18.55/18.49 [8597]~P1(f324(f324(f231(f845(a838,a832)),x85971),x85972))+P1(f324(f324(f231(f845(a1,a832)),f324(f304(a838,a1,f102(a1)),x85971)),f324(f304(a838,a1,f102(a1)),x85972)))
% 18.55/18.49 [8624]~P1(f324(f324(f232(a1),x86241),x86242))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x86241),x86241)),a99)),f324(f324(f82(a1),x86242),x86242)))
% 18.55/18.49 [8625]~P1(f324(f324(f232(a1),x86251),x86252))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x86251),x86251)),a99)),f324(f324(f82(a1),x86252),x86252)))
% 18.55/18.49 [8626]~P1(f324(f324(f232(a1),x86261),x86262))+P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x86261),x86261)),a99)),f324(f324(f82(a1),x86262),x86262)))
% 18.55/18.49 [8627]~P1(f324(f324(f232(a1),x86271),x86272))+P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x86271),x86271)),a99)),f324(f324(f82(a1),x86272),x86272)))
% 18.55/18.49 [8695]~P1(f324(f324(f326(a838),x86951),f324(f157(a838),x86952)))+P1(f324(f324(f231(a838),x86951),f324(f131(a838,a838,f82(a838),f2(a838)),x86952)))
% 18.55/18.49 [8769]P44(x87691,x87692)+~P1(f324(f324(f326(f844(x87691,x87691)),f324(f324(f247(x87691,x87691),f807(x87692,x87691)),f807(x87692,x87691))),x87692))
% 18.55/18.49 [8900]~P1(f324(f324(f232(f845(a1,a832)),f324(f304(a838,a1,f102(a1)),x89001)),f324(f304(a838,a1,f102(a1)),x89002)))+P1(f324(f324(f232(f845(a838,a832)),x89001),x89002))
% 18.55/18.49 [8901]~P1(f324(f324(f231(f845(a1,a832)),f324(f304(a838,a1,f102(a1)),x89011)),f324(f304(a838,a1,f102(a1)),x89012)))+P1(f324(f324(f231(f845(a838,a832)),x89011),x89012))
% 18.55/18.49 [8976]P1(f324(f324(f232(a1),x89761),x89762))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89761),x89761)),a99)),f324(f324(f82(a1),x89762),x89762)))
% 18.55/18.49 [8977]P1(f324(f324(f232(a1),x89771),x89772))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89771),x89771)),a99)),f324(f324(f82(a1),x89772),x89772)))
% 18.55/18.49 [8978]P1(f324(f324(f232(a1),x89781),x89782))+~P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89781),x89781)),a99)),f324(f324(f82(a1),x89782),x89782)))
% 18.55/18.49 [8979]P1(f324(f324(f232(a1),x89791),x89792))+~P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x89791),x89791)),a99)),f324(f324(f82(a1),x89792),x89792)))
% 18.55/18.49 [9841]~P1(f324(f64(x98411),x98412))+E(f324(f180(f839(x98411)),f92(f839(x98411),f324(f324(f20(f839(x98411),a832,a832),f324(f324(f10(a832,f845(a832,a832),f839(x98411)),a322),f324(f324(f9(f839(x98411),f845(x98411,a832),a832),f324(f324(f10(f845(x98411,a832),f845(f845(x98411,a832),a832),f839(x98411)),a321),f157(x98411))),x98412))),f127(x98411)))),f208(x98411,x98412))
% 18.55/18.49 [5875]E(f324(f324(f82(a838),f324(f324(f3(a838),x58751),x58752)),x58752),x58751)+~P1(f324(f324(f231(a838),x58752),x58751))
% 18.55/18.49 [5942]E(f324(f324(f42(a838),f324(f324(f83(a838),x59421),x59422)),x59422),x59421)+~P1(f324(f324(f232(a838),f2(a838)),x59422))
% 18.55/18.49 [5943]E(f324(f324(f42(a838),f324(f324(f83(a838),x59431),x59432)),x59431),x59432)+~P1(f324(f324(f232(a838),f2(a838)),x59431))
% 18.55/18.49 [5948]~P67(x59481)+E(f324(f324(f8(a838,x59481),f324(f149(x59481),x59482)),f324(f295(a838,f2(a838)),f324(f180(f839(x59481)),x59482))),f324(f151(x59481),x59482))
% 18.55/18.49 [6067]E(f51(a838,f324(a114,f324(f324(f83(a838),x60671),x60672)),x60671),f80(a838))+~P1(f324(f324(f232(a838),f80(a838)),x60671))
% 18.55/18.49 [6073]E(f324(a114,f324(f324(f82(a838),f324(f106(a838),x60731)),x60732)),f324(f324(f82(a838),f80(a838)),x60732))+~P1(f324(a185,f324(f106(a1),x60731)))
% 18.55/18.49 [6099]E(f324(a107,f324(f324(f240(a1),f324(f106(a1),x60991)),x60992)),f324(f324(f240(a838),f324(f106(a838),x60991)),x60992))+P1(f324(a185,f324(f106(a1),x60991)))
% 18.55/18.49 [6351]E(f324(f324(f3(a838),x63511),f324(f106(a838),f324(f324(f82(a1),x63512),a99))),f324(f324(f3(a838),f324(a114,x63511)),f324(f106(a838),x63512)))+~P1(f324(f324(f232(a1),a85),x63512))
% 18.55/18.49 [6432]E(x64321,f2(a838))+E(f324(a114,f324(f324(f82(a838),f324(f324(f3(a838),x64321),f80(a838))),x64322)),f324(f324(f82(a838),x64321),x64322))
% 18.55/18.49 [6477]E(x64771,f2(a1))+P1(f324(f324(f232(a1),f2(a1)),f324(f324(f240(a1),f324(f77(a1),x64771)),x64772)))
% 18.55/18.49 [6492]~E(x64922,f2(a838))+P1(f324(f324(f232(a1),f2(a1)),f324(f324(f240(a1),f324(f77(a1),x64921)),x64922)))
% 18.55/18.49 [6529]E(x65291,f2(a838))+E(f324(f324(f82(a838),x65292),f324(f324(f83(a838),f324(f324(f3(a838),x65291),f80(a838))),x65292)),f324(f324(f83(a838),x65291),x65292))
% 18.55/18.49 [6584]~P1(f324(f324(f231(a1),x65841),x65842))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x65841),a99)),x65842))
% 18.55/18.49 [6716]E(f324(f324(f139(a838),x67161),f129(a838,f324(f295(a838,f324(a114,x67161)),x67162))),f129(a838,f324(f295(a838,x67161),x67162)))+~P1(f324(f324(f232(a838),x67161),x67162))
% 18.55/18.49 [6717]E(f324(f324(f139(a838),x67171),f129(a838,f324(f295(a838,f324(a114,x67171)),x67172))),f129(a838,f324(f295(a838,x67171),x67172)))+~P1(f324(f324(f232(a838),x67171),x67172))
% 18.55/18.49 [6889]~P1(f324(f324(f280(a1),x68891),f324(f102(a1),x68892)))+P1(f324(f324(f280(a838),f324(a107,f324(f77(a1),x68891))),x68892))
% 18.55/18.49 [6923]E(x69231,x69232)+~E(f324(f324(f3(a1),f324(f324(f82(a1),x69231),x69231)),a99),f324(f324(f3(a1),f324(f324(f82(a1),x69232),x69232)),a99))
% 18.55/18.49 [6926]E(x69261,f115(x69262))+E(f264(x69262,f324(f324(f141(x69262,f844(a101,x69262)),f324(f247(a101,x69262),f80(a101))),x69261)),f271(x69262,x69261))
% 18.55/18.49 [7164]P1(f324(f324(f231(a1),x71641),x71642))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x71641),a99)),x71642))
% 18.55/18.49 [7306]P1(f324(f324(f280(a1),x73061),f324(f102(a1),x73062)))+~P1(f324(f324(f280(a838),f324(a107,f324(f77(a1),x73061))),x73062))
% 18.55/18.49 [7660]~P1(f324(f324(f232(a838),x76601),x76602))+P1(f324(f324(f326(f844(a838,a838)),f324(f324(f247(a838,a838),x76601),x76602)),a236))
% 18.55/18.49 [7891]~P1(f324(f324(f232(a101),f2(a101)),x78911))+P1(f324(f324(f232(a101),f324(f246(a101,f844(a101,a101)),f324(f265(x78911),x78912))),x78911))
% 18.55/18.49 [8199]~P78(x81991)+P1(f324(f324(f231(x81991),f324(f77(x81991),f324(f151(x81991),x81992))),f324(f151(x81991),f324(f324(f141(x81991,x81991),f77(x81991)),x81992))))
% 18.55/18.49 [8222]P1(f324(f324(f232(a838),x82221),x82222))+~P1(f324(f324(f326(f844(a838,a838)),f324(f324(f247(a838,a838),x82221),x82222)),a236))
% 18.55/18.49 [8382]E(f324(f324(f247(x83821,x83821),f360(x83822,x83821)),f360(x83822,x83821)),x83822)+~P1(f324(f324(f326(f844(x83821,x83821)),x83822),f301(x83821,f179(f845(f844(x83821,x83821),a832)))))
% 18.55/18.49 [8424]E(f324(f295(a838,x84241),f324(f324(f82(a838),x84241),f324(f41(a838),x84242))),x84242)+~P1(f324(f324(f231(f845(a838,a832)),x84242),f324(f295(a838,x84241),f324(f324(f82(a838),x84241),f324(f41(a838),x84242)))))
% 18.55/18.49 [8445]E(f324(f324(f139(a838),f324(f106(a838),x84451)),f129(a838,f324(f295(a838,f324(a114,f324(f106(a838),x84451))),f324(f106(a838),x84452)))),f129(a838,f324(f295(a838,f324(f106(a838),x84451)),f324(f106(a838),x84452))))+~P1(f324(f324(f232(a838),f324(f106(a838),x84451)),f324(f106(a838),x84452)))
% 18.55/18.49 [8728]E(f324(f324(f42(a1),f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),x87281),x87281)),a99))),f324(f106(a1),f324(f324(f82(a1),x87282),x87282))),f324(f324(f42(a1),f324(f106(a1),x87281)),f324(f106(a1),x87282)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x87282)))
% 18.55/18.49 [8834]E(f161(f839(x88341),f324(f324(f10(a832,a832,f839(x88341)),a320),f324(f324(f9(f839(x88341),f839(x88341),a832),a321),f115(x88341))),x88342),f163(x88341,f163(x88341,x88342)))+~P18(a838,f324(f154(a838),f324(f324(f141(f839(x88341),a838),f180(f839(x88341))),x88342)))
% 18.55/18.49 [8837]E(f324(f324(f42(a1),f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),x88371),x88371)),a99))),f324(f106(a1),f324(f324(f82(a1),x88372),x88372))),f324(f324(f42(a1),f324(f324(f82(a1),f324(f106(a1),x88371)),f80(a1))),f324(f106(a1),x88372)))+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x88372)))
% 18.55/18.49 [9612]P1(f324(a185,x96122))+E(f324(f324(f88(a1,a838),f324(f324(f3(a1),x96121),x96122)),f324(f324(f20(a1,a838,a838),f324(f324(f9(a1,a838,f845(a838,a838)),f324(f324(f10(a832,f845(a838,f845(a838,a838)),a1),f98(a838)),a185)),f2(a838))),a107)),f324(f324(f3(a838),f324(a107,x96121)),f324(a107,x96122)))
% 18.55/18.49 [9616]E(f324(f324(f88(a1,a838),f324(f106(a1),f324(f324(f82(a1),x96161),f324(f81(a1),x96162)))),f324(f324(f20(a1,a838,a838),f324(f324(f9(a1,a838,f845(a838,a838)),f324(f324(f10(a832,f845(a838,f845(a838,a838)),a1),f98(a838)),a185)),f2(a838))),a107)),f324(f324(f3(a838),f324(f106(a838),x96161)),f324(f106(a838),x96162)))+P1(f324(f324(f232(a1),x96162),a85))
% 18.55/18.49 [9617]~P30(x96171,x96172)+P1(f324(f324(f231(f845(f844(x96171,x96171),a832)),f324(f324(f282(x96171,x96171,x96171),f324(f246(f845(f844(x96171,x96171),a832),f845(f844(x96171,x96171),a832)),x96172)),f324(f251(f845(f844(x96171,x96171),a832),f845(f844(x96171,x96171),a832)),x96172))),f324(f246(f845(f844(x96171,x96171),a832),f845(f844(x96171,x96171),a832)),x96172)))
% 18.55/18.49 [9675]~E(f324(f41(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,f845(a838,a832),a832),f326(a838)),x96751))),f324(f324(f9(a838,a838,a832),f232(a838)),f324(a114,x96752))))),f2(a838))+~P1(f324(f324(f326(a838),f2(a838)),x96751))
% 18.55/18.49 [9686]E(f292(a838,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96861,x96862),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x96862),x96861))
% 18.55/18.49 [9692]E(f293(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96921,x96922),f179(f845(a838,a832)))+P1(f324(f324(f280(a838),x96921),x96922))
% 18.55/18.49 [9693]E(f290(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96931,x96932),f179(f845(a838,a832)))+P1(f324(f324(f280(a838),x96931),x96932))
% 18.55/18.49 [9694]E(f293(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96941,x96942),f179(f845(a838,a832)))+P1(f324(f324(f280(a838),x96941),x96942))
% 18.55/18.49 [9695]E(f290(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96951,x96952),f179(f845(a838,a832)))+P1(f324(f324(f280(a838),x96951),x96952))
% 18.55/18.49 [9696]E(f293(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96961,x96962),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x96962),x96961))
% 18.55/18.49 [9697]E(f290(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96971,x96972),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x96972),x96971))
% 18.55/18.49 [9698]E(f293(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96981,x96982),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x96982),x96981))
% 18.55/18.49 [9699]E(f293(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96991,x96992),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x96992),x96991))
% 18.55/18.49 [9700]E(f290(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97001,x97002),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x97002),x97001))
% 18.55/18.49 [9701]E(f290(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97011,x97012),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x97012),x97011))
% 18.55/18.49 [9744]E(f51(a1,f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),x97441),x97441)),a99)),f324(f106(a1),f324(f324(f82(a1),x97442),x97442))),f324(f324(f82(a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f51(a1,f324(f106(a1),x97441),f324(f106(a1),x97442)))),f80(a1)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x97442)))
% 18.55/18.49 [9753]E(f51(a1,f324(f106(a1),f324(f324(f3(a1),f324(f324(f82(a1),x97531),x97531)),a99)),f324(f106(a1),f324(f324(f82(a1),x97532),x97532))),f324(f324(f3(a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f51(a1,f324(f324(f82(a1),f324(f106(a1),x97531)),f80(a1)),f324(f106(a1),x97532)))),f80(a1)))+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x97532)))
% 18.55/18.49 [9810]~P9(x98101)+E(f43(x98101,f324(f257(x98101),f324(f324(f10(f845(x98101,a832),a832,x98101),f90(x98101)),f324(f324(f10(f845(x98101,a832),f845(x98101,a832),x98101),f324(f20(x98101,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98101),a327),f324(f324(f9(x98101,f845(x98101,a832),a832),f326(x98101)),x98102)))),f231(x98101))))),f44(x98101,x98102))
% 18.55/18.49 [9834]~P36(x98341,x98342)+P57(x98341,f324(f324(f9(x98341,f845(f844(x98341,x98341),a832),f845(x98341,a832)),f324(f324(f10(f845(x98341,f845(f845(f844(x98341,x98341),a832),a832)),f845(f845(f844(x98341,x98341),a832),f845(x98341,a832)),x98341),f9(x98341,f845(f844(x98341,x98341),a832),a832)),f324(f324(f10(f845(x98341,f844(x98341,x98341)),f845(x98341,f845(f845(f844(x98341,x98341),a832),a832)),x98341),f324(f10(f844(x98341,x98341),f845(f845(f844(x98341,x98341),a832),a832),x98341),f326(f844(x98341,x98341)))),f247(x98341,x98341)))),x98342))
% 18.55/18.49 [9835]~P12(x98351,f238(f845(x98351,a832)),x98352)+P11(x98351,f324(f324(f9(x98351,f845(f844(x98351,x98351),a832),f845(x98351,a832)),f324(f324(f10(f845(x98351,f845(f845(f844(x98351,x98351),a832),a832)),f845(f845(f844(x98351,x98351),a832),f845(x98351,a832)),x98351),f9(x98351,f845(f844(x98351,x98351),a832),a832)),f324(f324(f10(f845(x98351,f844(x98351,x98351)),f845(x98351,f845(f845(f844(x98351,x98351),a832),a832)),x98351),f324(f10(f844(x98351,x98351),f845(f845(f844(x98351,x98351),a832),a832),x98351),f326(f844(x98351,x98351)))),f247(x98351,x98351)))),x98352))
% 18.55/18.49 [9872]P36(x98721,x98722)+~P57(x98721,f324(f324(f9(x98721,f845(f844(x98721,x98721),a832),f845(x98721,a832)),f324(f324(f10(f845(x98721,f845(f845(f844(x98721,x98721),a832),a832)),f845(f845(f844(x98721,x98721),a832),f845(x98721,a832)),x98721),f9(x98721,f845(f844(x98721,x98721),a832),a832)),f324(f324(f10(f845(x98721,f844(x98721,x98721)),f845(x98721,f845(f845(f844(x98721,x98721),a832),a832)),x98721),f324(f10(f844(x98721,x98721),f845(f845(f844(x98721,x98721),a832),a832),x98721),f326(f844(x98721,x98721)))),f247(x98721,x98721)))),x98722))
% 18.55/18.49 [9873]P12(x98731,f238(f845(x98731,a832)),x98732)+~P11(x98731,f324(f324(f9(x98731,f845(f844(x98731,x98731),a832),f845(x98731,a832)),f324(f324(f10(f845(x98731,f845(f845(f844(x98731,x98731),a832),a832)),f845(f845(f844(x98731,x98731),a832),f845(x98731,a832)),x98731),f9(x98731,f845(f844(x98731,x98731),a832),a832)),f324(f324(f10(f845(x98731,f844(x98731,x98731)),f845(x98731,f845(f845(f844(x98731,x98731),a832),a832)),x98731),f324(f10(f844(x98731,x98731),f845(f845(f844(x98731,x98731),a832),a832),x98731),f326(f844(x98731,x98731)))),f247(x98731,x98731)))),x98732))
% 18.55/18.49 [7110]E(f324(f324(f82(a838),f324(f106(a838),f324(f324(f3(a1),x71101),a99))),x71102),f324(a114,f324(f324(f82(a838),f324(f106(a838),x71101)),x71102)))+P1(f324(a185,f324(f106(a1),x71101)))
% 18.55/18.49 [7578]~P89(x75781)+E(f324(f324(f82(x75781),f324(f324(f82(x75781),f80(x75781)),f324(f106(x75781),x75782))),f324(f106(x75781),x75782)),f324(f106(x75781),f324(f324(f3(a1),f324(f324(f82(a1),x75782),x75782)),a99)))
% 18.55/18.49 [8223]~P1(f324(f324(f231(a1),x82231),x82232))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x82231),x82231)),f324(f324(f3(a1),f324(f324(f82(a1),x82232),x82232)),a99)))
% 18.55/18.49 [8224]~P1(f324(f324(f231(a1),x82241),x82242))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x82241),x82241)),f324(f324(f3(a1),f324(f324(f82(a1),x82242),x82242)),a99)))
% 18.55/18.49 [8225]~P1(f324(f324(f231(a1),x82251),x82252))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x82251),x82251)),f324(f324(f3(a1),f324(f324(f82(a1),x82252),x82252)),a99)))
% 18.55/18.49 [8226]~P1(f324(f324(f231(a1),x82261),x82262))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x82261),x82261)),f324(f324(f3(a1),f324(f324(f82(a1),x82262),x82262)),a99)))
% 18.55/18.49 [8628]P1(f324(f324(f231(a1),x86281),x86282))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x86281),x86281)),f324(f324(f3(a1),f324(f324(f82(a1),x86282),x86282)),a99)))
% 18.55/18.49 [8629]P1(f324(f324(f231(a1),x86291),x86292))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),x86291),x86291)),f324(f324(f3(a1),f324(f324(f82(a1),x86292),x86292)),a99)))
% 18.55/18.49 [8630]P1(f324(f324(f231(a1),x86301),x86302))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x86301),x86301)),f324(f324(f3(a1),f324(f324(f82(a1),x86302),x86302)),a99)))
% 18.55/18.49 [8631]P1(f324(f324(f231(a1),x86311),x86312))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x86311),x86311)),f324(f324(f3(a1),f324(f324(f82(a1),x86312),x86312)),a99)))
% 18.55/18.49 [8890]~P1(f324(f324(f232(a1),x88901),x88902))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x88901),x88901)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x88902),x88902)),a99)))
% 18.55/18.49 [8891]~P1(f324(f324(f232(a1),x88911),x88912))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x88911),x88911)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x88912),x88912)),a99)))
% 18.55/18.49 [8892]~P1(f324(f324(f231(a1),x88921),x88922))+P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x88921),x88921)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x88922),x88922)),a99)))
% 18.55/18.49 [8893]~P1(f324(f324(f231(a1),x88931),x88932))+P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x88931),x88931)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x88932),x88932)),a99)))
% 18.55/18.49 [9122]P1(f324(f324(f232(a1),x91221),x91222))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x91221),x91221)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x91222),x91222)),a99)))
% 18.55/18.49 [9123]P1(f324(f324(f232(a1),x91231),x91232))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),x91231),x91231)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x91232),x91232)),a99)))
% 18.55/18.49 [9124]P1(f324(f324(f231(a1),x91241),x91242))+~P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x91241),x91241)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x91242),x91242)),a99)))
% 18.55/18.49 [9125]P1(f324(f324(f231(a1),x91251),x91252))+~P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),x91251),x91251)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),x91252),x91252)),a99)))
% 18.55/18.49 [9156]~P1(f324(f64(x91561),x91562))+P1(f324(f64(f845(x91561,a832)),f324(f257(f845(x91561,a832)),f324(f324(f9(f845(x91561,a832),f845(x91561,a832),a832),f231(f845(x91561,a832))),x91562))))
% 18.55/18.49 [9203]~E(f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),x92031),f179(f845(f844(a838,a838),a832)))),f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),x92032),f179(f845(f844(a838,a838),a832)))))+P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),x92031),x92032)),a111))
% 18.55/18.49 [9289]E(f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),x92891),f179(f845(f844(a838,a838),a832)))),f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),x92892),f179(f845(f844(a838,a838),a832)))))+~P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),x92891),x92892)),a111))
% 18.55/18.49 [9323]P1(f324(f324(f231(a1),f2(a1)),f348(x93231,x93232)))+E(f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x93231)),f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x93232)))
% 18.55/18.49 [9820]~P9(x98201)+E(f44(x98201,f324(f257(x98201),f324(f324(f10(f845(x98201,a832),a832,x98201),f90(x98201)),f324(f324(f10(f845(x98201,a832),f845(x98201,a832),x98201),f324(f20(x98201,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98201),a327),f324(f324(f9(x98201,f845(x98201,a832),a832),f326(x98201)),x98202)))),f324(f9(x98201,x98201,a832),f231(x98201)))))),f43(x98201,x98202))
% 18.55/18.49 [9840]P1(f324(f324(f326(a838),f2(a838)),x98401))+E(f324(f41(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,f845(a838,a832),a832),f324(f324(f10(a838,f845(f845(a838,a832),a832),a838),f326(a838)),a114)),x98401))),f324(f324(f9(a838,a838,a832),f232(a838)),x98402)))),f324(f41(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,f845(a838,a832),a832),f326(a838)),x98401))),f324(f324(f9(a838,a838,a832),f232(a838)),f324(a114,x98402))))))
% 18.55/18.49 [9887]P1(f324(f324(f280(a838),x98871),x98872))+~P1(f324(f324(f326(a838),x98872),f288(a838,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x98871)))
% 18.55/18.49 [9888]P1(f324(f324(f280(a838),x98881),x98882))+~P1(f324(f324(f326(a838),x98881),f291(a838,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x98882)))
% 18.55/18.49 [9889]~P1(f324(f324(f280(a838),x98891),x98892))+~P1(f324(f324(f326(a838),x98892),f291(a838,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x98891)))
% 18.55/18.49 [9890]~P1(f324(f324(f280(a838),x98901),x98902))+~P1(f324(f324(f326(a838),x98901),f288(a838,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x98902)))
% 18.55/18.49 [7445]~P89(x74451)+E(f324(f324(f83(x74451),x74452),f324(f106(x74451),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),x74452)
% 18.55/18.49 [7714]~P89(x77141)+E(f324(f324(f82(x77141),f324(f106(x77141),x77142)),f80(x77141)),f324(f106(x77141),f324(f324(f82(a1),x77142),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))
% 18.55/18.49 [7859]P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x78592)))+E(f324(f324(f240(a1),x78591),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x78592),x78592)),a99))),f80(a1))
% 18.55/18.49 [9180]~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x91802)))+E(f324(f324(f240(a1),x91801),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x91802),x91802)),a99))),f324(f324(f88(a1,a1),f324(f324(f240(a1),x91801),f324(f106(a838),x91802))),f324(f324(f20(a1,a1,a1),f324(f324(f10(a1,f845(a1,a1),a1),f83(a1)),f324(f83(a1),x91801))),f7(a1))))
% 18.55/18.49 [9665]~P1(f324(f324(f232(a838),f324(f106(a838),x96651)),f324(a114,x96652)))+P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x96651),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),f232(a838)),a107)),x96652))))
% 18.55/18.49 [9666]~P1(f324(f324(f231(a838),f324(f106(a838),x96661)),f324(a114,x96662)))+P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x96661),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),f231(a838)),a107)),x96662))))
% 18.55/18.49 [9728]P1(f324(f324(f232(a838),f324(f106(a838),x97281)),f324(a114,x97282)))+~P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x97281),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),f232(a838)),a107)),x97282))))
% 18.55/18.49 [9729]P1(f324(f324(f231(a838),f324(f106(a838),x97291)),f324(a114,x97292)))+~P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x97291),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),f231(a838)),a107)),x97292))))
% 18.55/18.49 [9759]~P1(f324(f324(f232(a838),f324(a114,x97592)),f324(f106(a838),x97591)))+P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x97591),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f10(a838,a832,a1),f324(f232(a838),x97592)),a107)))))
% 18.55/18.49 [9760]~P1(f324(f324(f231(a838),f324(a114,x97602)),f324(f106(a838),x97601)))+P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x97601),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f10(a838,a832,a1),f324(f231(a838),x97602)),a107)))))
% 18.55/18.49 [9808]P1(f324(f324(f232(a838),f324(a114,x98081)),f324(f106(a838),x98082)))+~P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x98082),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f10(a838,a832,a1),f324(f232(a838),x98081)),a107)))))
% 18.55/18.49 [9809]P1(f324(f324(f231(a838),f324(a114,x98091)),f324(f106(a838),x98092)))+~P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x98092),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f10(a838,a832,a1),f324(f231(a838),x98091)),a107)))))
% 18.55/18.49 [9880]~P1(f324(f324(f326(a838),f2(a838)),x98801))+E(f324(a114,f324(f41(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,f845(a838,a832),a832),f324(f324(f10(a838,f845(f845(a838,a832),a832),a838),f326(a838)),a114)),x98801))),f324(f324(f9(a838,a838,a832),f232(a838)),x98802))))),f324(f41(a838),f324(f257(a838),f324(f324(f20(a838,a832,a832),f324(f324(f10(a832,f845(a832,a832),a838),a322),f324(f324(f9(a838,f845(a838,a832),a832),f326(a838)),x98801))),f324(f324(f9(a838,a838,a832),f232(a838)),f324(a114,x98802))))))
% 18.55/18.49 [8408]~P89(x84081)+E(f324(f324(f83(x84081),f324(f106(x84081),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),x84082),x84082)
% 18.55/18.49 [8465]~P89(x84651)+E(f324(f324(f82(x84651),f80(x84651)),f324(f106(x84651),x84652)),f324(f106(x84651),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),x84652)))
% 18.55/18.49 [8511]~P89(x85111)+E(f324(f324(f3(x85111),f324(f106(x85111),x85112)),f80(x85111)),f324(f106(x85111),f324(f324(f82(a1),x85112),f324(f81(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.49 [8647]~P1(f324(f324(f232(a838),f324(f106(a838),a85)),x86472))+E(f324(f324(f3(a838),x86471),f324(f324(f3(a838),x86472),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f3(a838),f324(a114,x86471)),x86472))
% 18.55/18.49 [9219]~P105(x92191)+E(f324(f324(f83(x92191),x92192),x92192),f324(f324(f240(x92191),x92192),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.49 [9220]~P75(x92201)+E(f324(f324(f240(x92201),x92202),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f83(x92201),x92202),x92202))
% 18.55/18.49 [9222]~P89(x92221)+E(f324(f324(f83(x92221),x92222),f324(f106(x92221),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f82(x92221),x92222),x92222))
% 18.55/18.49 [9459]~P119(x94591)+E(f324(f324(f240(x94591),f324(f81(x94591),x94592)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f240(x94591),x94592),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.49 [9460]~P103(x94601)+E(f324(f324(f240(x94601),f324(f77(x94601),x94602)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f240(x94601),x94602),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.49 [9456]~P89(x94561)+E(f324(f324(f83(x94561),f324(f106(x94561),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x94562),f324(f324(f82(x94561),x94562),x94562))
% 18.55/18.49 [9571]~P103(x95711)+E(f324(f77(x95711),f324(f324(f240(x95711),x95712),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x95711),x95712),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.49 [9624]~P103(x96241)+P1(f324(f324(f231(x96241),f2(x96241)),f324(f324(f240(x96241),x96242),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.55/18.49 [9799]~E(f324(a114,x97992),f324(f106(a838),x97991))+P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x97991),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),a321),a107)),x97992)))))
% 18.55/18.49 [9800]~E(f324(f106(a838),x98001),f324(a114,x98002))+P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x98001),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),a321),a107)),x98002)))))
% 18.55/18.49 [9843]E(f324(a114,x98431),f324(f106(a838),x98432))+~P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x98432),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),a321),a107)),x98431)))))
% 18.55/18.49 [9844]E(f324(f106(a838),x98441),f324(a114,x98442))+~P1(f324(f324(f88(a1,a832),f324(f106(a1),f324(f324(f82(a1),x98441),a99))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a327),f324(f324(f10(a832,a832,a1),a320),a185))),f324(f324(f9(a1,a838,a832),f324(f324(f10(a838,f845(a838,a832),a1),a321),a107)),x98442)))))
% 18.55/18.49 [9622]~P89(x96221)+E(f324(f324(f240(x96221),f324(f106(x96221),a99)),f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x96222)),f80(x96221))
% 18.55/18.49 [9623]~P119(x96231)+E(f324(f324(f240(x96231),f324(f81(x96231),f80(x96231))),f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x96232)),f80(x96231))
% 18.55/18.49 [9626]~P75(x96261)+E(f324(f324(f240(x96261),x96262),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),a99))),f324(f324(f83(x96261),f324(f324(f83(x96261),x96262),x96262)),x96262))
% 18.55/18.49 [9823]~P1(f324(f324(f231(a1),f2(a1)),x98232))+E(f51(a1,f324(f324(f82(a1),f80(a1)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98231)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98232)),f324(f324(f82(a1),f80(a1)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f51(a1,x98231,x98232))))
% 18.55/18.49 [9846]~P1(f324(f324(f231(a1),f2(a1)),x98462))+E(f324(f324(f42(a1),f324(f324(f82(a1),f80(a1)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98461))),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98462)),f324(f324(f42(a1),x98461),x98462))
% 18.55/18.49 [9848]~P1(f324(f324(f231(a1),x98482),f2(a1)))+E(f324(f324(f42(a1),f324(f324(f82(a1),f80(a1)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98481))),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98482)),f324(f324(f42(a1),f324(f324(f82(a1),x98481),f80(a1))),x98482))
% 18.55/18.49 [9849]~P1(f324(f324(f231(a1),x98492),f2(a1)))+E(f51(a1,f324(f324(f82(a1),f80(a1)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98491)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98492)),f324(f324(f3(a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f51(a1,f324(f324(f82(a1),x98491),f80(a1)),x98492))),f80(a1)))
% 18.55/18.49 [9719]~P89(x97191)+E(f324(f324(f240(x97191),f324(f106(x97191),a99)),f324(a114,f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97192))),f324(f106(x97191),a99))
% 18.55/18.49 [9721]~P119(x97211)+E(f324(f324(f240(x97211),f324(f81(x97211),f80(x97211))),f324(a114,f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97212))),f324(f81(x97211),f80(x97211)))
% 18.55/18.49 [5928]E(x59281,x59282)+~P39(a25,x59281,x59283,x59282)
% 18.55/18.49 [4934]~P36(x49341,x49343)+P36(x49341,f319(x49341,x49342,x49343))
% 18.55/18.49 [5098]P31(x50981,x50982,x50983)+~P31(x50981,f324(a114,x50982),x50983)
% 18.55/18.49 [5181]~P12(x51811,x51812,x51813)+P12(f839(x51811),f147(x51811,x51812),f145(x51811,x51813))
% 18.55/18.49 [5182]~P47(x51821,x51822,x51823)+P47(f839(x51821),f147(x51821,x51822),f145(x51821,x51823))
% 18.55/18.49 [5291]P53(x52911,x52912,x52913)+~E(f333(x52913,x52912,x52911),f334(x52913,x52912,x52911))
% 18.55/18.49 [5292]P52(x52921,x52922,x52923)+~E(f605(x52923,x52922,x52921),f606(x52923,x52922,x52921))
% 18.55/18.49 [6250]P32(x62501,x62502,x62503)+~P31(x62501,f619(x62503,x62502,x62501),f625(x62503,x62502,x62501))
% 18.55/18.49 [4492]~E(x44921,f182(x44922))+~E(x44921,f324(f226(x44922),x44923))
% 18.55/18.49 [4493]~E(x44931,f182(x44932))+~E(x44931,f324(f226(x44932),x44933))
% 18.55/18.49 [4540]~E(f324(f154(x45402),x45401),x45403)+E(x45401,f324(f154(x45402),x45403))
% 18.55/18.49 [4541]~E(x45412,f324(f154(x45411),x45413))+E(f324(f154(x45411),x45412),x45413)
% 18.55/18.49 [4585]E(x45851,x45852)+~E(f324(f226(x45853),x45851),f324(f226(x45853),x45852))
% 18.55/18.49 [4586]E(x45861,x45862)+~E(f324(f154(x45863),x45861),f324(f154(x45863),x45862))
% 18.55/18.49 [4788]~P11(x47883,x47881)+P1(f324(f324(x47881,x47882),x47882))
% 18.55/18.49 [4789]~P49(x47893,x47891)+P1(f324(f324(x47891,x47892),x47892))
% 18.55/18.49 [4790]~P57(x47901,x47902)+P1(f324(f313(x47901,x47902),x47903))
% 18.55/18.49 [4791]~P57(x47911,x47912)+P1(f324(f313(x47911,x47912),x47913))
% 18.55/18.49 [4853]~P36(x48531,x48532)+P36(f839(x48531),f324(f132(x48531,x48532),x48533))
% 18.55/18.49 [4857]~P1(f324(x48572,x48573))+~E(f324(f257(x48571),x48572),f179(f845(x48571,a832)))
% 18.55/18.49 [4858]~P1(f324(x48582,x48583))+~E(f179(f845(x48581,a832)),f324(f257(x48581),x48582))
% 18.55/18.49 [4887]~P1(f324(x48871,x48873))+P1(f324(x48871,f92(x48872,x48871)))
% 18.55/18.49 [4888]~P1(f324(x48881,x48883))+P1(f324(x48881,f92(x48882,x48881)))
% 18.55/18.49 [4889]~P1(f324(x48891,x48893))+P1(f324(x48891,f92(x48892,x48891)))
% 18.55/18.49 [4890]~P1(f324(x48901,x48903))+P1(f324(x48901,f92(x48902,x48901)))
% 18.55/18.49 [5014]~E(x50142,x50143)+P1(f324(f324(f326(x50141),x50142),f324(a321,x50143)))
% 18.55/18.49 [5067]E(f324(f154(x50671),x50672),f324(f324(f139(x50671),x50673),f115(x50671)))+~E(x50672,f324(f324(f139(x50671),x50673),f115(x50671)))
% 18.55/18.49 [5068]~E(x50683,f324(f324(f139(x50681),x50682),f115(x50681)))+E(f324(f324(f139(x50681),x50682),f115(x50681)),f324(f154(x50681),x50683))
% 18.55/18.49 [5093]~E(x50933,f324(f18(f842(x50932),x50931),f182(x50932)))+E(f168(x50931,x50932,x50933),f179(f845(x50931,a832)))
% 18.55/18.49 [5114]E(f324(f41(x51141),f379(x51142,x51143,x51141)),x51142)+~E(f324(f41(x51141),x51143),f324(a114,x51142))
% 18.55/18.49 [5119]~P36(x51191,x51193)+P1(f324(f324(f326(x51191),x51192),f314(x51191,x51193)))
% 18.55/18.49 [5120]~P36(x51201,x51203)+P1(f324(f324(f326(x51201),x51202),f314(x51201,x51203)))
% 18.55/18.49 [5123]~E(f324(f154(x51232),x51231),f324(f324(f139(x51232),x51233),f115(x51232)))+E(x51231,f324(f324(f139(x51232),x51233),f115(x51232)))
% 18.55/18.49 [5124]~E(f324(f324(f139(x51242),x51243),f115(x51242)),f324(f154(x51242),x51241))+E(x51241,f324(f324(f139(x51242),x51243),f115(x51242)))
% 18.55/18.49 [5139]E(x51391,f324(f18(f842(x51392),x51393),f182(x51392)))+~E(f168(x51393,x51392,x51391),f179(f845(x51393,a832)))
% 18.55/18.49 [5145]E(f87(f844(a838,a838),f54(x51451,x51452)),x51453)+~P1(f324(f54(x51451,x51452),x51453))
% 18.55/18.49 [5153]~E(x51533,f324(f226(x51531),x51532))+P1(f324(f324(f326(x51531),x51532),f225(x51531,x51533)))
% 18.55/18.49 [5244]~E(x52442,f115(x52441))+P1(f324(f324(f326(f839(x52441)),x52442),f147(x52441,x52443)))
% 18.55/18.49 [5252]~P53(x52521,x52522,x52523)+P53(x52521,x52522,f324(f279(x52521,x52521),x52523))
% 18.55/18.49 [5253]~P47(x52531,x52532,x52533)+P47(x52531,x52532,f324(f279(x52531,x52531),x52533))
% 18.55/18.49 [5272]~P7(x52721)+E(f51(x52721,f51(x52721,x52722,x52723),x52723),f51(x52721,x52722,x52723))
% 18.55/18.49 [5370]E(x53701,x53702)+~P1(f324(f324(f326(x53703),x53701),f324(a321,x53702)))
% 18.55/18.49 [5414]~P2(x54141)+E(f181(x54141,x54142,f2(a838),x54143),x54143)
% 18.55/18.49 [5434]P53(x54341,x54342,x54343)+~P53(x54341,x54342,f324(f279(x54341,x54341),x54343))
% 18.55/18.49 [5435]P47(x54351,x54352,x54353)+~P47(x54351,x54352,f324(f279(x54351,x54351),x54353))
% 18.55/18.49 [5452]E(f155(x54521,x54522,f140(x54521,x54523)),f140(x54521,f155(x54521,x54522,x54523)))+~P1(f324(f127(x54521),x54523))
% 18.55/18.49 [5458]E(x54581,f324(f226(x54582),x54583))+~P1(f324(f324(f326(x54582),x54583),f225(x54582,x54581)))
% 18.55/18.49 [5540]~P1(f324(a26,x55403))+P1(f324(a26,f32(x55401,x55402,x55403)))
% 18.55/18.49 [5541]~P1(f324(a26,x55413))+P1(f324(a26,f32(x55411,x55412,x55413)))
% 18.55/18.49 [5553]E(f324(f126(x55531,x55532),x55533),f115(x55531))+P1(f324(x55532,f715(x55533,x55532,x55531)))
% 18.55/18.49 [5707]~P1(f324(f127(x57071),x57073))+P1(f324(f127(x57071),f155(x57071,x57072,x57073)))
% 18.55/18.49 [5708]~P1(f324(f127(x57081),x57082))+P1(f324(f127(x57081),f159(x57081,x57082,x57083)))
% 18.55/18.49 [5709]~P1(f324(f127(x57091),x57093))+P1(f324(f127(x57091),f161(x57091,x57092,x57093)))
% 18.55/18.49 [5710]~P139(x57101,x57102,x57103)+P1(f324(x57101,f51(a1,x57102,x57103)))
% 18.55/18.49 [5788]~P1(f324(f127(x57881),x57883))+P1(f324(f127(f839(x57881)),f61(x57881,x57882,x57883)))
% 18.55/18.49 [5810]P1(f324(a26,f31(x58101,x58102,x58103)))+~P1(f324(a26,f324(a27,x58102)))
% 18.55/18.49 [5811]P1(f324(a26,f31(x58111,x58112,x58113)))+~P1(f324(a26,f324(a27,x58112)))
% 18.55/18.49 [5823]~P85(x58231)+E(f324(f324(f104(f845(x58231,a832)),f324(f294(x58231),x58232)),f299(x58231,x58232,x58233)),f179(f845(x58231,a832)))
% 18.55/18.49 [5824]~P85(x58241)+E(f324(f324(f104(f845(x58241,a832)),f324(f294(x58241),x58242)),f298(x58241,x58242,x58243)),f179(f845(x58241,a832)))
% 18.55/18.49 [5825]~P85(x58251)+E(f324(f324(f104(f845(x58251,a832)),f324(f258(x58251),x58252)),f296(x58251,x58252,x58253)),f179(f845(x58251,a832)))
% 18.55/18.49 [5976]P1(f324(a26,x59761))+~P1(f324(a26,f32(x59762,x59763,x59761)))
% 18.55/18.49 [5977]P1(f324(a26,x59771))+~P1(f324(a26,f32(x59772,x59773,x59771)))
% 18.55/18.49 [5978]P1(f324(a26,x59781))+~P1(f324(a26,f33(x59782,x59783,x59781)))
% 18.55/18.49 [5979]P1(f324(a26,x59791))+~P1(f324(a26,f33(x59792,x59793,x59791)))
% 18.55/18.49 [5980]P1(f324(a26,x59801))+~P1(f324(a26,f33(x59802,x59801,x59803)))
% 18.55/18.49 [5981]P1(f324(a26,x59811))+~P1(f324(a26,f33(x59812,x59811,x59813)))
% 18.55/18.49 [6062]E(f324(f126(x60621,x60622),x60623),x60623)+~P1(f324(x60622,f747(x60623,x60622,x60621)))
% 18.55/18.49 [6064]E(f324(f324(f303(x60641),f384(x60642,x60643,x60641)),f379(x60642,x60643,x60641)),x60643)+~E(f324(f41(x60641),x60643),f324(a114,x60642))
% 18.55/18.49 [6079]P139(x60791,x60792,x60793)+~P1(f324(x60791,f51(a1,x60792,x60793)))
% 18.55/18.49 [6131]E(f161(x61311,x61312,x61313),x61313)+~P1(f324(x61312,f757(x61313,x61312,x61311)))
% 18.55/18.49 [6171]~P1(f324(a26,f31(x61712,x61711,x61713)))+P1(f324(a26,f324(a27,x61711)))
% 18.55/18.49 [6172]~P1(f324(a26,f31(x61722,x61721,x61723)))+P1(f324(a26,f324(a27,x61721)))
% 18.55/18.49 [6219]~P1(f324(x62192,f610(x62193,x62192,x62191)))+P1(f324(f243(x62191,x62192),x62193))
% 18.55/18.49 [6478]~P1(f324(f313(x64781,x64782),f791(x64783,x64782,x64781)))+P1(f324(f313(x64781,x64782),x64783))
% 18.55/18.49 [6479]~P1(f324(f313(x64791,x64792),f799(x64793,x64792,x64791)))+P1(f324(f313(x64791,x64792),x64793))
% 18.55/18.49 [7111]~P7(x71111)+E(f324(f324(f82(x71111),f324(f324(f83(x71111),x71112),f324(f324(f42(x71111),x71113),x71112))),f51(x71111,x71113,x71112)),x71113)
% 18.55/18.49 [7602]E(f324(f324(f247(x76021,x76021),f338(x76022,x76023,x76021)),f338(x76022,x76023,x76021)),x76023)+~P1(f324(f324(f326(f844(x76021,x76021)),x76023),f261(x76021,x76022)))
% 18.55/18.49 [7723]~P1(f324(f324(f326(x77231),f805(x77233,x77232,x77231)),f314(x77231,x77233)))+P1(f324(f324(f326(x77231),x77232),f314(x77231,x77233)))
% 18.55/18.49 [7724]~P1(f324(f324(f326(x77241),f809(x77243,x77242,x77241)),f314(x77241,x77243)))+P1(f324(f324(f326(x77241),x77242),f314(x77241,x77243)))
% 18.55/18.49 [7725]~P1(f324(f324(f326(x77251),f816(x77253,x77252,x77251)),f314(x77251,x77253)))+P1(f324(f324(f326(x77251),x77252),f314(x77251,x77253)))
% 18.55/18.49 [7913]~P7(x79131)+E(f324(f324(f82(x79131),f324(f324(f83(x79131),f324(f324(f42(x79131),x79132),x79133)),x79133)),f51(x79131,x79132,x79133)),x79132)
% 18.55/18.49 [7914]~P7(x79141)+E(f324(f324(f82(x79141),f324(f324(f83(x79141),f324(f324(f42(x79141),x79142),x79143)),x79143)),f51(x79141,x79142,x79143)),x79142)
% 18.55/18.49 [7956]~E(f324(f41(x79561),x79562),f324(a114,x79563))+~P1(f324(f324(f326(x79561),f384(x79563,x79562,x79561)),f379(x79563,x79562,x79561)))
% 18.55/18.49 [8560]P1(f324(f324(f231(f845(f844(x85601,x85601),a832)),f301(x85601,x85602)),f301(x85601,x85603)))+~P1(f324(f324(f231(f845(f844(x85601,x85601),a832)),x85602),f301(x85601,x85603)))
% 18.55/18.49 [8803]E(x88031,f115(x88032))+~P1(f324(f324(f326(f844(f839(x88032),f839(x88032))),f324(f324(f247(f839(x88032),f839(x88032)),x88031),f115(x88032))),f145(x88032,x88033)))
% 18.55/18.49 [8828]E(x88281,f115(x88282))+~P1(f324(f324(f326(f844(f839(x88282),f839(x88282))),f324(f324(f247(f839(x88282),f839(x88282)),f115(x88282)),x88281)),f145(x88282,x88283)))
% 18.55/18.49 [8948]E(f324(f324(f139(x89481),f738(x89482,x89483,x89481)),f739(x89482,x89483,x89481)),x89483)+~P1(f324(f324(f326(f844(f839(x89481),f839(x89481))),f324(f324(f247(f839(x89481),f839(x89481)),f115(x89481)),x89483)),f136(x89481,x89482)))
% 18.55/18.49 [9149]~P118(x91491)+~P1(f324(f324(f232(x91491),f324(f324(f82(x91491),f324(f324(f83(x91491),x91492),x91492)),f324(f324(f83(x91491),x91493),x91493))),f2(x91491)))
% 18.55/18.49 [9198]P1(f324(f64(x91981),x91982))+~P1(f324(f324(f326(f844(f845(x91981,a832),f845(x91981,a832))),f324(f324(f247(f845(x91981,a832),f845(x91981,a832)),x91983),x91982)),f300(x91981)))
% 18.55/18.49 [9480]~P45(x94801,x94802,x94803)+P1(f324(f324(f232(a1),f324(f324(f75(f844(a1,a1),a1,x94801,f246(a1,a1)),f206(x94801)),f223(x94801,x94802,f220(x94801,x94803)))),f2(a1)))
% 18.55/18.49 [9481]~P46(x94811,x94812,x94813)+P1(f324(f324(f231(a1),f324(f324(f75(f844(a1,a1),a1,x94811,f246(a1,a1)),f206(x94811)),f223(x94811,x94812,f220(x94811,x94813)))),f2(a1)))
% 18.55/18.49 [9597]P45(x95971,x95972,x95973)+~P1(f324(f324(f232(a1),f324(f324(f75(f844(a1,a1),a1,x95971,f246(a1,a1)),f206(x95971)),f223(x95971,x95972,f220(x95971,x95973)))),f2(a1)))
% 18.55/18.49 [9598]P46(x95981,x95982,x95983)+~P1(f324(f324(f231(a1),f324(f324(f75(f844(a1,a1),a1,x95981,f246(a1,a1)),f206(x95981)),f223(x95981,x95982,f220(x95981,x95983)))),f2(a1)))
% 18.55/18.49 [9927]~P103(x99271)+~P1(f324(f324(f232(x99271),f324(f324(f82(x99271),f324(f324(f240(x99271),x99272),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x99271),x99273),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f2(x99271)))
% 18.55/18.49 [4567]~E(x45673,f115(x45671))+E(f324(f324(f125(x45671),x45672),x45673),x45672)
% 18.55/18.49 [4568]~E(x45682,f115(x45681))+E(f324(f324(f125(x45681),x45682),x45683),x45683)
% 18.55/18.49 [4569]~E(x45693,f115(x45691))+E(f324(f324(f125(x45691),x45692),x45693),x45692)
% 18.55/18.49 [4570]~E(x45702,f115(x45701))+E(f324(f324(f125(x45701),x45702),x45703),x45703)
% 18.55/18.49 [4576]~E(x45762,f2(a838))+E(f324(f324(f158(x45761),x45762),x45763),f115(x45761))
% 18.55/18.49 [4580]~E(x45803,f115(x45801))+E(f324(f324(f158(x45801),x45802),x45803),f115(x45801))
% 18.55/18.49 [4620]~E(x46201,x46203)+E(x46201,f324(f324(f125(x46202),f115(x46202)),x46203))
% 18.55/18.49 [4704]~P100(x47042)+E(f324(f179(f845(x47041,x47042)),x47043),f179(x47042))
% 18.55/18.49 [4705]~P100(x47052)+E(f324(f179(f845(x47051,x47052)),x47053),f179(x47052))
% 18.55/18.49 [4706]~P110(x47062)+E(f324(f238(f845(x47061,x47062)),x47063),f238(x47062))
% 18.55/18.49 [4723]E(x47231,f115(x47232))+~E(f324(f324(f125(x47232),x47231),x47233),x47233)
% 18.55/18.49 [4724]E(x47241,f115(x47242))+~E(f324(f324(f125(x47242),x47243),x47241),x47243)
% 18.55/18.49 [4725]E(x47251,f115(x47252))+~E(f324(f324(f125(x47252),x47253),x47251),x47253)
% 18.55/18.49 [4726]E(x47261,f115(x47262))+~E(f324(f324(f125(x47262),x47261),x47263),x47263)
% 18.55/18.49 [4732]E(x47321,f115(x47322))+~E(f324(f324(f125(x47322),x47323),x47321),f115(x47322))
% 18.55/18.49 [4733]E(x47331,f115(x47332))+~E(f324(f324(f125(x47332),x47331),x47333),f115(x47332))
% 18.55/18.49 [4734]E(x47341,f115(x47342))+~E(f324(f324(f125(x47342),x47343),x47341),f115(x47342))
% 18.55/18.49 [4735]E(x47351,f115(x47352))+~E(f324(f324(f125(x47352),x47351),x47353),f115(x47352))
% 18.55/18.49 [4760]~E(x47602,f2(a838))+E(f324(f324(f83(a838),x47601),x47602),f324(f324(f83(a838),x47603),x47602))
% 18.55/18.49 [4761]~E(x47611,f2(a838))+E(f324(f324(f83(a838),x47611),x47612),f324(f324(f83(a838),x47611),x47613))
% 18.55/18.49 [4762]~E(x47621,f2(a838))+E(f324(f324(f83(a838),x47621),x47622),f324(f324(f83(a838),x47621),x47623))
% 18.55/18.49 [4815]~P105(x48151)+E(f324(f324(f83(x48151),x48152),x48153),f324(f324(f83(x48151),x48153),x48152))
% 18.55/18.49 [4816]~P105(x48161)+E(f324(f324(f82(x48161),x48162),x48163),f324(f324(f82(x48161),x48163),x48162))
% 18.55/18.49 [4817]~P86(x48171)+E(f324(f324(f235(x48171),x48172),x48173),f324(f324(f235(x48171),x48173),x48172))
% 18.55/18.49 [4818]~P86(x48181)+E(f324(f324(f235(x48181),x48182),x48183),f324(f324(f235(x48181),x48183),x48182))
% 18.55/18.49 [4819]~P86(x48191)+E(f324(f324(f178(x48191),x48192),x48193),f324(f324(f178(x48191),x48193),x48192))
% 18.55/18.49 [4820]~P86(x48201)+E(f324(f324(f178(x48201),x48202),x48203),f324(f324(f178(x48201),x48203),x48202))
% 18.55/18.49 [4821]~P93(x48211)+E(f324(f324(f103(x48211),x48212),x48213),f324(f324(f103(x48211),x48213),x48212))
% 18.55/18.49 [4822]~P93(x48221)+E(f324(f324(f103(x48221),x48222),x48223),f324(f324(f103(x48221),x48223),x48222))
% 18.55/18.49 [4823]~P94(x48231)+E(f324(f324(f103(x48231),x48232),x48233),f324(f324(f103(x48231),x48233),x48232))
% 18.55/18.49 [4824]~P94(x48241)+E(f324(f324(f104(x48241),x48242),x48243),f324(f324(f104(x48241),x48243),x48242))
% 18.55/18.49 [4825]~P99(x48251)+E(f324(f324(f104(x48251),x48252),x48253),f324(f324(f104(x48251),x48253),x48252))
% 18.55/18.49 [4826]~P99(x48261)+E(f324(f324(f104(x48261),x48262),x48263),f324(f324(f104(x48261),x48263),x48262))
% 18.55/18.49 [4885]E(f51(a838,x48851,x48852),f2(a838))+~E(x48851,f324(f324(f83(a838),x48852),x48853))
% 18.55/18.49 [4886]E(f51(a1,x48861,x48862),f2(a1))+~E(x48861,f324(f324(f83(a1),x48862),x48863))
% 18.55/18.49 [4946]E(x49461,x49462)+~E(f324(f324(f82(a838),x49463),x49461),f324(f324(f82(a838),x49463),x49462))
% 18.55/18.49 [4947]E(x49471,x49472)+~E(f324(f324(f82(a838),x49471),x49473),f324(f324(f82(a838),x49472),x49473))
% 18.55/18.49 [4957]~P63(x49571)+E(f324(f324(f82(x49571),x49572),f324(f81(x49571),x49573)),f324(f324(f3(x49571),x49572),x49573))
% 18.55/18.49 [4958]~P6(x49581)+E(f324(f324(f82(x49581),x49582),f324(f81(x49581),x49583)),f324(f324(f3(x49581),x49582),x49583))
% 18.55/18.49 [4959]~P107(x49591)+E(f324(f324(f82(x49591),x49592),f324(f81(x49591),x49593)),f324(f324(f3(x49591),x49592),x49593))
% 18.55/18.49 [4960]~P91(x49601)+E(f324(f324(f104(x49601),x49602),f324(f81(x49601),x49603)),f324(f324(f3(x49601),x49602),x49603))
% 18.55/18.49 [4961]~P63(x49611)+E(f324(f324(f3(x49611),x49612),f324(f81(x49611),x49613)),f324(f324(f82(x49611),x49612),x49613))
% 18.55/18.49 [5008]~P1(f324(x50083,x50082))+P1(f324(f324(f326(x50081),x50082),x50083))
% 18.55/18.49 [5009]~P68(x50092)+E(f324(f324(f11(x50091,x50092),x50093),f179(f845(x50091,a832))),f80(x50092))
% 18.55/18.49 [5010]~P68(x50102)+E(f324(f324(f11(x50101,x50102),x50103),f179(f845(x50101,a832))),f80(x50102))
% 18.55/18.49 [5011]~P67(x50112)+E(f324(f324(f8(x50111,x50112),x50113),f179(f845(x50111,a832))),f2(x50112))
% 18.55/18.49 [5012]~P67(x50122)+E(f324(f324(f8(x50121,x50122),x50123),f179(f845(x50121,a832))),f2(x50122))
% 18.55/18.49 [5057]~E(x50572,f324(f324(f82(a838),x50571),x50573))+P1(f324(f324(f231(a838),x50571),x50572))
% 18.55/18.49 [5059]~E(x50592,f179(f845(x50591,a832)))+E(f324(f324(f63(x50591),x50592),x50593),f179(f845(f845(x50591,a832),a832)))
% 18.55/18.49 [5060]~E(x50602,f179(f845(x50601,a832)))+E(f179(f845(f845(x50601,a832),a832)),f324(f324(f63(x50601),x50602),x50603))
% 18.55/18.49 [5127]~E(f324(f260(x51272,x51273),x51271),f179(f845(x51273,a832)))+E(x51271,f179(f845(f844(x51272,x51273),a832)))
% 18.55/18.49 [5128]~E(f324(f262(x51282,x51283),x51281),f179(f845(x51282,a832)))+E(x51281,f179(f845(f844(x51282,x51283),a832)))
% 18.55/18.49 [5159]E(f324(f260(x51591,x51592),x51593),f179(f845(x51592,a832)))+~E(x51593,f179(f845(f844(x51591,x51592),a832)))
% 18.55/18.49 [5160]E(f324(f262(x51601,x51602),x51603),f179(f845(x51601,a832)))+~E(x51603,f179(f845(f844(x51601,x51602),a832)))
% 18.55/18.49 [5163]E(f270(x51631,x51632,x51633),f324(f324(f3(a101),x51632),x51633))+P1(f324(f324(f232(a101),x51632),x51633))
% 18.55/18.49 [5179]P1(f324(x51791,x51792))+~P1(f324(f324(f326(x51793),x51792),x51791))
% 18.55/18.49 [5215]E(x52151,x52152)+~E(f324(f81(f845(x52153,a832)),x52151),f324(f81(f845(x52153,a832)),x52152))
% 18.55/18.49 [5220]E(f307(x52201,x52202,x52203),f182(f839(a831)))+~P1(f324(f324(f232(a1),x52202),x52203))
% 18.55/18.49 [5223]~E(x52231,f179(f845(x52232,a832)))+~P1(f324(f324(f326(x52232),x52233),x52231))
% 18.55/18.49 [5224]~E(x52241,f179(f845(x52242,a832)))+~P1(f324(f324(f326(x52242),x52243),x52241))
% 18.55/18.49 [5225]~E(x52251,f179(f845(x52252,a832)))+~P1(f324(f324(f326(x52252),x52253),x52251))
% 18.55/18.49 [5254]~E(x52542,f324(f324(f82(a1),x52541),f324(f102(a1),x52543)))+P1(f324(f324(f231(a1),x52541),x52542))
% 18.55/18.49 [5270]E(f324(f324(f303(x52701),x52702),x52703),x52703)+~P1(f324(f324(f326(x52701),x52702),x52703))
% 18.55/18.49 [5281]E(x52811,f179(f845(x52812,a832)))+~E(f324(f324(f63(x52812),x52811),x52813),f179(f845(f845(x52812,a832),a832)))
% 18.55/18.49 [5282]E(x52821,f179(f845(x52822,a832)))+~E(f179(f845(f845(x52822,a832),a832)),f324(f324(f63(x52822),x52821),x52823))
% 18.55/18.49 [5288]~P126(x52881)+E(f324(f324(f83(x52881),f324(f81(x52881),x52882)),f324(f81(x52881),x52883)),f324(f324(f83(x52881),x52882),x52883))
% 18.55/18.49 [5290]~P59(x52901)+E(f324(f324(f284(x52901),f324(f81(x52901),x52902)),f324(f81(x52901),x52903)),f324(f324(f284(x52901),x52902),x52903))
% 18.55/18.49 [5321]~P1(f324(x53213,x53212))+P1(f324(f324(f326(x53211),x53212),f324(f257(x53211),x53213)))
% 18.55/18.49 [5322]~P1(f324(x53223,x53222))+P1(f324(f324(f326(x53221),x53222),f324(f257(x53221),x53223)))
% 18.55/18.49 [5362]E(f155(x53621,x53622,x53623),x53623)+P1(f324(f324(f326(x53621),x53622),f324(f157(x53621),x53623)))
% 18.55/18.49 [5443]~P1(f324(f127(x54431),x54433))+P1(f324(f127(x54431),f324(f126(x54431,x54432),x54433)))
% 18.55/18.49 [5487]~P7(x54871)+E(f324(f324(f42(x54871),f51(x54871,x54872,x54873)),x54873),f2(x54871))
% 18.55/18.49 [5505]E(f159(x55051,f324(f324(f139(x55051),x55052),f115(x55051)),x55053),f115(x55051))+P1(f324(f324(f326(a838),f2(a838)),x55053))
% 18.55/18.49 [5570]E(x55701,x55702)+~E(f324(f324(f83(a838),f324(a114,x55703)),x55701),f324(f324(f83(a838),f324(a114,x55703)),x55702))
% 18.55/18.49 [5571]~E(x55712,f324(f324(f82(a1),x55711),f324(f102(a1),f324(a114,x55713))))+P1(f324(f324(f232(a1),x55711),x55712))
% 18.55/18.49 [5687]~E(x56873,f115(x56871))+E(f324(f324(f324(f172(f839(x56871),f839(x56871)),x56872),f153(x56871)),x56873),f115(x56871))
% 18.55/18.49 [5689]P1(f324(x56891,x56892))+~P1(f324(f324(f326(x56893),x56892),f324(f257(x56893),x56891)))
% 18.55/18.49 [5690]P1(f324(x56901,x56902))+~P1(f324(f324(f326(x56903),x56902),f324(f257(x56903),x56901)))
% 18.55/18.49 [5691]P1(f324(x56911,x56912))+~P1(f324(f324(f326(x56913),x56912),f324(f257(x56913),x56911)))
% 18.55/18.49 [5725]E(x57251,x57252)+~E(f324(f324(f303(x57253),x57251),f179(f845(x57253,a832))),f324(f324(f303(x57253),x57252),f179(f845(x57253,a832))))
% 18.55/18.49 [5735]~P85(x57351)+E(f324(f324(f104(f845(x57351,a832)),f324(f258(x57351),x57352)),f324(f295(x57351,x57352),x57353)),f179(f845(x57351,a832)))
% 18.55/18.49 [5797]~P70(x57971)+E(f324(f304(x57971,x57971,f81(x57971)),f324(f295(x57971,x57972),x57973)),f298(x57971,f324(f81(x57971),x57973),f324(f81(x57971),x57972)))
% 18.55/18.49 [5805]E(f324(f180(f839(x58051)),f155(x58051,x58052,x58053)),f324(f180(f839(x58051)),x58053))+P1(f324(f324(f326(x58051),x58052),f324(f157(x58051),x58053)))
% 18.55/18.49 [5826]P1(f324(x58261,x58262))+~P1(f324(f324(f326(x58263),x58262),f179(f845(x58263,a832))))
% 18.55/18.49 [5862]~P85(x58621)+E(f324(f324(f104(f845(x58621,a832)),f324(f295(x58621,x58622),x58623)),f324(f259(x58621),x58623)),f179(f845(x58621,a832)))
% 18.55/18.49 [5884]~P70(x58841)+E(f324(f304(x58841,x58841,f81(x58841)),f299(x58841,x58842,x58843)),f299(x58841,f324(f81(x58841),x58843),f324(f81(x58841),x58842)))
% 18.55/18.49 [5885]~P70(x58851)+E(f324(f304(x58851,x58851,f81(x58851)),f296(x58851,x58852,x58853)),f296(x58851,f324(f81(x58851),x58853),f324(f81(x58851),x58852)))
% 18.55/18.49 [5944]E(f159(x59441,f324(f324(f139(x59441),x59442),f115(x59441)),x59443),f324(f324(f139(x59441),x59442),f115(x59441)))+~P1(f324(f324(f326(a838),f2(a838)),x59443))
% 18.55/18.49 [5952]~P70(x59521)+E(f324(f304(x59521,x59521,f81(x59521)),f298(x59521,x59522,x59523)),f324(f295(x59521,f324(f81(x59521),x59523)),f324(f81(x59521),x59522)))
% 18.55/18.49 [5972]~P8(x59721)+E(f51(x59721,f324(f81(x59721),f51(x59721,x59722,x59723)),x59723),f51(x59721,f324(f81(x59721),x59722),x59723))
% 18.55/18.49 [6077]~P1(f324(f64(f844(x60772,x60771)),x60773))+P1(f324(f64(x60771),f324(f260(x60772,x60771),x60773)))
% 18.55/18.49 [6078]~P1(f324(f64(f844(x60781,x60782)),x60783))+P1(f324(f64(x60781),f324(f262(x60781,x60782),x60783)))
% 18.55/18.49 [6083]~P85(x60831)+E(f324(f324(f104(f845(x60831,a832)),f299(x60831,x60832,x60833)),f324(f259(x60831),x60833)),f179(f845(x60831,a832)))
% 18.55/18.49 [6084]~P85(x60841)+E(f324(f324(f104(f845(x60841,a832)),f298(x60841,x60842,x60843)),f324(f297(x60841),x60843)),f179(f845(x60841,a832)))
% 18.55/18.49 [6085]~P85(x60851)+E(f324(f324(f104(f845(x60851,a832)),f296(x60851,x60852,x60853)),f324(f297(x60851),x60853)),f179(f845(x60851,a832)))
% 18.55/18.49 [6154]E(f324(f324(f149(x61541),x61542),f716(x61542,x61543,x61541)),x61543)+~P1(f324(f324(f326(x61541),x61543),f324(f157(x61541),x61542)))
% 18.55/18.49 [6305]E(x63051,f115(x63052))+~E(f324(f324(f324(f172(f839(x63052),f839(x63052)),x63053),f153(x63052)),x63051),f115(x63052))
% 18.55/18.49 [6384]P39(x63841,x63842,f790(x63843,x63842,x63841),x63843)+~P1(f324(f324(f186(x63841),x63842),x63843))
% 18.55/18.49 [6385]P39(x63851,x63852,f804(x63853,x63852,x63851),x63853)+~P1(f324(f324(f186(x63851),x63852),x63853))
% 18.55/18.49 [6414]~P1(f324(f64(f844(x64142,x64141)),x64143))+P1(f324(f64(f844(x64141,x64142)),f324(f279(x64142,x64141),x64143)))
% 18.55/18.49 [6436]E(x64361,x64362)+~E(f283(a838,f280(a838),x64363,x64361),f324(f324(f303(a838),x64362),f179(f845(a838,a832))))
% 18.55/18.49 [6437]E(x64371,x64372)+~E(f283(a838,f280(a838),x64371,x64372),f324(f324(f303(a838),x64373),f179(f845(a838,a832))))
% 18.55/18.49 [6573]P53(x65731,x65732,x65733)+P1(f324(f324(f326(x65731),f334(x65733,x65732,x65731)),x65732))
% 18.55/18.49 [6574]P53(x65741,x65742,x65743)+P1(f324(f324(f326(x65741),f333(x65743,x65742,x65741)),x65742))
% 18.55/18.49 [6586]P1(f324(f313(x65861,x65862),x65863))+P1(f324(f324(x65862,f791(x65863,x65862,x65861)),x65863))
% 18.55/18.49 [6587]P1(f324(f313(x65871,x65872),x65873))+P1(f324(f324(x65872,f799(x65873,x65872,x65871)),x65873))
% 18.55/18.49 [6618]E(f324(f180(f839(x66181)),f155(x66181,x66182,x66183)),f324(f324(f3(a838),f324(f180(f839(x66181)),x66183)),f80(a838)))+~P1(f324(f324(f326(x66181),x66182),f324(f157(x66181),x66183)))
% 18.55/18.49 [6658]P1(f324(f243(x66581,x66582),x66583))+P1(f324(f324(f326(x66581),f610(x66583,x66582,x66581)),x66583))
% 18.55/18.49 [6670]~P1(f324(f64(f844(x66702,x66701)),f324(f279(x66701,x66702),x66703)))+P1(f324(f64(f844(x66701,x66702)),x66703))
% 18.55/18.49 [6731]~P1(f324(f324(f326(x67311),x67312),f324(f157(x67311),f116(x67311,x67313))))+P1(f324(f324(f326(x67311),x67312),f324(f157(x67311),x67313)))
% 18.55/18.49 [6738]P32(x67381,x67382,x67383)+P1(f324(f324(f326(f837(x67381)),f625(x67383,x67382,x67381)),x67383))
% 18.55/18.49 [6770]E(f324(f126(x67701,x67702),x67703),x67703)+P1(f324(f324(f326(x67701),f747(x67703,x67702,x67701)),f324(f157(x67701),x67703)))
% 18.55/18.49 [6787]E(f324(f126(x67871,x67872),x67873),f115(x67871))+P1(f324(f324(f326(x67871),f715(x67873,x67872,x67871)),f324(f157(x67871),x67873)))
% 18.55/18.49 [6815]E(f161(x68151,x68152,x68153),x68153)+P1(f324(f324(f326(x68151),f757(x68153,x68152,x68151)),f324(f157(x68151),x68153)))
% 18.55/18.49 [6936]P1(f324(f324(f326(x69361),x69362),f685(x69363,x69362,x69361)))+~P1(f324(f324(f326(x69361),x69362),f43(f845(x69361,a832),x69363)))
% 18.55/18.49 [6938]~P67(x69381)+E(f324(f324(f82(x69381),f324(f324(f8(a838,x69381),x69382),f324(f258(a838),x69383))),f324(x69382,x69383)),f324(f324(f8(a838,x69381),x69382),f324(f258(a838),f324(a114,x69383))))
% 18.55/18.49 [7042]~P1(f324(f324(f326(x70421),x70422),f686(x70422,x70423,x70421)))+P1(f324(f324(f326(x70421),x70422),f44(f845(x70421,a832),x70423)))
% 18.55/18.49 [7071]~P67(x70711)+E(f324(f324(f82(x70711),f324(f324(f8(a838,x70711),x70712),f324(f294(a838),x70713))),f324(x70712,f324(a114,x70713))),f324(f324(f8(a838,x70711),x70712),f324(f294(a838),f324(a114,x70713))))
% 18.55/18.49 [7224]P1(f324(f324(f326(f839(x72241)),x72242),f147(x72241,x72243)))+P1(f324(f324(f326(x72241),f736(x72243,x72242,x72241)),f324(f157(x72241),x72242)))
% 18.55/18.49 [7241]~P1(f324(f324(f326(f839(x72411)),x72412),f147(x72411,f314(x72411,x72413))))+P1(f324(f324(f326(f839(x72411)),x72412),f314(f839(x72411),f144(x72411,x72413))))
% 18.55/18.49 [7269]~P1(f324(f324(f326(f839(x72691)),x72692),f314(f839(x72691),f144(x72691,x72693))))+P1(f324(f324(f326(f839(x72691)),x72692),f147(x72691,f314(x72691,x72693))))
% 18.55/18.49 [7309]E(f324(f324(f324(f172(f839(x73091),f839(x73091)),x73092),f153(x73091)),x73093),x73093)+~P1(f324(f324(f231(a838),f324(f180(f839(x73091)),x73093)),f80(a838)))
% 18.55/18.49 [7365]~P29(x73651,x73652,x73653,f238(f845(x73651,a832)))+P29(f839(x73651),f839(x73652),f324(f141(x73651,x73652),x73653),f238(f845(f839(x73651),a832)))
% 18.55/18.49 [7366]~P29(x73661,x73662,x73663,f238(f845(x73661,a832)))+P29(f839(x73661),f839(x73662),f324(f141(x73661,x73662),x73663),f238(f845(f839(x73661),a832)))
% 18.55/18.49 [7523]E(x75231,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x75232)),x75233)),f324(f251(a838,a838),x75232)))+~P1(f324(f54(x75231,x75233),x75232))
% 18.55/18.49 [7530]P29(x75301,x75302,x75303,f238(f845(x75301,a832)))+~P29(f839(x75301),f839(x75302),f324(f141(x75301,x75302),x75303),f238(f845(f839(x75301),a832)))
% 18.55/18.49 [7531]P29(x75311,x75312,x75313,f238(f845(x75311,a832)))+~P29(f839(x75311),f839(x75312),f324(f141(x75311,x75312),x75313),f238(f845(f839(x75311),a832)))
% 18.55/18.49 [7574]P1(f324(f324(f326(f845(x75741,a832)),f686(x75742,x75743,x75741)),x75743))+P1(f324(f324(f326(x75741),x75742),f44(f845(x75741,a832),x75743)))
% 18.55/18.49 [7664]P1(f324(f324(f326(f839(x76641)),x76642),f147(x76641,x76643)))+~P1(f324(f324(f326(x76641),f736(x76643,x76642,x76641)),x76643))
% 18.55/18.49 [7797]E(x77971,x77972)+~E(f324(f324(f9(x77973,f845(x77973,a832),a832),f326(x77973)),x77971),f324(f324(f9(x77973,f845(x77973,a832),a832),f326(x77973)),x77972))
% 18.55/18.49 [7803]~P1(f324(f324(f326(f844(x78031,x78031)),x78033),f261(x78031,x78032)))+P1(f324(f324(f326(x78031),f338(x78032,x78033,x78031)),x78032))
% 18.55/18.49 [7805]~P1(f324(f324(f326(x78051),x78053),f43(f845(x78051,a832),x78052)))+P1(f324(f324(f326(f845(x78051,a832)),f685(x78052,x78053,x78051)),x78052))
% 18.55/18.49 [8071]E(f324(f228(f842(f839(a831)),f839(a831),f307(x80711,x80712,f324(f324(f82(a1),x80713),f80(a1))),f226(f839(a831))),f324(x80711,x80713)),f307(x80711,x80712,x80713))+P1(f324(f324(f232(a1),x80712),x80713))
% 18.55/18.49 [8172]E(x81721,f115(x81722))+P1(f324(f324(f326(x81722),f324(f246(x81722,f844(a101,a101)),f324(f271(x81722,x81721),x81723))),f324(f157(x81722),x81721)))
% 18.55/18.49 [8270]~P5(x82701)+E(f324(f131(x82701,x82701,f324(f9(x82701,x82701,x82701),f82(x82701)),x82702),f324(f154(x82701),x82703)),f324(f131(x82701,x82701,f82(x82701),x82702),x82703))
% 18.55/18.49 [8733]~P86(x87331)+E(f324(f157(x87331),f138(x87331,x87331,f7(x87331),x87332,x87333)),f324(f324(f303(x87331),x87332),f324(f157(x87331),x87333)))
% 18.55/18.49 [8742]P1(f324(f324(f232(a838),f2(a838)),f557(x87421,x87422,x87423)))+~P1(f324(f324(f326(f844(x87423,x87423)),x87422),f324(f324(f282(x87423,x87423,x87423),x87421),f301(x87423,x87421))))
% 18.55/18.49 [8998]~P55(x89981,x89982)+~P1(f324(f324(f326(f844(x89981,x89981)),f324(f324(f247(x89981,x89981),x89983),x89983)),f324(f324(f282(x89981,x89981,x89981),x89982),f301(x89981,x89982))))
% 18.55/18.49 [9110]~E(f324(f324(f104(f845(f844(x91101,x91101),a832)),f324(f279(x91101,x91101),x91102)),f301(x91101,x91102)),f179(f845(f844(x91101,x91101),a832)))+~P1(f324(f324(f326(f844(x91101,x91101)),f324(f324(f247(x91101,x91101),x91103),x91103)),f324(f324(f282(x91101,x91101,x91101),x91102),f301(x91101,x91102))))
% 18.55/18.49 [9285]~P1(f324(f64(x92851),x92852))+P1(f324(f324(f231(a838),f324(f41(x92851),f324(f324(f3(f845(x92851,a832)),x92852),f324(f324(f303(x92851),x92853),f179(f845(x92851,a832)))))),f324(f41(x92851),x92852)))
% 18.55/18.49 [4872]~E(x48723,f115(x48721))+E(f133(x48721,f324(f324(f139(x48721),x48722),x48723)),x48722)
% 18.55/18.49 [4873]~E(x48733,f115(x48731))+E(f133(x48731,f324(f324(f139(x48731),x48732),x48733)),x48732)
% 18.55/18.49 [4882]~E(x48823,f115(x48821))+E(f116(x48821,f324(f324(f139(x48821),x48822),x48823)),f115(x48821))
% 18.55/18.49 [4910]E(x49101,f115(x49102))+E(f133(x49102,f324(f324(f139(x49102),x49103),x49101)),f133(x49102,x49101))
% 18.55/18.49 [4911]E(x49111,f115(x49112))+E(f133(x49112,f324(f324(f139(x49112),x49113),x49111)),f133(x49112,x49111))
% 18.55/18.49 [4912]E(x49121,f115(x49122))+E(f133(x49122,f324(f324(f125(x49122),x49123),x49121)),f133(x49122,x49121))
% 18.55/18.49 [4913]E(x49131,f115(x49132))+E(f133(x49132,f324(f324(f125(x49132),x49133),x49131)),f133(x49132,x49131))
% 18.55/18.49 [4919]~E(x49193,f115(x49191))+E(f133(x49191,f324(f324(f125(x49191),x49192),x49193)),f133(x49191,x49192))
% 18.55/18.49 [4920]~E(x49203,f115(x49201))+E(f133(x49201,f324(f324(f125(x49201),x49202),x49203)),f133(x49201,x49202))
% 18.55/18.49 [4921]~E(x49213,f115(x49211))+E(f116(x49211,f324(f324(f125(x49211),x49212),x49213)),f116(x49211,x49212))
% 18.55/18.49 [4950]E(x49501,f115(x49502))+E(f324(f130(x49502),f324(f324(f125(x49502),x49501),x49503)),f324(f130(x49502),x49501))
% 18.55/18.49 [4951]E(x49511,f115(x49512))+E(f324(f130(x49512),f324(f324(f125(x49512),x49511),x49513)),f324(f130(x49512),x49511))
% 18.55/18.49 [4982]~E(x49822,f115(x49821))+E(f324(f130(x49821),f324(f324(f125(x49821),x49822),x49823)),f324(f130(x49821),x49823))
% 18.55/18.49 [5034]~P86(x50341)+E(f324(f324(f235(x50341),x50342),f324(f324(f178(x50341),x50342),x50343)),x50342)
% 18.55/18.49 [5035]~P86(x50351)+E(f324(f324(f178(x50351),x50352),f324(f324(f235(x50351),x50352),x50353)),x50352)
% 18.55/18.49 [5036]~P94(x50361)+E(f324(f324(f103(x50361),x50362),f324(f324(f104(x50361),x50362),x50363)),x50362)
% 18.55/18.49 [5037]~P94(x50371)+E(f324(f324(f104(x50371),x50372),f324(f324(f103(x50371),x50372),x50373)),x50372)
% 18.55/18.49 [5055]~P7(x50551)+E(f51(x50551,f324(f324(f83(x50551),x50552),x50553),x50553),f2(x50551))
% 18.55/18.49 [5056]~P7(x50561)+E(f51(x50561,f324(f324(f83(x50561),x50562),x50563),x50562),f2(x50561))
% 18.55/18.49 [5122]~P6(x51221)+E(f324(f81(x51221),f324(f324(f3(x51221),x51222),x51223)),f324(f324(f3(x51221),x51223),x51222))
% 18.55/18.49 [5183]E(x51831,f115(x51832))+E(f116(x51832,f324(f324(f139(x51832),x51833),x51831)),f324(f324(f139(x51832),x51833),f116(x51832,x51831)))
% 18.55/18.49 [5184]E(x51841,f115(x51842))+E(f116(x51842,f324(f324(f125(x51842),x51843),x51841)),f324(f324(f125(x51842),x51843),f116(x51842,x51841)))
% 18.55/18.49 [5185]~P9(x51851)+E(f44(x51851,f324(f324(f303(x51851),x51852),x51853)),f324(f324(f104(x51851),x51852),f44(x51851,x51853)))
% 18.55/18.49 [5186]~P9(x51861)+E(f43(x51861,f324(f324(f303(x51861),x51862),x51863)),f324(f324(f103(x51861),x51862),f43(x51861,x51863)))
% 18.55/18.49 [5229]~P92(x52291)+E(f324(f324(f83(x52291),x52292),f324(f324(f83(x52291),x52292),x52293)),f324(f324(f83(x52291),x52292),x52293))
% 18.55/18.49 [5230]~P86(x52301)+E(f324(f324(f235(x52301),x52302),f324(f324(f235(x52301),x52302),x52303)),f324(f324(f235(x52301),x52302),x52303))
% 18.55/18.49 [5231]~P86(x52311)+E(f324(f324(f235(x52311),x52312),f324(f324(f235(x52311),x52312),x52313)),f324(f324(f235(x52311),x52312),x52313))
% 18.55/18.49 [5232]~P86(x52321)+E(f324(f324(f178(x52321),x52322),f324(f324(f178(x52321),x52322),x52323)),f324(f324(f178(x52321),x52322),x52323))
% 18.55/18.49 [5233]~P86(x52331)+E(f324(f324(f178(x52331),x52332),f324(f324(f178(x52331),x52332),x52333)),f324(f324(f178(x52331),x52332),x52333))
% 18.55/18.49 [5234]~P93(x52341)+E(f324(f324(f103(x52341),x52342),f324(f324(f103(x52341),x52342),x52343)),f324(f324(f103(x52341),x52342),x52343))
% 18.55/18.49 [5235]~P93(x52351)+E(f324(f324(f103(x52351),x52352),f324(f324(f103(x52351),x52352),x52353)),f324(f324(f103(x52351),x52352),x52353))
% 18.55/18.49 [5236]~P94(x52361)+E(f324(f324(f103(x52361),x52362),f324(f324(f103(x52361),x52362),x52363)),f324(f324(f103(x52361),x52362),x52363))
% 18.55/18.49 [5237]~P94(x52371)+E(f324(f324(f104(x52371),x52372),f324(f324(f104(x52371),x52372),x52373)),f324(f324(f104(x52371),x52372),x52373))
% 18.55/18.49 [5238]~P99(x52381)+E(f324(f324(f104(x52381),x52382),f324(f324(f104(x52381),x52382),x52383)),f324(f324(f104(x52381),x52382),x52383))
% 18.55/18.49 [5239]~P99(x52391)+E(f324(f324(f104(x52391),x52392),f324(f324(f104(x52391),x52392),x52393)),f324(f324(f104(x52391),x52392),x52393))
% 18.55/18.49 [5247]~P7(x52471)+E(f51(x52471,f324(f324(f82(x52471),x52472),x52473),x52473),f51(x52471,x52472,x52473))
% 18.55/18.49 [5248]~P7(x52481)+E(f51(x52481,f324(f324(f82(x52481),x52482),x52483),x52482),f51(x52481,x52483,x52482))
% 18.55/18.49 [5255]~P126(x52551)+E(f324(f324(f83(x52551),x52552),f324(f81(x52551),x52553)),f324(f81(x52551),f324(f324(f83(x52551),x52552),x52553)))
% 18.55/18.49 [5256]~P59(x52561)+E(f324(f324(f284(x52561),x52562),f324(f81(x52561),x52563)),f324(f81(x52561),f324(f324(f284(x52561),x52562),x52563)))
% 18.55/18.49 [5257]~P72(x52571)+E(f324(f324(f82(x52571),x52572),f324(f151(x52571),x52573)),f324(f151(x52571),f324(f324(f139(x52571),x52572),x52573)))
% 18.55/18.49 [5287]~P126(x52871)+E(f324(f324(f83(x52871),f324(f81(x52871),x52872)),x52873),f324(f324(f83(x52871),x52872),f324(f81(x52871),x52873)))
% 18.55/18.49 [5293]~P12(x52931,x52932,x52933)+E(f43(f845(x52931,a832),f324(f324(f63(x52931),x52932),x52933)),x52932)
% 18.55/18.49 [5353]~P105(x53531)+E(f324(f324(f83(x53531),x53532),f324(f324(f240(x53531),x53532),x53533)),f324(f324(f240(x53531),x53532),f324(a114,x53533)))
% 18.55/18.49 [5354]~P108(x53541)+E(f324(f324(f83(x53541),x53542),f324(f324(f240(x53541),x53542),x53543)),f324(f324(f240(x53541),x53542),f324(a114,x53543)))
% 18.55/18.49 [5355]~P105(x53551)+E(f324(f324(f83(x53551),x53552),f324(f324(f240(x53551),x53552),x53553)),f324(f324(f240(x53551),x53552),f324(a114,x53553)))
% 18.55/18.49 [5365]~P63(x53651)+E(f324(f324(f82(x53651),f324(f81(x53651),x53652)),f324(f324(f82(x53651),x53652),x53653)),x53653)
% 18.55/18.49 [5386]~P2(x53861)+E(f324(f324(f240(x53861),f324(f102(x53861),x53862)),x53863),f324(f102(x53861),f324(f324(f240(a838),x53862),x53863)))
% 18.55/18.49 [5387]~P119(x53871)+E(f324(f324(f240(x53871),f324(f105(x53871),x53872)),x53873),f324(f105(x53871),f324(f324(f240(a1),x53872),x53873)))
% 18.55/18.49 [5392]~P78(x53921)+E(f324(f77(x53921),f324(f324(f3(x53921),x53922),x53923)),f324(f77(x53921),f324(f324(f3(x53921),x53923),x53922)))
% 18.55/18.49 [5395]~P103(x53951)+E(f324(f324(f83(x53951),f84(x53951,x53952)),f84(x53951,x53953)),f84(x53951,f324(f324(f83(x53951),x53952),x53953)))
% 18.55/18.49 [5399]E(x53991,f115(x53992))+E(f324(f324(f125(x53992),f324(f156(x53992),x53991)),x53993),f324(f156(x53992),f324(f324(f125(x53992),x53991),x53993)))
% 18.55/18.49 [5405]~E(x54052,f324(a114,f324(f324(f82(a838),x54051),x54053)))+P1(f324(f324(f232(a838),x54051),x54052))
% 18.55/18.49 [5406]~P126(x54061)+E(f324(f324(f83(x54061),f324(f81(x54061),x54062)),x54063),f324(f81(x54061),f324(f324(f83(x54061),x54062),x54063)))
% 18.55/18.49 [5407]~P114(x54071)+E(f324(f324(f284(x54071),f324(f81(x54071),x54072)),x54073),f324(f81(x54071),f324(f324(f284(x54071),x54072),x54073)))
% 18.55/18.49 [5408]~P103(x54081)+E(f324(f324(f240(x54081),f324(f77(x54081),x54082)),x54083),f324(f77(x54081),f324(f324(f240(x54081),x54082),x54083)))
% 18.55/18.49 [5504]E(f420(x55041,x55042,x55043),f423(x55041,x55042,x55043))+E(f324(f324(f104(f845(x55043,a832)),x55042),x55041),f179(f845(x55043,a832)))
% 18.55/18.49 [5518]~P68(x55182)+E(f324(f324(f11(x55181,x55182),f324(f18(x55182,x55181),f80(x55182))),x55183),f80(x55182))
% 18.55/18.49 [5519]~P67(x55192)+E(f324(f324(f8(x55191,x55192),f324(f18(x55192,x55191),f2(x55192))),x55193),f2(x55192))
% 18.55/18.49 [5521]~P2(x55211)+E(f324(f324(f83(x55211),f324(f102(x55211),x55212)),f324(f102(x55211),x55213)),f324(f102(x55211),f324(f324(f83(a838),x55212),x55213)))
% 18.55/18.49 [5522]~P2(x55221)+E(f324(f324(f82(x55221),f324(f102(x55221),x55222)),f324(f102(x55221),x55223)),f324(f102(x55221),f324(f324(f82(a838),x55222),x55223)))
% 18.55/18.49 [5523]~P119(x55231)+E(f324(f324(f83(x55231),f324(f105(x55231),x55232)),f324(f105(x55231),x55233)),f324(f105(x55231),f324(f324(f83(a1),x55232),x55233)))
% 18.55/18.49 [5524]~P119(x55241)+E(f324(f324(f82(x55241),f324(f105(x55241),x55242)),f324(f105(x55241),x55243)),f324(f105(x55241),f324(f324(f82(a1),x55242),x55243)))
% 18.55/18.49 [5525]~P119(x55251)+E(f324(f324(f3(x55251),f324(f105(x55251),x55252)),f324(f105(x55251),x55253)),f324(f105(x55251),f324(f324(f3(a1),x55252),x55253)))
% 18.55/18.49 [5526]~P89(x55261)+E(f324(f324(f83(x55261),f324(f106(x55261),x55262)),f324(f106(x55261),x55263)),f324(f106(x55261),f324(f324(f83(a1),x55262),x55263)))
% 18.55/18.49 [5527]~P89(x55271)+E(f324(f324(f82(x55271),f324(f106(x55271),x55272)),f324(f106(x55271),x55273)),f324(f106(x55271),f324(f324(f82(a1),x55272),x55273)))
% 18.55/18.49 [5528]~P89(x55281)+E(f324(f324(f3(x55281),f324(f106(x55281),x55282)),f324(f106(x55281),x55283)),f324(f106(x55281),f324(f324(f3(a1),x55282),x55283)))
% 18.55/18.49 [5529]~P89(x55291)+E(f324(f324(f83(x55291),f324(f106(x55291),x55292)),f324(f106(x55291),x55293)),f324(f106(x55291),f324(f324(f83(a1),x55292),x55293)))
% 18.55/18.49 [5530]~P89(x55301)+E(f324(f324(f82(x55301),f324(f106(x55301),x55302)),f324(f106(x55301),x55303)),f324(f106(x55301),f324(f324(f82(a1),x55302),x55303)))
% 18.55/18.49 [5577]~E(x55773,x55772)+P1(f324(f324(f231(f845(x55771,a832)),x55772),x55773))
% 18.55/18.49 [5578]~E(x55782,x55783)+P1(f324(f324(f231(f845(x55781,a832)),x55782),x55783))
% 18.55/18.49 [5579]~E(x55792,x55793)+P1(f324(f324(f231(f845(x55791,a832)),x55792),x55793))
% 18.55/18.49 [5580]~E(x55802,x55803)+P1(f324(f324(f231(f845(x55801,a832)),x55802),x55803))
% 18.55/18.49 [5581]~E(x55812,x55813)+P1(f324(f324(f231(f845(x55811,a832)),x55812),x55813))
% 18.55/18.49 [5582]~E(x55822,x55823)+P1(f324(f324(f231(f845(x55821,a832)),x55822),x55823))
% 18.55/18.49 [5583]~E(x55832,x55833)+P1(f324(f324(f231(f845(x55831,a832)),x55832),x55833))
% 18.55/18.49 [5588]~P63(x55881)+E(f324(f324(f82(x55881),f324(f81(x55881),x55882)),f324(f81(x55881),x55883)),f324(f81(x55881),f324(f324(f82(x55881),x55883),x55882)))
% 18.55/18.49 [5589]~P6(x55891)+E(f324(f324(f82(x55891),f324(f81(x55891),x55892)),f324(f81(x55891),x55893)),f324(f81(x55891),f324(f324(f82(x55891),x55892),x55893)))
% 18.55/18.49 [5590]~P69(x55901)+E(f324(f324(f178(x55901),f324(f81(x55901),x55902)),f324(f81(x55901),x55903)),f324(f81(x55901),f324(f324(f235(x55901),x55902),x55903)))
% 18.55/18.49 [5591]~P69(x55911)+E(f324(f324(f235(x55911),f324(f81(x55911),x55912)),f324(f81(x55911),x55913)),f324(f81(x55911),f324(f324(f178(x55911),x55912),x55913)))
% 18.55/18.49 [5592]~P91(x55921)+E(f324(f324(f104(x55921),f324(f81(x55921),x55922)),f324(f81(x55921),x55923)),f324(f81(x55921),f324(f324(f103(x55921),x55922),x55923)))
% 18.55/18.49 [5593]~P91(x55931)+E(f324(f324(f103(x55931),f324(f81(x55931),x55932)),f324(f81(x55931),x55933)),f324(f81(x55931),f324(f324(f104(x55931),x55932),x55933)))
% 18.55/18.49 [5594]~P103(x55941)+E(f324(f324(f83(x55941),f324(f77(x55941),x55942)),f324(f77(x55941),x55943)),f324(f77(x55941),f324(f324(f83(x55941),x55942),x55943)))
% 18.55/18.49 [5595]~P61(x55951)+E(f324(f324(f284(x55951),f324(f77(x55951),x55952)),f324(f77(x55951),x55953)),f324(f77(x55951),f324(f324(f284(x55951),x55952),x55953)))
% 18.55/18.49 [5596]~P72(x55961)+E(f324(f324(f82(x55961),f324(f151(x55961),x55962)),f324(f151(x55961),x55963)),f324(f151(x55961),f324(f324(f125(x55961),x55962),x55963)))
% 18.55/18.49 [5597]E(x55971,f179(f845(x55972,a832)))+~E(f324(f324(f103(f845(x55972,a832)),x55973),x55971),f179(f845(x55972,a832)))
% 18.55/18.49 [5598]E(x55981,f179(f845(x55982,a832)))+~E(f324(f324(f103(f845(x55982,a832)),x55981),x55983),f179(f845(x55982,a832)))
% 18.55/18.49 [5599]~P140(x55991,x55992,x55993)+P1(f324(x55991,f324(f324(f42(a1),x55992),x55993)))
% 18.55/18.49 [5658]~P1(f324(f64(x56581),x56583))+P1(f324(f64(x56581),f324(f324(f303(x56581),x56582),x56583)))
% 18.55/18.49 [5659]~P1(f324(f64(x56591),x56593))+P1(f324(f64(x56591),f324(f324(f303(x56591),x56592),x56593)))
% 18.55/18.49 [5660]~P1(f324(f127(x56601),x56603))+P1(f324(f127(x56601),f324(f324(f158(x56601),x56602),x56603)))
% 18.55/18.49 [5661]~P1(f324(f127(x56611),x56613))+P1(f324(f127(x56611),f324(f324(f128(x56611),x56612),x56613)))
% 18.55/18.49 [5692]~P86(x56921)+P1(f324(f324(f231(x56921),x56922),f324(f324(f178(x56921),x56923),x56922)))
% 18.55/18.49 [5693]~P86(x56931)+P1(f324(f324(f231(x56931),x56932),f324(f324(f178(x56931),x56932),x56933)))
% 18.55/18.49 [5694]~P93(x56941)+P1(f324(f324(f231(x56941),x56942),f324(f324(f103(x56941),x56943),x56942)))
% 18.55/18.49 [5695]~P94(x56951)+P1(f324(f324(f231(x56951),x56952),f324(f324(f103(x56951),x56953),x56952)))
% 18.55/18.49 [5696]~P93(x56961)+P1(f324(f324(f231(x56961),x56962),f324(f324(f103(x56961),x56962),x56963)))
% 18.55/18.49 [5697]~P94(x56971)+P1(f324(f324(f231(x56971),x56972),f324(f324(f103(x56971),x56972),x56973)))
% 18.55/18.49 [5698]~P105(x56981)+P1(f324(f324(f280(x56981),x56982),f324(f324(f83(x56981),x56983),x56982)))
% 18.55/18.49 [5699]~P105(x56991)+P1(f324(f324(f280(x56991),x56992),f324(f324(f83(x56991),x56992),x56993)))
% 18.55/18.49 [5712]~E(x57121,f2(a838))+E(f324(f324(f42(a838),f324(f324(f83(a838),x57121),x57122)),f324(f324(f83(a838),x57121),x57123)),f2(a838))
% 18.55/18.49 [5775]P1(f324(x57751,x57752))+P1(f324(f324(f186(f35(x57751,x57753)),x57752),x57752))
% 18.55/18.49 [5776]P1(f324(x57761,x57762))+P1(f324(f324(f186(f35(x57761,x57763)),x57762),x57762))
% 18.55/18.49 [5790]~P89(x57901)+E(f324(f324(f3(x57901),f324(f106(x57901),x57902)),f324(f106(x57901),x57903)),f324(f106(x57901),f324(f324(f82(a1),x57902),f324(f81(a1),x57903))))
% 18.55/18.49 [5846]E(x58461,f2(a838))+E(f324(f324(f42(a838),f324(f324(f83(a838),x58461),x58462)),f324(f324(f83(a838),x58461),x58463)),f324(f324(f42(a838),x58462),x58463))
% 18.55/18.49 [5882]E(f140(x58821,f324(f324(f139(x58821),x58822),x58823)),f324(f324(f139(x58821),x58822),f140(x58821,x58823)))+P1(f324(f324(f326(x58821),x58822),f324(f157(x58821),x58823)))
% 18.55/18.49 [5916]P140(x59161,x59162,x59163)+~P1(f324(x59161,f324(f324(f42(a1),x59162),x59163)))
% 18.55/18.49 [5993]E(x59931,f115(x59932))+E(f324(f324(f139(x59932),f324(f130(x59932),x59931)),f324(f324(f158(x59932),x59933),f324(f156(x59932),x59931))),f324(f324(f158(x59932),f324(a114,x59933)),x59931))
% 18.55/18.49 [6001]E(f324(f324(f3(f845(x60011,a832)),x60012),x60013),x60012)+~E(f324(f324(f104(f845(x60011,a832)),x60012),x60013),f179(f845(x60011,a832)))
% 18.55/18.49 [6014]E(f140(x60141,f324(f324(f139(x60141),x60142),x60143)),f140(x60141,x60143))+~P1(f324(f324(f326(x60141),x60142),f324(f157(x60141),x60143)))
% 18.55/18.49 [6045]~P1(f324(f324(f232(a838),x60451),x60453))+P1(f324(f324(f232(a838),x60451),f324(f324(f82(a838),x60452),x60453)))
% 18.55/18.49 [6046]~P1(f324(f324(f232(a838),x60461),x60463))+P1(f324(f324(f232(a838),x60461),f324(f324(f82(a838),x60462),x60463)))
% 18.55/18.49 [6047]~P1(f324(f324(f232(a838),x60471),x60472))+P1(f324(f324(f232(a838),x60471),f324(f324(f82(a838),x60472),x60473)))
% 18.55/18.49 [6048]~P1(f324(f324(f232(a838),x60481),x60482))+P1(f324(f324(f232(a838),x60481),f324(f324(f82(a838),x60482),x60483)))
% 18.55/18.49 [6049]~P1(f324(f324(f231(a838),x60491),x60493))+P1(f324(f324(f231(a838),x60491),f324(f324(f82(a838),x60492),x60493)))
% 18.55/18.49 [6050]~P1(f324(f324(f231(a838),x60501),x60503))+P1(f324(f324(f231(a838),x60501),f324(f324(f82(a838),x60502),x60503)))
% 18.55/18.49 [6051]~P1(f324(f324(f231(a838),x60511),x60512))+P1(f324(f324(f231(a838),x60511),f324(f324(f82(a838),x60512),x60513)))
% 18.55/18.49 [6052]~P1(f324(f324(f231(a838),x60521),x60522))+P1(f324(f324(f231(a838),x60521),f324(f324(f82(a838),x60522),x60523)))
% 18.55/18.49 [6091]P1(f324(f64(x60911),x60912))+~P1(f324(f64(x60911),f324(f324(f303(x60911),x60913),x60912)))
% 18.55/18.49 [6092]P1(f324(f127(x60921),x60922))+~P1(f324(f127(x60921),f324(f324(f139(x60921),x60923),x60922)))
% 18.55/18.49 [6093]P1(f324(f127(x60931),x60932))+~P1(f324(f127(x60931),f324(f324(f125(x60931),x60933),x60932)))
% 18.55/18.49 [6094]P1(f324(f127(x60941),x60942))+~P1(f324(f127(x60941),f324(f324(f125(x60941),x60942),x60943)))
% 18.55/18.49 [6139]~E(f51(a1,x61392,x61391),f51(a1,x61393,x61391))+P1(f324(f324(f280(a1),x61391),f324(f324(f3(a1),x61392),x61393)))
% 18.55/18.49 [6144]~P105(x61441)+E(f324(f324(f82(x61441),x61442),f324(f324(f83(x61441),x61443),x61442)),f324(f324(f83(x61441),f324(f324(f82(x61441),x61443),f80(x61441))),x61442))
% 18.55/18.49 [6193]~E(x61931,x61932)+~P1(f324(f324(f232(f845(x61933,a832)),x61931),x61932))
% 18.55/18.49 [6239]P1(f324(f324(f326(x62391),x62392),x62393))+P1(f324(f324(f326(x62391),x62392),f324(f81(f845(x62391,a832)),x62393)))
% 18.55/18.49 [6240]P1(f324(f324(f326(x62401),x62402),x62403))+P1(f324(f324(f326(x62401),x62402),f324(f81(f845(x62401,a832)),x62403)))
% 18.55/18.49 [6247]E(f133(x62471,f324(f324(f128(x62471),x62472),x62473)),f133(x62471,x62473))+~P1(f324(f324(f232(a838),x62472),f324(f180(f839(x62471)),x62473)))
% 18.55/18.49 [6248]E(f324(f324(f158(x62481),x62482),f116(x62481,x62483)),f324(f324(f158(x62481),x62482),x62483))+~P1(f324(f324(f232(a838),x62482),f324(f180(f839(x62481)),x62483)))
% 18.55/18.49 [6307]E(f324(f324(f324(f172(f839(x63071),f839(x63071)),x63072),f153(x63071)),x63073),x63073)+~E(f51(a838,x63072,f324(f180(f839(x63071)),x63073)),f2(a838))
% 18.55/18.49 [6316]~P12(x63161,x63163,x63162)+E(f324(f324(f282(x63161,x63161,x63161),f324(f279(x63161,x63161),x63162)),x63162),x63162)
% 18.55/18.49 [6359]~E(f324(f324(f103(f845(x63591,a832)),x63592),x63593),x63593)+P1(f324(f324(f231(f845(x63591,a832)),x63592),x63593))
% 18.55/18.49 [6364]~P52(x63641,x63641,x63643)+P52(x63641,x63641,f324(f324(f172(f844(x63641,x63641),a832),x63642),x63643))
% 18.55/18.49 [6366]~P1(f324(f324(f326(x63661),x63663),f324(f157(x63661),x63662)))+P1(f324(f324(f232(a838),f2(a838)),f324(f180(f839(x63661)),x63662)))
% 18.55/18.49 [6383]~E(x63832,x63833)+P1(f324(f324(f326(x63831),x63832),f324(f324(f303(x63831),x63833),f179(f845(x63831,a832)))))
% 18.55/18.49 [6396]~P78(x63961)+E(f324(f77(x63961),f324(f324(f82(x63961),f324(f77(x63961),x63962)),f324(f77(x63961),x63963))),f324(f324(f82(x63961),f324(f77(x63961),x63962)),f324(f77(x63961),x63963)))
% 18.55/18.49 [6407]E(f324(f324(f42(a838),f324(f324(f83(a838),x64071),x64072)),f324(f324(f83(a838),x64071),x64073)),f324(f324(f42(a838),x64072),x64073))+~P1(f324(f324(f232(a838),f2(a838)),x64071))
% 18.55/18.49 [6434]E(f51(a1,x64341,x64342),f51(a1,x64343,x64342))+~P1(f324(f324(f280(a1),x64342),f324(f324(f3(a1),x64341),x64343)))
% 18.55/18.49 [6548]~P1(f324(f64(x65481),x65483))+E(f324(f324(f67(x65481,f845(x65481,a832),f303(x65481)),x65482),x65483),f324(f324(f103(f845(x65481,a832)),x65483),x65482))
% 18.55/18.49 [6611]E(f324(f324(f103(f845(x66111,a832)),x66112),x66113),x66112)+~P1(f324(f324(f231(f845(x66111,a832)),x66113),x66112))
% 18.55/18.49 [6612]E(f324(f324(f103(f845(x66121,a832)),x66122),x66123),x66123)+~P1(f324(f324(f231(f845(x66121,a832)),x66122),x66123))
% 18.55/18.49 [6613]E(f324(f324(f103(f845(x66131,a832)),x66132),x66133),x66133)+~P1(f324(f324(f231(f845(x66131,a832)),x66132),x66133))
% 18.55/18.49 [6614]E(f324(f324(f104(f845(x66141,a832)),x66142),x66143),x66143)+~P1(f324(f324(f231(f845(x66141,a832)),x66143),x66142))
% 18.55/18.49 [6615]E(f324(f324(f104(f845(x66151,a832)),x66152),x66153),x66152)+~P1(f324(f324(f231(f845(x66151,a832)),x66152),x66153))
% 18.55/18.49 [6668]~P1(f324(f127(x66681),x66682))+E(f324(f324(f3(f845(x66681,a832)),f324(f157(x66681),x66682)),f324(f324(f303(x66681),x66683),f179(f845(x66681,a832)))),f324(f157(x66681),f155(x66681,x66683,x66682)))
% 18.55/18.49 [6726]P36(x67261,x67262)+~P36(x67261,f324(f324(f172(f844(x67261,x67261),a832),x67263),x67262))
% 18.55/18.49 [6745]~E(x67451,f2(a838))+P1(f324(f324(f280(a838),f324(f324(f83(a838),x67451),x67452)),f324(f324(f83(a838),x67451),x67453)))
% 18.55/18.49 [6799]P1(f324(f55(x67991,x67992),f324(a57,x67993)))+~P1(f324(f55(f324(f81(a1),x67991),f324(f81(a1),x67992)),x67993))
% 18.55/18.49 [6804]E(f324(f324(f3(f845(x68041,a832)),f324(f324(f303(x68041),x68042),x68043)),f324(f324(f303(x68041),x68042),f179(f845(x68041,a832)))),x68043)+P1(f324(f324(f326(x68041),x68042),x68043))
% 18.55/18.49 [6823]E(f324(f324(f104(f845(x68231,a832)),f324(f157(x68231),x68232)),f324(f157(x68231),x68233)),f179(f845(x68231,a832)))+~P1(f324(f127(x68231),f324(f324(f125(x68231),x68232),x68233)))
% 18.55/18.49 [6840]~P1(f324(f324(f326(x68401),x68402),f324(f157(x68401),x68403)))+~P1(f324(f127(x68401),f324(f324(f139(x68401),x68402),x68403)))
% 18.55/18.49 [6917]E(f324(f324(f104(f845(x69171,a832)),x69172),x69173),f179(f845(x69171,a832)))+P1(f324(f324(f326(x69171),f420(x69173,x69172,x69171)),x69172))
% 18.55/18.49 [6918]E(f324(f324(f104(f845(x69181,a832)),x69182),x69183),f179(f845(x69181,a832)))+P1(f324(f324(f326(x69181),f423(x69183,x69182,x69181)),x69183))
% 18.55/18.49 [6922]E(f116(x69221,f324(f324(f158(x69221),x69222),x69223)),f324(f324(f158(x69221),f324(f324(f3(a838),x69222),f80(a838))),x69223))+~P1(f324(f324(f231(a838),x69222),f324(f180(f839(x69221)),x69223)))
% 18.55/18.49 [7004]P1(f324(f324(f232(a838),f2(a838)),x70041))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x70042),x70041)),f324(f324(f83(a838),x70043),x70041)))
% 18.55/18.49 [7005]P1(f324(f324(f232(a838),f2(a838)),x70051))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x70051),x70052)),f324(f324(f83(a838),x70051),x70053)))
% 18.55/18.49 [7006]~P1(f324(f324(f326(x70061),x70062),x70063))+~P1(f324(f324(f326(x70061),x70062),f324(f81(f845(x70061,a832)),x70063)))
% 18.55/18.49 [7007]~P1(f324(f324(f326(x70071),x70072),x70073))+~P1(f324(f324(f326(x70071),x70072),f324(f81(f845(x70071,a832)),x70073)))
% 18.55/18.49 [7008]~P1(f324(f324(f326(x70081),x70082),x70083))+~P1(f324(f324(f326(x70081),x70082),f324(f81(f845(x70081,a832)),x70083)))
% 18.55/18.49 [7012]~P1(f324(f324(f232(f845(x70121,a832)),x70122),x70123))+P1(f324(f324(f231(f845(x70121,a832)),x70122),x70123))
% 18.55/18.49 [7013]~P1(f324(f324(f232(f845(x70131,a832)),x70132),x70133))+P1(f324(f324(f231(f845(x70131,a832)),x70132),x70133))
% 18.55/18.49 [7014]~P1(f324(f324(f232(f845(x70141,a832)),x70142),x70143))+P1(f324(f324(f231(f845(x70141,a832)),x70142),x70143))
% 18.55/18.49 [7118]~P1(f324(f324(f232(a838),x71182),x71183))+P1(f324(f324(f232(a838),f324(f324(f82(a838),x71181),x71182)),f324(f324(f82(a838),x71181),x71183)))
% 18.55/18.49 [7119]~P1(f324(f324(f232(a838),x71191),x71193))+P1(f324(f324(f232(a838),f324(f324(f82(a838),x71191),x71192)),f324(f324(f82(a838),x71193),x71192)))
% 18.55/18.49 [7120]~P1(f324(f324(f232(a1),x71201),x71203))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x71201),x71202)),f324(f324(f82(a1),x71203),x71202)))
% 18.55/18.49 [7123]~P1(f324(f324(f231(a838),x71232),x71233))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x71231),x71232)),f324(f324(f83(a838),x71231),x71233)))
% 18.55/18.49 [7124]~P1(f324(f324(f231(a838),x71242),x71243))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x71241),x71242)),f324(f324(f83(a838),x71241),x71243)))
% 18.55/18.49 [7125]~P1(f324(f324(f231(a838),x71251),x71253))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x71251),x71252)),f324(f324(f83(a838),x71253),x71252)))
% 18.55/18.49 [7126]~P1(f324(f324(f231(a838),x71261),x71263))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x71261),x71262)),f324(f324(f83(a838),x71263),x71262)))
% 18.55/18.49 [7127]~P1(f324(f324(f231(a838),x71272),x71273))+P1(f324(f324(f231(a838),f324(f324(f82(a838),x71271),x71272)),f324(f324(f82(a838),x71271),x71273)))
% 18.55/18.49 [7128]~P1(f324(f324(f231(a838),x71281),x71283))+P1(f324(f324(f231(a838),f324(f324(f82(a838),x71281),x71282)),f324(f324(f82(a838),x71283),x71282)))
% 18.55/18.49 [7129]~P1(f324(f324(f231(a838),x71291),x71293))+P1(f324(f324(f231(a838),f324(f324(f42(a838),x71291),x71292)),f324(f324(f42(a838),x71293),x71292)))
% 18.55/18.49 [7130]~P1(f324(f324(f231(a838),x71303),x71302))+P1(f324(f324(f231(a838),f324(f324(f3(a838),x71301),x71302)),f324(f324(f3(a838),x71301),x71303)))
% 18.55/18.49 [7131]~P1(f324(f324(f231(a838),x71311),x71313))+P1(f324(f324(f231(a838),f324(f324(f3(a838),x71311),x71312)),f324(f324(f3(a838),x71313),x71312)))
% 18.55/18.49 [7132]~P1(f324(f324(f231(a1),x71322),x71323))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x71321),x71322)),f324(f324(f82(a1),x71321),x71323)))
% 18.55/18.49 [7135]~P1(f324(f324(f280(a838),x71352),x71353))+P1(f324(f324(f280(a838),f324(f324(f83(a838),x71351),x71352)),f324(f324(f83(a838),x71351),x71353)))
% 18.55/18.49 [7222]E(x72221,x72222)+~P1(f324(f324(f326(x72223),x72221),f324(f324(f303(x72223),x72222),f179(f845(x72223,a832)))))
% 18.55/18.49 [7223]E(x72231,x72232)+~P1(f324(f324(f326(x72233),x72231),f324(f324(f303(x72233),x72232),f179(f845(x72233,a832)))))
% 18.55/18.49 [7225]~E(f324(f324(f104(f845(x72251,a832)),x72252),x72253),f179(f845(x72251,a832)))+P1(f324(f324(f231(f845(x72251,a832)),x72252),f324(f81(f845(x72251,a832)),x72253)))
% 18.55/18.49 [7231]P1(f324(f324(f326(f845(x72311,a832)),x72312),f324(f302(x72311),x72313)))+~P1(f324(f324(f231(f845(x72311,a832)),x72312),x72313))
% 18.55/18.49 [7232]P1(f324(f324(f326(f845(x72321,a832)),x72322),f324(f302(x72321),x72323)))+~P1(f324(f324(f231(f845(x72321,a832)),x72322),x72323))
% 18.55/18.49 [7289]E(f324(f324(f139(x72891),f324(f324(f149(x72891),x72892),x72893)),f324(f324(f128(x72891),f324(a114,x72893)),x72892)),f324(f324(f128(x72891),x72893),x72892))+~P1(f324(f324(f232(a838),x72893),f324(f180(f839(x72891)),x72892)))
% 18.55/18.49 [7319]P1(f324(f324(f326(f844(x73191,x73191)),x73192),f301(x73191,x73193)))+~P1(f324(f324(f326(f844(x73191,x73191)),x73192),x73193))
% 18.55/18.49 [7328]~P1(f324(f324(f326(f845(x73281,a832)),x73282),f324(f302(x73281),x73283)))+P1(f324(f324(f231(f845(x73281,a832)),x73282),x73283))
% 18.55/18.49 [7329]~P1(f324(f324(f326(f845(x73291,a832)),x73292),f324(f302(x73291),x73293)))+P1(f324(f324(f231(f845(x73291,a832)),x73292),x73293))
% 18.55/18.49 [7374]P1(f324(f324(f231(f845(x73741,a832)),x73742),f43(f845(x73741,a832),x73743)))+~P1(f324(f324(f326(f845(x73741,a832)),x73742),x73743))
% 18.55/18.49 [7402]~P119(x74021)+E(f324(f324(f83(x74021),f324(f324(f240(x74021),f324(f81(x74021),f80(x74021))),x74022)),f324(f324(f240(x74021),x74023),x74022)),f324(f324(f240(x74021),f324(f81(x74021),x74023)),x74022))
% 18.55/18.49 [7424]E(f324(f324(f149(x74241),x74242),f324(f324(f3(a838),f324(f180(f839(x74241)),x74242)),f324(a114,x74243))),f324(f324(f149(x74241),f324(f154(x74241),x74242)),x74243))+~P1(f324(f324(f232(a838),x74243),f324(f180(f839(x74241)),x74242)))
% 18.55/18.49 [7441]~E(f324(f324(f104(f845(x74411,a832)),f656(x74413,x74412,x74411)),x74413),f179(f845(x74411,a832)))+E(f324(f324(f104(f845(x74411,a832)),f43(f845(x74411,a832),x74412)),x74413),f179(f845(x74411,a832)))
% 18.55/18.49 [7505]~P1(f324(f324(f326(x75053),x75052),f324(f157(x75053),x75051)))+P1(f324(f324(f232(a838),f716(x75051,x75052,x75053)),f324(f180(f839(x75053)),x75051)))
% 18.55/18.49 [7513]P1(f324(f324(f326(x75131),f324(f324(f149(x75131),x75132),x75133)),f324(f157(x75131),x75132)))+~P1(f324(f324(f232(a838),x75133),f324(f180(f839(x75131)),x75132)))
% 18.55/18.49 [7613]~P1(f324(x76132,f764(x76133,x76132,x76131)))+E(f324(f324(f128(x76131),f324(f180(f839(x76131)),f161(x76131,x76132,x76133))),x76133),f115(x76131))
% 18.55/18.49 [7623]P1(f324(f324(f231(f845(f839(x76231),a832)),f147(x76231,x76232)),f147(x76231,x76233)))+~P1(f324(f324(f231(f845(x76231,a832)),x76232),x76233))
% 18.55/18.49 [7652]E(f324(f324(f104(f845(x76521,a832)),f43(f845(x76521,a832),x76522)),x76523),f179(f845(x76521,a832)))+P1(f324(f324(f326(f845(x76521,a832)),f656(x76523,x76522,x76521)),x76522))
% 18.55/18.49 [7654]~P1(f324(f324(f326(f845(x76541,a832)),x76543),x76542))+P1(f324(f324(f231(f845(x76541,a832)),f44(f845(x76541,a832),x76542)),x76543))
% 18.55/18.49 [7656]E(f324(f324(f104(f845(x76561,a832)),x76562),x76563),f179(f845(x76561,a832)))+~P1(f324(f324(f231(f845(x76561,a832)),x76562),f324(f81(f845(x76561,a832)),x76563)))
% 18.55/18.49 [7710]E(f324(f324(f3(a838),f324(f324(f82(a838),f324(f151(a838),x77101)),x77102)),f324(f324(f149(a838),x77101),x77103)),f324(f151(a838),f324(f324(f146(a838,x77101),x77103),x77102)))+~P1(f324(f324(f232(a838),x77103),f324(f180(f839(a838)),x77101)))
% 18.55/18.49 [7761]P1(f324(f324(f232(a838),x77611),x77612))+~P1(f324(f324(f232(a838),f324(f324(f82(a838),x77613),x77611)),f324(f324(f82(a838),x77613),x77612)))
% 18.55/18.49 [7762]P1(f324(f324(f232(a838),x77621),x77622))+~P1(f324(f324(f232(a838),f324(f324(f83(a838),x77623),x77621)),f324(f324(f83(a838),x77623),x77622)))
% 18.55/18.49 [7763]P1(f324(f324(f232(a838),x77631),x77632))+~P1(f324(f324(f232(a838),f324(f324(f83(a838),x77631),x77633)),f324(f324(f83(a838),x77632),x77633)))
% 18.55/18.49 [7766]P1(f324(f324(f231(a838),x77661),x77662))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x77663),x77661)),f324(f324(f82(a838),x77663),x77662)))
% 18.55/18.49 [7795]P1(f324(f324(f232(a838),f2(a838)),x77951))+~P1(f324(f324(f232(a838),f324(f324(f83(a838),x77952),x77951)),f324(f324(f83(a838),x77953),x77951)))
% 18.55/18.49 [7796]P1(f324(f324(f232(a838),f2(a838)),x77961))+~P1(f324(f324(f232(a838),f324(f324(f83(a838),x77961),x77962)),f324(f324(f83(a838),x77961),x77963)))
% 18.55/18.49 [7870]E(f242(x78701,x78702,x78703),x78702)+~P1(f324(f324(f231(f845(x78701,a832)),x78703),f324(f324(f303(x78701),x78702),f179(f845(x78701,a832)))))
% 18.55/18.49 [7946]E(f324(f324(f128(x79461),f324(f180(f839(x79461)),f161(x79461,x79462,x79463))),x79463),f115(x79461))+P1(f324(f324(f326(x79461),f764(x79463,x79462,x79461)),f324(f157(x79461),x79463)))
% 18.55/18.49 [7951]E(f324(f324(f125(x79511),f324(f324(f158(x79511),x79512),x79513)),f324(f324(f139(x79511),f324(f324(f149(x79511),x79513),x79512)),f115(x79511))),f324(f324(f158(x79511),f324(a114,x79512)),x79513))+~P1(f324(f324(f232(a838),x79512),f324(f180(f839(x79511)),x79513)))
% 18.55/18.49 [8021]P1(f324(f324(f231(f845(f845(x80211,a832),a832)),f243(x80211,x80212)),f243(x80211,x80213)))+~P1(f324(f324(f231(f845(x80211,a832)),x80212),x80213))
% 18.55/18.49 [8062]~P1(f324(f127(x80621),x80623))+P1(f324(f127(x80621),f324(f324(f324(f172(f839(x80621),f839(x80621)),x80622),f153(x80621)),x80623)))
% 18.55/18.49 [8067]~P1(f324(f324(f232(a838),x80672),x80673))+P1(f324(f324(f232(a838),f324(f324(f83(a838),f324(a114,x80671)),x80672)),f324(f324(f83(a838),f324(a114,x80671)),x80673)))
% 18.55/18.49 [8068]~P1(f324(f324(f231(a838),x80682),x80683))+P1(f324(f324(f231(a838),f324(f324(f83(a838),f324(a114,x80681)),x80682)),f324(f324(f83(a838),f324(a114,x80681)),x80683)))
% 18.55/18.49 [8090]P1(f324(f324(f231(f845(f845(x80901,a832),a832)),f324(f302(x80901),x80902)),f324(f302(x80901),x80903)))+~P1(f324(f324(f231(f845(x80901,a832)),x80902),x80903))
% 18.55/18.49 [8248]~P1(f324(f324(f231(f845(x82481,a832)),x82483),x82482))+P1(f324(f324(f231(f845(x82481,a832)),f324(f81(f845(x82481,a832)),x82482)),f324(f81(f845(x82481,a832)),x82483)))
% 18.55/18.49 [8249]~P1(f324(f324(f231(f845(x82491,a832)),x82493),x82492))+P1(f324(f324(f231(f845(x82491,a832)),f324(f81(f845(x82491,a832)),x82492)),f324(f81(f845(x82491,a832)),x82493)))
% 18.55/18.49 [8286]E(f324(f304(a838,a838,f324(f324(f9(a838,a838,a838),f3(a838)),x82861)),f324(f295(a838,x82862),x82863)),f324(f295(a838,f324(f324(f3(a838),x82862),x82861)),f324(f324(f3(a838),x82863),x82861)))+~P1(f324(f324(f232(a838),x82861),x82863))
% 18.55/18.49 [8312]~P72(x83121)+E(f324(f324(f82(x83121),x83122),f324(f131(x83121,x83121,f82(x83121),f2(x83121)),x83123)),f324(f131(x83121,x83121,f82(x83121),x83122),x83123))
% 18.55/18.49 [8395]~P78(x83951)+P1(f324(f324(f231(x83951),f324(f77(x83951),f324(f324(f82(x83951),x83952),x83953))),f324(f324(f82(x83951),f324(f77(x83951),x83952)),f324(f77(x83951),x83953))))
% 18.55/18.49 [8396]~P78(x83961)+P1(f324(f324(f231(x83961),f324(f77(x83961),f324(f324(f3(x83961),x83962),x83963))),f324(f324(f82(x83961),f324(f77(x83961),x83962)),f324(f77(x83961),x83963))))
% 18.55/18.49 [8406]E(f324(f324(f82(a1),f324(f324(f83(a1),x84061),f51(a1,f324(f324(f42(a1),x84062),x84061),x84063))),f51(a1,x84062,x84061)),f51(a1,x84062,f324(f324(f83(a1),x84061),x84063)))+~P1(f324(f324(f232(a1),f2(a1)),x84063))
% 18.55/18.49 [8412]E(f324(f324(f125(x84121),f324(f324(f158(x84121),x84122),x84123)),f324(f324(f139(x84121),f324(f130(x84121),f324(f324(f128(x84121),x84122),x84123))),f115(x84121))),f324(f324(f158(x84121),f324(a114,x84122)),x84123))+~P1(f324(f324(f232(a838),x84122),f324(f180(f839(x84121)),x84123)))
% 18.55/18.49 [8431]E(f324(f266(x84311,f324(f324(f141(x84311,f844(a101,x84311)),f324(f247(a101,x84311),f80(a101))),x84312)),f324(a5,x84313)),f324(f324(f149(x84311),x84312),x84313))+~P1(f324(f324(f232(a838),x84313),f324(f180(f839(x84311)),x84312)))
% 18.55/18.49 [8488]P1(f324(f324(f326(f844(x84881,x84881)),x84882),f324(f324(f282(x84881,x84881,x84881),x84883),f301(x84881,x84883))))+~P1(f324(f324(f326(f844(x84881,x84881)),x84882),x84883))
% 18.55/18.49 [8504]P1(f324(f324(f232(a838),x85041),x85042))+~P1(f324(f324(f232(a838),f324(f324(f83(a838),f324(a114,x85043)),x85041)),f324(f324(f83(a838),f324(a114,x85043)),x85042)))
% 18.55/18.49 [8505]P1(f324(f324(f231(a838),x85051),x85052))+~P1(f324(f324(f231(a838),f324(f324(f83(a838),f324(a114,x85053)),x85051)),f324(f324(f83(a838),f324(a114,x85053)),x85052)))
% 18.55/18.49 [8516]P1(f324(f324(f231(f845(x85161,a832)),x85162),x85163))+~P1(f324(f324(f231(f845(x85161,a832)),f324(f81(f845(x85161,a832)),x85163)),f324(f81(f845(x85161,a832)),x85162)))
% 18.55/18.49 [8534]P1(f324(f127(x85341),x85342))+~P1(f324(f127(x85341),f324(f324(f324(f172(f839(x85341),f839(x85341)),x85343),f153(x85341)),x85342)))
% 18.55/18.49 [8601]E(f324(f278(x86011,x86011,f301(x86011,x86012)),x86013),x86013)+~P1(f324(f324(f231(f845(x86011,a832)),f324(f278(x86011,x86011,x86012),x86013)),x86013))
% 18.55/18.49 [8603]E(f324(f304(f844(x86031,x86032),x86032,f251(x86031,x86032)),f324(f157(f844(x86031,x86032)),x86033)),f170(x86031,x86032,f165(x86031,x86032,x86033)))+~P1(f324(f127(x86031),f324(f324(f141(f844(x86031,x86032),x86031),f246(x86031,x86032)),x86033)))
% 18.55/18.49 [8644]~P86(x86441)+P18(x86441,f324(f126(x86441,f324(f324(f9(x86441,x86441,a832),a321),f324(x86442,x86443))),x86443))
% 18.55/18.49 [8649]~P1(f324(f324(f231(a838),x86491),x86492))+P1(f324(f324(f231(a838),x86491),f324(f131(a838,a838,f82(a838),x86492),x86493)))
% 18.55/18.49 [8721]~P1(f324(f324(f326(f844(x87211,x87211)),x87212),f301(x87211,x87213)))+P1(f324(f324(f326(f844(x87211,x87211)),x87212),f324(f324(f172(f844(x87211,x87211),a832),f556(x87213,x87212,x87211)),x87213)))
% 18.55/18.49 [8792]~P72(x87921)+E(f324(f324(f82(x87921),x87922),f324(f131(x87921,x87921,f324(f9(x87921,x87921,x87921),f82(x87921)),f2(x87921)),f324(f154(x87921),x87923))),f324(f131(x87921,x87921,f82(x87921),x87922),x87923))
% 18.55/18.49 [9043]P52(x90431,x90432,x90433)+P1(f324(f324(f326(f844(x90431,x90432)),f324(f324(f247(x90431,x90432),f604(x90433,x90432,x90431)),f606(x90433,x90432,x90431))),x90433))
% 18.55/18.49 [9044]P52(x90441,x90442,x90443)+P1(f324(f324(f326(f844(x90441,x90442)),f324(f324(f247(x90441,x90442),f604(x90443,x90442,x90441)),f605(x90443,x90442,x90441))),x90443))
% 18.55/18.49 [9099]~P1(f324(f324(f326(f844(x90991,x90991)),x90992),f324(f324(f282(x90991,x90991,x90991),x90993),f301(x90991,x90993))))+P1(f324(f324(f326(f844(x90991,x90991)),x90992),f324(f324(f172(f844(x90991,x90991),a832),f557(x90993,x90992,x90991)),x90993)))
% 18.55/18.49 [9100]~P1(f324(x91001,f324(f324(f149(x91002),x91003),f324(f180(f839(x91002)),f161(x91002,x91001,x91003)))))+~P1(f324(f324(f232(a838),f324(f180(f839(x91002)),f161(x91002,x91001,x91003))),f324(f180(f839(x91002)),x91003)))
% 18.55/18.49 [9178]~P1(f324(f324(f231(f845(x91781,a832)),x91782),x91783))+P1(f324(f324(f231(f845(x91781,a832)),f324(f324(f9(x91781,f845(x91781,a832),a832),f326(x91781)),x91782)),f324(f324(f9(x91781,f845(x91781,a832),a832),f326(x91781)),x91783)))
% 18.55/18.49 [9234]~P1(f324(f324(f326(f844(f845(x92341,a832),f845(x92341,a832))),f324(f324(f247(f845(x92341,a832),f845(x92341,a832)),x92342),x92343)),f300(x92341)))+P1(f324(f324(f232(f845(x92341,a832)),x92342),x92343))
% 18.55/18.49 [9260]P53(x92601,x92602,x92603)+~P1(f324(f324(f326(f844(x92601,x92601)),f324(f324(f247(x92601,x92601),f334(x92603,x92602,x92601)),f333(x92603,x92602,x92601))),x92603))
% 18.55/18.49 [9261]P53(x92611,x92612,x92613)+~P1(f324(f324(f326(f844(x92611,x92611)),f324(f324(f247(x92611,x92611),f333(x92613,x92612,x92611)),f334(x92613,x92612,x92611))),x92613))
% 18.55/18.49 [9295]~P1(f324(f324(f326(f844(f839(x92951),f839(x92951))),f324(f324(f247(f839(x92951),f839(x92951)),x92952),x92952)),f136(x92951,x92953)))+P1(f324(f324(f326(f844(x92951,x92951)),f324(f324(f247(x92951,x92951),f743(x92952,x92953,x92951)),f743(x92952,x92953,x92951))),x92953))
% 18.55/18.49 [9340]P1(f324(f324(f231(f845(x93401,a832)),x93402),x93403))+~P1(f324(f324(f231(f845(x93401,a832)),f324(f324(f9(x93401,f845(x93401,a832),a832),f326(x93401)),x93402)),f324(f324(f9(x93401,f845(x93401,a832),a832),f326(x93401)),x93403)))
% 18.55/18.49 [9427]E(f324(f324(f3(a838),f324(f324(f8(a838,a838),x94271),f324(f258(a838),x94272))),f324(f324(f8(a838,a838),x94273),f324(f258(a838),x94272))),f324(f324(f8(a838,a838),f324(f324(f20(a838,a838,a838),f324(f324(f10(a838,f845(a838,a838),a838),f3(a838)),x94271)),x94273)),f324(f258(a838),x94272)))+~P1(f324(f324(f231(a838),f324(x94273,f502(x94272,x94271,x94273))),f324(x94271,f502(x94272,x94271,x94273))))
% 18.55/18.49 [9716]E(f324(f257(f844(x97161,x97162)),f324(f252(x97161,x97162,a832),f324(f324(f9(x97161,f845(x97162,f842(x97162)),f845(x97162,a832)),f324(f324(f10(f845(f842(x97162),a832),f845(f845(x97162,f842(x97162)),f845(x97162,a832)),x97161),f10(f842(x97162),a832,x97162)),f324(f324(f10(f842(x97162),f845(f842(x97162),a832),x97161),a321),f165(x97161,x97162,x97163)))),f226(x97162)))),f324(f157(f844(x97161,x97162)),x97163))+~P1(f324(f127(x97161),f324(f324(f141(f844(x97161,x97162),x97161),f246(x97161,x97162)),x97163)))
% 18.55/18.49 [5440]~P63(x54401)+E(f324(f324(f82(x54401),f324(f324(f3(x54401),x54402),x54403)),x54403),x54402)
% 18.55/18.49 [5441]~P63(x54411)+E(f324(f324(f3(x54411),f324(f324(f82(x54411),x54412),x54413)),x54413),x54412)
% 18.55/18.49 [5667]~P63(x56671)+E(f324(f324(f82(x56671),x56672),f324(f324(f82(x56671),f324(f81(x56671),x56672)),x56673)),x56673)
% 18.55/18.49 [5750]~P75(x57501)+E(f324(f324(f83(x57501),f324(f324(f240(x57501),x57502),x57503)),x57502),f324(f324(f240(x57501),x57502),f324(a114,x57503)))
% 18.55/18.49 [5751]~P105(x57511)+E(f324(f324(f83(x57511),f324(f324(f240(x57511),x57512),x57513)),x57512),f324(f324(f240(x57511),x57512),f324(a114,x57513)))
% 18.55/18.49 [5969]~P103(x59691)+E(f324(f77(x59691),f324(f324(f240(x59691),f324(f81(x59691),x59692)),x59693)),f324(f77(x59691),f324(f324(f240(x59691),x59692),x59693)))
% 18.55/18.49 [6020]~P75(x60201)+E(f324(f324(f83(x60201),f324(f324(f240(x60201),x60202),x60203)),x60202),f324(f324(f83(x60201),x60202),f324(f324(f240(x60201),x60202),x60203)))
% 18.55/18.49 [6082]E(f324(f324(f3(a101),f324(f324(f82(a101),x60821),x60822)),x60823),f270(x60821,x60822,x60823))+~P1(f324(f324(f232(a101),x60822),x60823))
% 18.55/18.49 [6104]~E(f324(f324(f128(x61041),x61043),x61042),f115(x61041))+P1(f324(f324(f231(a838),f324(f180(f839(x61041)),x61042)),x61043))
% 18.55/18.49 [6245]E(f324(f324(f83(a838),f324(f106(a838),x62451)),f324(f324(f83(a838),f324(f106(a838),x62452)),x62453)),f2(a838))+~P1(f324(f324(f232(a1),x62451),a85))
% 18.55/18.49 [6261]~P59(x62611)+E(f324(f324(f240(x62611),f324(f324(f284(x62611),f80(x62611)),x62612)),x62613),f324(f324(f284(x62611),f80(x62611)),f324(f324(f240(x62611),x62612),x62613)))
% 18.55/18.49 [6345]E(f324(f324(f3(a838),f324(f324(f82(a838),x63451),x63452)),x63453),f324(f324(f82(a838),x63451),f324(f324(f3(a838),x63452),x63453)))+~P1(f324(f324(f231(a838),x63453),x63452))
% 18.55/18.49 [6346]E(f324(f324(f3(a838),f324(f324(f82(a838),x63461),x63462)),x63463),f324(f324(f3(a838),x63461),f324(f324(f3(a838),x63463),x63462)))+~P1(f324(f324(f231(a838),x63462),x63463))
% 18.55/18.49 [6347]E(f324(f324(f3(a838),f324(f324(f82(a838),x63471),x63472)),x63473),f324(f324(f82(a838),x63471),f324(f324(f3(a838),x63472),x63473)))+~P1(f324(f324(f231(a838),x63473),x63472))
% 18.55/18.49 [6387]~P86(x63871)+P1(f324(f324(f231(x63871),f324(f324(f235(x63871),x63872),x63873)),x63873))
% 18.55/18.49 [6388]~P86(x63881)+P1(f324(f324(f231(x63881),f324(f324(f235(x63881),x63882),x63883)),x63882))
% 18.55/18.49 [6389]~P94(x63891)+P1(f324(f324(f231(x63891),f324(f324(f104(x63891),x63892),x63893)),x63893))
% 18.55/18.49 [6390]~P99(x63901)+P1(f324(f324(f231(x63901),f324(f324(f104(x63901),x63902),x63903)),x63903))
% 18.55/18.49 [6391]~P94(x63911)+P1(f324(f324(f231(x63911),f324(f324(f104(x63911),x63912),x63913)),x63912))
% 18.55/18.49 [6392]~P99(x63921)+P1(f324(f324(f231(x63921),f324(f324(f104(x63921),x63922),x63923)),x63922))
% 18.55/18.49 [6406]E(f324(f324(f42(a1),f324(f324(f42(a1),x64061),x64062)),x64063),f324(f324(f42(a1),x64061),f324(f324(f83(a1),x64062),x64063)))+~P1(f324(f324(f232(a1),f2(a1)),x64063))
% 18.55/18.49 [6459]~P105(x64591)+E(f324(f324(f82(x64591),f324(f324(f83(x64591),x64592),x64593)),x64593),f324(f324(f83(x64591),f324(f324(f82(x64591),x64592),f80(x64591))),x64593))
% 18.55/18.49 [6460]~P89(x64601)+E(f324(f324(f83(x64601),f324(f81(x64601),f324(f106(x64601),x64602))),x64603),f324(f324(f83(x64601),f324(f106(x64601),f324(f81(a1),x64602))),x64603))
% 18.55/18.49 [6533]~P72(x65331)+E(f324(f151(x65331),f324(f324(f141(x65332,x65331),f324(f18(x65331,x65332),f2(x65331))),x65333)),f2(x65331))
% 18.55/18.49 [6552]E(f324(f324(f82(a838),f324(f106(a838),x65521)),f324(f324(f82(a838),f324(f106(a838),x65522)),x65523)),f324(f324(f82(a838),f324(f106(a838),x65522)),x65523))+~P1(f324(a185,f324(f106(a1),x65521)))
% 18.55/18.49 [6567]~P9(x65671)+E(f44(x65671,f324(f324(f303(x65671),x65672),f324(f324(f303(x65671),x65673),f179(f845(x65671,a832))))),f324(f324(f104(x65671),x65672),x65673))
% 18.55/18.49 [6568]~P9(x65681)+E(f43(x65681,f324(f324(f303(x65681),x65682),f324(f324(f303(x65681),x65683),f179(f845(x65681,a832))))),f324(f324(f103(x65681),x65682),x65683))
% 18.55/18.49 [6593]E(f324(f324(f158(x65931),x65932),x65933),x65933)+~P1(f324(f324(f231(a838),f324(f180(f839(x65931)),x65933)),x65932))
% 18.55/18.49 [6604]E(f324(f324(f128(x66041),x66042),x66043),f115(x66041))+~P1(f324(f324(f231(a838),f324(f180(f839(x66041)),x66043)),x66042))
% 18.55/18.49 [6605]E(f324(f324(f128(x66051),x66052),x66053),f115(x66051))+~P1(f324(f324(f231(a838),f324(f180(f839(x66051)),x66053)),x66052))
% 18.55/18.49 [6616]E(f324(f324(f3(a838),f324(f324(f82(a838),x66161),x66162)),x66163),f324(f324(f82(a838),f324(f324(f3(a838),x66161),x66163)),x66162))+~P1(f324(f324(f231(a838),x66163),x66161))
% 18.55/18.49 [6617]E(f324(f324(f3(a838),f324(f324(f82(a838),x66171),x66172)),x66173),f324(f324(f82(a838),f324(f324(f3(a838),x66171),x66173)),x66172))+~P1(f324(f324(f231(a838),x66173),x66171))
% 18.55/18.49 [6631]~P1(f324(f324(f232(a838),x66311),x66313))+P1(f324(f324(f232(a838),f324(f324(f3(a838),x66311),x66312)),x66313))
% 18.55/18.49 [6659]~P86(x66591)+E(f155(x66591,x66592,f324(f324(f137(x66591,x66591,f7(x66591)),x66592),x66593)),x66593)
% 18.55/18.49 [6759]E(f324(f324(f3(a838),f324(f324(f82(a838),x67591),x67592)),f324(a114,x67593)),f324(f324(f3(a838),x67591),f324(a114,f324(f324(f3(a838),x67593),x67592))))+~P1(f324(f324(f231(a838),x67592),x67593))
% 18.55/18.49 [6760]~P103(x67601)+P1(f324(f324(f231(x67601),f2(x67601)),f324(f324(f240(x67601),f324(f77(x67601),x67602)),x67603)))
% 18.55/18.49 [6811]P28(x68111,x68112,x68113)+~P1(f324(f324(f231(f845(f837(x68111),a832)),x68113),x68112))
% 18.55/18.49 [6852]~P1(f324(f64(x68521),x68522))+P1(f324(f64(x68521),f324(f324(f3(f845(x68521,a832)),x68522),x68523)))
% 18.55/18.49 [6853]~P1(f324(f64(x68531),x68533))+P1(f324(f64(x68531),f324(f324(f104(f845(x68531,a832)),x68532),x68533)))
% 18.55/18.49 [6854]~P1(f324(f64(x68541),x68542))+P1(f324(f64(x68541),f324(f324(f104(f845(x68541,a832)),x68542),x68543)))
% 18.55/18.49 [6993]~P36(x69931,x69933)+P36(x69931,f324(f324(f104(f845(f844(x69931,x69931),a832)),x69932),x69933))
% 18.55/18.49 [6994]~P36(x69941,x69942)+P36(x69941,f324(f324(f104(f845(f844(x69941,x69941),a832)),x69942),x69943))
% 18.55/18.49 [7113]~P94(x71131)+E(f12(x71131,f324(f157(x71131),f324(f324(f139(x71131),x71132),x71133))),f324(f131(x71131,x71131,f104(x71131),x71132),x71133))
% 18.55/18.49 [7114]~P86(x71141)+E(f16(x71141,f324(f157(x71141),f324(f324(f139(x71141),x71142),x71143))),f324(f131(x71141,x71141,f178(x71141),x71142),x71143))
% 18.55/18.49 [7115]~P86(x71151)+E(f17(x71151,f324(f157(x71151),f324(f324(f139(x71151),x71152),x71153))),f324(f131(x71151,x71151,f235(x71151),x71152),x71153))
% 18.55/18.49 [7116]~P94(x71161)+E(f15(x71161,f324(f157(x71161),f324(f324(f139(x71161),x71162),x71163))),f324(f131(x71161,x71161,f103(x71161),x71162),x71163))
% 18.55/18.49 [7117]~P1(f324(f324(f280(a1),x71171),x71172))+P1(f324(f324(f280(a1),x71171),f324(f324(f82(a1),x71172),f324(f324(f83(a1),x71171),x71173))))
% 18.55/18.49 [7187]~P1(f324(f64(x71871),x71872))+P1(f324(f324(f231(a838),f324(f41(x71871),x71872)),f324(f41(x71871),f324(f324(f303(x71871),x71873),x71872))))
% 18.55/18.49 [7194]E(f324(f324(f103(f845(a838,a832)),f324(f295(a838,x71941),x71942)),f324(f295(a838,x71942),f324(f324(f82(a838),x71942),x71943))),f324(f295(a838,x71941),f324(f324(f82(a838),x71942),x71943)))+~P1(f324(f324(f231(a838),x71941),x71942))
% 18.55/18.49 [7204]P1(f324(f324(f232(a838),x72041),x72042))+~P1(f324(f324(f232(a838),f324(f324(f82(a838),x72041),x72043)),x72042))
% 18.55/18.49 [7205]P1(f324(f324(f231(a838),x72051),x72052))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x72053),x72051)),x72052))
% 18.55/18.49 [7206]P1(f324(f324(f231(a838),x72061),x72062))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x72061),x72063)),x72062))
% 18.55/18.49 [7207]P1(f324(f324(f231(a838),x72071),x72072))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x72073),x72071)),x72072))
% 18.55/18.49 [7208]P1(f324(f324(f231(a838),x72081),x72082))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x72081),x72083)),x72082))
% 18.55/18.49 [7250]~P86(x72501)+E(f13(x72501,f178(x72501),f324(f157(x72501),f324(f324(f139(x72501),x72502),x72503))),f324(f131(x72501,x72501,f178(x72501),x72502),x72503))
% 18.55/18.49 [7251]~P86(x72511)+E(f14(x72511,f235(x72511),f324(f157(x72511),f324(f324(f139(x72511),x72512),x72513))),f324(f131(x72511,x72511,f235(x72511),x72512),x72513))
% 18.55/18.49 [7255]~E(x72552,f179(f845(f844(x72551,x72551),a832)))+P1(f324(f324(f231(f845(f844(x72551,x72551),a832)),x72552),x72553))
% 18.55/18.49 [7367]E(f324(f324(f103(f845(x73671,a832)),x73672),f324(f324(f3(f845(x73671,a832)),x73673),x73672)),x73673)+~P1(f324(f324(f231(f845(x73671,a832)),x73672),x73673))
% 18.55/18.49 [7370]~P1(f324(f324(f232(a838),x73701),f324(f324(f3(a838),x73703),x73702)))+P1(f324(f324(f232(a838),f324(f324(f82(a838),x73701),x73702)),x73703))
% 18.55/18.49 [7371]~P1(f324(f324(f231(a838),x73711),f324(f324(f82(a838),x73713),x73712)))+P1(f324(f324(f231(a838),f324(f324(f3(a838),x73711),x73712)),x73713))
% 18.55/18.49 [7431]E(x74311,f115(x74312))+E(f324(f130(x74312),f324(f324(f324(f172(f839(x74312),f839(x74312)),x74313),f153(x74312)),x74311)),f324(f324(f149(x74312),x74311),f51(a838,x74313,f324(f180(f839(x74312)),x74311))))
% 18.55/18.49 [7440]E(f324(f324(f303(x74401),x74402),f324(f324(f3(f845(x74401,a832)),x74403),f324(f324(f303(x74401),x74402),f179(f845(x74401,a832))))),x74403)+~P1(f324(f324(f326(x74401),x74402),x74403))
% 18.55/18.49 [7604]P1(f324(f324(f232(a838),x76041),f324(f324(f3(a838),x76042),x76043)))+~P1(f324(f324(f232(a838),f324(f324(f82(a838),x76041),x76043)),x76042))
% 18.55/18.49 [7605]P1(f324(f324(f231(a838),x76051),f324(f324(f82(a838),x76052),x76053)))+~P1(f324(f324(f231(a838),f324(f324(f3(a838),x76051),x76053)),x76052))
% 18.55/18.49 [7626]P1(f324(f64(x76261),x76262))+~P1(f324(f64(x76261),f324(f324(f103(f845(x76261,a832)),x76263),x76262)))
% 18.55/18.49 [7627]P1(f324(f64(x76271),x76272))+~P1(f324(f64(x76271),f324(f324(f103(f845(x76271,a832)),x76272),x76273)))
% 18.55/18.49 [7708]~P44(x77081,x77083)+P1(f324(f324(f326(f844(x77081,x77081)),f324(f324(f247(x77081,x77081),x77082),x77082)),x77083))
% 18.55/18.49 [7760]P1(f324(f324(f280(a1),x77601),x77602))+~P1(f324(f324(f280(a1),x77601),f324(f324(f82(a1),x77602),f324(f324(f83(a1),x77601),x77603))))
% 18.55/18.49 [7840]E(f324(f324(f149(a838),f129(a838,f324(f295(a838,x78401),x78402))),x78403),f324(f324(f82(a838),x78401),x78403))+~P1(f324(f324(f232(a838),f324(f324(f82(a838),x78401),x78403)),x78402))
% 18.55/18.49 [7911]~P1(f324(f324(f186(f324(a27,x79111)),x79112),x79113))+P1(f324(f324(f186(f324(f230(a833),f324(a30,x79111))),x79112),x79113))
% 18.55/18.49 [7912]~P1(f324(f324(f186(f324(a27,x79121)),x79122),x79123))+P1(f324(f324(f186(f324(f230(a833),f324(a30,x79121))),x79122),x79123))
% 18.55/18.49 [7916]E(f324(f324(f158(a838),x79161),f129(a838,f324(f295(a838,x79162),x79163))),f129(a838,f324(f295(a838,x79162),f324(f324(f82(a838),x79162),x79161))))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x79162),x79161)),x79163))
% 18.55/18.49 [7966]~P89(x79661)+E(f324(f324(f240(x79661),x79662),f324(f106(a838),f324(f324(f82(a1),x79663),x79663))),f324(f324(f88(x79661,x79661),f324(f324(f240(x79661),x79662),f324(f106(a838),x79663))),f324(f324(f20(x79661,x79661,x79661),f83(x79661)),f7(x79661))))
% 18.55/18.49 [8170]P1(f324(f324(f186(f324(a27,x81701)),x81702),x81703))+~P1(f324(f324(f186(f324(f230(a833),f324(a30,x81701))),x81702),x81703))
% 18.55/18.49 [8171]P1(f324(f324(f186(f324(a27,x81711)),x81712),x81713))+~P1(f324(f324(f186(f324(f230(a833),f324(a30,x81711))),x81712),x81713))
% 18.55/18.49 [8228]E(f324(f324(f125(x82281),f324(f324(f158(x82281),x82282),x82283)),f324(f324(f139(x82281),f324(f324(f149(x82281),x82283),x82282)),f324(f324(f128(x82281),f324(a114,x82282)),x82283))),x82283)+~P1(f324(f324(f232(a838),x82282),f324(f180(f839(x82281)),x82283)))
% 18.55/18.49 [8235]P1(f324(f324(f231(f845(x82351,a832)),f313(x82351,x82352)),f313(x82351,x82353)))+~P1(f324(f324(f231(f845(x82351,f845(x82351,a832))),x82353),x82352))
% 18.55/18.49 [8236]~P53(x82361,x82362,x82363)+P53(x82361,x82362,f324(f324(f3(f845(f844(x82361,x82361),a832)),x82363),f301(x82361,f179(f845(f844(x82361,x82361),a832)))))
% 18.55/18.49 [8258]P1(f324(f324(f231(f845(x82581,a832)),f314(x82581,x82582)),f314(x82581,x82583)))+~P1(f324(f324(f231(f845(f844(x82581,x82581),a832)),x82583),x82582))
% 18.55/18.49 [8265]~P118(x82651)+P1(f324(f324(f231(x82651),f2(x82651)),f324(f324(f82(x82651),f324(f324(f83(x82651),x82652),x82652)),f324(f324(f83(x82651),x82653),x82653))))
% 18.55/18.49 [8296]~P89(x82961)+E(f324(f324(f240(x82961),f324(f106(x82961),x82962)),f324(f106(a838),f324(f324(f82(a1),x82963),x82963))),f324(f324(f88(x82961,x82961),f324(f324(f240(x82961),f324(f106(x82961),x82962)),f324(f106(a838),x82963))),f324(f324(f20(x82961,x82961,x82961),f83(x82961)),f7(x82961))))
% 18.55/18.49 [8301]P1(f324(f324(f231(f845(x83011,a832)),f324(f277(x83011),x83012)),f324(f277(x83011),x83013)))+~P1(f324(f324(f231(f845(f844(x83011,x83011),a832)),x83012),x83013))
% 18.55/18.49 [8333]~P48(x83331,x83332)+~P1(f324(f324(f326(f844(x83331,x83331)),f324(f324(f247(x83331,x83331),x83333),x83333)),x83332))
% 18.55/18.49 [8334]~P36(x83341,x83342)+~P1(f324(f324(f326(f844(x83341,x83341)),f324(f324(f247(x83341,x83341),x83343),x83343)),x83342))
% 18.55/18.49 [8335]~P36(x83351,x83352)+~P1(f324(f324(f326(f844(x83351,x83351)),f324(f324(f247(x83351,x83351),x83353),x83353)),x83352))
% 18.55/18.49 [8376]~E(x83762,x83763)+P1(f324(f324(f326(f844(x83761,x83761)),f324(f324(f247(x83761,x83761),x83762),x83763)),f301(x83761,f179(f845(f844(x83761,x83761),a832)))))
% 18.55/18.49 [8397]P1(f324(f324(f231(f845(x83971,a832)),f44(f845(x83971,a832),x83972)),f44(f845(x83971,a832),x83973)))+~P1(f324(f324(f231(f845(f845(x83971,a832),a832)),x83973),x83972))
% 18.55/18.49 [8398]P1(f324(f324(f231(f845(x83981,a832)),f43(f845(x83981,a832),x83982)),f43(f845(x83981,a832),x83983)))+~P1(f324(f324(f231(f845(f845(x83981,a832),a832)),x83982),x83983))
% 18.55/18.49 [8450]~P12(x84501,x84503,x84502)+P1(f324(f324(f231(f845(f844(x84501,x84501),a832)),x84502),f324(f324(f249(x84501,x84501),x84503),f324(f18(f845(x84501,a832),x84501),x84503))))
% 18.55/18.49 [8451]~P47(x84511,x84513,x84512)+P1(f324(f324(f231(f845(f844(x84511,x84511),a832)),x84512),f324(f324(f249(x84511,x84511),x84513),f324(f18(f845(x84511,a832),x84511),x84513))))
% 18.55/18.49 [8489]~P78(x84891)+P1(f324(f324(f231(x84891),f324(f324(f3(x84891),f324(f77(x84891),x84892)),f324(f77(x84891),x84893))),f324(f77(x84891),f324(f324(f3(x84891),x84893),x84892))))
% 18.55/18.49 [8490]~P78(x84901)+P1(f324(f324(f231(x84901),f324(f324(f3(x84901),f324(f77(x84901),x84902)),f324(f77(x84901),x84903))),f324(f77(x84901),f324(f324(f3(x84901),x84902),x84903))))
% 18.55/18.49 [8514]P1(f324(f324(f231(f845(f844(x85141,x85141),a832)),f301(x85141,x85142)),f301(x85141,x85143)))+~P1(f324(f324(f231(f845(f844(x85141,x85141),a832)),x85142),x85143))
% 18.55/18.49 [8664]P53(x86641,x86642,x86643)+~P53(x86641,x86642,f324(f324(f3(f845(f844(x86641,x86641),a832)),x86643),f301(x86641,f179(f845(f844(x86641,x86641),a832)))))
% 18.55/18.49 [8683]P1(f324(f324(f231(f845(f844(f839(x86831),f839(x86831)),a832)),f145(x86831,x86832)),f145(x86831,x86833)))+~P1(f324(f324(f231(f845(f844(x86831,x86831),a832)),x86832),x86833))
% 18.55/18.49 [8684]P1(f324(f324(f231(f845(f844(f839(x86841),f839(x86841)),a832)),f144(x86841,x86842)),f144(x86841,x86843)))+~P1(f324(f324(f231(f845(f844(x86841,x86841),a832)),x86842),x86843))
% 18.55/18.49 [8701]~P47(x87011,x87013,x87012)+P1(f324(f324(f231(f845(f844(x87011,x87011),a832)),x87012),f324(f324(f282(x87011,x87011,x87011),f324(f279(x87011,x87011),x87012)),x87012)))
% 18.55/18.49 [8729]~P1(f324(f127(x87291),x87293))+P1(f324(f127(x87291),f324(f324(f128(x87291),f324(f180(f839(x87291)),f161(x87291,x87292,x87293))),x87293)))
% 18.55/18.49 [8743]~P1(f324(f127(x87431),x87432))+E(f324(f126(x87431,f324(f324(f9(x87431,f845(x87431,a832),a832),f326(x87431)),f324(f157(x87431),f159(x87431,x87432,x87433)))),x87432),f159(x87431,x87432,x87433))
% 18.55/18.49 [8790]E(x87901,x87902)+~P1(f324(f324(f326(f844(x87903,x87903)),f324(f324(f247(x87903,x87903),x87901),x87902)),f301(x87903,f179(f845(f844(x87903,x87903),a832)))))
% 18.55/18.49 [8870]P1(f324(f324(f326(x88701),x88702),f314(x88701,x88703)))+P1(f324(f324(f326(f844(x88701,x88701)),f324(f324(f247(x88701,x88701),f805(x88703,x88702,x88701)),x88702)),x88703))
% 18.55/18.49 [8871]P1(f324(f324(f326(x88711),x88712),f314(x88711,x88713)))+P1(f324(f324(f326(f844(x88711,x88711)),f324(f324(f247(x88711,x88711),f809(x88713,x88712,x88711)),x88712)),x88713))
% 18.55/18.49 [8872]P1(f324(f324(f326(x88721),x88722),f314(x88721,x88723)))+P1(f324(f324(f326(f844(x88721,x88721)),f324(f324(f247(x88721,x88721),f816(x88723,x88722,x88721)),x88722)),x88723))
% 18.55/18.49 [8970]P1(f324(x89703,x89702))+E(f324(f257(x89701),f324(f324(f20(x89701,a832,a832),f324(f324(f10(a832,f845(a832,a832),x89701),a322),f324(a321,x89702))),x89703)),f179(f845(x89701,a832)))
% 18.55/18.49 [8989]~P78(x89891)+P1(f324(f324(f231(x89891),f324(f77(x89891),f324(f324(f3(x89891),f324(f77(x89891),x89892)),f324(f77(x89891),x89893)))),f324(f77(x89891),f324(f324(f3(x89891),x89892),x89893))))
% 18.55/18.49 [9002]~P1(f324(x90023,x90022))+E(f324(f257(x90021),f324(f324(f20(x90021,a832,a832),f324(f324(f10(a832,f845(a832,a832),x90021),a322),f324(a321,x90022))),x90023)),f324(f324(f303(x90021),x90022),f179(f845(x90021,a832))))
% 18.55/18.49 [9008]~P1(f324(f324(f326(f845(x90081,a832)),x90083),f324(f302(x90081),x90082)))+P1(f324(f243(x90081,f324(f324(f9(x90081,f845(x90081,a832),a832),f326(x90081)),x90082)),x90083))
% 18.55/18.49 [9042]P36(x90421,x90422)+P1(f324(f324(f326(f844(x90421,x90421)),f324(f324(f247(x90421,x90421),f324(f353(x90422,x90421),f324(a114,x90423))),f324(f353(x90422,x90421),x90423))),x90422))
% 18.55/18.49 [9170]P1(f324(f324(f326(f845(x91701,a832)),x91702),f324(f302(x91701),x91703)))+~P1(f324(f243(x91701,f324(f324(f9(x91701,f845(x91701,a832),a832),f326(x91701)),x91703)),x91702))
% 18.55/18.49 [9230]P1(f324(f324(f326(x92301),f324(f266(x92301,x92302),x92303)),f324(f157(x92301),f324(f324(f141(f844(a101,x92301),x92301),f251(a101,x92301)),x92302))))+~P1(f324(f324(f232(a101),x92303),f324(f151(a101),f324(f324(f141(f844(a101,x92301),a101),f246(a101,x92301)),x92302))))
% 18.55/18.49 [9278]P1(f324(f324(f231(f845(f844(f839(x92781),f839(x92781)),a832)),f145(x92781,x92782)),f324(f324(f249(f839(x92781),f839(x92781)),f147(x92781,x92783)),f324(f18(f845(f839(x92781),a832),f839(x92781)),f147(x92781,x92783)))))+~P1(f324(f324(f231(f845(f844(x92781,x92781),a832)),x92782),f324(f324(f249(x92781,x92781),x92783),f324(f18(f845(x92781,a832),x92781),x92783))))
% 18.55/18.49 [9298]P1(f324(f324(f326(x92981),f324(f246(x92981,f844(a101,a101)),f324(f264(x92981,x92982),x92983))),f324(f157(x92981),f324(f324(f141(f844(a101,x92981),x92981),f251(a101,x92981)),x92982))))+~P1(f324(f324(f232(a101),f2(a101)),f324(f151(a101),f324(f324(f141(f844(a101,x92981),a101),f246(a101,x92981)),x92982))))
% 18.55/18.49 [9313]~P1(f324(f324(f231(f845(f844(x93131,x93131),a832)),x93132),f324(f324(f249(x93131,x93131),x93133),f324(f18(f845(x93131,a832),x93131),x93133))))+P1(f324(f324(f231(f845(f844(x93131,x93131),a832)),f324(f324(f282(x93131,x93131,x93131),x93132),f301(x93131,x93132))),f324(f324(f249(x93131,x93131),x93133),f324(f18(f845(x93131,a832),x93131),x93133))))
% 18.55/18.49 [9600]~P36(x96001,x96002)+~P1(f324(f324(f326(f844(x96001,x96001)),f324(f324(f247(x96001,x96001),f324(x96003,f324(a114,f354(x96002,x96001,x96003)))),f324(x96003,f354(x96002,x96001,x96003)))),x96002))
% 18.55/18.49 [9601]~P36(x96011,x96012)+~P1(f324(f324(f326(f844(x96011,x96011)),f324(f324(f247(x96011,x96011),f324(x96013,f324(a114,f364(x96013,x96012,x96011)))),f324(x96013,f364(x96013,x96012,x96011)))),x96012))
% 18.55/18.49 [9857]P1(f324(f324(f231(f845(f844(f845(x98571,a832),f845(x98571,a832)),a832)),f324(f324(f282(f845(x98571,a832),f845(x98571,a832),f845(x98571,a832)),f316(x98571,x98572)),f324(f324(f103(f845(f844(f845(x98571,a832),f845(x98571,a832)),a832)),f316(x98571,x98573)),f324(f324(f303(f844(f845(x98571,a832),f845(x98571,a832))),f324(f324(f247(f845(x98571,a832),f845(x98571,a832)),f179(f845(x98571,a832))),f179(f845(x98571,a832)))),f179(f845(f844(f845(x98571,a832),f845(x98571,a832)),a832)))))),f316(x98571,x98572)))+~P1(f324(f324(f231(f845(f844(x98571,x98571),a832)),f324(f324(f282(x98571,x98571,x98571),x98572),x98573)),x98572))
% 18.55/18.49 [9858]P1(f324(f324(f231(f845(f844(f845(x98581,a832),f845(x98581,a832)),a832)),f324(f324(f282(f845(x98581,a832),f845(x98581,a832),f845(x98581,a832)),f317(x98581,x98582)),f324(f324(f103(f845(f844(f845(x98581,a832),f845(x98581,a832)),a832)),f317(x98581,x98583)),f324(f324(f303(f844(f845(x98581,a832),f845(x98581,a832))),f324(f324(f247(f845(x98581,a832),f845(x98581,a832)),f179(f845(x98581,a832))),f179(f845(x98581,a832)))),f179(f845(f844(f845(x98581,a832),f845(x98581,a832)),a832)))))),f317(x98581,x98582)))+~P1(f324(f324(f231(f845(f844(x98581,x98581),a832)),f324(f324(f282(x98581,x98581,x98581),x98582),x98583)),x98582))
% 18.55/18.49 [7112]~P1(f324(f324(f231(a838),x71122),x71121))+E(f324(f324(f3(a838),f324(a114,f324(f324(f3(a838),x71121),x71122))),x71123),f324(f324(f3(a838),f324(a114,x71121)),f324(f324(f82(a838),x71122),x71123)))
% 18.55/18.49 [7152]~P7(x71521)+E(f324(f324(f82(x71521),f51(x71521,x71522,x71523)),f324(f324(f83(x71521),f324(f324(f42(x71521),x71522),x71523)),x71523)),x71522)
% 18.55/18.49 [7375]E(f324(f324(f83(a838),f324(f106(a838),x73751)),f324(f324(f83(a838),f324(f106(a838),x73752)),x73753)),f324(f324(f83(a838),f324(f106(a838),f324(f324(f83(a1),x73751),x73752))),x73753))+P1(f324(f324(f232(a1),x73751),a85))
% 18.55/18.49 [7851]~P1(f324(f324(f231(a838),x78513),x78512))+P1(f324(f324(f231(a838),x78511),f324(f324(f3(a838),f324(f324(f82(a838),x78512),x78511)),x78513)))
% 18.55/18.49 [8052]~P1(f324(f324(f231(a838),x80521),x80522))+E(f324(f324(f125(a838),f129(a838,f324(f295(a838,x80521),x80522))),f129(a838,f324(f295(a838,x80522),f324(f324(f82(a838),x80522),x80523)))),f129(a838,f324(f295(a838,x80521),f324(f324(f82(a838),x80522),x80523))))
% 18.55/18.49 [8309]~P1(f324(f64(x83091),x83092))+E(f324(a114,f324(f41(x83091),f324(f324(f3(f845(x83091,a832)),x83092),f324(f324(f303(x83091),x83093),f179(f845(x83091,a832)))))),f324(f41(x83091),f324(f324(f303(x83091),x83093),x83092)))
% 18.55/18.49 [8355]~P1(f324(f64(x83551),x83552))+E(f324(f324(f82(a838),f80(a838)),f324(f41(x83551),f324(f324(f3(f845(x83551,a832)),x83552),f324(f324(f303(x83551),x83553),f179(f845(x83551,a832)))))),f324(f41(x83551),f324(f324(f303(x83551),x83553),x83552)))
% 18.55/18.49 [8523]E(f324(f324(f3(a838),f324(f41(x85231),x85232)),f324(f41(x85231),f324(f324(f104(f845(x85231,a832)),x85232),x85233))),f324(f41(x85231),f324(f324(f3(f845(x85231,a832)),x85232),x85233)))+~P1(f324(f64(x85231),f324(f324(f104(f845(x85231,a832)),x85232),x85233)))
% 18.55/18.49 [8740]~P10(f324(x87402,f408(x87402,x87403,x87401)))+E(f324(f102(a1),f324(f324(f11(x87401,a838),f324(f324(f10(a1,a838,x87401),a107),x87402)),x87403)),f324(f324(f11(x87401,a1),x87402),x87403))
% 18.55/18.49 [8741]~P10(f324(x87412,f493(x87412,x87413,x87411)))+E(f324(f102(a1),f324(f324(f8(x87411,a838),f324(f324(f10(a1,a838,x87411),a107),x87412)),x87413)),f324(f324(f8(x87411,a1),x87412),x87413))
% 18.55/18.49 [8774]~P1(f324(f64(x87741),x87743))+P1(f324(f324(f231(a838),f324(f324(f3(a838),f324(f41(x87741),x87742)),f324(f41(x87741),x87743))),f324(f41(x87741),f324(f324(f3(f845(x87741,a832)),x87742),x87743))))
% 18.55/18.49 [8798]P1(f324(f324(f326(x87981),f408(x87982,x87983,x87981)),x87983))+E(f324(f102(a1),f324(f324(f11(x87981,a838),f324(f324(f10(a1,a838,x87981),a107),x87982)),x87983)),f324(f324(f11(x87981,a1),x87982),x87983))
% 18.55/18.49 [8799]P1(f324(f324(f326(x87991),f493(x87992,x87993,x87991)),x87993))+E(f324(f102(a1),f324(f324(f8(x87991,a838),f324(f324(f10(a1,a838,x87991),a107),x87992)),x87993)),f324(f324(f8(x87991,a1),x87992),x87993))
% 18.55/18.49 [8864]E(f87(x88641,f324(f324(f9(x88641,f845(x88641,a832),a832),f326(x88641)),f324(f324(f3(f845(x88641,a832)),x88642),f324(f324(f303(x88641),x88643),f179(f845(x88641,a832)))))),f242(x88641,x88643,x88642))+P1(f324(f324(f231(f845(x88641,a832)),x88642),f324(f324(f303(x88641),x88643),f179(f845(x88641,a832)))))
% 18.55/18.49 [9171]E(f324(f324(f141(f839(x91711),x91711),f324(f324(f9(f839(x91711),a838,x91711),f149(x91711)),x91712)),f324(f126(f839(x91711),f324(f324(f10(a838,a832,f839(x91711)),f324(f232(a838),x91712)),f180(f839(x91711)))),x91713)),f324(f324(f149(f839(x91711)),f163(x91711,x91713)),x91712))+~P1(f324(f324(f232(a838),x91712),f324(f180(f839(f839(x91711))),f163(x91711,x91713))))
% 18.55/18.49 [9382]E(f324(f324(f128(x93821),f324(f180(f839(x93821)),f161(x93821,x93822,x93823))),x93823),f115(x93821))+~P1(f324(x93822,f324(f130(x93821),f324(f324(f128(x93821),f324(f180(f839(x93821)),f161(x93821,x93822,x93823))),x93823))))
% 18.55/18.49 [9474]~P1(f324(f324(f326(f844(x94741,x94741)),x94742),f301(x94741,x94743)))+P1(f324(f324(f326(f844(x94741,x94741)),x94742),f324(f324(f45(a838,f845(f844(x94741,x94741),a832)),f238(f845(a838,a832))),f324(f324(f9(a838,f845(f844(x94741,x94741),a832),f845(f844(x94741,x94741),a832)),f172(f844(x94741,x94741),a832)),x94743))))
% 18.55/18.49 [9528]~P1(f324(f324(f231(f845(x95281,a832)),f324(f324(f45(a838,f845(x95281,a832)),f324(f295(a838,f2(a838)),f552(x95283,x95282,x95281))),x95282)),x95283))+P1(f324(f324(f231(f845(x95281,a832)),f324(f324(f45(a838,f845(x95281,a832)),f238(f845(a838,a832))),x95282)),x95283))
% 18.55/18.49 [9576]~P1(f324(f324(f232(a1),f2(a1)),x95763))+P1(f324(f324(f232(a1),x95761),f324(f324(f82(a1),x95762),f324(f324(f83(a1),f324(f324(f82(a1),f324(f77(a1),f324(f324(f3(a1),x95762),x95761))),f80(a1))),x95763))))
% 18.55/18.49 [9587]~P36(x95871,f324(f324(f103(f845(f844(x95871,x95871),a832)),x95872),x95873))+P36(x95871,f324(f324(f103(f845(f844(x95871,x95871),a832)),f324(f324(f103(f845(f844(x95871,x95871),a832)),f324(f324(f282(x95871,x95871,x95871),x95872),x95872)),f324(f324(f282(x95871,x95871,x95871),x95873),x95872))),x95873))
% 18.55/18.49 [9656]P36(x96561,f324(f324(f103(f845(f844(x96561,x96561),a832)),x96562),x96563))+~P36(x96561,f324(f324(f103(f845(f844(x96561,x96561),a832)),f324(f324(f103(f845(f844(x96561,x96561),a832)),f324(f324(f282(x96561,x96561,x96561),x96562),x96562)),f324(f324(f282(x96561,x96561,x96561),x96563),x96562))),x96563))
% 18.55/18.49 [9252]~P119(x92521)+E(f324(f105(x92521),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x92522),x92523)),f179(f845(f844(a838,a838),a832)))))),f324(f324(f3(x92521),f324(f102(x92521),x92522)),f324(f102(x92521),x92523)))
% 18.55/18.49 [9331]P1(f324(x93313,x93312))+E(f324(f257(x93311),f324(f324(f20(x93311,a832,a832),f324(f324(f10(a832,f845(a832,a832),x93311),a322),f324(f324(f9(x93311,x93311,a832),a321),x93312))),x93313)),f179(f845(x93311,a832)))
% 18.55/18.49 [9333]~P1(f324(x93333,x93332))+E(f324(f257(x93331),f324(f324(f20(x93331,a832,a832),f324(f324(f10(a832,f845(a832,a832),x93331),a322),f324(f324(f9(x93331,x93331,a832),a321),x93332))),x93333)),f324(f324(f303(x93331),x93332),f179(f845(x93331,a832))))
% 18.55/18.49 [9556]E(x95561,x95562)+P1(f324(f324(f239(x95563,x95563,f324(f324(f10(f845(x95563,a832),f845(x95563,a832),x95563),f324(f10(a832,a832,x95563),a320)),a321)),x95561),x95562))
% 18.55/18.49 [9634]~E(x96341,x96342)+~P1(f324(f324(f239(x96343,x96343,f324(f324(f10(f845(x96343,a832),f845(x96343,a832),x96343),f324(f10(a832,a832,x96343),a320)),a321)),x96341),x96342))
% 18.55/18.49 [9648]~P1(f324(f64(x96481),x96483))+E(f324(f324(f67(x96481,f845(x96481,a832),f324(f324(f10(f845(x96481,a832),f845(f845(x96481,a832),f845(x96481,a832)),x96481),f324(f9(f845(x96481,a832),f845(x96481,a832),f845(x96481,a832)),f3(f845(x96481,a832)))),f324(f324(f9(x96481,f845(x96481,a832),f845(x96481,a832)),f303(x96481)),f179(f845(x96481,a832))))),x96482),x96483),f324(f324(f3(f845(x96481,a832)),x96482),x96483))
% 18.55/18.49 [9680]~P1(f324(f324(f232(a1),f2(a1)),x96803))+P1(f324(f324(f232(a1),f324(f324(f3(a1),x96801),f324(f324(f83(a1),f324(f324(f82(a1),f324(f77(a1),f324(f324(f3(a1),x96801),x96802))),f80(a1))),x96803))),x96802))
% 18.55/18.49 [9923]~P1(f324(f324(f326(x99231),x99233),f314(x99231,x99232)))+P1(f324(f313(x99231,f324(f324(f9(x99231,f845(f844(x99231,x99231),a832),f845(x99231,a832)),f324(f324(f10(f845(x99231,f845(f845(f844(x99231,x99231),a832),a832)),f845(f845(f844(x99231,x99231),a832),f845(x99231,a832)),x99231),f9(x99231,f845(f844(x99231,x99231),a832),a832)),f324(f324(f10(f845(x99231,f844(x99231,x99231)),f845(x99231,f845(f845(f844(x99231,x99231),a832),a832)),x99231),f324(f10(f844(x99231,x99231),f845(f845(f844(x99231,x99231),a832),a832),x99231),f326(f844(x99231,x99231)))),f247(x99231,x99231)))),x99232)),x99233))
% 18.55/18.49 [9935]P1(f324(f324(f326(x99351),x99352),f314(x99351,x99353)))+~P1(f324(f313(x99351,f324(f324(f9(x99351,f845(f844(x99351,x99351),a832),f845(x99351,a832)),f324(f324(f10(f845(x99351,f845(f845(f844(x99351,x99351),a832),a832)),f845(f845(f844(x99351,x99351),a832),f845(x99351,a832)),x99351),f9(x99351,f845(f844(x99351,x99351),a832),a832)),f324(f324(f10(f845(x99351,f844(x99351,x99351)),f845(x99351,f845(f845(f844(x99351,x99351),a832),a832)),x99351),f324(f10(f844(x99351,x99351),f845(f845(f844(x99351,x99351),a832),a832),x99351),f326(f844(x99351,x99351)))),f247(x99351,x99351)))),x99353)),x99352))
% 18.55/18.49 [9526]~P1(f324(f64(x95261),f324(f257(x95261),x95263)))+P1(f324(f64(x95261),f324(f257(x95261),f324(f324(f20(x95261,a832,a832),f324(f324(f10(a832,f845(a832,a832),x95261),a322),x95262)),x95263))))
% 18.55/18.49 [9527]~P1(f324(f64(x95271),f324(f257(x95271),x95272)))+P1(f324(f64(x95271),f324(f257(x95271),f324(f324(f20(x95271,a832,a832),f324(f324(f10(a832,f845(a832,a832),x95271),a322),x95272)),x95273))))
% 18.55/18.49 [9614]P1(f324(f64(x96141),f324(f257(x96141),x96142)))+~P1(f324(f64(x96141),f324(f257(x96141),f324(f324(f20(x96141,a832,a832),f324(f324(f10(a832,f845(a832,a832),x96141),a323),x96143)),x96142))))
% 18.55/18.49 [9615]P1(f324(f64(x96151),f324(f257(x96151),x96152)))+~P1(f324(f64(x96151),f324(f257(x96151),f324(f324(f20(x96151,a832,a832),f324(f324(f10(a832,f845(a832,a832),x96151),a323),x96152)),x96153))))
% 18.55/18.49 [9909]~P1(f324(f64(x99091),x99092))+P1(f324(f64(f839(x99091)),f324(f257(f839(x99091)),f324(f324(f20(f839(x99091),a832,a832),f324(f324(f10(a832,f845(a832,a832),f839(x99091)),a322),f324(f324(f9(f839(x99091),f845(x99091,a832),a832),f324(f324(f10(f845(x99091,a832),f845(f845(x99091,a832),a832),f839(x99091)),f231(f845(x99091,a832))),f157(x99091))),x99092))),f324(f324(f9(f839(x99091),a838,a832),f324(f324(f10(a838,f845(a838,a832),f839(x99091)),a321),f180(f839(x99091)))),x99093)))))
% 18.55/18.49 [9910]~P1(f324(f64(x99101),x99102))+P1(f324(f64(f839(x99101)),f324(f257(f839(x99101)),f324(f324(f20(f839(x99101),a832,a832),f324(f324(f10(a832,f845(a832,a832),f839(x99101)),a322),f324(f324(f9(f839(x99101),f845(x99101,a832),a832),f324(f324(f10(f845(x99101,a832),f845(f845(x99101,a832),a832),f839(x99101)),f231(f845(x99101,a832))),f157(x99101))),x99102))),f324(f324(f9(f839(x99101),a838,a832),f324(f324(f10(a838,f845(a838,a832),f839(x99101)),f231(a838)),f180(f839(x99101)))),x99103)))))
% 18.55/18.49 [9628]~P105(x96281)+E(f324(f324(f240(x96281),x96282),f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x96283)),f324(f324(f83(x96281),f324(f324(f240(x96281),x96282),x96283)),f324(f324(f240(x96281),x96282),x96283)))
% 18.55/18.49 [9661]~P75(x96611)+E(f324(f324(f240(x96611),f324(f324(f240(x96611),x96612),x96613)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f240(x96611),x96612),f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x96613)))
% 18.55/18.49 [9720]~P119(x97201)+E(f324(f324(f240(x97201),f324(f81(x97201),x97202)),f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97203)),f324(f324(f240(x97201),x97202),f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97203)))
% 18.55/18.49 [9862]~P103(x98621)+P1(f324(f324(f231(x98621),f2(x98621)),f324(f324(f82(x98621),f324(f324(f240(x98621),x98622),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98621),x98623),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))))
% 18.55/18.49 [9730]~P105(x97301)+E(f324(f324(f240(x97301),x97302),f324(a114,f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97303))),f324(f324(f83(x97301),x97302),f324(f324(f83(x97301),f324(f324(f240(x97301),x97302),x97303)),f324(f324(f240(x97301),x97302),x97303))))
% 18.55/18.49 [9778]~P75(x97781)+E(f324(f324(f83(x97781),x97782),f324(f324(f240(x97781),f324(f324(f240(x97781),x97782),x97783)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x97781),x97782),f324(a114,f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97783))))
% 18.55/18.49 [9822]~P103(x98221)+P1(f324(f324(f231(x98221),f2(x98221)),f324(f324(f240(x98221),x98222),f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98223))))
% 18.55/18.49 [9891]~P89(x98911)+E(f324(f324(f82(x98911),f324(f324(f82(x98911),f324(f324(f240(x98911),x98912),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98911),x98913),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f324(f324(f83(x98911),f324(f324(f83(x98911),f324(f106(x98911),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98912)),x98913)),f324(f324(f240(x98911),f324(f324(f82(x98911),x98912),x98913)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.49 [9892]~P89(x98921)+E(f324(f324(f3(x98921),f324(f324(f82(x98921),f324(f324(f240(x98921),x98922),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98921),x98923),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f324(f324(f83(x98921),f324(f324(f83(x98921),f324(f106(x98921),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x98922)),x98923)),f324(f324(f240(x98921),f324(f324(f3(x98921),x98922),x98923)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.55/18.49 [4508]E(x45081,x45082)+~E(f28(x45083,x45081),f28(x45084,x45082))
% 18.55/18.49 [4509]E(x45091,x45092)+~E(f28(x45091,x45093),f28(x45092,x45094))
% 18.55/18.49 [4510]E(x45101,x45102)+~E(f36(x45103,x45101),f36(x45104,x45102))
% 18.55/18.49 [4511]E(x45111,x45112)+~E(f36(x45111,x45113),f36(x45112,x45114))
% 18.55/18.49 [4512]E(x45121,x45122)+~E(f35(x45123,x45121),f35(x45124,x45122))
% 18.55/18.49 [4513]E(x45131,x45132)+~E(f35(x45131,x45133),f35(x45132,x45134))
% 18.55/18.49 [5632]P39(f35(x56321,x56323),x56322,x56324,x56322)+P1(f324(x56321,x56322))
% 18.55/18.49 [5633]P39(f35(x56331,x56333),x56332,x56334,x56332)+P1(f324(x56331,x56332))
% 18.55/18.49 [6798]~P39(x67981,x67982,x67983,x67984)+P39(x67981,x67982,f324(a114,x67983),x67984)
% 18.55/18.49 [7646]P29(x76461,x76462,x76463,x76464)+~E(f520(x76464,x76463,x76462,x76461),f524(x76464,x76463,x76462,x76461))
% 18.55/18.49 [8156]~P29(x81561,f842(x81562),x81564,f168(x81561,x81562,x81564))+P29(x81561,f842(x81562),f169(x81561,x81562,x81563,x81564),f168(x81561,x81562,x81564))
% 18.55/18.49 [8370]~P29(x83701,f842(x83702),f169(x83701,x83702,x83704,x83703),f168(x83701,x83702,x83703))+P29(x83701,f842(x83702),x83703,f168(x83701,x83702,x83703))
% 18.55/18.49 [4878]~P21(x48783,x48781,x48784)+E(f324(f324(x48781,x48782),x48782),x48782)
% 18.55/18.49 [5155]~E(x51554,f179(f845(x51551,a832)))+E(f324(f304(x51551,x51552,x51553),x51554),f179(f845(x51552,a832)))
% 18.55/18.49 [5156]~E(x51564,f179(f845(x51561,a832)))+E(f324(f304(x51561,x51562,x51563),x51564),f179(f845(x51562,a832)))
% 18.55/18.49 [5420]~E(f324(f304(x54202,x54203,x54204),x54201),f179(f845(x54203,a832)))+E(x54201,f179(f845(x54202,a832)))
% 18.55/18.49 [5421]~E(f324(f304(x54212,x54213,x54214),x54211),f179(f845(x54213,a832)))+E(x54211,f179(f845(x54212,a832)))
% 18.55/18.49 [5713]~P86(x57132)+E(f324(f324(f137(x57131,x57132,x57133),x57134),f115(x57131)),f324(f324(f139(x57131),x57134),f115(x57131)))
% 18.55/18.49 [5748]E(f324(x57481,x57482),f182(x57483))+P1(f324(f324(f326(x57484),x57482),f168(x57484,x57483,x57481)))
% 18.55/18.49 [6076]~E(x60761,f179(f845(x60762,a832)))+~P1(f324(f65(x60762,x60763,x60761),x60764))
% 18.55/18.49 [6097]~P56(x60971,x60973,x60974,x60972)+P1(f324(f64(x60971),x60972))
% 18.55/18.49 [6098]~P56(x60981,x60983,x60982,x60984)+P1(f324(f64(x60981),x60982))
% 18.55/18.49 [6105]~P56(x61052,x61053,x61054,x61051)+~E(x61051,f179(f845(x61052,a832)))
% 18.55/18.49 [6137]~P85(x61371)+E(f324(f324(f104(f845(x61371,a832)),f324(f295(x61371,x61372),x61373)),f296(x61371,x61373,x61374)),f179(f845(x61371,a832)))
% 18.55/18.49 [6166]~P1(f324(f324(x61663,x61664),x61662))+P1(f324(f324(f326(x61661),x61662),f288(x61661,x61663,x61664)))
% 18.55/18.49 [6167]~P1(f324(f324(x61673,x61674),x61672))+P1(f324(f324(f326(x61671),x61672),f287(x61671,x61673,x61674)))
% 18.55/18.49 [6168]~P1(f324(f324(x61683,x61682),x61684))+P1(f324(f324(f326(x61681),x61682),f291(x61681,x61683,x61684)))
% 18.55/18.49 [6169]~P1(f324(f324(x61693,x61692),x61694))+P1(f324(f324(f326(x61691),x61692),f289(x61691,x61693,x61694)))
% 18.55/18.49 [6320]~P85(x63201)+E(f324(f324(f104(f845(x63201,a832)),f299(x63201,x63202,x63203)),f296(x63201,x63203,x63204)),f179(f845(x63201,a832)))
% 18.55/18.49 [6321]~P85(x63211)+E(f324(f324(f104(f845(x63211,a832)),f298(x63211,x63212,x63213)),f299(x63211,x63213,x63214)),f179(f845(x63211,a832)))
% 18.55/18.49 [6322]~P85(x63221)+E(f324(f324(f104(f845(x63221,a832)),f298(x63221,x63222,x63223)),f298(x63221,x63223,x63224)),f179(f845(x63221,a832)))
% 18.55/18.49 [6323]~P85(x63231)+E(f324(f324(f104(f845(x63231,a832)),f296(x63231,x63232,x63233)),f299(x63231,x63233,x63234)),f179(f845(x63231,a832)))
% 18.55/18.49 [6324]~P85(x63241)+E(f324(f324(f104(f845(x63241,a832)),f296(x63241,x63242,x63243)),f298(x63241,x63243,x63244)),f179(f845(x63241,a832)))
% 18.55/18.49 [6362]P1(f324(f324(x63621,x63622),f352(x63622,x63621)))+~P1(f324(f244(x63623,x63624,x63621),x63622))
% 18.55/18.49 [6415]~E(f324(x64151,x64152),f182(x64153))+~P1(f324(f324(f326(x64154),x64152),f168(x64154,x64153,x64151)))
% 18.55/18.49 [6497]~P2(x64971)+E(f181(x64971,x64972,f324(a114,x64973),x64974),f181(x64971,x64972,x64973,f324(x64972,x64974)))
% 18.55/18.49 [6561]~P1(f324(f324(f326(x65614),x65613),f288(x65614,x65611,x65612)))+P1(f324(f324(x65611,x65612),x65613))
% 18.55/18.49 [6562]~P1(f324(f324(f326(x65624),x65623),f287(x65624,x65621,x65622)))+P1(f324(f324(x65621,x65622),x65623))
% 18.55/18.49 [6563]~P1(f324(f324(f326(x65634),x65632),f291(x65634,x65631,x65633)))+P1(f324(f324(x65631,x65632),x65633))
% 18.55/18.49 [6564]~P1(f324(f324(f326(x65644),x65642),f289(x65644,x65641,x65643)))+P1(f324(f324(x65641,x65642),x65643))
% 18.55/18.49 [6646]E(f324(f41(f848(x66461,x66462)),f312(x66461,x66462,x66463,x66464)),f2(a838))+P1(f324(f64(x66462),x66464))
% 18.55/18.49 [6647]E(f324(f41(f848(x66471,x66472)),f312(x66471,x66472,x66473,x66474)),f2(a838))+P1(f324(f64(x66471),x66473))
% 18.55/18.49 [6860]~P19(x68604,x68601,x68602)+E(f324(f75(x68601,x68601,x68601,f324(x68602,x68603)),f324(x68602,x68603)),f324(x68602,x68603))
% 18.55/18.49 [7099]E(f273(x70991,x70992,x70993,x70994),f324(f247(f845(a101,f845(a832,f842(f840(x70991)))),f844(a101,a101)),f47(x70991)))+~P1(f324(f324(f231(a101),x70993),f2(a101)))
% 18.55/18.49 [7163]~P39(f324(a27,x71631),x71632,f324(a114,x71633),x71634)+P39(f324(f230(a833),f324(a30,x71631)),x71632,x71633,x71634)
% 18.55/18.49 [7199]P39(f324(a27,x71991),x71992,f324(a114,x71993),x71994)+~P39(f324(f230(a833),f324(a30,x71991)),x71992,x71993,x71994)
% 18.55/18.49 [7200]P39(f324(a27,x72001),x72002,f324(a114,x72003),x72004)+~P39(f324(f230(a833),f324(a30,x72001)),x72002,x72003,x72004)
% 18.55/18.49 [7503]~P39(f324(a27,x75034),x75033,x75032,x75031)+E(f324(a114,f788(x75031,x75032,x75033,x75034)),x75032)
% 18.55/18.49 [7776]~E(x77762,x77763)+P1(f324(f324(f326(f844(x77761,x77761)),f324(f324(f247(x77761,x77761),x77762),x77763)),f301(x77761,x77764)))
% 18.55/18.49 [7802]~P29(x78021,x78022,x78023,f238(f845(x78021,a832)))+E(f324(f79(x78021,x78022,f238(f845(x78021,a832)),x78023),f324(x78023,x78024)),x78024)
% 18.55/18.49 [7895]~P1(f324(f324(f326(f839(x78951)),f324(f324(f139(x78951),x78954),x78952)),f147(x78951,x78953)))+P1(f324(f324(f326(f839(x78951)),x78952),f147(x78951,x78953)))
% 18.55/18.49 [7896]~P1(f324(f324(f326(f839(x78961)),f324(f324(f125(x78961),x78964),x78962)),f147(x78961,x78963)))+P1(f324(f324(f326(f839(x78961)),x78962),f147(x78961,x78963)))
% 18.55/18.49 [7897]~P1(f324(f324(f326(f839(x78971)),f324(f324(f125(x78971),x78972),x78974)),f147(x78971,x78973)))+P1(f324(f324(f326(f839(x78971)),x78972),f147(x78971,x78973)))
% 18.55/18.49 [7973]~P39(f324(a27,x79731),x79732,x79734,x79733)+P39(f324(f230(a833),f324(a30,x79731)),x79732,f788(x79733,x79734,x79732,x79731),x79733)
% 18.55/18.49 [8011]P29(x80114,x80113,x80111,x80112)+E(f324(x80111,f520(x80112,x80111,x80113,x80114)),f324(x80111,f524(x80112,x80111,x80113,x80114)))
% 18.55/18.49 [8020]E(f169(x80201,x80202,x80203,x80204),f169(x80201,x80202,x80204,x80203))+~E(f324(f324(f104(f845(x80201,a832)),f168(x80201,x80202,x80203)),f168(x80201,x80202,x80204)),f179(f845(x80201,a832)))
% 18.55/18.49 [8119]~P29(x81192,x81191,x81194,x81193)+P29(x81191,x81192,f79(x81192,x81191,x81193,x81194),f324(f304(x81192,x81191,x81194),x81193))
% 18.55/18.49 [8256]P36(f844(x82562,x82564),f276(x82562,x82564,x82561,x82563))+P1(f324(x82561,f357(x82562,x82563,x82564,x82561)))
% 18.55/18.49 [8377]E(x83771,x83772)+~P1(f324(f324(f326(f844(x83773,x83773)),f324(f324(f247(x83773,x83773),x83771),x83772)),f261(x83773,x83774)))
% 18.55/18.49 [8440]~P1(f324(f64(f848(x84403,x84401)),f312(x84403,x84401,x84404,x84402)))+P1(f324(f64(x84401),x84402))
% 18.55/18.49 [8441]~P1(f324(f64(f848(x84411,x84413)),f312(x84411,x84413,x84412,x84414)))+P1(f324(f64(x84411),x84412))
% 18.55/18.49 [8442]~P1(f324(f64(f848(x84423,x84421)),f312(x84423,x84421,x84424,x84422)))+P1(f324(f64(x84421),x84422))
% 18.55/18.49 [8443]~P1(f324(f64(f848(x84431,x84433)),f312(x84431,x84433,x84432,x84434)))+P1(f324(f64(x84431),x84432))
% 18.55/18.49 [8605]P36(f844(x86051,x86052),f276(x86051,x86052,x86053,x86054))+~P36(x86052,f324(x86054,f357(x86051,x86054,x86052,x86053)))
% 18.55/18.49 [9103]E(f324(f324(f146(x91031,x91032),f730(x91033,x91034,x91032,x91031)),f726(x91033,x91034,x91032,x91031)),x91034)+~P1(f324(f324(f326(f844(f839(x91031),f839(x91031))),f324(f324(f247(f839(x91031),f839(x91031)),x91032),x91034)),f144(x91031,x91033)))
% 18.55/18.49 [9108]~P1(f324(f324(f326(f844(f839(x91081),f839(x91081))),f324(f324(f247(f839(x91081),f839(x91081)),x91082),x91083)),f134(x91081,x91084)))+P1(f324(f324(f326(f844(f839(x91081),f839(x91081))),f324(f324(f247(f839(x91081),f839(x91081)),x91082),x91083)),f136(x91081,x91084)))
% 18.55/18.49 [9206]P1(f324(f64(x92061),x92062))+~P1(f324(f324(f326(f844(f845(x92061,a832),f845(x92061,a832))),f324(f324(f247(f845(x92061,a832),f845(x92061,a832)),x92063),x92062)),f317(x92061,x92064)))
% 18.55/18.49 [9207]P1(f324(f64(x92071),x92072))+~P1(f324(f324(f326(f844(f845(x92071,a832),f845(x92071,a832))),f324(f324(f247(f845(x92071,a832),f845(x92071,a832)),x92072),x92073)),f317(x92071,x92074)))
% 18.55/18.49 [9210]~E(x92101,f179(f845(x92102,a832)))+~P1(f324(f324(f326(f844(f845(x92102,a832),f845(x92102,a832))),f324(f324(f247(f845(x92102,a832),f845(x92102,a832)),x92103),x92101)),f317(x92102,x92104)))
% 18.55/18.49 [9833]P16(x98331,x98332,x98333,x98334)+~P1(f324(f324(f252(x98331,x98331,a832),f324(f324(f9(x98331,f845(x98331,x98332),f845(x98331,a832)),f324(f324(f10(f845(x98332,a832),f845(f845(x98331,x98332),f845(x98331,a832)),x98331),f10(x98332,a832,x98331)),f324(f324(f10(x98332,f845(x98332,a832),x98331),a321),x98334))),x98334)),f611(x98334,x98333,x98332,x98331)))
% 18.55/18.49 [4780]~E(x47804,f115(x47801))+E(f324(f324(f141(x47801,x47802),x47803),x47804),f115(x47802))
% 18.55/18.49 [4781]~E(x47814,f115(x47811))+E(f324(f324(f141(x47811,x47812),x47813),x47814),f115(x47812))
% 18.55/18.49 [4782]~E(x47824,f182(x47821))+E(f324(f324(f195(x47821,x47822),x47823),x47824),f182(x47822))
% 18.55/18.49 [4783]~E(x47832,f115(x47831))+E(f324(f324(f146(x47831,x47832),x47833),x47834),f115(x47831))
% 18.55/18.49 [5015]E(x50151,f115(x50152))+~E(f324(f324(f141(x50152,x50153),x50154),x50151),f115(x50153))
% 18.55/18.49 [5016]E(x50161,f182(x50162))+~E(f324(f324(f195(x50162,x50163),x50164),x50161),f182(x50163))
% 18.55/18.49 [5017]E(x50171,f115(x50172))+~E(f324(f324(f141(x50172,x50173),x50174),x50171),f115(x50173))
% 18.55/18.49 [5018]E(x50181,f115(x50182))+~E(f324(f324(f146(x50182,x50181),x50183),x50184),f115(x50182))
% 18.55/18.49 [5048]E(x50481,x50482)+~E(f324(f324(f125(x50483),x50484),x50481),f324(f324(f125(x50483),x50484),x50482))
% 18.55/18.49 [5049]E(x50491,x50492)+~E(f324(f324(f125(x50493),x50491),x50494),f324(f324(f125(x50493),x50492),x50494))
% 18.55/18.49 [5191]P1(f324(x51913,x51912))+E(f155(x51911,x51912,f324(f126(x51911,x51913),x51914)),f324(f126(x51911,x51913),x51914))
% 18.55/18.49 [5202]E(x52021,x52022)+~E(f129(a838,f324(f295(a838,x52021),x52023)),f324(f324(f139(a838),x52022),x52024))
% 18.55/18.49 [5250]~P30(x52502,x52503)+P30(x52501,f324(f324(f76(x52502,x52501),x52503),x52504))
% 18.55/18.49 [5251]~P36(x52512,x52513)+P36(x52511,f324(f324(f281(x52512,x52511),x52513),x52514))
% 18.55/18.49 [5464]~E(x54641,f115(x54642))+~E(f324(f324(f125(x54642),x54643),f324(f324(f139(x54642),x54644),f115(x54642))),x54641)
% 18.55/18.49 [5497]E(f133(x54971,x54972),x54973)+~E(f324(f324(f125(x54971),x54974),f324(f324(f139(x54971),x54973),f115(x54971))),x54972)
% 18.55/18.49 [5498]E(f116(x54981,x54982),x54983)+~E(f324(f324(f125(x54981),x54983),f324(f324(f139(x54981),x54984),f115(x54981))),x54982)
% 18.55/18.49 [5606]~E(f129(a838,f324(f295(a838,x56061),x56062)),f324(f324(f139(a838),x56063),x56064))+P1(f324(f324(f232(a838),x56061),x56062))
% 18.55/18.49 [5703]~E(f324(f106(a838),x57034),f2(a838))+E(f324(f324(f149(x57031),f324(f324(f139(x57031),x57032),x57033)),f324(f106(a838),x57034)),x57032)
% 18.55/18.49 [5813]E(x58131,f324(f324(f125(x58132),f324(f154(x58132),x58133)),f324(f324(f139(x58132),x58134),f115(x58132))))+~E(f324(f154(x58132),x58131),f324(f324(f139(x58132),x58134),x58133))
% 18.55/18.49 [5997]~P85(x59971)+E(f324(f324(f104(f845(x59971,a832)),f324(f295(x59971,x59972),x59973)),f324(f295(x59971,x59973),x59974)),f179(f845(x59971,a832)))
% 18.55/18.49 [6033]~P67(x60331)+E(f324(f151(x60331),f324(f324(f141(a1,x60331),x60332),f162(x60333,x60334))),f324(f324(f8(a1,x60331),x60332),f324(f157(a1),f162(x60333,x60334))))
% 18.55/18.49 [6034]~P67(x60341)+E(f324(f324(f8(a1,x60341),x60342),f324(f157(a1),f162(x60343,x60344))),f324(f151(x60341),f324(f324(f141(a1,x60341),x60342),f162(x60343,x60344))))
% 18.55/18.49 [6181]~E(x61812,f324(f324(f125(x61811),f324(f154(x61811),x61814)),f324(f324(f139(x61811),x61813),f115(x61811))))+E(f324(f154(x61811),x61812),f324(f324(f139(x61811),x61813),x61814))
% 18.55/18.49 [6197]~P23(x61972,x61973,x61974,x61971)+E(f324(x61971,f179(f845(x61972,a832))),f37(x61973))
% 18.55/18.49 [6226]~P85(x62261)+E(f324(f324(f104(f845(x62261,a832)),f299(x62261,x62262,x62263)),f324(f295(x62261,x62263),x62264)),f179(f845(x62261,a832)))
% 18.55/18.49 [6312]~P39(x63121,x63122,x63124,x63123)+P1(f324(f324(f186(x63121),x63122),x63123))
% 18.55/18.49 [6313]~P39(x63131,x63132,x63134,x63133)+P1(f324(f324(f186(x63131),x63132),x63133))
% 18.55/18.49 [6446]E(x64461,f179(f845(x64462,a832)))+~E(f312(x64463,x64462,x64464,x64461),f179(f845(f848(x64463,x64462),a832)))
% 18.55/18.49 [6447]E(x64471,f179(f845(x64472,a832)))+~E(f312(x64472,x64473,x64471,x64474),f179(f845(f848(x64472,x64473),a832)))
% 18.55/18.49 [6527]~P1(f324(f245(x65273,x65274,x65271),x65272))+P1(f324(f324(x65271,f347(x65272,x65271)),x65272))
% 18.55/18.49 [6557]E(f324(f106(a838),x65571),f2(a838))+E(f324(f324(f149(x65572),f324(f324(f139(x65572),x65573),x65574)),f324(f106(a838),x65571)),f324(f324(f149(x65572),x65574),f324(f324(f3(a838),f324(f106(a838),x65571)),f80(a838))))
% 18.55/18.49 [6575]~P1(f324(f64(x65752),x65754))+P1(f324(f64(x65751),f324(f304(x65752,x65751,x65753),x65754)))
% 18.55/18.49 [6819]~P29(x68192,x68191,x68193,x68194)+E(f324(f41(x68191),f324(f304(x68192,x68191,x68193),x68194)),f324(f41(x68192),x68194))
% 18.55/18.49 [6839]E(f324(f304(x68391,x68392,x68393),f324(f305(x68391,x68392,x68393),x68394)),x68394)+~E(f324(f304(x68391,x68392,x68393),f238(f845(x68391,a832))),f238(f845(x68392,a832)))
% 18.55/18.49 [7264]~P29(x72641,x72642,x72643,f238(f845(x72641,a832)))+E(f324(f305(x72641,x72642,x72643),f324(f304(x72641,x72642,x72643),x72644)),x72644)
% 18.55/18.49 [7607]P1(f324(x76071,x76072))+~P1(f324(f324(f326(x76073),x76072),f324(f157(x76073),f161(x76073,x76071,x76074))))
% 18.55/18.49 [7719]~P1(f324(f324(f326(f839(x77191)),f324(f324(f139(x77191),x77192),x77194)),f147(x77191,x77193)))+P1(f324(f324(f326(x77191),x77192),x77193))
% 18.55/18.49 [7847]~P1(f324(f324(f326(x78471),x78472),f324(f157(x78471),f155(x78471,x78474,x78473))))+P1(f324(f324(f326(x78471),x78472),f324(f157(x78471),x78473)))
% 18.55/18.49 [7848]~P1(f324(f324(f326(x78481),x78482),f324(f157(x78481),f159(x78481,x78483,x78484))))+P1(f324(f324(f326(x78481),x78482),f324(f157(x78481),x78483)))
% 18.55/18.49 [7849]~P1(f324(f324(f326(x78491),x78492),f324(f157(x78491),f159(x78491,x78493,x78494))))+P1(f324(f324(f326(x78491),x78492),f324(f157(x78491),x78493)))
% 18.55/18.49 [7850]~P1(f324(f324(f326(x78501),x78502),f324(f157(x78501),f161(x78501,x78504,x78503))))+P1(f324(f324(f326(x78501),x78502),f324(f157(x78501),x78503)))
% 18.55/18.49 [7860]E(f324(f180(f839(x78601)),x78602),x78603)+~P1(f324(f324(f326(f839(x78601)),x78602),f324(f157(f839(x78601)),f61(x78601,x78603,x78604))))
% 18.55/18.49 [8069]E(f324(f324(f149(x80691),f161(x80691,x80692,x80693)),x80694),f324(f324(f149(x80691),x80693),x80694))+~P1(f324(f324(f232(a838),x80694),f324(f180(f839(x80691)),f161(x80691,x80692,x80693))))
% 18.55/18.49 [8154]~P67(x81541)+E(f324(f324(f8(a838,x81541),f324(f324(f10(a838,x81541,a838),x81542),a114)),f324(f295(a838,x81543),x81544)),f324(f324(f8(a838,x81541),x81542),f324(f295(a838,f324(a114,x81543)),f324(a114,x81544))))
% 18.55/18.49 [8163]~P67(x81631)+E(f324(f324(f8(a838,x81631),f324(f324(f10(a838,x81631,a838),x81632),a114)),f296(a838,x81633,x81634)),f324(f324(f8(a838,x81631),x81632),f296(a838,f324(a114,x81633),f324(a114,x81634))))
% 18.55/18.49 [8294]~P29(x82941,x82943,x82944,f238(f845(x82941,a832)))+P29(x82941,f845(x82942,x82943),f324(f324(f10(x82943,f845(x82942,x82943),x82941),f18(x82943,x82942)),x82944),f238(f845(x82941,a832)))
% 18.55/18.49 [8386]~P29(x83862,x83861,x83864,x83863)+E(f324(f304(x83861,x83862,f79(x83862,x83861,x83863,x83864)),f324(f304(x83862,x83861,x83864),x83863)),x83863)
% 18.55/18.49 [8444]~P1(f324(f324(f326(f844(x84441,x84441)),f324(f324(f247(x84441,x84441),x84442),x84444)),f261(x84441,x84443)))+P1(f324(f324(f326(x84441),x84442),x84443))
% 18.55/18.49 [8519]E(f324(f324(f324(f74(x85191,f842(x85192)),f324(f18(f842(x85192),x85191),f182(x85192))),x85193),f324(f226(x85192),f521(x85193,x85194,x85192,x85191))),x85194)+~E(f168(x85191,x85192,x85194),f324(f324(f303(x85191),x85193),f179(f845(x85191,a832))))
% 18.55/18.49 [8640]~E(f324(f324(f8(x86401,a838),x86404),x86403),f324(a114,x86402))+P1(f324(f324(f326(x86401),f627(x86402,x86403,x86404,x86401)),x86403))
% 18.55/18.49 [8657]~E(f324(f324(f8(x86574,a838),x86571),x86573),f324(a114,x86572))+P1(f324(f324(f232(a838),f2(a838)),f324(x86571,f627(x86572,x86573,x86571,x86574))))
% 18.55/18.49 [8667]~P1(f324(f64(x86672),x86674))+P1(f324(f324(f231(a838),f324(f41(x86671),f324(f304(x86672,x86671,x86673),x86674))),f324(f41(x86672),x86674)))
% 18.55/18.49 [8668]E(f324(f324(f247(x86681,x86682),f339(x86683,x86684,x86682,x86681)),f340(x86683,x86684,x86682,x86681)),x86684)+~P1(f324(f324(f326(f844(x86681,x86682)),x86684),f324(f279(x86682,x86681),x86683)))
% 18.55/18.49 [8677]P29(x86771,x86772,x86773,x86774)+P1(f324(f324(f326(x86771),f520(x86774,x86773,x86772,x86771)),x86774))
% 18.55/18.49 [8678]P29(x86781,x86782,x86783,x86784)+P1(f324(f324(f326(x86781),f524(x86784,x86783,x86782,x86781)),x86784))
% 18.55/18.49 [8732]P16(x87321,x87322,x87323,x87324)+P1(f324(f324(f326(f844(x87321,x87321)),f611(x87324,x87323,x87322,x87321)),x87323))
% 18.55/18.49 [8780]P1(f324(x87801,x87802))+~P1(f324(x87801,f324(f324(f247(x87803,x87804),f795(x87804,x87803,x87801)),f796(x87804,x87803,x87801))))
% 18.55/18.49 [8793]E(f324(f180(f839(x87931)),x87932),f324(f180(f839(x87931)),x87933))+~P1(f324(f324(f326(f844(f839(x87931),f839(x87931))),f324(f324(f247(f839(x87931),f839(x87931)),x87932),x87933)),f134(x87931,x87934)))
% 18.55/18.49 [8794]E(f324(f180(f839(x87941)),x87942),f324(f180(f839(x87941)),x87943))+~P1(f324(f324(f326(f844(f839(x87941),f839(x87941))),f324(f324(f247(f839(x87941),f839(x87941)),x87942),x87943)),f145(x87941,x87944)))
% 18.55/18.49 [8795]E(f324(f180(f839(x87951)),x87952),f324(f180(f839(x87951)),x87953))+~P1(f324(f324(f326(f844(f839(x87951),f839(x87951))),f324(f324(f247(f839(x87951),f839(x87951)),x87952),x87953)),f145(x87951,x87954)))
% 18.55/18.49 [8796]E(f324(f180(f839(x87961)),x87962),f324(f180(f839(x87961)),x87963))+~P1(f324(f324(f326(f844(f839(x87961),f839(x87961))),f324(f324(f247(f839(x87961),f839(x87961)),x87962),x87963)),f145(x87961,x87964)))
% 18.55/18.49 [8797]E(f324(f180(f839(x87971)),x87972),f324(f180(f839(x87971)),x87973))+~P1(f324(f324(f326(f844(f839(x87971),f839(x87971))),f324(f324(f247(f839(x87971),f839(x87971)),x87972),x87973)),f144(x87971,x87974)))
% 18.55/18.49 [8868]P1(f324(f324(f231(a838),f142(x88681,x88682,x88683)),f142(x88681,x88684,x88683)))+P1(f324(f324(f326(x88681),f746(x88684,x88682,x88683,x88681)),f324(f157(x88681),x88683)))
% 18.55/18.49 [8869]E(f324(f180(f839(x88691)),x88692),f324(f180(f839(x88691)),x88693))+~P1(f324(f324(f326(f844(f839(x88691),f839(x88691))),f324(f324(f247(f839(x88691),f839(x88691)),x88692),x88693)),f301(f839(x88691),f144(x88691,x88694))))
% 18.55/18.49 [8975]P1(f324(f324(f280(a838),x89751),x89752))+P1(f324(f324(f231(f845(a838,a832)),f283(a838,f280(a838),x89751,x89752)),f283(a838,f280(a838),x89753,x89754)))
% 18.55/18.49 [9083]~P29(x90831,x90832,x90833,x90834)+~P1(f324(f324(f232(a838),f324(f41(x90832),f324(f304(x90831,x90832,x90833),x90834))),f324(f41(x90831),x90834)))
% 18.55/18.49 [9115]~P1(f324(f324(f326(f844(f839(x91151),f839(x91151))),f324(f324(f247(f839(x91151),f839(x91151)),x91152),x91153)),f144(x91151,x91154)))+P1(f324(f324(f326(f844(f839(x91151),f839(x91151))),f324(f324(f247(f839(x91151),f839(x91151)),x91152),x91153)),f145(x91151,f301(x91151,x91154))))
% 18.55/18.49 [9118]~P1(f324(f324(f326(f844(f839(x91181),f839(x91181))),f324(f324(f247(f839(x91181),f839(x91181)),x91182),x91183)),f145(x91181,x91184)))+P1(f324(f324(f326(f844(f839(x91181),f839(x91181))),f324(f324(f247(f839(x91181),f839(x91181)),x91182),x91183)),f301(f839(x91181),f144(x91181,x91184))))
% 18.55/18.49 [9133]P1(f324(f324(f326(f844(x91331,x91331)),f324(f324(f247(x91331,x91331),x91332),x91333)),f301(x91331,x91334)))+~P1(f324(f324(f326(f844(x91331,x91331)),f324(f324(f247(x91331,x91331),x91332),x91333)),f324(f324(f282(x91331,x91331,x91331),x91334),f301(x91331,x91334))))
% 18.55/18.49 [9202]P1(f324(f324(f280(a838),x92021),x92022))+~P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x92023,x92024)),f283(a838,f280(a838),x92021,x92022)))
% 18.55/18.49 [9314]E(f324(f324(f125(x93141),f731(x93142,x93143,x93144,x93141)),f324(f324(f139(x93141),f732(x93142,x93143,x93144,x93141)),f734(x93142,x93143,x93144,x93141))),x93144)+~P1(f324(f324(f326(f844(f839(x93141),f839(x93141))),f324(f324(f247(f839(x93141),f839(x93141)),x93144),x93143)),f144(x93141,x93142)))
% 18.55/18.49 [9315]E(f324(f324(f125(x93151),f731(x93152,x93153,x93154,x93151)),f324(f324(f139(x93151),f733(x93152,x93153,x93154,x93151)),f734(x93152,x93153,x93154,x93151))),x93153)+~P1(f324(f324(f326(f844(f839(x93151),f839(x93151))),f324(f324(f247(f839(x93151),f839(x93151)),x93154),x93153)),f144(x93151,x93152)))
% 18.55/18.49 [9389]P1(f324(f324(f326(f844(x93891,x93891)),f324(f324(f247(x93891,x93891),x93892),f644(x93893,x93894,x93892,x93891))),f301(x93891,x93893)))+~P1(f324(f324(f326(f844(x93891,x93891)),f324(f324(f247(x93891,x93891),x93892),x93894)),f324(f324(f282(x93891,x93891,x93891),x93893),f301(x93891,x93893))))
% 18.55/18.49 [9457]P1(f324(f324(f231(a838),f142(x94571,x94572,x94573)),f142(x94571,x94574,x94573)))+~P1(f324(f324(f232(a838),f324(x94572,f746(x94574,x94572,x94573,x94571))),f324(x94574,f746(x94574,x94572,x94573,x94571))))
% 18.55/18.49 [9524]P1(f324(f324(f326(f844(x95241,x95241)),f324(f324(f247(x95241,x95241),f643(x95242,x95243,x95244,x95241)),x95243)),f301(x95241,x95242)))+~P1(f324(f324(f326(f844(x95241,x95241)),f324(f324(f247(x95241,x95241),x95244),x95243)),f324(f324(f282(x95241,x95241,x95241),x95242),f301(x95241,x95242))))
% 18.55/18.49 [5029]~E(x50292,x50293)+E(f155(x50291,x50292,f324(f324(f139(x50291),x50293),x50294)),x50294)
% 18.55/18.49 [5042]~E(x50422,f2(a838))+E(f324(f324(f158(x50421),x50422),f324(f324(f139(x50421),x50423),x50424)),f115(x50421))
% 18.55/18.49 [5148]P1(f324(x51482,x51483))+E(f161(x51481,x51482,f324(f324(f139(x51481),x51483),x51484)),f115(x51481))
% 18.55/18.49 [5213]~P81(x52132)+E(f324(f324(f81(f845(x52131,x52132)),x52133),x52134),f324(f81(x52132),f324(x52133,x52134)))
% 18.55/18.49 [5214]~P81(x52142)+E(f324(f324(f81(f845(x52141,x52142)),x52143),x52144),f324(f81(x52142),f324(x52143,x52144)))
% 18.55/18.49 [5226]~E(x52262,f2(a838))+E(f324(f324(f128(x52261),x52262),f324(f324(f139(x52261),x52263),x52264)),f324(f324(f139(x52261),x52263),x52264))
% 18.55/18.49 [5227]P1(f324(x52272,x52273))+E(f324(f126(x52271,x52272),f324(f324(f139(x52271),x52273),x52274)),f324(f126(x52271,x52272),x52274))
% 18.55/18.49 [5360]~E(x53602,x53604)+P1(f324(f324(f324(f303(x53601),x53602),x53603),x53604))
% 18.55/18.49 [5368]E(x53681,f115(x53682))+E(f133(x53683,f324(f324(f141(x53682,x53683),x53684),x53681)),f324(x53684,f133(x53682,x53681)))
% 18.55/18.49 [5380]~E(x53801,f66(x53802,x53804))+E(f324(x53801,f324(f324(f303(x53802),x53803),f179(f845(x53802,a832)))),x53803)
% 18.55/18.49 [5396]~E(f324(f106(a838),x53962),f2(a838))+E(f324(f324(f158(x53961),f324(f106(a838),x53962)),f324(f324(f139(x53961),x53963),x53964)),f115(x53961))
% 18.55/18.49 [5416]E(x54161,f115(x54162))+E(f324(f130(x54163),f324(f324(f141(x54162,x54163),x54164),x54161)),f324(x54164,f324(f130(x54162),x54161)))
% 18.55/18.49 [5516]~P1(f324(x55163,x55164))+P1(f324(f324(f324(f303(x55161),x55162),x55163),x55164))
% 18.55/18.49 [5623]~E(f324(f106(a838),x56232),f2(a838))+E(f324(f324(f128(x56231),f324(f106(a838),x56232)),f324(f324(f139(x56231),x56233),x56234)),f324(f324(f139(x56231),x56233),x56234))
% 18.55/18.49 [5639]~P22(x56392,x56394,x56391)+E(f324(x56391,f324(f324(f303(x56392),x56393),f179(f845(x56392,a832)))),x56393)
% 18.55/18.49 [5663]~E(x56632,x56633)+P1(f324(f324(f326(x56631),x56632),f324(f324(f303(x56631),x56633),x56634)))
% 18.55/18.49 [5664]~E(x56642,x56643)+P1(f324(f324(f326(x56641),x56642),f324(f324(f303(x56641),x56643),x56644)))
% 18.55/18.49 [5668]~P105(x56681)+E(f324(f324(f83(x56681),x56682),f324(f324(f83(x56681),x56683),x56684)),f324(f324(f83(x56681),x56683),f324(f324(f83(x56681),x56682),x56684)))
% 18.55/18.49 [5669]~P105(x56691)+E(f324(f324(f82(x56691),x56692),f324(f324(f82(x56691),x56693),x56694)),f324(f324(f82(x56691),x56693),f324(f324(f82(x56691),x56692),x56694)))
% 18.55/18.49 [5670]~P86(x56701)+E(f324(f324(f235(x56701),x56702),f324(f324(f235(x56701),x56703),x56704)),f324(f324(f235(x56701),x56703),f324(f324(f235(x56701),x56702),x56704)))
% 18.55/18.49 [5671]~P86(x56711)+E(f324(f324(f235(x56711),x56712),f324(f324(f235(x56711),x56713),x56714)),f324(f324(f235(x56711),x56713),f324(f324(f235(x56711),x56712),x56714)))
% 18.55/18.49 [5672]~P86(x56721)+E(f324(f324(f178(x56721),x56722),f324(f324(f178(x56721),x56723),x56724)),f324(f324(f178(x56721),x56723),f324(f324(f178(x56721),x56722),x56724)))
% 18.55/18.49 [5673]~P86(x56731)+E(f324(f324(f178(x56731),x56732),f324(f324(f178(x56731),x56733),x56734)),f324(f324(f178(x56731),x56733),f324(f324(f178(x56731),x56732),x56734)))
% 18.55/18.49 [5674]~P93(x56741)+E(f324(f324(f103(x56741),x56742),f324(f324(f103(x56741),x56743),x56744)),f324(f324(f103(x56741),x56743),f324(f324(f103(x56741),x56742),x56744)))
% 18.55/18.49 [5675]~P93(x56751)+E(f324(f324(f103(x56751),x56752),f324(f324(f103(x56751),x56753),x56754)),f324(f324(f103(x56751),x56753),f324(f324(f103(x56751),x56752),x56754)))
% 18.55/18.49 [5676]~P94(x56761)+E(f324(f324(f103(x56761),x56762),f324(f324(f103(x56761),x56763),x56764)),f324(f324(f103(x56761),x56763),f324(f324(f103(x56761),x56762),x56764)))
% 18.55/18.49 [5677]~P94(x56771)+E(f324(f324(f104(x56771),x56772),f324(f324(f104(x56771),x56773),x56774)),f324(f324(f104(x56771),x56773),f324(f324(f104(x56771),x56772),x56774)))
% 18.55/18.49 [5678]~P99(x56781)+E(f324(f324(f104(x56781),x56782),f324(f324(f104(x56781),x56783),x56784)),f324(f324(f104(x56781),x56783),f324(f324(f104(x56781),x56782),x56784)))
% 18.55/18.49 [5679]~P99(x56791)+E(f324(f324(f104(x56791),x56792),f324(f324(f104(x56791),x56793),x56794)),f324(f324(f104(x56791),x56793),f324(f324(f104(x56791),x56792),x56794)))
% 18.55/18.49 [5686]E(x56861,x56862)+E(f155(x56863,x56861,f324(f324(f139(x56863),x56862),x56864)),f324(f324(f139(x56863),x56862),f155(x56863,x56861,x56864)))
% 18.55/18.49 [5701]~P1(f324(x57012,x57013))+E(f324(f126(x57011,x57012),f324(f324(f139(x57011),x57013),x57014)),f324(f324(f139(x57011),x57013),f324(f126(x57011,x57012),x57014)))
% 18.55/18.49 [5789]~E(x57894,f179(f845(x57891,a832)))+E(f324(f304(x57891,x57892,f324(f18(x57892,x57891),x57893)),x57894),f179(f845(x57892,a832)))
% 18.55/18.49 [5834]~P1(f324(x58342,x58343))+E(f161(x58341,x58342,f324(f324(f139(x58341),x58343),x58344)),f324(f324(f139(x58341),x58343),f161(x58341,x58342,x58344)))
% 18.55/18.49 [5887]P28(x58871,x58872,x58873)+~P28(x58871,x58872,f324(f324(f303(f837(x58871)),x58874),x58873))
% 18.55/18.49 [5900]E(x59001,f179(f845(x59002,a832)))+E(f324(f324(f45(x59002,f845(x59003,a832)),x59001),f324(f18(f845(x59003,a832),x59002),x59004)),x59004)
% 18.55/18.49 [5901]E(x59011,f179(f845(x59012,a832)))+E(f324(f324(f46(x59012,f845(x59013,a832)),x59011),f324(f18(f845(x59013,a832),x59012),x59014)),x59014)
% 18.55/18.49 [5910]~E(x59104,f179(f845(x59102,a832)))+E(f324(f324(f249(x59101,x59102),x59103),f324(f18(f845(x59102,a832),x59101),x59104)),f179(f845(f844(x59101,x59102),a832)))
% 18.55/18.49 [5911]~E(x59113,f179(f845(x59111,a832)))+E(f324(f324(f249(x59111,x59112),x59113),f324(f18(f845(x59112,a832),x59111),x59114)),f179(f845(f844(x59111,x59112),a832)))
% 18.55/18.49 [5962]E(x59621,f2(a838))+E(f324(f324(f128(x59622),x59621),f324(f324(f139(x59622),x59623),x59624)),f324(f324(f128(x59622),f324(f324(f3(a838),x59621),f80(a838))),x59624))
% 18.55/18.49 [5989]E(x59891,f179(f845(x59892,a832)))+E(f324(f304(x59892,x59893,f324(f18(x59893,x59892),x59894)),x59891),f324(f324(f303(x59893),x59894),f179(f845(x59893,a832))))
% 18.55/18.49 [5992]E(f324(f305(x59921,x59922,f324(f18(x59922,x59921),x59923)),x59924),f179(f845(x59921,a832)))+P1(f324(f324(f326(x59922),x59923),x59924))
% 18.55/18.49 [6060]~E(x60603,f179(f845(x60601,a832)))+E(f324(f324(f45(x60601,f845(x60602,a832)),x60603),f324(f18(f845(x60602,a832),x60601),x60604)),f179(f845(x60602,a832)))
% 18.55/18.49 [6061]~E(x60613,f179(f845(x60611,a832)))+E(f324(f324(f46(x60611,f845(x60612,a832)),x60613),f324(f18(f845(x60612,a832),x60611),x60614)),f238(f845(x60612,a832)))
% 18.55/18.49 [6063]~P7(x60631)+E(f51(x60631,f324(f324(f83(x60631),x60632),x60633),f324(f324(f83(x60631),x60632),x60634)),f324(f324(f83(x60631),x60632),f51(x60631,x60633,x60634)))
% 18.55/18.49 [6236]E(f324(f305(x62361,x62362,f324(f18(x62362,x62361),x62363)),x62364),f238(f845(x62361,a832)))+~P1(f324(f324(f326(x62362),x62363),x62364))
% 18.55/18.49 [6257]~P1(f324(f324(f326(x62571),x62572),x62574))+P1(f324(f324(f326(x62571),x62572),f324(f324(f303(x62571),x62573),x62574)))
% 18.55/18.49 [6258]~P1(f324(f324(f326(x62581),x62582),x62584))+P1(f324(f324(f326(x62581),x62582),f324(f324(f303(x62581),x62583),x62584)))
% 18.55/18.49 [6259]~P1(f324(f324(f326(x62591),x62592),x62594))+P1(f324(f324(f326(x62591),x62592),f324(f324(f303(x62591),x62593),x62594)))
% 18.55/18.49 [6272]~E(x62723,f324(f324(f3(a838),f324(f180(f839(x62721)),x62722)),f80(a838)))+E(f116(x62721,f324(f324(f146(x62721,x62722),x62723),x62724)),f116(x62721,x62722))
% 18.55/18.49 [6297]~P86(x62971)+E(f324(f324(f104(f845(x62971,a832)),f324(f294(x62971),x62972)),f296(x62971,x62973,x62974)),f296(x62971,x62973,f324(f324(f235(x62971),x62972),x62974)))
% 18.55/18.49 [6298]~P86(x62981)+E(f324(f324(f104(f845(x62981,a832)),f324(f259(x62981),x62982)),f296(x62981,x62983,x62984)),f296(x62981,f324(f324(f178(x62981),x62982),x62983),x62984))
% 18.55/18.49 [6314]E(f324(f324(f104(f845(x63141,a832)),x63142),f324(f324(f303(x63141),x63143),x63144)),f324(f324(f104(f845(x63141,a832)),x63142),x63144))+P1(f324(f324(f326(x63141),x63143),x63142))
% 18.55/18.49 [6315]E(f324(f324(f104(f845(x63151,a832)),x63152),f324(f324(f303(x63151),x63153),x63154)),f324(f324(f104(f845(x63151,a832)),x63152),x63154))+P1(f324(f324(f326(x63151),x63153),x63152))
% 18.55/18.49 [6327]E(f155(x63271,x63272,f324(f324(f125(x63271),x63273),x63274)),f324(f324(f125(x63271),x63273),f155(x63271,x63272,x63274)))+P1(f324(f324(f326(x63271),x63272),f324(f157(x63271),x63273)))
% 18.55/18.49 [6332]~P75(x63321)+E(f324(f324(f83(x63321),f324(f324(f240(x63321),x63322),x63323)),f324(f324(f240(x63321),x63322),x63324)),f324(f324(f240(x63321),x63322),f324(f324(f82(a838),x63323),x63324)))
% 18.55/18.49 [6333]~P105(x63331)+E(f324(f324(f83(x63331),f324(f324(f240(x63331),x63332),x63333)),f324(f324(f240(x63331),x63332),x63334)),f324(f324(f240(x63331),x63332),f324(f324(f82(a838),x63333),x63334)))
% 18.55/18.49 [6369]~P105(x63691)+E(f324(f324(f82(x63691),f324(f324(f83(x63691),x63692),x63693)),f324(f324(f83(x63691),x63692),x63694)),f324(f324(f83(x63691),x63692),f324(f324(f82(x63691),x63693),x63694)))
% 18.55/18.49 [6370]~P86(x63701)+E(f324(f324(f178(x63701),f324(f324(f235(x63701),x63702),x63703)),f324(f324(f235(x63701),x63702),x63704)),f324(f324(f235(x63701),x63702),f324(f324(f178(x63701),x63703),x63704)))
% 18.55/18.49 [6371]~P86(x63711)+E(f324(f324(f235(x63711),f324(f324(f178(x63711),x63712),x63713)),f324(f324(f178(x63711),x63712),x63714)),f324(f324(f178(x63711),x63712),f324(f324(f235(x63711),x63713),x63714)))
% 18.55/18.49 [6372]~P97(x63721)+E(f324(f324(f104(x63721),f324(f324(f103(x63721),x63722),x63723)),f324(f324(f103(x63721),x63722),x63724)),f324(f324(f103(x63721),x63722),f324(f324(f104(x63721),x63723),x63724)))
% 18.55/18.49 [6373]~P97(x63731)+E(f324(f324(f103(x63731),f324(f324(f104(x63731),x63732),x63733)),f324(f324(f104(x63731),x63732),x63734)),f324(f324(f104(x63731),x63732),f324(f324(f103(x63731),x63733),x63734)))
% 18.55/18.49 [6409]~P7(x64091)+E(f51(x64091,f324(f324(f83(x64091),x64092),x64093),f324(f324(f83(x64091),x64094),x64093)),f324(f324(f83(x64091),f51(x64091,x64092,x64094)),x64093))
% 18.55/18.49 [6412]~E(f324(f180(f839(x64121)),x64123),f324(f180(f839(x64122)),x64124))+E(f324(f324(f141(f844(x64121,x64122),x64122),f251(x64121,x64122)),f324(f324(f166(x64121,x64122),x64123),x64124)),x64124)
% 18.55/18.49 [6413]~E(f324(f180(f839(x64131)),x64133),f324(f180(f839(x64132)),x64134))+E(f324(f324(f141(f844(x64131,x64132),x64131),f246(x64131,x64132)),f324(f324(f166(x64131,x64132),x64133),x64134)),x64133)
% 18.55/18.49 [6423]~P7(x64231)+E(f51(x64231,f324(f324(f83(x64231),x64232),f51(x64231,x64233,x64234)),x64234),f51(x64231,f324(f324(f83(x64231),x64232),x64233),x64234))
% 18.55/18.49 [6424]~P7(x64241)+E(f51(x64241,f324(f324(f82(x64241),x64242),f51(x64241,x64243,x64244)),x64244),f51(x64241,f324(f324(f82(x64241),x64242),x64243),x64244))
% 18.55/18.49 [6425]~P8(x64251)+E(f51(x64251,f324(f324(f3(x64251),x64252),f51(x64251,x64253,x64254)),x64254),f51(x64251,f324(f324(f3(x64251),x64252),x64253),x64254))
% 18.55/18.49 [6426]~P7(x64261)+E(f51(x64261,f324(f324(f82(x64261),x64262),f51(x64261,x64263,x64264)),x64264),f51(x64261,f324(f324(f82(x64261),x64262),x64263),x64264))
% 18.55/18.49 [6510]~P86(x65101)+E(f324(f324(f104(f845(x65101,a832)),f296(x65101,x65102,x65103)),f324(f294(x65101),x65104)),f296(x65101,x65102,f324(f324(f235(x65101),x65103),x65104)))
% 18.55/18.49 [6511]~P86(x65111)+E(f324(f324(f104(f845(x65111,a832)),f296(x65111,x65112,x65113)),f324(f259(x65111),x65114)),f296(x65111,f324(f324(f178(x65111),x65112),x65114),x65113))
% 18.55/18.49 [6514]~E(f324(f180(f839(x65141)),x65143),f324(f180(f839(x65142)),x65144))+E(f324(f324(f166(x65141,x65142),f324(f154(x65141),x65143)),f324(f154(x65142),x65144)),f324(f154(f844(x65141,x65142)),f324(f324(f166(x65141,x65142),x65143),x65144)))
% 18.55/18.49 [6523]E(x65231,f324(f324(f3(a838),f324(f180(f839(x65232)),x65233)),f80(a838)))+E(f116(x65232,f324(f324(f146(x65232,x65233),x65231),x65234)),f324(f324(f146(x65232,f116(x65232,x65233)),x65231),x65234))
% 18.55/18.49 [6540]~P1(f324(f127(x65402),x65404))+P1(f324(f127(f844(x65401,x65402)),f324(f324(f166(x65401,x65402),x65403),x65404)))
% 18.55/18.49 [6541]~P1(f324(f127(x65411),x65413))+P1(f324(f127(f844(x65411,x65412)),f324(f324(f166(x65411,x65412),x65413),x65414)))
% 18.55/18.49 [6639]E(x66391,f324(f324(f324(a188,x66392),x66393),f324(x66394,x66392)))+~P1(f324(f324(f186(f28(x66393,x66394)),x66392),x66391))
% 18.55/18.49 [6822]E(f324(f324(f42(a838),x68221),x68222),x68223)+~P1(f324(f54(x68221,x68222),f324(f324(f247(a838,a838),x68223),x68224)))
% 18.55/18.49 [6848]E(f51(a838,x68481,x68482),x68483)+~P1(f324(f54(x68481,x68482),f324(f324(f247(a838,a838),x68484),x68483)))
% 18.55/18.49 [6851]P1(f324(f127(x68511),x68512))+~P1(f324(f127(x68513),f324(f324(f141(x68511,x68513),x68514),x68512)))
% 18.55/18.49 [6859]~P28(x68591,x68592,f324(f324(f303(f837(x68591)),x68593),x68594))+P28(x68591,x68592,f324(f324(f303(f837(x68591)),x68593),f179(f845(f837(x68591),a832))))
% 18.55/18.49 [6931]E(f155(x69311,x69312,f324(f324(f125(x69311),x69313),x69314)),f324(f324(f125(x69311),f155(x69311,x69312,x69313)),x69314))+~P1(f324(f324(f326(x69311),x69312),f324(f157(x69311),x69313)))
% 18.55/18.49 [6999]E(f324(f106(a838),x69991),f2(a838))+E(f324(f324(f128(x69992),f324(f106(a838),x69991)),f324(f324(f139(x69992),x69993),x69994)),f324(f324(f128(x69992),f324(f324(f3(a838),f324(f106(a838),x69991)),f80(a838))),x69994))
% 18.55/18.49 [7025]~P7(x70251)+E(f51(x70251,f324(f324(f83(x70251),f51(x70251,x70252,x70253)),x70254),x70253),f51(x70251,f324(f324(f83(x70251),x70252),x70254),x70253))
% 18.55/18.49 [7026]~P7(x70261)+E(f51(x70261,f324(f324(f82(x70261),f51(x70261,x70262,x70263)),x70264),x70263),f51(x70261,f324(f324(f82(x70261),x70262),x70264),x70263))
% 18.55/18.49 [7027]~P8(x70271)+E(f51(x70271,f324(f324(f3(x70271),f51(x70271,x70272,x70273)),x70274),x70273),f51(x70271,f324(f324(f3(x70271),x70272),x70274),x70273))
% 18.55/18.49 [7028]~P7(x70281)+E(f51(x70281,f324(f324(f83(x70281),f51(x70281,x70282,x70283)),x70284),x70283),f51(x70281,f324(f324(f83(x70281),x70282),x70284),x70283))
% 18.55/18.49 [7029]~P7(x70291)+E(f51(x70291,f324(f324(f82(x70291),f51(x70291,x70292,x70293)),x70294),x70293),f51(x70291,f324(f324(f82(x70291),x70292),x70294),x70293))
% 18.55/18.49 [7234]~E(x72341,f324(f324(f139(x72342),x72343),x72344))+~P1(f324(f324(f231(a838),f324(f180(f839(x72342)),x72341)),f324(f180(f839(x72342)),x72344)))
% 18.55/18.49 [7409]~E(f165(x74091,x74092,x74093),f165(x74091,x74092,x74094))+E(f324(f304(f844(x74091,x74092),x74091,f246(x74091,x74092)),f324(f157(f844(x74091,x74092)),x74093)),f324(f304(f844(x74091,x74092),x74091,f246(x74091,x74092)),f324(f157(f844(x74091,x74092)),x74094)))
% 18.55/18.49 [7452]P29(x74521,x74522,x74523,f324(f157(x74521),x74524))+~P1(f324(f127(x74522),f324(f324(f141(x74521,x74522),x74523),x74524)))
% 18.55/18.49 [7529]~P1(f324(f324(f231(f845(x75291,a832)),x75292),x75294))+P1(f324(f324(f231(f845(x75291,a832)),x75292),f324(f324(f303(x75291),x75293),x75294)))
% 18.55/18.49 [7564]~P7(x75641)+E(f51(x75641,f324(f324(f83(x75641),f51(x75641,x75642,x75643)),f51(x75641,x75644,x75643)),x75643),f51(x75641,f324(f324(f83(x75641),x75642),x75644),x75643))
% 18.55/18.49 [7565]~P7(x75651)+E(f51(x75651,f324(f324(f82(x75651),f51(x75651,x75652,x75653)),f51(x75651,x75654,x75653)),x75653),f51(x75651,f324(f324(f82(x75651),x75652),x75654),x75653))
% 18.55/18.49 [7566]~P8(x75661)+E(f51(x75661,f324(f324(f3(x75661),f51(x75661,x75662,x75663)),f51(x75661,x75664,x75663)),x75663),f51(x75661,f324(f324(f3(x75661),x75662),x75664),x75663))
% 18.55/18.49 [7668]~E(f324(x76684,f529(x76684,x76683,x76681,x76682)),f179(f845(x76682,a832)))+E(f324(f324(f45(x76681,f845(x76682,a832)),x76683),x76684),f179(f845(x76682,a832)))
% 18.55/18.49 [7669]~E(f324(x76694,f657(x76694,x76693,x76691,x76692)),f238(f845(x76692,a832)))+E(f324(f324(f46(x76691,f845(x76692,a832)),x76693),x76694),f238(f845(x76692,a832)))
% 18.55/18.49 [7670]~E(f324(x76704,f530(x76704,x76703,x76702,x76701)),f179(f845(x76702,a832)))+E(f324(f324(f45(x76701,f845(x76702,a832)),x76703),x76704),f179(f845(x76702,a832)))
% 18.55/18.49 [7671]~E(f324(x76714,f662(x76714,x76713,x76712,x76711)),f238(f845(x76712,a832)))+E(f324(f324(f46(x76711,f845(x76712,a832)),x76713),x76714),f238(f845(x76712,a832)))
% 18.55/18.49 [8070]P1(f324(x80701,x80702))+~P1(f324(f324(f326(x80703),x80702),f324(f324(f104(f845(x80703,a832)),x80704),f324(f257(x80703),x80701))))
% 18.55/18.49 [8109]~P1(f324(f324(f231(f845(x81091,a832)),x81093),x81094))+P1(f324(f324(f231(f845(x81091,a832)),f324(f324(f303(x81091),x81092),x81093)),f324(f324(f303(x81091),x81092),x81094)))
% 18.55/18.49 [8152]P1(f324(f324(f326(x81521),x81522),x81523))+~P1(f324(f324(f326(x81521),x81522),f324(f324(f104(f845(x81521,a832)),x81523),f324(f257(x81521),x81524))))
% 18.55/18.49 [8278]P1(f324(f324(f186(x82781),x82782),f675(x82783,x82782,x82784,x82781)))+~P1(f324(f324(f186(f36(x82781,x82784)),x82782),x82783))
% 18.55/18.49 [8287]P1(f324(x82872,x82873))+E(f324(f324(f128(x82871),f324(f180(f839(x82871)),f161(x82871,x82872,f324(f324(f139(x82871),x82873),x82874)))),f324(f324(f139(x82871),x82873),x82874)),f324(f324(f139(x82871),x82873),x82874))
% 18.55/18.49 [8400]~P1(f324(f324(f232(a838),f324(x84004,x84002)),f324(x84004,x84003)))+P1(f324(f324(f326(f844(x84001,x84001)),f324(f324(f247(x84001,x84001),x84002),x84003)),f324(f324(f281(a838,x84001),a236),x84004)))
% 18.55/18.49 [8545]P29(f839(x85451),f839(x85452),f324(f141(x85451,x85452),x85453),x85454)+~P29(x85451,x85452,x85453,f43(f845(x85451,a832),f324(f304(f839(x85451),f845(x85451,a832),f157(x85451)),x85454)))
% 18.55/18.49 [8611]~P1(f324(x86112,x86113))+E(f324(f324(f128(x86111),f324(f180(f839(x86111)),f161(x86111,x86112,f324(f324(f139(x86111),x86113),x86114)))),f324(f324(f139(x86111),x86113),x86114)),f324(f324(f128(x86111),f324(f180(f839(x86111)),f161(x86111,x86112,x86114))),x86114))
% 18.55/18.49 [8658]E(f324(f324(f45(x86581,f845(x86582,a832)),x86583),x86584),f179(f845(x86582,a832)))+P1(f324(f324(f326(x86581),f529(x86584,x86583,x86581,x86582)),x86583))
% 18.55/18.49 [8659]E(f324(f324(f46(x86591,f845(x86592,a832)),x86593),x86594),f238(f845(x86592,a832)))+P1(f324(f324(f326(x86591),f657(x86594,x86593,x86591,x86592)),x86593))
% 18.55/18.49 [8660]E(f324(f324(f45(x86601,f845(x86602,a832)),x86603),x86604),f179(f845(x86602,a832)))+P1(f324(f324(f326(x86601),f530(x86604,x86603,x86602,x86601)),x86603))
% 18.55/18.49 [8661]E(f324(f324(f46(x86611,f845(x86612,a832)),x86613),x86614),f238(f845(x86612,a832)))+P1(f324(f324(f326(x86611),f662(x86614,x86613,x86612,x86611)),x86613))
% 18.55/18.49 [8696]P1(f324(f324(f232(a838),f324(x86961,x86962)),f324(x86961,x86963)))+~P1(f324(f324(f326(f844(x86964,x86964)),f324(f324(f247(x86964,x86964),x86962),x86963)),f324(f324(f281(a838,x86964),a236),x86961)))
% 18.55/18.49 [8746]P1(f324(f324(f186(x87461),f675(x87462,x87463,x87461,x87464)),x87462))+~P1(f324(f324(f186(f36(x87464,x87461)),x87463),x87462))
% 18.55/18.49 [8857]P1(f324(f324(f326(x88571),f523(x88572,x88573,x88574,x88571)),x88573))+~P1(f324(f324(f326(f845(x88571,a832)),x88574),f324(f324(f63(x88571),x88573),x88572)))
% 18.55/18.49 [8860]E(x88601,x88602)+~P1(f324(f324(f326(f844(x88603,x88603)),f324(f324(f247(x88603,x88603),x88601),x88602)),f324(f324(f172(f844(x88603,x88603),a832),f2(a838)),x88604)))
% 18.55/18.49 [8932]E(f324(f278(x89321,x89321,x89322),f324(f324(f303(x89321),f523(x89322,x89323,x89324,x89321)),f179(f845(x89321,a832)))),x89324)+~P1(f324(f324(f326(f845(x89321,a832)),x89324),f324(f324(f63(x89321),x89323),x89322)))
% 18.55/18.49 [8939]~P1(f324(f324(f326(f844(x89391,x89391)),f324(f324(f247(x89391,x89391),x89393),x89392)),f301(x89391,x89394)))+P1(f324(f324(f326(f844(x89391,x89391)),f324(f324(f247(x89391,x89391),x89392),x89393)),f301(x89391,f324(f279(x89391,x89391),x89394))))
% 18.55/18.49 [8950]~P7(x89501)+E(f324(f324(f82(x89501),f324(f324(f82(x89501),f324(f324(f83(x89501),x89502),f324(f324(f42(x89501),x89503),x89502))),f51(x89501,x89503,x89502))),x89504),f324(f324(f82(x89501),x89503),x89504))
% 18.55/18.49 [8957]~P1(f324(f324(f326(x89571),x89573),x89574))+P1(f324(f324(f326(f845(x89571,a832)),f324(f278(x89571,x89571,x89572),f324(f324(f303(x89571),x89573),f179(f845(x89571,a832))))),f324(f324(f63(x89571),x89574),x89572)))
% 18.55/18.49 [8967]P1(f324(f324(f326(f844(x89671,x89671)),f324(f324(f247(x89671,x89671),x89672),x89673)),f301(x89671,x89674)))+~P1(f324(f324(f326(f844(x89671,x89671)),f324(f324(f247(x89671,x89671),x89673),x89672)),f301(x89671,f324(f279(x89671,x89671),x89674))))
% 18.55/18.49 [9050]E(f324(f324(f146(x90501,f324(f154(x90501),x90502)),f324(f324(f3(a838),f324(f324(f3(a838),f324(f180(f839(x90501)),x90502)),x90503)),f80(a838))),x90504),f324(f154(x90501),f324(f324(f146(x90501,x90502),x90503),x90504)))+~P1(f324(f324(f232(a838),x90503),f324(f180(f839(x90501)),x90502)))
% 18.55/18.49 [9087]~P29(x90872,x90871,x90873,f238(f845(x90872,a832)))+P1(f324(f324(f231(f845(x90871,a832)),f324(f304(x90872,x90871,x90873),f324(f81(f845(x90872,a832)),x90874))),f324(f81(f845(x90871,a832)),f324(f304(x90872,x90871,x90873),x90874))))
% 18.55/18.49 [9095]~P9(x90951)+E(f324(f131(x90951,x90952,f324(f9(x90952,x90951,x90951),f324(f324(f10(x90951,f845(x90951,x90951),x90952),f103(x90951)),x90953)),f179(x90951)),x90954),f324(f324(f45(x90952,x90951),f324(f157(x90952),x90954)),x90953))
% 18.55/18.49 [9096]~P9(x90961)+E(f324(f131(x90961,x90962,f324(f9(x90962,x90961,x90961),f324(f324(f10(x90961,f845(x90961,x90961),x90962),f104(x90961)),x90963)),f238(x90961)),x90964),f324(f324(f46(x90962,x90961),f324(f157(x90962),x90964)),x90963))
% 18.55/18.49 [9164]~P1(f324(f324(f326(f844(f839(x91644),f839(x91644))),f324(f324(f247(f839(x91644),f839(x91644)),x91643),x91642)),f144(x91644,x91641)))+P1(f324(f324(f232(a838),f730(x91641,x91642,x91643,x91644)),f324(f180(f839(x91644)),x91643)))
% 18.55/18.49 [9165]~P7(x91651)+E(f324(f324(f82(x91651),f324(f324(f82(x91651),f324(f324(f83(x91651),f324(f324(f42(x91651),x91652),x91653)),x91653)),f51(x91651,x91652,x91653))),x91654),f324(f324(f82(x91651),x91652),x91654))
% 18.55/18.49 [9194]~P1(f324(f324(f326(f844(f839(x91941),f839(x91941))),f324(f324(f247(f839(x91941),f839(x91941)),x91942),x91943)),f324(f279(f839(x91941),f839(x91941)),f144(x91941,x91944))))+P1(f324(f324(f326(f844(f839(x91941),f839(x91941))),f324(f324(f247(f839(x91941),f839(x91941)),x91942),x91943)),f144(x91941,f324(f279(x91941,x91941),x91944))))
% 18.55/18.49 [9195]P1(f324(f324(f326(f844(f839(x91951),f839(x91951))),f324(f324(f247(f839(x91951),f839(x91951)),x91952),x91953)),f324(f279(f839(x91951),f839(x91951)),f144(x91951,x91954))))+~P1(f324(f324(f326(f844(f839(x91951),f839(x91951))),f324(f324(f247(f839(x91951),f839(x91951)),x91952),x91953)),f144(x91951,f324(f279(x91951,x91951),x91954))))
% 18.55/18.49 [9232]~P1(f324(f324(f326(x92321),x92323),f324(f262(x92321,x92322),x92324)))+P1(f324(f324(f326(f844(x92321,x92322)),f324(f324(f247(x92321,x92322),x92323),f349(x92324,x92322,x92323,x92321))),x92324))
% 18.55/18.49 [9233]~P1(f324(f324(f326(x92331),x92333),f324(f262(x92331,x92332),x92334)))+P1(f324(f324(f326(f844(x92331,x92332)),f324(f324(f247(x92331,x92332),x92333),f350(x92334,x92332,x92333,x92331))),x92334))
% 18.55/18.49 [9359]~P1(f324(f64(f842(x93591)),f324(f304(x93592,f842(x93591),x93593),f238(f845(x93592,a832)))))+P1(f324(f64(f842(x93591)),f324(f304(x93592,f842(x93591),f169(x93592,x93591,x93593,f165(x93592,x93591,x93594))),f238(f845(x93592,a832)))))
% 18.55/18.49 [9384]~P1(f324(f324(f326(f844(x93841,x93841)),f324(f324(f247(x93841,x93841),x93842),x93844)),f324(f324(f282(x93841,x93841,x93841),x93843),f301(x93841,x93843))))+P1(f324(f324(f326(f844(x93841,x93841)),f324(f324(f247(x93841,x93841),x93842),f643(x93843,x93844,x93842,x93841))),x93843))
% 18.55/18.49 [9546]~P1(f324(f324(f326(f844(x95462,x95461)),x95464),f324(f279(x95461,x95462),x95463)))+P1(f324(f324(f326(f844(x95461,x95462)),f324(f324(f247(x95461,x95462),f340(x95463,x95464,x95461,x95462)),f339(x95463,x95464,x95461,x95462))),x95463))
% 18.55/18.49 [9570]~P1(f324(f324(f326(f844(f839(x95701),f839(x95701))),f324(f324(f247(f839(x95701),f839(x95701)),x95704),x95703)),f144(x95701,x95702)))+P1(f324(f324(f326(f844(x95701,x95701)),f324(f324(f247(x95701,x95701),f732(x95702,x95703,x95704,x95701)),f733(x95702,x95703,x95704,x95701))),x95702))
% 18.55/18.49 [9650]~P1(f324(f324(f326(f844(f839(x96501),f839(x96501))),f324(f324(f247(f839(x96501),f839(x96501)),x96502),x96504)),f144(x96501,x96503)))+P1(f324(f324(f326(f844(x96501,x96501)),f324(f324(f247(x96501,x96501),f324(f324(f149(x96501),x96502),f730(x96503,x96504,x96502,x96501))),f726(x96503,x96504,x96502,x96501))),x96503))
% 18.55/18.49 [9672]~P1(f324(f64(x96722),x96724))+E(f324(f324(f324(f68(f845(x96721,a832),x96722,f103(f845(x96721,a832))),f324(f324(f9(x96722,f845(x96721,a832),f845(x96721,a832)),f324(f324(f10(x96721,f845(f845(x96721,a832),f845(x96721,a832)),x96722),f303(x96721)),x96723)),f179(f845(x96721,a832)))),f179(f845(x96721,a832))),x96724),f324(f304(x96722,x96721,x96723),x96724))
% 18.55/18.49 [9785]~P29(x97851,x97852,x97853,f238(f845(x97851,a832)))+P1(f324(f324(f231(f845(x97851,a832)),f324(f305(x97851,x97852,x97853),f324(f324(f303(x97852),x97854),f179(f845(x97852,a832))))),f324(f324(f303(x97851),f87(x97851,f324(f324(f9(x97851,x97852,a832),f324(f324(f10(x97852,f845(x97852,a832),x97851),a321),x97853)),x97854))),f179(f845(x97851,a832)))))
% 18.55/18.49 [5425]~E(f324(f324(f125(x54251),x54252),x54254),x54253)+E(f324(f324(f158(x54251),f324(f180(f839(x54251)),x54252)),x54253),x54252)
% 18.55/18.49 [5426]~E(f324(f324(f125(x54262),x54263),x54261),x54264)+E(x54261,f324(f324(f128(x54262),f324(f180(f839(x54262)),x54263)),x54264))
% 18.55/18.49 [5437]~E(x54374,f2(a838))+E(f324(f324(f149(x54371),f324(f324(f139(x54371),x54372),x54373)),x54374),x54372)
% 18.55/18.49 [5973]~P105(x59731)+E(f324(f324(f240(x59731),f324(f324(f240(x59731),x59732),x59733)),x59734),f324(f324(f240(x59731),x59732),f324(f324(f83(a838),x59733),x59734)))
% 18.55/18.49 [5974]~P75(x59741)+E(f324(f324(f240(x59741),f324(f324(f240(x59741),x59742),x59743)),x59744),f324(f324(f240(x59741),x59742),f324(f324(f83(a838),x59743),x59744)))
% 18.55/18.49 [5990]E(x59901,f2(a838))+E(f324(f324(f149(x59902),f324(f324(f139(x59902),x59903),x59904)),x59901),f324(f324(f149(x59902),x59904),f324(f324(f3(a838),x59901),f80(a838))))
% 18.55/18.49 [6015]~P105(x60151)+E(f324(f324(f83(x60151),f324(f324(f83(x60151),x60152),x60153)),x60154),f324(f324(f83(x60151),x60152),f324(f324(f83(x60151),x60153),x60154)))
% 18.55/18.49 [6016]~P114(x60161)+E(f324(f324(f284(x60161),f324(f324(f83(x60161),x60162),x60163)),x60164),f324(f324(f83(x60161),x60162),f324(f324(f284(x60161),x60163),x60164)))
% 18.55/18.49 [6017]~P105(x60171)+E(f324(f324(f82(x60171),f324(f324(f82(x60171),x60172),x60173)),x60174),f324(f324(f82(x60171),x60172),f324(f324(f82(x60171),x60173),x60174)))
% 18.55/18.49 [6018]~P4(x60181)+E(f324(f324(f83(x60181),f324(f324(f83(x60181),x60182),x60183)),x60184),f324(f324(f83(x60181),x60182),f324(f324(f83(x60181),x60183),x60184)))
% 18.55/18.49 [6019]~P105(x60191)+E(f324(f324(f83(x60191),f324(f324(f83(x60191),x60192),x60193)),x60194),f324(f324(f83(x60191),x60192),f324(f324(f83(x60191),x60193),x60194)))
% 18.55/18.49 [6021]~P105(x60211)+E(f324(f324(f82(x60211),f324(f324(f82(x60211),x60212),x60213)),x60214),f324(f324(f82(x60211),x60212),f324(f324(f82(x60211),x60213),x60214)))
% 18.55/18.49 [6022]~P5(x60221)+E(f324(f324(f82(x60221),f324(f324(f82(x60221),x60222),x60223)),x60224),f324(f324(f82(x60221),x60222),f324(f324(f82(x60221),x60223),x60224)))
% 18.55/18.49 [6023]~P86(x60231)+E(f324(f324(f235(x60231),f324(f324(f235(x60231),x60232),x60233)),x60234),f324(f324(f235(x60231),x60232),f324(f324(f235(x60231),x60233),x60234)))
% 18.55/18.49 [6024]~P86(x60241)+E(f324(f324(f235(x60241),f324(f324(f235(x60241),x60242),x60243)),x60244),f324(f324(f235(x60241),x60242),f324(f324(f235(x60241),x60243),x60244)))
% 18.55/18.49 [6025]~P86(x60251)+E(f324(f324(f178(x60251),f324(f324(f178(x60251),x60252),x60253)),x60254),f324(f324(f178(x60251),x60252),f324(f324(f178(x60251),x60253),x60254)))
% 18.55/18.49 [6026]~P86(x60261)+E(f324(f324(f178(x60261),f324(f324(f178(x60261),x60262),x60263)),x60264),f324(f324(f178(x60261),x60262),f324(f324(f178(x60261),x60263),x60264)))
% 18.55/18.49 [6027]~P93(x60271)+E(f324(f324(f103(x60271),f324(f324(f103(x60271),x60272),x60273)),x60274),f324(f324(f103(x60271),x60272),f324(f324(f103(x60271),x60273),x60274)))
% 18.55/18.49 [6028]~P93(x60281)+E(f324(f324(f103(x60281),f324(f324(f103(x60281),x60282),x60283)),x60284),f324(f324(f103(x60281),x60282),f324(f324(f103(x60281),x60283),x60284)))
% 18.55/18.49 [6029]~P94(x60291)+E(f324(f324(f103(x60291),f324(f324(f103(x60291),x60292),x60293)),x60294),f324(f324(f103(x60291),x60292),f324(f324(f103(x60291),x60293),x60294)))
% 18.55/18.49 [6030]~P94(x60301)+E(f324(f324(f104(x60301),f324(f324(f104(x60301),x60302),x60303)),x60304),f324(f324(f104(x60301),x60302),f324(f324(f104(x60301),x60303),x60304)))
% 18.55/18.49 [6031]~P99(x60311)+E(f324(f324(f104(x60311),f324(f324(f104(x60311),x60312),x60313)),x60314),f324(f324(f104(x60311),x60312),f324(f324(f104(x60311),x60313),x60314)))
% 18.55/18.49 [6032]~P99(x60321)+E(f324(f324(f104(x60321),f324(f324(f104(x60321),x60322),x60323)),x60324),f324(f324(f104(x60321),x60322),f324(f324(f104(x60321),x60323),x60324)))
% 18.55/18.49 [6043]~P7(x60431)+E(f51(x60431,f324(f324(f82(x60431),x60432),f324(f324(f83(x60431),x60433),x60434)),x60434),f51(x60431,x60432,x60434))
% 18.55/18.49 [6044]~P7(x60441)+E(f51(x60441,f324(f324(f82(x60441),x60442),f324(f324(f83(x60441),x60443),x60444)),x60443),f51(x60441,x60442,x60443))
% 18.55/18.49 [6182]E(f324(f324(f149(x61821),f324(f324(f158(x61821),x61822),x61823)),x61824),f324(f324(f149(x61821),x61823),x61824))+~P1(f324(f324(f232(a838),x61824),x61822))
% 18.55/18.49 [6367]~P105(x63671)+E(f324(f324(f83(x63671),f324(f324(f83(x63671),x63672),x63673)),x63674),f324(f324(f83(x63671),f324(f324(f83(x63671),x63672),x63674)),x63673))
% 18.55/18.49 [6368]~P105(x63681)+E(f324(f324(f82(x63681),f324(f324(f82(x63681),x63682),x63683)),x63684),f324(f324(f82(x63681),f324(f324(f82(x63681),x63682),x63684)),x63683))
% 18.55/18.49 [6429]~P2(x64292)+E(f324(f324(f8(x64291,x64292),f324(f18(x64292,x64291),x64293)),x64294),f324(f324(f83(x64292),f324(f102(x64292),f324(f41(x64291),x64294))),x64293))
% 18.55/18.49 [6607]E(f324(f324(f104(f845(x66071,a832)),f324(f324(f303(x66071),x66072),x66073)),x66074),f324(f324(f104(f845(x66071,a832)),x66073),x66074))+P1(f324(f324(f326(x66071),x66072),x66074))
% 18.55/18.49 [6608]E(f324(f324(f104(f845(x66081,a832)),f324(f324(f303(x66081),x66082),x66083)),x66084),f324(f324(f104(f845(x66081,a832)),x66083),x66084))+P1(f324(f324(f326(x66081),x66082),x66084))
% 18.55/18.49 [6682]~P105(x66821)+E(f324(f324(f82(x66821),f324(f324(f83(x66821),x66822),x66823)),f324(f324(f83(x66821),x66824),x66823)),f324(f324(f83(x66821),f324(f324(f82(x66821),x66822),x66824)),x66823))
% 18.55/18.49 [6683]~P106(x66831)+E(f324(f324(f82(x66831),f324(f324(f83(x66831),x66832),x66833)),f324(f324(f83(x66831),x66834),x66833)),f324(f324(f83(x66831),f324(f324(f82(x66831),x66832),x66834)),x66833))
% 18.55/18.49 [6684]~P76(x66841)+E(f324(f324(f235(x66841),f324(f324(f82(x66841),x66842),x66843)),f324(f324(f82(x66841),x66844),x66843)),f324(f324(f82(x66841),f324(f324(f235(x66841),x66842),x66844)),x66843))
% 18.55/18.49 [6685]~P76(x66851)+E(f324(f324(f178(x66851),f324(f324(f82(x66851),x66852),x66853)),f324(f324(f82(x66851),x66854),x66853)),f324(f324(f82(x66851),f324(f324(f178(x66851),x66852),x66854)),x66853))
% 18.55/18.49 [6686]~P70(x66861)+E(f324(f324(f235(x66861),f324(f324(f3(x66861),x66862),x66863)),f324(f324(f3(x66861),x66864),x66863)),f324(f324(f3(x66861),f324(f324(f235(x66861),x66862),x66864)),x66863))
% 18.55/18.49 [6687]~P70(x66871)+E(f324(f324(f178(x66871),f324(f324(f3(x66871),x66872),x66873)),f324(f324(f3(x66871),x66874),x66873)),f324(f324(f3(x66871),f324(f324(f178(x66871),x66872),x66874)),x66873))
% 18.55/18.49 [6688]~P105(x66881)+E(f324(f324(f83(x66881),f324(f324(f240(x66881),x66882),x66883)),f324(f324(f240(x66881),x66884),x66883)),f324(f324(f240(x66881),f324(f324(f83(x66881),x66882),x66884)),x66883))
% 18.55/18.49 [6689]~P68(x66891)+E(f324(f324(f83(x66891),f324(f324(f240(x66891),x66892),x66893)),f324(f324(f240(x66891),x66894),x66893)),f324(f324(f240(x66891),f324(f324(f83(x66891),x66892),x66894)),x66893))
% 18.55/18.49 [6690]~P59(x66901)+E(f324(f324(f284(x66901),f324(f324(f240(x66901),x66902),x66903)),f324(f324(f240(x66901),x66904),x66903)),f324(f324(f240(x66901),f324(f324(f284(x66901),x66902),x66904)),x66903))
% 18.55/18.49 [6691]~P114(x66911)+E(f324(f324(f82(x66911),f324(f324(f284(x66911),x66912),x66913)),f324(f324(f284(x66911),x66914),x66913)),f324(f324(f284(x66911),f324(f324(f82(x66911),x66912),x66914)),x66913))
% 18.55/18.49 [6692]~P114(x66921)+E(f324(f324(f3(x66921),f324(f324(f284(x66921),x66922),x66923)),f324(f324(f284(x66921),x66924),x66923)),f324(f324(f284(x66921),f324(f324(f3(x66921),x66922),x66924)),x66923))
% 18.55/18.49 [6693]~P86(x66931)+E(f324(f324(f178(x66931),f324(f324(f235(x66931),x66932),x66933)),f324(f324(f235(x66931),x66934),x66933)),f324(f324(f235(x66931),f324(f324(f178(x66931),x66932),x66934)),x66933))
% 18.55/18.49 [6694]~P86(x66941)+E(f324(f324(f235(x66941),f324(f324(f178(x66941),x66942),x66943)),f324(f324(f178(x66941),x66944),x66943)),f324(f324(f178(x66941),f324(f324(f235(x66941),x66942),x66944)),x66943))
% 18.55/18.49 [6695]~P97(x66951)+E(f324(f324(f104(x66951),f324(f324(f103(x66951),x66952),x66953)),f324(f324(f103(x66951),x66954),x66953)),f324(f324(f103(x66951),f324(f324(f104(x66951),x66952),x66954)),x66953))
% 18.55/18.49 [6696]~P97(x66961)+E(f324(f324(f103(x66961),f324(f324(f104(x66961),x66962),x66963)),f324(f324(f104(x66961),x66964),x66963)),f324(f324(f104(x66961),f324(f324(f103(x66961),x66962),x66964)),x66963))
% 18.55/18.49 [6697]~P105(x66971)+E(f324(f324(f82(x66971),f324(f324(f83(x66971),x66972),x66973)),f324(f324(f83(x66971),x66974),x66973)),f324(f324(f83(x66971),f324(f324(f82(x66971),x66972),x66974)),x66973))
% 18.55/18.49 [6732]E(f324(f324(f146(x67321,x67322),x67323),x67324),x67322)+~P1(f324(f324(f231(a838),f324(f180(f839(x67321)),x67322)),x67323))
% 18.55/18.49 [6761]~P1(f324(x67613,x67614))+P1(f324(f324(f324(f103(f845(x67611,a832)),x67612),x67613),x67614))
% 18.55/18.49 [6762]~P1(f324(x67623,x67624))+P1(f324(f324(f324(f103(f845(x67621,a832)),x67622),x67623),x67624))
% 18.55/18.49 [6763]~P1(f324(x67632,x67634))+P1(f324(f324(f324(f103(f845(x67631,a832)),x67632),x67633),x67634))
% 18.55/18.49 [6764]~P1(f324(x67642,x67644))+P1(f324(f324(f324(f103(f845(x67641,a832)),x67642),x67643),x67644))
% 18.55/18.49 [6786]E(f324(f324(f149(x67861),f324(f324(f125(x67861),x67862),x67863)),x67864),f324(f324(f149(x67861),x67862),x67864))+~P1(f324(f324(f232(a838),x67864),f324(f180(f839(x67861)),x67862)))
% 18.55/18.49 [6795]E(f324(f324(f3(f845(x67951,a832)),f324(f324(f303(x67951),x67952),x67953)),x67954),f324(f324(f3(f845(x67951,a832)),x67953),x67954))+~P1(f324(f324(f326(x67951),x67952),x67954))
% 18.55/18.49 [6796]E(f324(f324(f3(f845(x67961,a832)),f324(f324(f303(x67961),x67962),x67963)),x67964),f324(f324(f3(f845(x67961,a832)),x67963),x67964))+~P1(f324(f324(f326(x67961),x67962),x67964))
% 18.55/18.49 [6837]~E(f129(a838,f324(f295(a838,x68371),x68372)),f324(f324(f139(a838),x68374),x68373))+E(f129(a838,f324(f295(a838,f324(f324(f82(a838),x68371),f80(a838))),x68372)),x68373)
% 18.55/18.49 [6906]E(x69061,f2(a838))+E(f324(f324(f139(x69062),x69063),f324(f324(f158(x69062),f324(f324(f3(a838),x69061),f80(a838))),x69064)),f324(f324(f158(x69062),x69061),f324(f324(f139(x69062),x69063),x69064)))
% 18.55/18.49 [7010]E(f324(f324(f149(x70101),x70102),f324(f324(f3(a838),x70103),f324(f180(f839(x70101)),x70104))),f324(f324(f149(x70101),f324(f324(f125(x70101),x70104),x70102)),x70103))+P1(f324(f324(f232(a838),x70103),f324(f180(f839(x70101)),x70104)))
% 18.55/18.49 [7037]E(f324(f324(f104(f845(x70371,a832)),x70372),f324(f324(f303(x70371),x70373),x70374)),f324(f324(f303(x70371),x70373),f324(f324(f104(f845(x70371,a832)),x70372),x70374)))+~P1(f324(f324(f326(x70371),x70373),x70372))
% 18.55/18.49 [7038]E(f324(f324(f104(f845(x70381,a832)),x70382),f324(f324(f303(x70381),x70383),x70384)),f324(f324(f303(x70381),x70383),f324(f324(f104(f845(x70381,a832)),x70382),x70384)))+~P1(f324(f324(f326(x70381),x70383),x70382))
% 18.55/18.49 [7072]E(f324(f324(f149(x70721),f324(f324(f146(x70721,x70722),x70723),x70724)),x70723),x70724)+~P1(f324(f324(f232(a838),x70723),f324(f180(f839(x70721)),x70722)))
% 18.55/18.49 [7094]E(x70941,f179(f845(x70942,a832)))+E(f324(f304(f844(x70943,x70942),x70943,f246(x70943,x70942)),f324(f324(f249(x70943,x70942),x70944),f324(f18(f845(x70942,a832),x70943),x70941))),x70944)
% 18.55/18.49 [7095]E(x70951,f179(f845(x70952,a832)))+E(f324(f304(f844(x70952,x70953),x70953,f251(x70952,x70953)),f324(f324(f249(x70952,x70953),x70951),f324(f18(f845(x70953,a832),x70952),x70954))),x70954)
% 18.55/18.49 [7177]E(f324(f324(f3(f845(x71771,a832)),f324(f324(f303(x71771),x71772),x71773)),x71774),f324(f324(f303(x71771),x71772),f324(f324(f3(f845(x71771,a832)),x71773),x71774)))+P1(f324(f324(f326(x71771),x71772),x71774))
% 18.55/18.49 [7218]~E(x72184,f179(f845(x72182,a832)))+E(f324(f304(f844(x72181,x72182),x72181,f246(x72181,x72182)),f324(f324(f249(x72181,x72182),x72183),f324(f18(f845(x72182,a832),x72181),x72184))),f179(f845(x72181,a832)))
% 18.55/18.49 [7219]~E(x72193,f179(f845(x72191,a832)))+E(f324(f304(f844(x72191,x72192),x72192,f251(x72191,x72192)),f324(f324(f249(x72191,x72192),x72193),f324(f18(f845(x72192,a832),x72191),x72194))),f179(f845(x72192,a832)))
% 18.55/18.49 [7276]~P1(f324(f324(f326(x72761),x72762),x72764))+P1(f324(f324(f326(x72761),x72762),f324(f324(f103(f845(x72761,a832)),x72763),x72764)))
% 18.55/18.49 [7277]~P1(f324(f324(f326(x72771),x72772),x72774))+P1(f324(f324(f326(x72771),x72772),f324(f324(f103(f845(x72771,a832)),x72773),x72774)))
% 18.55/18.49 [7278]~P1(f324(f324(f326(x72781),x72782),x72784))+P1(f324(f324(f326(x72781),x72782),f324(f324(f103(f845(x72781,a832)),x72783),x72784)))
% 18.55/18.49 [7279]~P1(f324(f324(f326(x72791),x72792),x72793))+P1(f324(f324(f326(x72791),x72792),f324(f324(f103(f845(x72791,a832)),x72793),x72794)))
% 18.55/18.49 [7280]~P1(f324(f324(f326(x72801),x72802),x72803))+P1(f324(f324(f326(x72801),x72802),f324(f324(f103(f845(x72801,a832)),x72803),x72804)))
% 18.55/18.49 [7281]~P1(f324(f324(f326(x72811),x72812),x72813))+P1(f324(f324(f326(x72811),x72812),f324(f324(f103(f845(x72811,a832)),x72813),x72814)))
% 18.55/18.49 [7302]E(f324(f324(f104(f845(x73021,a832)),f324(f324(f303(x73021),x73022),x73023)),x73024),f324(f324(f303(x73021),x73022),f324(f324(f104(f845(x73021,a832)),x73023),x73024)))+~P1(f324(f324(f326(x73021),x73022),x73024))
% 18.55/18.49 [7303]E(f324(f324(f104(f845(x73031,a832)),f324(f324(f303(x73031),x73032),x73033)),x73034),f324(f324(f303(x73031),x73032),f324(f324(f104(f845(x73031,a832)),x73033),x73034)))+~P1(f324(f324(f326(x73031),x73032),x73034))
% 18.55/18.49 [7583]P1(f324(x75831,x75832))+~P1(f324(f324(f324(f104(f845(x75833,a832)),x75834),x75831),x75832))
% 18.55/18.49 [7584]P1(f324(x75841,x75842))+~P1(f324(f324(f324(f104(f845(x75843,a832)),x75841),x75844),x75842))
% 18.55/18.49 [7585]P1(f324(x75851,x75852))+~P1(f324(f324(f324(f104(f845(x75853,a832)),x75854),x75851),x75852))
% 18.55/18.49 [7586]P1(f324(x75861,x75862))+~P1(f324(f324(f324(f104(f845(x75863,a832)),x75861),x75864),x75862))
% 18.55/18.49 [7589]E(f324(f324(f8(x75891,a838),x75892),f324(f324(f3(f845(x75891,a832)),x75893),f324(f324(f303(x75891),x75894),f179(f845(x75891,a832))))),f324(f324(f8(x75891,a838),x75892),x75893))+P1(f324(f324(f326(x75891),x75894),x75893))
% 18.55/18.49 [7595]~P67(x75951)+E(f324(f151(x75951),f324(f324(f141(a838,x75951),x75952),f129(a838,f324(f295(a838,x75953),x75954)))),f324(f324(f8(a838,x75951),x75952),f324(f157(a838),f129(a838,f324(f295(a838,x75953),x75954)))))
% 18.55/18.49 [7596]~P67(x75961)+E(f324(f324(f8(a838,x75961),x75962),f324(f157(a838),f129(a838,f324(f295(a838,x75963),x75964)))),f324(f151(x75961),f324(f324(f141(a838,x75961),x75962),f129(a838,f324(f295(a838,x75963),x75964)))))
% 18.55/18.49 [7712]~E(x77123,x77124)+P1(f324(f65(x77121,x77122,f324(f324(f303(x77121),x77123),f179(f845(x77121,a832)))),x77124))
% 18.55/18.49 [7809]P1(f324(f324(f326(x78091),x78092),f324(f157(x78091),x78093)))+~P1(f324(f324(f326(x78091),x78092),f324(f157(x78091),f324(f324(f158(x78091),x78094),x78093))))
% 18.55/18.49 [7810]P1(f324(f324(f326(x78101),x78102),f324(f157(x78101),x78103)))+~P1(f324(f324(f326(x78101),x78102),f324(f157(x78101),f324(f324(f128(x78101),x78104),x78103))))
% 18.55/18.49 [7882]P1(f324(f324(f326(x78821),x78822),x78823))+~P1(f324(f324(f326(x78821),x78822),f324(f324(f104(f845(x78821,a832)),x78824),x78823)))
% 18.55/18.49 [7883]P1(f324(f324(f326(x78831),x78832),x78833))+~P1(f324(f324(f326(x78831),x78832),f324(f324(f3(f845(x78831,a832)),x78833),x78834)))
% 18.55/18.49 [7884]P1(f324(f324(f326(x78841),x78842),x78843))+~P1(f324(f324(f326(x78841),x78842),f324(f324(f3(f845(x78841,a832)),x78843),x78844)))
% 18.55/18.49 [7885]P1(f324(f324(f326(x78851),x78852),x78853))+~P1(f324(f324(f326(x78851),x78852),f324(f324(f3(f845(x78851,a832)),x78853),x78854)))
% 18.55/18.49 [7886]P1(f324(f324(f326(x78861),x78862),x78863))+~P1(f324(f324(f326(x78861),x78862),f324(f324(f104(f845(x78861,a832)),x78864),x78863)))
% 18.55/18.49 [7887]P1(f324(f324(f326(x78871),x78872),x78873))+~P1(f324(f324(f326(x78871),x78872),f324(f324(f104(f845(x78871,a832)),x78874),x78873)))
% 18.55/18.49 [7888]P1(f324(f324(f326(x78881),x78882),x78883))+~P1(f324(f324(f326(x78881),x78882),f324(f324(f104(f845(x78881,a832)),x78883),x78884)))
% 18.55/18.49 [7889]P1(f324(f324(f326(x78891),x78892),x78893))+~P1(f324(f324(f326(x78891),x78892),f324(f324(f104(f845(x78891,a832)),x78893),x78894)))
% 18.55/18.49 [7890]P1(f324(f324(f326(x78901),x78902),x78903))+~P1(f324(f324(f326(x78901),x78902),f324(f324(f104(f845(x78901,a832)),x78903),x78904)))
% 18.55/18.49 [7908]E(f324(f324(f125(x79081),f324(f324(f158(x79081),x79082),x79083)),f324(f324(f139(x79081),x79084),f324(f324(f128(x79081),f324(a114,x79082)),x79083))),f324(f324(f146(x79081,x79083),x79082),x79084))+~P1(f324(f324(f232(a838),x79082),f324(f180(f839(x79081)),x79083)))
% 18.55/18.49 [7931]P1(f324(f324(f326(x79311),x79312),x79313))+~P1(f324(f324(f231(f845(x79311,a832)),f324(f324(f303(x79311),x79312),x79314)),x79313))
% 18.55/18.49 [7960]~P1(f324(f324(f326(x79601),x79602),x79603))+~P1(f324(f324(f326(x79601),x79602),f324(f324(f3(f845(x79601,a832)),x79604),x79603)))
% 18.55/18.49 [7961]~P1(f324(f324(f326(x79611),x79612),x79613))+~P1(f324(f324(f326(x79611),x79612),f324(f324(f3(f845(x79611,a832)),x79614),x79613)))
% 18.55/18.49 [7962]~P1(f324(f324(f326(x79621),x79622),x79623))+~P1(f324(f324(f326(x79621),x79622),f324(f324(f3(f845(x79621,a832)),x79624),x79623)))
% 18.55/18.49 [7996]~P1(f324(f324(f232(a838),x79964),f324(f180(f839(x79961)),x79963)))+P1(f324(f324(f326(x79961),x79962),f324(f157(x79961),f324(f324(f146(x79961,x79963),x79964),x79962))))
% 18.55/18.49 [8039]E(f324(f106(a838),x80391),f2(a838))+E(f324(f324(f139(x80392),x80393),f324(f324(f158(x80392),f324(f324(f3(a838),f324(f106(a838),x80391)),f80(a838))),x80394)),f324(f324(f158(x80392),f324(f106(a838),x80391)),f324(f324(f139(x80392),x80393),x80394)))
% 18.55/18.49 [8048]E(f324(f324(f149(x80481),f324(f324(f128(x80481),x80482),x80483)),x80484),f324(f324(f149(x80481),x80483),f324(f324(f82(a838),x80482),x80484)))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x80482),x80484)),f324(f180(f839(x80481)),x80483)))
% 18.55/18.49 [8057]~P2(x80572)+E(f324(f324(f8(x80571,x80572),f324(f324(f10(a838,x80572,x80571),f102(x80572)),x80573)),x80574),f324(f102(x80572),f324(f324(f8(x80571,a838),x80573),x80574)))
% 18.55/18.49 [8058]~P119(x80582)+E(f324(f324(f8(x80581,x80582),f324(f324(f10(a1,x80582,x80581),f105(x80582)),x80583)),x80584),f324(f105(x80582),f324(f324(f8(x80581,a1),x80583),x80584)))
% 18.55/18.49 [8111]~P62(x81112)+E(f324(f324(f11(x81111,x81112),f324(f324(f10(x81112,x81112,x81111),f77(x81112)),x81113)),x81114),f324(f77(x81112),f324(f324(f11(x81111,x81112),x81113),x81114)))
% 18.55/18.49 [8112]~P6(x81122)+E(f324(f324(f8(x81121,x81122),f324(f324(f10(x81122,x81122,x81121),f81(x81122)),x81123)),x81124),f324(f81(x81122),f324(f324(f8(x81121,x81122),x81123),x81124)))
% 18.55/18.49 [8114]E(f324(f324(f8(x81141,a838),x81142),f324(f324(f3(f845(x81141,a832)),x81143),f324(f324(f303(x81141),x81144),f179(f845(x81141,a832))))),f324(f324(f3(a838),f324(f324(f8(x81141,a838),x81142),x81143)),f324(x81142,x81144)))+~P1(f324(f324(f326(x81141),x81144),x81143))
% 18.55/18.49 [8133]P1(f324(f324(f231(f845(x81331,a832)),x81332),x81333))+~P1(f324(f324(f231(f845(x81331,a832)),f324(f324(f303(x81331),x81334),x81332)),x81333))
% 18.55/18.49 [8343]P36(x83431,x83432)+~P36(x83431,f324(f324(f303(f844(x83431,x83431)),f324(f324(f247(x83431,x83431),x83433),x83434)),x83432))
% 18.55/18.49 [8344]P55(x83441,x83442)+~P55(x83441,f324(f324(f303(f844(x83441,x83441)),f324(f324(f247(x83441,x83441),x83443),x83444)),x83442))
% 18.55/18.49 [8352]~P86(x83521)+E(f324(f324(f137(x83521,x83521,f7(x83521)),x83522),f324(f324(f137(x83521,x83521,f7(x83521)),x83523),x83524)),f324(f324(f137(x83521,x83521,f7(x83521)),x83523),f324(f324(f137(x83521,x83521,f7(x83521)),x83522),x83524)))
% 18.55/18.49 [8362]E(x83621,x83622)+~P1(f324(f65(x83623,x83624,f324(f324(f303(x83623),x83621),f179(f845(x83623,a832)))),x83622))
% 18.55/18.49 [8367]E(f324(f165(x83671,x83672,x83673),x83674),f182(x83672))+P1(f324(f324(f326(x83671),x83674),f324(f304(f844(x83671,x83672),x83671,f246(x83671,x83672)),f324(f157(f844(x83671,x83672)),x83673))))
% 18.55/18.49 [8373]E(f324(f324(f125(x83731),f324(f324(f158(x83731),x83732),x83733)),f324(f324(f158(x83731),x83734),f324(f324(f128(x83731),x83732),x83733))),f324(f324(f158(x83731),f324(f324(f82(a838),x83732),x83734)),x83733))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x83732),x83734)),f324(f180(f839(x83731)),x83733)))
% 18.55/18.49 [8413]P1(f324(f64(x84131),x84132))+~E(x84132,f324(f304(a838,x84131,x84133),f324(f257(a838),f324(f324(f9(a838,a838,a832),f232(a838)),x84134))))
% 18.55/18.49 [8414]P1(f324(f64(x84141),x84142))+~E(x84142,f324(f304(a838,x84141,x84143),f324(f257(a838),f324(f324(f9(a838,a838,a832),f232(a838)),x84144))))
% 18.55/18.49 [8434]~P83(x84341)+E(f324(f131(x84341,x84341,f82(x84341),f324(f324(f82(x84341),x84342),x84343)),x84344),f324(f324(f82(x84341),x84342),f324(f131(x84341,x84341,f82(x84341),x84343),x84344)))
% 18.55/18.49 [8466]P1(f324(f324(f231(f845(x84661,a832)),f324(f262(x84661,x84662),x84663)),f324(f262(x84661,x84662),x84664)))+~P1(f324(f324(f231(f845(f844(x84661,x84662),a832)),x84663),x84664))
% 18.55/18.49 [8477]~P1(f324(f324(f231(a838),x84772),x84774))+P1(f324(f324(f231(f845(x84771,a832)),f324(f157(x84771),f324(f324(f158(x84771),x84772),x84773))),f324(f157(x84771),f324(f324(f158(x84771),x84774),x84773))))
% 18.55/18.49 [8478]~P1(f324(f324(f231(a838),x84784),x84782))+P1(f324(f324(f231(f845(x84781,a832)),f324(f157(x84781),f324(f324(f128(x84781),x84782),x84783))),f324(f157(x84781),f324(f324(f128(x84781),x84784),x84783))))
% 18.55/18.49 [8521]~P1(f324(f64(x85211),f324(f324(f3(f845(x85211,a832)),x85212),x85214)))+P1(f324(f64(x85211),f324(f324(f3(f845(x85211,a832)),x85212),f324(f324(f303(x85211),x85213),x85214))))
% 18.55/18.49 [8555]P1(f324(f324(f326(f844(x85551,x85551)),x85552),f301(x85551,x85553)))+~P1(f324(f324(f326(f844(x85551,x85551)),x85552),f324(f324(f172(f844(x85551,x85551),a832),x85554),x85553)))
% 18.55/18.49 [8556]P1(f324(f324(f326(f844(x85561,x85561)),x85562),f301(x85561,x85563)))+~P1(f324(f324(f326(f844(x85561,x85561)),x85562),f324(f324(f172(f844(x85561,x85561),a832),x85564),x85563)))
% 18.55/18.49 [8633]~P1(f324(f64(x86331),f324(f324(f3(f845(x86331,a832)),x86332),f324(f324(f303(x86331),x86334),x86333))))+P1(f324(f64(x86331),f324(f324(f3(f845(x86331,a832)),x86332),x86333)))
% 18.55/18.49 [8700]P1(f324(f324(f326(f844(x87001,x87002)),f324(f324(f247(x87001,x87002),x87003),x87004)),f179(f845(f844(x87001,x87002),a832))))+~P1(f324(f324(f179(f845(x87001,f845(x87002,a832))),x87003),x87004))
% 18.55/18.49 [8779]~E(f324(f165(x87791,x87792,x87793),x87794),f182(x87792))+~P1(f324(f324(f326(x87791),x87794),f324(f304(f844(x87791,x87792),x87791,f246(x87791,x87792)),f324(f157(f844(x87791,x87792)),x87793))))
% 18.55/18.49 [8816]~P86(x88161)+P1(f324(f324(f231(x88161),f324(f324(f178(x88161),x88162),f324(f324(f235(x88161),x88163),x88164))),f324(f324(f235(x88161),f324(f324(f178(x88161),x88162),x88163)),f324(f324(f178(x88161),x88162),x88164))))
% 18.55/18.49 [8817]~P94(x88171)+P1(f324(f324(f231(x88171),f324(f324(f103(x88171),x88172),f324(f324(f104(x88171),x88173),x88174))),f324(f324(f104(x88171),f324(f324(f103(x88171),x88172),x88173)),f324(f324(f103(x88171),x88172),x88174))))
% 18.55/18.49 [8835]~P1(f324(f324(f326(f844(x88351,x88352)),f324(f324(f247(x88351,x88352),x88353),x88354)),f179(f845(f844(x88351,x88352),a832))))+P1(f324(f324(f179(f845(x88351,f845(x88352,a832))),x88353),x88354))
% 18.55/18.49 [8953]E(x89531,x89532)+~P1(f324(f324(f326(f844(x89533,x89533)),f324(f324(f247(x89533,x89533),x89531),x89532)),f324(f157(f844(x89533,x89533)),f324(f324(f166(x89533,x89533),x89534),x89534))))
% 18.55/18.49 [8983]~P1(f324(f324(f326(f844(x89831,x89831)),f324(f324(f247(x89831,x89831),x89833),x89832)),f301(x89831,x89834)))+~P36(x89831,f324(f324(f303(f844(x89831,x89831)),f324(f324(f247(x89831,x89831),x89832),x89833)),x89834))
% 18.55/18.49 [8984]~P1(f324(f324(f326(f844(x89841,x89841)),f324(f324(f247(x89841,x89841),x89843),x89842)),f301(x89841,x89844)))+~P55(x89841,f324(f324(f303(f844(x89841,x89841)),f324(f324(f247(x89841,x89841),x89842),x89843)),x89844))
% 18.55/18.49 [8997]P1(f324(f324(f326(x89971),x89972),f324(f157(x89971),x89973)))+~P1(f324(f324(f326(f844(x89971,x89971)),f324(f324(f247(x89971,x89971),x89972),x89974)),f324(f157(f844(x89971,x89971)),f324(f324(f166(x89971,x89971),x89973),x89973))))
% 18.55/18.49 [9028]~P86(x90281)+P1(f324(f324(f231(x90281),f324(f324(f178(x90281),f324(f324(f235(x90281),x90282),x90283)),f324(f324(f235(x90281),x90282),x90284))),f324(f324(f235(x90281),x90282),f324(f324(f178(x90281),x90283),x90284))))
% 18.55/18.49 [9029]~P94(x90291)+P1(f324(f324(f231(x90291),f324(f324(f103(x90291),f324(f324(f104(x90291),x90292),x90293)),f324(f324(f104(x90291),x90292),x90294))),f324(f324(f104(x90291),x90292),f324(f324(f103(x90291),x90293),x90294))))
% 18.55/18.49 [9063]P1(f324(f324(f326(f844(x90631,x90631)),f324(f324(f247(x90631,x90631),x90632),x90633)),f324(f324(f282(x90631,x90631,x90631),x90634),f301(x90631,x90634))))+~P1(f324(f324(f326(f844(x90631,x90631)),f324(f324(f247(x90631,x90631),x90632),x90633)),x90634))
% 18.55/18.49 [9092]~E(f324(f304(x90922,x90921,x90923),f238(f845(x90922,a832))),f238(f845(x90921,a832)))+P1(f324(f324(f231(f845(x90921,a832)),f324(f81(f845(x90921,a832)),f324(f304(x90922,x90921,x90923),x90924))),f324(f304(x90922,x90921,x90923),f324(f81(f845(x90922,a832)),x90924))))
% 18.55/18.49 [9398]P1(f324(f324(f326(f844(x93981,x93981)),f324(f324(f247(x93981,x93981),x93982),x93983)),f324(f279(x93981,x93981),f324(f324(f282(x93981,x93981,x93981),x93984),f301(x93981,x93984)))))+~P1(f324(f324(f326(f844(x93981,x93981)),f324(f324(f247(x93981,x93981),x93982),x93983)),f324(f324(f282(x93981,x93981,x93981),f324(f279(x93981,x93981),x93984)),f301(x93981,f324(f279(x93981,x93981),x93984)))))
% 18.55/18.49 [9399]~P1(f324(f324(f326(f844(x93991,x93991)),f324(f324(f247(x93991,x93991),x93992),x93993)),f324(f279(x93991,x93991),f324(f324(f282(x93991,x93991,x93991),x93994),f301(x93991,x93994)))))+P1(f324(f324(f326(f844(x93991,x93991)),f324(f324(f247(x93991,x93991),x93992),x93993)),f324(f324(f282(x93991,x93991,x93991),f324(f279(x93991,x93991),x93994)),f301(x93991,f324(f279(x93991,x93991),x93994)))))
% 18.55/18.49 [9424]~P1(f324(f324(f326(x94242),x94244),f324(f260(x94241,x94242),x94243)))+P1(f324(f324(f326(f844(x94241,x94242)),f324(f324(f247(x94241,x94242),f341(x94243,x94241,x94244,x94242)),x94244)),x94243))
% 18.55/18.49 [9425]~P1(f324(f324(f326(x94252),x94254),f324(f260(x94251,x94252),x94253)))+P1(f324(f324(f326(f844(x94251,x94252)),f324(f324(f247(x94251,x94252),f342(x94253,x94251,x94254,x94252)),x94254)),x94253))
% 18.55/18.49 [9446]~P1(f324(f324(f326(x94461),x94464),f324(f324(f103(f845(x94461,a832)),x94462),x94463)))+P1(f324(f324(f324(f103(f845(x94461,a832)),f324(f324(f9(x94461,f845(x94461,a832),a832),f326(x94461)),x94462)),f324(f324(f9(x94461,f845(x94461,a832),a832),f326(x94461)),x94463)),x94464))
% 18.55/18.49 [9447]~P1(f324(f324(f326(x94471),x94474),f324(f324(f104(f845(x94471,a832)),x94472),x94473)))+P1(f324(f324(f324(f104(f845(x94471,a832)),f324(f324(f9(x94471,f845(x94471,a832),a832),f326(x94471)),x94472)),f324(f324(f9(x94471,f845(x94471,a832),a832),f326(x94471)),x94473)),x94474))
% 18.55/18.49 [9522]~P1(f324(f324(f326(f844(x95221,x95221)),f324(f324(f247(x95221,x95221),x95224),x95223)),f324(f324(f282(x95221,x95221,x95221),x95222),f301(x95221,x95222))))+P1(f324(f324(f326(f844(x95221,x95221)),f324(f324(f247(x95221,x95221),f644(x95222,x95223,x95224,x95221)),x95223)),x95222))
% 18.55/18.49 [9558]P1(f324(f324(f326(x95581),x95582),f324(f324(f103(f845(x95581,a832)),x95583),x95584)))+~P1(f324(f324(f324(f103(f845(x95581,a832)),f324(f324(f9(x95581,f845(x95581,a832),a832),f326(x95581)),x95583)),f324(f324(f9(x95581,f845(x95581,a832),a832),f326(x95581)),x95584)),x95582))
% 18.55/18.49 [9559]P1(f324(f324(f326(x95591),x95592),f324(f324(f104(f845(x95591,a832)),x95593),x95594)))+~P1(f324(f324(f324(f104(f845(x95591,a832)),f324(f324(f9(x95591,f845(x95591,a832),a832),f326(x95591)),x95593)),f324(f324(f9(x95591,f845(x95591,a832),a832),f326(x95591)),x95594)),x95592))
% 18.55/18.49 [9838]P34(x98381,f324(f324(f9(x98381,f845(f844(x98381,x98381),a832),f845(x98381,a832)),f324(f324(f10(f845(x98381,f845(f845(f844(x98381,x98381),a832),a832)),f845(f845(f844(x98381,x98381),a832),f845(x98381,a832)),x98381),f9(x98381,f845(f844(x98381,x98381),a832),a832)),f324(f324(f10(f845(x98381,f844(x98381,x98381)),f845(x98381,f845(f845(f844(x98381,x98381),a832),a832)),x98381),f324(f10(f844(x98381,x98381),f845(f845(f844(x98381,x98381),a832),a832),x98381),f326(f844(x98381,x98381)))),f247(x98381,x98381)))),x98382),x98383,x98384)+~P1(f324(f324(f326(f844(f839(x98381),f839(x98381))),f324(f324(f247(f839(x98381),f839(x98381)),x98383),x98384)),f145(x98381,x98382)))
% 18.55/18.49 [9842]P56(x98421,f324(f324(f9(x98421,f845(f844(x98421,x98421),a832),f845(x98421,a832)),f324(f324(f10(f845(x98421,f845(f845(f844(x98421,x98421),a832),a832)),f845(f845(f844(x98421,x98421),a832),f845(x98421,a832)),x98421),f9(x98421,f845(f844(x98421,x98421),a832),a832)),f324(f324(f10(f845(x98421,f844(x98421,x98421)),f845(x98421,f845(f845(f844(x98421,x98421),a832),a832)),x98421),f324(f10(f844(x98421,x98421),f845(f845(f844(x98421,x98421),a832),a832),x98421),f326(f844(x98421,x98421)))),f247(x98421,x98421)))),x98422),x98423,x98424)+~P1(f324(f324(f326(f844(f845(x98421,a832),f845(x98421,a832))),f324(f324(f247(f845(x98421,a832),f845(x98421,a832)),x98423),x98424)),f317(x98421,x98422)))
% 18.55/18.49 [9871]E(x98711,x98712)+~E(f324(f324(f9(x98713,f845(f844(x98713,x98714),a832),f845(x98714,a832)),f324(f324(f10(f845(x98714,f845(f845(f844(x98713,x98714),a832),a832)),f845(f845(f844(x98713,x98714),a832),f845(x98714,a832)),x98713),f9(x98714,f845(f844(x98713,x98714),a832),a832)),f324(f324(f10(f845(x98714,f844(x98713,x98714)),f845(x98714,f845(f845(f844(x98713,x98714),a832),a832)),x98713),f324(f10(f844(x98713,x98714),f845(f845(f844(x98713,x98714),a832),a832),x98714),f326(f844(x98713,x98714)))),f247(x98713,x98714)))),x98711),f324(f324(f9(x98713,f845(f844(x98713,x98714),a832),f845(x98714,a832)),f324(f324(f10(f845(x98714,f845(f845(f844(x98713,x98714),a832),a832)),f845(f845(f844(x98713,x98714),a832),f845(x98714,a832)),x98713),f9(x98714,f845(f844(x98713,x98714),a832),a832)),f324(f324(f10(f845(x98714,f844(x98713,x98714)),f845(x98714,f845(f845(f844(x98713,x98714),a832),a832)),x98713),f324(f10(f844(x98713,x98714),f845(f845(f844(x98713,x98714),a832),a832),x98714),f326(f844(x98713,x98714)))),f247(x98713,x98714)))),x98712))
% 18.55/18.49 [9874]~P34(x98741,f324(f324(f9(x98741,f845(f844(x98741,x98741),a832),f845(x98741,a832)),f324(f324(f10(f845(x98741,f845(f845(f844(x98741,x98741),a832),a832)),f845(f845(f844(x98741,x98741),a832),f845(x98741,a832)),x98741),f9(x98741,f845(f844(x98741,x98741),a832),a832)),f324(f324(f10(f845(x98741,f844(x98741,x98741)),f845(x98741,f845(f845(f844(x98741,x98741),a832),a832)),x98741),f324(f10(f844(x98741,x98741),f845(f845(f844(x98741,x98741),a832),a832),x98741),f326(f844(x98741,x98741)))),f247(x98741,x98741)))),x98744),x98742,x98743)+P1(f324(f324(f326(f844(f839(x98741),f839(x98741))),f324(f324(f247(f839(x98741),f839(x98741)),x98742),x98743)),f145(x98741,x98744)))
% 18.55/18.49 [9875]~P56(x98751,f324(f324(f9(x98751,f845(f844(x98751,x98751),a832),f845(x98751,a832)),f324(f324(f10(f845(x98751,f845(f845(f844(x98751,x98751),a832),a832)),f845(f845(f844(x98751,x98751),a832),f845(x98751,a832)),x98751),f9(x98751,f845(f844(x98751,x98751),a832),a832)),f324(f324(f10(f845(x98751,f844(x98751,x98751)),f845(x98751,f845(f845(f844(x98751,x98751),a832),a832)),x98751),f324(f10(f844(x98751,x98751),f845(f845(f844(x98751,x98751),a832),a832),x98751),f326(f844(x98751,x98751)))),f247(x98751,x98751)))),x98754),x98752,x98753)+P1(f324(f324(f326(f844(f845(x98751,a832),f845(x98751,a832))),f324(f324(f247(f845(x98751,a832),f845(x98751,a832)),x98752),x98753)),f317(x98751,x98754)))
% 18.55/18.49 [7351]~P89(x73511)+E(f324(f324(f83(x73511),f324(f106(x73511),x73512)),f324(f324(f83(x73511),f324(f106(x73511),x73513)),x73514)),f324(f324(f83(x73511),f324(f106(x73511),f324(f324(f83(a1),x73512),x73513))),x73514))
% 18.55/18.49 [7352]~P89(x73521)+E(f324(f324(f82(x73521),f324(f106(x73521),x73522)),f324(f324(f82(x73521),f324(f106(x73521),x73523)),x73524)),f324(f324(f82(x73521),f324(f106(x73521),f324(f324(f82(a1),x73522),x73523))),x73524))
% 18.55/18.49 [7353]~P89(x73531)+E(f324(f324(f82(x73531),f324(f106(x73531),x73532)),f324(f324(f3(x73531),f324(f106(x73531),x73533)),x73534)),f324(f324(f3(x73531),f324(f106(x73531),f324(f324(f82(a1),x73532),x73533))),x73534))
% 18.55/18.49 [7403]~P2(x74031)+E(f324(f151(x74031),f324(f324(f141(x74032,x74031),f324(f18(x74031,x74032),x74033)),x74034)),f324(f324(f83(x74031),f324(f102(x74031),f324(f180(f839(x74032)),x74034))),x74033))
% 18.55/18.49 [7640]E(f324(f266(x76401,f324(f324(f139(f844(a101,x76401)),x76402),x76403)),x76404),f324(f251(a101,x76401),x76402))+~P1(f324(f324(f232(a101),x76404),f324(f246(a101,x76401),x76402)))
% 18.55/18.49 [7688]~P89(x76881)+E(f324(f324(f82(x76881),f324(f106(x76881),x76882)),f324(f324(f3(x76881),x76883),f324(f106(x76881),x76884))),f324(f324(f82(x76881),f324(f106(x76881),f324(f324(f82(a1),x76882),f324(f81(a1),x76884)))),x76883))
% 18.55/18.49 [7821]E(f324(f266(x78211,x78212),f324(f324(f3(a101),x78213),f324(f246(a101,x78211),x78214))),f324(f266(x78211,f324(f324(f139(f844(a101,x78211)),x78214),x78212)),x78213))+P1(f324(f324(f232(a101),x78213),f324(f246(a101,x78211),x78214)))
% 18.55/18.49 [8260]~P1(f324(f324(f326(x82601),x82602),f324(f157(x82601),f116(x82601,x82604))))+P1(f324(f324(f326(x82601),x82602),f324(f157(x82601),f116(x82601,f324(f324(f125(x82601),x82603),x82604)))))
% 18.55/18.49 [8261]~P1(f324(f324(f326(x82611),x82612),f324(f157(x82611),f116(x82611,x82613))))+P1(f324(f324(f326(x82611),x82612),f324(f157(x82611),f116(x82611,f324(f324(f125(x82611),x82613),x82614)))))
% 18.55/18.49 [8282]E(f324(f324(f103(f845(x82821,a832)),f324(f324(f104(f845(x82821,a832)),x82822),x82823)),x82824),f324(f324(f104(f845(x82821,a832)),x82822),f324(f324(f103(f845(x82821,a832)),x82823),x82824)))+~P1(f324(f324(f231(f845(x82821,a832)),x82824),x82822))
% 18.55/18.49 [8569]~E(f324(f324(f103(f845(x85691,a832)),f324(f324(f104(f845(x85691,a832)),x85693),x85694)),x85692),f324(f324(f104(f845(x85691,a832)),x85693),f324(f324(f103(f845(x85691,a832)),x85694),x85692)))+P1(f324(f324(f231(f845(x85691,a832)),x85692),x85693))
% 18.55/18.49 [8822]~P1(f324(f324(f231(f845(x88221,a832)),x88222),f324(f324(f103(f845(x88221,a832)),x88223),x88224)))+P1(f324(f324(f231(f845(x88221,a832)),f324(f324(f3(f845(x88221,a832)),x88222),x88223)),x88224))
% 18.55/18.49 [8937]P1(f324(f324(f231(f845(x89371,a832)),x89372),f324(f324(f103(f845(x89371,a832)),x89373),x89374)))+~P1(f324(f324(f231(f845(x89371,a832)),f324(f324(f3(f845(x89371,a832)),x89372),x89373)),x89374))
% 18.55/18.49 [9010]~P78(x90101)+E(f324(f77(x90101),f324(f324(f8(x90102,x90101),f324(f324(f10(x90101,x90101,x90102),f77(x90101)),x90103)),x90104)),f324(f324(f8(x90102,x90101),f324(f324(f10(x90101,x90101,x90102),f77(x90101)),x90103)),x90104))
% 18.55/18.49 [9157]~P78(x91571)+P1(f324(f324(f231(x91571),f2(x91571)),f324(f324(f8(x91572,x91571),f324(f324(f10(x91571,x91571,x91572),f77(x91571)),x91573)),x91574)))
% 18.55/18.49 [9160]~P6(x91601)+E(f324(f151(x91601),f324(f324(f141(x91602,x91601),f324(f75(x91601,x91601,x91602,f81(x91601)),x91603)),x91604)),f324(f81(x91601),f324(f151(x91601),f324(f324(f141(x91602,x91601),x91603),x91604))))
% 18.55/18.49 [9297]~P78(x92971)+P1(f324(f324(f231(x92971),f324(f77(x92971),f324(f324(f8(x92972,x92971),x92973),x92974))),f324(f324(f8(x92972,x92971),f324(f324(f10(x92971,x92971,x92972),f77(x92971)),x92973)),x92974)))
% 18.55/18.49 [9325]~E(f324(f324(f82(a838),x93251),x93254),f324(f324(f82(a838),x93253),x93252))+P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),f324(f324(f247(a838,a838),x93251),x93252)),f324(f324(f247(a838,a838),x93253),x93254))),a111))
% 18.55/18.49 [9326]~P1(f324(f324(f232(a838),x93261),x93263))+P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),f324(f324(f247(a838,a838),x93261),x93262)),f324(f324(f247(a838,a838),x93263),x93264))),a38))
% 18.55/18.49 [9327]~P1(f324(f324(f232(a838),x93271),x93273))+P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),f324(f324(f247(a838,a838),x93271),x93272)),f324(f324(f247(a838,a838),x93273),x93274))),a72))
% 18.55/18.49 [9470]E(f324(f324(f82(a838),x94701),x94702),f324(f324(f82(a838),x94703),x94704))+~P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),f324(f324(f247(a838,a838),x94701),x94704)),f324(f324(f247(a838,a838),x94703),x94702))),a111))
% 18.55/18.49 [9495]E(f324(f324(f149(x94951),f324(f324(f128(x94951),f324(f180(f839(x94951)),f161(x94951,x94952,x94953))),x94953)),x94954),f324(f324(f149(x94951),x94953),f324(f324(f82(a838),x94954),f324(f180(f839(x94951)),f161(x94951,x94952,x94953)))))+~P1(f324(f324(f232(a838),x94954),f324(f180(f839(x94951)),f324(f324(f128(x94951),f324(f180(f839(x94951)),f161(x94951,x94952,x94953))),x94953))))
% 18.55/18.49 [9515]~P1(f324(f324(f326(x95152),x95154),f324(f324(f45(x95151,f845(x95152,a832)),f238(f845(x95151,a832))),x95153)))+P1(f324(f324(f324(f45(x95151,f845(x95152,a832)),f238(f845(x95151,a832))),f324(f324(f10(f845(x95152,a832),f845(x95152,a832),x95151),f324(f9(x95152,f845(x95152,a832),a832),f326(x95152))),x95153)),x95154))
% 18.55/18.49 [9516]~P1(f324(f324(f326(x95162),x95164),f324(f324(f46(x95161,f845(x95162,a832)),f238(f845(x95161,a832))),x95163)))+P1(f324(f324(f324(f46(x95161,f845(x95162,a832)),f238(f845(x95161,a832))),f324(f324(f10(f845(x95162,a832),f845(x95162,a832),x95161),f324(f9(x95162,f845(x95162,a832),a832),f326(x95162))),x95163)),x95164))
% 18.55/18.49 [9583]~P1(f324(f55(x95831,x95832),f324(f324(f247(a1,a1),x95834),x95833)))+P1(f324(f55(f324(f81(a1),x95831),x95832),f324(f324(f247(a1,a1),f324(f324(f324(f98(a1),f324(f324(a321,x95833),f2(a1))),f324(f81(a1),x95834)),f324(f324(f3(a1),f324(f81(a1),x95834)),f80(a1)))),f324(f324(f324(f98(a1),f324(f324(a321,x95833),f2(a1))),f2(a1)),f324(f324(f3(a1),x95832),x95833)))))
% 18.55/18.49 [9592]P1(f324(f324(f326(x95921),x95922),f324(f324(f45(x95923,f845(x95921,a832)),f238(f845(x95923,a832))),x95924)))+~P1(f324(f324(f324(f45(x95923,f845(x95921,a832)),f238(f845(x95923,a832))),f324(f324(f10(f845(x95921,a832),f845(x95921,a832),x95923),f324(f9(x95921,f845(x95921,a832),a832),f326(x95921))),x95924)),x95922))
% 18.55/18.49 [9593]P1(f324(f324(f326(x95931),x95932),f324(f324(f46(x95933,f845(x95931,a832)),f238(f845(x95933,a832))),x95934)))+~P1(f324(f324(f324(f46(x95933,f845(x95931,a832)),f238(f845(x95933,a832))),f324(f324(f10(f845(x95931,a832),f845(x95931,a832),x95933),f324(f9(x95931,f845(x95931,a832),a832),f326(x95931))),x95934)),x95932))
% 18.55/18.49 [9605]E(f324(f324(f45(a838,f845(x96051,a832)),f238(f845(a838,a832))),x96052),f324(f324(f45(a838,f845(x96051,a832)),f238(f845(a838,a832))),x96053))+~E(f324(f324(f45(a838,f845(x96051,a832)),f324(f295(a838,f2(a838)),f549(x96052,x96054,x96053,x96051))),x96053),f324(f324(f45(a838,f845(x96051,a832)),f324(f295(a838,f2(a838)),f324(f324(f82(a838),f549(x96052,x96054,x96053,x96051)),x96054))),x96052))
% 18.55/18.49 [9933]~P1(f324(f324(f231(f845(f844(x99331,x99332),a832)),x99333),x99334))+P1(f324(f324(f231(f845(x99331,f845(x99332,a832))),f324(f324(f9(x99331,f845(f844(x99331,x99332),a832),f845(x99332,a832)),f324(f324(f10(f845(x99332,f845(f845(f844(x99331,x99332),a832),a832)),f845(f845(f844(x99331,x99332),a832),f845(x99332,a832)),x99331),f9(x99332,f845(f844(x99331,x99332),a832),a832)),f324(f324(f10(f845(x99332,f844(x99331,x99332)),f845(x99332,f845(f845(f844(x99331,x99332),a832),a832)),x99331),f324(f10(f844(x99331,x99332),f845(f845(f844(x99331,x99332),a832),a832),x99332),f326(f844(x99331,x99332)))),f247(x99331,x99332)))),x99333)),f324(f324(f9(x99331,f845(f844(x99331,x99332),a832),f845(x99332,a832)),f324(f324(f10(f845(x99332,f845(f845(f844(x99331,x99332),a832),a832)),f845(f845(f844(x99331,x99332),a832),f845(x99332,a832)),x99331),f9(x99332,f845(f844(x99331,x99332),a832),a832)),f324(f324(f10(f845(x99332,f844(x99331,x99332)),f845(x99332,f845(f845(f844(x99331,x99332),a832),a832)),x99331),f324(f10(f844(x99331,x99332),f845(f845(f844(x99331,x99332),a832),a832),x99332),f326(f844(x99331,x99332)))),f247(x99331,x99332)))),x99334)))
% 18.55/18.49 [9950]P1(f324(f324(f231(f845(f844(x99501,x99502),a832)),x99503),x99504))+~P1(f324(f324(f231(f845(x99501,f845(x99502,a832))),f324(f324(f9(x99501,f845(f844(x99501,x99502),a832),f845(x99502,a832)),f324(f324(f10(f845(x99502,f845(f845(f844(x99501,x99502),a832),a832)),f845(f845(f844(x99501,x99502),a832),f845(x99502,a832)),x99501),f9(x99502,f845(f844(x99501,x99502),a832),a832)),f324(f324(f10(f845(x99502,f844(x99501,x99502)),f845(x99502,f845(f845(f844(x99501,x99502),a832),a832)),x99501),f324(f10(f844(x99501,x99502),f845(f845(f844(x99501,x99502),a832),a832),x99502),f326(f844(x99501,x99502)))),f247(x99501,x99502)))),x99503)),f324(f324(f9(x99501,f845(f844(x99501,x99502),a832),f845(x99502,a832)),f324(f324(f10(f845(x99502,f845(f845(f844(x99501,x99502),a832),a832)),f845(f845(f844(x99501,x99502),a832),f845(x99502,a832)),x99501),f9(x99502,f845(f844(x99501,x99502),a832),a832)),f324(f324(f10(f845(x99502,f844(x99501,x99502)),f845(x99502,f845(f845(f844(x99501,x99502),a832),a832)),x99501),f324(f10(f844(x99501,x99502),f845(f845(f844(x99501,x99502),a832),a832),x99502),f326(f844(x99501,x99502)))),f247(x99501,x99502)))),x99504)))
% 18.55/18.49 [9055]~P1(f324(f324(f326(f844(x90551,x90551)),x90552),f301(x90551,x90554)))+P1(f324(f324(f326(f844(x90551,x90551)),x90552),f301(x90551,f324(f324(f103(f845(f844(x90551,x90551),a832)),x90553),x90554))))
% 18.55/18.49 [9056]~P1(f324(f324(f326(f844(x90561,x90561)),x90562),f301(x90561,x90563)))+P1(f324(f324(f326(f844(x90561,x90561)),x90562),f301(x90561,f324(f324(f103(f845(f844(x90561,x90561),a832)),x90563),x90564))))
% 18.55/18.49 [9390]~E(f324(f157(x93901),x93904),f168(x93901,x93902,x93903))+E(f165(x93901,x93902,f324(f324(f141(x93901,f844(x93901,x93902)),f324(f324(f20(x93901,x93902,f844(x93901,x93902)),f247(x93901,x93902)),f324(f324(f10(f842(x93902),x93902,x93901),f230(x93902)),x93903))),x93904)),x93903)
% 18.55/18.49 [9688]~P1(f324(f324(f232(a838),f324(f324(f82(a838),x96881),x96884)),f324(f324(f82(a838),x96883),x96882)))+P1(f324(f324(f232(a1),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x96881),x96882)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x96883),x96884)),f179(f845(f844(a838,a838),a832)))))))
% 18.55/18.49 [9689]~P1(f324(f324(f231(a838),f324(f324(f82(a838),x96891),x96894)),f324(f324(f82(a838),x96893),x96892)))+P1(f324(f324(f231(a1),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x96891),x96892)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x96893),x96894)),f179(f845(f844(a838,a838),a832)))))))
% 18.55/18.49 [9776]P1(f324(f324(f232(a838),f324(f324(f82(a838),x97761),x97762)),f324(f324(f82(a838),x97763),x97764)))+~P1(f324(f324(f232(a1),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x97761),x97764)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x97763),x97762)),f179(f845(f844(a838,a838),a832)))))))
% 18.55/18.49 [9777]P1(f324(f324(f231(a838),f324(f324(f82(a838),x97771),x97772)),f324(f324(f82(a838),x97773),x97774)))+~P1(f324(f324(f231(a1),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x97771),x97774)),f179(f845(f844(a838,a838),a832)))))),f324(a91,f324(f278(f844(a838,a838),f844(a838,a838),a111),f324(f324(f303(f844(a838,a838)),f324(f324(f247(a838,a838),x97773),x97772)),f179(f845(f844(a838,a838),a832)))))))
% 18.55/18.49 [9824]P1(f324(f324(f231(f845(x98241,a832)),f324(f324(f45(a838,f845(x98241,a832)),f238(f845(a838,a832))),x98242)),f324(f324(f45(a838,f845(x98241,a832)),f238(f845(a838,a832))),x98243)))+~P1(f324(f324(f231(f845(x98241,a832)),f324(f324(f45(a838,f845(x98241,a832)),f324(f295(a838,f2(a838)),f550(x98243,x98244,x98242,x98241))),x98242)),f324(f324(f45(a838,f845(x98241,a832)),f324(f295(a838,f2(a838)),f324(f324(f82(a838),f550(x98243,x98244,x98242,x98241)),x98244))),x98243)))
% 18.55/18.49 [9877]P1(f324(f324(f231(a101),x98774),f2(a101)))+E(f324(f324(f254(f844(a101,a101),f844(x98771,f845(a841,a831)),f844(a101,a101),f844(f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101))),f324(x98772,x98773)),f324(f324(f10(f845(f845(a101,f845(a832,f842(f840(x98771)))),f845(f844(a101,a101),f844(f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101)))),f845(f844(a101,a101),f844(f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101))),f844(x98771,f845(a841,a831))),f324(f254(f844(a101,a101),f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101),f844(f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101))),f273(x98771,x98772,f324(f324(f3(a101),x98774),f80(a101)),x98773))),f324(f324(f10(f845(f845(a101,f845(a832,f842(f840(x98771)))),f845(a101,f845(a832,f842(f840(x98771))))),f845(f845(a101,f845(a832,f842(f840(x98771)))),f845(f844(a101,a101),f844(f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101)))),f844(x98771,f845(a841,a831))),f324(f10(f845(a101,f845(a832,f842(f840(x98771)))),f845(f844(a101,a101),f844(f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101))),f845(a101,f845(a832,f842(f840(x98771))))),f247(f845(a101,f845(a832,f842(f840(x98771)))),f844(a101,a101)))),f324(f324(f10(f845(a101,f845(a832,f842(f840(x98771)))),f845(f845(a101,f845(a832,f842(f840(x98771)))),f845(a101,f845(a832,f842(f840(x98771))))),f844(x98771,f845(a841,a831))),f50(x98771)),f324(f324(f10(x98771,f845(a101,f845(a832,f842(f840(x98771)))),f844(x98771,f845(a841,a831))),f48(x98771)),f246(x98771,f845(a841,a831))))))),f273(x98771,x98772,x98774,x98773))
% 18.55/18.49 [9924]~P1(f324(f324(f326(x99242),x99244),f324(f260(x99241,x99242),x99243)))+P1(f324(f245(x99241,x99242,f324(f324(f9(x99241,f845(f844(x99241,x99242),a832),f845(x99242,a832)),f324(f324(f10(f845(x99242,f845(f845(f844(x99241,x99242),a832),a832)),f845(f845(f844(x99241,x99242),a832),f845(x99242,a832)),x99241),f9(x99242,f845(f844(x99241,x99242),a832),a832)),f324(f324(f10(f845(x99242,f844(x99241,x99242)),f845(x99242,f845(f845(f844(x99241,x99242),a832),a832)),x99241),f324(f10(f844(x99241,x99242),f845(f845(f844(x99241,x99242),a832),a832),x99242),f326(f844(x99241,x99242)))),f247(x99241,x99242)))),x99243)),x99244))
% 18.55/18.49 [9925]~P1(f324(f324(f326(x99251),x99254),f324(f262(x99251,x99252),x99253)))+P1(f324(f244(x99251,x99252,f324(f324(f9(x99251,f845(f844(x99251,x99252),a832),f845(x99252,a832)),f324(f324(f10(f845(x99252,f845(f845(f844(x99251,x99252),a832),a832)),f845(f845(f844(x99251,x99252),a832),f845(x99252,a832)),x99251),f9(x99252,f845(f844(x99251,x99252),a832),a832)),f324(f324(f10(f845(x99252,f844(x99251,x99252)),f845(x99252,f845(f845(f844(x99251,x99252),a832),a832)),x99251),f324(f10(f844(x99251,x99252),f845(f845(f844(x99251,x99252),a832),a832),x99252),f326(f844(x99251,x99252)))),f247(x99251,x99252)))),x99253)),x99254))
% 18.55/18.49 [9936]P1(f324(f324(f326(x99361),x99362),f324(f260(x99363,x99361),x99364)))+~P1(f324(f245(x99363,x99361,f324(f324(f9(x99363,f845(f844(x99363,x99361),a832),f845(x99361,a832)),f324(f324(f10(f845(x99361,f845(f845(f844(x99363,x99361),a832),a832)),f845(f845(f844(x99363,x99361),a832),f845(x99361,a832)),x99363),f9(x99361,f845(f844(x99363,x99361),a832),a832)),f324(f324(f10(f845(x99361,f844(x99363,x99361)),f845(x99361,f845(f845(f844(x99363,x99361),a832),a832)),x99363),f324(f10(f844(x99363,x99361),f845(f845(f844(x99363,x99361),a832),a832),x99361),f326(f844(x99363,x99361)))),f247(x99363,x99361)))),x99364)),x99362))
% 18.55/18.49 [9937]P1(f324(f324(f326(x99371),x99372),f324(f262(x99371,x99373),x99374)))+~P1(f324(f244(x99371,x99373,f324(f324(f9(x99371,f845(f844(x99371,x99373),a832),f845(x99373,a832)),f324(f324(f10(f845(x99373,f845(f845(f844(x99371,x99373),a832),a832)),f845(f845(f844(x99371,x99373),a832),f845(x99373,a832)),x99371),f9(x99373,f845(f844(x99371,x99373),a832),a832)),f324(f324(f10(f845(x99373,f844(x99371,x99373)),f845(x99373,f845(f845(f844(x99371,x99373),a832),a832)),x99371),f324(f10(f844(x99371,x99373),f845(f845(f844(x99371,x99373),a832),a832),x99373),f326(f844(x99371,x99373)))),f247(x99371,x99373)))),x99374)),x99372))
% 18.55/18.49 [9702]~P105(x97021)+E(f324(f324(f83(x97021),f324(f324(f82(x97021),f80(x97021)),f80(x97021))),f324(f324(f8(a838,x97021),f324(f324(f10(x97021,x97021,a838),f324(f82(x97021),x97022)),f324(f324(f9(a838,x97021,x97021),f324(f324(f10(x97021,f845(x97021,x97021),a838),f83(x97021)),f102(x97021))),x97023))),f324(f258(a838),x97024))),f324(f324(f83(x97021),f324(f102(x97021),x97024)),f324(f324(f82(x97021),x97022),f324(f324(f82(x97021),x97022),f324(f324(f83(x97021),f324(f102(x97021),f324(f324(f3(a838),x97024),f80(a838)))),x97023)))))
% 18.55/18.49 [9845]P1(f324(x98451,f355(x98452,x98453,x98454,x98451)))+P36(x98452,f324(f257(f844(x98452,x98452)),f324(f252(x98452,x98452,a832),f324(f324(f10(f845(x98452,a832),f845(x98452,a832),x98452),f324(f20(x98452,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98452),a322),x98451))),f324(f324(f9(x98452,f845(x98452,x98452),f845(x98452,a832)),f324(f324(f10(f845(x98452,a832),f845(f845(x98452,x98452),f845(x98452,a832)),x98452),f10(x98452,a832,x98452)),a321)),x98453)))))
% 18.55/18.49 [9859]~P1(f324(f324(f232(a838),f324(x98594,f324(x98593,f355(x98591,x98593,x98594,x98592)))),f324(x98594,f355(x98591,x98593,x98594,x98592))))+P36(x98591,f324(f257(f844(x98591,x98591)),f324(f252(x98591,x98591,a832),f324(f324(f10(f845(x98591,a832),f845(x98591,a832),x98591),f324(f20(x98591,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98591),a322),x98592))),f324(f324(f9(x98591,f845(x98591,x98591),f845(x98591,a832)),f324(f324(f10(f845(x98591,a832),f845(f845(x98591,x98591),f845(x98591,a832)),x98591),f10(x98591,a832,x98591)),a321)),x98593)))))
% 18.55/18.49 [9963]~P1(f324(f324(f326(f844(x99631,x99631)),f324(f324(f247(x99631,x99631),x99633),x99634)),f324(f324(f103(f845(f844(x99631,x99631),a832)),x99632),f301(x99631,f179(f845(f844(x99631,x99631),a832))))))+P1(f324(f324(f324(f324(f103(f845(x99631,f845(x99631,a832))),f324(f324(f9(x99631,f845(f844(x99631,x99631),a832),f845(x99631,a832)),f324(f324(f10(f845(x99631,f845(f845(f844(x99631,x99631),a832),a832)),f845(f845(f844(x99631,x99631),a832),f845(x99631,a832)),x99631),f9(x99631,f845(f844(x99631,x99631),a832),a832)),f324(f324(f10(f845(x99631,f844(x99631,x99631)),f845(x99631,f845(f845(f844(x99631,x99631),a832),a832)),x99631),f324(f10(f844(x99631,x99631),f845(f845(f844(x99631,x99631),a832),a832),x99631),f326(f844(x99631,x99631)))),f247(x99631,x99631)))),x99632)),a321),x99633),x99634))
% 18.55/18.49 [9972]P1(f324(f324(f326(f844(x99721,x99721)),f324(f324(f247(x99721,x99721),x99722),x99723)),f324(f324(f103(f845(f844(x99721,x99721),a832)),x99724),f301(x99721,f179(f845(f844(x99721,x99721),a832))))))+~P1(f324(f324(f324(f324(f103(f845(x99721,f845(x99721,a832))),f324(f324(f9(x99721,f845(f844(x99721,x99721),a832),f845(x99721,a832)),f324(f324(f10(f845(x99721,f845(f845(f844(x99721,x99721),a832),a832)),f845(f845(f844(x99721,x99721),a832),f845(x99721,a832)),x99721),f9(x99721,f845(f844(x99721,x99721),a832),a832)),f324(f324(f10(f845(x99721,f844(x99721,x99721)),f845(x99721,f845(f845(f844(x99721,x99721),a832),a832)),x99721),f324(f10(f844(x99721,x99721),f845(f845(f844(x99721,x99721),a832),a832),x99721),f326(f844(x99721,x99721)))),f247(x99721,x99721)))),x99724)),a321),x99722),x99723))
% 18.55/18.49 [9921]E(f324(f324(f139(f839(x99211)),f324(f324(f139(x99211),x99212),f324(f131(f839(x99211),f839(x99211),f125(x99211),f115(x99211)),f324(f324(f141(f839(x99211),f839(x99211)),f143(f839(x99211),x99211,f115(x99211),f324(f324(f10(f839(x99211),f845(f839(x99211),f839(x99211)),x99211),f18(f839(x99211),f839(x99211))),f324(f324(f9(x99211,f839(x99211),f839(x99211)),f139(x99211)),f115(x99211))))),x99213)))),f163(x99211,f324(f324(f139(f839(x99211)),x99214),f324(f131(f839(f839(x99211)),f839(f839(x99211)),f125(f839(x99211)),f115(f839(x99211))),f324(f324(f141(f839(x99211),f839(f839(x99211))),f143(f839(f839(x99211)),x99211,f115(f839(x99211)),f324(f18(f845(f839(x99211),f839(f839(x99211))),x99211),f324(f324(f9(f839(x99211),f839(f839(x99211)),f839(f839(x99211))),f139(f839(x99211))),f115(f839(x99211)))))),x99213))))),f163(x99211,f324(f324(f139(f839(x99211)),f324(f324(f139(x99211),x99212),x99214)),x99213)))+~P1(f324(f313(f839(f839(x99211)),f164(x99211)),f324(f324(f139(f839(x99211)),f324(f324(f139(x99211),x99212),x99214)),x99213)))
% 18.55/18.49 [9962]~P1(f324(f64(x99622),f324(f257(x99622),x99624)))+P1(f324(f64(x99621),f324(f257(x99621),f324(f324(f10(f845(x99622,a832),a832,x99621),f89(x99622)),f324(f324(f9(x99621,f845(x99622,a832),f845(x99622,a832)),f324(f324(f10(f845(x99622,f845(a832,a832)),f845(f845(x99622,a832),f845(x99622,a832)),x99621),f20(x99622,a832,a832)),f324(f324(f10(f845(x99622,a832),f845(x99622,f845(a832,a832)),x99621),f324(f10(a832,f845(a832,a832),x99622),a322)),f324(f324(f9(x99621,f845(x99622,x99621),f845(x99622,a832)),f324(f324(f10(f845(x99621,a832),f845(f845(x99622,x99621),f845(x99622,a832)),x99621),f10(x99621,a832,x99622)),a321)),x99623)))),x99624)))))
% 18.55/18.49 [8934]~P39(f36(x89341,x89345),x89342,x89343,x89344)+P39(x89341,x89342,x89343,f664(x89344,x89343,x89342,x89345,x89341))
% 18.55/18.49 [8935]~P39(f36(x89355,x89351),x89354,x89353,x89352)+P39(x89351,f664(x89352,x89353,x89354,x89351,x89355),x89353,x89352)
% 18.55/18.49 [5450]E(f324(f324(f303(x54501),x54502),f168(x54501,x54503,x54504)),f168(x54501,x54503,x54504))+~E(f324(x54504,x54502),f324(f226(x54503),x54505))
% 18.55/18.49 [5865]P1(f324(f245(x58651,x58652,x58653),x58654))+~P1(f324(f324(x58653,x58655),x58654))
% 18.55/18.49 [5866]P1(f324(f245(x58661,x58662,x58663),x58664))+~P1(f324(f324(x58663,x58665),x58664))
% 18.55/18.49 [5867]P1(f324(f244(x58671,x58672,x58673),x58674))+~P1(f324(f324(x58673,x58674),x58675))
% 18.55/18.49 [5868]P1(f324(f244(x58681,x58682,x58683),x58684))+~P1(f324(f324(x58683,x58684),x58685))
% 18.55/18.49 [5871]~E(f324(x58714,x58712),f324(f226(x58713),x58715))+P1(f324(f324(f326(x58711),x58712),f168(x58711,x58713,x58714)))
% 18.55/18.49 [5872]~E(f324(x58724,x58725),f324(f226(x58721),x58722))+P1(f324(f324(f326(x58721),x58722),f170(x58723,x58721,x58724)))
% 18.55/18.49 [6357]~E(x63575,f2(a101))+E(f324(f192(x63571,x63572,x63573,x63574),x63575),f117(x63572))
% 18.55/18.49 [6358]~E(x63585,f2(a101))+E(f324(f190(x63581,x63582,x63583,x63584),x63585),f124(x63582))
% 18.55/18.49 [6453]~P39(f28(x64533,x64534),x64532,x64535,x64531)+E(x64531,f324(f324(f324(a188,x64532),x64533),f324(x64534,x64532)))
% 18.55/18.49 [6498]~E(x64983,f2(a101))+E(f324(f269(x64981,x64982,x64983,x64984),x64985),f324(f247(x64981,x64982),x64985))
% 18.55/18.49 [6577]~E(f324(x65774,x65775),f182(x65772))+E(f324(f228(f842(x65771),x65772,f182(x65771),x65773),f324(x65774,x65775)),f182(x65771))
% 18.55/18.49 [6578]~E(f324(x65784,x65785),f182(x65782))+E(f324(f228(f842(x65781),x65782,f182(x65781),x65783),f324(x65784,x65785)),f182(x65781))
% 18.55/18.49 [7229]E(f324(x72291,x72292),f182(x72293))+~E(f324(f169(x72294,x72293,x72295,x72291),x72292),f182(x72293))
% 18.55/18.49 [7230]E(f324(x72301,x72302),f182(x72303))+~E(f324(f169(x72304,x72303,x72301,x72305),x72302),f182(x72303))
% 18.55/18.49 [7270]E(f324(f169(x72701,x72702,x72703,x72704),x72705),f324(x72703,x72705))+P1(f324(f324(f326(x72701),x72705),f168(x72701,x72702,x72704)))
% 18.55/18.49 [7271]E(f324(f169(x72711,x72712,x72713,x72714),x72715),f324(x72714,x72715))+P1(f324(f324(f326(x72711),x72715),f168(x72711,x72712,x72713)))
% 18.55/18.49 [7600]~P24(x76004,x76001,x76002,x76005)+E(f324(f75(x76001,x76001,x76001,f324(x76002,x76003)),f324(x76002,x76003)),f324(x76002,x76003))
% 18.55/18.49 [7644]E(f324(f169(x76441,x76442,x76443,x76444),x76445),f324(x76444,x76445))+~P1(f324(f324(f326(x76441),x76445),f168(x76441,x76442,x76444)))
% 18.55/18.49 [7997]~P20(x79975,x79971,x79972)+E(f324(f75(x79971,x79971,x79971,f324(x79972,x79973)),f324(x79972,x79974)),f324(f75(x79971,x79971,x79971,f324(x79972,x79974)),f324(x79972,x79973)))
% 18.55/18.49 [8322]P1(f324(f324(f326(f844(x83221,x83221)),f324(f324(f247(x83221,x83221),x83222),x83223)),f319(x83221,x83224,x83225)))+~P1(f324(f324(f232(a838),f324(x83224,x83222)),f324(x83224,x83223)))
% 18.55/18.49 [8420]~P1(f324(f324(f326(x84204),x84203),f292(x84204,x84201,x84202,x84205)))+P1(f324(f324(x84201,x84202),x84203))
% 18.55/18.49 [8421]~P1(f324(f324(f326(x84214),x84213),f283(x84214,x84211,x84212,x84215)))+P1(f324(f324(x84211,x84212),x84213))
% 18.55/18.49 [8422]~P1(f324(f324(f326(x84224),x84222),f292(x84224,x84221,x84225,x84223)))+P1(f324(f324(x84221,x84222),x84223))
% 18.55/18.49 [8423]~P1(f324(f324(f326(x84234),x84232),f283(x84234,x84231,x84235,x84233)))+P1(f324(f324(x84231,x84232),x84233))
% 18.55/18.49 [8546]~P54(x85462,x85461,x85465,x85463,x85464)+E(f324(f304(x85461,x85462,x85463),x85464),f238(f845(x85462,a832)))
% 18.55/18.49 [9316]P1(f324(f324(f326(f844(f839(x93161),f839(x93161))),f324(f324(f247(f839(x93161),f839(x93161)),f324(f324(f139(x93161),x93162),x93163)),f324(f324(f139(x93161),x93162),x93164))),f144(x93161,x93165)))+~P1(f324(f324(f326(f844(f839(x93161),f839(x93161))),f324(f324(f247(f839(x93161),f839(x93161)),x93163),x93164)),f144(x93161,x93165)))
% 18.55/18.49 [9317]P1(f324(f324(f326(f844(f839(x93171),f839(x93171))),f324(f324(f247(f839(x93171),f839(x93171)),f324(f324(f125(x93171),x93172),x93173)),f324(f324(f125(x93171),x93172),x93174))),f136(x93171,x93175)))+~P1(f324(f324(f326(f844(f839(x93171),f839(x93171))),f324(f324(f247(f839(x93171),f839(x93171)),x93173),x93174)),f136(x93171,x93175)))
% 18.55/18.49 [9498]E(f324(f324(f139(x94981),f705(x94982,x94983,x94984,x94985,x94981)),f706(x94982,x94983,x94984,x94985,x94981)),x94985)+~P1(f324(f324(f326(f844(f839(x94981),f839(x94981))),f324(f324(f247(f839(x94981),f839(x94981)),x94985),f324(f324(f139(x94981),x94984),x94983))),f145(x94981,x94982)))
% 18.55/18.49 [9525]E(f324(f324(f139(x95251),f707(x95252,x95253,x95254,x95255,x95251)),f708(x95252,x95253,x95254,x95255,x95251)),x95253)+~P1(f324(f324(f326(f844(f839(x95251),f839(x95251))),f324(f324(f247(f839(x95251),f839(x95251)),f324(f324(f139(x95251),x95255),x95254)),x95253)),f145(x95251,x95252)))
% 18.55/18.49 [9662]~P1(f324(f324(f326(f844(f839(x96621),f839(x96621))),f324(f324(f247(f839(x96621),f839(x96621)),f324(f324(f139(x96621),x96625),x96622)),x96624)),f145(x96621,x96623)))+P1(f324(f324(f326(f844(f839(x96621),f839(x96621))),f324(f324(f247(f839(x96621),f839(x96621)),x96622),f708(x96623,x96624,x96622,x96625,x96621))),f145(x96621,x96623)))
% 18.55/18.49 [9745]~P1(f324(f324(f326(f844(f839(x97451),f839(x97451))),f324(f324(f247(f839(x97451),f839(x97451)),x97455),f324(f324(f139(x97451),x97454),x97453))),f145(x97451,x97452)))+P1(f324(f324(f326(f844(f839(x97451),f839(x97451))),f324(f324(f247(f839(x97451),f839(x97451)),f706(x97452,x97453,x97454,x97455,x97451)),x97453)),f145(x97451,x97452)))
% 18.55/18.49 [9916]P1(f324(f324(f326(f844(x99161,x99161)),f324(f324(f247(x99161,x99161),f324(x99162,f324(f324(f82(a838),x99163),x99164))),f324(x99162,x99163))),f301(x99161,x99165)))+~P1(f324(f324(f326(f844(x99161,x99161)),f324(f324(f247(x99161,x99161),f324(x99162,f324(a114,f436(x99164,x99163,x99165,x99162,x99161)))),f324(x99162,f436(x99164,x99163,x99165,x99162,x99161)))),f301(x99161,x99165)))
% 18.55/18.49 [9939]E(x99391,f2(a101))+E(f324(f228(f844(f839(x99392),x99393),f844(x99392,x99393),f324(f324(f247(f839(x99392),x99393),f115(x99392)),x99394),f324(f252(x99392,x99393,f844(f839(x99392),x99393)),f324(f324(f9(x99392,f845(x99393,f844(f839(x99392),x99393)),f845(x99393,f844(f839(x99392),x99393))),f324(f324(f10(f845(f844(f839(x99392),x99393),f844(f839(x99392),x99393)),f845(f845(x99393,f844(f839(x99392),x99393)),f845(x99393,f844(f839(x99392),x99393))),x99392),f10(f844(f839(x99392),x99393),f844(f839(x99392),x99393),x99393)),f324(f324(f10(f845(f839(x99392),f845(x99393,f844(f839(x99392),x99393))),f845(f844(f839(x99392),x99393),f844(f839(x99392),x99393)),x99392),f252(f839(x99392),x99393,f844(f839(x99392),x99393))),f324(f324(f10(f845(f839(x99392),f839(x99392)),f845(f839(x99392),f845(x99393,f844(f839(x99392),x99393))),x99392),f324(f10(f839(x99392),f845(x99393,f844(f839(x99392),x99393)),f839(x99392)),f247(f839(x99392),x99393))),f139(x99392))))),f119(x99393,x99392,x99395,f324(f324(f3(a101),x99391),f80(a101)))))),f324(x99395,x99394)),f324(f119(x99393,x99392,x99395,x99391),x99394))
% 18.55/18.49 [5050]E(x50501,x50502)+~E(f324(f324(f139(x50503),x50504),x50501),f324(f324(f139(x50503),x50505),x50502))
% 18.55/18.49 [5051]E(x50511,x50512)+~E(f324(f324(f139(x50513),x50511),x50514),f324(f324(f139(x50513),x50512),x50515))
% 18.55/18.49 [5246]~E(f324(f324(f128(x52461),x52463),x52462),f324(f324(f139(x52461),x52464),x52465))+E(f324(f324(f149(x52461),x52462),x52463),x52464)
% 18.55/18.49 [5379]~P19(x53794,x53795,x53791)+E(f324(f324(x53791,x53792),f324(f324(x53791,x53792),x53793)),f324(f324(x53791,x53792),x53793))
% 18.55/18.49 [5746]~E(f324(x57463,x57464),f324(f226(x57462),x57465))+E(f324(f324(f324(f74(x57461,f842(x57462)),x57463),x57464),f324(f226(x57462),x57465)),x57463)
% 18.55/18.49 [6000]~P86(x60002)+~E(f324(f324(f137(x60001,x60002,x60003),x60004),x60005),f115(x60001))
% 18.55/18.49 [6399]E(x63991,x63992)+~E(f324(f324(f125(x63993),x63994),f324(f324(f139(x63993),x63991),f115(x63993))),f324(f324(f125(x63993),x63995),f324(f324(f139(x63993),x63992),f115(x63993))))
% 18.55/18.49 [6400]E(x64001,x64002)+~E(f324(f324(f125(x64003),x64001),f324(f324(f139(x64003),x64004),f115(x64003))),f324(f324(f125(x64003),x64002),f324(f324(f139(x64003),x64005),f115(x64003))))
% 18.55/18.49 [6660]E(f324(f171(x66601,x66602,x66603,x66604),x66605),f182(x66602))+P1(f324(f324(f326(x66601),x66605),x66604))
% 18.55/18.49 [6661]E(f324(f171(x66611,x66612,x66613,x66614),x66615),f182(x66612))+P1(f324(f324(f326(x66611),x66615),x66614))
% 18.55/18.49 [6730]E(f324(f324(f303(x67301),f324(x67302,x67303)),f324(f304(x67304,x67301,x67302),x67305)),f324(f304(x67304,x67301,x67302),x67305))+~P1(f324(f324(f326(x67304),x67303),x67305))
% 18.55/18.49 [6739]~P1(f324(x67394,f324(x67393,x67395)))+P1(f324(f324(f305(x67391,x67392,x67393),x67394),x67395))
% 18.55/18.49 [6740]~P1(f324(f324(x67403,x67405),x67404))+P1(f324(f324(f239(x67401,x67402,x67403),x67404),x67405))
% 18.55/18.49 [6741]~P1(f324(f324(x67413,x67415),x67414))+P1(f324(f324(f239(x67411,x67412,x67413),x67414),x67415))
% 18.55/18.49 [6742]~P1(f324(f324(x67423,x67425),x67424))+P1(f324(f324(f239(x67421,x67422,x67423),x67424),x67425))
% 18.55/18.49 [6747]~E(x67474,f2(a101))+E(f324(f119(x67471,x67472,x67473,x67474),x67475),f324(f324(f247(f839(x67472),x67471),f115(x67472)),x67475))
% 18.55/18.49 [6841]~E(f324(f304(x68411,x68412,x68413),x68414),x68415)+E(f324(f304(f845(x68411,a832),f845(x68412,a832),f304(x68411,x68412,x68413)),f324(f302(x68411),x68414)),f324(f302(x68412),x68415))
% 18.55/18.49 [6871]E(f324(f171(x68711,x68712,x68713,x68714),x68715),f324(x68713,x68715))+~P1(f324(f324(f326(x68711),x68715),x68714))
% 18.55/18.49 [6872]E(f324(f171(x68721,x68722,x68723,x68724),x68725),f324(x68723,x68725))+~P1(f324(f324(f326(x68721),x68725),x68724))
% 18.55/18.49 [7186]P29(x71861,x71862,x71863,x71864)+~P29(x71861,x71862,x71863,f324(f324(f303(x71861),x71865),x71864))
% 18.55/18.49 [7257]P1(f324(x72571,x72572))+~P1(f324(f324(f94(x72573,x72574,x72571),x72575),x72572))
% 18.55/18.49 [7308]~P1(f324(f324(f326(x73084),x73083),x73085))+P1(f324(f324(f326(x73081),f324(x73082,x73083)),f324(f304(x73084,x73081,x73082),x73085)))
% 18.55/18.49 [7360]P1(f324(x73601,f324(x73602,x73603)))+~P1(f324(f324(f305(x73604,x73605,x73602),x73601),x73603))
% 18.55/18.49 [7361]P1(f324(f324(x73611,x73612),x73613))+~P1(f324(f324(f239(x73614,x73615,x73611),x73613),x73612))
% 18.55/18.49 [7362]P1(f324(f324(x73621,x73622),x73623))+~P1(f324(f324(f239(x73624,x73625,x73621),x73623),x73622))
% 18.55/18.49 [7363]P1(f324(f324(x73631,x73632),x73633))+~P1(f324(f324(f239(x73634,x73635,x73631),x73633),x73632))
% 18.55/18.49 [7364]P1(f324(f324(x73641,x73642),x73643))+~P1(f324(f324(f94(x73644,x73641,x73645),x73642),x73643))
% 18.55/18.49 [7432]~P1(f324(f324(f326(x74323),f324(x74324,x74322)),x74325))+P1(f324(f324(f326(x74321),x74322),f324(f305(x74321,x74323,x74324),x74325)))
% 18.55/18.49 [7433]~P1(f324(f324(f326(x74333),f324(x74334,x74332)),x74335))+P1(f324(f324(f326(x74331),x74332),f324(f305(x74331,x74333,x74334),x74335)))
% 18.55/18.49 [7834]~P1(f324(f324(f326(x78345),x78343),f324(f305(x78345,x78341,x78342),x78344)))+P1(f324(f324(f326(x78341),f324(x78342,x78343)),x78344))
% 18.55/18.49 [7835]~P1(f324(f324(f326(x78355),x78353),f324(f305(x78355,x78351,x78352),x78354)))+P1(f324(f324(f326(x78351),f324(x78352,x78353)),x78354))
% 18.55/18.49 [8059]~E(x80593,f324(f324(f324(f74(x80591,f842(x80592)),f324(f18(f842(x80592),x80591),f182(x80592))),x80594),f324(f226(x80592),x80595)))+E(f168(x80591,x80592,x80593),f324(f324(f303(x80591),x80594),f179(f845(x80591,a832))))
% 18.55/18.49 [8138]~P20(x81382,x81381,x81383)+E(f324(f131(x81381,x81382,f324(f9(x81382,x81381,x81381),x81383),x81384),f140(x81382,x81385)),f324(f324(f67(x81382,x81381,x81383),x81384),f324(f157(x81382),x81385)))
% 18.55/18.49 [8157]E(f324(x81571,f821(x81572,x81571,x81573,x81574)),x81574)+~P1(f324(f324(f326(x81575),x81574),f324(f304(x81573,x81575,x81571),x81572)))
% 18.55/18.49 [8464]~E(x84642,f324(f324(f139(x84641),x84644),x84645))+P1(f324(f324(f326(f844(f839(x84641),f839(x84641))),f324(f324(f247(f839(x84641),f839(x84641)),f115(x84641)),x84642)),f136(x84641,x84643)))
% 18.55/18.49 [8515]P1(f324(f324(f231(f845(x85151,a832)),f324(f324(f46(x85152,f845(x85151,a832)),x85153),x85154)),f324(x85154,x85155)))+~P1(f324(f324(f326(x85152),x85155),x85153))
% 18.55/18.49 [8562]~P54(x85621,x85622,x85623,x85625,x85624)+E(f324(f304(x85621,x85622,x85623),f238(f845(x85621,a832))),x85624)
% 18.55/18.49 [8754]E(f324(f324(f324(f74(x87541,f842(x87542)),f171(x87541,x87542,x87543,x87544)),x87545),f182(x87542)),f171(x87541,x87542,x87543,x87544))+P1(f324(f324(f326(x87541),x87545),x87544))
% 18.55/18.49 [8759]E(f324(x87591,f696(x87592,x87593,x87591,x87594,x87595)),x87592)+~E(f324(f324(f195(x87595,x87594),x87591),x87593),f324(f226(x87594),x87592))
% 18.55/18.49 [8762]E(f324(f226(x87621),f696(x87622,x87623,x87624,x87625,x87621)),x87623)+~E(f324(f324(f195(x87621,x87625),x87624),x87623),f324(f226(x87625),x87622))
% 18.55/18.49 [8844]E(f324(f180(f839(x88441)),x88442),x88443)+~P1(f324(f324(f326(f844(f839(x88441),f839(x88441))),f324(f324(f247(f839(x88441),f839(x88441)),x88444),x88442)),f324(f132(x88441,x88445),x88443)))
% 18.55/18.49 [8845]E(f324(f180(f839(x88451)),x88452),x88453)+~P1(f324(f324(f326(f844(f839(x88451),f839(x88451))),f324(f324(f247(f839(x88451),f839(x88451)),x88452),x88454)),f324(f132(x88451,x88455),x88453)))
% 18.55/18.49 [8906]P1(f324(f324(f326(x89061),f821(x89062,x89063,x89061,x89064)),x89062))+~P1(f324(f324(f326(x89065),x89064),f324(f304(x89061,x89065,x89063),x89062)))
% 18.55/18.49 [9053]E(f324(f304(x90531,x90532,x90533),f822(x90534,x90533,x90531,x90535,x90532)),x90535)+~P1(f324(f324(f231(f845(x90532,a832)),x90535),f324(f304(x90531,x90532,x90533),x90534)))
% 18.55/18.49 [9288]E(f324(x92881,f542(x92882,x92881,x92883,x92884,x92885)),f324(f226(x92885),x92884))+~P1(f324(f324(f326(x92885),x92884),f170(x92883,x92885,f171(x92883,x92885,x92881,x92882))))
% 18.55/18.49 [9332]P1(f324(f324(f326(f844(f839(x93321),f839(x93321))),f324(f324(f247(f839(x93321),f839(x93321)),f324(f324(f139(x93321),x93322),x93323)),f324(f324(f139(x93321),x93322),x93324))),f301(f839(x93321),f144(x93321,x93325))))+~P1(f324(f324(f326(f844(f839(x93321),f839(x93321))),f324(f324(f247(f839(x93321),f839(x93321)),x93323),x93324)),f301(f839(x93321),f144(x93321,x93325))))
% 18.55/18.49 [9361]~E(f324(x93613,f697(x93615,x93614,x93613,x93612,x93611)),f324(x93615,f697(x93615,x93614,x93613,x93612,x93611)))+E(f324(f324(f141(x93611,x93612),x93613),x93614),f324(f324(f141(x93611,x93612),x93615),x93614))
% 18.55/18.49 [9442]E(f324(f324(f141(x94421,x94422),x94423),x94424),f324(f324(f141(x94421,x94422),x94425),x94424))+P1(f324(f324(f326(x94421),f697(x94423,x94424,x94425,x94422,x94421)),f324(f157(x94421),x94424)))
% 18.55/18.49 [9471]~P1(f324(f324(f326(x94715),x94714),f324(f278(x94711,x94715,x94713),x94712)))+P1(f324(f324(f326(x94711),f511(x94712,x94713,x94711,x94714,x94715)),x94712))
% 18.55/18.49 [9472]~P1(f324(f324(f326(x94725),x94724),f324(f278(x94721,x94725,x94723),x94722)))+P1(f324(f324(f326(x94721),f518(x94722,x94723,x94721,x94724,x94725)),x94722))
% 18.55/18.49 [9496]~P1(f324(f324(f231(f845(x94965,a832)),x94964),f324(f304(x94961,x94965,x94963),x94962)))+P1(f324(f324(f231(f845(x94961,a832)),f822(x94962,x94963,x94961,x94964,x94965)),x94962))
% 18.55/18.49 [9540]~P1(f324(f324(f326(x95405),x95404),f170(x95401,x95405,f171(x95401,x95405,x95403,x95402))))+P1(f324(f324(f326(x95401),f542(x95402,x95403,x95401,x95404,x95405)),x95402))
% 18.55/18.49 [5259]~E(f324(x52593,x52594),x52595)+E(f324(f324(f324(f74(x52591,x52592),x52593),x52594),x52595),x52593)
% 18.55/18.49 [5260]~E(f324(x52603,x52604),x52605)+E(f324(f324(f324(f74(x52601,x52602),x52603),x52604),x52605),x52603)
% 18.55/18.49 [5711]E(f324(x57111,x57112),x57113)+~E(f324(f324(f324(f74(x57114,x57115),x57111),x57112),x57113),x57111)
% 18.55/18.49 [5802]E(x58021,x58022)+~E(f324(f251(x58023,x58024),f324(f324(f247(x58023,x58024),x58025),x58021)),x58022)
% 18.55/18.49 [5803]E(x58031,x58032)+~E(f324(f246(x58033,x58034),f324(f324(f247(x58033,x58034),x58031),x58035)),x58032)
% 18.55/18.49 [6486]E(f324(f304(x64861,x64862,f324(f18(x64862,x64861),x64863)),x64864),f324(f324(f303(x64862),x64863),f179(f845(x64862,a832))))+~P1(f324(f324(f326(x64861),x64865),x64864))
% 18.55/18.49 [6560]E(f324(f324(f103(f845(x65601,a832)),f324(f157(x65601),x65602)),f324(f157(x65601),x65603)),f324(f157(x65601),x65604))+~E(f152(x65601,x65605,x65604),f324(f324(f247(f839(x65601),f839(x65601)),x65602),x65603))
% 18.55/18.49 [6667]~P86(x66672)+E(f324(f180(f839(x66671)),f324(f324(f137(x66671,x66672,x66673),x66674),x66675)),f324(a114,f324(f180(f839(x66671)),x66675)))
% 18.55/18.49 [6681]~P86(x66812)+E(f324(f157(x66811),f324(f324(f137(x66811,x66812,x66813),x66814),x66815)),f324(f324(f303(x66811),x66814),f324(f157(x66811),x66815)))
% 18.55/18.49 [6962]~P105(x69621)+E(f324(f324(f83(x69621),f324(f324(f83(x69621),x69622),x69623)),f324(f324(f83(x69621),x69624),x69625)),f324(f324(f83(x69621),f324(f324(f83(x69621),x69622),x69624)),f324(f324(f83(x69621),x69623),x69625)))
% 18.55/18.49 [6963]~P105(x69631)+E(f324(f324(f82(x69631),f324(f324(f82(x69631),x69632),x69633)),f324(f324(f82(x69631),x69634),x69635)),f324(f324(f82(x69631),f324(f324(f82(x69631),x69632),x69634)),f324(f324(f82(x69631),x69633),x69635)))
% 18.55/18.49 [6964]~P59(x69641)+E(f324(f324(f284(x69641),f324(f324(f83(x69641),x69642),x69643)),f324(f324(f83(x69641),x69644),x69645)),f324(f324(f83(x69641),f324(f324(f284(x69641),x69642),x69644)),f324(f324(f284(x69641),x69643),x69645)))
% 18.55/18.49 [6978]~P86(x69781)+E(f299(x69781,f324(f324(f178(x69781),x69782),x69783),f324(f324(f235(x69781),x69784),x69785)),f324(f324(f104(f845(x69781,a832)),f299(x69781,x69782,x69784)),f299(x69781,x69783,x69785)))
% 18.55/18.49 [6979]~P86(x69791)+E(f298(x69791,f324(f324(f178(x69791),x69792),x69793),f324(f324(f235(x69791),x69794),x69795)),f324(f324(f104(f845(x69791,a832)),f298(x69791,x69792,x69794)),f298(x69791,x69793,x69795)))
% 18.55/18.49 [6980]~P86(x69801)+E(f296(x69801,f324(f324(f178(x69801),x69802),x69803),f324(f324(f235(x69801),x69804),x69805)),f324(f324(f104(f845(x69801,a832)),f296(x69801,x69802,x69804)),f296(x69801,x69803,x69805)))
% 18.55/18.49 [6981]~P86(x69811)+E(f324(f324(f104(f845(x69811,a832)),f324(f295(x69811,x69812),x69813)),f324(f295(x69811,x69814),x69815)),f324(f295(x69811,f324(f324(f178(x69811),x69812),x69814)),f324(f324(f235(x69811),x69813),x69815)))
% 18.55/18.49 [7100]~P1(f324(x71001,f792(x71003,x71002,x71001)))+P1(f324(x71001,f324(f324(f247(x71002,x71003),x71004),x71005)))
% 18.55/18.49 [7198]~E(f324(x71983,x71984),f182(x71982))+E(f170(x71981,x71982,f324(f324(f324(f74(x71981,f842(x71982)),x71983),x71984),f324(f226(x71982),x71985))),f324(f324(f303(x71982),x71985),f170(x71981,x71982,x71983)))
% 18.55/18.49 [7221]~E(x72212,f324(x72214,x72215))+P1(f324(f324(f326(x72211),x72212),f324(f304(x72213,x72211,x72214),f238(f845(x72213,a832)))))
% 18.55/18.49 [7282]~E(f324(x72823,x72824),f182(x72822))+E(f324(f324(f3(f845(x72821,a832)),f168(x72821,x72822,x72823)),f324(f324(f303(x72821),x72824),x72825)),f324(f324(f3(f845(x72821,a832)),f168(x72821,x72822,x72823)),x72825))
% 18.55/18.49 [7304]~P19(x73043,x73042,x73044)+P19(x73041,x73042,f324(f324(f10(x73043,f845(x73042,x73042),x73041),x73044),x73045))
% 18.55/18.49 [7305]~P20(x73053,x73052,x73054)+P20(x73051,x73052,f324(f324(f10(x73053,f845(x73052,x73052),x73051),x73054),x73055))
% 18.55/18.49 [7449]~P29(x74491,x74492,x74493,x74494)+P29(x74491,x74492,x74493,f324(f324(f3(f845(x74491,a832)),x74494),x74495))
% 18.55/18.49 [7608]~P1(f324(f324(x76083,x76084),x76085))+P1(f324(f324(f252(x76081,x76082,a832),x76083),f324(f324(f247(x76081,x76082),x76084),x76085)))
% 18.55/18.49 [7609]~P1(f324(f324(x76093,x76094),x76095))+P1(f324(f324(f252(x76091,x76092,a832),x76093),f324(f324(f247(x76091,x76092),x76094),x76095)))
% 18.55/18.49 [7726]~P1(f324(x77262,x77264))+~E(f324(f324(f128(x77261),f324(f180(f839(x77261)),f161(x77261,x77262,x77263))),x77263),f324(f324(f139(x77261),x77264),x77265))
% 18.55/18.49 [7746]P29(x77461,x77462,x77463,x77464)+~P29(x77461,x77462,x77463,f324(f324(f103(f845(x77461,a832)),x77465),x77464))
% 18.55/18.49 [7747]P29(x77471,x77472,x77473,x77474)+~P29(x77471,x77472,x77473,f324(f324(f103(f845(x77471,a832)),x77474),x77475))
% 18.55/18.49 [7955]~P31(x79551,f324(a114,x79552),f324(f324(f324(f93(x79551),x79553),f324(a27,x79554)),x79555))+P31(x79551,x79552,f324(f324(f324(f93(x79551),x79553),f324(f230(a833),f324(a30,x79554))),x79555))
% 18.55/18.49 [8086]P31(x80861,f324(a114,x80862),f324(f324(f324(f93(x80861),x80863),f324(a27,x80864)),x80865))+~P31(x80861,x80862,f324(f324(f324(f93(x80861),x80863),f324(f230(a833),f324(a30,x80864))),x80865))
% 18.55/18.49 [8115]~P19(x81152,x81151,x81153)+E(f324(f131(x81151,x81152,f324(f9(x81152,x81151,x81151),x81153),x81154),x81155),f324(f324(f67(x81152,x81151,x81153),x81154),f324(f157(x81152),x81155)))
% 18.55/18.49 [8144]~E(f324(f324(f128(x81441),f324(f180(f839(x81441)),f161(x81441,x81442,x81443))),x81443),f324(f324(f139(x81441),x81444),x81445))+E(f324(f324(f125(x81441),f161(x81441,x81442,x81443)),f324(f324(f139(x81441),x81444),x81445)),x81443)
% 18.55/18.49 [8167]P1(f324(f324(x81671,x81672),x81673))+~P1(f324(f324(f252(x81674,x81675,a832),x81671),f324(f324(f247(x81674,x81675),x81672),x81673)))
% 18.55/18.49 [8238]P39(x82384,f663(x82385,x82384,x82383,x82382),x82382,f775(x82385,x82384,x82383,x82382))+P31(x82381,x82382,f324(f324(f324(f93(x82381),x82383),x82384),x82385))
% 18.55/18.49 [8253]~E(f324(f165(x82531,x82532,x82535),x82533),f324(f226(x82532),x82534))+P1(f324(f324(f326(f844(x82531,x82532)),f324(f324(f247(x82531,x82532),x82533),x82534)),f324(f157(f844(x82531,x82532)),x82535)))
% 18.55/18.49 [8254]~E(f324(f165(x82541,x82542,x82545),x82543),f324(f226(x82542),x82544))+P1(f324(f324(f326(f844(x82541,x82542)),f324(f324(f247(x82541,x82542),x82543),x82544)),f324(f157(f844(x82541,x82542)),x82545)))
% 18.55/18.49 [8616]P1(f324(f324(f231(f845(x86161,a832)),f324(f304(x86162,x86161,x86163),x86164)),f324(f304(x86162,x86161,x86163),x86165)))+~P1(f324(f324(f231(f845(x86162,a832)),x86164),x86165))
% 18.55/18.49 [8617]P1(f324(f324(f231(f845(x86171,a832)),f324(f305(x86171,x86172,x86173),x86174)),f324(f305(x86171,x86172,x86173),x86175)))+~P1(f324(f324(f231(f845(x86172,a832)),x86174),x86175))
% 18.55/18.49 [8690]E(x86901,f2(a101))+E(f324(f324(f254(x86902,x86903,x86902,f844(x86903,x86902)),f324(x86904,x86905)),f269(x86903,x86902,f324(f324(f3(a101),x86901),f80(a101)),x86904)),f324(f269(x86903,x86902,x86901,x86904),x86905))
% 18.55/18.49 [8778]P1(f324(f324(f250(x87781,x87782,a832,x87783),x87784),x87785))+~P1(f324(x87783,f324(f324(f247(x87781,x87782),x87784),x87785)))
% 18.55/18.49 [8971]P31(x89711,x89712,f324(f324(f324(f93(x89711),x89713),x89714),x89715))+P1(f324(f324(x89713,f551(x89715,x89714,x89713,x89712)),f663(x89715,x89714,x89713,x89712)))
% 18.55/18.49 [9031]~P1(f324(f324(f250(x90312,x90313,a832,x90311),x90314),x90315))+P1(f324(x90311,f324(f324(f247(x90312,x90313),x90314),x90315)))
% 18.55/18.49 [9032]~P1(f324(f324(f250(x90322,x90323,a832,x90321),x90324),x90325))+P1(f324(x90321,f324(f324(f247(x90322,x90323),x90324),x90325)))
% 18.55/18.49 [9143]E(f324(f226(x91431),f702(x91432,x91433,x91434,x91431,x91435)),f324(f165(x91435,x91431,x91432),x91434))+~P1(f324(f324(f326(f844(x91435,x91431)),f324(f324(f247(x91435,x91431),x91434),x91433)),f324(f157(f844(x91435,x91431)),x91432)))
% 18.55/18.49 [9186]P31(x91861,x91862,f324(f324(f324(f93(x91861),x91863),x91864),x91865))+~P1(f324(f324(x91865,f551(x91865,x91864,x91863,x91862)),f775(x91865,x91864,x91863,x91862)))
% 18.55/18.49 [9253]~P28(x92531,x92532,f324(f324(f303(f837(x92531)),f324(f324(f324(f93(x92531),x92533),f324(f230(a833),f324(a30,x92534))),x92535)),f179(f845(f837(x92531),a832))))+P28(x92531,x92532,f324(f324(f303(f837(x92531)),f324(f324(f324(f93(x92531),x92533),f324(a27,x92534)),x92535)),f179(f845(f837(x92531),a832))))
% 18.55/18.49 [9280]~P1(f324(f64(x92803),f324(f304(x92802,x92803,x92805),f238(f845(x92802,a832)))))+P1(f324(f64(x92801),f324(f304(x92802,x92801,f324(f324(f10(x92803,x92801,x92802),x92804),x92805)),f238(f845(x92802,a832)))))
% 18.55/18.49 [9302]P1(f324(f324(f231(f845(f845(x93021,a832),a832)),f324(f304(f845(x93022,a832),f845(x93021,a832),f304(x93022,x93021,x93023)),f324(f302(x93022),x93024))),f324(f302(x93021),x93025)))+~P1(f324(f324(f231(f845(x93021,a832)),f324(f304(x93022,x93021,x93023),x93024)),x93025))
% 18.55/18.49 [9312]~P1(f324(f64(f842(x93121)),f324(f304(x93122,f842(x93121),x93123),f238(f845(x93122,a832)))))+P1(f324(f64(f842(x93121)),f324(f304(x93122,f842(x93121),f324(f324(f324(f74(x93122,f842(x93121)),x93123),x93124),f324(f226(x93121),x93125))),f238(f845(x93122,a832)))))
% 18.55/18.49 [9370]E(x93701,x93702)+~P1(f324(f69(x93703,x93704,x93705,x93701,f179(f845(x93703,a832))),x93702))
% 18.55/18.49 [9385]E(f324(f324(f247(x93851,x93852),f591(x93853,x93854,x93855,x93852,x93851)),f592(x93853,x93854,x93855,x93852,x93851)),x93855)+~P1(f324(f324(f326(f844(x93851,x93852)),x93855),f324(f324(f249(x93851,x93852),x93854),x93853)))
% 18.55/18.49 [9476]P1(f324(f324(f326(x94761),f591(x94762,x94763,x94764,x94765,x94761)),x94763))+~P1(f324(f324(f326(f844(x94761,x94765)),x94764),f324(f324(f249(x94761,x94765),x94763),x94762)))
% 18.55/18.49 [9573]P28(x95735,x95734,f324(f324(f303(f837(x95735)),f324(f324(f324(f93(x95735),x95731),x95733),x95732)),f179(f845(f837(x95735),a832))))+P1(f324(f324(x95731,f435(x95732,x95733,x95734,x95735,x95731)),f437(x95732,x95733,x95734,x95735,x95731)))
% 18.55/18.49 [9618]P1(f324(f324(f326(x96181),f592(x96182,x96183,x96184,x96181,x96185)),f324(x96182,f591(x96182,x96183,x96184,x96181,x96185))))+~P1(f324(f324(f326(f844(x96185,x96181)),x96184),f324(f324(f249(x96185,x96181),x96183),x96182)))
% 18.55/18.49 [9638]P1(f324(f324(f326(f844(x96381,x96381)),f324(f324(f247(x96381,x96381),x96382),f639(x96383,x96384,x96385,x96382,x96381))),x96383))+~P1(f324(f324(f326(f844(x96381,x96381)),f324(f324(f247(x96381,x96381),x96382),x96385)),f324(f324(f172(f844(x96381,x96381),a832),f324(a114,x96384)),x96383)))
% 18.55/18.49 [9639]P1(f324(f324(f326(f844(x96391,x96391)),f324(f324(f247(x96391,x96391),x96392),f641(x96393,x96394,x96395,x96392,x96391))),x96393))+~P1(f324(f324(f326(f844(x96391,x96391)),f324(f324(f247(x96391,x96391),x96392),x96395)),f324(f324(f172(f844(x96391,x96391),a832),f324(a114,x96394)),x96393)))
% 18.55/18.49 [9657]~P1(f324(f324(f326(f844(f839(x96571),f839(x96571))),f324(f324(f247(f839(x96571),f839(x96571)),f324(f324(f139(x96571),x96572),x96575)),x96574)),f145(x96571,x96573)))+P1(f324(f324(f326(f844(x96571,x96571)),f324(f324(f247(x96571,x96571),x96572),f707(x96573,x96574,x96575,x96572,x96571))),x96573))
% 18.55/18.49 [9659]~P28(x96591,x96592,f324(f324(f303(f837(x96591)),f324(f324(f324(f93(x96591),f94(x96591,x96593,x96594)),x96595),x96593)),f179(f845(f837(x96591),a832))))+P28(x96591,x96592,f324(f324(f303(f837(x96591)),f324(f324(f324(f93(x96591),x96593),f35(x96594,x96595)),f94(x96591,x96593,f324(f75(a832,a832,a835,a320),x96594)))),f179(f845(f837(x96591),a832))))
% 18.55/18.49 [9660]~P32(x96601,x96602,f324(f324(f303(f837(x96601)),f324(f324(f324(f93(x96601),f94(x96601,x96603,x96604)),x96605),x96603)),f179(f845(f837(x96601),a832))))+P32(x96601,x96602,f324(f324(f303(f837(x96601)),f324(f324(f324(f93(x96601),x96603),f35(x96604,x96605)),f94(x96601,x96603,f324(f75(a832,a832,a835,a320),x96604)))),f179(f845(f837(x96601),a832))))
% 18.55/18.49 [9940]P28(x99401,x99402,f324(f324(f303(f837(x99401)),f324(f324(f324(f93(x99401),x99403),x99404),x99405)),f179(f845(f837(x99401),a832))))+~P28(x99401,x99402,f324(f324(f303(f837(x99401)),f324(f324(f324(f93(x99401),f324(f18(f845(a835,a832),x99401),f324(f324(f9(a835,a835,a832),a321),f437(x99405,x99404,x99402,x99401,x99403)))),x99404),f324(f18(f845(a835,a832),x99401),f324(x99405,f435(x99405,x99404,x99402,x99401,x99403))))),f179(f845(f837(x99401),a832))))
% 18.55/18.49 [6152]P1(f324(x61522,x61524))+E(f161(x61521,x61522,f324(f324(f125(x61521),x61523),f324(f324(f139(x61521),x61524),x61525))),f161(x61521,x61522,x61523))
% 18.55/18.49 [6201]~P73(x62012)+E(f324(f324(f324(f3(f845(x62011,x62012)),x62013),x62014),x62015),f324(f324(f3(x62012),f324(x62013,x62015)),f324(x62014,x62015)))
% 18.55/18.49 [6202]~P73(x62022)+E(f324(f324(f324(f3(f845(x62021,x62022)),x62023),x62024),x62025),f324(f324(f3(x62022),f324(x62023,x62025)),f324(x62024,x62025)))
% 18.55/18.49 [6203]~P94(x62032)+E(f324(f324(f324(f103(f845(x62031,x62032)),x62033),x62034),x62035),f324(f324(f103(x62032),f324(x62033,x62035)),f324(x62034,x62035)))
% 18.55/18.49 [6204]~P94(x62042)+E(f324(f324(f324(f103(f845(x62041,x62042)),x62043),x62044),x62045),f324(f324(f103(x62042),f324(x62043,x62045)),f324(x62044,x62045)))
% 18.55/18.49 [6205]~P94(x62052)+E(f324(f324(f324(f104(f845(x62051,x62052)),x62053),x62054),x62055),f324(f324(f104(x62052),f324(x62053,x62055)),f324(x62054,x62055)))
% 18.55/18.49 [6206]~P94(x62062)+E(f324(f324(f324(f104(f845(x62061,x62062)),x62063),x62064),x62065),f324(f324(f104(x62062),f324(x62063,x62065)),f324(x62064,x62065)))
% 18.55/18.49 [6227]E(x62271,x62272)+E(f324(f324(f149(x62273),f324(f324(f146(x62273,x62274),x62271),x62275)),x62272),f324(f324(f149(x62273),x62274),x62272))
% 18.55/18.49 [6503]~E(x65034,f179(f845(x65033,a832)))+E(f324(f324(f3(f845(x65031,a832)),x65032),f324(f324(f45(x65033,f845(x65031,a832)),x65034),x65035)),x65032)
% 18.55/18.49 [6504]~E(x65044,f179(f845(x65043,a832)))+E(f324(f324(f103(f845(x65041,a832)),x65042),f324(f324(f45(x65043,f845(x65041,a832)),x65044),x65045)),x65042)
% 18.55/18.49 [6505]~E(x65054,f179(f845(x65053,a832)))+E(f324(f324(f104(f845(x65051,a832)),x65052),f324(f324(f46(x65053,f845(x65051,a832)),x65054),x65055)),x65052)
% 18.55/18.49 [6519]~E(x65194,f179(f845(x65193,a832)))+E(f324(f324(f303(x65191),x65192),f324(f324(f45(x65193,f845(x65191,a832)),x65194),x65195)),f324(f324(f303(x65191),x65192),f179(f845(x65191,a832))))
% 18.55/18.49 [6961]~P105(x69611)+E(f324(f324(f83(x69611),f324(f324(f83(x69611),x69612),x69613)),f324(f324(f83(x69611),x69614),x69615)),f324(f324(f83(x69611),x69612),f324(f324(f83(x69611),x69613),f324(f324(f83(x69611),x69614),x69615))))
% 18.55/18.49 [7349]E(f324(f324(f149(x73491),f324(f324(f141(x73492,x73491),x73493),x73494)),x73495),f324(x73493,f324(f324(f149(x73492),x73494),x73495)))+~P1(f324(f324(f232(a838),x73495),f324(f180(f839(x73492)),x73494)))
% 18.55/18.49 [7421]E(f324(f324(f103(f845(x74211,a832)),f324(x74212,x74213)),f324(f324(f45(x74214,f845(x74211,a832)),x74215),x74212)),f324(f324(f45(x74214,f845(x74211,a832)),x74215),x74212))+~P1(f324(f324(f326(x74214),x74213),x74215))
% 18.55/18.49 [7422]E(f324(f324(f104(f845(x74221,a832)),f324(x74222,x74223)),f324(f324(f46(x74224,f845(x74221,a832)),x74225),x74222)),f324(f324(f46(x74224,f845(x74221,a832)),x74225),x74222))+~P1(f324(f324(f326(x74224),x74223),x74225))
% 18.55/18.49 [8034]~E(x80343,f179(f845(x80341,a832)))+E(f324(f324(f45(x80341,f845(x80342,a832)),x80343),f324(f324(f10(f845(x80342,a832),f845(x80342,a832),x80341),f324(f303(x80342),x80344)),x80345)),f179(f845(x80342,a832)))
% 18.55/18.49 [8040]~P1(f324(f324(f326(x80404),x80403),x80405))+P1(f324(f324(f231(f845(x80401,a832)),f324(x80402,x80403)),f324(f324(f45(x80404,f845(x80401,a832)),x80405),x80402)))
% 18.55/18.49 [8166]~E(f324(x81664,x81662),x81665)+P1(f324(f324(f326(x81661),x81662),f324(f305(x81661,x81663,x81664),f324(f324(f303(x81663),x81665),f179(f845(x81663,a832))))))
% 18.55/18.49 [8212]~P52(x82121,x82122,f324(f279(x82122,x82121),x82123))+E(f324(f324(f104(f845(x82121,a832)),f324(f278(x82122,x82121,x82123),x82124)),f324(f278(x82122,x82121,x82123),x82125)),f324(f278(x82122,x82121,x82123),f324(f324(f104(f845(x82122,a832)),x82124),x82125)))
% 18.55/18.49 [8237]E(x82371,f2(a101))+E(f118(x82372,x82373,f324(x82374,f324(f324(f3(a101),x82371),f80(a101))),f324(f324(f9(x82372,a101,f840(x82373)),x82375),x82371)),f324(f192(x82372,x82373,x82374,x82375),x82371))
% 18.55/18.49 [8331]E(x83311,f179(f845(x83312,a832)))+E(f324(f324(f45(x83312,f845(x83313,a832)),x83311),f324(f324(f10(f845(x83313,a832),f845(x83313,a832),x83312),f324(f303(x83313),x83314)),x83315)),f324(f324(f303(x83313),x83314),f324(f324(f45(x83312,f845(x83313,a832)),x83311),x83315)))
% 18.55/18.49 [8332]E(x83321,f179(f845(x83322,a832)))+E(f324(f324(f45(x83322,f845(x83323,a832)),x83321),f324(f324(f10(f845(x83323,a832),f845(x83323,a832),x83322),f324(f303(x83323),x83324)),x83325)),f324(f324(f303(x83323),x83324),f324(f324(f45(x83322,f845(x83323,a832)),x83321),x83325)))
% 18.55/18.49 [8387]~P29(x83872,x83871,x83873,f238(f845(x83872,a832)))+E(f324(f324(f3(f845(x83871,a832)),f324(f304(x83872,x83871,x83873),x83874)),f324(f304(x83872,x83871,x83873),x83875)),f324(f304(x83872,x83871,x83873),f324(f324(f3(f845(x83872,a832)),x83874),x83875)))
% 18.55/18.49 [8388]~P29(x83882,x83881,x83883,f238(f845(x83882,a832)))+E(f324(f324(f104(f845(x83881,a832)),f324(f304(x83882,x83881,x83883),x83884)),f324(f304(x83882,x83881,x83883),x83885)),f324(f304(x83882,x83881,x83883),f324(f324(f104(f845(x83882,a832)),x83884),x83885)))
% 18.55/18.49 [8452]~P1(f324(f324(f70(x84521,x84522,x84525),x84523),x84524))+P1(f324(f324(f326(f844(x84521,x84522)),f324(f324(f247(x84521,x84522),x84523),x84524)),x84525))
% 18.55/18.49 [8479]P1(f324(f324(f326(x84791),x84792),f324(f260(x84793,x84791),x84794)))+~P1(f324(f324(f326(f844(x84793,x84791)),f324(f324(f247(x84793,x84791),x84795),x84792)),x84794))
% 18.55/18.49 [8480]P1(f324(f324(f326(x84801),x84802),f324(f260(x84803,x84801),x84804)))+~P1(f324(f324(f326(f844(x84803,x84801)),f324(f324(f247(x84803,x84801),x84805),x84802)),x84804))
% 18.55/18.49 [8481]P1(f324(f324(f326(x84811),x84812),f324(f262(x84811,x84813),x84814)))+~P1(f324(f324(f326(f844(x84811,x84813)),f324(f324(f247(x84811,x84813),x84812),x84815)),x84814))
% 18.55/18.49 [8482]P1(f324(f324(f326(x84821),x84822),f324(f262(x84821,x84823),x84824)))+~P1(f324(f324(f326(f844(x84821,x84823)),f324(f324(f247(x84821,x84823),x84822),x84825)),x84824))
% 18.55/18.49 [8604]P1(f324(f324(f70(x86041,x86042,x86043),x86044),x86045))+~P1(f324(f324(f326(f844(x86041,x86042)),f324(f324(f247(x86041,x86042),x86044),x86045)),x86043))
% 18.55/18.49 [8639]E(f324(x86391,x86392),x86393)+~P1(f324(f324(f326(x86394),x86392),f324(f305(x86394,x86395,x86391),f324(f324(f303(x86395),x86393),f179(f845(x86395,a832))))))
% 18.55/18.49 [8840]P1(f324(f324(f326(f844(x88401,x88402)),f324(f324(f247(x88401,x88402),x88403),x88404)),f324(f279(x88402,x88401),x88405)))+~P1(f324(f324(f326(f844(x88402,x88401)),f324(f324(f247(x88402,x88401),x88404),x88403)),x88405))
% 18.55/18.49 [8841]P1(f324(f324(f326(f844(x88411,x88412)),f324(f324(f247(x88411,x88412),x88413),x88414)),f324(f279(x88412,x88411),x88415)))+~P1(f324(f324(f326(f844(x88412,x88411)),f324(f324(f247(x88412,x88411),x88414),x88413)),x88415))
% 18.55/18.49 [8859]~P1(f324(f324(x88591,x88595),x88594))+P1(f324(f324(x88591,f324(f251(x88592,x88593),f324(f324(f247(x88592,x88593),x88594),x88595))),f324(f246(x88592,x88593),f324(f324(f247(x88592,x88593),x88594),x88595))))
% 18.77/18.49 [8885]~P1(f324(f324(f326(f844(x88852,x88851)),f324(f324(f247(x88852,x88851),x88854),x88853)),f324(f279(x88851,x88852),x88855)))+P1(f324(f324(f326(f844(x88851,x88852)),f324(f324(f247(x88851,x88852),x88853),x88854)),x88855))
% 18.77/18.49 [8886]~P1(f324(f324(f326(f844(x88862,x88861)),f324(f324(f247(x88862,x88861),x88864),x88863)),f324(f279(x88861,x88862),x88865)))+P1(f324(f324(f326(f844(x88861,x88862)),f324(f324(f247(x88861,x88862),x88863),x88864)),x88865))
% 18.77/18.49 [8914]~P1(f324(f324(f326(f844(x89143,x89141)),f324(f324(f247(x89143,x89141),x89145),x89142)),x89144))+P1(f324(f324(f326(x89141),x89142),f324(f278(x89143,x89141,x89144),f324(f324(f303(x89143),x89145),f179(f845(x89143,a832))))))
% 18.77/18.49 [8955]P1(f324(f324(f326(f844(x89551,x89552)),f324(f324(f247(x89551,x89552),x89553),x89554)),x89555))+~P1(f324(f324(f326(x89552),x89554),f324(f278(x89551,x89552,x89555),f324(f324(f303(x89551),x89553),f179(f845(x89551,a832))))))
% 18.77/18.49 [8974]E(f324(f324(f324(f74(x89741,f842(x89742)),f171(x89741,x89742,x89743,x89744)),x89745),f182(x89742)),f171(x89741,x89742,x89743,f324(f324(f3(f845(x89741,a832)),x89744),f324(f324(f303(x89741),x89745),f179(f845(x89741,a832))))))+~P1(f324(f324(f326(x89741),x89745),x89744))
% 18.77/18.49 [9038]~P67(x90381)+E(f324(f324(f8(a838,x90381),x90382),f296(a838,f324(f324(f82(a838),x90383),x90384),f324(f324(f82(a838),x90385),x90384))),f324(f324(f8(a838,x90381),f324(f324(f10(a838,x90381,a838),x90382),f324(f324(f9(a838,a838,a838),f82(a838)),x90384))),f296(a838,x90383,x90385)))
% 18.77/18.49 [9057]~P67(x90571)+E(f324(f324(f8(a838,x90571),x90572),f324(f295(a838,f324(f324(f82(a838),x90573),x90574)),f324(f324(f82(a838),x90575),x90574))),f324(f324(f8(a838,x90571),f324(f324(f10(a838,x90571,a838),x90572),f324(f324(f9(a838,a838,a838),f82(a838)),x90574))),f324(f295(a838,x90573),x90575)))
% 18.77/18.49 [9268]P1(f324(f324(f326(f844(f839(x92681),f839(x92681))),f324(f324(f247(f839(x92681),f839(x92681)),f324(f324(f139(x92681),x92682),x92683)),f324(f324(f139(x92681),x92684),x92683))),f144(x92681,x92685)))+~P1(f324(f324(f326(f844(x92681,x92681)),f324(f324(f247(x92681,x92681),x92682),x92684)),x92685))
% 18.77/18.49 [9368]P28(x93681,x93682,f324(f324(f303(f837(x93681)),f324(f324(f324(f93(x93681),x93683),f324(a27,x93684)),x93685)),f179(f845(f837(x93681),a832))))+~P28(x93681,f324(f324(f303(f837(x93681)),f324(f324(f324(f93(x93681),x93683),f324(a27,x93684)),x93685)),x93682),f324(f324(f303(f837(x93681)),f324(f324(f324(f93(x93681),x93683),f324(f230(a833),f324(a30,x93684))),x93685)),f179(f845(f837(x93681),a832))))
% 18.77/18.49 [9380]E(f324(f324(f303(x93801),f566(x93802,x93803,x93804,x93805,x93801)),f571(x93802,x93803,x93804,x93805,x93801)),f324(f324(f303(x93801),x93804),x93803))+~P1(f324(f65(x93801,x93805,f324(f324(f303(x93801),x93804),x93803)),x93802))
% 18.77/18.49 [9381]E(f324(f324(f303(x93811),f572(x93812,x93813,x93814,x93815,x93811)),f576(x93812,x93813,x93814,x93815,x93811)),f324(f324(f303(x93811),x93814),x93813))+~P1(f324(f65(x93811,x93815,f324(f324(f303(x93811),x93814),x93813)),x93812))
% 18.77/18.49 [9462]P1(f324(f324(f326(x94621),f668(x94622,x94623,x94624,x94625,x94621)),x94624))+P1(f324(f324(f324(f46(x94621,f845(x94625,a832)),x94624),x94623),x94622))
% 18.77/18.49 [9467]P1(f324(f324(f326(x94671),f658(x94672,x94673,x94671,x94674,x94675)),x94673))+P1(f324(f324(f326(x94675),x94674),f324(f324(f46(x94671,f845(x94675,a832)),x94673),x94672)))
% 18.77/18.49 [9475]P1(f324(f324(f326(x94751),f667(x94752,x94753,x94751,x94754,x94755)),x94753))+P1(f324(f324(f231(f845(x94755,a832)),x94754),f324(f324(f46(x94751,f845(x94755,a832)),x94753),x94752)))
% 18.77/18.49 [9477]P1(f324(f324(x94771,f528(x94772,x94771,x94773,x94774,x94775)),x94772))+~P1(f324(f324(f324(f45(x94775,f845(x94774,a832)),x94773),x94771),x94772))
% 18.77/18.49 [9479]P1(f324(f324(f326(x94791),f528(x94792,x94793,x94794,x94795,x94791)),x94794))+~P1(f324(f324(f324(f45(x94791,f845(x94795,a832)),x94794),x94793),x94792))
% 18.77/18.49 [9489]P1(f324(f324(f326(x94891),f536(x94892,x94893,x94891,x94894,x94895)),x94893))+~P1(f324(f324(f326(x94895),x94894),f324(f324(f45(x94891,f845(x94895,a832)),x94893),x94892)))
% 18.77/18.49 [9494]P1(f324(f324(f326(x94941),x94942),f324(x94943,f536(x94943,x94944,x94945,x94942,x94941))))+~P1(f324(f324(f326(x94941),x94942),f324(f324(f45(x94945,f845(x94941,a832)),x94944),x94943)))
% 18.77/18.49 [9577]~P1(f324(f324(x95774,f668(x95775,x95774,x95773,x95772,x95771)),x95775))+P1(f324(f324(f324(f46(x95771,f845(x95772,a832)),x95773),x95774),x95775))
% 18.77/18.49 [9580]~P1(f324(f324(f326(x95801),x95802),f324(x95805,f658(x95805,x95804,x95803,x95802,x95801))))+P1(f324(f324(f326(x95801),x95802),f324(f324(f46(x95803,f845(x95801,a832)),x95804),x95805)))
% 18.77/18.49 [9584]~P1(f324(f324(f231(f845(x95841,a832)),x95842),f324(x95845,f667(x95845,x95844,x95843,x95842,x95841))))+P1(f324(f324(f231(f845(x95841,a832)),x95842),f324(f324(f46(x95843,f845(x95841,a832)),x95844),x95845)))
% 18.77/18.49 [9642]~P1(f324(f324(f326(x96421),f566(x96425,x96424,x96423,x96422,x96421)),f571(x96425,x96424,x96423,x96422,x96421)))+~P1(f324(f65(x96421,x96422,f324(f324(f303(x96421),x96423),x96424)),x96425))
% 18.77/18.49 [9643]~P1(f324(f324(f326(x96431),f572(x96435,x96434,x96433,x96432,x96431)),f576(x96435,x96434,x96433,x96432,x96431)))+~P1(f324(f65(x96431,x96432,f324(f324(f303(x96431),x96433),x96434)),x96435))
% 18.77/18.49 [9644]~P1(f324(f324(f326(f844(x96441,x96441)),f324(f324(f247(x96441,x96441),x96442),x96445)),f324(f324(f172(f844(x96441,x96441),a832),f324(a114,x96444)),x96443)))+P1(f324(f324(f326(f844(x96441,x96441)),f324(f324(f247(x96441,x96441),x96442),f640(x96443,x96444,x96445,x96442,x96441))),f324(f324(f172(f844(x96441,x96441),a832),x96444),x96443)))
% 18.77/18.49 [9651]P1(f324(f69(x96511,x96511,x96512,f566(x96513,x96514,x96515,x96512,x96511),f571(x96513,x96514,x96515,x96512,x96511)),x96513))+~P1(f324(f65(x96511,x96512,f324(f324(f303(x96511),x96515),x96514)),x96513))
% 18.77/18.49 [9652]P1(f324(f69(x96521,x96521,x96522,f572(x96523,x96524,x96525,x96522,x96521),f576(x96523,x96524,x96525,x96522,x96521)),x96523))+~P1(f324(f65(x96521,x96522,f324(f324(f303(x96521),x96525),x96524)),x96523))
% 18.77/18.49 [9664]~P86(x96641)+P18(x96641,f324(f324(f141(x96642,x96641),x96643),f324(f126(x96642,f324(f324(f9(x96642,x96641,a832),f324(f324(f10(x96641,f845(x96641,a832),x96642),a321),x96643)),f324(x96644,x96645))),x96645)))
% 18.77/18.49 [9717]~P1(f324(f324(f326(x97172),x97175),f324(f278(x97171,x97172,x97174),x97173)))+P1(f324(f324(f326(f844(x97171,x97172)),f324(f324(f247(x97171,x97172),f511(x97173,x97174,x97171,x97175,x97172)),x97175)),x97174))
% 18.77/18.49 [9718]~P1(f324(f324(f326(x97182),x97185),f324(f278(x97181,x97182,x97184),x97183)))+P1(f324(f324(f326(f844(x97181,x97182)),f324(f324(f247(x97181,x97182),f518(x97183,x97184,x97181,x97185,x97182)),x97185)),x97184))
% 18.77/18.49 [9738]~P1(f324(f324(f326(f844(x97381,x97381)),f324(f324(f247(x97381,x97381),x97385),x97384)),f324(f324(f172(f844(x97381,x97381),a832),f324(a114,x97383)),x97382)))+P1(f324(f324(f326(f844(x97381,x97381)),f324(f324(f247(x97381,x97381),f640(x97382,x97383,x97384,x97385,x97381)),x97384)),x97382))
% 18.77/18.49 [9741]~P1(f324(f324(f326(f844(x97411,x97411)),f324(f324(f247(x97411,x97411),x97415),x97414)),f324(f324(f172(f844(x97411,x97411),a832),f324(a114,x97413)),x97412)))+P1(f324(f324(f326(f844(x97411,x97411)),f324(f324(f247(x97411,x97411),f639(x97412,x97413,x97414,x97415,x97411)),x97414)),f324(f324(f172(f844(x97411,x97411),a832),x97413),x97412)))
% 18.77/18.49 [9742]~P1(f324(f324(f326(f844(x97421,x97421)),f324(f324(f247(x97421,x97421),x97425),x97424)),f324(f324(f172(f844(x97421,x97421),a832),f324(a114,x97423)),x97422)))+P1(f324(f324(f326(f844(x97421,x97421)),f324(f324(f247(x97421,x97421),f641(x97422,x97423,x97424,x97425,x97421)),x97424)),f324(f324(f172(f844(x97421,x97421),a832),x97423),x97422)))
% 18.77/18.49 [9743]~P1(f324(f324(f326(f844(f839(x97431),f839(x97431))),f324(f324(f247(f839(x97431),f839(x97431)),x97435),f324(f324(f139(x97431),x97434),x97433))),f145(x97431,x97432)))+P1(f324(f324(f326(f844(x97431,x97431)),f324(f324(f247(x97431,x97431),f705(x97432,x97433,x97434,x97435,x97431)),x97434)),x97432))
% 18.77/18.49 [6921]E(x69211,f182(x69212))+E(f168(x69213,x69212,f324(f324(f324(f74(x69213,f842(x69212)),x69214),x69215),x69211)),f324(f324(f303(x69213),x69215),f168(x69213,x69212,x69214)))
% 18.77/18.49 [7442]~E(x74423,f179(f845(x74422,a832)))+E(f324(f324(f103(f845(x74421,a832)),f324(f324(f45(x74422,f845(x74421,a832)),x74423),x74424)),x74425),x74425)
% 18.77/18.49 [7443]~E(x74433,f179(f845(x74432,a832)))+E(f324(f324(f104(f845(x74431,a832)),f324(f324(f46(x74432,f845(x74431,a832)),x74433),x74434)),x74435),x74435)
% 18.77/18.49 [7495]~P105(x74951)+E(f324(f324(f83(x74951),f324(f324(f83(x74951),x74952),x74953)),f324(f324(f83(x74951),x74954),x74955)),f324(f324(f83(x74951),x74954),f324(f324(f83(x74951),f324(f324(f83(x74951),x74952),x74953)),x74955)))
% 18.77/18.49 [7808]~E(x78085,f182(x78082))+E(f168(x78081,x78082,f324(f324(f324(f74(x78081,f842(x78082)),x78083),x78084),x78085)),f324(f324(f3(f845(x78081,a832)),f168(x78081,x78082,x78083)),f324(f324(f303(x78081),x78084),f179(f845(x78081,a832)))))
% 18.77/18.49 [7879]~E(x78793,f179(f845(x78792,a832)))+E(f324(f324(f3(f845(x78791,a832)),f324(f324(f46(x78792,f845(x78791,a832)),x78793),x78794)),x78795),f324(f324(f3(f845(x78791,a832)),f238(f845(x78791,a832))),x78795))
% 18.77/18.49 [8009]E(f324(f324(f146(x80091,f324(f324(f125(x80091),x80092),x80093)),x80094),x80095),f324(f324(f125(x80091),f324(f324(f146(x80091,x80092),x80094),x80095)),x80093))+~P1(f324(f324(f232(a838),x80094),f324(f180(f839(x80091)),x80092)))
% 18.77/18.49 [8010]E(f324(f324(f146(x80101,f324(f324(f125(x80101),x80102),x80103)),x80104),x80105),f324(f324(f125(x80101),f324(f324(f146(x80101,x80102),x80104),x80105)),x80103))+~P1(f324(f324(f232(a838),x80104),f324(f180(f839(x80101)),x80102)))
% 18.77/18.49 [8143]P1(f324(f324(f326(x81431),x81435),f324(f157(x81431),x81433)))+E(f324(f165(x81431,x81432,f324(f324(f166(x81431,x81432),x81433),f324(f324(f141(x81431,x81432),x81434),x81433))),x81435),f182(x81432))
% 18.77/18.49 [8252]~P1(f324(f324(f326(x82521),x82525),f324(f157(x82521),x82523)))+E(f324(f165(x82521,x82522,f324(f324(f166(x82521,x82522),x82523),f324(f324(f141(x82521,x82522),x82524),x82523))),x82525),f324(f226(x82522),f324(x82524,x82525)))
% 18.77/18.49 [8281]E(f324(f324(f149(x82811),f324(f324(f141(a838,x82811),x82812),f129(a838,f324(f295(a838,x82813),x82814)))),x82815),f324(x82812,f324(f324(f82(a838),x82813),x82815)))+~P1(f324(f324(f232(a838),x82815),f324(f324(f3(a838),x82814),x82813)))
% 18.77/18.49 [8295]E(x82951,f2(a101))+E(f122(x82952,x82953,f324(x82954,f324(f324(f3(a101),x82951),f80(a101))),f324(f324(f9(x82952,a101,f840(f842(x82953))),x82955),x82951)),f324(f190(x82952,x82953,x82954,x82955),x82951))
% 18.77/18.49 [8319]~E(x83193,f179(f845(x83191,a832)))+E(f324(f324(f45(x83191,f845(x83192,a832)),x83193),f324(f324(f10(f845(x83192,a832),f845(x83192,a832),x83191),f324(f103(f845(x83192,a832)),x83194)),x83195)),f179(f845(x83192,a832)))
% 18.77/18.49 [8320]~E(x83203,f179(f845(x83201,a832)))+E(f324(f324(f46(x83201,f845(x83202,a832)),x83203),f324(f324(f10(f845(x83202,a832),f845(x83202,a832),x83201),f324(f3(f845(x83202,a832)),x83204)),x83205)),f238(f845(x83202,a832)))
% 18.77/18.49 [8321]~E(x83213,f179(f845(x83211,a832)))+E(f324(f324(f46(x83211,f845(x83212,a832)),x83213),f324(f324(f10(f845(x83212,a832),f845(x83212,a832),x83211),f324(f104(f845(x83212,a832)),x83214)),x83215)),f238(f845(x83212,a832)))
% 18.77/18.49 [8326]~P135(x83262)+E(f324(f324(f8(x83261,x83262),f324(f324(f10(x83262,x83262,x83261),f324(f83(x83262),x83263)),x83264)),x83265),f324(f324(f83(x83262),x83263),f324(f324(f8(x83261,x83262),x83264),x83265)))
% 18.77/18.49 [8586]E(x85861,f179(f845(x85862,a832)))+E(f324(f324(f46(x85862,f845(x85863,a832)),x85861),f324(f324(f10(f845(x85863,a832),f845(x85863,a832),x85862),f324(f3(f845(x85863,a832)),x85864)),x85865)),f324(f324(f3(f845(x85863,a832)),x85864),f324(f324(f45(x85862,f845(x85863,a832)),x85861),x85865)))
% 18.77/18.49 [8587]E(x85871,f179(f845(x85872,a832)))+E(f324(f324(f45(x85872,f845(x85873,a832)),x85871),f324(f324(f10(f845(x85873,a832),f845(x85873,a832),x85872),f324(f103(f845(x85873,a832)),x85874)),x85875)),f324(f324(f103(f845(x85873,a832)),x85874),f324(f324(f45(x85872,f845(x85873,a832)),x85871),x85875)))
% 18.77/18.49 [8588]E(x85881,f179(f845(x85882,a832)))+E(f324(f324(f46(x85882,f845(x85883,a832)),x85881),f324(f324(f10(f845(x85883,a832),f845(x85883,a832),x85882),f324(f104(f845(x85883,a832)),x85884)),x85885)),f324(f324(f104(f845(x85883,a832)),x85884),f324(f324(f46(x85882,f845(x85883,a832)),x85881),x85885)))
% 18.77/18.49 [8589]E(x85891,f179(f845(x85892,a832)))+E(f324(f324(f45(x85892,f845(x85893,a832)),x85891),f324(f324(f10(f845(x85893,a832),f845(x85893,a832),x85892),f324(f103(f845(x85893,a832)),x85894)),x85895)),f324(f324(f103(f845(x85893,a832)),x85894),f324(f324(f45(x85892,f845(x85893,a832)),x85891),x85895)))
% 18.77/18.49 [8590]E(x85901,f179(f845(x85902,a832)))+E(f324(f324(f46(x85902,f845(x85903,a832)),x85901),f324(f324(f10(f845(x85903,a832),f845(x85903,a832),x85902),f324(f3(f845(x85903,a832)),x85904)),x85905)),f324(f324(f3(f845(x85903,a832)),x85904),f324(f324(f45(x85902,f845(x85903,a832)),x85901),x85905)))
% 18.77/18.49 [8591]E(x85911,f179(f845(x85912,a832)))+E(f324(f324(f46(x85912,f845(x85913,a832)),x85911),f324(f324(f10(f845(x85913,a832),f845(x85913,a832),x85912),f324(f104(f845(x85913,a832)),x85914)),x85915)),f324(f324(f104(f845(x85913,a832)),x85914),f324(f324(f46(x85912,f845(x85913,a832)),x85911),x85915)))
% 18.77/18.49 [9007]~P29(x90072,x90071,x90073,f324(f324(f103(f845(x90072,a832)),x90074),x90075))+E(f324(f324(f104(f845(x90071,a832)),f324(f304(x90072,x90071,x90073),f324(f324(f3(f845(x90072,a832)),x90074),x90075))),f324(f304(x90072,x90071,x90073),f324(f324(f3(f845(x90072,a832)),x90075),x90074))),f179(f845(x90071,a832)))
% 18.77/18.49 [9264]~P1(f324(f324(f231(f845(x92643,a832)),f324(f278(x92641,x92643,x92644),x92642)),x92645))+P1(f324(f324(f231(f845(x92641,a832)),x92642),f324(f81(f845(x92641,a832)),f324(f278(x92643,x92641,f324(f279(x92641,x92643),x92644)),f324(f81(f845(x92643,a832)),x92645)))))
% 18.77/18.49 [9287]~P29(x92871,x92872,x92873,f324(f324(f303(x92871),x92874),x92875))+~P1(f324(f324(f326(x92872),f324(x92873,x92874)),f324(f304(x92871,x92872,x92873),f324(f324(f3(f845(x92871,a832)),x92875),f324(f324(f303(x92871),x92874),f179(f845(x92871,a832)))))))
% 18.77/18.49 [9336]P1(f324(f324(f231(f845(x93361,a832)),f324(f278(x93362,x93361,x93363),x93364)),x93365))+~P1(f324(f324(f231(f845(x93362,a832)),x93364),f324(f81(f845(x93362,a832)),f324(f278(x93361,x93362,f324(f279(x93362,x93361),x93363)),f324(f81(f845(x93361,a832)),x93365)))))
% 18.77/18.49 [9410]~P78(x94101)+P1(f324(f324(f231(x94101),f324(f77(x94101),f324(f324(f3(x94101),f324(f324(f82(x94101),x94102),x94103)),f324(f324(f82(x94101),x94104),x94105)))),f324(f324(f82(x94101),f324(f77(x94101),f324(f324(f3(x94101),x94102),x94104))),f324(f77(x94101),f324(f324(f3(x94101),x94103),x94105)))))
% 18.77/18.49 [9507]P1(f324(f324(f326(x95071),f537(x95072,x95073,x95074,x95071,x95075)),x95074))+P1(f324(f324(f231(f845(x95075,a832)),f324(f324(f45(x95071,f845(x95075,a832)),x95074),x95073)),x95072))
% 18.77/18.49 [9682]~P1(f324(f324(f231(f845(x96821,a832)),f324(x96824,f537(x96825,x96824,x96823,x96822,x96821))),x96825))+P1(f324(f324(f231(f845(x96821,a832)),f324(f324(f45(x96822,f845(x96821,a832)),x96823),x96824)),x96825))
% 18.77/18.49 [8433]E(f324(f324(f125(x84331),x84332),f324(f324(f146(x84331,x84333),f324(f324(f3(a838),x84334),f324(f180(f839(x84331)),x84332))),x84335)),f324(f324(f146(x84331,f324(f324(f125(x84331),x84332),x84333)),x84334),x84335))+P1(f324(f324(f232(a838),x84334),f324(f180(f839(x84331)),x84332)))
% 18.77/18.49 [8458]~P134(x84581)+E(f324(f324(f82(x84581),f324(f324(f83(x84581),x84582),x84583)),f324(f324(f82(x84581),f324(f324(f83(x84581),x84584),x84583)),x84585)),f324(f324(f82(x84581),f324(f324(f83(x84581),f324(f324(f82(x84581),x84582),x84584)),x84583)),x84585))
% 18.77/18.49 [8964]~P135(x89641)+E(f324(f151(x89641),f324(f324(f141(x89642,x89641),f324(f324(f10(x89641,x89641,x89642),f324(f83(x89641),x89643)),x89644)),x89645)),f324(f324(f83(x89641),x89643),f324(f151(x89641),f324(f324(f141(x89642,x89641),x89644),x89645))))
% 18.77/18.49 [9343]~P135(x93432)+E(f324(f324(f8(x93431,x93432),f324(f324(f9(x93431,x93432,x93432),f324(f324(f10(x93432,f845(x93432,x93432),x93431),f83(x93432)),x93433)),x93434)),x93435),f324(f324(f83(x93432),f324(f324(f8(x93431,x93432),x93433),x93435)),x93434))
% 18.77/18.49 [9344]~P60(x93442)+E(f324(f324(f8(x93441,x93442),f324(f324(f9(x93441,x93442,x93442),f324(f324(f10(x93442,f845(x93442,x93442),x93441),f284(x93442)),x93443)),x93444)),x93445),f324(f324(f284(x93442),f324(f324(f8(x93441,x93442),x93443),x93445)),x93444))
% 18.77/18.49 [9351]~P68(x93512)+E(f324(f324(f11(x93511,x93512),f324(f324(f20(x93511,x93512,x93512),f324(f324(f10(x93512,f845(x93512,x93512),x93511),f83(x93512)),x93513)),x93514)),x93515),f324(f324(f83(x93512),f324(f324(f11(x93511,x93512),x93513),x93515)),f324(f324(f11(x93511,x93512),x93514),x93515)))
% 18.77/18.49 [9352]~P67(x93522)+E(f324(f324(f8(x93521,x93522),f324(f324(f20(x93521,x93522,x93522),f324(f324(f10(x93522,f845(x93522,x93522),x93521),f82(x93522)),x93523)),x93524)),x93525),f324(f324(f82(x93522),f324(f324(f8(x93521,x93522),x93523),x93525)),f324(f324(f8(x93521,x93522),x93524),x93525)))
% 18.77/18.49 [9353]~P6(x93532)+E(f324(f324(f8(x93531,x93532),f324(f324(f20(x93531,x93532,x93532),f324(f324(f10(x93532,f845(x93532,x93532),x93531),f3(x93532)),x93533)),x93534)),x93535),f324(f324(f3(x93532),f324(f324(f8(x93531,x93532),x93533),x93535)),f324(f324(f8(x93531,x93532),x93534),x93535)))
% 18.77/18.49 [9393]~E(x93933,f179(f845(x93931,a832)))+E(f324(f324(f45(x93931,f845(x93932,a832)),x93933),f324(f324(f9(x93931,f845(x93932,a832),f845(x93932,a832)),f324(f324(f10(f845(x93932,a832),f845(f845(x93932,a832),f845(x93932,a832)),x93931),f103(f845(x93932,a832))),x93934)),x93935)),f179(f845(x93932,a832)))
% 18.77/18.49 [9394]~E(x93943,f179(f845(x93941,a832)))+E(f324(f324(f46(x93941,f845(x93942,a832)),x93943),f324(f324(f9(x93941,f845(x93942,a832),f845(x93942,a832)),f324(f324(f10(f845(x93942,a832),f845(f845(x93942,a832),f845(x93942,a832)),x93941),f3(f845(x93942,a832))),x93944)),x93945)),f238(f845(x93942,a832)))
% 18.77/18.49 [9395]~E(x93953,f179(f845(x93951,a832)))+E(f324(f324(f46(x93951,f845(x93952,a832)),x93953),f324(f324(f9(x93951,f845(x93952,a832),f845(x93952,a832)),f324(f324(f10(f845(x93952,a832),f845(f845(x93952,a832),f845(x93952,a832)),x93951),f104(f845(x93952,a832))),x93954)),x93955)),f238(f845(x93952,a832)))
% 18.77/18.49 [9417]E(x94171,f179(f845(x94172,a832)))+E(f324(f324(f46(x94172,f845(x94173,a832)),x94171),f324(f324(f9(x94172,f845(x94173,a832),f845(x94173,a832)),f324(f324(f10(f845(x94173,a832),f845(f845(x94173,a832),f845(x94173,a832)),x94172),f3(f845(x94173,a832))),x94174)),x94175)),f324(f324(f3(f845(x94173,a832)),f324(f324(f46(x94172,f845(x94173,a832)),x94171),x94174)),x94175))
% 18.77/18.49 [9418]E(x94181,f179(f845(x94182,a832)))+E(f324(f324(f45(x94182,f845(x94183,a832)),x94181),f324(f324(f9(x94182,f845(x94183,a832),f845(x94183,a832)),f324(f324(f10(f845(x94183,a832),f845(f845(x94183,a832),f845(x94183,a832)),x94182),f103(f845(x94183,a832))),x94184)),x94185)),f324(f324(f103(f845(x94183,a832)),f324(f324(f45(x94182,f845(x94183,a832)),x94181),x94184)),x94185))
% 18.77/18.49 [9419]E(x94191,f179(f845(x94192,a832)))+E(f324(f324(f46(x94192,f845(x94193,a832)),x94191),f324(f324(f9(x94192,f845(x94193,a832),f845(x94193,a832)),f324(f324(f10(f845(x94193,a832),f845(f845(x94193,a832),f845(x94193,a832)),x94192),f104(f845(x94193,a832))),x94194)),x94195)),f324(f324(f104(f845(x94193,a832)),f324(f324(f46(x94192,f845(x94193,a832)),x94191),x94194)),x94195))
% 18.77/18.49 [9420]E(x94201,f179(f845(x94202,a832)))+E(f324(f324(f45(x94202,f845(x94203,a832)),x94201),f324(f324(f9(x94202,f845(x94203,a832),f845(x94203,a832)),f324(f324(f10(f845(x94203,a832),f845(f845(x94203,a832),f845(x94203,a832)),x94202),f103(f845(x94203,a832))),x94204)),x94205)),f324(f324(f103(f845(x94203,a832)),f324(f324(f45(x94202,f845(x94203,a832)),x94201),x94204)),x94205))
% 18.77/18.49 [9421]E(x94211,f179(f845(x94212,a832)))+E(f324(f324(f46(x94212,f845(x94213,a832)),x94211),f324(f324(f9(x94212,f845(x94213,a832),f845(x94213,a832)),f324(f324(f10(f845(x94213,a832),f845(f845(x94213,a832),f845(x94213,a832)),x94212),f3(f845(x94213,a832))),x94214)),x94215)),f324(f324(f3(f845(x94213,a832)),f324(f324(f46(x94212,f845(x94213,a832)),x94211),x94214)),x94215))
% 18.77/18.50 [9422]E(x94221,f179(f845(x94222,a832)))+E(f324(f324(f46(x94222,f845(x94223,a832)),x94221),f324(f324(f9(x94222,f845(x94223,a832),f845(x94223,a832)),f324(f324(f10(f845(x94223,a832),f845(f845(x94223,a832),f845(x94223,a832)),x94222),f104(f845(x94223,a832))),x94224)),x94225)),f324(f324(f104(f845(x94223,a832)),f324(f324(f46(x94222,f845(x94223,a832)),x94221),x94224)),x94225))
% 18.77/18.50 [9011]~P1(f324(f324(f231(a838),x90111),x90114))+E(f324(f324(f3(a838),f324(f324(f82(a838),f324(f324(f83(a838),x90111),x90112)),x90113)),f324(f324(f82(a838),f324(f324(f83(a838),x90114),x90112)),x90115)),f324(f324(f3(a838),x90113),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x90114),x90111)),x90112)),x90115)))
% 18.77/18.50 [9561]~P135(x95611)+E(f324(f151(x95611),f324(f324(f141(x95612,x95611),f324(f324(f9(x95612,x95611,x95611),f324(f324(f10(x95611,f845(x95611,x95611),x95612),f83(x95611)),x95613)),x95614)),x95615)),f324(f324(f83(x95611),f324(f151(x95611),f324(f324(f141(x95612,x95611),x95613),x95615))),x95614))
% 18.77/18.50 [9567]~P67(x95671)+E(f324(f151(x95671),f324(f324(f141(x95672,x95671),f324(f324(f20(x95672,x95671,x95671),f324(f324(f10(x95671,f845(x95671,x95671),x95672),f82(x95671)),x95673)),x95674)),x95675)),f324(f324(f82(x95671),f324(f151(x95671),f324(f324(f141(x95672,x95671),x95673),x95675))),f324(f151(x95671),f324(f324(f141(x95672,x95671),x95674),x95675))))
% 18.77/18.50 [9568]~P6(x95681)+E(f324(f151(x95681),f324(f324(f141(x95682,x95681),f324(f324(f20(x95682,x95681,x95681),f324(f324(f10(x95681,f845(x95681,x95681),x95682),f3(x95681)),x95683)),x95684)),x95685)),f324(f324(f3(x95681),f324(f151(x95681),f324(f324(f141(x95682,x95681),x95683),x95685))),f324(f151(x95681),f324(f324(f141(x95682,x95681),x95684),x95685))))
% 18.77/18.50 [9949]~P1(f324(f324(f326(f844(x99492,x99491)),f324(f324(f247(x99492,x99491),x99494),x99495)),f324(f279(x99491,x99492),x99493)))+P1(f324(f324(f239(x99491,x99492,f324(f324(f9(x99491,f845(f844(x99491,x99492),a832),f845(x99492,a832)),f324(f324(f10(f845(x99492,f845(f845(f844(x99491,x99492),a832),a832)),f845(f845(f844(x99491,x99492),a832),f845(x99492,a832)),x99491),f9(x99492,f845(f844(x99491,x99492),a832),a832)),f324(f324(f10(f845(x99492,f844(x99491,x99492)),f845(x99492,f845(f845(f844(x99491,x99492),a832),a832)),x99491),f324(f10(f844(x99491,x99492),f845(f845(f844(x99491,x99492),a832),a832),x99492),f326(f844(x99491,x99492)))),f247(x99491,x99492)))),x99493)),x99494),x99495))
% 18.77/18.50 [9958]P1(f324(f324(f326(f844(x99581,x99582)),f324(f324(f247(x99581,x99582),x99583),x99584)),f324(f279(x99582,x99581),x99585)))+~P1(f324(f324(f239(x99582,x99581,f324(f324(f9(x99582,f845(f844(x99582,x99581),a832),f845(x99581,a832)),f324(f324(f10(f845(x99581,f845(f845(f844(x99582,x99581),a832),a832)),f845(f845(f844(x99582,x99581),a832),f845(x99581,a832)),x99582),f9(x99581,f845(f844(x99582,x99581),a832),a832)),f324(f324(f10(f845(x99581,f844(x99582,x99581)),f845(x99581,f845(f845(f844(x99582,x99581),a832),a832)),x99582),f324(f10(f844(x99582,x99581),f845(f845(f844(x99582,x99581),a832),a832),x99581),f326(f844(x99582,x99581)))),f247(x99582,x99581)))),x99585)),x99583),x99584))
% 18.77/18.50 [9231]~P1(f324(f324(f231(a838),x92314),x92311))+E(f324(f324(f3(a838),f324(f324(f82(a838),f324(f324(f83(a838),x92311),x92312)),x92313)),f324(f324(f82(a838),f324(f324(f83(a838),x92314),x92312)),x92315)),f324(f324(f3(a838),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x92311),x92314)),x92312)),x92313)),x92315))
% 18.77/18.50 [9967]P28(x99671,x99672,f324(f304(a834,f837(x99671),f324(f324(f20(a834,f845(x99671,f845(a835,a832)),f837(x99671)),f324(f324(f20(a834,a833,f845(f845(x99671,f845(a835,a832)),f837(x99671))),f324(f324(f10(f845(x99671,f845(a835,a832)),f845(a833,f845(f845(x99671,f845(a835,a832)),f837(x99671))),a834),f93(x99671)),x99673)),a27)),x99674)),x99675))+~P28(x99671,f324(f324(f103(f845(f837(x99671),a832)),x99672),f324(f304(a834,f837(x99671),f324(f324(f20(a834,f845(x99671,f845(a835,a832)),f837(x99671)),f324(f324(f20(a834,a833,f845(f845(x99671,f845(a835,a832)),f837(x99671))),f324(f324(f10(f845(x99671,f845(a835,a832)),f845(a833,f845(f845(x99671,f845(a835,a832)),f837(x99671))),a834),f93(x99671)),x99673)),a27)),x99674)),x99675)),f324(f304(a834,f837(x99671),f324(f324(f20(a834,f845(x99671,f845(a835,a832)),f837(x99671)),f324(f324(f20(a834,a833,f845(f845(x99671,f845(a835,a832)),f837(x99671))),f324(f324(f10(f845(x99671,f845(a835,a832)),f845(a833,f845(f845(x99671,f845(a835,a832)),f837(x99671))),a834),f93(x99671)),x99673)),f324(f324(f10(f842(a833),a833,a834),f230(a833)),a30))),x99674)),x99675))
% 18.77/18.50 [5075]E(x50751,x50752)+~E(f31(x50753,x50754,x50751),f31(x50755,x50756,x50752))
% 18.77/18.50 [5076]E(x50761,x50762)+~E(f31(x50763,x50761,x50764),f31(x50765,x50762,x50766))
% 18.77/18.50 [5077]E(x50771,x50772)+~E(f31(x50771,x50773,x50774),f31(x50772,x50775,x50776))
% 18.77/18.50 [5078]E(x50781,x50782)+~E(f33(x50783,x50784,x50781),f33(x50785,x50786,x50782))
% 18.77/18.50 [5079]E(x50791,x50792)+~E(f33(x50793,x50791,x50794),f33(x50795,x50792,x50796))
% 18.77/18.50 [5080]E(x50801,x50802)+~E(f33(x50801,x50803,x50804),f33(x50802,x50805,x50806))
% 18.77/18.50 [5081]E(x50811,x50812)+~E(f32(x50813,x50814,x50811),f32(x50815,x50816,x50812))
% 18.77/18.50 [5082]E(x50821,x50822)+~E(f32(x50823,x50821,x50824),f32(x50825,x50822,x50826))
% 18.77/18.50 [5083]E(x50831,x50832)+~E(f32(x50831,x50833,x50834),f32(x50832,x50835,x50836))
% 18.77/18.50 [7108]E(x71081,x71082)+~E(f214(x71083,x71084,x71085,x71081),f214(x71083,x71084,x71086,x71082))
% 18.77/18.50 [7109]E(x71091,x71092)+~E(f214(x71093,x71094,x71091,x71095),f214(x71093,x71094,x71092,x71096))
% 18.77/18.50 [6549]E(f324(f169(x65491,x65492,x65493,x65494),x65495),f324(f226(x65492),x65496))+~E(f324(x65494,x65495),f324(f226(x65492),x65496))
% 18.77/18.50 [6550]E(f324(f169(x65501,x65502,x65503,x65504),x65505),f324(f226(x65502),x65506))+~E(f324(x65504,x65505),f324(f226(x65502),x65506))
% 18.77/18.50 [6701]E(f324(f228(f842(x67011),x67012,f182(x67011),x67013),f324(x67014,x67015)),f324(x67013,x67016))+~E(f324(x67014,x67015),f324(f226(x67012),x67016))
% 18.77/18.50 [8263]~P23(x82635,x82631,x82632,x82636)+E(f324(f75(x82631,x82631,x82631,f324(x82632,x82633)),f324(x82632,x82634)),f324(f75(x82631,x82631,x82631,f324(x82632,x82634)),f324(x82632,x82633)))
% 18.77/18.50 [8493]~P54(x84934,x84935,x84932,x84931,x84936)+E(f324(x84931,f324(x84932,x84933)),x84933)
% 18.77/18.50 [8637]P29(x86371,x86372,x86373,x86374)+~P29(x86371,x86375,f324(f75(x86372,x86375,x86371,x86376),x86373),x86374)
% 18.77/18.50 [8715]~P29(x87154,x87152,f324(f75(x87151,x87152,x87154,x87153),x87155),x87156)+P29(x87151,x87152,x87153,f324(f304(x87154,x87151,x87155),x87156))
% 18.77/18.50 [9354]P1(f324(f64(x93541),x93542))+~P1(f324(f69(x93541,x93543,x93544,x93545,x93542),x93546))
% 18.77/18.50 [9364]~P1(f324(f324(f326(x93644),x93643),f293(x93644,x93645,x93641,x93642,x93646)))+P1(f324(f324(x93641,x93642),x93643))
% 18.77/18.50 [9365]~P1(f324(f324(f326(x93654),x93653),f290(x93654,x93651,x93655,x93652,x93656)))+P1(f324(f324(x93651,x93652),x93653))
% 18.77/18.50 [9366]~P1(f324(f324(f326(x93664),x93662),f293(x93664,x93661,x93665,x93666,x93663)))+P1(f324(f324(x93661,x93662),x93663))
% 18.77/18.50 [9367]~P1(f324(f324(f326(x93674),x93672),f290(x93674,x93675,x93671,x93676,x93673)))+P1(f324(f324(x93671,x93672),x93673))
% 18.77/18.50 [5566]E(x55661,x55662)+~E(f324(f324(f247(x55663,x55664),x55665),x55661),f324(f324(f247(x55663,x55664),x55666),x55662))
% 18.77/18.50 [5567]E(x55671,x55672)+~E(f324(f324(f247(x55673,x55674),x55675),x55671),f324(f324(f247(x55673,x55674),x55676),x55672))
% 18.77/18.50 [5568]E(x55681,x55682)+~E(f324(f324(f247(x55683,x55684),x55681),x55685),f324(f324(f247(x55683,x55684),x55682),x55686))
% 18.77/18.50 [5569]E(x55691,x55692)+~E(f324(f324(f247(x55693,x55694),x55691),x55695),f324(f324(f247(x55693,x55694),x55692),x55696))
% 18.77/18.50 [5706]~P20(x57065,x57066,x57061)+E(f324(f324(x57061,x57062),f324(f324(x57061,x57063),x57064)),f324(f324(x57061,x57063),f324(f324(x57061,x57062),x57064)))
% 18.77/18.50 [7179]~P34(x71794,x71791,f324(f324(f139(x71794),x71792),x71795),f324(f324(f139(x71794),x71793),x71796))+P1(f324(f324(x71791,x71792),x71793))
% 18.77/18.50 [7561]P34(x75611,x75612,x75613,x75614)+~P34(x75611,x75612,f324(f324(f139(x75611),x75615),x75613),f324(f324(f139(x75611),x75616),x75614))
% 18.77/18.50 [8580]~P54(x85805,x85801,x85802,x85806,x85804)+P1(f324(f324(f326(x85801),f324(x85802,x85803)),x85804))
% 18.77/18.50 [8737]E(f324(f78(x87371,x87372,x87373,x87374,x87375),x87376),f324(x87373,x87376))+P1(f324(f324(f326(x87371),x87376),x87375))
% 18.77/18.50 [8738]E(f324(f78(x87381,x87382,x87383,x87384,x87385),x87386),f324(x87383,x87386))+P1(f324(f324(f326(x87381),x87386),x87385))
% 18.77/18.50 [8757]~E(x87573,f324(f324(f139(x87571),x87575),x87576))+P1(f324(f324(f326(f844(f839(x87571),f839(x87571))),f324(f324(f247(f839(x87571),f839(x87571)),x87572),f324(f324(f125(x87571),x87572),x87573))),f136(x87571,x87574)))
% 18.77/18.50 [8760]E(f324(f78(x87601,x87602,x87603,x87604,x87605),x87606),f324(x87604,x87606))+~P1(f324(f324(f326(x87601),x87606),x87605))
% 18.77/18.50 [8761]E(f324(f78(x87611,x87612,x87613,x87614,x87615),x87616),f324(x87614,x87616))+~P1(f324(f324(f326(x87611),x87616),x87615))
% 18.77/18.50 [9432]~P27(x94324,x94322,x94325,x94323,x94326,x94321)+E(f324(x94321,f179(f845(x94322,a832))),x94323)
% 18.77/18.50 [9645]~E(f324(x96454,f324(f246(x96451,x96453),x96455)),f324(x96456,f324(f246(x96451,x96453),x96455)))+E(f324(f253(x96451,x96452,x96453,x96453,x96454,f37(x96453)),x96455),f324(f253(x96451,x96452,x96453,x96453,x96456,f37(x96453)),x96455))
% 18.77/18.50 [9646]~E(f324(x96464,f324(f251(x96461,x96462),x96465)),f324(x96466,f324(f251(x96461,x96462),x96465)))+E(f324(f253(x96461,x96461,x96462,x96463,f37(x96461),x96464),x96465),f324(f253(x96461,x96461,x96462,x96463,f37(x96461),x96466),x96465))
% 18.77/18.50 [9705]~E(f324(f253(x97052,x97056,x97053,x97053,x97051,f37(x97053)),x97054),f324(f253(x97052,x97056,x97053,x97053,x97055,f37(x97053)),x97054))+E(f324(x97051,f324(f246(x97052,x97053),x97054)),f324(x97055,f324(f246(x97052,x97053),x97054)))
% 18.77/18.50 [9706]~E(f324(f253(x97062,x97062,x97063,x97066,f37(x97062),x97061),x97064),f324(f253(x97062,x97062,x97063,x97066,f37(x97062),x97065),x97064))+E(f324(x97061,f324(f251(x97062,x97063),x97064)),f324(x97065,f324(f251(x97062,x97063),x97064)))
% 18.77/18.50 [8670]P1(f324(f324(f326(x86701),x86702),x86703))+~P1(f324(f324(f326(f844(x86701,x86704)),f324(f324(f247(x86701,x86704),x86702),x86705)),f324(f324(f249(x86701,x86704),x86703),x86706)))
% 18.77/18.50 [8671]P1(f324(f324(f326(x86711),x86712),x86713))+~P1(f324(f324(f326(f844(x86711,x86714)),f324(f324(f247(x86711,x86714),x86712),x86715)),f324(f324(f249(x86711,x86714),x86713),x86716)))
% 18.77/18.50 [8672]P1(f324(f324(f326(x86721),x86722),x86723))+~P1(f324(f324(f326(f844(x86721,x86724)),f324(f324(f247(x86721,x86724),x86722),x86725)),f324(f324(f249(x86721,x86724),x86723),x86726)))
% 18.77/18.50 [8685]P1(f324(f324(f326(x86851),x86852),f324(x86853,x86854)))+~P1(f324(f324(f326(f844(x86855,x86851)),f324(f324(f247(x86855,x86851),x86854),x86852)),f324(f324(f249(x86855,x86851),x86856),x86853)))
% 18.77/18.50 [8686]P1(f324(f324(f326(x86861),x86862),f324(x86863,x86864)))+~P1(f324(f324(f326(f844(x86865,x86861)),f324(f324(f247(x86865,x86861),x86864),x86862)),f324(f324(f249(x86865,x86861),x86866),x86863)))
% 18.77/18.50 [8687]P1(f324(f324(f326(x86871),x86872),f324(x86873,x86874)))+~P1(f324(f324(f326(f844(x86875,x86871)),f324(f324(f247(x86875,x86871),x86874),x86872)),f324(f324(f249(x86875,x86871),x86876),x86873)))
% 18.77/18.50 [8987]P1(f324(f324(f326(x89871),x89874),f168(x89871,x89872,x89876)))+E(f169(x89871,x89872,f324(f324(f324(f74(x89871,f842(x89872)),x89873),x89874),f324(f226(x89872),x89875)),x89876),f324(f324(f324(f74(x89871,f842(x89872)),f169(x89871,x89872,x89873,x89876)),x89874),f324(f226(x89872),x89875)))
% 18.77/18.50 [9076]P1(f324(f324(f326(f844(x90761,x90761)),f324(f324(f247(x90761,x90761),f324(x90762,x90763)),f324(x90762,x90764))),x90765))+~P1(f324(f324(f326(f844(x90766,x90766)),f324(f324(f247(x90766,x90766),x90763),x90764)),f324(f324(f281(x90761,x90766),x90765),x90762)))
% 18.77/18.50 [9090]~P1(f324(f324(f326(f844(x90904,x90904)),f324(f324(f247(x90904,x90904),f324(x90906,x90902)),f324(x90906,x90903))),x90905))+P1(f324(f324(f326(f844(x90901,x90901)),f324(f324(f247(x90901,x90901),x90902),x90903)),f324(f324(f281(x90904,x90901),x90905),x90906)))
% 18.77/18.50 [9708]E(f324(f324(f247(x97081,x97082),f374(x97083,x97084,x97085,x97086,x97082,x97081)),f375(x97083,x97084,x97085,x97086,x97082,x97081)),x97086)+~P1(f324(f324(f326(f844(x97081,x97082)),x97086),f324(f324(f282(x97081,x97085,x97082),x97084),x97083)))
% 18.77/18.50 [9914]~P1(f324(f324(f326(f844(x99141,x99146)),x99145),f324(f324(f282(x99141,x99142,x99146),x99144),x99143)))+P1(f324(f324(f326(f844(x99141,x99142)),f324(f324(f247(x99141,x99142),f374(x99143,x99144,x99142,x99145,x99146,x99141)),f376(x99143,x99144,x99142,x99145,x99146,x99141))),x99144))
% 18.77/18.50 [9915]~P1(f324(f324(f326(f844(x99156,x99152)),x99155),f324(f324(f282(x99156,x99151,x99152),x99154),x99153)))+P1(f324(f324(f326(f844(x99151,x99152)),f324(f324(f247(x99151,x99152),f376(x99153,x99154,x99151,x99155,x99152,x99156)),f375(x99153,x99154,x99151,x99155,x99152,x99156))),x99153))
% 18.77/18.50 [5986]~E(x59866,x59864)+E(f324(f324(f324(f324(f74(x59861,x59862),x59863),x59864),x59865),x59866),x59865)
% 18.77/18.50 [5987]~E(x59876,x59874)+E(f324(f324(f324(f324(f74(x59871,x59872),x59873),x59874),x59875),x59876),x59875)
% 18.77/18.50 [6035]E(x60351,x60352)+E(f324(f324(f324(f324(f74(x60353,x60354),x60355),x60352),x60356),x60351),f324(x60355,x60351))
% 18.77/18.50 [6036]E(x60361,x60362)+E(f324(f324(f324(f324(f74(x60363,x60364),x60365),x60362),x60366),x60361),f324(x60365,x60361))
% 18.77/18.50 [6037]E(x60371,x60372)+E(f324(f324(f324(f324(f74(x60373,x60374),x60375),x60372),x60376),x60371),f324(x60375,x60371))
% 18.77/18.50 [7628]~P9(x76282)+E(f324(f324(f45(x76281,x76282),x76283),f324(f324(f9(x76281,x76284,x76282),x76285),x76286)),f324(f324(f324(f45(x76281,f845(x76284,x76282)),x76283),x76285),x76286))
% 18.77/18.50 [7629]~P9(x76292)+E(f324(f324(f46(x76291,x76292),x76293),f324(f324(f9(x76291,x76294,x76292),x76295),x76296)),f324(f324(f324(f46(x76291,f845(x76294,x76292)),x76293),x76295),x76296))
% 18.77/18.50 [8227]E(f324(f304(x82271,f842(x82272),f324(f324(f324(f74(x82271,f842(x82272)),x82273),x82274),f324(f226(x82272),x82275))),x82276),f324(f304(x82271,f842(x82272),x82273),x82276))+P1(f324(f324(f326(x82271),x82274),x82276))
% 18.77/18.50 [8415]E(f324(f324(f45(x84151,f845(x84152,a832)),x84153),f324(f324(f10(f845(x84152,a832),f845(x84152,a832),x84151),f324(f303(x84152),x84154)),x84155)),f324(f324(f303(x84152),x84154),f324(f324(f45(x84151,f845(x84152,a832)),x84153),x84155)))+~P1(f324(f324(f326(x84151),x84156),x84153))
% 18.77/18.50 [8416]E(f324(f324(f46(x84161,f845(x84162,a832)),x84163),f324(f324(f10(f845(x84162,a832),f845(x84162,a832),x84161),f324(f303(x84162),x84164)),x84165)),f324(f324(f303(x84162),x84164),f324(f324(f46(x84161,f845(x84162,a832)),x84163),x84165)))+~P1(f324(f324(f326(x84161),x84166),x84163))
% 18.77/18.50 [8801]~P9(x88012)+E(f324(f324(f45(x88011,x88012),x88013),f324(f324(f10(f845(x88014,x88012),x88012,x88011),f324(f45(x88014,x88012),x88015)),f324(f9(x88014,x88011,x88012),x88016))),f324(f324(f45(x88014,x88012),x88015),f324(f324(f10(f845(x88011,x88012),x88012,x88014),f324(f45(x88011,x88012),x88013)),x88016)))
% 18.77/18.50 [8802]~P9(x88022)+E(f324(f324(f46(x88021,x88022),x88023),f324(f324(f10(f845(x88024,x88022),x88022,x88021),f324(f46(x88024,x88022),x88025)),f324(f9(x88024,x88021,x88022),x88026))),f324(f324(f46(x88024,x88022),x88025),f324(f324(f10(f845(x88021,x88022),x88022,x88024),f324(f46(x88021,x88022),x88023)),x88026)))
% 18.77/18.50 [8993]P1(f324(f324(f326(x89931),x89932),f324(f157(x89931),x89933)))+~P1(f324(f324(f326(f844(x89934,x89931)),f324(f324(f247(x89934,x89931),x89935),x89932)),f324(f157(f844(x89934,x89931)),f324(f324(f166(x89934,x89931),x89936),x89933))))
% 18.77/18.50 [8994]P1(f324(f324(f326(x89941),x89942),f324(f157(x89941),x89943)))+~P1(f324(f324(f326(f844(x89941,x89944)),f324(f324(f247(x89941,x89944),x89942),x89945)),f324(f157(f844(x89941,x89944)),f324(f324(f166(x89941,x89944),x89943),x89946))))
% 18.77/18.50 [8995]P1(f324(f324(f326(x89951),x89952),f324(f157(x89951),x89953)))+~P1(f324(f324(f326(f844(x89954,x89951)),f324(f324(f247(x89954,x89951),x89955),x89952)),f324(f157(f844(x89954,x89951)),f324(f324(f166(x89954,x89951),x89956),x89953))))
% 18.77/18.50 [8996]P1(f324(f324(f326(x89961),x89962),f324(f157(x89961),x89963)))+~P1(f324(f324(f326(f844(x89961,x89964)),f324(f324(f247(x89961,x89964),x89962),x89965)),f324(f157(f844(x89961,x89964)),f324(f324(f166(x89961,x89964),x89963),x89966))))
% 18.77/18.50 [9088]P1(f324(f324(f231(f845(x90881,a832)),f324(f278(x90882,x90881,x90883),x90884)),x90885))+~P1(f324(f324(f231(f845(f844(x90882,x90881),a832)),x90883),f324(f324(f249(x90882,x90881),x90886),f324(f18(f845(x90881,a832),x90882),x90885))))
% 18.77/18.50 [9267]P1(f324(f324(f326(f844(f839(x92671),f839(x92671))),f324(f324(f247(f839(x92671),f839(x92671)),f324(f324(f139(x92671),x92672),x92673)),f324(f324(f139(x92671),x92674),x92675))),f136(x92671,x92676)))+~P1(f324(f324(f326(f844(x92671,x92671)),f324(f324(f247(x92671,x92671),x92672),x92674)),x92676))
% 18.77/18.50 [9704]E(f324(f324(f247(x97041,x97042),f812(x97043,x97044,x97045,x97042,x97041,x97046)),f815(x97043,x97044,x97045,x97042,x97041,x97046)),x97046)+P1(f324(f324(f326(x97045),x97044),f324(f324(f252(x97041,x97042,f845(x97045,a832)),x97043),x97046)))
% 18.77/18.50 [9709]E(f324(f324(f247(x97091,x97092),f813(x97093,x97094,x97092,x97091,x97095,x97096)),f814(x97093,x97094,x97092,x97091,x97095,x97096)),x97093)+~P1(f324(f324(f326(x97096),x97095),f324(f324(f252(x97091,x97092,f845(x97096,a832)),x97094),x97093)))
% 18.77/18.50 [9870]P1(f324(f324(f326(x98701),x98702),f324(f324(x98703,f813(x98704,x98703,x98705,x98706,x98702,x98701)),f814(x98704,x98703,x98705,x98706,x98702,x98701))))+~P1(f324(f324(f326(x98701),x98702),f324(f324(f252(x98706,x98705,f845(x98701,a832)),x98703),x98704)))
% 18.77/18.50 [9893]~P1(f324(f324(f326(x98931),x98932),f324(f324(x98935,f812(x98935,x98932,x98931,x98934,x98933,x98936)),f815(x98935,x98932,x98931,x98934,x98933,x98936))))+P1(f324(f324(f326(x98931),x98932),f324(f324(f252(x98933,x98934,f845(x98931,a832)),x98935),x98936)))
% 18.77/18.50 [7755]P1(f324(f324(f326(x77551),x77554),x77556))+E(f171(x77551,x77552,f324(f324(f324(f74(x77551,f842(x77552)),x77553),x77554),x77555),x77556),f171(x77551,x77552,x77553,x77556))
% 18.77/18.50 [7830]P1(f324(f324(f326(x78301),x78304),x78306))+E(f324(f304(x78301,x78302,f324(f324(f324(f74(x78301,x78302),x78303),x78304),x78305)),x78306),f324(f304(x78301,x78302,x78303),x78306))
% 18.77/18.50 [7858]P1(f324(f324(f326(x78581),x78584),f324(f157(x78581),x78586)))+E(f324(f324(f141(x78581,x78582),f324(f324(f324(f74(x78581,x78582),x78583),x78584),x78585)),x78586),f324(f324(f141(x78581,x78582),x78583),x78586))
% 18.77/18.50 [8311]E(x83111,x83112)+E(f324(f324(f146(x83113,f324(f324(f146(x83113,x83114),x83111),x83115)),x83112),x83116),f324(f324(f146(x83113,f324(f324(f146(x83113,x83114),x83112),x83116)),x83111),x83115))
% 18.77/18.50 [8807]~P1(f324(f324(f326(x88073),x88076),x88075))+E(f324(f324(f303(x88071),x88072),f324(f304(x88073,x88071,x88074),f324(f324(f3(f845(x88073,a832)),x88075),f324(f324(f303(x88073),x88076),f179(f845(x88073,a832)))))),f324(f304(x88073,x88071,f324(f324(f324(f74(x88073,x88071),x88074),x88076),x88072)),x88075))
% 18.77/18.50 [8632]~E(x86323,x86326)+E(f324(f165(x86321,x86322,f324(f324(f139(f844(x86321,x86322)),f324(f324(f247(x86321,x86322),x86323),x86324)),x86325)),x86326),f324(f226(x86322),x86324))
% 18.77/18.50 [8674]E(x86741,x86742)+E(f324(f165(x86743,x86744,f324(f324(f139(f844(x86743,x86744)),f324(f324(f247(x86743,x86744),x86741),x86745)),x86746)),x86742),f324(f165(x86743,x86744,x86746),x86742))
% 18.77/18.50 [8879]~P1(f324(f324(x88794,x88795),x88796))+P1(f324(f324(f324(f324(f103(f845(x88791,f845(x88792,a832))),x88793),x88794),x88795),x88796))
% 18.77/18.50 [8880]~P1(f324(f324(x88804,x88805),x88806))+P1(f324(f324(f324(f324(f103(f845(x88801,f845(x88802,a832))),x88803),x88804),x88805),x88806))
% 18.77/18.50 [8881]~P1(f324(f324(x88813,x88815),x88816))+P1(f324(f324(f324(f324(f103(f845(x88811,f845(x88812,a832))),x88813),x88814),x88815),x88816))
% 18.77/18.50 [8882]~P1(f324(f324(x88823,x88825),x88826))+P1(f324(f324(f324(f324(f103(f845(x88821,f845(x88822,a832))),x88823),x88824),x88825),x88826))
% 18.77/18.50 [8898]P1(f324(f324(f326(x88981),x88986),f324(f157(x88981),x88984)))+E(f324(f169(x88981,x88982,x88983,f165(x88981,x88982,f324(f154(f844(x88981,x88982)),f324(f324(f166(x88981,x88982),x88984),x88985)))),x88986),f324(x88983,x88986))
% 18.77/18.50 [9041]~E(f324(f180(f839(x90411)),x90414),f324(f180(f839(x90412)),x90415))+E(f169(x90411,x90412,x90413,f165(x90411,x90412,f324(f154(f844(x90411,x90412)),f324(f324(f166(x90411,x90412),x90414),f324(f324(f125(x90412),x90415),x90416))))),f169(x90411,x90412,x90413,f165(x90411,x90412,f324(f154(f844(x90411,x90412)),f324(f324(f166(x90411,x90412),x90414),x90415)))))
% 18.77/18.50 [9128]P1(f324(f324(x91281,x91282),x91283))+~P1(f324(f324(f324(f324(f104(f845(x91284,f845(x91285,a832))),x91286),x91281),x91282),x91283))
% 18.77/18.50 [9129]P1(f324(f324(x91291,x91292),x91293))+~P1(f324(f324(f324(f324(f104(f845(x91294,f845(x91295,a832))),x91291),x91296),x91292),x91293))
% 18.77/18.50 [9130]P1(f324(f324(x91301,x91302),x91303))+~P1(f324(f324(f324(f324(f104(f845(x91304,f845(x91305,a832))),x91306),x91301),x91302),x91303))
% 18.77/18.50 [9131]P1(f324(f324(x91311,x91312),x91313))+~P1(f324(f324(f324(f324(f104(f845(x91314,f845(x91315,a832))),x91311),x91316),x91312),x91313))
% 18.77/18.50 [9549]~P68(x95492)+E(f324(f324(f11(x95491,x95492),f324(f324(f9(x95491,f845(x95493,a832),x95492),f324(f324(f10(f845(x95493,x95492),f845(f845(x95493,a832),x95492),x95491),f11(x95493,x95492)),x95494)),x95495)),x95496),f324(f324(f11(f844(x95491,x95493),x95492),f324(f252(x95491,x95493,x95492),x95494)),f324(f324(f249(x95491,x95493),x95496),f324(f18(f845(x95493,a832),x95491),x95495))))
% 18.77/18.50 [9550]~P67(x95502)+E(f324(f324(f8(x95501,x95502),f324(f324(f9(x95501,f845(x95503,a832),x95502),f324(f324(f10(f845(x95503,x95502),f845(f845(x95503,a832),x95502),x95501),f8(x95503,x95502)),x95504)),x95505)),x95506),f324(f324(f8(f844(x95501,x95503),x95502),f324(f252(x95501,x95503,x95502),x95504)),f324(f324(f249(x95501,x95503),x95506),f324(f18(f845(x95503,a832),x95501),x95505))))
% 18.77/18.50 [9673]~P67(x96732)+E(f324(f324(f8(x96731,x96732),f324(f324(f9(x96731,f845(x96733,a832),x96732),f324(f324(f10(f845(x96733,x96732),f845(f845(x96733,a832),x96732),x96731),f8(x96733,x96732)),f324(f9(x96733,x96731,x96732),x96734))),x96735)),x96736),f324(f324(f8(x96733,x96732),f324(f324(f9(x96733,f845(x96731,a832),x96732),f324(f324(f10(f845(x96731,x96732),f845(f845(x96731,a832),x96732),x96733),f8(x96731,x96732)),x96734)),x96736)),x96735))
% 18.77/18.50 [9132]~E(f324(f180(f839(x91321)),x91324),f324(f180(f839(x91322)),x91326))+E(f169(x91321,x91322,x91323,f165(x91321,x91322,f324(f154(f844(x91321,x91322)),f324(f324(f166(x91321,x91322),f324(f324(f125(x91321),x91324),x91325)),x91326)))),f169(x91321,x91322,x91323,f165(x91321,x91322,f324(f154(f844(x91321,x91322)),f324(f324(f166(x91321,x91322),x91324),x91326)))))
% 18.77/18.50 [9397]~P1(f324(f324(f326(x93971),x93975),x93974))+E(f324(f324(f324(f74(x93971,f842(x93972)),f171(x93971,x93972,x93973,f324(f324(f3(f845(x93971,a832)),x93974),f324(f324(f303(x93971),x93975),f179(f845(x93971,a832)))))),x93975),x93976),f171(x93971,x93972,f324(f324(f324(f74(x93971,f842(x93972)),x93973),x93975),x93976),x93974))
% 18.77/18.50 [9451]~P1(f324(f324(f326(x94511),x94515),x94514))+E(f324(f324(f324(f74(x94511,f842(x94512)),f171(x94511,x94512,x94513,f324(f324(f3(f845(x94511,a832)),x94514),f324(f324(f303(x94511),x94515),f179(f845(x94511,a832)))))),x94515),x94516),f324(f324(f324(f74(x94511,f842(x94512)),f171(x94511,x94512,x94513,x94514)),x94515),x94516))
% 18.77/18.50 [9611]E(f169(x96111,x96112,x96113,f165(x96111,x96112,f324(f154(f844(x96111,x96112)),f324(f324(f166(x96111,x96112),f324(f324(f125(x96111),x96114),f324(f324(f139(x96111),x96115),f115(x96111)))),x96116)))),f324(f324(f324(f74(x96111,f842(x96112)),f169(x96111,x96112,x96113,f165(x96111,x96112,f324(f154(f844(x96111,x96112)),f324(f324(f166(x96111,x96112),x96114),x96116))))),x96115),f324(f226(x96112),f324(f324(f149(x96112),x96116),f324(f180(f839(x96111)),x96114)))))+~P1(f324(f324(f232(a838),f324(f180(f839(x96111)),x96114)),f324(f180(f839(x96112)),x96116)))
% 18.77/18.50 [9970]~P1(f324(f324(f326(f844(x99701,x99702)),f324(f324(f247(x99701,x99702),x99705),x99706)),f324(f324(f103(f845(f844(x99701,x99702),a832)),x99703),x99704)))+P1(f324(f324(f324(f324(f103(f845(x99701,f845(x99702,a832))),f324(f324(f9(x99701,f845(f844(x99701,x99702),a832),f845(x99702,a832)),f324(f324(f10(f845(x99702,f845(f845(f844(x99701,x99702),a832),a832)),f845(f845(f844(x99701,x99702),a832),f845(x99702,a832)),x99701),f9(x99702,f845(f844(x99701,x99702),a832),a832)),f324(f324(f10(f845(x99702,f844(x99701,x99702)),f845(x99702,f845(f845(f844(x99701,x99702),a832),a832)),x99701),f324(f10(f844(x99701,x99702),f845(f845(f844(x99701,x99702),a832),a832),x99702),f326(f844(x99701,x99702)))),f247(x99701,x99702)))),x99703)),f324(f324(f9(x99701,f845(f844(x99701,x99702),a832),f845(x99702,a832)),f324(f324(f10(f845(x99702,f845(f845(f844(x99701,x99702),a832),a832)),f845(f845(f844(x99701,x99702),a832),f845(x99702,a832)),x99701),f9(x99702,f845(f844(x99701,x99702),a832),a832)),f324(f324(f10(f845(x99702,f844(x99701,x99702)),f845(x99702,f845(f845(f844(x99701,x99702),a832),a832)),x99701),f324(f10(f844(x99701,x99702),f845(f845(f844(x99701,x99702),a832),a832),x99702),f326(f844(x99701,x99702)))),f247(x99701,x99702)))),x99704)),x99705),x99706))
% 18.77/18.50 [9971]~P1(f324(f324(f326(f844(x99711,x99712)),f324(f324(f247(x99711,x99712),x99715),x99716)),f324(f324(f104(f845(f844(x99711,x99712),a832)),x99713),x99714)))+P1(f324(f324(f324(f324(f104(f845(x99711,f845(x99712,a832))),f324(f324(f9(x99711,f845(f844(x99711,x99712),a832),f845(x99712,a832)),f324(f324(f10(f845(x99712,f845(f845(f844(x99711,x99712),a832),a832)),f845(f845(f844(x99711,x99712),a832),f845(x99712,a832)),x99711),f9(x99712,f845(f844(x99711,x99712),a832),a832)),f324(f324(f10(f845(x99712,f844(x99711,x99712)),f845(x99712,f845(f845(f844(x99711,x99712),a832),a832)),x99711),f324(f10(f844(x99711,x99712),f845(f845(f844(x99711,x99712),a832),a832),x99712),f326(f844(x99711,x99712)))),f247(x99711,x99712)))),x99713)),f324(f324(f9(x99711,f845(f844(x99711,x99712),a832),f845(x99712,a832)),f324(f324(f10(f845(x99712,f845(f845(f844(x99711,x99712),a832),a832)),f845(f845(f844(x99711,x99712),a832),f845(x99712,a832)),x99711),f9(x99712,f845(f844(x99711,x99712),a832),a832)),f324(f324(f10(f845(x99712,f844(x99711,x99712)),f845(x99712,f845(f845(f844(x99711,x99712),a832),a832)),x99711),f324(f10(f844(x99711,x99712),f845(f845(f844(x99711,x99712),a832),a832),x99712),f326(f844(x99711,x99712)))),f247(x99711,x99712)))),x99714)),x99715),x99716))
% 18.77/18.50 [9976]P1(f324(f324(f326(f844(x99761,x99762)),f324(f324(f247(x99761,x99762),x99763),x99764)),f324(f324(f103(f845(f844(x99761,x99762),a832)),x99765),x99766)))+~P1(f324(f324(f324(f324(f103(f845(x99761,f845(x99762,a832))),f324(f324(f9(x99761,f845(f844(x99761,x99762),a832),f845(x99762,a832)),f324(f324(f10(f845(x99762,f845(f845(f844(x99761,x99762),a832),a832)),f845(f845(f844(x99761,x99762),a832),f845(x99762,a832)),x99761),f9(x99762,f845(f844(x99761,x99762),a832),a832)),f324(f324(f10(f845(x99762,f844(x99761,x99762)),f845(x99762,f845(f845(f844(x99761,x99762),a832),a832)),x99761),f324(f10(f844(x99761,x99762),f845(f845(f844(x99761,x99762),a832),a832),x99762),f326(f844(x99761,x99762)))),f247(x99761,x99762)))),x99765)),f324(f324(f9(x99761,f845(f844(x99761,x99762),a832),f845(x99762,a832)),f324(f324(f10(f845(x99762,f845(f845(f844(x99761,x99762),a832),a832)),f845(f845(f844(x99761,x99762),a832),f845(x99762,a832)),x99761),f9(x99762,f845(f844(x99761,x99762),a832),a832)),f324(f324(f10(f845(x99762,f844(x99761,x99762)),f845(x99762,f845(f845(f844(x99761,x99762),a832),a832)),x99761),f324(f10(f844(x99761,x99762),f845(f845(f844(x99761,x99762),a832),a832),x99762),f326(f844(x99761,x99762)))),f247(x99761,x99762)))),x99766)),x99763),x99764))
% 18.77/18.50 [9977]P1(f324(f324(f326(f844(x99771,x99772)),f324(f324(f247(x99771,x99772),x99773),x99774)),f324(f324(f104(f845(f844(x99771,x99772),a832)),x99775),x99776)))+~P1(f324(f324(f324(f324(f104(f845(x99771,f845(x99772,a832))),f324(f324(f9(x99771,f845(f844(x99771,x99772),a832),f845(x99772,a832)),f324(f324(f10(f845(x99772,f845(f845(f844(x99771,x99772),a832),a832)),f845(f845(f844(x99771,x99772),a832),f845(x99772,a832)),x99771),f9(x99772,f845(f844(x99771,x99772),a832),a832)),f324(f324(f10(f845(x99772,f844(x99771,x99772)),f845(x99772,f845(f845(f844(x99771,x99772),a832),a832)),x99771),f324(f10(f844(x99771,x99772),f845(f845(f844(x99771,x99772),a832),a832),x99772),f326(f844(x99771,x99772)))),f247(x99771,x99772)))),x99775)),f324(f324(f9(x99771,f845(f844(x99771,x99772),a832),f845(x99772,a832)),f324(f324(f10(f845(x99772,f845(f845(f844(x99771,x99772),a832),a832)),f845(f845(f844(x99771,x99772),a832),f845(x99772,a832)),x99771),f9(x99772,f845(f844(x99771,x99772),a832),a832)),f324(f324(f10(f845(x99772,f844(x99771,x99772)),f845(x99772,f845(f845(f844(x99771,x99772),a832),a832)),x99771),f324(f10(f844(x99771,x99772),f845(f845(f844(x99771,x99772),a832),a832),x99772),f326(f844(x99771,x99772)))),f247(x99771,x99772)))),x99776)),x99773),x99774))
% 18.77/18.50 [9965]~P1(f324(f324(f326(f844(x99652,x99653)),f324(f324(f247(x99652,x99653),x99655),x99656)),f324(f324(f45(x99651,f845(f844(x99652,x99653),a832)),f238(f845(x99651,a832))),x99654)))+P1(f324(f324(f324(f324(f45(x99651,f845(x99652,f845(x99653,a832))),f238(f845(x99651,a832))),f324(f324(f10(f845(f844(x99652,x99653),a832),f845(x99652,f845(x99653,a832)),x99651),f324(f9(x99652,f845(f844(x99652,x99653),a832),f845(x99653,a832)),f324(f324(f10(f845(x99653,f845(f845(f844(x99652,x99653),a832),a832)),f845(f845(f844(x99652,x99653),a832),f845(x99653,a832)),x99652),f9(x99653,f845(f844(x99652,x99653),a832),a832)),f324(f324(f10(f845(x99653,f844(x99652,x99653)),f845(x99653,f845(f845(f844(x99652,x99653),a832),a832)),x99652),f324(f10(f844(x99652,x99653),f845(f845(f844(x99652,x99653),a832),a832),x99653),f326(f844(x99652,x99653)))),f247(x99652,x99653))))),x99654)),x99655),x99656))
% 18.77/18.50 [9966]~P1(f324(f324(f326(f844(x99662,x99663)),f324(f324(f247(x99662,x99663),x99665),x99666)),f324(f324(f46(x99661,f845(f844(x99662,x99663),a832)),f238(f845(x99661,a832))),x99664)))+P1(f324(f324(f324(f324(f46(x99661,f845(x99662,f845(x99663,a832))),f238(f845(x99661,a832))),f324(f324(f10(f845(f844(x99662,x99663),a832),f845(x99662,f845(x99663,a832)),x99661),f324(f9(x99662,f845(f844(x99662,x99663),a832),f845(x99663,a832)),f324(f324(f10(f845(x99663,f845(f845(f844(x99662,x99663),a832),a832)),f845(f845(f844(x99662,x99663),a832),f845(x99663,a832)),x99662),f9(x99663,f845(f844(x99662,x99663),a832),a832)),f324(f324(f10(f845(x99663,f844(x99662,x99663)),f845(x99663,f845(f845(f844(x99662,x99663),a832),a832)),x99662),f324(f10(f844(x99662,x99663),f845(f845(f844(x99662,x99663),a832),a832),x99663),f326(f844(x99662,x99663)))),f247(x99662,x99663))))),x99664)),x99665),x99666))
% 18.77/18.50 [9974]P1(f324(f324(f326(f844(x99741,x99742)),f324(f324(f247(x99741,x99742),x99743),x99744)),f324(f324(f45(x99745,f845(f844(x99741,x99742),a832)),f238(f845(x99745,a832))),x99746)))+~P1(f324(f324(f324(f324(f45(x99745,f845(x99741,f845(x99742,a832))),f238(f845(x99745,a832))),f324(f324(f10(f845(f844(x99741,x99742),a832),f845(x99741,f845(x99742,a832)),x99745),f324(f9(x99741,f845(f844(x99741,x99742),a832),f845(x99742,a832)),f324(f324(f10(f845(x99742,f845(f845(f844(x99741,x99742),a832),a832)),f845(f845(f844(x99741,x99742),a832),f845(x99742,a832)),x99741),f9(x99742,f845(f844(x99741,x99742),a832),a832)),f324(f324(f10(f845(x99742,f844(x99741,x99742)),f845(x99742,f845(f845(f844(x99741,x99742),a832),a832)),x99741),f324(f10(f844(x99741,x99742),f845(f845(f844(x99741,x99742),a832),a832),x99742),f326(f844(x99741,x99742)))),f247(x99741,x99742))))),x99746)),x99743),x99744))
% 18.77/18.50 [9975]P1(f324(f324(f326(f844(x99751,x99752)),f324(f324(f247(x99751,x99752),x99753),x99754)),f324(f324(f46(x99755,f845(f844(x99751,x99752),a832)),f238(f845(x99755,a832))),x99756)))+~P1(f324(f324(f324(f324(f46(x99755,f845(x99751,f845(x99752,a832))),f238(f845(x99755,a832))),f324(f324(f10(f845(f844(x99751,x99752),a832),f845(x99751,f845(x99752,a832)),x99755),f324(f9(x99751,f845(f844(x99751,x99752),a832),f845(x99752,a832)),f324(f324(f10(f845(x99752,f845(f845(f844(x99751,x99752),a832),a832)),f845(f845(f844(x99751,x99752),a832),f845(x99752,a832)),x99751),f9(x99752,f845(f844(x99751,x99752),a832),a832)),f324(f324(f10(f845(x99752,f844(x99751,x99752)),f845(x99752,f845(f845(f844(x99751,x99752),a832),a832)),x99751),f324(f10(f844(x99751,x99752),f845(f845(f844(x99751,x99752),a832),a832),x99752),f326(f844(x99751,x99752)))),f247(x99751,x99752))))),x99756)),x99753),x99754))
% 18.77/18.50 [7297]E(f324(x72971,f324(x72972,x72973)),f324(x72974,x72973))+~E(f324(f75(x72975,x72976,x72977,x72971),x72972),x72974)
% 18.77/18.50 [9431]~P26(x94313,x94314,x94311,x94315,x94316,x94317)+E(f324(f324(x94311,x94312),x94312),x94312)
% 18.77/18.50 [9788]~E(f324(f228(f842(x97887),x97881,f182(x97887),x97885),f324(x97884,x97883)),f324(f226(x97887),x97882))+E(f324(f226(x97881),f699(x97882,x97883,x97884,x97885,x97886,x97887,x97881)),f324(x97884,x97883))
% 18.77/18.50 [9789]~E(f324(f228(f842(x97896),x97897,f182(x97896),x97891),f324(x97894,x97893)),f324(f226(x97896),x97892))+E(f324(x97891,f699(x97892,x97893,x97894,x97891,x97895,x97896,x97897)),f324(f226(x97896),x97892))
% 18.77/18.50 [5804]~E(f324(f324(f141(x58041,x58045),x58046),x58042),f324(f324(f141(x58043,x58045),x58047),x58044))+E(f324(f180(f839(x58041)),x58042),f324(f180(f839(x58043)),x58044))
% 18.77/18.50 [7376]E(x73761,x73762)+~E(f324(f324(f324(f74(x73763,f842(x73764)),x73765),x73766),f324(f226(x73764),x73761)),f324(f324(f324(f74(x73763,f842(x73764)),x73767),x73766),f324(f226(x73764),x73762)))
% 18.77/18.50 [8348]E(f324(x83481,f324(x83482,x83483)),f324(x83484,x83483))+~E(f324(f75(x83485,x83486,x83487,x83481),x83482),f324(f75(x83486,x83486,x83487,f37(x83486)),x83484))
% 18.77/18.50 [9581]P1(f324(f324(x95811,x95812),f351(x95813,x95812,x95814,x95811)))+~P1(f324(f324(f248(x95815,x95816,x95817,x95811,x95814),x95812),x95813))
% 18.77/18.50 [9602]P1(f324(f324(x96021,f351(x96022,x96023,x96021,x96024)),x96022))+~P1(f324(f324(f248(x96025,x96026,x96027,x96024,x96021),x96023),x96022))
% 18.77/18.50 [5851]E(x58511,x58512)+~E(f324(f324(f324(f93(x58513),x58514),x58515),x58511),f324(f324(f324(f93(x58513),x58516),x58517),x58512))
% 18.77/18.50 [5852]E(x58521,x58522)+~E(f324(f324(f324(f93(x58523),x58524),x58521),x58525),f324(f324(f324(f93(x58523),x58526),x58522),x58527))
% 18.77/18.50 [5853]E(x58531,x58532)+~E(f324(f324(f324(f93(x58533),x58531),x58534),x58535),f324(f324(f324(f93(x58533),x58532),x58536),x58537))
% 18.77/18.50 [8764]~P24(x87646,x87641,x87643,x87647)+E(f324(f75(x87641,x87641,x87642,f324(x87643,x87644)),f324(f75(x87641,x87641,x87642,f324(x87643,x87644)),x87645)),f324(f75(x87641,x87641,x87642,f324(x87643,x87644)),x87645))
% 18.77/18.50 [8763]~P1(f324(f324(f326(x87631),x87632),f324(f324(x87635,x87636),x87637)))+P1(f324(f324(f326(x87631),x87632),f324(f324(f252(x87633,x87634,f845(x87631,a832)),x87635),f324(f324(f247(x87633,x87634),x87636),x87637))))
% 18.77/18.50 [9022]P1(f324(f324(f324(x90221,x90222),x90223),x90224))+~P1(f324(f324(f324(f252(x90225,x90226,f845(x90227,a832)),x90221),f324(f324(f247(x90225,x90226),x90222),x90223)),x90224))
% 18.77/18.50 [9144]P1(f324(f324(f326(x91441),f324(f324(x91442,x91443),x91444)),f324(f304(f844(x91445,x91446),x91441,f324(f252(x91445,x91446,x91441),x91442)),x91447)))+~P1(f324(f324(f326(f844(x91445,x91446)),f324(f324(f247(x91445,x91446),x91443),x91444)),x91447))
% 18.77/18.50 [9473]P1(f324(f324(f326(f844(f839(x94731),f839(x94731))),f324(f324(f247(f839(x94731),f839(x94731)),f324(f324(f125(x94731),x94732),f324(f324(f139(x94731),x94733),x94734))),f324(f324(f125(x94731),x94732),f324(f324(f139(x94731),x94735),x94736)))),f136(x94731,x94737)))+~P1(f324(f324(f326(f844(x94731,x94731)),f324(f324(f247(x94731,x94731),x94733),x94735)),x94737))
% 18.77/18.50 [9538]P1(f324(f324(f326(x95381),x95384),f324(f157(x95381),x95386)))+E(f169(x95381,x95382,f324(f324(f324(f74(x95381,f842(x95382)),x95383),x95384),f324(f226(x95382),x95385)),f165(x95381,x95382,f324(f154(f844(x95381,x95382)),f324(f324(f166(x95381,x95382),x95386),x95387)))),f324(f324(f324(f74(x95381,f842(x95382)),f169(x95381,x95382,x95383,f165(x95381,x95382,f324(f154(f844(x95381,x95382)),f324(f324(f166(x95381,x95382),x95386),x95387))))),x95384),f324(f226(x95382),x95385)))
% 18.77/18.50 [9017]E(x90171,x90172)+E(f324(f324(f324(f74(x90173,x90174),f324(f324(f324(f74(x90173,x90174),x90175),x90171),x90176)),x90172),x90177),f324(f324(f324(f74(x90173,x90174),f324(f324(f324(f74(x90173,x90174),x90175),x90172),x90177)),x90171),x90176))
% 18.77/18.50 [9271]E(f169(x92711,x92712,f324(f324(f324(f74(x92711,f842(x92712)),x92713),x92714),f324(f226(x92712),x92715)),f165(x92711,x92712,f324(f154(f844(x92711,x92712)),f324(f324(f166(x92711,x92712),x92716),x92717)))),f169(x92711,x92712,x92713,f165(x92711,x92712,f324(f154(f844(x92711,x92712)),f324(f324(f166(x92711,x92712),x92716),x92717)))))+~P1(f324(f324(f326(x92711),x92714),f324(f157(x92711),f324(f324(f158(x92711),f324(f180(f839(x92712)),x92717)),x92716))))
% 18.77/18.50 [9557]E(f169(x95571,x95572,f324(f324(f324(f74(x95571,f842(x95572)),x95573),x95574),f324(f226(x95572),x95575)),f165(x95571,x95572,f324(f154(f844(x95571,x95572)),f324(f324(f166(x95571,x95572),x95576),x95577)))),f324(f324(f324(f74(x95571,f842(x95572)),f169(x95571,x95572,x95573,f165(x95571,x95572,f324(f154(f844(x95571,x95572)),f324(f324(f166(x95571,x95572),x95576),x95577))))),x95574),f324(f226(x95572),x95575)))+P1(f324(f324(f326(x95571),x95574),f324(f157(x95571),f324(f324(f158(x95571),f324(f180(f839(x95572)),x95577)),x95576))))
% 18.77/18.50 [9903]P1(f324(f324(f326(x99031),f669(x99032,x99033,x99034,x99035,x99036,x99037,x99031)),x99035))+P1(f324(f324(f324(f324(f46(x99031,f845(x99037,f845(x99036,a832))),x99035),x99034),x99033),x99032))
% 18.77/18.50 [9904]P1(f324(f324(f326(x99041),f547(x99042,x99043,x99044,x99045,x99046,x99047,x99041)),x99045))+~P1(f324(f324(f324(f324(f45(x99041,f845(x99047,f845(x99046,a832))),x99045),x99044),x99043),x99042))
% 18.77/18.50 [9930]P1(f324(f324(f324(x99301,f547(x99302,x99303,x99301,x99304,x99305,x99306,x99307)),x99303),x99302))+~P1(f324(f324(f324(f324(f45(x99307,f845(x99306,f845(x99305,a832))),x99304),x99301),x99303),x99302))
% 18.77/18.50 [9947]~P1(f324(f324(f324(x99475,f669(x99477,x99476,x99475,x99474,x99473,x99472,x99471)),x99476),x99477))+P1(f324(f324(f324(f324(f46(x99471,f845(x99472,f845(x99473,a832))),x99474),x99475),x99476),x99477))
% 18.77/18.50 [9964]~P1(f324(f324(f326(f844(x99641,x99643)),f324(f324(f247(x99641,x99643),x99646),x99647)),f324(f324(f282(x99641,x99642,x99643),x99644),x99645)))+P1(f324(f324(f248(x99641,x99642,x99643,f324(f324(f9(x99641,f845(f844(x99641,x99642),a832),f845(x99642,a832)),f324(f324(f10(f845(x99642,f845(f845(f844(x99641,x99642),a832),a832)),f845(f845(f844(x99641,x99642),a832),f845(x99642,a832)),x99641),f9(x99642,f845(f844(x99641,x99642),a832),a832)),f324(f324(f10(f845(x99642,f844(x99641,x99642)),f845(x99642,f845(f845(f844(x99641,x99642),a832),a832)),x99641),f324(f10(f844(x99641,x99642),f845(f845(f844(x99641,x99642),a832),a832),x99642),f326(f844(x99641,x99642)))),f247(x99641,x99642)))),x99644),f324(f324(f9(x99642,f845(f844(x99642,x99643),a832),f845(x99643,a832)),f324(f324(f10(f845(x99643,f845(f845(f844(x99642,x99643),a832),a832)),f845(f845(f844(x99642,x99643),a832),f845(x99643,a832)),x99642),f9(x99643,f845(f844(x99642,x99643),a832),a832)),f324(f324(f10(f845(x99643,f844(x99642,x99643)),f845(x99643,f845(f845(f844(x99642,x99643),a832),a832)),x99642),f324(f10(f844(x99642,x99643),f845(f845(f844(x99642,x99643),a832),a832),x99643),f326(f844(x99642,x99643)))),f247(x99642,x99643)))),x99645)),x99646),x99647))
% 18.77/18.50 [9973]P1(f324(f324(f326(f844(x99731,x99732)),f324(f324(f247(x99731,x99732),x99733),x99734)),f324(f324(f282(x99731,x99735,x99732),x99736),x99737)))+~P1(f324(f324(f248(x99731,x99735,x99732,f324(f324(f9(x99731,f845(f844(x99731,x99735),a832),f845(x99735,a832)),f324(f324(f10(f845(x99735,f845(f845(f844(x99731,x99735),a832),a832)),f845(f845(f844(x99731,x99735),a832),f845(x99735,a832)),x99731),f9(x99735,f845(f844(x99731,x99735),a832),a832)),f324(f324(f10(f845(x99735,f844(x99731,x99735)),f845(x99735,f845(f845(f844(x99731,x99735),a832),a832)),x99731),f324(f10(f844(x99731,x99735),f845(f845(f844(x99731,x99735),a832),a832),x99735),f326(f844(x99731,x99735)))),f247(x99731,x99735)))),x99736),f324(f324(f9(x99735,f845(f844(x99735,x99732),a832),f845(x99732,a832)),f324(f324(f10(f845(x99732,f845(f845(f844(x99735,x99732),a832),a832)),f845(f845(f844(x99735,x99732),a832),f845(x99732,a832)),x99735),f9(x99732,f845(f844(x99735,x99732),a832),a832)),f324(f324(f10(f845(x99732,f844(x99735,x99732)),f845(x99732,f845(f845(f844(x99735,x99732),a832),a832)),x99735),f324(f10(f844(x99735,x99732),f845(f845(f844(x99735,x99732),a832),a832),x99732),f326(f844(x99735,x99732)))),f247(x99735,x99732)))),x99737)),x99733),x99734))
% 18.77/18.50 [9913]~P135(x99132)+E(f324(f324(f8(x99131,x99132),f324(f324(f9(x99131,f845(x99133,a832),x99132),f324(f324(f10(f845(x99133,x99132),f845(f845(x99133,a832),x99132),x99131),f8(x99133,x99132)),f324(f324(f9(x99131,f845(x99133,x99132),f845(x99133,x99132)),f324(f324(f10(f845(x99132,x99132),f845(f845(x99133,x99132),f845(x99133,x99132)),x99131),f10(x99132,x99132,x99133)),f324(f324(f10(x99132,f845(x99132,x99132),x99131),f83(x99132)),x99134))),x99135))),x99136)),x99137),f324(f324(f83(x99132),f324(f324(f8(x99131,x99132),x99134),x99137)),f324(f324(f8(x99133,x99132),x99135),x99136)))
% 18.77/18.50 [9054]~P23(x90547,x90541,x90543,x90548)+E(f324(f75(x90541,x90541,x90542,f324(x90543,x90544)),f324(f75(x90541,x90541,x90542,f324(x90543,x90545)),x90546)),f324(f75(x90541,x90541,x90542,f324(x90543,x90545)),f324(f75(x90541,x90541,x90542,f324(x90543,x90544)),x90546)))
% 18.77/18.50 [9968]E(f324(f324(f247(x99681,x99682),f324(x99683,f593(x99684,x99685,x99683,x99686,x99687,x99688,x99682,x99681))),f324(x99685,f594(x99684,x99685,x99683,x99686,x99687,x99688,x99682,x99681))),x99688)+~P1(f324(f324(f326(f844(x99681,x99682)),x99688),f324(f304(f844(x99687,x99686),f844(x99681,x99682),f253(x99687,x99681,x99686,x99682,x99683,x99685)),x99684)))
% 18.77/18.50 [9981]~P1(f324(f324(f326(f844(x99818,x99817)),x99816),f324(f304(f844(x99811,x99812),f844(x99818,x99817),f253(x99811,x99818,x99812,x99817,x99815,x99814)),x99813)))+P1(f324(f324(f326(f844(x99811,x99812)),f324(f324(f247(x99811,x99812),f593(x99813,x99814,x99815,x99812,x99811,x99816,x99817,x99818)),f594(x99813,x99814,x99815,x99812,x99811,x99816,x99817,x99818))),x99813))
% 18.77/18.50 [9463]P1(f324(f324(f326(f844(f844(x94631,x94632),f844(x94631,x94632))),f324(f324(f247(f844(x94631,x94632),f844(x94631,x94632)),f324(f324(f247(x94631,x94632),x94633),x94634)),f324(f324(f247(x94631,x94632),x94635),x94636))),f318(x94631,x94632,x94637,x94638)))+~P1(f324(f324(f326(f844(x94631,x94631)),f324(f324(f247(x94631,x94631),x94633),x94635)),x94637))
% 18.77/18.50 [8353]E(f324(x83531,f324(x83532,x83533)),f324(x83534,f324(x83535,x83533)))+~E(f324(f75(x83536,x83537,x83538,x83531),x83532),f324(f75(x83539,x83537,x83538,x83534),x83535))
% 18.77/18.50 [8354]E(f324(x83541,f324(x83542,x83543)),f324(x83544,f324(x83545,x83543)))+~E(f324(f75(x83546,x83547,x83548,x83541),x83542),f324(f75(x83549,x83547,x83548,x83544),x83545))
% 18.77/18.50 [9839]P1(f324(f324(f326(f844(x98391,x98392)),f324(f324(f247(x98391,x98392),f324(x98393,x98394)),f324(x98395,x98396))),f324(f304(f844(x98397,x98398),f844(x98391,x98392),f253(x98397,x98391,x98398,x98392,x98393,x98395)),x98399)))+~P1(f324(f324(f326(f844(x98397,x98398)),f324(f324(f247(x98397,x98398),x98394),x98396)),x98399))
% 18.77/18.50 [8612]~E(f324(x86124,f324(x86125,x86126)),f324(x86129,f324(x861210,x861211)))+E(f324(f324(f75(x86121,x86122,x86123,x86124),x86125),x86126),f324(f324(f75(x86127,x86122,x86128,x86129),x861210),x861211))
% 18.77/18.50 [9117]~P23(x91178,x91179,x911710,x911711)+E(f324(f75(x91171,x91172,x91173,x91174),f324(f75(x91175,x91171,x91173,x91176),x91177)),f324(f75(x91175,x91172,x91173,f324(f75(x91171,x91172,x91175,x91174),x91176)),x91177))
% 18.77/18.50 [4419]~P86(x44191)+~P93(x44191)+E(f178(x44191),f103(x44191))
% 18.77/18.50 [4420]~P86(x44201)+~P99(x44201)+E(f235(x44201),f104(x44201))
% 18.77/18.50 [4658]~P103(x46581)+~P89(x46581)+E(f324(f77(x46581),f324(f106(x46581),a99)),f80(x46581))
% 18.77/18.50 [4931]E(x49311,f2(a1))+E(f84(a1,x49311),f324(f81(a1),f80(a1)))+P1(f324(f324(f232(a1),f2(a1)),x49311))
% 18.77/18.50 [5133]E(x51331,f2(a1))+E(f84(a1,x51331),f80(a1))+~P1(f324(f324(f232(a1),f2(a1)),x51331))
% 18.77/18.50 [6456]~P38(x64561)+~P1(f324(f64(a1),x64561))+P1(f324(f64(a838),f324(f304(a1,a838,a107),x64561)))
% 18.77/18.50 [6838]E(f53(f80(a1),f324(f106(a1),x68381)),f324(f324(f247(a1,a1),f2(a1)),f80(a1)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x68381)))+~P1(f324(f324(f232(a1),f80(a1)),f324(f106(a1),x68381)))
% 18.77/18.50 [7184]~P38(x71841)+P1(f324(f64(a1),x71841))+~P1(f324(f64(a838),f324(f304(a1,a838,a107),x71841)))
% 18.77/18.50 [8050]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f82(a1),f80(a1)),f324(f106(a1),x80501))),f56(f80(a1),f324(f106(a1),x80501)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x80501)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f80(a1)),f324(f106(a1),x80501))))
% 18.77/18.50 [8457]~P13(a500)+~P1(f324(f324(f326(f844(a834,a833)),x84571),f324(f157(f844(a834,a833)),a29)))+P1(f324(f324(f252(a834,a833,a832),f324(f18(f845(a833,a832),a834),a26)),x84571))
% 18.77/18.50 [9727]E(f324(f49(f324(f106(a1),x97271)),f53(f80(a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f106(a1),x97271)))),f53(f80(a1),f324(f106(a1),x97271)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x97271)))+P1(f324(f324(f232(a1),f80(a1)),f324(f106(a1),x97271)))
% 18.77/18.50 [9733]E(f324(f49(f324(f106(a1),x97331)),f56(f80(a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f106(a1),x97331)))),f56(f80(a1),f324(f106(a1),x97331)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x97331)))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f80(a1)),f324(f106(a1),x97331))))
% 18.77/18.50 [9430]E(x94301,f179(f845(f844(a838,a838),a832)))+~P1(f324(f64(f844(a838,a838)),x94301))+P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),f179(f845(f844(a838,a838),a832))),x94301)),a40))
% 18.77/18.50 [9582]E(x95821,f2(a838))+E(x95821,f324(a114,f2(a838)))+~P1(f324(f324(f232(a838),x95821),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.77/18.50 [9865]E(x98651,f2(a101))+E(f324(f324(f82(a1),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(a23,f324(f324(f42(a101),x98651),f324(f106(a101),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))),f80(a1)),f324(a23,x98651))+E(f51(a101,x98651,f324(f106(a101),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f2(a101))
% 18.77/18.50 [9713]E(x97131,f2(a101))+~E(f51(a101,x97131,f324(f106(a101),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f2(a101))+E(f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(a23,f324(f324(f42(a101),x97131),f324(f106(a101),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f324(a23,x97131))
% 18.77/18.50 [4494]~P55(x44941,x44942)+P42(x44941,x44942)+~P43(a832)
% 18.77/18.50 [4432]~P2(x44321)+P33(x44321,x44322)+~E(x44322,f2(x44321))
% 18.77/18.50 [4441]~P103(x44411)+~E(x44412,f2(x44411))+E(f84(x44411,x44412),f2(x44411))
% 18.77/18.50 [4442]~P82(x44421)+~E(x44422,f2(x44421))+E(f84(x44421,x44422),f2(x44421))
% 18.77/18.50 [4450]~P2(x44502)+~P33(x44502,x44501)+E(x44501,f2(x44502))
% 18.77/18.50 [4484]~P103(x44842)+~E(f84(x44842,x44841),f2(x44842))+E(x44841,f2(x44842))
% 18.77/18.50 [4501]~P10(x45012)+~P10(x45011)+P10(f187(x45011,x45012))
% 18.77/18.50 [4502]~P58(x45022)+~P58(x45021)+P58(f845(x45021,x45022))
% 18.77/18.50 [4503]~P58(x45032)+~P58(x45031)+P58(f844(x45031,x45032))
% 18.77/18.50 [4504]~P58(x45042)+~P58(x45041)+P58(f848(x45041,x45042))
% 18.77/18.50 [4505]~P138(x45052)+~P138(x45051)+P138(f844(x45051,x45052))
% 18.77/18.50 [4630]~P86(x46301)+~P18(x46301,x46302)+P18(x46301,f140(x46301,x46302))
% 18.77/18.50 [4863]~P10(x48632)+~P10(x48631)+P10(f51(a1,x48631,x48632))
% 18.77/18.50 [4451]~P69(x44511)+~E(x44512,f2(x44511))+E(f324(f81(x44511),x44512),x44512)
% 18.77/18.50 [4452]~P69(x44521)+~E(x44522,f2(x44521))+E(f324(f81(x44521),x44522),x44522)
% 18.77/18.50 [4455]~P88(x44551)+~E(x44552,f2(a1))+E(f324(f105(x44551),x44552),f2(x44551))
% 18.77/18.50 [4456]~P119(x44561)+~E(x44562,f2(a1))+E(f324(f105(x44561),x44562),f2(x44561))
% 18.77/18.50 [4457]~P88(x44571)+~E(x44572,f2(a1))+E(f324(f105(x44571),x44572),f2(x44571))
% 18.77/18.50 [4481]~P63(x44811)+~E(f2(x44811),x44812)+E(f324(f81(x44811),x44812),f2(x44811))
% 18.77/18.50 [4482]~P63(x44821)+~E(x44822,f2(x44821))+E(f324(f81(x44821),x44822),f2(x44821))
% 18.77/18.50 [4483]~P78(x44831)+~E(x44832,f2(x44831))+E(f324(f77(x44831),x44832),f2(x44831))
% 18.77/18.50 [4506]~P69(x45062)+E(x45061,f2(x45062))+~E(f324(f81(x45062),x45061),x45061)
% 18.77/18.50 [4507]~P69(x45072)+E(x45071,f2(x45072))+~E(f324(f81(x45072),x45071),x45071)
% 18.77/18.50 [4515]E(x45151,f324(a107,x45152))+~E(x45151,f2(a838))+~E(x45152,f324(f102(a1),x45151))
% 18.77/18.50 [4516]E(f324(a107,x45161),x45162)+~E(x45162,f2(a838))+~E(x45161,f324(f102(a1),x45162))
% 18.77/18.50 [4519]~P88(x45192)+E(x45191,f2(a1))+~E(f324(f105(x45192),x45191),f2(x45192))
% 18.77/18.50 [4520]~P88(x45202)+E(x45201,f2(a1))+~E(f324(f105(x45202),x45201),f2(x45202))
% 18.77/18.50 [4525]~P63(x45252)+E(x45251,f2(x45252))+~E(f324(f81(x45252),x45251),f2(x45252))
% 18.77/18.50 [4526]~P78(x45262)+E(x45261,f2(x45262))+~E(f324(f77(x45262),x45261),f2(x45262))
% 18.77/18.50 [4527]~P63(x45271)+E(f2(x45271),x45272)+~E(f324(f81(x45271),x45272),f2(x45271))
% 18.77/18.50 [4662]~P13(a500)+~E(f324(a30,x46622),f324(f226(a833),x46621))+P1(f324(a26,x46621))
% 18.77/18.50 [4703]~P86(x47031)+~P18(x47031,x47032)+P18(x47031,f324(f156(x47031),x47032))
% 18.77/18.50 [4729]~P1(x47292)+~P1(x47291)+P1(f324(f324(a322,x47291),x47292))
% 18.77/18.50 [4763]~E(f80(a838),f2(a838))+E(f324(f41(x47631),x47632),f2(a838))+~P1(f324(f64(x47631),x47632))
% 18.77/18.50 [4794]~P108(x47941)+~P135(x47941)+E(f324(f324(f240(x47941),f2(x47941)),f324(a114,x47942)),f2(x47941))
% 18.77/18.50 [4834]~P86(x48341)+P18(x48341,f129(x48341,x48342))+~P1(f324(f64(x48341),x48342))
% 18.77/18.50 [4854]~P86(x48541)+E(f324(f157(x48541),f129(x48541,x48542)),x48542)+~P1(f324(f64(x48541),x48542))
% 18.77/18.50 [4884]P1(x48841)+P1(x48842)+~P1(f324(f324(a323,x48842),x48841))
% 18.77/18.50 [4896]E(x48961,f179(f845(x48962,a832)))+~E(f324(f41(x48962),x48961),f2(a838))+~P1(f324(f64(x48962),x48961))
% 18.77/18.50 [4901]P1(x49011)+~P1(x49012)+~P1(f324(f324(a327,x49012),x49011))
% 18.77/18.50 [4949]~P66(x49491)+E(f324(f77(x49491),x49492),x49492)+P1(f324(f324(f232(x49491),x49492),f2(x49491)))
% 18.77/18.50 [5045]~P1(f324(a26,x50452))+~P1(f324(a26,x50451))+P1(f324(a26,f36(x50451,x50452)))
% 18.77/18.50 [5046]~P1(f324(a26,x50462))+~P1(f324(a26,x50461))+P1(f324(a26,f36(x50461,x50462)))
% 18.77/18.50 [5053]E(x50531,f115(x50532))+P1(f324(f127(x50532),f116(x50532,x50531)))+~P1(f324(f127(x50532),x50531))
% 18.77/18.50 [5058]~P86(x50581)+~P1(f324(f64(x50581),x50582))+P1(f324(f127(x50581),f129(x50581,x50582)))
% 18.77/18.50 [5064]~P119(x50641)+E(f324(f102(x50641),f324(a107,x50642)),f324(f105(x50641),x50642))+P1(f324(f324(f232(a1),x50642),f2(a1)))
% 18.77/18.50 [5090]P11(x50902,x50901)+E(f324(x50901,f539(x50901)),f324(x50901,f553(x50901)))+P1(f324(f324(x50901,f539(x50901)),f553(x50901)))
% 18.77/18.50 [5103]E(f324(f102(a1),f452(x51031,x51032)),x51031)+P1(f324(x51032,f324(a107,x51031)))+~P1(f324(x51032,f2(a838)))
% 18.77/18.50 [5143]~P103(x51431)+~E(f84(x51431,x51432),f324(f81(x51431),f80(x51431)))+P1(f324(f324(f232(x51431),x51432),f2(x51431)))
% 18.77/18.50 [5216]~E(x52162,f2(a1))+E(f209(x52161,x52162),f324(f324(f247(a1,a1),f2(a1)),f80(a1)))+P1(f324(f324(f232(a1),x52162),f2(a1)))
% 18.77/18.50 [5217]~E(x52171,f2(a1))+E(f209(x52171,x52172),f324(f324(f247(a1,a1),f2(a1)),f80(a1)))+P1(f324(f324(f232(a1),x52172),f2(a1)))
% 18.77/18.50 [5240]~P1(f324(x52401,x52402))+~P1(f324(x52401,f823(x52402,x52401)))+P1(f324(x52401,f2(a838)))
% 18.77/18.50 [5269]E(f324(f102(a1),f452(x52691,x52692)),x52691)+P1(f324(x52692,f324(a107,x52691)))+P1(f324(f324(f232(a1),x52691),f2(a1)))
% 18.77/18.50 [5333]~P103(x53331)+E(f84(x53331,x53332),f324(f81(x53331),f80(x53331)))+~P1(f324(f324(f232(x53331),x53332),f2(x53331)))
% 18.77/18.50 [5334]~P103(x53341)+E(f84(x53341,x53342),f324(f81(x53341),f80(x53341)))+~P1(f324(f324(f232(x53341),x53342),f2(x53341)))
% 18.77/18.50 [5335]~P78(x53351)+E(f324(f77(x53351),x53352),f324(f81(x53351),x53352))+~P1(f324(f324(f232(x53351),x53352),f2(x53351)))
% 18.77/18.50 [5336]~P78(x53361)+E(f324(f77(x53361),x53362),f324(f81(x53361),x53362))+~P1(f324(f324(f231(x53361),x53362),f2(x53361)))
% 18.77/18.50 [5337]~P66(x53371)+E(f324(f77(x53371),x53372),f324(f81(x53371),x53372))+~P1(f324(f324(f232(x53371),x53372),f2(x53371)))
% 18.77/18.50 [5369]~P2(x53691)+E(f324(f102(x53691),f393(x53692,x53691)),x53692)+~P1(f324(f324(f326(x53691),x53692),f175(x53691)))
% 18.77/18.50 [5431]~P1(f324(x54311,f452(x54312,x54311)))+P1(f324(x54311,f324(a107,x54312)))+~P1(f324(x54311,f2(a838)))
% 18.77/18.50 [5438]E(x54381,f2(a838))+E(f324(a114,f345(x54382,x54381)),x54381)+~P1(f324(f324(f232(a838),x54381),f324(a114,x54382)))
% 18.77/18.50 [5442]P11(x54421,x54422)+~E(f324(x54422,f539(x54422)),f324(x54422,f553(x54422)))+~P1(f324(f324(x54422,f539(x54422)),f553(x54422)))
% 18.77/18.50 [5462]~P86(x54621)+P18(x54621,x54622)+P1(f324(f324(f231(a838),f749(x54622,x54621)),f750(x54622,x54621)))
% 18.77/18.50 [5463]~P86(x54631)+P18(x54631,x54632)+P1(f324(f324(f231(a838),f756(x54632,x54631)),f766(x54632,x54631)))
% 18.77/18.50 [5549]~P78(x55491)+~E(x55492,f2(x55491))+P1(f324(f324(f231(x55491),f324(f77(x55491),x55492)),f2(x55491)))
% 18.77/18.50 [5637]~P1(f324(x56371,f452(x56372,x56371)))+P1(f324(x56371,f324(a107,x56372)))+P1(f324(f324(f232(a1),x56372),f2(a1)))
% 18.77/18.50 [5662]~P1(f324(x56621,f324(a107,x56622)))+P1(f324(x56621,f2(a838)))+~P1(f324(f324(f232(a1),x56622),f2(a1)))
% 18.77/18.50 [6009]~P103(x60091)+~P1(f324(f324(f232(x60091),x60092),f2(x60091)))+P1(f324(f324(f232(x60091),f84(x60091,x60092)),f2(x60091)))
% 18.77/18.50 [6127]~P103(x61271)+P1(f324(f324(f232(x61271),f324(f105(x61271),x61272)),f2(x61271)))+~P1(f324(f324(f232(a1),x61272),f2(a1)))
% 18.77/18.50 [6128]~P103(x61281)+P1(f324(f324(f231(x61281),f324(f105(x61281),x61282)),f2(x61281)))+~P1(f324(f324(f231(a1),x61282),f2(a1)))
% 18.77/18.50 [6133]~P78(x61332)+E(x61331,f2(x61332))+~P1(f324(f324(f231(x61332),f324(f77(x61332),x61331)),f2(x61332)))
% 18.77/18.50 [6217]~P119(x62171)+~P1(f324(f324(f326(x62171),x62172),f112(x62171)))+P1(f324(f324(f326(x62171),f324(f81(x62171),x62172)),f112(x62171)))
% 18.77/18.50 [6249]~P103(x62491)+~P1(f324(f324(f232(x62491),f84(x62491,x62492)),f2(x62491)))+P1(f324(f324(f232(x62491),x62492),f2(x62491)))
% 18.77/18.50 [6330]~P85(x63301)+P50(a838,x63301,f280(a838),x63302)+P1(f324(f324(f280(a838),f335(x63302,x63301)),f337(x63302,x63301)))
% 18.77/18.50 [6427]~P103(x64272)+~P1(f324(f324(f232(x64272),f324(f105(x64272),x64271)),f2(x64272)))+P1(f324(f324(f232(a1),x64271),f2(a1)))
% 18.77/18.50 [6428]~P103(x64282)+~P1(f324(f324(f231(x64282),f324(f105(x64282),x64281)),f2(x64282)))+P1(f324(f324(f231(a1),x64281),f2(a1)))
% 18.77/18.50 [6955]~P103(x69551)+~P1(f324(f324(f232(x69551),x69552),f2(x69551)))+P1(f324(f324(f232(x69551),f324(f324(f82(x69551),x69552),x69552)),f2(x69551)))
% 18.77/18.50 [6956]~P69(x69561)+~P1(f324(f324(f232(x69561),x69562),f2(x69561)))+P1(f324(f324(f232(x69561),f324(f324(f82(x69561),x69562),x69562)),f2(x69561)))
% 18.77/18.50 [6957]~P69(x69571)+~P1(f324(f324(f231(x69571),x69572),f2(x69571)))+P1(f324(f324(f231(x69571),f324(f324(f82(x69571),x69572),x69572)),f2(x69571)))
% 18.77/18.50 [7554]~P103(x75541)+~P1(f324(f324(f232(x75541),f324(f324(f82(x75541),x75542),x75542)),f2(x75541)))+P1(f324(f324(f232(x75541),x75542),f2(x75541)))
% 18.77/18.50 [7555]~P69(x75551)+~P1(f324(f324(f232(x75551),f324(f324(f82(x75551),x75552),x75552)),f2(x75551)))+P1(f324(f324(f232(x75551),x75552),f2(x75551)))
% 18.77/18.50 [7556]~P69(x75561)+~P1(f324(f324(f231(x75561),f324(f324(f82(x75561),x75562),x75562)),f2(x75561)))+P1(f324(f324(f231(x75561),x75562),f2(x75561)))
% 18.77/18.50 [4562]~E(x45622,f80(a838))+~E(x45621,f80(a838))+E(f324(f324(f83(a838),x45621),x45622),f80(a838))
% 18.77/18.50 [4563]~E(x45632,f80(a838))+~E(x45631,f80(a838))+E(f324(f324(f83(a838),x45631),x45632),f80(a838))
% 18.77/18.50 [4564]~E(x45642,f80(a1))+~E(x45641,f80(a1))+E(f324(f324(f83(a1),x45641),x45642),f80(a1))
% 18.77/18.50 [4565]~E(x45652,f2(a838))+~E(x45651,f2(a838))+E(f324(f324(f82(a838),x45651),x45652),f2(a838))
% 18.77/18.50 [4616]~P7(x46162)+E(x46161,f2(x46162))+E(f324(f324(f42(x46162),x46161),x46161),f80(x46162))
% 18.77/18.50 [4617]~P114(x46172)+E(x46171,f2(x46172))+E(f324(f324(f284(x46172),x46171),x46171),f80(x46172))
% 18.77/18.50 [4618]~P115(x46182)+E(x46181,f2(x46182))+E(f324(f324(f284(x46182),x46181),x46181),f80(x46182))
% 18.77/18.50 [4633]~P69(x46331)+~E(x46332,f2(x46331))+E(f324(f324(f82(x46331),x46332),x46332),f2(x46331))
% 18.77/18.50 [4636]~P133(x46361)+~E(x46362,f80(x46361))+E(f324(f324(f83(x46361),x46362),x46362),f80(x46361))
% 18.77/18.50 [4637]~P69(x46371)+~E(x46372,f2(x46371))+E(f324(f324(f82(x46371),x46372),x46372),f2(x46371))
% 18.77/18.50 [4638]~P115(x46381)+~E(x46382,f2(x46381))+E(f324(f324(f284(x46381),x46382),x46382),f2(x46381))
% 18.77/18.50 [4682]~E(x46822,f2(a838))+~E(x46821,f2(a838))+E(f324(f81(a1),f324(f102(a1),x46821)),f324(f102(a1),x46822))
% 18.77/18.50 [4700]E(x47001,f80(a838))+E(x47002,f2(a838))+~E(f324(f324(f83(a838),x47002),x47001),x47002)
% 18.77/18.50 [4710]E(x47101,f2(a838))+E(x47102,f2(a838))+~E(f324(f324(f83(a838),x47102),x47101),f2(a838))
% 18.77/18.50 [4736]~E(x47362,f2(a838))+~E(x47361,f324(a114,f2(a838)))+E(f324(f324(f82(a838),x47361),x47362),f324(a114,f2(a838)))
% 18.77/18.50 [4737]~E(x47371,f2(a838))+~E(x47372,f324(a114,f2(a838)))+E(f324(f324(f82(a838),x47371),x47372),f324(a114,f2(a838)))
% 18.77/18.50 [4738]~E(x47382,f2(a838))+~E(x47381,f324(a114,f2(a838)))+E(f324(f324(f82(a838),x47381),x47382),f324(a114,f2(a838)))
% 18.77/18.50 [4739]~E(x47391,f2(a838))+~E(x47392,f324(a114,f2(a838)))+E(f324(f324(f82(a838),x47391),x47392),f324(a114,f2(a838)))
% 18.77/18.50 [4744]E(x47441,f80(a1))+E(x47442,f324(f106(a1),a99))+~E(f324(f324(f83(a1),x47441),x47442),f80(a1))
% 18.77/18.50 [4745]E(x47451,f80(a1))+E(x47452,f324(f106(a1),a99))+~E(f324(f324(f83(a1),x47452),x47451),f80(a1))
% 18.77/18.50 [4746]E(x47461,f80(a1))+E(x47461,f324(f106(a1),a99))+~E(f324(f324(f83(a1),x47462),x47461),f80(a1))
% 18.77/18.50 [4747]E(x47471,f80(a1))+E(x47471,f324(f106(a1),a99))+~E(f324(f324(f83(a1),x47471),x47472),f80(a1))
% 18.77/18.50 [4748]E(x47481,f80(a1))+E(x47481,f324(f106(a1),a99))+~E(f324(f324(f83(a1),x47481),x47482),f80(a1))
% 18.77/18.50 [4766]~P69(x47662)+E(x47661,f2(x47662))+~E(f324(f324(f82(x47662),x47661),x47661),f2(x47662))
% 18.77/18.50 [4767]~P69(x47672)+E(x47671,f2(x47672))+~E(f324(f324(f82(x47672),x47671),x47671),f2(x47672))
% 18.77/18.50 [4773]~E(x47731,f324(f106(a1),a99))+~E(x47732,f324(f106(a1),a99))+E(f324(f324(f83(a1),x47731),x47732),f80(a1))
% 18.77/18.50 [4784]E(x47841,f2(a838))+E(x47842,f2(a838))+~E(f324(f324(f82(a838),x47842),x47841),f324(a114,f2(a838)))
% 18.77/18.50 [4785]E(x47851,f2(a838))+E(x47852,f2(a838))+~E(f324(f324(f82(a838),x47852),x47851),f324(a114,f2(a838)))
% 18.77/18.50 [4793]~P89(x47931)+~P59(x47931)+E(f324(f324(f284(x47931),x47932),f324(f106(x47931),a85)),f2(x47931))
% 18.77/18.50 [4800]~P133(x48001)+~E(x48002,f324(f81(x48001),f80(x48001)))+E(f324(f324(f83(x48001),x48002),x48002),f80(x48001))
% 18.77/18.50 [4805]~P10(x48052)+~P10(x48051)+P10(f324(f324(f83(a1),x48051),x48052))
% 18.77/18.50 [4806]~P10(x48062)+~P10(x48061)+P10(f324(f324(f82(a1),x48061),x48062))
% 18.77/18.50 [4807]~P10(x48072)+~P10(x48071)+P10(f324(f324(f42(a1),x48071),x48072))
% 18.77/18.50 [4808]~E(x48082,f2(a1))+E(x48081,f2(a1))+E(f52(x48081,x48082),f324(f324(f247(a1,a1),f2(a1)),x48081))
% 18.77/18.50 [4809]~E(x48092,f2(a1))+E(x48091,f2(a1))+E(f52(x48091,x48092),f324(f324(f247(a1,a1),f2(a1)),x48091))
% 18.77/18.50 [4832]~E(x48322,f324(a114,f2(a838)))+~E(x48321,f324(a114,f2(a838)))+E(f324(f324(f83(a838),x48321),x48322),f324(a114,f2(a838)))
% 18.77/18.50 [4843]E(x48431,f2(a838))+E(x48431,f324(a114,f2(a838)))+~E(f324(f324(f82(a838),x48432),x48431),f324(a114,f2(a838)))
% 18.77/18.50 [4844]E(x48441,f2(a838))+E(x48441,f324(a114,f2(a838)))+~E(f324(f324(f82(a838),x48441),x48442),f324(a114,f2(a838)))
% 18.77/18.50 [4845]E(x48451,f2(a838))+E(x48452,f324(a114,f2(a838)))+~E(f324(f324(f240(a838),x48452),x48451),f324(a114,f2(a838)))
% 18.77/18.50 [4846]E(x48461,f2(a838))+E(x48461,f324(a114,f2(a838)))+~E(f324(f324(f82(a838),x48462),x48461),f324(a114,f2(a838)))
% 18.77/18.50 [4847]E(x48471,f2(a838))+E(x48471,f324(a114,f2(a838)))+~E(f324(f324(f82(a838),x48471),x48472),f324(a114,f2(a838)))
% 18.77/18.50 [4855]~P89(x48551)+~P59(x48551)+E(f324(f324(f284(x48551),x48552),f324(f106(x48551),a99)),f324(f81(x48551),x48552))
% 18.77/18.50 [4876]E(x48761,f324(a107,x48762))+~E(x48761,f2(a838))+P1(f324(f324(f231(a1),f2(a1)),x48762))
% 18.77/18.50 [4877]E(f324(a107,x48771),x48772)+~E(x48772,f2(a838))+P1(f324(f324(f231(a1),f2(a1)),x48771))
% 18.77/18.50 [4891]E(x48911,f324(a114,f2(a838)))+E(x48912,f324(a114,f2(a838)))+~E(f324(f324(f82(a838),x48911),x48912),f324(a114,f2(a838)))
% 18.77/18.50 [4892]E(x48921,f324(a114,f2(a838)))+E(x48922,f324(a114,f2(a838)))+~E(f324(f324(f82(a838),x48921),x48922),f324(a114,f2(a838)))
% 18.77/18.50 [4903]~E(x49031,f324(a107,x49032))+E(x49031,f2(a838))+P1(f324(f324(f231(a1),f2(a1)),x49032))
% 18.77/18.50 [4904]~E(f324(a107,x49042),x49041)+E(x49041,f2(a838))+P1(f324(f324(f231(a1),f2(a1)),x49042))
% 18.77/18.50 [4927]~P94(x49271)+E(f324(f66(x49271,f104(x49271)),x49272),f12(x49271,x49272))+~P1(f324(f64(x49271),x49272))
% 18.77/18.50 [4928]~P86(x49281)+E(f324(f66(x49281,f178(x49281)),x49282),f16(x49281,x49282))+~P1(f324(f64(x49281),x49282))
% 18.77/18.50 [4929]~P86(x49291)+E(f324(f66(x49291,f235(x49291)),x49292),f17(x49291,x49292))+~P1(f324(f64(x49291),x49292))
% 18.77/18.50 [4930]~P94(x49301)+E(f324(f66(x49301,f103(x49301)),x49302),f15(x49301,x49302))+~P1(f324(f64(x49301),x49302))
% 18.77/18.50 [5013]E(x50131,x50132)+~E(f324(f324(f3(a838),x50132),x50131),f2(a838))+~E(f324(f324(f3(a838),x50131),x50132),f2(a838))
% 18.77/18.50 [5024]P10(x50241)+~P38(x50242)+~P1(f324(f324(f326(a1),x50241),x50242))
% 18.77/18.50 [5054]~P103(x50541)+~E(f84(x50541,x50542),f80(x50541))+P1(f324(f324(f232(x50541),f2(x50541)),x50542))
% 18.77/18.50 [5065]~P89(x50651)+E(f324(f102(x50651),f324(f106(a838),x50652)),f324(f106(x50651),x50652))+P1(f324(a185,f324(f106(a1),x50652)))
% 18.77/18.50 [5070]~P42(x50701,x50702)+P43(a832)+P1(f324(f64(f844(x50701,x50701)),x50702))
% 18.77/18.50 [5135]~P86(x51351)+E(f324(f66(x51351,f178(x51351)),x51352),f13(x51351,f178(x51351),x51352))+~P1(f324(f64(x51351),x51352))
% 18.77/18.50 [5136]~P86(x51361)+E(f324(f66(x51361,f235(x51361)),x51362),f14(x51361,f235(x51361),x51362))+~P1(f324(f64(x51361),x51362))
% 18.77/18.50 [5149]E(x51491,x51492)+P1(f324(f324(f232(a838),x51492),x51491))+P1(f324(f324(f232(a838),x51491),x51492))
% 18.77/18.50 [5150]E(x51501,x51502)+P1(f324(f324(f232(a838),x51502),x51501))+P1(f324(f324(f232(a838),x51501),x51502))
% 18.77/18.50 [5151]E(x51511,x51512)+P1(f324(f324(f232(a1),x51512),x51511))+P1(f324(f324(f232(a1),x51511),x51512))
% 18.77/18.50 [5203]~P89(x52031)+E(f324(f102(x52031),f324(f106(a838),x52032)),f2(x52031))+~P1(f324(a185,f324(f106(a1),x52032)))
% 18.77/18.50 [5206]~E(x52062,f324(a107,x52061))+E(x52061,f324(f102(a1),x52062))+~P1(f324(f324(f231(a1),f2(a1)),x52061))
% 18.77/18.50 [5207]~E(f324(a107,x52071),x52072)+E(x52071,f324(f102(a1),x52072))+~P1(f324(f324(f231(a1),f2(a1)),x52071))
% 18.77/18.50 [5208]~E(x52081,f324(a107,x52082))+E(f324(f102(a1),x52081),x52082)+~P1(f324(f324(f231(a1),f2(a1)),x52082))
% 18.77/18.50 [5218]E(x52181,f324(a107,x52182))+~E(x52182,f324(f102(a1),x52181))+~P1(f324(f324(f231(a1),f2(a1)),x52182))
% 18.77/18.50 [5219]E(f324(a107,x52191),x52192)+~E(x52191,f324(f102(a1),x52192))+~P1(f324(f324(f231(a1),f2(a1)),x52191))
% 18.77/18.50 [5249]~P105(x52492)+E(x52491,f2(x52492))+~P1(f324(f324(f280(x52492),f2(x52492)),x52491))
% 18.77/18.50 [5258]~P78(x52582)+E(x52581,f2(x52582))+P1(f324(f324(f232(x52582),f2(x52582)),f324(f77(x52582),x52581)))
% 18.77/18.50 [5324]~P103(x53241)+E(f84(x53241,x53242),f80(x53241))+~P1(f324(f324(f232(x53241),f2(x53241)),x53242))
% 18.77/18.50 [5325]~P103(x53251)+E(f84(x53251,x53252),f80(x53251))+~P1(f324(f324(f232(x53251),f2(x53251)),x53252))
% 18.77/18.50 [5331]~P89(x53311)+E(f324(f102(x53311),f324(f106(a838),x53312)),f2(x53311))+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x53312)))
% 18.77/18.50 [5338]~P78(x53381)+E(f324(f77(x53381),x53382),x53382)+~P1(f324(f324(f232(x53381),f2(x53381)),x53382))
% 18.77/18.50 [5339]~P78(x53391)+E(f324(f77(x53391),x53392),x53392)+~P1(f324(f324(f231(x53391),f2(x53391)),x53392))
% 18.77/18.50 [5346]E(x53461,f2(a838))+~E(f129(a838,f324(f295(a838,x53462),x53461)),f115(a838))+P1(f324(f324(f231(a838),x53461),x53462))
% 18.77/18.50 [5356]~P67(x53561)+E(f324(f324(f8(x53561,x53561),f7(x53561)),f324(f157(x53561),x53562)),f324(f151(x53561),x53562))+~P1(f324(f127(x53561),x53562))
% 18.77/18.50 [5359]~P119(x53591)+E(f324(f102(x53591),f324(a107,x53592)),f324(f105(x53591),x53592))+~P1(f324(f324(f231(a1),f2(a1)),x53592))
% 18.77/18.50 [5361]~E(x53611,x53612)+P1(f324(f324(f232(a838),x53611),f324(a114,x53612)))+P1(f324(f324(f232(a838),x53611),x53612))
% 18.77/18.50 [5382]E(x53821,x53822)+P1(f324(f324(f232(a838),x53821),x53822))+~P1(f324(f324(f231(a838),x53821),x53822))
% 18.77/18.50 [5383]E(x53831,x53832)+P1(f324(f324(f232(a838),x53831),x53832))+~P1(f324(f324(f231(a838),x53831),x53832))
% 18.77/18.50 [5384]E(x53841,x53842)+P1(f324(f324(f232(a838),x53841),x53842))+~P1(f324(f324(f231(a838),x53841),x53842))
% 18.77/18.50 [5385]E(x53851,x53852)+P1(f324(f324(f232(a1),x53851),x53852))+~P1(f324(f324(f231(a1),x53851),x53852))
% 18.77/18.50 [5388]E(x53881,f80(a1))+~E(f324(f324(f83(a1),x53882),x53881),f80(a1))+~P1(f324(f324(f232(a1),f2(a1)),x53882))
% 18.77/18.50 [5389]E(x53891,f80(a1))+~E(f324(f324(f83(a1),x53891),x53892),f80(a1))+~P1(f324(f324(f232(a1),f2(a1)),x53891))
% 18.77/18.50 [5427]~P38(x54272)+P1(f324(f324(f231(a1),f2(a1)),x54271))+~P1(f324(f324(f326(a1),x54271),x54272))
% 18.77/18.50 [5428]~P38(x54282)+P1(f324(f324(f231(a1),f2(a1)),x54281))+~P1(f324(f324(f326(a1),x54281),x54282))
% 18.77/18.50 [5439]~P1(f324(x54391,x54392))+P1(f324(x54391,f2(a838)))+P1(f324(x54391,f324(a114,f823(x54392,x54391))))
% 18.77/18.50 [5446]~P55(x54461,x54462)+P36(x54461,x54462)+~P1(f324(f64(f844(x54461,x54461)),x54462))
% 18.77/18.50 [5447]~P55(x54471,x54472)+P36(x54471,x54472)+~P1(f324(f64(f844(x54471,x54471)),x54472))
% 18.77/18.50 [5448]~P36(x54481,x54482)+P55(x54481,x54482)+~P1(f324(f64(f844(x54481,x54481)),x54482))
% 18.77/18.50 [5449]~P55(x54491,x54492)+P42(x54491,x54492)+~P1(f324(f64(f844(x54491,x54491)),x54492))
% 18.77/18.50 [5491]E(x54911,f179(f845(x54912,a832)))+~P1(f324(f64(x54912),x54911))+P1(f324(f324(f232(a838),f2(a838)),f324(f41(x54912),x54911)))
% 18.77/18.50 [5517]~P1(f324(x55171,x55172))+P1(f324(x55171,f2(a838)))+P1(f324(f324(f232(a838),f632(x55172,x55171)),x55172))
% 18.77/18.50 [5542]E(x55421,f2(a838))+~E(f324(f151(a838),x55422),f2(a838))+~P1(f324(f324(f326(a838),x55421),f324(f157(a838),x55422)))
% 18.77/18.50 [5575]~E(x55751,x55752)+P1(f324(f324(f232(a838),x55751),f324(a114,x55752)))+~P1(f324(f324(f231(a838),x55752),x55751))
% 18.77/18.50 [5604]~E(x56042,f2(a838))+P1(f324(f324(f231(a1),f2(a1)),x56041))+P1(f324(f324(f280(a838),f324(a107,x56041)),x56042))
% 18.77/18.50 [5607]E(x56071,x56072)+~P1(f324(f324(f231(a838),x56072),x56071))+~P1(f324(f324(f231(a838),x56071),x56072))
% 18.77/18.50 [5608]E(x56081,x56082)+~P1(f324(f324(f231(a1),x56082),x56081))+~P1(f324(f324(f231(a1),x56081),x56082))
% 18.77/18.50 [5609]E(x56091,x56092)+~P1(f324(f324(f280(a838),x56092),x56091))+~P1(f324(f324(f280(a838),x56091),x56092))
% 18.77/18.50 [5610]E(x56101,x56102)+~P1(f324(f324(f280(a838),x56102),x56101))+~P1(f324(f324(f280(a838),x56101),x56102))
% 18.77/18.50 [5611]E(x56111,x56112)+~P1(f324(f324(f280(a838),x56112),x56111))+~P1(f324(f324(f280(a838),x56111),x56112))
% 18.77/18.50 [5612]E(x56121,x56122)+~P1(f324(f324(f280(a838),x56122),x56121))+~P1(f324(f324(f280(a838),x56121),x56122))
% 18.77/18.50 [5613]E(x56131,x56132)+~P1(f324(f324(f280(a838),x56132),x56131))+~P1(f324(f324(f280(a838),x56131),x56132))
% 18.77/18.50 [5614]E(x56141,x56142)+~P1(f324(f324(f280(a838),x56142),x56141))+~P1(f324(f324(f280(a838),x56141),x56142))
% 18.77/18.50 [5615]E(x56151,x56152)+~P1(f324(f324(f280(a838),x56152),x56151))+~P1(f324(f324(f280(a838),x56151),x56152))
% 18.77/18.50 [5616]E(x56161,x56162)+~P1(f324(f324(f280(a838),x56162),x56161))+~P1(f324(f324(f280(a838),x56161),x56162))
% 18.77/18.50 [5617]E(x56171,x56172)+~P1(f324(f324(f280(a838),x56172),x56171))+~P1(f324(f324(f280(a838),x56171),x56172))
% 18.77/18.50 [5618]E(f324(f41(x56181),x56182),f2(a838))+~P1(f324(f64(x56181),x56182))+P1(f324(f324(f326(x56181),f633(x56182,x56181)),x56182))
% 18.77/18.50 [5624]E(f56(x56241,x56242),f52(x56241,x56242))+P1(f324(f324(f231(a1),f2(a1)),x56241))+~P1(f324(f324(f232(a1),f2(a1)),x56242))
% 18.77/18.50 [5651]~P1(f324(x56511,f515(x56511)))+P1(f324(x56511,f324(a107,x56512)))+~P1(f324(f324(f231(a1),f2(a1)),x56512))
% 18.77/18.50 [5653]P1(f324(f324(f232(a838),x56531),f383(x56532)))+~P1(f324(f64(a838),x56532))+~P1(f324(f324(f326(a838),x56531),x56532))
% 18.77/18.50 [5654]P1(f324(f324(f231(a838),x56541),f381(x56542)))+~P1(f324(f64(a838),x56542))+~P1(f324(f324(f326(a838),x56541),x56542))
% 18.77/18.50 [5680]E(x56801,x56802)+~P1(f324(f324(f232(a838),x56801),f324(a114,x56802)))+P1(f324(f324(f232(a838),x56801),x56802))
% 18.77/18.50 [5681]E(x56811,x56812)+~P1(f324(f324(f232(a838),x56811),f324(a114,x56812)))+P1(f324(f324(f232(a838),x56811),x56812))
% 18.77/18.50 [5682]E(x56821,x56822)+~P1(f324(f324(f232(a838),x56821),f324(a114,x56822)))+P1(f324(f324(f232(a838),x56821),x56822))
% 18.77/18.50 [5683]E(x56831,x56832)+~P1(f324(f324(f232(a838),x56831),f324(a114,x56832)))+P1(f324(f324(f232(a838),x56831),x56832))
% 18.77/18.50 [5720]E(x57201,f324(a114,x57202))+~P1(f324(f324(f231(a838),x57201),f324(a114,x57202)))+P1(f324(f324(f231(a838),x57201),x57202))
% 18.77/18.50 [5721]E(x57211,f324(a114,x57212))+~P1(f324(f324(f231(a838),x57211),f324(a114,x57212)))+P1(f324(f324(f231(a838),x57211),x57212))
% 18.77/18.50 [5731]P1(f324(x57311,f540(x57311)))+~P1(f324(x57311,f324(a107,x57312)))+~P1(f324(f324(f231(a1),f2(a1)),x57312))
% 18.77/18.50 [5733]E(f324(f77(a1),x57331),f324(f77(a1),x57332))+~P1(f324(f324(f280(a1),x57332),x57331))+~P1(f324(f324(f280(a1),x57331),x57332))
% 18.77/18.50 [5745]~P1(f324(x57451,x57452))+~P1(f324(f324(f231(a1),f2(a1)),x57452))+P1(f324(x57451,f324(f102(a1),f555(x57451))))
% 18.77/18.50 [5757]~P78(x57572)+~E(x57571,f2(x57572))+~P1(f324(f324(f232(x57572),f2(x57572)),f324(f77(x57572),x57571)))
% 18.77/18.50 [5783]~P55(x57831,x57832)+P36(x57831,f324(f279(x57831,x57831),x57832))+~P1(f324(f64(f844(x57831,x57831)),x57832))
% 18.77/18.50 [5792]~P89(x57921)+E(f324(f102(x57921),f324(f106(a838),x57922)),f324(f106(x57921),x57922))+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x57922)))
% 18.77/18.50 [5796]E(f324(a114,x57961),x57962)+~P1(f324(f324(f232(a838),x57961),x57962))+P1(f324(f324(f232(a838),f324(a114,x57961)),x57962))
% 18.77/18.50 [5808]E(f324(f324(f42(a1),x58081),x58082),f2(a1))+~P1(f324(f324(f231(a1),x58081),f2(a1)))+~P1(f324(f324(f232(a1),x58082),x58081))
% 18.77/18.50 [5809]E(f324(f324(f42(a1),x58091),x58092),f2(a1))+~P1(f324(f324(f231(a1),x58091),f2(a1)))+~P1(f324(f324(f232(a1),x58092),x58091))
% 18.77/18.50 [5822]E(f51(a1,x58221,x58222),x58221)+~P1(f324(f324(f231(a1),x58221),f2(a1)))+~P1(f324(f324(f232(a1),x58222),x58221))
% 18.77/18.50 [5835]E(f53(x58351,x58352),f52(x58351,x58352))+~P1(f324(f324(f231(a1),f2(a1)),x58351))+~P1(f324(f324(f231(a1),f2(a1)),x58352))
% 18.77/18.50 [5841]E(f324(f324(f42(a838),x58411),x58412),f2(a838))+~P1(f324(f324(f232(a838),f2(a838)),x58412))+~P1(f324(f324(f232(a838),x58411),x58412))
% 18.77/18.50 [5842]E(f324(f324(f42(a1),x58421),x58422),f2(a1))+~P1(f324(f324(f231(a1),f2(a1)),x58421))+~P1(f324(f324(f232(a1),x58421),x58422))
% 18.77/18.50 [5843]E(f324(f324(f42(a1),x58431),x58432),f2(a1))+~P1(f324(f324(f231(a1),f2(a1)),x58431))+~P1(f324(f324(f232(a1),x58431),x58432))
% 18.77/18.50 [5857]E(f51(a838,f324(f106(a838),x58571),f324(f106(a838),x58572)),f324(f106(a838),x58571))+P1(f324(a185,f324(f106(a1),x58571)))+~P1(f324(a185,f324(f106(a1),x58572)))
% 18.77/18.50 [5859]E(f51(a1,x58591,x58592),x58591)+~P1(f324(f324(f231(a1),f2(a1)),x58591))+~P1(f324(f324(f232(a1),x58591),x58592))
% 18.77/18.50 [5861]E(x58611,x58612)+~P1(f324(f324(f232(a838),x58611),f324(a114,x58612)))+~P1(f324(f324(f231(a838),x58612),x58611))
% 18.77/18.50 [5873]E(f324(f106(a1),x58731),f324(f102(a1),x58732))+~E(x58732,f324(a107,f324(f106(a1),x58731)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x58731)))
% 18.77/18.50 [5877]~P103(x58771)+~P1(f324(f324(f232(x58771),x58772),f2(x58771)))+P1(f324(f324(f232(x58771),x58772),f324(f81(x58771),x58772)))
% 18.77/18.50 [5878]~P69(x58781)+~P1(f324(f324(f231(x58781),x58782),f2(x58781)))+P1(f324(f324(f231(x58781),x58782),f324(f81(x58781),x58782)))
% 18.77/18.50 [5888]~P9(x58881)+E(f324(f324(f67(x58881,x58881,f104(x58881)),f238(x58881)),x58882),f44(x58881,x58882))+~P1(f324(f64(x58881),x58882))
% 18.77/18.50 [5889]~P9(x58891)+E(f324(f324(f67(x58891,x58891,f103(x58891)),f179(x58891)),x58892),f43(x58891,x58892))+~P1(f324(f64(x58891),x58892))
% 18.77/18.50 [5903]~P84(x59031)+~P1(f324(f324(f232(a838),f2(a838)),x59032))+P1(f324(f324(f232(x59031),f2(x59031)),f324(f102(x59031),x59032)))
% 18.77/18.50 [5904]~P103(x59041)+~P1(f324(f324(f232(a1),f2(a1)),x59042))+P1(f324(f324(f232(x59041),f2(x59041)),f324(f105(x59041),x59042)))
% 18.77/18.50 [5905]~P103(x59051)+~P1(f324(f324(f231(a1),f2(a1)),x59052))+P1(f324(f324(f231(x59051),f2(x59051)),f324(f105(x59051),x59052)))
% 18.77/18.50 [5908]~P10(x59082)+~P10(x59081)+E(f324(f304(a838,a1,f102(a1)),f296(a838,f324(a107,x59081),f324(a107,x59082))),f296(a1,x59081,x59082))
% 18.77/18.50 [5914]P1(f324(x59141,x59142))+~P1(f324(f324(f231(a1),f2(a1)),x59142))+~P1(f324(x59141,f324(f102(a1),f584(x59141))))
% 18.77/18.50 [5941]E(f324(f324(f82(a838),f324(f106(a838),x59411)),f324(f106(a838),x59412)),f324(f106(a838),x59411))+P1(f324(f324(f232(a1),x59411),a85))+~P1(f324(f324(f232(a1),x59412),a85))
% 18.77/18.50 [5945]~P103(x59451)+P1(f324(f324(f232(x59451),f2(x59451)),f84(x59451,x59452)))+~P1(f324(f324(f232(x59451),f2(x59451)),x59452))
% 18.77/18.50 [5959]~P70(x59591)+~P1(f324(f324(f232(x59591),x59592),f2(x59591)))+P1(f324(f324(f232(x59591),f2(x59591)),f324(f81(x59591),x59592)))
% 18.77/18.50 [5960]~P70(x59601)+~P1(f324(f324(f231(x59601),x59602),f2(x59601)))+P1(f324(f324(f231(x59601),f2(x59601)),f324(f81(x59601),x59602)))
% 18.77/18.50 [5963]E(x59631,f2(a838))+P1(f324(f324(f231(a1),f2(a1)),x59632))+~P1(f324(f324(f280(a838),f324(a107,x59632)),x59631))
% 18.77/18.50 [5964]E(x59641,f238(f845(x59642,a832)))+~E(f324(f41(x59642),x59641),f324(f41(x59642),f238(f845(x59642,a832))))+~P1(f324(f64(x59642),f238(f845(x59642,a832))))
% 18.77/18.50 [5995]~P1(f324(f324(f232(a838),f2(a838)),x59952))+~P1(f324(f324(f280(a838),x59951),x59952))+P1(f324(f324(f231(a838),x59951),x59952))
% 18.77/18.50 [5996]~P1(f324(f324(f232(a1),f2(a1)),x59962))+~P1(f324(f324(f280(a1),x59961),x59962))+P1(f324(f324(f231(a1),x59961),x59962))
% 18.77/18.50 [6002]~P103(x60021)+P1(f324(f324(f232(x60021),x60022),f2(x60021)))+~P1(f324(f324(f232(x60021),x60022),f324(f81(x60021),x60022)))
% 18.77/18.50 [6003]~P69(x60031)+P1(f324(f324(f231(x60031),x60032),f2(x60031)))+~P1(f324(f324(f231(x60031),x60032),f324(f81(x60031),x60032)))
% 18.77/18.50 [6008]E(f53(x60081,x60082),f324(f324(f247(a1,a1),f2(a1)),x60081))+~P1(f324(f324(f232(a1),f2(a1)),x60082))+~P1(f324(f324(f232(a1),x60081),x60082))
% 18.77/18.50 [6011]~P89(x60111)+P1(f324(f324(f326(x60111),f324(f106(x60111),x60112)),f175(x60111)))+~P1(f324(f324(f231(a1),a85),x60112))
% 18.77/18.50 [6042]E(x60421,f2(a838))+~P1(f324(f324(f232(a838),x60421),f324(a114,x60422)))+P1(f324(f324(f232(a838),f345(x60422,x60421)),x60422))
% 18.77/18.50 [6066]~P103(x60661)+~P1(f324(f324(f232(x60661),f2(x60661)),f84(x60661,x60662)))+P1(f324(f324(f232(x60661),f2(x60661)),x60662))
% 18.77/18.50 [6068]~E(f324(f106(a838),x60682),f324(f106(a838),x60681))+P1(f324(f324(f231(a1),f324(f106(a1),x60681)),f2(a1)))+~P1(f324(a185,f324(f106(a1),x60682)))
% 18.77/18.50 [6096]E(f324(f246(a1,a1),f56(x60961,x60962)),f324(f324(f42(a1),x60961),x60962))+~P1(f324(f324(f232(a1),x60961),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x60962))
% 18.77/18.50 [6130]E(f324(f251(a1,a1),f56(x61301,x61302)),f51(a1,x61301,x61302))+~P1(f324(f324(f232(a1),x61301),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x61302))
% 18.77/18.50 [6132]E(x61321,f2(a1))+~P1(f324(f324(f280(a1),x61322),x61321))+P1(f324(f324(f231(a1),f324(f77(a1),x61322)),f324(f77(a1),x61321)))
% 18.77/18.50 [6134]~P84(x61342)+~P1(f324(f324(f232(x61342),f2(x61342)),f324(f102(x61342),x61341)))+P1(f324(f324(f232(a838),f2(a838)),x61341))
% 18.77/18.50 [6135]~P103(x61352)+~P1(f324(f324(f232(x61352),f2(x61352)),f324(f105(x61352),x61351)))+P1(f324(f324(f232(a1),f2(a1)),x61351))
% 18.77/18.50 [6136]~P103(x61362)+~P1(f324(f324(f231(x61362),f2(x61362)),f324(f105(x61362),x61361)))+P1(f324(f324(f231(a1),f2(a1)),x61361))
% 18.77/18.50 [6140]~E(x61402,f2(a838))+P1(f324(f324(f280(a838),f324(a107,x61401)),x61402))+~P1(f324(f324(f280(a1),x61401),f324(f102(a1),x61402)))
% 18.77/18.50 [6141]E(f324(f246(a1,a1),f53(x61411,x61412)),f324(f324(f42(a1),x61411),x61412))+~P1(f324(f324(f232(a1),f2(a1)),x61411))+~P1(f324(f324(f231(a1),f2(a1)),x61412))
% 18.77/18.50 [6155]E(f324(f251(a1,a1),f53(x61551,x61552)),f51(a1,x61551,x61552))+~P1(f324(f324(f232(a1),f2(a1)),x61551))+~P1(f324(f324(f231(a1),f2(a1)),x61552))
% 18.77/18.50 [6173]~P70(x61731)+P1(f324(f324(f232(x61731),x61732),f2(x61731)))+~P1(f324(f324(f232(x61731),f2(x61731)),f324(f81(x61731),x61732)))
% 18.77/18.50 [6174]~P70(x61741)+P1(f324(f324(f231(x61741),x61742),f2(x61741)))+~P1(f324(f324(f231(x61741),f2(x61741)),f324(f81(x61741),x61742)))
% 18.77/18.50 [6200]P1(f324(f55(x62001,x62002),f56(x62001,x62002)))+~P1(f324(f324(f232(a1),x62001),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x62002))
% 18.77/18.50 [6215]~P1(f324(f324(f232(a838),f2(a838)),x62151))+~P1(f324(f324(f280(a838),x62152),x62151))+~P1(f324(f324(f232(a838),x62151),x62152))
% 18.77/18.50 [6216]~P1(f324(f324(f232(a1),f2(a1)),x62161))+~P1(f324(f324(f280(a1),x62162),x62161))+~P1(f324(f324(f232(a1),x62161),x62162))
% 18.77/18.50 [6228]P1(f324(f55(x62281,x62282),f53(x62281,x62282)))+~P1(f324(f324(f232(a1),f2(a1)),x62282))+~P1(f324(f324(f231(a1),f2(a1)),x62281))
% 18.77/18.50 [6270]~P70(x62701)+P1(f324(f324(f232(x62701),f324(f81(x62701),x62702)),f2(x62701)))+~P1(f324(f324(f232(x62701),f2(x62701)),x62702))
% 18.77/18.50 [6271]~P70(x62711)+P1(f324(f324(f231(x62711),f324(f81(x62711),x62712)),f2(x62711)))+~P1(f324(f324(f231(x62711),f2(x62711)),x62712))
% 18.77/18.50 [6293]E(f324(f324(f3(a838),f324(a107,x62931)),f324(a107,x62932)),f324(a107,f187(x62931,x62932)))+~P1(f324(f324(f231(a1),f2(a1)),x62932))+~P1(f324(f324(f231(a1),f2(a1)),x62931))
% 18.77/18.50 [6311]P1(f324(f324(f231(a1),f2(a1)),f187(x63111,x63112)))+~P1(f324(f324(f231(a1),f2(a1)),x63112))+~P1(f324(f324(f231(a1),f2(a1)),x63111))
% 18.77/18.50 [6350]~P1(f324(x63501,x63502))+P1(f324(x63501,f2(a838)))+P1(f324(x63501,f324(f324(f82(a838),f632(x63502,x63501)),f80(a838))))
% 18.77/18.50 [6356]E(f283(a838,f280(a838),x63561,x63562),f179(f845(a838,a832)))+P1(f324(f324(f280(a838),x63561),x63562))+~P1(f324(f324(f280(a838),x63562),x63561))
% 18.77/18.50 [6435]E(f324(f106(a838),x64351),f324(f106(a838),x64352))+~P1(f324(f324(f231(a1),f324(f106(a1),x64352)),f2(a1)))+~P1(f324(a185,f324(f106(a1),x64351)))
% 18.77/18.50 [6448]~E(x64481,f2(a838))+~E(f717(x64482,x64481),f2(a838))+E(f324(f131(a838,a838,f82(a838),x64481),x64482),f2(a838))
% 18.77/18.50 [6474]~P1(f324(f64(x64741),f651(x64742,x64741)))+~P1(f324(f64(f845(x64741,a832)),x64742))+P1(f324(f64(x64741),f43(f845(x64741,a832),x64742)))
% 18.77/18.50 [6480]E(x64801,x64802)+P1(f324(f324(f232(a1),x64801),x64802))+~P1(f324(f324(f232(a1),x64801),f324(f324(f82(a1),x64802),f80(a1))))
% 18.77/18.50 [6481]P1(f324(f324(f232(a838),f324(a107,x64811)),f324(a107,x64812)))+~P1(f324(f324(f232(a1),f2(a1)),x64812))+~P1(f324(f324(f232(a1),x64811),x64812))
% 18.77/18.50 [6482]P1(f324(f324(f232(a838),f324(a107,x64821)),f324(a107,x64822)))+~P1(f324(f324(f232(a1),f2(a1)),x64822))+~P1(f324(f324(f232(a1),x64821),x64822))
% 18.77/18.50 [6483]P1(f324(f324(f232(a838),f324(a107,x64831)),f324(a107,x64832)))+~P1(f324(f324(f231(a1),f2(a1)),x64831))+~P1(f324(f324(f232(a1),x64831),x64832))
% 18.77/18.50 [6484]P1(f324(f324(f231(a838),f324(a107,x64841)),f324(a107,x64842)))+~P1(f324(f324(f232(a1),f2(a1)),x64841))+~P1(f324(f324(f231(a1),x64841),x64842))
% 18.77/18.50 [6485]P1(f324(f324(f231(a838),f324(a107,x64851)),f324(a107,x64852)))+~P1(f324(f324(f231(a1),f2(a1)),x64852))+~P1(f324(f324(f231(a1),x64851),x64852))
% 18.77/18.50 [6495]E(f51(a838,f324(a107,x64951),f324(a107,x64952)),f324(a107,f51(a1,x64951,x64952)))+~P1(f324(f324(f231(a1),f2(a1)),x64952))+~P1(f324(f324(f231(a1),f2(a1)),x64951))
% 18.77/18.50 [6496]E(f51(a838,f324(a107,x64961),f324(a107,x64962)),f324(a107,f51(a1,x64961,x64962)))+~P1(f324(f324(f231(a1),f2(a1)),x64962))+~P1(f324(f324(f231(a1),f2(a1)),x64961))
% 18.77/18.50 [6517]~P70(x65171)+~P1(f324(f324(f232(x65171),f324(f81(x65171),x65172)),f2(x65171)))+P1(f324(f324(f232(x65171),f2(x65171)),x65172))
% 18.77/18.50 [6518]~P70(x65181)+~P1(f324(f324(f231(x65181),f324(f81(x65181),x65182)),f2(x65181)))+P1(f324(f324(f231(x65181),f2(x65181)),x65182))
% 18.77/18.50 [6535]~P1(f324(f324(f232(a1),a85),x65352))+~P1(f324(f324(f232(a1),x65351),x65352))+P1(f324(f324(f232(a838),f324(f106(a838),x65351)),f324(f106(a838),x65352)))
% 18.77/18.50 [6632]~P1(f324(f324(f231(a1),f2(a1)),x66321))+P1(f324(f324(f232(a838),f324(a107,x66321)),x66322))+~P1(f324(f324(f232(a1),x66321),f324(f102(a1),x66322)))
% 18.77/18.50 [6633]~P1(f324(f324(f231(a1),f2(a1)),x66331))+P1(f324(f324(f280(a838),f324(a107,x66331)),x66332))+~P1(f324(f324(f280(a1),x66331),f324(f102(a1),x66332)))
% 18.77/18.50 [6649]E(x66491,f2(a1))+E(f51(a1,x66492,x66491),f2(a1))+E(f324(f324(f3(a1),f324(f81(a1),f324(f324(f42(a1),x66492),x66491))),f80(a1)),f324(f324(f42(a1),x66492),f324(f81(a1),x66491)))
% 18.77/18.50 [6665]~P1(f324(f324(f231(a1),f2(a1)),x66651))+~P1(f324(f324(f232(a838),f324(a107,x66651)),x66652))+P1(f324(f324(f232(a1),x66651),f324(f102(a1),x66652)))
% 18.77/18.50 [6666]~P1(f324(f324(f231(a1),f2(a1)),x66661))+~P1(f324(f324(f280(a838),f324(a107,x66661)),x66662))+P1(f324(f324(f280(a1),x66661),f324(f102(a1),x66662)))
% 18.77/18.50 [6703]~P1(f324(f324(f232(a838),f324(a107,x67031)),f324(a107,x67032)))+~P1(f324(f324(f232(a1),f2(a1)),x67032))+P1(f324(f324(f232(a1),x67031),x67032))
% 18.77/18.50 [6704]~P1(f324(f324(f232(a838),f324(a107,x67041)),f324(a107,x67042)))+~P1(f324(f324(f231(a1),f2(a1)),x67041))+P1(f324(f324(f232(a1),x67041),x67042))
% 18.77/18.50 [6705]~P1(f324(f324(f231(a838),f324(a107,x67051)),f324(a107,x67052)))+~P1(f324(f324(f232(a1),f2(a1)),x67051))+P1(f324(f324(f231(a1),x67051),x67052))
% 18.77/18.50 [6706]~P1(f324(f324(f231(a838),f324(a107,x67061)),f324(a107,x67062)))+~P1(f324(f324(f231(a1),f2(a1)),x67062))+P1(f324(f324(f231(a1),x67061),x67062))
% 18.77/18.50 [6737]P1(f324(f324(f231(a1),x67371),x67372))+~P1(f324(f324(f231(a838),f324(f106(a838),x67371)),f324(f106(a838),x67372)))+P1(f324(f324(f231(a1),x67371),a85))
% 18.77/18.50 [6767]P1(f324(f324(f231(a1),f2(a1)),f51(a1,x67671,x67672)))+~P1(f324(f324(f231(a1),f2(a1)),x67672))+~P1(f324(f324(f231(a1),f2(a1)),x67671))
% 18.77/18.50 [6866]P1(f324(f324(f232(a1),a85),x68661))+~P1(f324(f324(f232(a1),x68662),x68661))+~P1(f324(f324(f232(a838),f324(f106(a838),x68662)),f324(f106(a838),x68661)))
% 18.77/18.50 [6914]E(f324(f324(f247(a1,a1),f324(f324(f42(a1),x69141),x69142)),f51(a1,x69141,x69142)),f56(x69141,x69142))+~P1(f324(f324(f232(a1),x69141),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x69142))
% 18.77/18.50 [6935]E(f324(f324(f247(a1,a1),f324(f324(f42(a1),x69351),x69352)),f51(a1,x69351,x69352)),f53(x69351,x69352))+~P1(f324(f324(f231(a1),f2(a1)),x69352))+~P1(f324(f324(f231(a1),f2(a1)),x69351))
% 18.77/18.50 [6990]~P92(x69902)+E(x69901,f115(x69902))+E(f324(f131(x69902,x69902,f83(x69902),f324(f130(x69902),x69901)),f324(f156(x69902),x69901)),f324(f66(x69902,f83(x69902)),f324(f157(x69902),x69901)))
% 18.77/18.50 [7105]~E(x71051,f2(a838))+E(f324(f131(a838,a838,f82(a838),x71051),x71052),f2(a838))+P1(f324(f324(f326(a838),f717(x71052,x71051)),f324(f157(a838),x71052)))
% 18.77/18.50 [7157]~P1(f324(f324(f232(a1),x71572),f2(a1)))+P1(f324(f324(f232(a1),f324(f324(f42(a1),x71571),x71572)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x71571))
% 18.77/18.50 [7158]~P1(f324(f324(f232(a1),x71581),f2(a1)))+P1(f324(f324(f232(a1),f324(f324(f42(a1),x71581),x71582)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x71582))
% 18.77/18.50 [7159]~P1(f324(f324(f232(a1),x71591),f2(a1)))+P1(f324(f324(f232(a1),f324(f324(f42(a1),x71591),x71592)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x71592))
% 18.77/18.50 [7160]~P1(f324(f324(f232(a1),x71602),f2(a1)))+P1(f324(f324(f231(a1),f324(f324(f42(a1),x71601),x71602)),f2(a1)))+~P1(f324(f324(f231(a1),f2(a1)),x71601))
% 18.77/18.50 [7161]~P1(f324(f324(f231(a1),x71611),f2(a1)))+P1(f324(f324(f231(a1),f324(f324(f42(a1),x71611),x71612)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x71612))
% 18.77/18.50 [7170]P1(f324(f324(f326(f845(x71701,a832)),f651(x71702,x71701)),x71702))+~P1(f324(f64(f845(x71701,a832)),x71702))+P1(f324(f64(x71701),f43(f845(x71701,a832),x71702)))
% 18.77/18.50 [7275]P29(x72751,x72751,x72752,f238(f845(x72751,a832)))+~E(f324(f304(x72751,x72751,x72752),f238(f845(x72751,a832))),f238(f845(x72751,a832)))+~P1(f324(f64(x72751),f238(f845(x72751,a832))))
% 18.77/18.50 [7407]~P29(x74071,x74071,x74072,f238(f845(x74071,a832)))+E(f324(f304(x74071,x74071,x74072),f238(f845(x74071,a832))),f238(f845(x74071,a832)))+~P1(f324(f64(x74071),f238(f845(x74071,a832))))
% 18.77/18.50 [7430]E(f53(f324(f106(a1),x74301),f324(f106(a1),x74302)),f324(f324(f247(a1,a1),f2(a1)),f324(f106(a1),x74301)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x74302)))+~P1(f324(f324(f232(a1),f324(f106(a1),x74301)),f324(f106(a1),x74302)))
% 18.77/18.50 [7548]E(f324(f324(f42(a1),x75481),x75482),f324(f106(a1),a99))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x75481),x75482)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x75481))
% 18.77/18.50 [7606]~P1(f324(f324(f232(a1),x76062),f2(a1)))+~P1(f324(f324(f232(a1),f324(f324(f42(a1),x76061),x76062)),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x76061))
% 18.77/18.50 [7611]E(f324(f324(f82(a1),x76111),x76112),f51(a1,x76111,x76112))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),x76111),x76112)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x76111))
% 18.77/18.50 [7614]P1(f324(f324(f232(a1),x76141),f2(a1)))+~P1(f324(f324(f232(a1),f324(f324(f42(a1),x76141),x76142)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x76142))
% 18.77/18.50 [7869]~P85(x78691)+P50(a838,x78691,f280(a838),x78692)+~P1(f324(f324(f231(x78691),f324(x78692,f335(x78692,x78691))),f324(x78692,f337(x78692,x78691))))
% 18.77/18.50 [8316]~P86(x83161)+P18(x83161,x83162)+~P1(f324(f324(f231(x83161),f324(f324(f149(x83161),x83162),f749(x83162,x83161))),f324(f324(f149(x83161),x83162),f750(x83162,x83161))))
% 18.77/18.50 [8317]~P86(x83171)+P18(x83171,x83172)+~P1(f324(f324(f231(x83171),f324(f324(f149(x83171),x83172),f756(x83172,x83171))),f324(f324(f149(x83171),x83172),f766(x83172,x83171))))
% 18.77/18.50 [5485]E(x54851,f2(a1))+~E(f51(a1,x54852,x54851),f2(a1))+E(f324(f324(f42(a1),x54852),f324(f81(a1),x54851)),f324(f81(a1),f324(f324(f42(a1),x54852),x54851)))
% 18.77/18.50 [5502]~P38(x55022)+~P38(x55021)+P38(f324(f324(f103(f845(a1,a832)),x55021),x55022))
% 18.77/18.50 [5503]~P38(x55032)+~P38(x55031)+P38(f324(f324(f104(f845(a1,a832)),x55031),x55032))
% 18.77/18.50 [5520]~P89(x55201)+~P59(x55201)+E(f324(f81(x55201),f324(f324(f284(x55201),f80(x55201)),x55202)),f324(f324(f284(x55201),f324(f106(x55201),a99)),x55202))
% 18.77/18.50 [5643]E(x56431,f2(a1))+~E(f51(a1,x56432,x56431),f2(a1))+E(f324(f324(f42(a1),f324(f81(a1),x56432)),x56431),f324(f81(a1),f324(f324(f42(a1),x56432),x56431)))
% 18.77/18.50 [5777]~P86(x57771)+P18(x57771,x57772)+P1(f324(f324(f232(a838),f750(x57772,x57771)),f324(f180(f839(x57771)),x57772)))
% 18.77/18.50 [5778]~P86(x57781)+P18(x57781,x57782)+P1(f324(f324(f232(a838),f766(x57782,x57781)),f324(f180(f839(x57781)),x57782)))
% 18.77/18.50 [5937]~P89(x59371)+~E(f324(f106(x59371),x59372),f2(x59371))+P33(x59371,f324(f106(x59371),f324(f324(f82(a1),x59372),f324(f81(a1),a85))))
% 18.77/18.50 [5938]~P89(x59381)+~E(f324(f106(x59381),x59382),f2(x59381))+P33(x59381,f324(f106(x59381),f324(f324(f82(a1),a85),f324(f81(a1),x59382))))
% 18.77/18.50 [5940]E(f324(a57,f53(f324(f81(a1),x59401),f324(f81(a1),x59402))),f52(x59401,x59402))+P1(f324(f324(f232(a1),f2(a1)),x59402))+P1(f324(f324(f231(a1),f2(a1)),x59401))
% 18.77/18.50 [6074]~E(x60742,f2(a838))+~E(x60741,f2(a838))+P1(f324(f324(f231(a1),f324(f102(a1),x60741)),f324(f81(a1),f324(f102(a1),x60742))))
% 18.77/18.50 [6100]E(f324(f324(f82(a838),f324(f106(a838),x61001)),f324(f106(a838),x61002)),f324(f106(a838),f324(f324(f82(a1),x61001),x61002)))+P1(f324(f324(f232(a1),x61001),a85))+P1(f324(f324(f232(a1),x61002),a85))
% 18.77/18.50 [6237]~P69(x62371)+~P1(f324(f324(f232(x62371),f2(x62371)),x62372))+P1(f324(f324(f232(x62371),f324(f81(x62371),x62372)),x62372))
% 18.77/18.50 [6238]~P69(x62381)+~P1(f324(f324(f231(x62381),f2(x62381)),x62382))+P1(f324(f324(f231(x62381),f324(f81(x62381),x62382)),x62382))
% 18.77/18.50 [6420]E(f324(f324(f3(a838),f324(a107,x64201)),f324(a107,x64202)),f324(a107,f324(f324(f3(a1),x64201),x64202)))+~P1(f324(f324(f231(a1),f2(a1)),x64202))+~P1(f324(f324(f231(a1),x64202),x64201))
% 18.77/18.50 [6457]E(f324(a107,f51(a1,f324(f106(a1),x64571),f324(f106(a1),x64572))),f51(a838,f324(f106(a838),x64571),f324(f106(a838),x64572)))+P1(f324(a185,f324(f106(a1),x64571)))+P1(f324(a185,f324(f106(a1),x64572)))
% 18.77/18.50 [6475]~P69(x64751)+P1(f324(f324(f232(x64751),f2(x64751)),x64752))+~P1(f324(f324(f232(x64751),f324(f81(x64751),x64752)),x64752))
% 18.77/18.50 [6476]~P69(x64761)+P1(f324(f324(f231(x64761),f2(x64761)),x64762))+~P1(f324(f324(f231(x64761),f324(f81(x64761),x64762)),x64762))
% 18.77/18.50 [6487]~P69(x64871)+~P1(f324(f324(f232(x64871),f2(x64871)),x64872))+P1(f324(f324(f232(x64871),f2(x64871)),f324(f324(f82(x64871),x64872),x64872)))
% 18.77/18.50 [6489]~P69(x64891)+~P1(f324(f324(f231(x64891),f2(x64891)),x64892))+P1(f324(f324(f231(x64891),f2(x64891)),f324(f324(f82(x64891),x64892),x64892)))
% 18.77/18.50 [6499]E(f324(f324(f82(a838),f324(a107,x64991)),f324(a107,x64992)),f324(a107,f324(f324(f82(a1),x64991),x64992)))+~P1(f324(f324(f231(a1),f2(a1)),x64992))+~P1(f324(f324(f231(a1),f2(a1)),x64991))
% 18.77/18.50 [6500]E(f324(f324(f83(a838),f324(a107,x65001)),f324(a107,x65002)),f324(a107,f324(f324(f83(a1),x65001),x65002)))+~P1(f324(f324(f231(a1),f2(a1)),x65002))+~P1(f324(f324(f231(a1),f2(a1)),x65001))
% 18.77/18.50 [6501]E(f324(f324(f82(a838),f324(a107,x65011)),f324(a107,x65012)),f324(a107,f324(f324(f82(a1),x65011),x65012)))+~P1(f324(f324(f231(a1),f2(a1)),x65012))+~P1(f324(f324(f231(a1),f2(a1)),x65011))
% 18.77/18.50 [6502]E(f324(f324(f42(a838),f324(a107,x65021)),f324(a107,x65022)),f324(a107,f324(f324(f42(a1),x65021),x65022)))+~P1(f324(f324(f231(a1),f2(a1)),x65022))+~P1(f324(f324(f231(a1),f2(a1)),x65021))
% 18.77/18.50 [6513]E(x65131,f2(a838))+P1(f324(f324(f232(a838),f2(a838)),x65132))+~P1(f324(f324(f232(a838),f2(a838)),f324(f324(f240(a838),x65132),x65131)))
% 18.77/18.50 [6546]~P89(x65461)+E(f324(f106(x65461),x65462),f2(x65461))+~P33(x65461,f324(f106(x65461),f324(f324(f82(a1),a85),f324(f81(a1),x65462))))
% 18.77/18.50 [6547]~P89(x65471)+E(f324(f106(x65471),x65472),f2(x65471))+~P33(x65471,f324(f106(x65471),f324(f324(f82(a1),x65472),f324(f81(a1),a85))))
% 18.77/18.50 [6609]~P1(f324(f64(x66091),x66092))+~P1(f324(f64(x66091),f238(f845(x66091,a832))))+P1(f324(f64(x66091),f324(f81(f845(x66091,a832)),x66092)))
% 18.77/18.50 [6634]~P1(f324(f324(f232(a1),f2(a1)),x66342))+~P1(f324(f324(f231(a1),x66342),x66341))+P1(f324(f324(f232(a1),f2(a1)),f324(f324(f42(a1),x66341),x66342)))
% 18.77/18.50 [6635]~P1(f324(f324(f232(a1),x66352),f2(a1)))+~P1(f324(f324(f231(a1),x66351),f2(a1)))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f42(a1),x66351),x66352)))
% 18.77/18.50 [6676]~P1(f324(f324(f232(a838),f2(a838)),x66762))+~P1(f324(f324(f232(a838),f2(a838)),x66761))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f83(a838),x66761),x66762)))
% 18.77/18.50 [6677]~P1(f324(f324(f231(a1),f2(a1)),x66772))+~P1(f324(f324(f231(a1),f2(a1)),x66771))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f83(a1),x66771),x66772)))
% 18.77/18.50 [6678]~P1(f324(f324(f231(a1),f2(a1)),x66782))+~P1(f324(f324(f231(a1),f2(a1)),x66781))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),x66781),x66782)))
% 18.77/18.50 [6679]~P1(f324(f324(f232(a1),f2(a1)),x66792))+~P1(f324(f324(f231(a1),f2(a1)),x66791))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f42(a1),x66791),x66792)))
% 18.77/18.50 [6680]~P1(f324(f324(f231(a1),f2(a1)),x66802))+~P1(f324(f324(f231(a1),f2(a1)),x66801))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f42(a1),x66801),x66802)))
% 18.77/18.50 [6752]E(x67521,f2(a1))+E(f51(a1,x67522,x67521),f2(a1))+E(f324(f324(f3(a1),f324(f81(a1),f324(f324(f42(a1),x67522),x67521))),f80(a1)),f324(f324(f42(a1),f324(f81(a1),x67522)),x67521))
% 18.77/18.50 [6812]P1(f324(f324(f232(a838),f2(a838)),x68121))+P1(f324(f324(f232(a838),f2(a838)),x68122))+~P1(f324(f324(f232(a838),f2(a838)),f324(f324(f82(a838),x68122),x68121)))
% 18.77/18.50 [6813]~P69(x68131)+P1(f324(f324(f232(x68131),f2(x68131)),x68132))+~P1(f324(f324(f232(x68131),f2(x68131)),f324(f324(f82(x68131),x68132),x68132)))
% 18.77/18.50 [6814]~P69(x68141)+P1(f324(f324(f231(x68141),f2(x68141)),x68142))+~P1(f324(f324(f231(x68141),f2(x68141)),f324(f324(f82(x68141),x68142),x68142)))
% 18.77/18.50 [6867]~P1(f324(f64(x68671),x68672))+P1(f324(f64(x68671),f238(f845(x68671,a832))))+~P1(f324(f64(x68671),f324(f81(f845(x68671,a832)),x68672)))
% 18.77/18.50 [6927]P1(f324(f324(f231(a1),x69271),f2(a1)))+~P1(f324(f324(f232(a1),x69272),f2(a1)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f42(a1),x69271),x69272)))
% 18.77/18.50 [6933]~P1(f324(f324(f232(a1),f2(a1)),x69331))+P1(f324(f324(f231(a1),x69331),x69332))+~P1(f324(f324(f232(a1),f2(a1)),f324(f324(f42(a1),x69332),x69331)))
% 18.77/18.50 [6934]~P1(f324(f324(f231(a1),f2(a1)),x69342))+P1(f324(f324(f231(a1),x69341),x69342))+~P1(f324(f324(f232(a1),f2(a1)),f324(f324(f42(a1),x69342),x69341)))
% 18.77/18.50 [6966]P1(f324(f324(f232(a1),f2(a1)),x69661))+~P1(f324(f324(f231(a1),f2(a1)),x69662))+~P1(f324(f324(f232(a1),f2(a1)),f324(f324(f42(a1),x69662),x69661)))
% 18.77/18.50 [6967]P1(f324(f324(f231(a1),f2(a1)),x69671))+~P1(f324(f324(f232(a1),f2(a1)),x69672))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f42(a1),x69671),x69672)))
% 18.77/18.50 [7067]E(f210(x70671,x70672),x70671)+~E(x70672,f2(a838))+~P1(f324(f313(f844(a838,a838),a213),f324(f324(f247(a838,a838),x70671),x70672)))
% 18.77/18.50 [7295]E(f162(x72951,x72952),f115(a1))+P1(f324(f324(f231(a1),x72951),x72952))+~P1(f324(f313(f844(a1,a1),a167),f324(f324(f247(a1,a1),x72951),x72952)))
% 18.77/18.50 [7320]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f82(a1),x73201),x73202)),f56(x73201,x73202))+~P1(f324(f324(f232(a1),f2(a1)),x73202))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),x73201),x73202)))
% 18.77/18.50 [7347]E(x73471,f2(a838))+E(f210(x73471,f51(a838,x73472,x73471)),f210(x73472,x73471))+~P1(f324(f313(f844(a838,a838),a213),f324(f324(f247(a838,a838),x73472),x73471)))
% 18.77/18.50 [7438]~P1(f324(f64(x74382),f238(f845(x74382,a832))))+~P1(f324(f64(x74381),f238(f845(x74381,a832))))+P1(f324(f64(f844(x74381,x74382)),f238(f845(f844(x74381,x74382),a832))))
% 18.77/18.50 [7439]~P1(f324(f64(x74392),f238(f845(x74392,a832))))+~P1(f324(f64(x74391),f238(f845(x74391,a832))))+P1(f324(f64(f848(x74391,x74392)),f238(f845(f848(x74391,x74392),a832))))
% 18.77/18.50 [7511]~P1(f324(f324(f232(a838),f324(a114,f2(a838))),x75111))+~P1(f324(f324(f232(a838),f324(a114,f2(a838))),x75112))+P1(f324(f324(f232(a838),x75111),f324(f324(f83(a838),x75112),x75111)))
% 18.77/18.50 [7512]~P1(f324(f324(f232(a838),f324(a114,f2(a838))),x75121))+~P1(f324(f324(f232(a838),f324(a114,f2(a838))),x75122))+P1(f324(f324(f232(a838),x75121),f324(f324(f83(a838),x75121),x75122)))
% 18.77/18.50 [7547]E(f324(f41(x75471),f238(f845(x75471,a832))),f324(a114,f2(a838)))+P1(f324(f64(x75472),f238(f845(x75472,a832))))+~P1(f324(f64(f845(x75472,x75471)),f238(f845(f845(x75472,x75471),a832))))
% 18.77/18.50 [7599]E(f53(x75991,x75992),f324(f324(f247(a1,a1),f2(a1)),x75991))+~P1(f324(f324(f232(a1),x75991),x75992))+~P1(f324(f313(f844(a1,a1),a62),f324(f324(f247(a1,a1),x75991),x75992)))
% 18.77/18.50 [7603]E(f209(f324(f81(a1),x76031),f324(f81(a1),x76032)),f209(x76031,x76032))+~P1(f324(f324(f232(a1),x76032),f2(a1)))+~P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),x76031),x76032)))
% 18.77/18.50 [7621]E(f53(x76211,x76212),f324(f324(f247(a1,a1),f2(a1)),x76211))+~P1(f324(f324(f231(a1),x76212),f2(a1)))+~P1(f324(f313(f844(a1,a1),a62),f324(f324(f247(a1,a1),x76211),x76212)))
% 18.77/18.50 [7673]~P1(f324(f324(f232(a838),f324(a114,f2(a838))),x76732))+~P1(f324(f324(f232(a838),f324(a114,f2(a838))),x76731))+P1(f324(f324(f232(a838),f324(a114,f2(a838))),f324(f324(f83(a838),x76731),x76732)))
% 18.77/18.50 [7674]~P1(f324(f324(f231(a838),f324(a114,f2(a838))),x76741))+~P1(f324(f324(f231(a838),f324(a114,f2(a838))),x76742))+P1(f324(f324(f231(a838),f324(a114,f2(a838))),f324(f324(f83(a838),x76741),x76742)))
% 18.77/18.50 [7838]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f82(a1),x78381),x78382)),f56(x78381,x78382))+~P1(f324(f324(f231(a1),x78382),f2(a1)))+~P1(f324(f313(f844(a1,a1),a58),f324(f324(f247(a1,a1),x78381),x78382)))
% 18.77/18.50 [7880]E(f324(f324(f139(a1),x78801),f162(f324(f324(f82(a1),x78801),f80(a1)),x78802)),f162(x78801,x78802))+~P1(f324(f324(f231(a1),x78801),x78802))+~P1(f324(f313(f844(a1,a1),a167),f324(f324(f247(a1,a1),x78801),x78802)))
% 18.77/18.50 [8159]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f82(a1),x81591),x81592)),f56(x81591,x81592))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),x81591),x81592)))+~P1(f324(f313(f844(a1,a1),a58),f324(f324(f247(a1,a1),x81591),x81592)))
% 18.77/18.50 [8365]E(x83651,f115(x83652))+~P1(f324(f127(x83652),x83651))+E(f161(x83652,f324(f324(f10(a832,a832,x83652),a320),f324(f324(f9(x83652,x83652,a832),a321),f133(x83652,x83651))),x83651),f116(x83652,x83651))
% 18.77/18.50 [8439]E(f324(f324(f247(a1,a1),f324(f106(a1),a99)),f324(f324(f82(a1),f324(f106(a1),x84391)),f324(f106(a1),x84392))),f56(f324(f106(a1),x84391),f324(f106(a1),x84392)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x84392)))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f324(f106(a1),x84391)),f324(f106(a1),x84392))))
% 18.77/18.50 [8460]~P38(x84602)+~P38(x84601)+E(f324(f304(a838,a1,f102(a1)),f324(f324(f103(f845(a838,a832)),f324(f304(a1,a838,a107),x84601)),f324(f304(a1,a838,a107),x84602))),f324(f324(f103(f845(a1,a832)),x84601),x84602))
% 18.77/18.50 [8461]~P38(x84612)+~P38(x84611)+E(f324(f304(a838,a1,f102(a1)),f324(f324(f104(f845(a838,a832)),f324(f304(a1,a838,a107),x84611)),f324(f304(a1,a838,a107),x84612))),f324(f324(f104(f845(a1,a832)),x84611),x84612))
% 18.77/18.50 [9048]~P89(x90481)+~E(f324(f106(x90481),x90482),f80(x90481))+P33(x90481,f324(f106(x90481),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f81(a1),x90482))))
% 18.77/18.50 [9265]~P89(x92651)+E(f324(f106(x92651),x92652),f80(x92651))+~P33(x92651,f324(f106(x92651),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f81(a1),x92652))))
% 18.77/18.50 [9687]~P85(x96872)+P51(a838,x96872,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96871)+P1(f324(f324(f280(a838),f829(x96871,x96872)),f336(x96871,x96872)))
% 18.77/18.50 [9690]~P85(x96901)+P51(a838,x96901,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96902)+~P1(f324(f324(f280(a838),f336(x96902,x96901)),f829(x96902,x96901)))
% 18.77/18.50 [9691]~P85(x96911)+P51(a838,x96911,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x96912)+~P1(f324(f324(f232(x96911),f324(x96912,f829(x96912,x96911))),f324(x96912,f336(x96912,x96911))))
% 18.77/18.50 [9779]~P85(x97791)+P50(a838,x97791,f280(a838),x97792)+~P51(a838,x97791,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97792)
% 18.77/18.50 [9979]E(x99791,f2(a1))+E(x99792,f2(a1))+E(f324(f253(a1,a1,a1,a1,f37(a1),f324(f83(a1),f84(a1,x99792))),f324(f324(f324(f98(f844(a1,a1)),f324(f324(a321,f84(a1,x99791)),f84(a1,x99792))),f59(x99791,x99792)),f324(f324(f252(a1,a1,f844(a1,a1)),f324(f324(f20(a1,f845(a1,f844(a1,a1)),f845(a1,f844(a1,a1))),f324(f324(f10(f845(a1,f845(f844(a1,a1),f844(a1,a1))),f845(f845(a1,f844(a1,a1)),f845(a1,f844(a1,a1))),a1),f20(a1,f844(a1,a1),f844(a1,a1))),f324(f324(f10(f844(a1,a1),f845(a1,f845(f844(a1,a1),f844(a1,a1))),a1),f324(f9(a1,f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),f324(f324(f10(a832,f845(f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),a1),f98(f844(a1,a1))),f324(f324(f9(a1,a1,a832),a321),f2(a1))))),f324(f324(f9(a1,a1,f844(a1,a1)),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f81(a1))),f2(a1))))),f324(f324(f9(a1,f845(a1,a1),f845(a1,f844(a1,a1))),f324(f324(f10(f845(a1,f844(a1,a1)),f845(f845(a1,a1),f845(a1,f844(a1,a1))),a1),f10(a1,f844(a1,a1),a1)),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f324(f324(f9(a1,a1,a1),f324(f324(f10(a1,f845(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f324(f3(a1),f324(f77(a1),x99792))))),f59(x99791,x99792)))),f52(x99791,x99792))
% 18.77/18.50 [9980]E(x99801,f2(a1))+E(x99802,f2(a1))+E(f324(f253(a1,a1,a1,a1,f37(a1),f324(f83(a1),f84(a1,x99802))),f324(f324(f324(f98(f844(a1,a1)),f324(f324(a323,f324(f324(a322,f324(f324(f232(a1),f2(a1)),x99802)),f324(f324(f231(a1),f2(a1)),x99801))),f324(f324(a322,f324(f324(f232(a1),x99802),f2(a1))),f324(f324(f232(a1),x99801),f2(a1))))),f59(x99801,x99802)),f324(f324(f252(a1,a1,f844(a1,a1)),f324(f324(f20(a1,f845(a1,f844(a1,a1)),f845(a1,f844(a1,a1))),f324(f324(f10(f845(a1,f845(f844(a1,a1),f844(a1,a1))),f845(f845(a1,f844(a1,a1)),f845(a1,f844(a1,a1))),a1),f20(a1,f844(a1,a1),f844(a1,a1))),f324(f324(f10(f844(a1,a1),f845(a1,f845(f844(a1,a1),f844(a1,a1))),a1),f324(f9(a1,f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),f324(f324(f10(a832,f845(f844(a1,a1),f845(f844(a1,a1),f844(a1,a1))),a1),f98(f844(a1,a1))),f324(f324(f9(a1,a1,a832),a321),f2(a1))))),f324(f324(f9(a1,a1,f844(a1,a1)),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f81(a1))),f2(a1))))),f324(f324(f9(a1,f845(a1,a1),f845(a1,f844(a1,a1))),f324(f324(f10(f845(a1,f844(a1,a1)),f845(f845(a1,a1),f845(a1,f844(a1,a1))),a1),f10(a1,f844(a1,a1),a1)),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f324(f324(f9(a1,a1,a1),f324(f324(f10(a1,f845(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f324(f3(a1),f324(f77(a1),x99802))))),f59(x99801,x99802)))),f52(x99801,x99802))
% 18.77/18.50 [5510]~P103(x55101)+~P89(x55101)+E(f324(f77(x55101),f324(f324(f240(x55101),f324(f106(x55101),a99)),x55102)),f80(x55101))
% 18.77/18.50 [6012]~P119(x60121)+~P1(f324(f324(f232(a1),x60122),f2(a1)))+E(f324(f81(x60121),f324(f102(x60121),f324(a107,f324(f81(a1),x60122)))),f324(f105(x60121),x60122))
% 18.77/18.50 [6221]P1(f324(f324(f231(a101),x62211),f80(a101)))+E(f324(f324(f82(a101),f80(a101)),f268(x62211,f324(f324(f42(a101),x62212),x62211))),f268(x62211,x62212))+P1(f324(f324(f232(a101),x62212),x62211))
% 18.77/18.50 [6294]E(x62941,f2(a1))+~E(f324(f77(a1),x62942),f80(a1))+P1(f324(f324(f280(a1),f324(f324(f83(a1),x62941),x62942)),x62941))
% 18.77/18.50 [6718]~E(x67182,f80(a838))+~P1(f324(f324(f232(a838),f2(a838)),x67181))+P1(f324(f324(f280(a838),f324(f324(f83(a838),x67181),x67182)),x67181))
% 18.77/18.50 [6719]~E(x67191,f80(a838))+~P1(f324(f324(f232(a838),f2(a838)),x67192))+P1(f324(f324(f280(a838),f324(f324(f83(a838),x67191),x67192)),x67192))
% 18.77/18.50 [6855]~P88(x68551)+~P1(f324(f324(f326(x68551),x68552),f112(x68551)))+~E(f324(f324(f82(x68551),f324(f324(f82(x68551),f80(x68551)),x68552)),x68552),f2(x68551))
% 18.77/18.50 [6968]~P1(f324(f324(f232(a1),x69681),f2(a1)))+~P1(f324(f324(f231(a1),x69682),f2(a1)))+E(f324(f246(a1,a1),f324(a57,f53(f324(f81(a1),x69681),f324(f81(a1),x69682)))),f324(f324(f42(a1),x69681),x69682))
% 18.77/18.50 [6984]~P1(f324(f324(f232(a1),x69841),f2(a1)))+~P1(f324(f324(f231(a1),x69842),f2(a1)))+E(f324(f251(a1,a1),f324(a57,f53(f324(f81(a1),x69841),f324(f81(a1),x69842)))),f51(a1,x69841,x69842))
% 18.77/18.50 [6992]~P1(f324(f324(f232(a1),x69922),f2(a1)))+E(f324(f246(a1,a1),f324(a57,f56(f324(f81(a1),x69921),f324(f81(a1),x69922)))),f324(f324(f42(a1),x69921),x69922))+~P1(f324(f324(f232(a1),f2(a1)),x69921))
% 18.77/18.50 [6996]E(x69961,f2(a1))+E(f324(f77(a1),x69962),f80(a1))+~P1(f324(f324(f280(a1),f324(f324(f83(a1),x69961),x69962)),x69961))
% 18.77/18.50 [7011]~P1(f324(f324(f232(a1),x70112),f2(a1)))+E(f324(f251(a1,a1),f324(a57,f56(f324(f81(a1),x70111),f324(f81(a1),x70112)))),f51(a1,x70111,x70112))+~P1(f324(f324(f232(a1),f2(a1)),x70111))
% 18.77/18.50 [7062]E(f324(f324(f42(a1),f324(f324(f240(a1),x70621),x70622)),x70621),f324(f324(f240(a1),x70621),f324(f324(f3(a838),x70622),f324(a114,f2(a838)))))+~P1(f324(f324(f232(a838),f2(a838)),x70622))+~P1(f324(f324(f232(a1),f2(a1)),x70621))
% 18.77/18.50 [7166]~P1(f324(f324(f232(a838),f2(a838)),x71661))+~P1(f324(f324(f232(a838),f80(a838)),x71662))+P1(f324(f324(f232(a838),f324(f324(f42(a838),x71661),x71662)),x71661))
% 18.77/18.50 [7167]~P1(f324(f324(f232(a838),f2(a838)),x71671))+~P1(f324(f324(f232(a838),f2(a838)),x71672))+P1(f324(f324(f232(a838),f324(f324(f3(a838),x71671),x71672)),x71671))
% 18.77/18.50 [7168]~P1(f324(f324(f232(a1),f2(a1)),x71681))+~P1(f324(f324(f232(a1),f80(a1)),x71682))+P1(f324(f324(f232(a1),f324(f324(f42(a1),x71681),x71682)),x71681))
% 18.77/18.50 [7327]E(x73271,f2(a838))+~E(x73272,f2(a1))+~P1(f324(f324(f232(a1),f2(a1)),f324(f324(f240(a1),f324(f77(a1),x73272)),x73271)))
% 18.77/18.50 [7368]E(x73681,f80(a838))+~P1(f324(f324(f232(a838),f2(a838)),x73682))+~P1(f324(f324(f280(a838),f324(f324(f83(a838),x73682),x73681)),x73682))
% 18.77/18.50 [7369]E(x73691,f80(a838))+~P1(f324(f324(f232(a838),f2(a838)),x73692))+~P1(f324(f324(f280(a838),f324(f324(f83(a838),x73691),x73692)),x73692))
% 18.77/18.50 [7758]~E(x77582,f115(f839(x77581)))+E(f324(f180(f839(f839(x77581))),f163(x77581,x77582)),f2(a838))+~P18(a838,f324(f154(a838),f324(f324(f141(f839(x77581),a838),f180(f839(x77581))),x77582)))
% 18.77/18.50 [8012]P1(f324(x80121,x80122))+~P1(f324(x80121,f324(a110,f599(x80121,x80122))))+~P1(f324(f324(f326(f845(f844(a838,a838),a832)),x80122),a100))
% 18.77/18.50 [8027]E(x80271,f115(f839(x80272)))+E(f324(f180(f839(x80272)),f324(f324(f149(f839(x80272)),x80271),f2(a838))),f324(f180(f839(f839(x80272))),f163(x80272,x80271)))+~P18(a838,f324(f154(a838),f324(f324(f141(f839(x80272),a838),f180(f839(x80272))),x80271)))
% 18.77/18.50 [8703]~P1(f324(f64(x87031),f324(f257(x87031),x87032)))+~P1(f324(f64(x87031),f238(f845(x87031,a832))))+P1(f324(f64(x87031),f324(f257(x87031),f324(f324(f10(a832,a832,x87031),a320),x87032))))
% 18.77/18.50 [8758]E(f324(f324(f247(a838,a838),f324(a114,f324(f324(f42(a838),f324(f324(f3(a838),x87581),x87582)),x87582))),f51(a838,f324(f324(f3(a838),x87581),x87582),x87582)),f87(f844(a838,a838),f54(x87581,x87582)))+~P1(f324(f324(f232(a838),f2(a838)),x87582))+~P1(f324(f324(f231(a838),x87582),x87581))
% 18.77/18.50 [9015]~P1(f324(f64(x90151),f324(f257(x90151),x90152)))+P1(f324(f64(x90151),f238(f845(x90151,a832))))+~P1(f324(f64(x90151),f324(f257(x90151),f324(f324(f10(a832,a832,x90151),a320),x90152))))
% 18.77/18.50 [9684]P30(x96841,x96842)+~P36(x96841,f324(f246(f845(f844(x96841,x96841),a832),f845(f844(x96841,x96841),a832)),x96842))+~P1(f324(f324(f231(f845(f844(x96841,x96841),a832)),f324(f324(f282(x96841,x96841,x96841),f324(f246(f845(f844(x96841,x96841),a832),f845(f844(x96841,x96841),a832)),x96842)),f324(f251(f845(f844(x96841,x96841),a832),f845(f844(x96841,x96841),a832)),x96842))),f324(f246(f845(f844(x96841,x96841),a832),f845(f844(x96841,x96841),a832)),x96842)))
% 18.77/18.50 [9731]E(f324(f49(f324(f106(a1),x97311)),f53(f324(f106(a1),x97312),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f106(a1),x97311)))),f53(f324(f106(a1),x97312),f324(f106(a1),x97311)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x97311)))+P1(f324(f324(f232(a1),f324(f106(a1),x97312)),f324(f106(a1),x97311)))
% 18.77/18.50 [9737]E(f324(f49(f324(f106(a1),x97371)),f56(f324(f106(a1),x97372),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f106(a1),x97371)))),f56(f324(f106(a1),x97372),f324(f106(a1),x97371)))+~P1(f324(f324(f232(a1),f2(a1)),f324(f106(a1),x97371)))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f324(f106(a1),x97372)),f324(f106(a1),x97371))))
% 18.77/18.50 [9781]~E(f293(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97812,x97811),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x97812),x97811))+P1(f324(f324(f280(a838),x97811),x97812))
% 18.77/18.50 [9782]~E(f290(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97822,x97821),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x97822),x97821))+P1(f324(f324(f280(a838),x97821),x97822))
% 18.77/18.50 [9783]~E(f293(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97832,x97831),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x97832),x97831))+P1(f324(f324(f280(a838),x97831),x97832))
% 18.77/18.50 [9784]~E(f290(a838,f280(a838),f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97842,x97841),f179(f845(a838,a832)))+~P1(f324(f324(f280(a838),x97842),x97841))+P1(f324(f324(f280(a838),x97841),x97842))
% 18.77/18.50 [7085]~P1(f324(f324(f232(a838),f2(a838)),x70852))+P1(f324(f324(f232(a838),x70851),x70852))+E(f324(a114,f324(f324(f42(a838),f324(f324(f3(a838),x70851),x70852)),x70852)),f324(f324(f42(a838),x70851),x70852))
% 18.77/18.50 [7086]~P1(f324(f324(f232(a838),f2(a838)),x70862))+P1(f324(f324(f232(a838),x70861),x70862))+E(f324(a114,f324(f324(f42(a838),f324(f324(f3(a838),x70861),x70862)),x70862)),f324(f324(f42(a838),x70861),x70862))
% 18.77/18.50 [7242]~P1(f324(f324(f232(a838),f2(a838)),x72422))+~P1(f324(f324(f231(a838),x72422),x72421))+E(f324(a114,f324(f324(f42(a838),f324(f324(f3(a838),x72421),x72422)),x72422)),f324(f324(f42(a838),x72421),x72422))
% 18.77/18.50 [8229]~P89(x82291)+~P88(x82291)+~P33(x82291,f324(f106(x82291),f324(f324(f3(a1),f324(f324(f82(a1),x82292),x82292)),a99)))
% 18.77/18.50 [8931]E(x89311,f2(a838))+E(f324(f324(f252(a838,a838,f844(a838,a838)),f324(f324(f10(a838,f845(a838,f844(a838,a838)),a838),f247(a838,a838)),a114)),f87(f844(a838,a838),f54(f324(f324(f3(a838),x89312),x89311),x89311))),f87(f844(a838,a838),f54(x89312,x89311)))+P1(f324(f324(f232(a838),x89312),x89311))
% 18.77/18.50 [9324]P1(f324(x93242,f348(x93242,x93241)))+P1(f324(x93241,f348(x93242,x93241)))+E(f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x93241)),f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x93242)))
% 18.77/18.50 [9328]~P1(f324(x93282,f348(x93282,x93281)))+~P1(f324(x93281,f348(x93282,x93281)))+E(f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x93281)),f324(f257(a1),f324(f324(f20(a1,a832,a832),f324(f324(f10(a832,f845(a832,a832),a1),a322),f324(f231(a1),f2(a1)))),x93282)))
% 18.77/18.50 [9866]~P1(f324(f324(f280(a838),x98662),x98661))+P1(f324(f324(f280(a838),x98661),x98662))+P1(f324(f324(f326(a838),x98661),f288(a838,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x98662)))
% 18.77/18.50 [9867]~P1(f324(f324(f280(a838),x98672),x98671))+P1(f324(f324(f280(a838),x98671),x98672))+P1(f324(f324(f326(a838),x98672),f291(a838,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x98671)))
% 18.77/18.50 [7467]~P89(x74671)+~P60(x74671)+E(f324(f324(f284(x74671),x74672),f324(f106(x74671),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),x74672)
% 18.77/18.50 [7468]~P89(x74681)+~P60(x74681)+E(f324(f324(f284(x74681),x74682),f324(f106(x74681),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))),x74682)
% 18.77/18.50 [9047]~P89(x90471)+~E(f324(f106(x90471),x90472),f80(x90471))+P33(x90471,f324(f106(x90471),f324(f324(f82(a1),x90472),f324(f81(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.77/18.50 [9204]~P133(x92041)+~E(x92042,f2(x92041))+E(f324(f324(f240(x92041),x92042),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f2(x92041))
% 18.77/18.50 [9205]~P133(x92051)+~E(x92052,f80(x92051))+E(f324(f324(f240(x92051),x92052),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f80(x92051))
% 18.77/18.50 [9218]~P133(x92181)+~E(x92182,f324(f81(x92181),f80(x92181)))+E(f324(f324(f240(x92181),x92182),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f80(x92181))
% 18.77/18.50 [9238]~P75(x92381)+~P90(x92381)+E(f324(f324(f240(x92381),f324(f106(x92381),x92382)),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f83(x92381),f324(f106(x92381),x92382)),f324(f106(x92381),x92382)))
% 18.77/18.50 [9266]~P89(x92661)+E(f324(f106(x92661),x92662),f80(x92661))+~P33(x92661,f324(f106(x92661),f324(f324(f82(a1),x92662),f324(f81(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.77/18.50 [9376]~P133(x93762)+E(x93761,f2(x93762))+~E(f324(f324(f240(x93762),x93761),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f2(x93762))
% 18.77/18.50 [9625]~P103(x96252)+E(x96251,f2(x96252))+P1(f324(f324(f232(x96252),f2(x96252)),f324(f324(f240(x96252),x96251),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.77/18.50 [9683]~P103(x96832)+~E(x96831,f2(x96832))+~P1(f324(f324(f232(x96832),f2(x96832)),f324(f324(f240(x96832),x96831),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.77/18.50 [9722]P1(f324(f324(f231(a1),x97221),f2(a1)))+P1(f324(f324(f232(a1),x97222),x97221))+E(f324(f49(x97221),f53(x97222,f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97221))),f53(x97222,x97221))
% 18.77/18.50 [9723]~P1(f324(f324(f232(a1),f2(a1)),x97231))+P1(f324(f324(f232(a1),x97232),x97231))+E(f324(f49(x97231),f53(x97232,f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97231))),f53(x97232,x97231))
% 18.77/18.50 [9724]P1(f324(f324(f231(a1),x97241),f2(a1)))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),x97242),x97241)))+E(f324(f49(x97241),f56(x97242,f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97241))),f56(x97242,x97241))
% 18.77/18.50 [9725]~P1(f324(f324(f232(a1),f2(a1)),x97251))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),x97252),x97251)))+E(f324(f49(x97251),f56(x97252,f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97251))),f56(x97252,x97251))
% 18.77/18.50 [9726]~P2(x97261)+~P1(f324(f324(f231(a1),f2(a1)),x97262))+E(f324(f102(x97261),f324(a107,f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97262))),f324(f324(f82(x97261),f324(f102(x97261),f324(a107,x97262))),f324(f102(x97261),f324(a107,x97262))))
% 18.77/18.50 [4864]~P139(x48641,x48642,x48643)+~E(x48643,f2(a1))+P1(f324(x48641,x48642))
% 18.77/18.50 [4986]~P86(x49861)+~P18(x49861,x49863)+P18(x49861,f155(x49861,x49862,x49863))
% 18.77/18.50 [4987]~P86(x49871)+~P18(x49871,x49873)+P18(x49871,f161(x49871,x49872,x49873))
% 18.77/18.50 [4572]~P63(x45722)+~E(x45723,f324(f81(x45722),x45721))+E(x45721,f324(f81(x45722),x45723))
% 18.77/18.50 [4573]~P63(x45732)+~E(x45733,f324(f81(x45732),x45731))+E(x45731,f324(f81(x45732),x45733))
% 18.77/18.50 [4574]~P63(x45741)+~E(f324(f81(x45741),x45743),x45742)+E(f324(f81(x45741),x45742),x45743)
% 18.77/18.50 [4575]~P63(x45751)+~E(f324(f81(x45751),x45753),x45752)+E(f324(f81(x45751),x45752),x45753)
% 18.77/18.50 [4648]~P87(x46483)+E(x46481,x46482)+~E(f324(f102(x46483),x46481),f324(f102(x46483),x46482))
% 18.77/18.50 [4649]~P88(x46493)+E(x46491,x46492)+~E(f324(f105(x46493),x46491),f324(f105(x46493),x46492))
% 18.77/18.50 [4650]~P63(x46503)+E(x46501,x46502)+~E(f324(f81(x46503),x46501),f324(f81(x46503),x46502))
% 18.77/18.50 [4651]~P91(x46513)+E(x46511,x46512)+~E(f324(f81(x46513),x46511),f324(f81(x46513),x46512))
% 18.77/18.50 [4652]~P86(x46523)+E(x46521,x46522)+~E(f324(f294(x46523),x46521),f324(f294(x46523),x46522))
% 18.77/18.50 [4653]~P86(x46533)+E(x46531,x46532)+~E(f324(f258(x46533),x46531),f324(f258(x46533),x46532))
% 18.77/18.50 [4654]~P86(x46543)+E(x46541,x46542)+~E(f324(f259(x46543),x46541),f324(f259(x46543),x46542))
% 18.77/18.50 [4655]~P86(x46553)+E(x46551,x46552)+~E(f324(f297(x46553),x46551),f324(f297(x46553),x46552))
% 18.77/18.50 [4883]~P140(x48831,x48833,x48832)+~E(x48832,f2(a1))+P1(f324(x48831,f2(a1)))
% 18.77/18.50 [4922]~E(x49221,f2(a838))+E(f379(x49221,x49222,x49223),f179(f845(x49223,a832)))+~E(f324(f41(x49223),x49222),f324(a114,x49221))
% 18.77/18.50 [5069]~E(x50692,f2(a838))+E(f324(f246(a838,a838),x50691),f2(a838))+~P1(f324(f54(x50693,x50692),x50691))
% 18.77/18.50 [5113]P1(f324(x51131,x51132))+~E(x51133,f324(f102(a1),x51132))+~P1(f324(x51131,f324(a107,x51133)))
% 18.77/18.50 [5572]~E(x55723,f2(a838))+~P1(f324(x55721,x55722))+P1(f324(x55721,f51(a838,x55722,x55723)))
% 18.77/18.50 [5716]~P1(f324(a26,x57163))+~P1(f324(a26,x57162))+P1(f324(a26,f33(x57161,x57162,x57163)))
% 18.77/18.50 [5717]~P1(f324(a26,x57173))+~P1(f324(a26,x57172))+P1(f324(a26,f33(x57171,x57172,x57173)))
% 18.77/18.50 [5994]~E(x59943,f2(a838))+P1(f324(x59941,x59942))+~P1(f324(x59941,f51(a838,x59942,x59943)))
% 18.77/18.50 [6702]E(x67021,f2(a838))+~P1(f324(x67022,f779(x67021,x67023,x67022)))+P1(f324(x67022,f51(a838,x67023,x67021)))
% 18.77/18.50 [6818]~P9(x68181)+~P1(f324(f324(f231(x68181),x68182),f653(x68183,x68182,x68181)))+P1(f324(f324(f231(x68181),x68182),f44(x68181,x68183)))
% 18.77/18.50 [6820]~P1(f324(x68201,x68202))+~P1(f324(x68201,f779(x68203,x68202,x68201)))+P1(f324(x68201,f51(a838,x68202,x68203)))
% 18.77/18.50 [6920]E(x69201,f115(x69202))+E(f324(f324(f139(x69202),f735(x69203,x69201,x69202)),f744(x69203,x69201,x69202)),x69201)+~P1(f324(f324(f326(f839(x69202)),x69201),f147(x69202,x69203)))
% 18.77/18.50 [6954]~P119(x69541)+~P1(f324(f324(f326(x69541),x69542),f112(x69541)))+P1(f324(f324(f326(x69541),f324(f324(f240(x69541),x69542),x69543)),f112(x69541)))
% 18.77/18.50 [7294]P36(x72941,x72942)+~P1(f324(f324(f326(x72941),x72943),f368(x72942,x72941)))+P1(f324(f324(f326(x72941),f370(x72942,x72941,x72943)),f368(x72942,x72941)))
% 18.77/18.50 [7573]E(x75731,f115(x75732))+~P1(f324(f324(f326(f839(x75732)),x75731),f147(x75732,x75733)))+P1(f324(f324(f326(f839(x75732)),f744(x75733,x75731,x75732)),f147(x75732,x75733)))
% 18.77/18.50 [7624]E(x76241,f2(a838))+E(f324(f324(f82(a838),f324(f324(f83(a838),x76241),f780(x76241,x76242,x76243))),f779(x76241,x76242,x76243)),x76242)+P1(f324(x76243,f51(a838,x76242,x76241)))
% 18.77/18.50 [7667]~P1(f324(x76673,x76672))+E(f324(f324(f82(a838),f324(f324(f83(a838),x76671),f780(x76671,x76672,x76673))),f779(x76671,x76672,x76673)),x76672)+P1(f324(x76673,f51(a838,x76672,x76671)))
% 18.77/18.50 [7813]P1(f324(f324(f232(a1),x78131),f718(x78132,x78133,x78131)))+P1(f324(f324(x78133,f324(f324(f42(a1),x78132),x78131)),f51(a1,x78132,x78131)))+~P1(f324(f324(f232(a1),x78131),f2(a1)))
% 18.77/18.50 [8085]P1(f324(f324(x80852,f324(f324(f42(a1),x80851),x80853)),f51(a1,x80851,x80853)))+~P1(f324(f324(f232(a1),x80853),f2(a1)))+P1(f324(f324(f231(a1),f718(x80851,x80852,x80853)),f2(a1)))
% 18.77/18.50 [8266]E(f324(f324(f82(a1),f324(f324(f83(a1),x82661),f719(x82662,x82663,x82661))),f718(x82662,x82663,x82661)),x82662)+P1(f324(f324(x82663,f324(f324(f42(a1),x82662),x82661)),f51(a1,x82662,x82661)))+~P1(f324(f324(f232(a1),x82661),f2(a1)))
% 18.77/18.50 [8498]~P1(f324(f324(x84981,f719(x84982,x84981,x84983)),f718(x84982,x84981,x84983)))+P1(f324(f324(x84981,f324(f324(f42(a1),x84982),x84983)),f51(a1,x84982,x84983)))+~P1(f324(f324(f232(a1),x84983),f2(a1)))
% 18.77/18.50 [8713]~P86(x87131)+~P18(x87131,x87133)+P18(x87131,f138(x87131,x87131,f7(x87131),x87132,x87133))
% 18.77/18.50 [9154]~P117(x91542)+E(x91541,f2(x91542))+~P1(f324(f324(f231(x91542),f324(f324(f82(x91542),f324(f324(f83(x91542),x91543),x91543)),f324(f324(f83(x91542),x91541),x91541))),f2(x91542)))
% 18.77/18.50 [9155]~P117(x91552)+E(x91551,f2(x91552))+~P1(f324(f324(f231(x91552),f324(f324(f82(x91552),f324(f324(f83(x91552),x91551),x91551)),f324(f324(f83(x91552),x91553),x91553))),f2(x91552)))
% 18.77/18.50 [9919]~P103(x99191)+~P1(f324(f324(f232(x99191),x99192),f2(x99191)))+P1(f324(f324(f232(x99191),f324(f324(f240(x99191),x99192),f324(a114,f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x99193)))),f2(x99191)))
% 18.77/18.50 [9928]~P103(x99282)+E(x99281,f2(x99282))+~P1(f324(f324(f231(x99282),f324(f324(f82(x99282),f324(f324(f240(x99282),x99283),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x99282),x99281),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f2(x99282)))
% 18.77/18.50 [9929]~P103(x99292)+E(x99291,f2(x99292))+~P1(f324(f324(f231(x99292),f324(f324(f82(x99292),f324(f324(f240(x99292),x99291),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x99292),x99293),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f2(x99292)))
% 18.77/18.50 [4605]~E(x46052,x46053)+~P63(x46051)+E(f324(f324(f3(x46051),x46052),x46053),f2(x46051))
% 18.77/18.50 [4606]~E(x46062,x46063)+~P6(x46061)+E(f324(f324(f3(x46061),x46062),x46063),f2(x46061))
% 18.77/18.50 [4619]~P136(x46191)+~E(x46193,f2(x46191))+E(f324(f324(f82(x46191),x46192),x46193),x46192)
% 18.77/18.50 [4634]~P132(x46341)+~E(x46343,f2(x46341))+E(f324(f324(f83(x46341),x46342),x46343),f2(x46341))
% 18.77/18.50 [4635]~P132(x46351)+~E(x46352,f2(x46351))+E(f324(f324(f83(x46351),x46352),x46353),f2(x46351))
% 18.77/18.50 [4656]~E(x46563,f115(x46561))+~E(x46562,f115(x46561))+E(f324(f324(f125(x46561),x46562),x46563),f115(x46561))
% 18.77/18.50 [4657]~E(x46573,f115(x46571))+~E(x46572,f115(x46571))+E(f324(f324(f125(x46571),x46572),x46573),f115(x46571))
% 18.77/18.50 [4742]~P136(x47422)+E(x47421,f2(x47422))+~E(f324(f324(f82(x47422),x47423),x47421),x47423)
% 18.77/18.50 [4743]~P63(x47431)+~E(x47432,f324(f81(x47431),x47433))+E(f324(f324(f82(x47431),x47432),x47433),f2(x47431))
% 18.77/18.50 [4750]E(x47501,f115(x47502))+E(x47503,f2(a838))+~E(f324(f324(f158(x47502),x47503),x47501),f115(x47502))
% 18.77/18.50 [4758]~P63(x47583)+E(x47581,x47582)+~E(f324(f324(f3(x47583),x47581),x47582),f2(x47583))
% 18.77/18.50 [4759]~P6(x47593)+E(x47591,x47592)+~E(f324(f324(f3(x47593),x47591),x47592),f2(x47593))
% 18.77/18.50 [4768]~P133(x47682)+E(x47681,f2(x47682))+~E(f324(f324(f240(x47682),x47681),x47683),f2(x47682))
% 18.77/18.50 [4769]~P95(x47692)+E(x47691,f179(x47692))+~E(f324(f324(f103(x47692),x47693),x47691),f179(x47692))
% 18.77/18.50 [4770]~P95(x47702)+E(x47701,f179(x47702))+~E(f324(f324(f103(x47702),x47701),x47703),f179(x47702))
% 18.77/18.50 [4771]~P98(x47712)+E(x47711,f238(x47712))+~E(f324(f324(f104(x47712),x47713),x47711),f238(x47712))
% 18.77/18.50 [4772]~P98(x47722)+E(x47721,f238(x47722))+~E(f324(f324(f104(x47722),x47721),x47723),f238(x47722))
% 18.77/18.50 [4837]~P63(x48372)+E(x48371,f324(f81(x48372),x48373))+~E(f324(f324(f82(x48372),x48371),x48373),f2(x48372))
% 18.77/18.50 [4838]~P63(x48381)+E(f324(f81(x48381),x48382),x48383)+~E(f324(f324(f82(x48381),x48382),x48383),f2(x48381))
% 18.77/18.50 [4839]~E(x48392,x48393)+~P85(x48391)+P1(f324(f324(f231(x48391),x48392),x48393))
% 18.77/18.50 [4840]~E(x48402,x48403)+~P85(x48401)+P1(f324(f324(f231(x48401),x48402),x48403))
% 18.77/18.50 [4841]~E(x48412,x48413)+~P85(x48411)+P1(f324(f324(f231(x48411),x48412),x48413))
% 18.77/18.50 [4842]~E(x48422,x48423)+~P102(x48421)+P1(f324(f324(f231(x48421),x48422),x48423))
% 18.77/18.50 [4936]~P112(x49361)+~E(x49362,f324(f81(x49361),x49363))+E(f324(f324(f83(x49361),x49362),x49362),f324(f324(f83(x49361),x49363),x49363))
% 18.77/18.50 [4944]~P86(x49441)+~P18(x49441,x49443)+P18(x49441,f324(f324(f158(x49441),x49442),x49443))
% 18.77/18.50 [4945]~P86(x49451)+~P18(x49451,x49453)+P18(x49451,f324(f324(f128(x49451),x49452),x49453))
% 18.77/18.50 [4983]E(x49831,x49832)+E(x49833,f2(a838))+~E(f324(f324(f83(a838),x49833),x49831),f324(f324(f83(a838),x49833),x49832))
% 18.77/18.50 [4984]E(x49841,x49842)+E(x49843,f2(a838))+~E(f324(f324(f83(a838),x49843),x49841),f324(f324(f83(a838),x49843),x49842))
% 18.77/18.50 [4985]E(x49851,x49852)+E(x49853,f2(a838))+~E(f324(f324(f83(a838),x49851),x49853),f324(f324(f83(a838),x49852),x49853))
% 18.77/18.50 [5061]~E(x50612,x50613)+~P85(x50611)+E(f296(x50611,x50612,x50613),f324(f324(f303(x50611),x50612),f179(f845(x50611,a832))))
% 18.77/18.50 [5101]~P103(x51011)+~E(f324(f77(x51011),x51012),f324(f77(x51011),x51013))+P1(f324(f324(f280(x51011),x51012),x51013))
% 18.77/18.50 [5105]~E(x51051,x51052)+~P85(x51053)+~P1(f324(f324(f232(x51053),x51051),x51052))
% 18.77/18.50 [5106]~E(x51061,x51062)+~P85(x51063)+~P1(f324(f324(f232(x51063),x51061),x51062))
% 18.77/18.50 [5107]~E(x51071,x51072)+~P85(x51073)+~P1(f324(f324(f232(x51073),x51071),x51072))
% 18.77/18.50 [5108]~E(x51081,x51082)+~P86(x51083)+~P1(f324(f324(f232(x51083),x51081),x51082))
% 18.77/18.50 [5109]~E(x51091,x51092)+~P86(x51093)+~P1(f324(f324(f232(x51093),x51091),x51092))
% 18.77/18.50 [5110]~E(x51101,x51102)+~P85(x51103)+~P1(f324(f324(f232(x51103),x51101),x51102))
% 18.77/18.50 [5111]~E(x51111,x51112)+~P86(x51113)+~P1(f324(f324(f232(x51113),x51111),x51112))
% 18.77/18.50 [5117]~P85(x51171)+E(f324(f295(x51171,x51172),x51173),f179(f845(x51171,a832)))+P1(f324(f324(f232(x51171),x51172),x51173))
% 18.77/18.50 [5118]~P85(x51181)+E(f324(f295(x51181,x51182),x51183),f179(f845(x51181,a832)))+P1(f324(f324(f232(x51181),x51182),x51183))
% 18.77/18.50 [5164]~P85(x51641)+E(f298(x51641,x51642,x51643),f179(f845(x51641,a832)))+P1(f324(f324(f232(x51641),x51642),x51643))
% 18.77/18.50 [5165]~P85(x51651)+E(f296(x51651,x51652,x51653),f179(f845(x51651,a832)))+P1(f324(f324(f231(x51651),x51652),x51653))
% 18.77/18.50 [5166]~P85(x51661)+E(f179(f845(x51661,a832)),f298(x51661,x51662,x51663))+P1(f324(f324(f232(x51661),x51662),x51663))
% 18.77/18.50 [5167]~P85(x51671)+E(f179(f845(x51671,a832)),f296(x51671,x51672,x51673))+P1(f324(f324(f231(x51671),x51672),x51673))
% 18.77/18.50 [5175]~P86(x51751)+~E(f324(f324(f235(x51751),x51752),x51753),x51752)+P1(f324(f324(f231(x51751),x51752),x51753))
% 18.77/18.50 [5176]~P86(x51761)+~E(f324(f324(f178(x51761),x51762),x51763),x51763)+P1(f324(f324(f231(x51761),x51762),x51763))
% 18.77/18.50 [5177]~P93(x51771)+~E(f324(f324(f103(x51771),x51772),x51773),x51773)+P1(f324(f324(f231(x51771),x51772),x51773))
% 18.77/18.50 [5178]~P99(x51781)+~E(f324(f324(f104(x51781),x51782),x51783),x51782)+P1(f324(f324(f231(x51781),x51782),x51783))
% 18.77/18.50 [5193]~P86(x51931)+P18(x51931,x51932)+~P18(x51931,f324(f324(f139(x51931),x51933),x51932))
% 18.77/18.50 [5194]~P86(x51941)+P18(x51941,x51942)+~P18(x51941,f324(f324(f139(x51941),x51943),x51942))
% 18.77/18.50 [5195]~P86(x51951)+P18(x51951,x51952)+~P18(x51951,f324(f324(f125(x51951),x51953),x51952))
% 18.77/18.50 [5196]~P86(x51961)+P18(x51961,x51962)+~P18(x51961,f324(f324(f125(x51961),x51962),x51963))
% 18.77/18.50 [5201]~P7(x52011)+~E(f51(x52011,x52013,x52012),f2(x52011))+P1(f324(f324(f280(x52011),x52012),x52013))
% 18.77/18.50 [5261]~P86(x52611)+P1(f324(f324(f231(x52611),x52613),x52612))+P1(f324(f324(f232(x52611),x52612),x52613))
% 18.77/18.50 [5262]~P86(x52621)+P1(f324(f324(f231(x52621),x52623),x52622))+P1(f324(f324(f232(x52621),x52622),x52623))
% 18.77/18.50 [5263]~P86(x52631)+P1(f324(f324(f231(x52631),x52633),x52632))+P1(f324(f324(f232(x52631),x52632),x52633))
% 18.77/18.50 [5264]~P86(x52641)+P1(f324(f324(f231(x52641),x52643),x52642))+P1(f324(f324(f232(x52641),x52642),x52643))
% 18.77/18.50 [5265]~P86(x52651)+P1(f324(f324(f231(x52651),x52653),x52652))+P1(f324(f324(f232(x52651),x52652),x52653))
% 18.77/18.50 [5266]~P86(x52661)+P1(f324(f324(f231(x52661),x52663),x52662))+P1(f324(f324(f231(x52661),x52662),x52663))
% 18.77/18.50 [5267]~P86(x52671)+P1(f324(f324(f231(x52671),x52673),x52672))+P1(f324(f324(f231(x52671),x52672),x52673))
% 18.77/18.50 [5305]~P86(x53051)+E(f324(f324(f235(x53051),x53052),x53053),x53053)+~P1(f324(f324(f231(x53051),x53053),x53052))
% 18.77/18.50 [5306]~P86(x53061)+E(f324(f324(f235(x53061),x53062),x53063),x53062)+~P1(f324(f324(f231(x53061),x53062),x53063))
% 18.77/18.50 [5307]~P86(x53071)+E(f324(f324(f235(x53071),x53072),x53073),x53072)+~P1(f324(f324(f231(x53071),x53072),x53073))
% 18.77/18.50 [5308]~P86(x53081)+E(f324(f324(f178(x53081),x53082),x53083),x53082)+~P1(f324(f324(f231(x53081),x53083),x53082))
% 18.77/18.50 [5309]~P86(x53091)+E(f324(f324(f178(x53091),x53092),x53093),x53093)+~P1(f324(f324(f231(x53091),x53092),x53093))
% 18.77/18.50 [5310]~P86(x53101)+E(f324(f324(f178(x53101),x53102),x53103),x53103)+~P1(f324(f324(f231(x53101),x53102),x53103))
% 18.77/18.50 [5311]~P93(x53111)+E(f324(f324(f103(x53111),x53112),x53113),x53112)+~P1(f324(f324(f231(x53111),x53113),x53112))
% 18.77/18.50 [5312]~P93(x53121)+E(f324(f324(f103(x53121),x53122),x53123),x53123)+~P1(f324(f324(f231(x53121),x53122),x53123))
% 18.77/18.50 [5313]~P93(x53131)+E(f324(f324(f103(x53131),x53132),x53133),x53133)+~P1(f324(f324(f231(x53131),x53132),x53133))
% 18.77/18.50 [5314]~P99(x53141)+E(f324(f324(f104(x53141),x53142),x53143),x53143)+~P1(f324(f324(f231(x53141),x53143),x53142))
% 18.77/18.50 [5315]~P99(x53151)+E(f324(f324(f104(x53151),x53152),x53153),x53152)+~P1(f324(f324(f231(x53151),x53152),x53153))
% 18.77/18.50 [5316]~P99(x53161)+E(f324(f324(f104(x53161),x53162),x53163),x53162)+~P1(f324(f324(f231(x53161),x53162),x53163))
% 18.77/18.50 [5323]~P114(x53232)+E(x53231,f2(x53232))+E(f324(f324(f284(x53232),f324(f81(x53232),x53233)),f324(f81(x53232),x53231)),f324(f324(f284(x53232),x53233),x53231))
% 18.77/18.50 [5329]~P7(x53291)+E(f51(x53291,x53292,x53293),f2(x53291))+~P1(f324(f324(f280(x53291),x53293),x53292))
% 18.77/18.50 [5330]~P7(x53301)+E(f51(x53301,x53302,x53303),f2(x53301))+~P1(f324(f324(f280(x53301),x53303),x53302))
% 18.77/18.50 [5371]~P85(x53711)+E(f324(f295(x53711,x53712),x53713),f179(f845(x53711,a832)))+~P1(f324(f324(f231(x53711),x53713),x53712))
% 18.77/18.50 [5401]~P85(x54011)+E(f299(x54011,x54012,x54013),f179(f845(x54011,a832)))+~P1(f324(f324(f231(x54011),x54013),x54012))
% 18.77/18.50 [5402]~P85(x54021)+E(f298(x54021,x54022,x54023),f179(f845(x54021,a832)))+~P1(f324(f324(f231(x54021),x54023),x54022))
% 18.77/18.50 [5403]~P85(x54031)+E(f296(x54031,x54032,x54033),f179(f845(x54031,a832)))+~P1(f324(f324(f232(x54031),x54033),x54032))
% 18.77/18.50 [5454]~E(f324(f324(f3(a838),x54541),x54543),x54542)+E(x54541,f324(f324(f82(a838),x54542),x54543))+~P1(f324(f324(f231(a838),x54543),x54541))
% 18.77/18.50 [5455]~E(x54551,f324(f324(f82(a838),x54553),x54552))+E(f324(f324(f3(a838),x54551),x54552),x54553)+~P1(f324(f324(f231(a838),x54552),x54551))
% 18.77/18.50 [5499]~P1(f324(x54991,x54993))+P1(f324(x54991,f442(x54991,x54992)))+~P1(f324(f324(f231(a838),x54993),x54992))
% 18.77/18.50 [5500]~P1(f324(x55001,x55003))+P1(f324(x55001,f475(x55001,x55002)))+~P1(f324(f324(f232(a838),x55003),x55002))
% 18.77/18.50 [5507]~P85(x55071)+~E(f324(f295(x55071,x55072),x55073),f179(f845(x55071,a832)))+~P1(f324(f324(f232(x55071),x55072),x55073))
% 18.77/18.50 [5508]~P85(x55081)+~E(f324(f295(x55081,x55082),x55083),f179(f845(x55081,a832)))+~P1(f324(f324(f232(x55081),x55082),x55083))
% 18.77/18.50 [5511]~P85(x55111)+~P1(f324(f324(f232(x55111),x55112),x55113))+P1(f324(f324(f231(x55111),x55112),x55113))
% 18.77/18.50 [5512]~P85(x55121)+~P1(f324(f324(f232(x55121),x55122),x55123))+P1(f324(f324(f231(x55121),x55122),x55123))
% 18.77/18.50 [5513]~P102(x55131)+~P1(f324(f324(f232(x55131),x55132),x55133))+P1(f324(f324(f231(x55131),x55132),x55133))
% 18.77/18.50 [5514]~P102(x55141)+~P1(f324(f324(f232(x55141),x55142),x55143))+P1(f324(f324(f231(x55141),x55142),x55143))
% 18.77/18.50 [5627]~P85(x56271)+~E(f298(x56271,x56272,x56273),f179(f845(x56271,a832)))+~P1(f324(f324(f232(x56271),x56272),x56273))
% 18.77/18.50 [5628]~P85(x56281)+~E(f296(x56281,x56282,x56283),f179(f845(x56281,a832)))+~P1(f324(f324(f231(x56281),x56282),x56283))
% 18.77/18.50 [5629]~P85(x56291)+~E(f179(f845(x56291,a832)),f298(x56291,x56292,x56293))+~P1(f324(f324(f232(x56291),x56292),x56293))
% 18.77/18.50 [5630]~P85(x56301)+~E(f179(f845(x56301,a832)),f296(x56301,x56302,x56303))+~P1(f324(f324(f231(x56301),x56302),x56303))
% 18.77/18.50 [5641]P1(f324(x56411,x56412))+~P1(f324(x56411,f447(x56411,x56413)))+~P1(f324(f324(f231(a838),x56412),x56413))
% 18.77/18.50 [5642]P1(f324(x56421,x56422))+~P1(f324(x56421,f476(x56421,x56423)))+~P1(f324(f324(f232(a838),x56422),x56423))
% 18.77/18.50 [5650]~E(x56501,f324(a114,x56503))+P1(f324(f324(f232(a838),x56501),f324(a114,x56502)))+~P1(f324(f324(f232(a838),x56503),x56502))
% 18.77/18.50 [5666]E(x56661,x56662)+~E(f324(f324(f83(a838),x56663),x56661),f324(f324(f83(a838),x56663),x56662))+~P1(f324(f324(f232(a838),f2(a838)),x56663))
% 18.77/18.50 [5727]E(f324(x57271,f485(x57271,x57272,x57273)),f80(a838))+~E(f324(f324(f8(x57273,a838),x57271),x57272),f80(a838))+~P1(f324(f64(x57273),x57272))
% 18.77/18.50 [5737]~P9(x57371)+P1(f324(f324(f231(x57371),x57372),f43(x57371,x57373)))+~P1(f324(f324(f326(x57371),x57372),x57373))
% 18.77/18.50 [5761]~P85(x57611)+~P1(f324(f324(f232(x57611),x57613),x57612))+~P1(f324(f324(f232(x57611),x57612),x57613))
% 18.77/18.50 [5762]~P102(x57621)+~P1(f324(f324(f232(x57621),x57623),x57622))+~P1(f324(f324(f232(x57621),x57622),x57623))
% 18.77/18.50 [5763]~P102(x57631)+~P1(f324(f324(f232(x57631),x57633),x57632))+~P1(f324(f324(f232(x57631),x57632),x57633))
% 18.77/18.50 [5764]~P102(x57641)+~P1(f324(f324(f232(x57641),x57643),x57642))+~P1(f324(f324(f232(x57641),x57642),x57643))
% 18.77/18.50 [5765]~P102(x57651)+~P1(f324(f324(f232(x57651),x57653),x57652))+~P1(f324(f324(f232(x57651),x57652),x57653))
% 18.77/18.50 [5766]~P102(x57661)+~P1(f324(f324(f231(x57661),x57663),x57662))+~P1(f324(f324(f232(x57661),x57662),x57663))
% 18.77/18.50 [5767]~P86(x57671)+~P1(f324(f324(f232(x57671),x57673),x57672))+~P1(f324(f324(f232(x57671),x57672),x57673))
% 18.77/18.50 [5768]~P86(x57681)+~P1(f324(f324(f231(x57681),x57683),x57682))+~P1(f324(f324(f232(x57681),x57682),x57683))
% 18.77/18.50 [5769]~P86(x57691)+~P1(f324(f324(f231(x57691),x57693),x57692))+~P1(f324(f324(f232(x57691),x57692),x57693))
% 18.77/18.50 [5770]~P86(x57701)+~P1(f324(f324(f231(x57701),x57703),x57702))+~P1(f324(f324(f232(x57701),x57702),x57703))
% 18.77/18.50 [5791]~E(x57912,x57913)+~E(x57911,x57912)+E(f283(a838,f280(a838),x57911,x57912),f324(f324(f303(a838),x57913),f179(f845(a838,a832))))
% 18.77/18.50 [5799]~E(f324(x57992,f394(x57992,x57993,x57991)),f80(a838))+E(f324(f324(f11(x57991,a838),x57992),x57993),f80(a838))+~P1(f324(f64(x57991),x57993))
% 18.77/18.50 [5800]~E(f324(x58002,f486(x58002,x58003,x58001)),f2(a838))+E(f324(f324(f8(x58001,a838),x58002),x58003),f2(a838))+~P1(f324(f64(x58001),x58003))
% 18.77/18.50 [5814]~P101(x58141)+~P1(f324(f324(f231(x58141),x58143),x58142))+P1(f324(f324(f326(x58141),x58142),f324(f259(x58141),x58143)))
% 18.77/18.50 [5815]~P101(x58151)+~P1(f324(f324(f232(x58151),x58153),x58152))+P1(f324(f324(f326(x58151),x58152),f324(f297(x58151),x58153)))
% 18.77/18.50 [5816]~P101(x58161)+~P1(f324(f324(f231(x58161),x58162),x58163))+P1(f324(f324(f326(x58161),x58162),f324(f294(x58161),x58163)))
% 18.77/18.50 [5817]~P101(x58171)+~P1(f324(f324(f232(x58171),x58172),x58173))+P1(f324(f324(f326(x58171),x58172),f324(f258(x58171),x58173)))
% 18.77/18.50 [5818]~P107(x58181)+~P1(f324(f324(f280(x58181),x58182),x58183))+P1(f324(f324(f280(x58181),x58182),f324(f81(x58181),x58183)))
% 18.77/18.50 [5819]~P103(x58191)+~P1(f324(f324(f280(x58191),x58192),x58193))+P1(f324(f324(f280(x58191),x58192),f324(f77(x58191),x58193)))
% 18.77/18.50 [5830]E(f324(x58301,f489(x58301,x58302,x58303)),f324(a114,f2(a838)))+~E(f324(f324(f8(x58303,a838),x58301),x58302),f324(a114,f2(a838)))+~P1(f324(f64(x58303),x58302))
% 18.77/18.50 [5915]~P9(x59151)+~P1(f324(f324(f326(x59151),x59153),x59152))+P1(f324(f324(f231(x59151),f44(x59151,x59152)),x59153))
% 18.77/18.50 [5933]~P1(f324(f324(f231(a838),x59331),x59333))+P1(f324(f324(f231(a838),x59331),x59332))+~P1(f324(f324(f231(a838),x59333),x59332))
% 18.77/18.50 [5934]~P1(f324(f324(f231(a1),x59341),x59343))+P1(f324(f324(f231(a1),x59341),x59342))+~P1(f324(f324(f231(a1),x59343),x59342))
% 18.77/18.50 [5935]~P1(f324(f324(f280(a838),x59351),x59353))+P1(f324(f324(f280(a838),x59351),x59352))+~P1(f324(f324(f280(a838),x59353),x59352))
% 18.77/18.50 [5953]~P101(x59531)+~P1(f324(f324(f326(x59531),x59533),f324(f297(x59531),x59532)))+P1(f324(f324(f232(x59531),x59532),x59533))
% 18.77/18.50 [5954]~P101(x59541)+~P1(f324(f324(f326(x59541),x59542),f324(f258(x59541),x59543)))+P1(f324(f324(f232(x59541),x59542),x59543))
% 18.77/18.50 [5955]~P101(x59551)+~P1(f324(f324(f326(x59551),x59553),f324(f259(x59551),x59552)))+P1(f324(f324(f231(x59551),x59552),x59553))
% 18.77/18.50 [5956]~P101(x59561)+~P1(f324(f324(f326(x59561),x59562),f324(f294(x59561),x59563)))+P1(f324(f324(f231(x59561),x59562),x59563))
% 18.77/18.50 [5957]~P103(x59571)+~P1(f324(f324(f280(x59571),x59572),f324(f77(x59571),x59573)))+P1(f324(f324(f280(x59571),x59572),x59573))
% 18.77/18.50 [5958]~P107(x59581)+~P1(f324(f324(f280(x59581),x59582),f324(f81(x59581),x59583)))+P1(f324(f324(f280(x59581),x59582),x59583))
% 18.77/18.50 [6183]~P61(x61831)+P1(f324(f324(f232(x61831),f2(x61831)),f783(x61833,x61832,x61831)))+P1(f324(f324(f231(x61831),x61832),x61833))
% 18.77/18.50 [6184]~P62(x61841)+P1(f324(f324(f232(x61841),f2(x61841)),f820(x61843,x61842,x61841)))+P1(f324(f324(f231(x61841),x61842),x61843))
% 18.77/18.50 [6253]~P70(x62531)+~P1(f324(f324(f232(x62531),x62533),f324(f81(x62531),x62532)))+P1(f324(f324(f232(x62531),x62532),f324(f81(x62531),x62533)))
% 18.77/18.50 [6254]~P70(x62541)+~P1(f324(f324(f232(x62541),x62543),f324(f81(x62541),x62542)))+P1(f324(f324(f232(x62541),x62542),f324(f81(x62541),x62543)))
% 18.77/18.50 [6255]~P70(x62551)+~P1(f324(f324(f231(x62551),x62553),f324(f81(x62551),x62552)))+P1(f324(f324(f231(x62551),x62552),f324(f81(x62551),x62553)))
% 18.77/18.50 [6256]~P70(x62561)+~P1(f324(f324(f231(x62561),x62563),f324(f81(x62561),x62562)))+P1(f324(f324(f231(x62561),x62562),f324(f81(x62561),x62563)))
% 18.77/18.50 [6267]~P1(f324(f324(f232(a838),x62671),x62673))+~P1(f324(f324(f232(a838),x62673),x62672))+P1(f324(f324(f232(a838),f324(a114,x62671)),x62672))
% 18.77/18.50 [6299]~P84(x62991)+P1(f324(f324(f232(x62991),f324(f102(x62991),x62992)),f324(f102(x62991),x62993)))+~P1(f324(f324(f232(a838),x62992),x62993))
% 18.77/18.50 [6300]~P103(x63001)+P1(f324(f324(f232(x63001),f324(f105(x63001),x63002)),f324(f105(x63001),x63003)))+~P1(f324(f324(f232(a1),x63002),x63003))
% 18.77/18.50 [6301]~P84(x63011)+P1(f324(f324(f232(x63011),f324(f102(x63011),x63012)),f324(f102(x63011),x63013)))+~P1(f324(f324(f232(a838),x63012),x63013))
% 18.77/18.50 [6302]~P84(x63021)+P1(f324(f324(f231(x63021),f324(f102(x63021),x63022)),f324(f102(x63021),x63023)))+~P1(f324(f324(f231(a838),x63022),x63023))
% 18.77/18.50 [6303]~P103(x63031)+P1(f324(f324(f231(x63031),f324(f105(x63031),x63032)),f324(f105(x63031),x63033)))+~P1(f324(f324(f231(a1),x63032),x63033))
% 18.77/18.50 [6309]~P86(x63091)+E(f324(f324(f103(f845(x63091,a832)),f324(f258(x63091),x63092)),f324(f295(x63091,x63092),x63093)),f324(f258(x63091),x63093))+~P1(f324(f324(f231(x63091),x63092),x63093))
% 18.77/18.50 [6340]~P70(x63401)+~P1(f324(f324(f232(x63401),x63403),x63402))+P1(f324(f324(f232(x63401),f324(f81(x63401),x63402)),f324(f81(x63401),x63403)))
% 18.77/18.50 [6341]~P70(x63411)+~P1(f324(f324(f231(x63411),x63413),x63412))+P1(f324(f324(f231(x63411),f324(f81(x63411),x63412)),f324(f81(x63411),x63413)))
% 18.77/18.50 [6342]~P70(x63421)+~P1(f324(f324(f231(x63421),x63423),x63422))+P1(f324(f324(f231(x63421),f324(f81(x63421),x63422)),f324(f81(x63421),x63423)))
% 18.77/18.50 [6343]~P91(x63431)+~P1(f324(f324(f231(x63431),x63433),x63432))+P1(f324(f324(f231(x63431),f324(f81(x63431),x63432)),f324(f81(x63431),x63433)))
% 18.77/18.50 [6344]~P91(x63441)+~P1(f324(f324(f231(x63441),x63443),x63442))+P1(f324(f324(f231(x63441),f324(f81(x63441),x63442)),f324(f81(x63441),x63443)))
% 18.77/18.50 [6379]~P86(x63791)+E(f324(f324(f103(f845(x63791,a832)),f324(f294(x63791),x63792)),f299(x63791,x63792,x63793)),f324(f258(x63791),x63793))+~P1(f324(f324(f232(x63791),x63792),x63793))
% 18.77/18.50 [6380]~P86(x63801)+E(f324(f324(f103(f845(x63801,a832)),f324(f294(x63801),x63802)),f298(x63801,x63802,x63803)),f324(f294(x63801),x63803))+~P1(f324(f324(f231(x63801),x63802),x63803))
% 18.77/18.50 [6381]~P86(x63811)+E(f324(f324(f103(f845(x63811,a832)),f324(f258(x63811),x63812)),f296(x63811,x63812,x63813)),f324(f294(x63811),x63813))+~P1(f324(f324(f231(x63811),x63812),x63813))
% 18.77/18.50 [6418]~P86(x64181)+E(f324(f324(f103(f845(x64181,a832)),f324(f295(x64181,x64182),x64183)),f324(f259(x64181),x64183)),f324(f259(x64181),x64182))+~P1(f324(f324(f231(x64181),x64182),x64183))
% 18.77/18.50 [6581]~P86(x65811)+E(f324(f324(f103(f845(x65811,a832)),f299(x65811,x65812,x65813)),f324(f259(x65811),x65813)),f324(f297(x65811),x65812))+~P1(f324(f324(f232(x65811),x65812),x65813))
% 18.77/18.50 [6582]~P86(x65821)+E(f324(f324(f103(f845(x65821,a832)),f298(x65821,x65822,x65823)),f324(f297(x65821),x65823)),f324(f297(x65821),x65822))+~P1(f324(f324(f231(x65821),x65822),x65823))
% 18.77/18.50 [6583]~P86(x65831)+E(f324(f324(f103(f845(x65831,a832)),f296(x65831,x65832,x65833)),f324(f297(x65831),x65833)),f324(f259(x65831),x65832))+~P1(f324(f324(f231(x65831),x65832),x65833))
% 18.77/18.50 [6600]P1(f324(x66001,x66002))+~P1(f324(f324(f231(a838),x66002),x66003))+P1(f324(f324(f326(a838),f447(x66001,x66003)),f296(a838,f2(a838),x66003)))
% 18.77/18.50 [6610]P1(f324(f324(f280(a1),x66101),f51(a1,x66102,x66103)))+~P1(f324(f324(f280(a1),x66101),x66102))+~P1(f324(f324(f280(a1),x66101),x66103))
% 18.77/18.50 [6636]E(x66361,x66362)+~E(f324(f324(f149(x66363),x66361),f711(x66363,x66362,x66361)),f324(f324(f149(x66363),x66362),f711(x66363,x66362,x66361)))+~E(f324(f180(f839(x66363)),x66361),f324(f180(f839(x66363)),x66362))
% 18.77/18.50 [6642]~E(x66423,f324(f324(f42(a838),x66421),x66422))+~P1(f324(f324(f232(a838),f2(a838)),x66422))+P1(f324(f324(f232(a838),x66421),f324(f324(f83(a838),x66422),f324(a114,x66423))))
% 18.77/18.50 [6657]~P1(f324(x66571,x66573))+~P1(f324(f324(f231(a838),x66573),x66572))+P1(f324(f324(f326(a838),f442(x66571,x66572)),f296(a838,f2(a838),x66572)))
% 18.77/18.50 [6699]~P1(f324(x66991,x66993))+P1(f324(x66991,f448(x66991,x66992)))+~P1(f324(f324(f326(a838),x66993),f296(a838,f2(a838),x66992)))
% 18.77/18.50 [6721]~P84(x67213)+~P1(f324(f324(f232(x67213),f324(f102(x67213),x67211)),f324(f102(x67213),x67212)))+P1(f324(f324(f232(a838),x67211),x67212))
% 18.77/18.50 [6722]~P84(x67223)+~P1(f324(f324(f232(x67223),f324(f102(x67223),x67221)),f324(f102(x67223),x67222)))+P1(f324(f324(f232(a838),x67221),x67222))
% 18.77/18.50 [6723]~P103(x67233)+~P1(f324(f324(f232(x67233),f324(f105(x67233),x67231)),f324(f105(x67233),x67232)))+P1(f324(f324(f232(a1),x67231),x67232))
% 18.77/18.50 [6724]~P84(x67243)+~P1(f324(f324(f231(x67243),f324(f102(x67243),x67241)),f324(f102(x67243),x67242)))+P1(f324(f324(f231(a838),x67241),x67242))
% 18.77/18.50 [6725]~P103(x67253)+~P1(f324(f324(f231(x67253),f324(f105(x67253),x67251)),f324(f105(x67253),x67252)))+P1(f324(f324(f231(a1),x67251),x67252))
% 18.77/18.50 [6744]~P84(x67441)+~P1(f324(f324(f232(x67441),f80(x67441)),x67442))+P1(f324(f324(f232(x67441),f80(x67441)),f324(f324(f240(x67441),x67442),f324(a114,x67443))))
% 18.77/18.50 [6748]~P70(x67481)+~P1(f324(f324(f232(x67481),f324(f81(x67481),x67483)),f324(f81(x67481),x67482)))+P1(f324(f324(f232(x67481),x67482),x67483))
% 18.77/18.50 [6749]~P70(x67491)+~P1(f324(f324(f231(x67491),f324(f81(x67491),x67493)),f324(f81(x67491),x67492)))+P1(f324(f324(f231(x67491),x67492),x67493))
% 18.77/18.50 [6750]~P91(x67501)+~P1(f324(f324(f231(x67501),f324(f81(x67501),x67503)),f324(f81(x67501),x67502)))+P1(f324(f324(f231(x67501),x67502),x67503))
% 18.77/18.50 [6776]P1(f324(x67761,x67762))+~P1(f324(x67761,f449(x67761,x67763)))+~P1(f324(f324(f326(a838),x67762),f296(a838,f2(a838),x67763)))
% 18.77/18.50 [6797]~P61(x67971)+P1(f324(f324(f232(x67971),f783(x67973,x67972,x67971)),f80(x67971)))+P1(f324(f324(f231(x67971),x67972),x67973))
% 18.77/18.50 [6816]~E(f51(a838,x68163,x68162),f51(a838,x68161,x68162))+E(f324(f324(f82(a838),x68161),f324(f324(f83(a838),x68162),f786(x68161,x68162,x68163))),x68163)+~P1(f324(f324(f231(a838),x68161),x68163))
% 18.77/18.50 [6834]E(f324(x68341,f626(x68341,x68342,x68343)),f182(x68342))+~P1(f324(f64(x68343),f168(x68343,x68342,x68341)))+P1(f324(f64(x68343),f238(f845(x68343,a832))))
% 18.77/18.50 [6875]E(f324(f324(f11(x68751,a838),x68752),x68753),f80(a838))+~P1(f324(f64(x68751),x68753))+P1(f324(f324(f326(x68751),f394(x68752,x68753,x68751)),x68753))
% 18.77/18.50 [6876]E(f324(f324(f8(x68761,a838),x68762),x68763),f2(a838))+~P1(f324(f64(x68761),x68763))+P1(f324(f324(f326(x68761),f486(x68762,x68763,x68761)),x68763))
% 18.77/18.50 [6898]~P86(x68981)+~P1(f324(f324(f232(x68981),x68982),x68983))+P1(f324(f324(f232(f845(x68981,a832)),f324(f258(x68981),x68982)),f324(f258(x68981),x68983)))
% 18.77/18.50 [6899]~P85(x68991)+~P1(f324(f324(f231(x68991),x68992),x68993))+P1(f324(f324(f231(f845(x68991,a832)),f324(f294(x68991),x68992)),f324(f294(x68991),x68993)))
% 18.77/18.50 [6900]~P86(x69001)+~P1(f324(f324(f231(x69001),x69002),x69003))+P1(f324(f324(f231(f845(x69001,a832)),f324(f258(x69001),x69002)),f324(f258(x69001),x69003)))
% 18.77/18.50 [6901]~P85(x69011)+~P1(f324(f324(f231(x69011),x69013),x69012))+P1(f324(f324(f231(f845(x69011,a832)),f324(f259(x69011),x69012)),f324(f259(x69011),x69013)))
% 18.77/18.50 [6902]~P86(x69021)+~P1(f324(f324(f231(x69021),x69023),x69022))+P1(f324(f324(f231(f845(x69021,a832)),f324(f297(x69021),x69022)),f324(f297(x69021),x69023)))
% 18.77/18.50 [6907]~P9(x69071)+P1(f324(f324(f231(x69071),x69072),f44(x69071,x69073)))+P1(f324(f324(f326(x69071),f653(x69073,x69072,x69071)),x69073))
% 18.77/18.50 [6912]~P70(x69121)+P1(f324(f324(f232(x69121),f324(f324(f3(x69121),x69122),x69123)),f2(x69121)))+~P1(f324(f324(f232(x69121),x69122),x69123))
% 18.77/18.50 [6913]~P70(x69131)+P1(f324(f324(f231(x69131),f324(f324(f3(x69131),x69132),x69133)),f2(x69131)))+~P1(f324(f324(f231(x69131),x69132),x69133))
% 18.77/18.50 [6951]~P1(f324(f324(f280(a1),x69511),f51(a1,x69512,x69513)))+~P1(f324(f324(f280(a1),x69511),x69513))+P1(f324(f324(f280(a1),x69511),x69512))
% 18.77/18.50 [6958]P1(f324(x69581,x69582))+P1(f324(f324(f231(a838),f449(x69581,x69583)),x69583))+~P1(f324(f324(f326(a838),x69582),f296(a838,f2(a838),x69583)))
% 18.77/18.50 [7000]~E(f324(f324(f8(x70001,a838),x70002),x70003),f80(a838))+~P1(f324(f64(x70001),x70003))+P1(f324(f324(f326(x70001),f485(x70002,x70003,x70001)),x70003))
% 18.77/18.50 [7001]~P1(f324(x70011,x70013))+P1(f324(f324(f231(a838),f448(x70011,x70012)),x70012))+~P1(f324(f324(f326(a838),x70013),f296(a838,f2(a838),x70012)))
% 18.77/18.50 [7039]~P9(x70391)+P1(f324(f324(f326(x70391),f654(x70393,x70392,x70391)),x70392))+P1(f324(f324(f231(x70391),f43(x70391,x70392)),x70393))
% 18.77/18.50 [7069]~E(f324(f324(f8(x70691,a838),x70692),x70693),f324(a114,f2(a838)))+~P1(f324(f64(x70691),x70693))+P1(f324(f324(f326(x70691),f489(x70692,x70693,x70691)),x70693))
% 18.77/18.50 [7080]E(x70801,f2(a838))+P1(f324(x70802,f51(a838,x70803,x70801)))+P1(f324(f324(f232(a838),f779(x70801,x70803,x70802)),x70801))
% 18.77/18.50 [7203]~P1(f324(x72031,x72032))+P1(f324(x72031,f51(a838,x72032,x72033)))+P1(f324(f324(f232(a838),f779(x72033,x72032,x72031)),x72033))
% 18.77/18.50 [7330]E(x73301,f115(x73302))+~P1(f324(f324(f326(f839(x73302)),x73301),f147(x73302,x73303)))+P1(f324(f324(f326(x73302),f735(x73303,x73301,x73302)),x73303))
% 18.77/18.50 [7350]~P86(x73501)+E(f324(f324(f103(f845(x73501,a832)),f324(f324(f303(x73501),x73502),f179(f845(x73501,a832)))),f299(x73501,x73502,x73503)),f324(f295(x73501,x73502),x73503))+~P1(f324(f324(f232(x73501),x73502),x73503))
% 18.77/18.50 [7378]~P86(x73781)+E(f324(f324(f103(f845(x73781,a832)),f324(f324(f303(x73781),x73782),f179(f845(x73781,a832)))),f298(x73781,x73782,x73783)),f296(x73781,x73782,x73783))+~P1(f324(f324(f231(x73781),x73782),x73783))
% 18.77/18.50 [7490]~P86(x74901)+P1(f324(f324(f232(x74901),x74902),x74903))+~P1(f324(f324(f232(f845(x74901,a832)),f324(f258(x74901),x74902)),f324(f258(x74901),x74903)))
% 18.77/18.50 [7491]~P85(x74911)+P1(f324(f324(f231(x74911),x74912),x74913))+~P1(f324(f324(f231(f845(x74911,a832)),f324(f259(x74911),x74913)),f324(f259(x74911),x74912)))
% 18.77/18.50 [7492]~P86(x74921)+P1(f324(f324(f231(x74921),x74922),x74923))+~P1(f324(f324(f231(f845(x74921,a832)),f324(f297(x74921),x74923)),f324(f297(x74921),x74922)))
% 18.77/18.50 [7493]~P85(x74931)+P1(f324(f324(f231(x74931),x74932),x74933))+~P1(f324(f324(f231(f845(x74931,a832)),f324(f294(x74931),x74932)),f324(f294(x74931),x74933)))
% 18.77/18.50 [7494]~P86(x74941)+P1(f324(f324(f231(x74941),x74942),x74943))+~P1(f324(f324(f231(f845(x74941,a832)),f324(f258(x74941),x74942)),f324(f258(x74941),x74943)))
% 18.77/18.50 [7518]~P70(x75181)+~P1(f324(f324(f232(x75181),f324(f324(f3(x75181),x75182),x75183)),f2(x75181)))+P1(f324(f324(f232(x75181),x75182),x75183))
% 18.77/18.50 [7519]~P70(x75191)+~P1(f324(f324(f231(x75191),f324(f324(f3(x75191),x75192),x75193)),f2(x75191)))+P1(f324(f324(f231(x75191),x75192),x75193))
% 18.77/18.50 [7680]E(x76801,f2(a838))+~E(f324(f131(a838,a838,f82(a838),x76802),x76803),f2(a838))+~P1(f324(f324(f326(a838),x76801),f324(f157(a838),x76803)))
% 18.77/18.50 [7684]~P9(x76841)+~P1(f324(f324(f231(x76841),f654(x76843,x76842,x76841)),x76843))+P1(f324(f324(f231(x76841),f43(x76841,x76842)),x76843))
% 18.77/18.50 [7837]P1(f324(f324(f231(a1),f2(a1)),f700(x78371,x78372,x78373)))+P1(f324(f324(x78372,f324(f324(f42(a1),x78371),x78373)),f51(a1,x78371,x78373)))+~P1(f324(f324(f232(a1),f2(a1)),x78373))
% 18.77/18.50 [7932]E(x79321,x79322)+~E(f324(f180(f839(x79323)),x79321),f324(f180(f839(x79323)),x79322))+~P1(f324(f324(f252(x79323,x79323,a832),a321),f701(x79323,x79321,x79322)))
% 18.77/18.50 [8000]~P36(x80002,x80003)+E(x80001,f179(f845(x80002,a832)))+~P1(f324(f324(f231(f845(x80002,a832)),x80001),f324(f278(x80002,x80002,x80003),x80001)))
% 18.77/18.50 [8029]~P62(x80291)+~P1(f324(f324(f231(x80291),x80292),f324(f324(f82(x80291),x80293),f820(x80293,x80292,x80291))))+P1(f324(f324(f231(x80291),x80292),x80293))
% 18.77/18.50 [8066]P47(x80661,x80662,x80663)+P1(f324(f324(f326(x80661),f608(x80663,x80662,x80661)),x80662))+P1(f324(f324(f326(f844(x80661,x80661)),f609(x80663,x80662,x80661)),x80663))
% 18.77/18.50 [8089]P1(f324(f324(x80892,f324(f324(f42(a1),x80891),x80893)),f51(a1,x80891,x80893)))+~P1(f324(f324(f232(a1),f2(a1)),x80893))+P1(f324(f324(f232(a1),f700(x80891,x80892,x80893)),x80893))
% 18.77/18.50 [8113]E(f324(f304(a838,a838,f324(f324(f9(a838,a838,a838),f3(a838)),x81131)),f324(f295(a838,x81132),x81133)),f179(f845(a838,a832)))+P1(f324(f324(f232(a838),x81131),x81133))+P1(f324(f324(f232(a838),x81132),x81133))
% 18.77/18.50 [8217]E(f324(f304(a838,a838,f324(f324(f9(a838,a838,a838),f3(a838)),x82171)),f324(f295(a838,x82172),x82173)),f324(f324(f303(a838),f2(a838)),f179(f845(a838,a832))))+P1(f324(f324(f232(a838),x82171),x82173))+~P1(f324(f324(f232(a838),x82172),x82173))
% 18.77/18.50 [8232]~P86(x82321)+E(f138(x82321,x82321,f7(x82321),x82322,x82323),x82323)+~P1(f324(f324(f326(x82321),x82322),f324(f157(x82321),x82323)))
% 18.77/18.50 [8247]P29(x82471,x82471,x82472,x82473)+~P1(f324(f64(x82471),x82473))+~P1(f324(f324(f231(f845(x82471,a832)),x82473),f324(f304(x82471,x82471,x82472),x82473)))
% 18.77/18.50 [8274]E(f324(f324(f82(a1),f324(f324(f83(a1),x82741),f690(x82742,x82743,x82741))),f700(x82742,x82743,x82741)),x82742)+P1(f324(f324(x82743,f324(f324(f42(a1),x82742),x82741)),f51(a1,x82742,x82741)))+~P1(f324(f324(f232(a1),f2(a1)),x82741))
% 18.77/18.50 [8503]~P1(f324(f324(x85031,f690(x85032,x85031,x85033)),f700(x85032,x85031,x85033)))+P1(f324(f324(x85031,f324(f324(f42(a1),x85032),x85033)),f51(a1,x85032,x85033)))+~P1(f324(f324(f232(a1),f2(a1)),x85033))
% 18.77/18.50 [9293]~P1(f324(f64(x92931),x92932))+~P1(f324(f324(f326(x92931),x92933),x92932))+P1(f324(f324(f232(a838),f324(f41(x92931),f324(f324(f3(f845(x92931,a832)),x92932),f324(f324(f303(x92931),x92933),f179(f845(x92931,a832)))))),f324(f41(x92931),x92932)))
% 18.77/18.50 [9876]P47(x98761,x98762,x98763)+~P1(f324(f324(f252(x98761,x98761,a832),f324(f324(f9(x98761,f845(x98761,a832),f845(x98761,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x98761,a832),f845(x98761,a832)),x98761),f10(a832,a832,x98761)),f324(f324(f10(a832,f845(a832,a832),x98761),a322),f324(f324(f9(x98761,f845(x98761,a832),a832),f326(x98761)),x98762)))),f324(f324(f9(x98761,f845(x98761,a832),a832),f326(x98761)),x98762))),f609(x98763,x98762,x98761)))+P1(f324(f324(f326(x98761),f608(x98763,x98762,x98761)),x98762))
% 18.77/18.50 [5284]~P114(x52842)+E(x52841,f2(x52842))+E(f324(f324(f284(x52842),x52843),f324(f81(x52842),x52841)),f324(f81(x52842),f324(f324(f284(x52842),x52843),x52841)))
% 18.77/18.50 [5417]~E(x54173,f179(f845(x54171,a832)))+~E(x54172,f179(f845(x54171,a832)))+E(f324(f324(f103(f845(x54171,a832)),x54172),x54173),f179(f845(x54171,a832)))
% 18.77/18.50 [5473]~E(x54733,f2(a838))+~P1(f324(x54731,f2(a838)))+P1(f324(x54731,f324(f324(f42(a838),x54732),x54733)))
% 18.77/18.50 [5474]~E(x54743,f2(a838))+~P1(f324(x54741,f2(a838)))+P1(f324(x54741,f324(f324(f42(a838),x54742),x54743)))
% 18.77/18.50 [5622]~P62(x56222)+E(x56221,f2(x56222))+E(f324(f324(f284(x56222),f324(f77(x56222),x56223)),f324(f77(x56222),x56221)),f324(f77(x56222),f324(f324(f284(x56222),x56223),x56221)))
% 18.77/18.50 [5715]~P105(x57151)+~E(x57152,f80(x57151))+P1(f324(f324(f280(x57151),x57152),f324(f324(f240(x57151),x57152),x57153)))
% 18.77/18.50 [5732]~P7(x57321)+E(f324(f324(f83(x57321),x57322),f324(f324(f42(x57321),x57323),x57322)),x57323)+~P1(f324(f324(f280(x57321),x57322),x57323))
% 18.77/18.50 [5786]~P1(f324(f64(x57861),x57863))+E(f324(f41(x57861),f324(f324(f303(x57861),x57862),x57863)),f324(a114,f324(f41(x57861),x57863)))+P1(f324(f324(f326(x57861),x57862),x57863))
% 18.77/18.50 [5787]~P1(f324(f64(x57871),x57873))+E(f324(f41(x57871),f324(f324(f303(x57871),x57872),x57873)),f324(a114,f324(f41(x57871),x57873)))+P1(f324(f324(f326(x57871),x57872),x57873))
% 18.77/18.50 [5864]~E(x58642,f2(a838))+P1(f324(x58641,f2(a838)))+~P1(f324(x58641,f324(f324(f42(a838),x58643),x58642)))
% 18.77/18.50 [5883]~P1(f324(f64(x58831),x58833))+E(f324(f41(x58831),f324(f324(f303(x58831),x58832),x58833)),f324(f41(x58831),x58833))+~P1(f324(f324(f326(x58831),x58832),x58833))
% 18.77/18.50 [5917]~P1(f324(f64(x59171),x59173))+E(f324(f41(x59171),f324(f324(f303(x59171),x59172),x59173)),f324(f324(f82(a838),f80(a838)),f324(f41(x59171),x59173)))+P1(f324(f324(f326(x59171),x59172),x59173))
% 18.77/18.50 [5924]~P8(x59241)+E(f324(f324(f42(x59241),x59242),f324(f81(x59241),x59243)),f324(f81(x59241),f324(f324(f42(x59241),x59242),x59243)))+~P1(f324(f324(f280(x59241),x59243),x59242))
% 18.77/18.50 [6040]E(f324(f324(f82(a838),x60401),f777(x60401,x60402,x60403)),x60402)+~P1(f324(x60403,f2(a838)))+P1(f324(x60403,f324(f324(f3(a838),x60402),x60401)))
% 18.77/18.50 [6041]E(f324(f324(f82(a838),x60411),f782(x60411,x60412,x60413)),x60412)+~P1(f324(x60413,f2(a838)))+P1(f324(x60413,f324(f324(f3(a838),x60412),x60411)))
% 18.77/18.50 [6065]~P8(x60651)+E(f324(f324(f42(x60651),f324(f81(x60651),x60652)),x60653),f324(f81(x60651),f324(f324(f42(x60651),x60652),x60653)))+~P1(f324(f324(f280(x60651),x60653),x60652))
% 18.77/18.50 [6088]~P9(x60881)+~P1(f324(f64(x60881),x60883))+E(f324(f324(f67(x60881,x60881,f103(x60881)),x60882),x60883),f324(f324(f103(x60881),x60882),f43(x60881,x60883)))
% 18.77/18.50 [6089]~P9(x60891)+~P1(f324(f64(x60891),x60893))+E(f324(f324(f67(x60891,x60891,f104(x60891)),x60892),x60893),f324(f324(f104(x60891),x60892),f44(x60891,x60893)))
% 18.77/18.50 [6095]~P89(x60951)+~E(f324(f106(x60951),x60952),f324(f106(x60951),x60953))+P33(x60951,f324(f106(x60951),f324(f324(f82(a1),x60952),f324(f81(a1),x60953))))
% 18.77/18.50 [6102]~P119(x61021)+E(f324(f324(f3(x61021),f324(f102(x61021),x61022)),f324(f102(x61021),x61023)),f324(f102(x61021),f324(f324(f3(a838),x61022),x61023)))+~P1(f324(f324(f231(a838),x61023),x61022))
% 18.77/18.50 [6108]~P107(x61081)+~P1(f324(f324(f280(x61081),x61082),x61083))+P1(f324(f324(f280(x61081),f324(f81(x61081),x61082)),x61083))
% 18.77/18.50 [6109]~P103(x61091)+~P1(f324(f324(f280(x61091),x61092),x61093))+P1(f324(f324(f280(x61091),f324(f77(x61091),x61092)),x61093))
% 18.77/18.50 [6194]E(f324(f324(f82(a838),x61941),f777(x61941,x61942,x61943)),x61942)+P1(f324(f324(f232(a838),x61942),x61941))+P1(f324(x61943,f324(f324(f3(a838),x61942),x61941)))
% 18.77/18.50 [6195]E(f324(f324(f82(a838),x61951),f782(x61951,x61952,x61953)),x61952)+P1(f324(f324(f232(a838),x61952),x61951))+P1(f324(x61953,f324(f324(f3(a838),x61952),x61951)))
% 18.77/18.50 [6212]~P103(x62121)+E(f324(f324(f83(x62121),f324(f77(x62121),x62122)),x62123),f324(f77(x62121),f324(f324(f83(x62121),x62122),x62123)))+~P1(f324(f324(f231(x62121),f2(x62121)),x62123))
% 18.77/18.50 [6213]~P61(x62131)+E(f324(f324(f284(x62131),f324(f77(x62131),x62132)),x62133),f324(f77(x62131),f324(f324(f284(x62131),x62132),x62133)))+~P1(f324(f324(f232(x62131),f2(x62131)),x62133))
% 18.77/18.50 [6222]~P94(x62221)+~P1(f324(f64(x62221),x62223))+E(f324(f324(f67(x62221,x62221,f104(x62221)),x62222),x62223),f12(x62221,f324(f324(f303(x62221),x62222),x62223)))
% 18.77/18.50 [6223]~P86(x62231)+~P1(f324(f64(x62231),x62233))+E(f324(f324(f67(x62231,x62231,f178(x62231)),x62232),x62233),f16(x62231,f324(f324(f303(x62231),x62232),x62233)))
% 18.77/18.50 [6224]~P86(x62241)+~P1(f324(f64(x62241),x62243))+E(f324(f324(f67(x62241,x62241,f235(x62241)),x62242),x62243),f17(x62241,f324(f324(f303(x62241),x62242),x62243)))
% 18.77/18.50 [6225]~P94(x62251)+~P1(f324(f64(x62251),x62253))+E(f324(f324(f67(x62251,x62251,f103(x62251)),x62252),x62253),f15(x62251,f324(f324(f303(x62251),x62252),x62253)))
% 18.77/18.50 [6269]E(x62691,f115(x62692))+~E(f163(x62692,x62693),f115(f839(x62692)))+~P1(f324(f324(f326(f839(x62692)),x62691),f324(f157(f839(x62692)),x62693)))
% 18.77/18.50 [6288]~P105(x62881)+~P1(f324(f324(f232(a838),f2(a838)),x62883))+P1(f324(f324(f280(x62881),x62882),f324(f324(f240(x62881),x62882),x62883)))
% 18.77/18.50 [6319]~P1(f324(f127(x63191),x63193))+P1(f324(f324(f326(x63191),x63192),f324(f157(x63191),x63193)))+P1(f324(f127(x63191),f324(f324(f139(x63191),x63192),x63193)))
% 18.77/18.50 [6331]~P92(x63311)+~P1(f324(f64(x63311),x63313))+E(f324(f66(x63311,f83(x63311)),f324(f324(f303(x63311),x63312),x63313)),f324(f324(f67(x63311,x63311,f83(x63311)),x63312),x63313))
% 18.77/18.50 [6352]~P86(x63521)+~P1(f324(f64(x63521),x63523))+E(f13(x63521,f178(x63521),f324(f324(f303(x63521),x63522),x63523)),f324(f324(f67(x63521,x63521,f178(x63521)),x63522),x63523))
% 18.77/18.50 [6353]~P86(x63531)+~P1(f324(f64(x63531),x63533))+E(f14(x63531,f235(x63531),f324(f324(f303(x63531),x63532),x63533)),f324(f324(f67(x63531,x63531,f235(x63531)),x63532),x63533))
% 18.77/18.50 [6354]P1(f324(x63541,f2(a838)))+~P1(f324(f324(f232(a838),x63542),x63543))+~P1(f324(x63541,f324(f324(f3(a838),x63542),x63543)))
% 18.77/18.50 [6355]P1(f324(x63551,f2(a838)))+~P1(f324(f324(f232(a838),x63552),x63553))+~P1(f324(x63551,f324(f324(f3(a838),x63552),x63553)))
% 18.77/18.50 [6374]~P103(x63741)+P1(f324(f324(f232(x63741),x63742),x63743))+~P1(f324(f324(f232(x63741),f324(f77(x63741),x63742)),x63743))
% 18.77/18.50 [6375]~P78(x63751)+P1(f324(f324(f231(x63751),x63752),x63753))+~P1(f324(f324(f231(x63751),f324(f77(x63751),x63752)),x63753))
% 18.77/18.50 [6376]~P78(x63761)+P1(f324(f324(f231(x63761),x63762),x63763))+~P1(f324(f324(f231(x63761),f324(f77(x63761),x63762)),x63763))
% 18.77/18.50 [6377]~P103(x63771)+P1(f324(f324(f280(x63771),x63772),x63773))+~P1(f324(f324(f280(x63771),f324(f77(x63771),x63772)),x63773))
% 18.77/18.50 [6378]~P107(x63781)+P1(f324(f324(f280(x63781),x63782),x63783))+~P1(f324(f324(f280(x63781),f324(f81(x63781),x63782)),x63783))
% 18.77/18.50 [6397]E(x63971,f115(x63972))+E(f324(f130(x63972),f324(f324(f128(x63972),x63973),x63971)),f324(f324(f149(x63972),x63971),x63973))+~P1(f324(f324(f232(a838),x63973),f324(f180(f839(x63972)),x63971)))
% 18.77/18.50 [6450]~P1(f324(x64501,x64503))+P1(f324(x64501,f478(x64501,x64502)))+~P1(f324(f324(f326(a838),x64503),f324(f295(a838,f2(a838)),x64502)))
% 18.77/18.50 [6473]P1(f324(x64731,x64732))+~P1(f324(f324(f232(a838),x64732),x64733))+P1(f324(f324(f326(a838),f476(x64731,x64733)),f324(f295(a838,f2(a838)),x64733)))
% 18.77/18.50 [6488]~P84(x64881)+~P1(f324(f324(f232(x64881),f2(x64881)),x64882))+P1(f324(f324(f232(x64881),f2(x64881)),f324(f324(f240(x64881),x64882),x64883)))
% 18.77/18.50 [6490]~P84(x64901)+~P1(f324(f324(f231(x64901),f2(x64901)),x64902))+P1(f324(f324(f231(x64901),f2(x64901)),f324(f324(f240(x64901),x64902),x64903)))
% 18.77/18.50 [6491]~P84(x64911)+~P1(f324(f324(f231(x64911),f80(x64911)),x64912))+P1(f324(f324(f231(x64911),f80(x64911)),f324(f324(f240(x64911),x64912),x64913)))
% 18.77/18.50 [6516]~P1(f324(x65161,x65163))+~P1(f324(f324(f232(a838),x65163),x65162))+P1(f324(f324(f326(a838),f475(x65161,x65162)),f324(f295(a838,f2(a838)),x65162)))
% 18.77/18.50 [6520]P1(f324(f64(x65201),x65202))+~P1(f324(f64(x65201),x65203))+~P1(f324(f324(f231(f845(x65201,a832)),x65202),x65203))
% 18.77/18.50 [6521]P1(f324(f64(x65211),x65212))+~P1(f324(f64(x65211),x65213))+~P1(f324(f324(f231(f845(x65211,a832)),x65212),x65213))
% 18.77/18.50 [6530]~P1(f324(f324(f280(a838),x65301),x65302))+~P1(f324(f324(f280(a838),x65301),x65303))+P1(f324(f324(f280(a838),x65301),f324(f324(f3(a838),x65302),x65303)))
% 18.77/18.50 [6531]P1(f324(x65311,x65312))+~P1(f324(x65311,f477(x65311,x65313)))+~P1(f324(f324(f326(a838),x65312),f324(f295(a838,f2(a838)),x65313)))
% 18.77/18.50 [6544]E(x65441,f2(a838))+P1(f324(x65442,f778(x65441,x65443,x65442)))+~P1(f324(x65442,f324(f324(f42(a838),x65443),x65441)))
% 18.77/18.50 [6553]~P117(x65532)+E(x65531,f2(x65532))+~E(f324(f324(f82(x65532),f324(f324(f83(x65532),x65533),x65533)),f324(f324(f83(x65532),x65531),x65531)),f2(x65532))
% 18.77/18.50 [6554]~P117(x65542)+E(x65541,f2(x65542))+~E(f324(f324(f82(x65542),f324(f324(f83(x65542),x65541),x65541)),f324(f324(f83(x65542),x65543),x65543)),f2(x65542))
% 18.77/18.50 [6601]E(x66011,f2(a838))+~P1(f324(x66012,f785(x66011,x66013,x66012)))+P1(f324(x66012,f324(f324(f42(a838),x66013),x66011)))
% 18.77/18.50 [6606]~P86(x66061)+~P18(x66061,x66063)+P18(x66061,f324(f324(f137(x66061,x66061,f7(x66061)),x66062),x66063))
% 18.77/18.50 [6650]P1(f324(x66501,f778(x66502,x66503,x66501)))+P1(f324(x66501,f2(a838)))+~P1(f324(x66501,f324(f324(f42(a838),x66503),x66502)))
% 18.77/18.50 [6656]~P89(x66561)+E(f324(f106(x66561),x66562),f324(f106(x66561),x66563))+~P33(x66561,f324(f106(x66561),f324(f324(f82(a1),x66562),f324(f81(a1),x66563))))
% 18.77/18.50 [6728]E(x67281,f2(a1))+E(x67282,f2(a1))+~P1(f324(f55(x67282,x67282),f324(f324(f247(a1,a1),x67283),x67281)))
% 18.77/18.50 [6729]E(x67291,f80(a1))+E(x67292,f2(a1))+~P1(f324(f55(x67292,x67292),f324(f324(f247(a1,a1),x67291),x67293)))
% 18.77/18.50 [6746]P1(f324(x67461,x67462))+P1(f324(f324(f232(a838),f477(x67461,x67463)),x67463))+~P1(f324(f324(f326(a838),x67462),f324(f295(a838,f2(a838)),x67463)))
% 18.77/18.50 [6771]~P1(f324(x67711,f785(x67713,x67712,x67711)))+~P1(f324(x67711,f2(a838)))+P1(f324(x67711,f324(f324(f42(a838),x67712),x67713)))
% 18.77/18.50 [6772]~P1(f324(x67721,f777(x67723,x67722,x67721)))+~P1(f324(x67721,f2(a838)))+P1(f324(x67721,f324(f324(f3(a838),x67722),x67723)))
% 18.77/18.50 [6773]~P1(f324(x67731,f782(x67733,x67732,x67731)))+~P1(f324(x67731,f2(a838)))+P1(f324(x67731,f324(f324(f3(a838),x67732),x67733)))
% 18.77/18.50 [6793]~P1(f324(x67931,x67933))+P1(f324(f324(f232(a838),f478(x67931,x67932)),x67932))+~P1(f324(f324(f326(a838),x67933),f324(f295(a838,f2(a838)),x67932)))
% 18.77/18.50 [6794]E(f324(f324(f3(a838),f324(f324(f3(a838),x67941),x67942)),f324(f324(f3(a838),x67943),x67942)),f324(f324(f3(a838),x67941),x67943))+~P1(f324(f324(f231(a838),x67942),x67941))+~P1(f324(f324(f231(a838),x67942),x67943))
% 18.77/18.50 [6827]~P70(x68271)+~P1(f324(f324(f232(x68271),f324(f81(x68271),x68273)),x68272))+P1(f324(f324(f232(x68271),f324(f81(x68271),x68272)),x68273))
% 18.77/18.50 [6828]~P70(x68281)+~P1(f324(f324(f232(x68281),f324(f81(x68281),x68283)),x68282))+P1(f324(f324(f232(x68281),f324(f81(x68281),x68282)),x68283))
% 18.77/18.50 [6829]~P103(x68291)+~P1(f324(f324(f232(x68291),f324(f77(x68291),x68292)),x68293))+P1(f324(f324(f232(x68291),f324(f81(x68291),x68292)),x68293))
% 18.77/18.50 [6830]~P70(x68301)+~P1(f324(f324(f231(x68301),f324(f81(x68301),x68303)),x68302))+P1(f324(f324(f231(x68301),f324(f81(x68301),x68302)),x68303))
% 18.77/18.50 [6831]~P70(x68311)+~P1(f324(f324(f231(x68311),f324(f81(x68311),x68313)),x68312))+P1(f324(f324(f231(x68311),f324(f81(x68311),x68312)),x68313))
% 18.77/18.50 [6832]~P78(x68321)+~P1(f324(f324(f231(x68321),f324(f77(x68321),x68322)),x68323))+P1(f324(f324(f231(x68321),f324(f81(x68321),x68322)),x68323))
% 18.77/18.50 [6833]~P78(x68331)+~P1(f324(f324(f231(x68331),f324(f77(x68331),x68332)),x68333))+P1(f324(f324(f231(x68331),f324(f81(x68331),x68332)),x68333))
% 18.77/18.50 [6836]~P1(f324(f324(f280(a1),x68361),x68363))+P1(f324(f324(f280(a1),x68361),x68362))+~P1(f324(f324(f280(a1),x68361),f324(f324(f3(a1),x68362),x68363)))
% 18.77/18.50 [6869]~P1(f324(x68693,f777(x68692,x68691,x68693)))+P1(f324(f324(f232(a838),x68691),x68692))+P1(f324(x68693,f324(f324(f3(a838),x68691),x68692)))
% 18.77/18.50 [6870]~P1(f324(x68703,f782(x68702,x68701,x68703)))+P1(f324(f324(f232(a838),x68701),x68702))+P1(f324(x68703,f324(f324(f3(a838),x68701),x68702)))
% 18.77/18.50 [6916]~E(f676(x69163,x69162,x69161),f677(x69163,x69162,x69161))+E(f324(f324(f104(f845(x69161,a832)),x69162),f43(f845(x69161,a832),x69163)),f179(f845(x69161,a832)))+P1(f324(f324(f326(f845(x69161,a832)),x69162),x69163))
% 18.77/18.50 [6925]~P1(f324(f64(x69251),x69253))+P1(f324(f64(x69251),f44(f845(x69251,a832),x69252)))+~P1(f324(f324(f326(f845(x69251,a832)),x69253),x69252))
% 18.77/18.50 [6986]~P86(x69861)+E(f324(f324(f103(f845(x69861,a832)),f324(f295(x69861,x69862),x69863)),f324(f324(f303(x69861),x69863),f179(f845(x69861,a832)))),f296(x69861,x69862,x69863))+~P1(f324(f324(f231(x69861),x69862),x69863))
% 18.77/18.50 [6989]E(x69891,f2(a838))+P1(f324(f324(f232(a838),f787(x69891,x69893,x69892)),x69891))+P1(f324(x69892,f324(f324(f42(a838),x69893),x69891)))
% 18.77/18.50 [7023]E(x70231,x70232)+~P1(f324(f324(f231(f845(x70233,a832)),x70231),x70232))+P1(f324(f324(f232(f845(x70233,a832)),x70231),x70232))
% 18.77/18.50 [7024]E(x70241,x70242)+~P1(f324(f324(f231(f845(x70243,a832)),x70241),x70242))+P1(f324(f324(f232(f845(x70243,a832)),x70241),x70242))
% 18.77/18.50 [7036]E(x70361,x70362)+~E(f324(f180(f839(x70363)),x70361),f324(f180(f839(x70363)),x70362))+P1(f324(f324(f232(a838),f711(x70363,x70361,x70362)),f324(f180(f839(x70363)),x70362)))
% 18.77/18.50 [7081]P12(x70811,x70812,x70813)+~E(f324(f262(x70811,x70811),x70813),x70812)+~E(f324(f324(f282(x70811,x70811,x70811),f324(f279(x70811,x70811),x70813)),x70813),x70813)
% 18.77/18.50 [7162]E(x71621,f2(a1))+~P1(f324(f324(f280(a1),x71622),x71623))+P1(f324(f324(f280(a1),f324(f324(f83(a1),x71621),x71622)),f324(f324(f83(a1),x71621),x71623)))
% 18.77/18.50 [7165]~P1(f324(x71651,f2(a838)))+P1(f324(f324(f232(a838),f787(x71653,x71652,x71651)),x71653))+P1(f324(x71651,f324(f324(f42(a838),x71652),x71653)))
% 18.77/18.50 [7178]~P86(x71781)+E(f324(f324(f103(f845(x71781,a832)),f299(x71781,x71782,x71783)),f324(f324(f303(x71781),x71783),f179(f845(x71781,a832)))),f298(x71781,x71782,x71783))+~P1(f324(f324(f232(x71781),x71782),x71783))
% 18.77/18.50 [7283]~P1(f324(f64(x72831),x72833))+P1(f324(f324(f232(a838),f324(f41(x72831),x72832)),f324(f41(x72831),x72833)))+~P1(f324(f324(f232(f845(x72831,a832)),x72832),x72833))
% 18.77/18.50 [7284]~P1(f324(f64(x72841),x72843))+P1(f324(f324(f231(a838),f324(f41(x72841),x72842)),f324(f41(x72841),x72843)))+~P1(f324(f324(f231(f845(x72841,a832)),x72842),x72843))
% 18.77/18.50 [7325]~P1(f324(x73253,x73252))+P1(f324(f324(f186(x73251),x73252),f774(x73252,x73251,x73253)))+~P1(f324(f324(f186(f35(x73253,x73251)),x73252),x73252))
% 18.77/18.50 [7425]E(x74251,x74252)+~P1(f324(f324(f231(f845(x74253,a832)),x74252),x74251))+~P1(f324(f324(f231(f845(x74253,a832)),x74251),x74252))
% 18.77/18.50 [7426]E(x74261,x74262)+~P1(f324(f324(f231(f845(x74263,a832)),x74262),x74261))+~P1(f324(f324(f231(f845(x74263,a832)),x74261),x74262))
% 18.77/18.50 [7429]~P86(x74291)+P18(x74291,x74292)+~P18(x74291,f324(f324(f137(x74291,x74291,f7(x74291)),x74293),x74292))
% 18.77/18.50 [7498]~P1(f324(f324(f232(a838),x74983),x74982))+~P1(f324(f324(f232(a838),x74983),x74981))+P1(f324(f324(f232(a838),f324(f324(f3(a838),x74981),x74982)),f324(f324(f3(a838),x74981),x74983)))
% 18.77/18.50 [7499]~P1(f324(f324(f232(a838),x74991),x74993))+~P1(f324(f324(f231(a838),x74992),x74991))+P1(f324(f324(f232(a838),f324(f324(f3(a838),x74991),x74992)),f324(f324(f3(a838),x74993),x74992)))
% 18.77/18.50 [7516]~P1(f324(f324(f232(a1),x75162),f2(a1)))+~P1(f324(f324(f231(a1),x75163),x75161))+P1(f324(f324(f231(a1),f324(f324(f42(a1),x75161),x75162)),f324(f324(f42(a1),x75163),x75162)))
% 18.77/18.50 [7533]~P1(f324(f324(f232(a838),f2(a838)),x75331))+~P1(f324(f324(f232(a838),x75332),x75333))+P1(f324(f324(f232(a838),f324(f324(f83(a838),x75331),x75332)),f324(f324(f83(a838),x75331),x75333)))
% 18.77/18.50 [7534]~P1(f324(f324(f232(a838),f2(a838)),x75341))+~P1(f324(f324(f232(a838),x75342),x75343))+P1(f324(f324(f232(a838),f324(f324(f83(a838),x75341),x75342)),f324(f324(f83(a838),x75341),x75343)))
% 18.77/18.50 [7535]~P1(f324(f324(f232(a838),f2(a838)),x75352))+~P1(f324(f324(f232(a838),x75351),x75353))+P1(f324(f324(f232(a838),f324(f324(f83(a838),x75351),x75352)),f324(f324(f83(a838),x75353),x75352)))
% 18.77/18.50 [7536]~P1(f324(f324(f232(a838),f2(a838)),x75362))+~P1(f324(f324(f232(a838),x75361),x75363))+P1(f324(f324(f232(a838),f324(f324(f83(a838),x75361),x75362)),f324(f324(f83(a838),x75363),x75362)))
% 18.77/18.50 [7537]~P1(f324(f324(f232(a838),f2(a838)),x75371))+~P1(f324(f324(f232(a838),x75372),x75373))+P1(f324(f324(f232(a838),f324(f324(f83(a838),x75371),x75372)),f324(f324(f83(a838),x75371),x75373)))
% 18.77/18.50 [7538]~P1(f324(f324(f232(a1),f2(a1)),x75381))+~P1(f324(f324(f232(a1),x75382),x75383))+P1(f324(f324(f232(a1),f324(f324(f83(a1),x75381),x75382)),f324(f324(f83(a1),x75381),x75383)))
% 18.77/18.50 [7539]~P1(f324(f324(f232(a838),f2(a838)),x75391))+~P1(f324(f324(f231(a838),x75392),x75393))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x75391),x75392)),f324(f324(f83(a838),x75391),x75393)))
% 18.77/18.50 [7540]~P1(f324(f324(f232(a838),f2(a838)),x75403))+~P1(f324(f324(f231(a838),x75403),x75402))+P1(f324(f324(f231(a838),f324(f324(f42(a838),x75401),x75402)),f324(f324(f42(a838),x75401),x75403)))
% 18.77/18.50 [7541]~P1(f324(f324(f232(a1),f2(a1)),x75412))+~P1(f324(f324(f231(a1),x75411),x75413))+P1(f324(f324(f231(a1),f324(f324(f42(a1),x75411),x75412)),f324(f324(f42(a1),x75413),x75412)))
% 18.77/18.50 [7542]~P1(f324(f324(f232(a838),f2(a838)),x75421))+~P1(f324(f324(f280(a838),x75422),x75423))+P1(f324(f324(f280(a838),f324(f324(f83(a838),x75421),x75422)),f324(f324(f83(a838),x75421),x75423)))
% 18.77/18.50 [7590]E(x75901,f2(a838))+E(f324(f324(f82(a838),f324(f324(f83(a838),x75901),f785(x75901,x75902,x75903))),f787(x75901,x75902,x75903)),x75902)+P1(f324(x75903,f324(f324(f42(a838),x75902),x75901)))
% 18.77/18.50 [7649]E(f324(f324(f82(a838),f324(f324(f83(a838),x76491),f785(x76491,x76492,x76493))),f787(x76491,x76492,x76493)),x76492)+~P1(f324(x76493,f2(a838)))+P1(f324(x76493,f324(f324(f42(a838),x76492),x76491)))
% 18.77/18.50 [7665]~P1(f324(f64(x76651),x76653))+P1(f324(f324(f326(x76651),f407(x76652,x76653,x76651)),x76653))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f11(x76651,a838),x76652),x76653)))
% 18.77/18.50 [7666]~P1(f324(f64(x76661),x76663))+P1(f324(f324(f326(x76661),f596(x76662,x76663,x76661)),x76663))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f11(x76661,a838),x76662),x76663)))
% 18.77/18.50 [7773]E(x77731,f2(a838))+P1(f324(f324(f280(a838),x77732),x77733))+~P1(f324(f324(f280(a838),f324(f324(f83(a838),x77731),x77732)),f324(f324(f83(a838),x77731),x77733)))
% 18.77/18.50 [7774]E(x77741,f2(a1))+P1(f324(f324(f280(a1),x77742),x77743))+~P1(f324(f324(f280(a1),f324(f324(f83(a1),x77741),x77742)),f324(f324(f83(a1),x77741),x77743)))
% 18.77/18.50 [7775]E(x77751,f2(a1))+P1(f324(f324(f280(a1),x77752),x77753))+~P1(f324(f324(f280(a1),f324(f324(f83(a1),x77751),x77752)),f324(f324(f83(a1),x77751),x77753)))
% 18.77/18.50 [7964]E(x79641,f179(f845(x79642,a832)))+E(x79641,f324(f324(f303(x79642),x79643),f179(f845(x79642,a832))))+~P1(f324(f324(f231(f845(x79642,a832)),x79641),f324(f324(f303(x79642),x79643),f179(f845(x79642,a832)))))
% 18.77/18.50 [7989]~P86(x79891)+~P18(x79891,x79893)+P18(x79891,f324(f324(f128(x79891),f324(f180(f839(x79891)),f161(x79891,x79892,x79893))),x79893))
% 18.77/18.50 [8001]~P1(f324(f324(f232(a838),f2(a838)),x80013))+P1(f324(f324(f232(a838),x80011),x80012))+~P1(f324(f324(f232(a838),f324(f324(f83(a838),x80013),x80011)),f324(f324(f83(a838),x80013),x80012)))
% 18.77/18.50 [8002]~P1(f324(f324(f232(a838),f2(a838)),x80023))+P1(f324(f324(f232(a838),x80021),x80022))+~P1(f324(f324(f232(a838),f324(f324(f240(a838),x80023),x80021)),f324(f324(f240(a838),x80023),x80022)))
% 18.77/18.50 [8003]~P1(f324(f324(f232(a838),f2(a838)),x80033))+P1(f324(f324(f231(a838),x80031),x80032))+~P1(f324(f324(f231(a838),f324(f324(f83(a838),x80033),x80031)),f324(f324(f83(a838),x80033),x80032)))
% 18.77/18.50 [8004]~P1(f324(f324(f232(a838),f2(a838)),x80043))+P1(f324(f324(f231(a838),x80041),x80042))+~P1(f324(f324(f231(a838),f324(f324(f83(a838),x80043),x80041)),f324(f324(f83(a838),x80043),x80042)))
% 18.77/18.50 [8005]~P1(f324(f324(f232(a838),f80(a838)),x80053))+P1(f324(f324(f231(a838),x80051),x80052))+~P1(f324(f324(f280(a838),f324(f324(f240(a838),x80053),x80051)),f324(f324(f240(a838),x80053),x80052)))
% 18.77/18.50 [8006]~P1(f324(f324(f232(a838),f2(a838)),x80063))+P1(f324(f324(f231(a838),x80061),x80062))+~P1(f324(f324(f231(a838),f324(f324(f83(a838),x80061),x80063)),f324(f324(f83(a838),x80062),x80063)))
% 18.77/18.50 [8007]~P1(f324(f324(f232(a838),f2(a838)),x80073))+P1(f324(f324(f280(a838),x80071),x80072))+~P1(f324(f324(f280(a838),f324(f324(f83(a838),x80073),x80071)),f324(f324(f83(a838),x80073),x80072)))
% 18.77/18.50 [8008]~P1(f324(f324(f232(a838),f2(a838)),x80083))+P1(f324(f324(f280(a838),x80081),x80082))+~P1(f324(f324(f280(a838),f324(f324(f83(a838),x80083),x80081)),f324(f324(f83(a838),x80083),x80082)))
% 18.77/18.50 [8038]~P1(f324(x80381,x80383))+P1(f324(f324(f186(f35(x80381,x80382)),f774(x80383,x80382,x80381)),x80383))+~P1(f324(f324(f186(f35(x80381,x80382)),x80383),x80383))
% 18.77/18.50 [8046]~E(f324(f324(f104(f845(x80461,a832)),f677(x80463,x80462,x80461)),f676(x80463,x80462,x80461)),f179(f845(x80461,a832)))+E(f324(f324(f104(f845(x80461,a832)),x80462),f43(f845(x80461,a832),x80463)),f179(f845(x80461,a832)))+P1(f324(f324(f326(f845(x80461,a832)),x80462),x80463))
% 18.77/18.50 [8060]E(x80601,f115(x80602))+~E(f324(f131(f839(x80602),f839(x80602),f125(x80602),f115(x80602)),x80603),f115(x80602))+~P1(f324(f324(f326(f839(x80602)),x80601),f324(f157(f839(x80602)),x80603)))
% 18.77/18.50 [8061]E(x80611,f115(x80612))+~E(f324(f131(f839(x80612),f839(x80612),f125(x80612),f115(x80612)),x80613),f115(x80612))+~P1(f324(f324(f326(f839(x80612)),x80611),f324(f157(f839(x80612)),x80613)))
% 18.77/18.50 [8118]E(x81181,f179(f845(f845(x81182,a832),a832)))+P1(f324(f324(f326(f845(x81182,a832)),f678(x81183,x81181,x81182)),x81181))+P1(f324(f324(f231(f845(x81182,a832)),f44(f845(x81182,a832),x81181)),x81183))
% 18.77/18.50 [8124]~P67(x81241)+~P68(x81241)+E(f324(f324(f11(a1,x81241),f324(f324(f10(a838,x81241,a1),x81242),a107)),f324(f304(a838,a1,f102(a1)),x81243)),f324(f324(f11(a838,x81241),x81242),x81243))
% 18.77/18.50 [8125]~P67(x81251)+~P68(x81251)+E(f324(f324(f8(a1,x81251),f324(f324(f10(a838,x81251,a1),x81252),a107)),f324(f304(a838,a1,f102(a1)),x81253)),f324(f324(f8(a838,x81251),x81252),x81253))
% 18.77/18.50 [8164]~P1(f324(f64(x81641),x81643))+~P1(f324(f324(f232(a838),f2(a838)),f324(x81642,f407(x81642,x81643,x81641))))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f11(x81641,a838),x81642),x81643)))
% 18.77/18.50 [8165]~P1(f324(f64(x81651),x81653))+~P1(f324(f324(f232(a838),f2(a838)),f324(x81652,f596(x81652,x81653,x81651))))+P1(f324(f324(f232(a838),f2(a838)),f324(f324(f11(x81651,a838),x81652),x81653)))
% 18.77/18.50 [8200]~P60(x82002)+E(x82001,f80(x82002))+E(f324(f324(f284(x82002),f324(f324(f3(x82002),f324(f324(f240(x82002),x82001),x82003)),f80(x82002))),f324(f324(f3(x82002),x82001),f80(x82002))),f324(f324(f8(a838,x82002),f324(f240(x82002),x82001)),f324(f295(a838,f2(a838)),x82003)))
% 18.77/18.50 [8259]E(x82591,f2(a838))+~P1(f324(x82593,f324(f324(f42(a838),x82592),x82591)))+P1(f324(f324(f232(a838),x82592),f324(f324(f83(a838),x82591),f324(a114,f778(x82591,x82592,x82593)))))
% 18.77/18.50 [8279]P1(f324(x82791,f2(a838)))+~P1(f324(x82791,f324(f324(f42(a838),x82792),x82793)))+P1(f324(f324(f232(a838),x82792),f324(f324(f83(a838),x82793),f324(a114,f778(x82793,x82792,x82791)))))
% 18.77/18.50 [8318]E(x83181,f2(a838))+~P1(f324(x83183,f324(f324(f42(a838),x83182),x83181)))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x83181),f778(x83181,x83182,x83183))),x83182))
% 18.77/18.50 [8356]P1(f324(x83561,f2(a838)))+~P1(f324(x83561,f324(f324(f42(a838),x83563),x83562)))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x83562),f778(x83562,x83563,x83561))),x83563))
% 18.77/18.50 [8359]~P86(x83591)+E(f324(f324(f137(x83591,x83591,f7(x83591)),x83592),x83593),f138(x83591,x83591,f7(x83591),x83592,x83593))+P1(f324(f324(f326(x83591),x83592),f324(f157(x83591),x83593)))
% 18.77/18.50 [8399]~E(f324(x83993,f622(x83992,x83993,x83991)),f324(x83993,f624(x83992,x83993,x83991)))+~P57(x83991,f324(x83993,f623(x83992,x83993,x83991)))+P57(x83991,f324(f324(f45(x83992,f845(x83991,f845(x83991,a832))),f238(f845(x83992,a832))),x83993))
% 18.77/18.50 [8407]E(x84071,f179(f845(f845(x84072,a832),a832)))+~P1(f324(f324(f231(f845(x84072,a832)),f678(x84073,x84071,x84072)),x84073))+P1(f324(f324(f231(f845(x84072,a832)),f44(f845(x84072,a832),x84071)),x84073))
% 18.77/18.50 [8463]~P62(x84631)+~P1(f324(f324(f232(x84631),x84632),x84633))+P1(f324(f324(f232(x84631),x84632),f324(f324(f284(x84631),f324(f324(f82(x84631),x84632),x84633)),f324(f324(f82(x84631),f80(x84631)),f80(x84631)))))
% 18.77/18.50 [8506]~P1(f324(f324(x85061,f800(x85061,x85063,x85062)),f801(x85061,x85063,x85062)))+P1(f324(f324(x85061,x85062),x85063))+~P1(f324(f313(f844(a1,a1),a58),f324(f324(f247(a1,a1),x85062),x85063)))
% 18.77/18.50 [8507]~P1(f324(f324(x85071,f802(x85071,x85073,x85072)),f803(x85071,x85073,x85072)))+P1(f324(f324(x85071,x85072),x85073))+~P1(f324(f313(f844(a1,a1),a62),f324(f324(f247(a1,a1),x85072),x85073)))
% 18.77/18.50 [8508]~P1(f324(f324(x85081,f806(x85081,x85083,x85082)),f808(x85081,x85083,x85082)))+P1(f324(f324(x85081,x85082),x85083))+~P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),x85082),x85083)))
% 18.77/18.50 [8509]~P1(f324(f324(x85091,f810(x85091,x85093,x85092)),f811(x85091,x85093,x85092)))+P1(f324(f324(x85091,x85092),x85093))+~P1(f324(f313(f844(a838,a838),a213),f324(f324(f247(a838,a838),x85092),x85093)))
% 18.77/18.50 [8510]~P1(f324(f324(x85101,f720(x85101,x85103,x85102)),f723(x85101,x85103,x85102)))+P1(f324(f324(x85101,x85102),x85103))+~P1(f324(f313(f844(a1,a1),a167),f324(f324(f247(a1,a1),x85102),x85103)))
% 18.77/18.50 [8748]P1(f324(f324(x87481,x87482),x87483))+P1(f324(f313(f844(a838,a838),a213),f324(f324(f247(a838,a838),f810(x87481,x87483,x87482)),f811(x87481,x87483,x87482))))+~P1(f324(f313(f844(a838,a838),a213),f324(f324(f247(a838,a838),x87482),x87483)))
% 18.77/18.50 [8749]P1(f324(f324(x87491,x87492),x87493))+P1(f324(f313(f844(a1,a1),a58),f324(f324(f247(a1,a1),f800(x87491,x87493,x87492)),f801(x87491,x87493,x87492))))+~P1(f324(f313(f844(a1,a1),a58),f324(f324(f247(a1,a1),x87492),x87493)))
% 18.77/18.50 [8750]P1(f324(f324(x87501,x87502),x87503))+P1(f324(f313(f844(a1,a1),a62),f324(f324(f247(a1,a1),f802(x87501,x87503,x87502)),f803(x87501,x87503,x87502))))+~P1(f324(f313(f844(a1,a1),a62),f324(f324(f247(a1,a1),x87502),x87503)))
% 18.77/18.50 [8751]P1(f324(f324(x87511,x87512),x87513))+P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),f806(x87511,x87513,x87512)),f808(x87511,x87513,x87512))))+~P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),x87512),x87513)))
% 18.77/18.50 [8752]P1(f324(f324(x87521,x87522),x87523))+P1(f324(f313(f844(a1,a1),a167),f324(f324(f247(a1,a1),f720(x87521,x87523,x87522)),f723(x87521,x87523,x87522))))+~P1(f324(f313(f844(a1,a1),a167),f324(f324(f247(a1,a1),x87522),x87523)))
% 18.77/18.50 [9058]~P1(f324(f64(x90581),x90583))+P1(f324(f324(f326(f844(f845(x90581,a832),f845(x90581,a832))),f324(f324(f247(f845(x90581,a832),f845(x90581,a832)),x90582),x90583)),f300(x90581)))+~P1(f324(f324(f232(f845(x90581,a832)),x90582),x90583))
% 18.77/18.50 [9113]~P57(x91131,f324(x91133,f623(x91132,x91133,x91131)))+P57(x91131,f324(f324(f45(x91132,f845(x91131,f845(x91131,a832))),f238(f845(x91132,a832))),x91133))+~E(f324(f324(f104(f845(x91131,a832)),f244(x91131,x91131,f324(x91133,f622(x91132,x91133,x91131)))),f245(x91131,x91131,f324(x91133,f624(x91132,x91133,x91131)))),f179(f845(x91131,a832)))
% 18.77/18.50 [9306]P47(x93061,x93062,x93063)+P1(f324(f324(f326(f844(x93061,x93061)),f609(x93063,x93062,x93061)),x93063))+~P1(f324(f324(f326(f844(x93061,x93061)),f324(f324(f247(x93061,x93061),f608(x93063,x93062,x93061)),f608(x93063,x93062,x93061))),x93063))
% 18.77/18.50 [9878]P47(x98781,x98782,x98783)+~P1(f324(f324(f252(x98781,x98781,a832),f324(f324(f9(x98781,f845(x98781,a832),f845(x98781,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x98781,a832),f845(x98781,a832)),x98781),f10(a832,a832,x98781)),f324(f324(f10(a832,f845(a832,a832),x98781),a322),f324(f324(f9(x98781,f845(x98781,a832),a832),f326(x98781)),x98782)))),f324(f324(f9(x98781,f845(x98781,a832),a832),f326(x98781)),x98782))),f609(x98783,x98782,x98781)))+~P1(f324(f324(f326(f844(x98781,x98781)),f324(f324(f247(x98781,x98781),f608(x98783,x98782,x98781)),f608(x98783,x98782,x98781))),x98783))
% 18.77/18.50 [5456]~P7(x54562)+E(x54561,f2(x54562))+E(f324(f324(f42(x54562),f324(f324(f83(x54562),x54563),x54561)),x54561),x54563)
% 18.77/18.50 [5457]~P7(x54572)+E(x54571,f2(x54572))+E(f324(f324(f42(x54572),f324(f324(f83(x54572),x54571),x54573)),x54571),x54573)
% 18.77/18.50 [6103]~P7(x61031)+E(f324(f324(f83(x61031),f324(f324(f42(x61031),x61032),x61033)),x61033),x61032)+~P1(f324(f324(f280(x61031),x61033),x61032))
% 18.77/18.50 [6268]~P67(x62681)+~E(f324(x62682,f2(a838)),f2(x62681))+E(f324(f324(f8(a838,x62681),x62682),f324(f295(a838,f324(a114,f2(a838))),x62683)),f324(f324(f8(a838,x62681),x62682),f324(f295(a838,f2(a838)),x62683)))
% 18.77/18.50 [6410]~P7(x64102)+E(x64101,f2(x64102))+E(f324(f324(f42(x64102),f324(f324(f82(x64102),x64103),x64101)),x64101),f324(f324(f82(x64102),f324(f324(f42(x64102),x64103),x64101)),f80(x64102)))
% 18.77/18.50 [6411]~P7(x64112)+E(x64111,f2(x64112))+E(f324(f324(f42(x64112),f324(f324(f82(x64112),x64111),x64113)),x64111),f324(f324(f82(x64112),f324(f324(f42(x64112),x64113),x64111)),f80(x64112)))
% 18.77/18.50 [6640]~P1(f324(x66403,f2(a1)))+P1(f324(f324(f231(a838),x66401),x66402))+P1(f324(x66403,f324(f102(a1),f324(f324(f3(a838),x66402),x66401))))
% 18.77/18.50 [6753]P1(f324(f324(f231(a838),x67532),x67531))+P1(f324(f324(f232(a838),x67531),x67532))+P1(f324(x67533,f324(f102(a1),f324(f324(f3(a838),x67531),x67532))))
% 18.77/18.50 [6826]E(f324(f324(f82(a838),f324(f106(a838),x68261)),f324(f324(f82(a838),f324(f106(a838),x68262)),x68263)),f324(f324(f82(a838),f324(f106(a838),x68261)),x68263))+P1(f324(a185,f324(f106(a1),x68261)))+~P1(f324(a185,f324(f106(a1),x68262)))
% 18.77/18.50 [6904]~E(x69042,f324(f324(f42(a838),x69043),x69041))+~P1(f324(f324(f232(a838),f2(a838)),x69041))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x69041),x69042)),x69043))
% 18.77/18.50 [7020]~P1(f324(f64(x70201),x70203))+~P1(f324(f64(x70201),x70202))+P1(f324(f64(x70201),f324(f324(f3(f845(x70201,a832)),x70202),x70203)))
% 18.77/18.50 [7021]~P1(f324(f64(x70211),x70213))+~P1(f324(f64(x70211),x70212))+P1(f324(f64(x70211),f324(f324(f103(f845(x70211,a832)),x70212),x70213)))
% 18.77/18.50 [7022]~P1(f324(f64(x70221),x70223))+~P1(f324(f64(x70221),x70222))+P1(f324(f64(x70221),f324(f324(f103(f845(x70221,a832)),x70222),x70223)))
% 18.77/18.50 [7336]~P86(x73361)+~P1(f324(f64(x73361),x73362))+E(f129(x73361,f324(f324(f3(f845(x73361,a832)),x73362),f324(f324(f303(x73361),x73363),f179(f845(x73361,a832))))),f155(x73361,x73363,f129(x73361,x73362)))
% 18.77/18.50 [7405]P1(f324(x74051,f2(a1)))+~P1(f324(f324(f232(a838),x74052),x74053))+~P1(f324(x74051,f324(f102(a1),f324(f324(f3(a838),x74052),x74053))))
% 18.77/18.50 [7423]~P1(f324(f64(x74231),x74232))+E(f324(f41(x74231),f324(f324(f3(f845(x74231,a832)),x74232),f324(f324(f303(x74231),x74233),f179(f845(x74231,a832))))),f324(f41(x74231),x74232))+P1(f324(f324(f326(x74231),x74233),x74232))
% 18.77/18.50 [7557]~P84(x75571)+~P1(f324(f324(f232(x75571),f80(x75571)),x75572))+P1(f324(f324(f232(x75571),f80(x75571)),f324(f324(f83(x75571),x75572),f324(f324(f240(x75571),x75572),x75573))))
% 18.77/18.50 [7601]~P1(f324(f64(x76011),x76013))+E(f324(f324(f3(a838),f324(f41(x76011),x76012)),f324(f41(x76011),x76013)),f324(f41(x76011),f324(f324(f3(f845(x76011,a832)),x76012),x76013)))+~P1(f324(f324(f231(f845(x76011,a832)),x76013),x76012))
% 18.77/18.50 [7657]~P1(f324(f324(f231(a838),x76572),x76573))+~P1(f324(f324(f231(a838),x76571),f324(f324(f3(a838),x76573),x76572)))+P1(f324(f324(f231(a838),f324(f324(f82(a838),x76571),x76572)),x76573))
% 18.77/18.50 [7715]P1(f324(f64(x77151),x77152))+~P1(f324(f64(x77151),x77153))+~P1(f324(f64(x77151),f324(f324(f3(f845(x77151,a832)),x77152),x77153)))
% 18.77/18.50 [7721]~P1(f324(f64(x77211),x77212))+E(f324(f41(x77211),f324(f324(f3(f845(x77211,a832)),x77212),f324(f324(f303(x77211),x77213),f179(f845(x77211,a832))))),f324(f324(f3(a838),f324(f41(x77211),x77212)),f80(a838)))+~P1(f324(f324(f326(x77211),x77213),x77212))
% 18.77/18.50 [7722]~P1(f324(f64(x77221),x77222))+E(f324(f41(x77221),f324(f324(f3(f845(x77221,a832)),x77222),f324(f324(f303(x77221),x77223),f179(f845(x77221,a832))))),f324(f324(f3(a838),f324(f41(x77221),x77222)),f80(a838)))+~P1(f324(f324(f326(x77221),x77223),x77222))
% 18.77/18.50 [7798]P57(x77981,x77982)+~P57(x77981,x77983)+~P1(f324(f324(f231(f845(x77981,f845(x77981,a832))),x77982),x77983))
% 18.77/18.50 [7836]~P1(f324(f324(f231(a838),x78363),x78362))+P1(f324(f324(f231(a838),x78361),f324(f324(f3(a838),x78362),x78363)))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),x78361),x78363)),x78362))
% 18.77/18.50 [7856]P36(x78561,x78562)+~P36(x78561,x78563)+~P1(f324(f324(f231(f845(f844(x78561,x78561),a832)),x78562),x78563))
% 18.77/18.50 [7857]P55(x78571,x78572)+~P55(x78571,x78573)+~P1(f324(f324(f231(f845(f844(x78571,x78571),a832)),x78572),x78573))
% 18.77/18.50 [8096]~P84(x80961)+~P1(f324(f324(f232(x80961),f80(x80961)),x80962))+P1(f324(f324(f232(x80961),f324(f324(f240(x80961),x80962),x80963)),f324(f324(f83(x80961),x80962),f324(f324(f240(x80961),x80962),x80963))))
% 18.77/18.50 [8184]~P1(f324(x81841,f2(a1)))+~P1(f324(x81841,f324(f324(f3(a1),f324(f102(a1),x81842)),f324(f102(a1),x81843))))+P1(f324(x81841,f324(f102(a1),f324(f324(f3(a838),x81842),x81843))))
% 18.77/18.50 [8197]~P1(f324(f324(f231(a838),x81973),x81972))+P1(f324(x81971,f324(f324(f3(a1),f324(f102(a1),x81972)),f324(f102(a1),x81973))))+~P1(f324(x81971,f324(f102(a1),f324(f324(f3(a838),x81972),x81973))))
% 18.77/18.50 [8214]P1(f324(f324(f232(a838),x82141),x82142))+~P1(f324(x82143,f324(f324(f3(a1),f324(f102(a1),x82141)),f324(f102(a1),x82142))))+P1(f324(x82143,f324(f102(a1),f324(f324(f3(a838),x82141),x82142))))
% 18.77/18.50 [8271]~P117(x82712)+E(x82711,f2(x82712))+P1(f324(f324(f232(x82712),f2(x82712)),f324(f324(f82(x82712),f324(f324(f83(x82712),x82713),x82713)),f324(f324(f83(x82712),x82711),x82711))))
% 18.77/18.50 [8272]~P117(x82722)+E(x82721,f2(x82722))+P1(f324(f324(f232(x82722),f2(x82722)),f324(f324(f82(x82722),f324(f324(f83(x82722),x82721),x82721)),f324(f324(f83(x82722),x82723),x82723))))
% 18.77/18.50 [8378]~P1(f324(f324(f232(a838),f2(a838)),x83781))+~P1(f324(f324(f232(a1),x83782),x83783))+P1(f324(f324(f232(a1),f324(f324(f83(a1),f324(f102(a1),x83781)),x83782)),f324(f324(f83(a1),f324(f102(a1),x83781)),x83783)))
% 18.77/18.50 [8435]E(f324(f324(f104(f845(x84351,a832)),x84352),f43(f845(x84351,a832),x84353)),f179(f845(x84351,a832)))+P1(f324(f324(f326(f845(x84351,a832)),x84352),x84353))+P1(f324(f324(f326(f845(x84351,a832)),f677(x84353,x84352,x84351)),f324(f324(f303(f845(x84351,a832)),x84352),x84353)))
% 18.77/18.50 [8436]E(f324(f324(f104(f845(x84361,a832)),x84362),f43(f845(x84361,a832),x84363)),f179(f845(x84361,a832)))+P1(f324(f324(f326(f845(x84361,a832)),x84362),x84363))+P1(f324(f324(f326(f845(x84361,a832)),f676(x84363,x84362,x84361)),f324(f324(f303(f845(x84361,a832)),x84362),x84363)))
% 18.77/18.50 [8462]E(x84621,x84622)+~E(f324(f180(f839(x84623)),x84621),f324(f180(f839(x84623)),x84622))+P1(f324(f324(f326(f844(x84623,x84623)),f701(x84623,x84621,x84622)),f324(f157(f844(x84623,x84623)),f324(f324(f166(x84623,x84623),x84622),x84621))))
% 18.77/18.50 [8676]E(f301(x86761,x86762),f301(x86761,x86763))+~P1(f324(f324(f231(f845(f844(x86761,x86761),a832)),x86763),f301(x86761,x86762)))+~P1(f324(f324(f231(f845(f844(x86761,x86761),a832)),x86762),x86763))
% 18.77/18.50 [8730]~P47(x87301,f238(f845(x87301,a832)),x87303)+P1(f324(f324(f231(f845(f844(f839(x87301),f839(x87301)),a832)),f144(x87301,x87302)),f145(x87301,x87303)))+~P1(f324(f324(f231(f845(f844(x87301,x87301),a832)),x87302),x87303))
% 18.77/18.50 [8908]P36(x89081,x89082)+~P1(f324(f324(f326(x89081),x89083),f368(x89082,x89081)))+P1(f324(f324(f326(f844(x89081,x89081)),f324(f324(f247(x89081,x89081),f370(x89082,x89081,x89083)),x89083)),x89082))
% 18.77/18.50 [8942]~P1(f324(f64(x89421),x89422))+P1(f324(f64(f845(x89421,a832)),f324(f324(f63(x89421),x89422),x89423)))+~P1(f324(f324(f231(f845(f844(x89421,x89421),a832)),x89423),f324(f324(f249(x89421,x89421),x89422),f324(f18(f845(x89421,a832),x89421),x89422))))
% 18.77/18.50 [8972]P47(x89721,x89722,x89723)+P1(f324(f324(f326(x89721),f597(x89723,x89722,x89721)),x89722))+~P1(f324(f324(f231(f845(f844(x89721,x89721),a832)),x89723),f324(f324(f249(x89721,x89721),x89722),f324(f18(f845(x89721,a832),x89721),x89722))))
% 18.77/18.50 [8973]P47(x89731,x89732,x89733)+P1(f324(f324(f326(x89731),f598(x89732,x89733,x89731)),x89732))+~P1(f324(f324(f231(f845(f844(x89731,x89731),a832)),x89733),f324(f324(f249(x89731,x89731),x89732),f324(f18(f845(x89731,a832),x89731),x89732))))
% 18.77/18.50 [9006]~P62(x90061)+~P1(f324(f324(f232(x90061),x90062),x90063))+P1(f324(f324(f232(x90061),f324(f324(f284(x90061),f324(f324(f82(x90061),x90062),x90063)),f324(f324(f82(x90061),f80(x90061)),f80(x90061)))),x90063))
% 18.77/18.50 [9033]~P61(x90331)+P1(f324(f324(f231(x90331),x90332),x90333))+~P1(f324(f324(f231(x90331),f324(f324(f83(x90331),f783(x90333,x90332,x90331)),x90332)),x90333))
% 18.77/18.50 [9142]E(f307(x91421,x91422,x91423),f182(f839(a831)))+~P1(f324(f324(f232(a1),x91422),x91423))+~P1(f324(f313(f844(f845(a1,f842(f839(a831))),f844(a1,a1)),a311),f324(f324(f247(f845(a1,f842(f839(a831))),f844(a1,a1)),x91421),f324(f324(f247(a1,a1),x91422),x91423))))
% 18.77/18.50 [9145]E(f324(f180(f839(f839(x91451))),f324(f126(f839(x91451),f324(f324(f10(a838,a832,f839(x91451)),f324(f232(a838),x91452)),f180(f839(x91451)))),f163(x91451,x91453))),f324(f180(f839(x91451)),f324(f324(f149(f839(x91451)),x91453),x91452)))+~P18(a838,f324(f154(a838),f324(f324(f141(f839(x91451),a838),f180(f839(x91451))),x91453)))+~P1(f324(f324(f232(a838),x91452),f324(f180(f839(f839(x91451))),x91453)))
% 18.77/18.50 [9256]~P36(x92561,x92562)+P30(x92561,f324(f324(f247(f845(f844(x92561,x92561),a832),f845(f844(x92561,x92561),a832)),x92562),x92563))+~P1(f324(f324(f231(f845(f844(x92561,x92561),a832)),f324(f324(f282(x92561,x92561,x92561),x92562),x92563)),x92562))
% 18.77/18.50 [9258]E(f324(f228(f842(f839(a831)),f839(a831),f307(x92581,x92582,f324(f324(f82(a1),x92583),f80(a1))),f226(f839(a831))),f324(x92581,x92583)),f307(x92581,x92582,x92583))+P1(f324(f324(f232(a1),x92582),x92583))+~P1(f324(f313(f844(f845(a1,f842(f839(a831))),f844(a1,a1)),a311),f324(f324(f247(f845(a1,f842(f839(a831))),f844(a1,a1)),x92581),f324(f324(f247(a1,a1),x92582),x92583))))
% 18.77/18.50 [9263]E(f324(f324(f141(f839(x92631),x92631),f324(f324(f9(f839(x92631),a838,x92631),f149(x92631)),x92632)),f324(f126(f839(x92631),f324(f324(f10(a838,a832,f839(x92631)),f324(f232(a838),x92632)),f180(f839(x92631)))),f163(x92631,x92633))),f324(f324(f149(f839(x92631)),x92633),x92632))+~P18(a838,f324(f154(a838),f324(f324(f141(f839(x92631),a838),f180(f839(x92631))),x92633)))+~P1(f324(f324(f232(a838),x92632),f324(f180(f839(f839(x92631))),x92633)))
% 18.77/18.50 [9391]P47(x93911,x93912,x93913)+~P1(f324(f324(f326(f844(x93911,x93911)),f324(f324(f247(x93911,x93911),f597(x93913,x93912,x93911)),f597(x93913,x93912,x93911))),x93913))+~P1(f324(f324(f231(f845(f844(x93911,x93911),a832)),x93913),f324(f324(f249(x93911,x93911),x93912),f324(f18(f845(x93911,a832),x93911),x93912))))
% 18.77/18.50 [9392]P47(x93921,x93922,x93923)+~P1(f324(f324(f326(f844(x93921,x93921)),f324(f324(f247(x93921,x93921),f598(x93922,x93923,x93921)),f598(x93922,x93923,x93921))),x93923))+~P1(f324(f324(f231(f845(f844(x93921,x93921),a832)),x93923),f324(f324(f249(x93921,x93921),x93922),f324(f18(f845(x93921,a832),x93921),x93922))))
% 18.77/18.50 [9555]~P119(x95551)+~P116(x95551)+E(f324(f324(f284(x95551),f324(f105(x95551),f324(f324(f75(f844(a1,a1),a1,x95552,f246(a1,a1)),f206(x95552)),x95553))),f324(f105(x95551),f324(f324(f75(f844(a1,a1),a1,x95552,f251(a1,a1)),f206(x95552)),x95553))),f216(x95552,x95551,x95553))
% 18.77/18.50 [9754]~E(x97543,f2(a838))+~E(f324(f180(f839(x97541)),f324(f324(f149(f839(x97541)),x97542),f759(x97543,x97541,x97542))),x97543)+E(f324(f324(f141(a838,f839(x97541)),f324(f324(f9(a838,f839(a838),f839(x97541)),f324(f324(f10(f845(a838,x97541),f845(f839(a838),f839(x97541)),a838),f141(a838,x97541)),f324(f9(a838,a838,x97541),f324(f324(f10(f839(x97541),f845(a838,x97541),a838),f149(x97541)),f324(f149(f839(x97541)),x97542))))),f129(a838,f324(f295(a838,f2(a838)),f324(f180(f839(f839(x97541))),x97542))))),f129(a838,f324(f295(a838,f2(a838)),x97543))),f163(x97541,x97542))
% 18.77/18.50 [9755]E(x97551,f115(f839(x97552)))+~E(f324(f180(f839(x97552)),f324(f324(f149(f839(x97552)),x97551),f759(x97553,x97552,x97551))),x97553)+E(f324(f324(f141(a838,f839(x97552)),f324(f324(f9(a838,f839(a838),f839(x97552)),f324(f324(f10(f845(a838,x97552),f845(f839(a838),f839(x97552)),a838),f141(a838,x97552)),f324(f9(a838,a838,x97552),f324(f324(f10(f839(x97552),f845(a838,x97552),a838),f149(x97552)),f324(f149(f839(x97552)),x97551))))),f129(a838,f324(f295(a838,f2(a838)),f324(f180(f839(f839(x97552))),x97551))))),f129(a838,f324(f295(a838,f2(a838)),x97553))),f163(x97552,x97551))
% 18.77/18.50 [9756]~E(x97563,f2(a838))+E(f324(f324(f141(a838,f839(x97561)),f324(f324(f9(a838,f839(a838),f839(x97561)),f324(f324(f10(f845(a838,x97561),f845(f839(a838),f839(x97561)),a838),f141(a838,x97561)),f324(f9(a838,a838,x97561),f324(f324(f10(f839(x97561),f845(a838,x97561),a838),f149(x97561)),f324(f149(f839(x97561)),x97562))))),f129(a838,f324(f295(a838,f2(a838)),f324(f180(f839(f839(x97561))),x97562))))),f129(a838,f324(f295(a838,f2(a838)),x97563))),f163(x97561,x97562))+P1(f324(f324(f232(a838),f759(x97563,x97561,x97562)),f324(f180(f839(f839(x97561))),x97562)))
% 18.77/18.50 [9757]E(x97571,f115(f839(x97572)))+E(f324(f324(f141(a838,f839(x97572)),f324(f324(f9(a838,f839(a838),f839(x97572)),f324(f324(f10(f845(a838,x97572),f845(f839(a838),f839(x97572)),a838),f141(a838,x97572)),f324(f9(a838,a838,x97572),f324(f324(f10(f839(x97572),f845(a838,x97572),a838),f149(x97572)),f324(f149(f839(x97572)),x97571))))),f129(a838,f324(f295(a838,f2(a838)),f324(f180(f839(f839(x97572))),x97571))))),f129(a838,f324(f295(a838,f2(a838)),x97573))),f163(x97572,x97571))+P1(f324(f324(f232(a838),f759(x97573,x97572,x97571)),f324(f180(f839(f839(x97572))),x97571)))
% 18.77/18.50 [7598]E(f324(f324(f82(a838),f324(f106(a838),x75981)),f324(f324(f82(a838),f324(f106(a838),x75982)),x75983)),f324(f324(f82(a838),f324(f106(a838),f324(f324(f82(a1),x75981),x75982))),x75983))+P1(f324(a185,f324(f106(a1),x75981)))+P1(f324(a185,f324(f106(a1),x75982)))
% 18.77/18.50 [8369]~P1(f324(f64(x83691),x83692))+~P1(f324(f324(f326(x83691),x83693),x83692))+E(f324(a114,f324(f41(x83691),f324(f324(f3(f845(x83691,a832)),x83692),f324(f324(f303(x83691),x83693),f179(f845(x83691,a832)))))),f324(f41(x83691),x83692))
% 18.77/18.50 [8389]~P1(f324(f64(x83891),x83892))+~P1(f324(f324(f326(x83891),x83893),x83892))+E(f324(f324(f82(a838),f80(a838)),f324(f41(x83891),f324(f324(f3(f845(x83891,a832)),x83892),f324(f324(f303(x83891),x83893),f179(f845(x83891,a832)))))),f324(f41(x83891),x83892))
% 18.77/18.50 [8470]~P86(x84701)+~P1(f324(f64(x84701),x84703))+E(f324(f324(f137(x84701,x84701,f7(x84701)),x84702),f129(x84701,f324(f324(f3(f845(x84701,a832)),x84703),f324(f324(f303(x84701),x84702),f179(f845(x84701,a832)))))),f129(x84701,f324(f324(f303(x84701),x84702),x84703)))
% 18.77/18.50 [8608]~P1(f324(f64(x86081),x86083))+~P1(f324(f64(x86081),x86082))+E(f324(f324(f82(a838),f324(f41(x86081),f324(f324(f103(f845(x86081,a832)),x86082),x86083))),f324(f41(x86081),f324(f324(f104(f845(x86081,a832)),x86082),x86083))),f324(f324(f82(a838),f324(f41(x86081),x86082)),f324(f41(x86081),x86083)))
% 18.77/18.50 [8609]~P1(f324(f64(x86091),x86093))+~P1(f324(f64(x86091),x86092))+E(f324(f324(f82(a838),f324(f41(x86091),f324(f324(f103(f845(x86091,a832)),x86092),x86093))),f324(f41(x86091),f324(f324(f104(f845(x86091,a832)),x86092),x86093))),f324(f324(f82(a838),f324(f41(x86091),x86092)),f324(f41(x86091),x86093)))
% 18.77/18.50 [9703]~P29(x97031,f845(f845(x97031,a832),a832),f324(f324(f9(x97031,f845(f844(x97031,x97031),a832),f845(f845(x97031,a832),a832)),f324(f324(f10(f845(x97031,a832),f845(f845(f844(x97031,x97031),a832),f845(f845(x97031,a832),a832)),x97031),f63(x97031)),f324(f324(f9(x97031,f845(x97031,a832),f845(x97031,a832)),f303(x97031)),f179(f845(x97031,a832))))),x97033),x97032)+~P1(f324(f64(x97031),x97032))+E(f324(f41(f845(x97031,a832)),f324(f324(f63(x97031),x97032),x97033)),f324(f41(x97031),x97032))
% 18.77/18.50 [7874]~P89(x78741)+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x78743)))+E(f324(f324(f240(x78741),x78742),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x78743),x78743)),a99))),f80(x78741))
% 18.77/18.50 [7965]~P89(x79651)+P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x79653)))+E(f324(f324(f240(x79651),f324(f106(x79651),x79652)),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x79653),x79653)),a99))),f80(x79651))
% 18.77/18.50 [9239]~P89(x92391)+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x92393)))+E(f324(f324(f240(x92391),x92392),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x92393),x92393)),a99))),f324(f324(f88(x92391,x92391),f324(f324(f240(x92391),x92392),f324(f106(a838),x92393))),f324(f324(f20(x92391,x92391,x92391),f324(f324(f10(x92391,f845(x92391,x92391),x92391),f83(x92391)),f324(f83(x92391),x92392))),f7(x92391))))
% 18.77/18.50 [9305]~P89(x93051)+~P1(f324(f324(f231(a1),f2(a1)),f324(f106(a1),x93053)))+E(f324(f324(f240(x93051),f324(f106(x93051),x93052)),f324(f106(a838),f324(f324(f3(a1),f324(f324(f82(a1),x93053),x93053)),a99))),f324(f324(f88(x93051,x93051),f324(f324(f240(x93051),f324(f106(x93051),x93052)),f324(f106(a838),x93053))),f324(f324(f20(x93051,x93051,x93051),f324(f324(f10(x93051,f845(x93051,x93051),x93051),f83(x93051)),f324(f83(x93051),f324(f106(x93051),x93052)))),f7(x93051))))
% 18.77/18.50 [9610]~P1(f324(f127(x96101),x96103))+~P1(f324(f324(f326(x96101),x96102),f324(f157(x96101),x96103)))+E(f324(f324(f128(x96101),f324(f180(f839(x96101)),f161(x96101,f324(f324(f10(a832,a832,x96101),a320),f324(f324(f9(x96101,x96101,a832),a321),x96102)),f324(f154(x96101),x96103)))),f324(f154(x96101),x96103)),f324(f324(f139(x96101),x96102),f324(f154(x96101),f161(x96101,f324(f324(f10(a832,a832,x96101),a320),f324(f324(f9(x96101,x96101,a832),a321),x96102)),x96103))))
% 18.77/18.50 [9670]P1(f324(f324(f231(f845(f844(x96701,x96701),a832)),f301(x96701,x96702)),x96703))+~P1(f324(f324(f231(f845(f844(x96701,x96701),a832)),f301(x96701,f179(f845(f844(x96701,x96701),a832)))),x96703))+~P1(f324(f324(f231(f845(f844(x96701,x96701),a832)),f324(f324(f282(x96701,x96701,x96701),f324(f324(f104(f845(f844(x96701,x96701),a832)),f301(x96701,x96702)),x96703)),x96702)),x96703))
% 18.77/18.50 [9531]~P1(f324(f64(x95311),f324(f257(x95311),x95313)))+~P1(f324(f64(x95311),f324(f257(x95311),x95312)))+P1(f324(f64(x95311),f324(f257(x95311),f324(f324(f20(x95311,a832,a832),f324(f324(f10(a832,f845(a832,a832),x95311),a323),x95312)),x95313))))
% 18.77/18.50 [9821]P1(f324(f324(f231(f845(f844(x98211,x98211),a832)),f324(f324(f282(x98211,x98211,x98211),x98212),f301(x98211,x98212))),x98213))+~P1(f324(f324(f231(f845(f844(x98211,x98211),a832)),x98212),x98213))+~P1(f324(f324(f231(f845(f844(x98211,x98211),a832)),f324(f324(f282(x98211,x98211,x98211),f324(f324(f104(f845(f844(x98211,x98211),a832)),f324(f324(f282(x98211,x98211,x98211),x98212),f301(x98211,x98212))),x98213)),x98212)),x98213))
% 18.77/18.50 [9768]~P103(x97682)+E(x97681,f2(x97682))+~E(f324(f324(f82(x97682),f324(f324(f240(x97682),x97683),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x97682),x97681),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f2(x97682))
% 18.77/18.50 [9769]~P103(x97692)+E(x97691,f2(x97692))+~E(f324(f324(f82(x97692),f324(f324(f240(x97692),x97691),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x97692),x97693),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f2(x97692))
% 18.77/18.50 [9775]~P1(f324(f127(x97751),x97753))+~P1(f324(f324(f326(x97751),x97752),f324(f157(x97751),x97753)))+E(f324(f154(x97751),f324(f156(x97751),f324(f324(f128(x97751),f324(f180(f839(x97751)),f161(x97751,f324(f324(f10(a832,a832,x97751),a320),f324(f324(f9(x97751,x97751,a832),a321),x97752)),x97753))),x97753))),f161(x97751,f324(f324(f10(a832,a832,x97751),a320),f324(f324(f9(x97751,x97751,a832),a321),x97752)),f324(f154(x97751),x97753)))
% 18.77/18.50 [9863]~P103(x98632)+E(x98631,f2(x98632))+P1(f324(f324(f232(x98632),f2(x98632)),f324(f324(f82(x98632),f324(f324(f240(x98632),x98633),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98632),x98631),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))))
% 18.77/18.50 [9864]~P103(x98642)+E(x98641,f2(x98642))+P1(f324(f324(f232(x98642),f2(x98642)),f324(f324(f82(x98642),f324(f324(f240(x98642),x98641),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98642),x98643),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))))
% 18.77/18.50 [9911]~P103(x99111)+P1(f324(f324(f231(x99111),f2(x99111)),x99112))+~P1(f324(f324(f231(x99111),f2(x99111)),f324(f324(f240(x99111),x99112),f324(a114,f324(f324(f83(a838),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x99113)))))
% 18.77/18.50 [5297]~P28(x52971,x52974,x52973)+P28(x52971,x52972,x52973)+~P28(x52971,x52972,x52974)
% 18.77/18.50 [4778]~E(x47782,f92(x47783,x47781))+P1(f324(x47781,x47782))+~P1(f324(x47781,x47784))
% 18.77/18.50 [6545]~P36(x65452,x65454)+~P36(x65451,x65453)+P36(f844(x65451,x65452),f318(x65451,x65452,x65453,x65454))
% 18.77/18.50 [7947]~P39(f35(x79474,x79471),x79472,x79473,x79472)+P39(x79471,x79472,x79473,f737(x79473,x79472,x79471,x79474))+~P1(f324(x79474,x79472))
% 18.77/18.50 [7974]~P39(f35(x79741,x79742),x79744,x79743,x79744)+P39(f35(x79741,x79742),f737(x79743,x79744,x79742,x79741),x79743,x79744)+~P1(f324(x79741,x79744))
% 18.77/18.50 [4955]~P11(x49554,x49551)+~E(f324(x49551,x49552),f324(x49551,x49553))+P1(f324(f324(x49551,x49552),x49553))
% 18.77/18.50 [5116]~P11(x51164,x51161)+E(f324(x51161,x51162),f324(x51161,x51163))+~P1(f324(f324(x51161,x51162),x51163))
% 18.77/18.50 [5204]~P22(x52043,x52044,x52041)+E(f324(x52041,x52042),f324(f66(x52043,x52044),x52042))+~P1(f324(f64(x52043),x52042))
% 18.77/18.50 [5205]~P14(x52053,x52054,x52051)+E(f324(x52051,x52052),f324(f66(x52053,x52054),x52052))+~P1(f324(f64(x52053),x52052))
% 18.77/18.50 [5332]~P11(x53324,x53321)+~P1(f324(f324(x53321,x53323),x53322))+P1(f324(f324(x53321,x53322),x53323))
% 18.77/18.50 [5397]E(x53971,x53972)+~E(f324(f246(x53973,x53974),x53971),f324(f246(x53973,x53974),x53972))+~E(f324(f251(x53973,x53974),x53971),f324(f251(x53973,x53974),x53972))
% 18.77/18.50 [5398]E(x53981,x53982)+~E(f324(f246(x53983,x53984),x53981),f324(f246(x53983,x53984),x53982))+~E(f324(f251(x53983,x53984),x53981),f324(f251(x53983,x53984),x53982))
% 18.77/18.50 [5424]E(x54241,x54242)+~P1(f324(f54(x54243,x54244),x54242))+~P1(f324(f54(x54243,x54244),x54241))
% 18.77/18.50 [5621]~P67(x56212)+E(f224(x56211,x56212,x56213,x56214),f2(x56212))+P1(f324(f64(x56211),x56214))
% 18.77/18.50 [5754]~P1(f324(f313(x57541,x57542),x57544))+P1(f324(f313(x57541,x57542),x57543))+~P1(f324(f324(x57542,x57543),x57544))
% 18.77/18.50 [5755]~P1(f324(f313(x57551,x57552),x57554))+P1(f324(f313(x57551,x57552),x57553))+~P1(f324(f324(x57552,x57553),x57554))
% 18.77/18.50 [5756]~P1(f324(f313(x57561,x57562),x57564))+P1(f324(f313(x57561,x57562),x57563))+~P1(f324(f324(x57562,x57563),x57564))
% 18.77/18.50 [8018]~P1(f324(f64(x80182),x80184))+~P1(f324(f64(x80181),x80183))+P1(f324(f64(f848(x80181,x80182)),f312(x80181,x80182,x80183,x80184)))
% 18.77/18.50 [8019]~P1(f324(f64(x80192),x80194))+~P1(f324(f64(x80191),x80193))+P1(f324(f64(f848(x80191,x80192)),f312(x80191,x80192,x80193,x80194)))
% 18.77/18.50 [8023]P1(f324(f324(f326(f839(x80231)),f324(f324(f125(x80231),x80232),x80233)),f147(x80231,x80234)))+~P1(f324(f324(f326(f839(x80231)),x80233),f147(x80231,x80234)))+~P1(f324(f324(f326(f839(x80231)),x80232),f147(x80231,x80234)))
% 18.77/18.50 [8339]P1(f324(x83391,x83392))+~E(x83393,f324(f226(x83394),x83392))+~P1(f324(x83391,f492(x83392,x83391,x83393,x83394)))
% 18.77/18.50 [8598]~P1(f324(f324(f326(f844(x85981,x85981)),f324(f324(f247(x85981,x85981),x85982),x85984)),f301(x85981,x85983)))+P1(f324(f324(f326(x85981),x85982),f314(x85981,x85983)))+~P1(f324(f324(f326(x85981),x85984),f314(x85981,x85983)))
% 18.77/18.50 [8599]~P1(f324(f324(f326(f844(x85991,x85991)),f324(f324(f247(x85991,x85991),x85992),x85994)),f301(x85991,x85993)))+P1(f324(f324(f326(x85991),x85992),f314(x85991,x85993)))+~P1(f324(f324(f326(x85991),x85994),f314(x85991,x85993)))
% 18.77/18.50 [8618]~E(x86184,f324(f226(x86183),x86182))+P1(f324(x86181,x86182))+P1(f324(f324(f326(x86183),f492(x86182,x86181,x86184,x86183)),f225(x86183,x86184)))
% 18.77/18.50 [4937]~P68(x49372)+E(f324(f324(f11(x49371,x49372),x49373),x49374),f80(x49372))+P1(f324(f64(x49371),x49374))
% 18.77/18.50 [4938]~P68(x49382)+E(f324(f324(f11(x49381,x49382),x49383),x49384),f80(x49382))+P1(f324(f64(x49381),x49384))
% 18.77/18.50 [4939]~P68(x49392)+E(f324(f324(f11(x49391,x49392),x49393),x49394),f80(x49392))+P1(f324(f64(x49391),x49394))
% 18.77/18.50 [4940]~P67(x49402)+E(f324(f324(f8(x49401,x49402),x49403),x49404),f2(x49402))+P1(f324(f64(x49401),x49404))
% 18.77/18.50 [4941]~P67(x49412)+E(f324(f324(f8(x49411,x49412),x49413),x49414),f2(x49412))+P1(f324(f64(x49411),x49414))
% 18.77/18.50 [4942]~P67(x49422)+E(f324(f324(f8(x49421,x49422),x49423),x49424),f2(x49422))+P1(f324(f64(x49421),x49424))
% 18.77/18.50 [5084]~P64(x50843)+E(x50841,x50842)+~E(f324(f324(f82(x50843),x50844),x50841),f324(f324(f82(x50843),x50844),x50842))
% 18.77/18.50 [5085]~P64(x50853)+E(x50851,x50852)+~E(f324(f324(f82(x50853),x50854),x50851),f324(f324(f82(x50853),x50854),x50852))
% 18.77/18.50 [5086]~P65(x50863)+E(x50861,x50862)+~E(f324(f324(f82(x50863),x50864),x50861),f324(f324(f82(x50863),x50864),x50862))
% 18.77/18.50 [5087]~P64(x50873)+E(x50871,x50872)+~E(f324(f324(f82(x50873),x50871),x50874),f324(f324(f82(x50873),x50872),x50874))
% 18.77/18.50 [5088]~P64(x50883)+E(x50881,x50882)+~E(f324(f324(f82(x50883),x50881),x50884),f324(f324(f82(x50883),x50882),x50884))
% 18.77/18.50 [5174]~P113(x51741)+~E(x51743,f324(f324(f83(x51741),x51742),x51744))+P1(f324(f324(f280(x51741),x51742),x51743))
% 18.77/18.50 [5199]~P9(x51993)+E(x51991,f179(f845(x51992,a832)))+E(f324(f324(f45(x51992,x51993),x51991),f324(f18(x51993,x51992),x51994)),x51994)
% 18.77/18.50 [5200]~P9(x52003)+E(x52001,f179(f845(x52002,a832)))+E(f324(f324(f46(x52002,x52003),x52001),f324(f18(x52003,x52002),x52004)),x52004)
% 18.77/18.50 [5412]~P85(x54123)+E(x54121,x54122)+~E(f296(x54123,x54124,x54121),f324(f324(f303(x54123),x54122),f179(f845(x54123,a832))))
% 18.77/18.50 [5413]~P85(x54133)+E(x54131,x54132)+~E(f296(x54133,x54131,x54132),f324(f324(f303(x54133),x54134),f179(f845(x54133,a832))))
% 18.77/18.50 [5718]P1(f324(x57181,x57182))+~P1(f324(f243(x57183,x57181),x57184))+~P1(f324(f324(f326(x57183),x57182),x57184))
% 18.77/18.50 [5747]E(x57471,x57472)+~P1(f324(f324(f186(x57473),x57474),x57472))+~P1(f324(f324(f186(x57473),x57474),x57471))
% 18.77/18.50 [5831]~P67(x58311)+E(f324(f324(f8(a838,x58311),x58312),f324(f295(a838,x58313),f324(a114,x58314))),f2(x58311))+~P1(f324(f324(f232(a838),x58314),x58313))
% 18.77/18.50 [5836]~P8(x58361)+~E(f51(x58361,x58362,x58363),f51(x58361,x58364,x58363))+E(f51(x58361,f324(f81(x58361),x58362),x58363),f51(x58361,f324(f81(x58361),x58364),x58363))
% 18.77/18.50 [5906]P1(f324(x59061,x59062))+~E(f324(f126(x59063,x59061),x59064),x59064)+~P1(f324(f324(f326(x59063),x59062),f324(f157(x59063),x59064)))
% 18.77/18.50 [5925]~E(f324(f324(f82(a838),x59253),x59252),f324(f324(f82(a838),x59251),x59254))+~P1(f324(f324(f232(a838),x59253),x59254))+P1(f324(f324(f232(a838),x59251),x59252))
% 18.77/18.50 [5932]~P7(x59321)+E(f51(x59321,f51(x59321,x59322,x59323),x59324),f51(x59321,x59322,x59324))+~P1(f324(f324(f280(x59321),x59324),x59323))
% 18.77/18.50 [5970]~E(f324(f126(x59701,x59702),x59703),f115(x59701))+~P1(f324(x59702,x59704))+~P1(f324(f324(f326(x59701),x59704),f324(f157(x59701),x59703)))
% 18.77/18.50 [5971]~E(f161(x59713,x59711,x59714),x59714)+P1(f324(x59711,x59712))+~P1(f324(f324(f326(x59713),x59712),f324(f157(x59713),x59714)))
% 18.77/18.50 [6006]~E(x60064,f179(f845(x60062,a832)))+~E(x60063,f179(f845(x60061,a832)))+E(f312(x60061,x60062,x60063,x60064),f179(f845(f848(x60061,x60062),a832)))
% 18.77/18.50 [6439]~P67(x64391)+E(f324(f324(f8(a838,x64391),x64392),f296(a838,x64393,f324(a114,x64394))),f2(x64391))+~P1(f324(f324(f232(a838),f324(a114,x64394)),x64393))
% 18.77/18.50 [6588]~P86(x65881)+E(f324(f324(f3(f845(x65881,a832)),f324(f295(x65881,x65882),x65883)),f324(f295(x65881,x65882),x65884)),f324(f295(x65881,x65884),x65883))+~P1(f324(f324(f231(x65881),x65882),x65884))
% 18.77/18.50 [6952]~P1(f324(f324(f326(f839(x69521)),x69524),f147(x69521,x69523)))+P1(f324(f324(f326(x69521),x69522),x69523))+~P1(f324(f324(f326(x69521),x69522),f324(f157(x69521),x69524)))
% 18.77/18.50 [6959]~P36(x69591,x69592)+P1(f324(f324(f326(x69591),f369(x69592,x69591,x69593)),x69593))+~P1(f324(f324(f326(x69591),x69594),x69593))
% 18.77/18.50 [6991]~P29(x69912,x69911,x69913,x69914)+E(f324(f41(x69911),f324(f304(x69912,x69911,x69913),x69914)),f324(f41(x69912),x69914))+~P1(f324(f64(x69912),x69914))
% 18.77/18.50 [7015]~P68(x70151)+E(f324(f324(f324(f68(x70151,x70152,f83(x70151)),x70153),f80(x70151)),x70154),f324(f324(f11(x70152,x70151),x70153),x70154))+~P1(f324(f64(x70152),x70154))
% 18.77/18.50 [7016]~P68(x70161)+E(f324(f324(f324(f68(x70161,x70162,f83(x70161)),x70163),f80(x70161)),x70164),f324(f324(f11(x70162,x70161),x70163),x70164))+~P1(f324(f64(x70162),x70164))
% 18.77/18.50 [7017]~P67(x70171)+E(f324(f324(f324(f68(x70171,x70172,f82(x70171)),x70173),f2(x70171)),x70174),f324(f324(f8(x70172,x70171),x70173),x70174))+~P1(f324(f64(x70172),x70174))
% 18.77/18.50 [7018]~P67(x70181)+E(f324(f324(f324(f68(x70181,x70182,f82(x70181)),x70183),f2(x70181)),x70184),f324(f324(f8(x70182,x70181),x70183),x70184))+~P1(f324(f64(x70182),x70184))
% 18.77/18.50 [7044]P29(x70441,x70442,x70443,x70444)+~E(f324(f41(x70442),f324(f304(x70441,x70442,x70443),x70444)),f324(f41(x70441),x70444))+~P1(f324(f64(x70441),x70444))
% 18.77/18.50 [7045]P29(x70451,x70452,x70453,x70454)+~E(f324(f41(x70452),f324(f304(x70451,x70452,x70453),x70454)),f324(f41(x70451),x70454))+~P1(f324(f64(x70451),x70454))
% 18.77/18.50 [7248]~P67(x72481)+E(f324(f324(f82(x72481),f324(x72482,x72483)),f324(f324(f8(a838,x72481),x72482),f298(a838,x72483,x72484))),f324(f324(f8(a838,x72481),x72482),f296(a838,x72483,x72484)))+~P1(f324(f324(f231(a838),x72483),x72484))
% 18.77/18.50 [7258]~P68(x72581)+~P29(x72582,x72581,x72583,x72584)+E(f324(f324(f11(x72581,x72581),f37(x72581)),f324(f304(x72582,x72581,x72583),x72584)),f324(f324(f11(x72582,x72581),x72583),x72584))
% 18.77/18.50 [7259]~P67(x72591)+~P29(x72592,x72591,x72593,x72594)+E(f324(f324(f8(x72591,x72591),f37(x72591)),f324(f304(x72592,x72591,x72593),x72594)),f324(f324(f8(x72592,x72591),x72593),x72594))
% 18.77/18.50 [7317]E(f324(f41(f848(x73171,x73172)),f312(x73171,x73172,x73173,x73174)),f324(f324(f82(a838),f324(f41(x73171),x73173)),f324(f41(x73172),x73174)))+~P1(f324(f64(x73172),x73174))+~P1(f324(f64(x73171),x73173))
% 18.77/18.50 [7318]E(f324(f41(f848(x73181,x73182)),f312(x73181,x73182,x73183,x73184)),f324(f324(f82(a838),f324(f41(x73181),x73183)),f324(f41(x73182),x73184)))+~P1(f324(f64(x73182),x73184))+~P1(f324(f64(x73181),x73183))
% 18.77/18.50 [7406]E(x74061,x74062)+P1(f324(f324(f326(x74063),x74061),f324(f157(x74063),f155(x74063,x74062,x74064))))+~P1(f324(f324(f326(x74063),x74061),f324(f157(x74063),x74064)))
% 18.77/18.50 [7633]~P67(x76331)+E(f324(f324(f82(x76331),f324(f324(f8(a838,x76331),x76332),f324(f295(a838,x76333),x76334))),f324(x76332,x76334)),f324(f324(f8(a838,x76331),x76332),f324(f295(a838,x76333),f324(a114,x76334))))+P1(f324(f324(f232(a838),x76334),x76333))
% 18.77/18.50 [7690]~P29(x76901,x76902,x76903,f238(f845(x76901,a832)))+~P1(f324(f64(x76902),x76904))+P1(f324(f64(x76901),f324(f305(x76901,x76902,x76903),x76904)))
% 18.77/18.50 [7806]P1(f324(f324(f326(f839(x78061)),f324(f324(f139(x78061),x78062),x78063)),f147(x78061,x78064)))+~P1(f324(f324(f326(f839(x78061)),x78063),f147(x78061,x78064)))+~P1(f324(f324(f326(x78061),x78062),x78064))
% 18.77/18.50 [7855]E(x78551,x78552)+~P1(f324(f324(f326(x78553),x78551),f324(f157(x78553),f155(x78553,x78552,x78554))))+P1(f324(f324(f326(x78553),x78551),f324(f157(x78553),x78554)))
% 18.77/18.50 [7898]~E(f324(f304(x78983,x78981,x78984),f238(f845(x78983,a832))),f238(f845(x78981,a832)))+P1(f324(f64(x78981),x78982))+~P1(f324(f64(x78983),f324(f305(x78983,x78981,x78984),x78982)))
% 18.77/18.50 [7991]~P29(x79911,x79913,x79914,x79912)+P1(f324(f64(x79911),x79912))+~P1(f324(f64(x79913),f324(f304(x79911,x79913,x79914),x79912)))
% 18.77/18.50 [8013]~E(x80132,x80133)+P1(f324(f324(f326(f844(x80131,x80131)),f324(f324(f247(x80131,x80131),x80132),x80133)),f261(x80131,x80134)))+~P1(f324(f324(f326(x80131),x80132),x80134))
% 18.77/18.50 [8014]~E(x80142,x80143)+P1(f324(f324(f326(f844(x80141,x80141)),f324(f324(f247(x80141,x80141),x80142),x80143)),f261(x80141,x80144)))+~P1(f324(f324(f326(x80141),x80142),x80144))
% 18.77/18.50 [8047]~P67(x80471)+E(f324(f324(f82(x80471),f324(f324(f8(a838,x80471),x80472),f296(a838,x80473,x80474))),f324(x80472,f324(a114,x80474))),f324(f324(f8(a838,x80471),x80472),f296(a838,x80473,f324(a114,x80474))))+P1(f324(f324(f232(a838),f324(a114,x80474)),x80473))
% 18.77/18.50 [8108]~E(x81082,x81084)+P1(f324(f324(f326(f844(x81081,x81081)),f324(f324(f247(x81081,x81081),x81082),x81084)),f301(x81081,x81083)))+P1(f324(f324(f326(x81081),x81082),f324(f262(x81081,x81081),x81083)))
% 18.77/18.50 [8110]P1(f324(x81101,x81102))+~P1(f324(x81101,f324(f324(f149(x81103),x81104),f713(x81101,x81104,x81103))))+~P1(f324(f324(f326(x81103),x81102),f324(f157(x81103),x81104)))
% 18.77/18.50 [8246]~P1(f324(f324(f326(x82461),x82462),f314(x82461,x82464)))+P1(f324(f324(f326(f839(x82461)),f324(f324(f139(x82461),x82462),x82463)),f314(f839(x82461),f144(x82461,x82464))))+~P1(f324(f324(f326(f839(x82461)),x82463),f314(f839(x82461),f144(x82461,x82464))))
% 18.77/18.50 [8262]~P29(x82622,x82623,x82624,f679(x82624,x82623,x82622,x82621))+P29(x82622,x82623,x82624,f44(f845(x82622,a832),x82621))+E(x82621,f179(f845(f845(x82622,a832),a832)))
% 18.77/18.50 [8520]E(x85201,x85202)+~P1(f324(f324(f326(f844(x85203,x85203)),f324(f324(f247(x85203,x85203),x85201),x85202)),f301(x85203,x85204)))+P1(f324(f324(f326(x85203),x85201),f324(f262(x85203,x85203),x85204)))
% 18.77/18.50 [8773]P29(x87732,x87733,x87734,f44(f845(x87732,a832),x87731))+E(x87731,f179(f845(f845(x87732,a832),a832)))+P1(f324(f324(f326(f845(x87732,a832)),f679(x87734,x87733,x87732,x87731)),x87731))
% 18.77/18.50 [8899]P1(f324(f64(x88991),x88992))+~P1(f324(f64(x88994),f324(f304(x88991,x88994,x88993),x88992)))+P1(f324(f324(f326(x88991),f602(x88993,x88994,x88992,x88991)),x88992))
% 18.77/18.50 [8985]~P9(x89852)+E(f324(f324(f67(x89851,x89852,f324(f324(f10(x89852,f845(x89852,x89852),x89851),f103(x89852)),x89853)),f179(x89852)),x89854),f324(f324(f45(x89851,x89852),x89854),x89853))+~P1(f324(f64(x89851),x89854))
% 18.77/18.50 [8986]~P9(x89862)+E(f324(f324(f67(x89861,x89862,f324(f324(f10(x89862,f845(x89862,x89862),x89861),f104(x89862)),x89863)),f238(x89862)),x89864),f324(f324(f46(x89861,x89862),x89864),x89863))+~P1(f324(f64(x89861),x89864))
% 18.77/18.50 [9012]~P1(f324(f324(f280(a838),x90123),x90124))+P1(f324(f324(f280(a838),x90121),x90122))+P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x90121,x90122)),f283(a838,f280(a838),x90123,x90124)))
% 18.77/18.50 [9023]~P1(f324(f324(f280(a838),x90232),x90234))+~P1(f324(f324(f280(a838),x90233),x90231))+P1(f324(f324(f231(f845(a838,a832)),f283(a838,f280(a838),x90231,x90232)),f283(a838,f280(a838),x90233,x90234)))
% 18.77/18.50 [9078]E(x90781,x90782)+~P1(f324(f324(f326(f844(x90783,x90783)),f324(f324(f247(x90783,x90783),x90781),x90782)),f301(x90783,x90784)))+P1(f324(f324(f326(f844(x90783,x90783)),f324(f324(f247(x90783,x90783),x90781),x90782)),f324(f324(f282(x90783,x90783,x90783),x90784),f301(x90783,x90784))))
% 18.77/18.50 [9079]E(x90791,x90792)+~P1(f324(f324(f326(f844(x90793,x90793)),f324(f324(f247(x90793,x90793),x90791),x90792)),f301(x90793,x90794)))+P1(f324(f324(f326(f844(x90793,x90793)),f324(f324(f247(x90793,x90793),x90791),x90792)),f324(f324(f282(x90793,x90793,x90793),x90794),f301(x90793,x90794))))
% 18.77/18.50 [9114]~E(f324(f180(f839(x91141)),x91142),f324(f180(f839(x91141)),x91143))+~P1(f324(f324(f326(f844(f839(x91141),f839(x91141))),f324(f324(f247(f839(x91141),f839(x91141)),x91142),x91143)),f136(x91141,x91144)))+P1(f324(f324(f326(f844(f839(x91141),f839(x91141))),f324(f324(f247(f839(x91141),f839(x91141)),x91142),x91143)),f134(x91141,x91144)))
% 18.77/18.50 [9134]E(x91341,x91342)+P1(f324(f324(f326(f844(x91343,x91343)),f324(f324(f247(x91343,x91343),x91341),x91342)),f301(x91343,x91344)))+~P1(f324(f324(f326(f844(x91343,x91343)),f324(f324(f247(x91343,x91343),x91341),x91342)),f324(f324(f282(x91343,x91343,x91343),x91344),f301(x91343,x91344))))
% 18.77/18.50 [9226]P1(f324(f324(f280(a838),x92261),x92262))+~P1(f324(f324(f280(a838),x92263),x92261))+~P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x92263,x92261)),f283(a838,f280(a838),x92264,x92262)))
% 18.77/18.50 [9227]P1(f324(f324(f280(a838),x92271),x92272))+~P1(f324(f324(f280(a838),x92273),x92271))+~P1(f324(f324(f231(f845(a838,a832)),f283(a838,f280(a838),x92273,x92271)),f283(a838,f280(a838),x92274,x92272)))
% 18.77/18.50 [9228]P1(f324(f324(f280(a838),x92281),x92282))+~P1(f324(f324(f280(a838),x92282),x92283))+~P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x92282,x92283)),f283(a838,f280(a838),x92281,x92284)))
% 18.77/18.50 [9229]P1(f324(f324(f280(a838),x92291),x92292))+~P1(f324(f324(f280(a838),x92292),x92293))+~P1(f324(f324(f231(f845(a838,a832)),f283(a838,f280(a838),x92292,x92293)),f283(a838,f280(a838),x92291,x92294)))
% 18.77/18.50 [9534]~P6(x95341)+E(f324(f324(f8(a838,x95341),f324(f324(f20(a838,x95341,x95341),f324(f324(f10(x95341,f845(x95341,x95341),a838),f3(x95341)),x95342)),f324(f324(f10(a838,x95341,a838),x95342),f324(f324(f9(a838,a838,a838),f82(a838)),f80(a838))))),f296(a838,x95343,x95344)),f2(x95341))+P1(f324(f324(f231(a838),x95343),x95344))
% 18.77/18.50 [9767]~P36(x97672,x97674)+~P29(x97672,x97671,x97673,f238(f845(x97672,a832)))+P36(x97671,f324(f304(f844(x97672,x97672),f844(x97671,x97671),f253(x97672,x97671,x97672,x97671,x97673,x97673)),x97674))
% 18.77/18.50 [9938]~E(f324(f180(f839(x99381)),x99383),f324(f180(f839(x99381)),x99382))+P1(f324(f324(f326(f844(f839(x99381),f839(x99381))),f324(f324(f247(f839(x99381),f839(x99381)),x99382),x99383)),f145(x99381,x99384)))+~P1(f324(f324(f252(x99381,x99381,a832),f324(f324(f9(x99381,f845(f844(x99381,x99381),a832),f845(x99381,a832)),f324(f324(f10(f845(x99381,f845(f845(f844(x99381,x99381),a832),a832)),f845(f845(f844(x99381,x99381),a832),f845(x99381,a832)),x99381),f9(x99381,f845(f844(x99381,x99381),a832),a832)),f324(f324(f10(f845(x99381,f844(x99381,x99381)),f845(x99381,f845(f845(f844(x99381,x99381),a832),a832)),x99381),f324(f10(f844(x99381,x99381),f845(f845(f844(x99381,x99381),a832),a832),x99381),f326(f844(x99381,x99381)))),f247(x99381,x99381)))),x99384)),f704(x99384,x99383,x99382,x99381)))
% 18.77/18.50 [5795]~E(x57954,x57952)+P1(f324(x57951,x57952))+P1(f324(f324(f186(f35(x57951,x57953)),x57952),x57954))
% 18.77/18.50 [5890]~P7(x58901)+~E(x58902,f2(x58901))+E(f324(f324(f42(x58901),f324(f324(f83(x58901),x58902),x58903)),f324(f324(f83(x58901),x58902),x58904)),f2(x58901))
% 18.77/18.50 [5929]E(x59291,f115(x59292))+E(x59293,f324(f324(f3(a838),f324(f180(f839(x59292)),x59291)),f80(a838)))+E(f133(x59292,f324(f324(f146(x59292,x59291),x59293),x59294)),f133(x59292,x59291))
% 18.77/18.50 [5961]E(x59611,x59612)+P1(f324(x59613,x59612))+~P1(f324(f324(f324(f303(x59614),x59611),x59613),x59612))
% 18.77/18.50 [5975]~P67(x59751)+~P1(f324(f127(x59752),x59754))+E(f324(f151(x59751),f324(f324(f141(x59752,x59751),x59753),x59754)),f324(f324(f8(x59752,x59751),x59753),f324(f157(x59752),x59754)))
% 18.77/18.50 [5999]~P68(x59992)+~P1(f324(f64(x59991),x59994))+E(f324(f324(f11(x59991,x59992),f324(f18(x59992,x59991),x59993)),x59994),f324(f324(f240(x59992),x59993),f324(f41(x59991),x59994)))
% 18.77/18.50 [6054]~P7(x60542)+E(x60541,f2(x60542))+E(f324(f324(f42(x60542),f324(f324(f83(x60542),x60543),x60541)),f324(f324(f83(x60542),x60544),x60541)),f324(f324(f42(x60542),x60543),x60544))
% 18.77/18.50 [6055]~P7(x60552)+E(x60551,f2(x60552))+E(f324(f324(f42(x60552),f324(f324(f83(x60552),x60551),x60553)),f324(f324(f83(x60552),x60551),x60554)),f324(f324(f42(x60552),x60553),x60554))
% 18.77/18.50 [6056]~P59(x60562)+E(x60561,f2(x60562))+E(f324(f324(f284(x60562),f324(f324(f83(x60562),x60563),x60561)),f324(f324(f83(x60562),x60564),x60561)),f324(f324(f284(x60562),x60563),x60564))
% 18.77/18.50 [6057]~P59(x60572)+E(x60571,f2(x60572))+E(f324(f324(f284(x60572),f324(f324(f83(x60572),x60571),x60573)),f324(f324(f83(x60572),x60571),x60574)),f324(f324(f284(x60572),x60573),x60574))
% 18.77/18.50 [6058]~P7(x60582)+E(x60581,f2(x60582))+E(f324(f324(f42(x60582),f324(f324(f83(x60582),x60581),x60583)),f324(f324(f83(x60582),x60581),x60584)),f324(f324(f42(x60582),x60583),x60584))
% 18.77/18.50 [6123]P1(f324(x61231,x61232))+~E(x61233,f324(f324(f82(a838),x61234),x61232))+~P1(f324(x61231,f324(f324(f3(a838),x61233),x61234)))
% 18.77/18.50 [6124]P1(f324(x61241,x61242))+~E(x61243,f324(f324(f82(a838),x61244),x61242))+~P1(f324(x61241,f324(f324(f3(a838),x61243),x61244)))
% 18.77/18.50 [6207]P32(x62071,x62072,x62073)+P31(x62071,f619(x62073,x62072,x62071),x62074)+~P1(f324(f324(f326(f837(x62071)),x62074),x62072))
% 18.77/18.50 [6252]E(x62521,f115(x62522))+~E(x62523,f324(f324(f3(a838),f324(f180(f839(x62522)),x62521)),f80(a838)))+E(f133(x62522,f324(f324(f146(x62522,x62521),x62523),x62524)),x62524)
% 18.77/18.50 [6274]~P86(x62741)+~P1(f324(f324(f232(x62741),x62742),x62744))+P1(f324(f324(f232(x62741),x62742),f324(f324(f178(x62741),x62743),x62744)))
% 18.77/18.50 [6275]~P86(x62751)+~P1(f324(f324(f232(x62751),x62752),x62754))+P1(f324(f324(f232(x62751),x62752),f324(f324(f178(x62751),x62753),x62754)))
% 18.77/18.50 [6276]~P86(x62761)+~P1(f324(f324(f232(x62761),x62762),x62763))+P1(f324(f324(f232(x62761),x62762),f324(f324(f178(x62761),x62763),x62764)))
% 18.77/18.50 [6277]~P86(x62771)+~P1(f324(f324(f232(x62771),x62772),x62773))+P1(f324(f324(f232(x62771),x62772),f324(f324(f178(x62771),x62773),x62774)))
% 18.77/18.50 [6278]~P93(x62781)+~P1(f324(f324(f232(x62781),x62782),x62784))+P1(f324(f324(f232(x62781),x62782),f324(f324(f103(x62781),x62783),x62784)))
% 18.77/18.50 [6279]~P93(x62791)+~P1(f324(f324(f232(x62791),x62792),x62793))+P1(f324(f324(f232(x62791),x62792),f324(f324(f103(x62791),x62793),x62794)))
% 18.77/18.50 [6280]~P86(x62801)+~P1(f324(f324(f231(x62801),x62802),x62804))+P1(f324(f324(f231(x62801),x62802),f324(f324(f178(x62801),x62803),x62804)))
% 18.77/18.50 [6281]~P86(x62811)+~P1(f324(f324(f231(x62811),x62812),x62814))+P1(f324(f324(f231(x62811),x62812),f324(f324(f178(x62811),x62813),x62814)))
% 18.77/18.50 [6282]~P86(x62821)+~P1(f324(f324(f231(x62821),x62822),x62823))+P1(f324(f324(f231(x62821),x62822),f324(f324(f178(x62821),x62823),x62824)))
% 18.77/18.50 [6283]~P86(x62831)+~P1(f324(f324(f231(x62831),x62832),x62833))+P1(f324(f324(f231(x62831),x62832),f324(f324(f178(x62831),x62833),x62834)))
% 18.77/18.50 [6284]~P93(x62841)+~P1(f324(f324(f231(x62841),x62842),x62844))+P1(f324(f324(f231(x62841),x62842),f324(f324(f103(x62841),x62843),x62844)))
% 18.77/18.50 [6285]~P93(x62851)+~P1(f324(f324(f231(x62851),x62852),x62853))+P1(f324(f324(f231(x62851),x62852),f324(f324(f103(x62851),x62853),x62854)))
% 18.77/18.50 [6286]~P105(x62861)+~P1(f324(f324(f280(x62861),x62862),x62864))+P1(f324(f324(f280(x62861),x62862),f324(f324(f83(x62861),x62863),x62864)))
% 18.77/18.50 [6287]~P105(x62871)+~P1(f324(f324(f280(x62871),x62872),x62873))+P1(f324(f324(f280(x62871),x62872),f324(f324(f83(x62871),x62873),x62874)))
% 18.77/18.50 [6382]~E(f324(f324(f149(x63821),x63822),x63823),x63824)+E(f324(f324(f146(x63821,x63822),x63823),x63824),x63822)+~P1(f324(f324(f232(a838),x63823),f324(f180(f839(x63821)),x63822)))
% 18.77/18.50 [6401]E(x64011,x64012)+P1(f324(x64013,x64011))+~P1(f324(f324(f186(f35(x64013,x64014)),x64011),x64012))
% 18.77/18.50 [6421]P1(f324(x64211,x64212))+~P1(f324(x64213,x64212))+~P1(f324(f324(f231(f845(x64214,a832)),x64213),x64211))
% 18.77/18.50 [6422]P1(f324(x64221,x64222))+~P1(f324(x64223,x64222))+~P1(f324(f324(f231(f845(x64224,a832)),x64223),x64221))
% 18.77/18.50 [6458]~E(f324(f324(f146(x64581,x64582),x64583),x64584),x64582)+E(f324(f324(f149(x64581),x64582),x64583),x64584)+~P1(f324(f324(f232(a838),x64583),f324(f180(f839(x64581)),x64582)))
% 18.77/18.50 [6576]P31(x65761,x65762,x65763)+~P31(x65761,f324(a114,x65762),f617(x65762,x65764,x65761))+~P1(f324(f324(f326(f837(x65761)),x65763),x65764))
% 18.77/18.50 [6585]E(x65851,f179(f845(x65852,a832)))+E(x65853,f179(f845(x65854,a832)))+~E(f324(f324(f249(x65854,x65852),x65853),f324(f18(f845(x65852,a832),x65854),x65851)),f179(f845(f844(x65854,x65852),a832)))
% 18.77/18.50 [6602]E(x66021,x66022)+P1(f324(f324(f326(x66023),x66021),x66024))+~P1(f324(f324(f326(x66023),x66021),f324(f324(f303(x66023),x66022),x66024)))
% 18.77/18.50 [6603]E(x66031,x66032)+P1(f324(f324(f326(x66033),x66031),x66034))+~P1(f324(f324(f326(x66033),x66031),f324(f324(f303(x66033),x66032),x66034)))
% 18.77/18.50 [6620]~P86(x66201)+P1(f324(f324(f232(x66201),x66202),x66203))+~P1(f324(f324(f232(x66201),x66202),f324(f324(f235(x66201),x66204),x66203)))
% 18.77/18.50 [6621]~P86(x66211)+P1(f324(f324(f232(x66211),x66212),x66213))+~P1(f324(f324(f232(x66211),x66212),f324(f324(f235(x66211),x66213),x66214)))
% 18.77/18.50 [6622]~P86(x66221)+P1(f324(f324(f231(x66221),x66222),x66223))+~P1(f324(f324(f231(x66221),x66222),f324(f324(f235(x66221),x66224),x66223)))
% 18.77/18.50 [6623]~P86(x66231)+P1(f324(f324(f231(x66231),x66232),x66233))+~P1(f324(f324(f231(x66231),x66232),f324(f324(f235(x66231),x66234),x66233)))
% 18.77/18.50 [6624]~P86(x66241)+P1(f324(f324(f231(x66241),x66242),x66243))+~P1(f324(f324(f231(x66241),x66242),f324(f324(f235(x66241),x66243),x66244)))
% 18.77/18.50 [6625]~P86(x66251)+P1(f324(f324(f231(x66251),x66252),x66253))+~P1(f324(f324(f231(x66251),x66252),f324(f324(f235(x66251),x66253),x66254)))
% 18.77/18.50 [6626]~P99(x66261)+P1(f324(f324(f231(x66261),x66262),x66263))+~P1(f324(f324(f231(x66261),x66262),f324(f324(f104(x66261),x66264),x66263)))
% 18.77/18.50 [6627]~P99(x66271)+P1(f324(f324(f231(x66271),x66272),x66273))+~P1(f324(f324(f231(x66271),x66272),f324(f324(f104(x66271),x66274),x66273)))
% 18.77/18.50 [6628]~P99(x66281)+P1(f324(f324(f231(x66281),x66282),x66283))+~P1(f324(f324(f231(x66281),x66282),f324(f324(f104(x66281),x66283),x66284)))
% 18.77/18.50 [6629]~P99(x66291)+P1(f324(f324(f231(x66291),x66292),x66293))+~P1(f324(f324(f231(x66291),x66292),f324(f324(f104(x66291),x66293),x66294)))
% 18.77/18.50 [6651]~E(f324(f324(f149(x66511),x66513),x66514),x66512)+P1(f324(f324(f326(x66511),x66512),f324(f157(x66511),x66513)))+~P1(f324(f324(f232(a838),x66514),f324(f180(f839(x66511)),x66513)))
% 18.77/18.50 [6663]~P86(x66631)+~P18(x66631,f324(f324(f139(x66631),x66632),f324(f324(f139(x66631),x66633),x66634)))+P1(f324(f324(f231(x66631),x66632),x66633))
% 18.77/18.50 [6720]~P86(x67201)+P18(x67201,f324(f324(f139(x67201),x67202),x67203))+~P18(x67201,f324(f324(f139(x67201),x67204),f324(f324(f139(x67201),x67202),x67203)))
% 18.77/18.50 [6835]E(x68351,f2(a1))+E(f324(f324(f42(a1),x68352),x68351),x68353)+~P1(f324(f55(x68352,x68351),f324(f324(f247(a1,a1),x68353),x68354)))
% 18.77/18.50 [6858]E(f51(a1,x68582,x68581),x68583)+E(x68581,f2(a1))+~P1(f324(f55(x68582,x68581),f324(f324(f247(a1,a1),x68584),x68583)))
% 18.77/18.50 [6973]P1(f324(f324(f326(x69731),x69732),x69733))+~P1(f324(f324(f326(x69731),x69732),x69734))+~P1(f324(f324(f232(f845(x69731,a832)),x69734),x69733))
% 18.77/18.50 [6974]P1(f324(f324(f326(x69741),x69742),x69743))+~P1(f324(f324(f326(x69741),x69742),x69744))+~P1(f324(f324(f231(f845(x69741,a832)),x69744),x69743))
% 18.77/18.50 [6975]P1(f324(f324(f326(x69751),x69752),x69753))+~P1(f324(f324(f326(x69751),x69752),x69754))+~P1(f324(f324(f231(f845(x69751,a832)),x69754),x69753))
% 18.77/18.50 [6976]P1(f324(f324(f326(x69761),x69762),x69763))+~P1(f324(f324(f326(x69761),x69762),x69764))+~P1(f324(f324(f231(f845(x69761,a832)),x69764),x69763))
% 18.77/18.50 [6977]P1(f324(f324(f326(x69771),x69772),x69773))+~P1(f324(f324(f326(x69771),x69772),x69774))+~P1(f324(f324(f231(f845(x69771,a832)),x69774),x69773))
% 18.77/18.50 [6987]~P112(x69871)+~E(x69873,f2(x69871))+P1(f324(f324(f280(x69871),f324(f324(f83(x69871),x69872),x69873)),f324(f324(f83(x69871),x69874),x69873)))
% 18.77/18.50 [6988]~P112(x69881)+~E(x69882,f2(x69881))+P1(f324(f324(f280(x69881),f324(f324(f83(x69881),x69882),x69883)),f324(f324(f83(x69881),x69882),x69884)))
% 18.77/18.50 [7212]~P101(x72122)+~P1(f324(f324(f232(f845(x72121,x72122)),x72123),x72124))+P1(f324(f324(f231(f845(x72121,x72122)),x72123),x72124))
% 18.77/18.50 [7307]~P28(x73071,x73072,x73074)+P28(x73071,x73072,f324(f324(f303(f837(x73071)),x73073),x73074))+~P28(x73071,x73072,f324(f324(f303(f837(x73071)),x73073),f179(f845(f837(x73071),a832))))
% 18.77/18.50 [7346]~P1(f324(f324(f326(x73461),x73462),x73464))+P1(f324(f324(f326(x73461),x73462),f43(f845(x73461,a832),x73463)))+~P1(f324(f324(f326(f845(x73461,a832)),x73464),x73463))
% 18.77/18.50 [7348]~P105(x73481)+~P1(f324(f324(f231(a838),x73483),x73484))+P1(f324(f324(f280(x73481),f324(f324(f240(x73481),x73482),x73483)),f324(f324(f240(x73481),x73482),x73484)))
% 18.77/18.50 [7359]P31(x73591,x73592,x73593)+P1(f324(f324(f326(f837(x73591)),f617(x73592,x73594,x73591)),x73594))+~P1(f324(f324(f326(f837(x73591)),x73593),x73594))
% 18.77/18.50 [7381]~P76(x73811)+~P1(f324(f324(f232(x73811),x73813),x73814))+P1(f324(f324(f232(x73811),f324(f324(f82(x73811),x73812),x73813)),f324(f324(f82(x73811),x73812),x73814)))
% 18.77/18.50 [7382]~P79(x73821)+~P1(f324(f324(f232(x73821),x73823),x73824))+P1(f324(f324(f232(x73821),f324(f324(f82(x73821),x73822),x73823)),f324(f324(f82(x73821),x73822),x73824)))
% 18.77/18.50 [7383]~P76(x73831)+~P1(f324(f324(f232(x73831),x73832),x73834))+P1(f324(f324(f232(x73831),f324(f324(f82(x73831),x73832),x73833)),f324(f324(f82(x73831),x73834),x73833)))
% 18.77/18.50 [7384]~P79(x73841)+~P1(f324(f324(f232(x73841),x73842),x73844))+P1(f324(f324(f232(x73841),f324(f324(f82(x73841),x73842),x73843)),f324(f324(f82(x73841),x73844),x73843)))
% 18.77/18.50 [7385]~P76(x73851)+~P1(f324(f324(f231(x73851),x73853),x73854))+P1(f324(f324(f231(x73851),f324(f324(f82(x73851),x73852),x73853)),f324(f324(f82(x73851),x73852),x73854)))
% 18.77/18.50 [7386]~P77(x73861)+~P1(f324(f324(f231(x73861),x73863),x73864))+P1(f324(f324(f231(x73861),f324(f324(f82(x73861),x73862),x73863)),f324(f324(f82(x73861),x73862),x73864)))
% 18.77/18.50 [7387]~P76(x73871)+~P1(f324(f324(f231(x73871),x73872),x73874))+P1(f324(f324(f231(x73871),f324(f324(f82(x73871),x73872),x73873)),f324(f324(f82(x73871),x73874),x73873)))
% 18.77/18.50 [7388]~P77(x73881)+~P1(f324(f324(f231(x73881),x73882),x73884))+P1(f324(f324(f231(x73881),f324(f324(f82(x73881),x73882),x73883)),f324(f324(f82(x73881),x73884),x73883)))
% 18.77/18.50 [7389]~P112(x73891)+~P1(f324(f324(f280(x73891),x73893),x73894))+P1(f324(f324(f280(x73891),f324(f324(f83(x73891),x73892),x73893)),f324(f324(f83(x73891),x73892),x73894)))
% 18.77/18.50 [7390]~P112(x73901)+~P1(f324(f324(f280(x73901),x73902),x73904))+P1(f324(f324(f280(x73901),f324(f324(f83(x73901),x73902),x73903)),f324(f324(f83(x73901),x73904),x73903)))
% 18.77/18.50 [7391]~P105(x73911)+~P1(f324(f324(f280(x73911),x73912),x73914))+P1(f324(f324(f280(x73911),f324(f324(f240(x73911),x73912),x73913)),f324(f324(f240(x73911),x73914),x73913)))
% 18.77/18.50 [7400]~P134(x74001)+~P90(x74001)+E(f324(f324(f82(x74001),f324(f324(f83(x74001),x74002),f324(f106(x74001),x74003))),f324(f324(f83(x74001),x74004),f324(f106(x74001),x74003))),f324(f324(f83(x74001),f324(f324(f82(x74001),x74002),x74004)),f324(f106(x74001),x74003)))
% 18.77/18.50 [7401]~P126(x74011)+~P90(x74011)+E(f324(f324(f3(x74011),f324(f324(f83(x74011),x74012),f324(f106(x74011),x74013))),f324(f324(f83(x74011),x74014),f324(f106(x74011),x74013))),f324(f324(f83(x74011),f324(f324(f3(x74011),x74012),x74014)),f324(f106(x74011),x74013)))
% 18.77/18.50 [7437]~P67(x74371)+E(f324(f324(f82(x74371),f324(x74372,x74373)),f324(f324(f8(a838,x74371),x74372),f296(a838,f324(a114,x74373),x74374))),f324(f324(f8(a838,x74371),x74372),f296(a838,x74373,x74374)))+~P1(f324(f324(f231(a838),x74373),x74374))
% 18.77/18.50 [7448]~P29(x74482,x74481,x74483,f324(f157(x74482),x74484))+~P1(f324(f127(x74482),x74484))+P1(f324(f127(x74481),f324(f324(f141(x74482,x74481),x74483),x74484)))
% 18.77/18.50 [7497]~P1(f324(f324(f232(a838),x74972),x74974))+~P1(f324(f324(f232(a838),x74971),x74973))+P1(f324(f324(f232(a838),f324(f324(f82(a838),x74971),x74972)),f324(f324(f82(a838),x74973),x74974)))
% 18.77/18.50 [7500]~P1(f324(f324(f232(a1),x75001),x75003))+~P1(f324(f324(f231(a1),x75002),x75004))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x75001),x75002)),f324(f324(f82(a1),x75003),x75004)))
% 18.77/18.50 [7501]~P1(f324(f324(f231(a838),x75012),x75014))+~P1(f324(f324(f231(a838),x75011),x75013))+P1(f324(f324(f231(a838),f324(f324(f83(a838),x75011),x75012)),f324(f324(f83(a838),x75013),x75014)))
% 18.77/18.50 [7502]~P1(f324(f324(f231(a838),x75022),x75024))+~P1(f324(f324(f231(a838),x75021),x75023))+P1(f324(f324(f231(a838),f324(f324(f82(a838),x75021),x75022)),f324(f324(f82(a838),x75023),x75024)))
% 18.77/18.50 [7551]P1(f324(f324(f326(x75511),x75512),x75513))+~P1(f324(f324(f326(x75511),x75512),f44(f845(x75511,a832),x75514)))+~P1(f324(f324(f326(f845(x75511,a832)),x75513),x75514))
% 18.77/18.50 [7552]P1(f324(f324(f326(x75521),x75522),x75523))+~P1(f324(f324(f326(x75521),x75522),f44(f845(x75521,a832),x75524)))+~P1(f324(f324(f326(f845(x75521,a832)),x75523),x75524))
% 18.77/18.50 [7568]~P1(f324(x75681,f712(x75681,x75683,x75682)))+P1(f324(x75681,f324(f324(f149(x75682),x75683),x75684)))+~P1(f324(f324(f232(a838),x75684),f324(f180(f839(x75682)),x75683)))
% 18.77/18.50 [7572]P1(f324(x75721,x75722))+~P1(f324(f324(f326(x75724),x75722),f324(f157(x75724),x75723)))+P1(f324(f324(f232(a838),f713(x75721,x75723,x75724)),f324(f180(f839(x75724)),x75723)))
% 18.77/18.50 [7591]~P1(f324(f324(f186(x75912),x75913),x75914))+~P1(f324(f324(f186(f35(x75911,x75912)),x75914),x75913))+P1(f324(f324(f186(f35(x75911,x75912)),x75913),x75913))
% 18.77/18.50 [7620]~P101(x76201)+~P1(f324(f324(f231(f845(x76202,x76201)),x76204),x76203))+~P1(f324(f324(f232(f845(x76202,x76201)),x76203),x76204))
% 18.77/18.50 [7663]~P1(f324(x76634,x76632))+~P1(f324(f324(f326(x76631),x76632),x76633))+P1(f324(f324(f326(x76631),x76632),f324(f324(f104(f845(x76631,a832)),x76633),f324(f257(x76631),x76634))))
% 18.77/18.50 [7682]P1(f324(f324(f326(x76821),x76822),x76823))+~P1(f324(f324(f231(f845(x76821,a832)),x76823),x76824))+P1(f324(f324(f231(f845(x76821,a832)),x76823),f324(f324(f303(x76821),x76822),x76824)))
% 18.77/18.50 [7683]P1(f324(f324(f326(x76831),x76832),x76833))+~P1(f324(f324(f231(f845(x76831,a832)),x76833),x76834))+P1(f324(f324(f231(f845(x76831,a832)),x76833),f324(f324(f303(x76831),x76832),x76834)))
% 18.77/18.50 [7814]~P1(f324(f324(f326(x78141),x78143),x78144))+~P1(f324(f324(f232(f845(x78141,a832)),x78142),x78144))+P1(f324(f324(f232(f845(x78141,a832)),x78142),f324(f324(f303(x78141),x78143),x78144)))
% 18.77/18.50 [7816]E(f324(f324(f104(f845(x78161,a832)),x78162),x78163),f179(f845(x78161,a832)))+~E(f324(f324(f104(f845(x78161,a832)),f43(f845(x78161,a832),x78164)),x78163),f179(f845(x78161,a832)))+~P1(f324(f324(f326(f845(x78161,a832)),x78162),x78164))
% 18.77/18.50 [7893]P1(f324(f324(f326(x78931),x78932),x78933))+~P1(f324(f324(f231(f845(x78931,a832)),x78933),f324(f324(f303(x78931),x78932),x78934)))+P1(f324(f324(f231(f845(x78931,a832)),x78933),x78934))
% 18.77/18.50 [7894]P1(f324(f324(f326(x78941),x78942),x78943))+~P1(f324(f324(f231(f845(x78941,a832)),x78943),f324(f324(f303(x78941),x78942),x78944)))+P1(f324(f324(f231(f845(x78941,a832)),x78943),x78944))
% 18.77/18.50 [7915]P1(f324(f324(f326(x79152),f712(x79151,x79153,x79152)),f324(f157(x79152),x79153)))+P1(f324(x79151,f324(f324(f149(x79152),x79153),x79154)))+~P1(f324(f324(f232(a838),x79154),f324(f180(f839(x79152)),x79153)))
% 18.77/18.50 [7923]~P1(f324(f324(f232(f845(x79231,a832)),x79232),x79234))+P1(f324(f324(f232(f845(x79231,a832)),x79232),x79233))+~P1(f324(f324(f232(f845(x79231,a832)),x79234),x79233))
% 18.77/18.50 [7924]~P1(f324(f324(f231(f845(x79241,a832)),x79242),x79244))+P1(f324(f324(f232(f845(x79241,a832)),x79242),x79243))+~P1(f324(f324(f232(f845(x79241,a832)),x79244),x79243))
% 18.77/18.50 [7925]~P1(f324(f324(f231(f845(x79251,a832)),x79254),x79253))+~P1(f324(f324(f232(f845(x79251,a832)),x79252),x79254))+P1(f324(f324(f232(f845(x79251,a832)),x79252),x79253))
% 18.77/18.50 [7926]~P1(f324(f324(f231(f845(x79261,a832)),x79262),x79264))+P1(f324(f324(f231(f845(x79261,a832)),x79262),x79263))+~P1(f324(f324(f231(f845(x79261,a832)),x79264),x79263))
% 18.77/18.50 [7963]~P1(f324(f324(f326(x79631),x79634),x79633))+~P1(f324(f324(f232(f845(x79631,a832)),x79632),f324(f324(f303(x79631),x79634),x79633)))+P1(f324(f324(f232(f845(x79631,a832)),x79632),x79633))
% 18.77/18.50 [7975]~P76(x79751)+P1(f324(f324(f232(x79751),x79752),x79753))+~P1(f324(f324(f232(x79751),f324(f324(f82(x79751),x79754),x79752)),f324(f324(f82(x79751),x79754),x79753)))
% 18.77/18.50 [7976]~P76(x79761)+P1(f324(f324(f232(x79761),x79762),x79763))+~P1(f324(f324(f232(x79761),f324(f324(f82(x79761),x79764),x79762)),f324(f324(f82(x79761),x79764),x79763)))
% 18.77/18.50 [7977]~P76(x79771)+P1(f324(f324(f232(x79771),x79772),x79773))+~P1(f324(f324(f232(x79771),f324(f324(f82(x79771),x79772),x79774)),f324(f324(f82(x79771),x79773),x79774)))
% 18.77/18.50 [7978]~P76(x79781)+P1(f324(f324(f232(x79781),x79782),x79783))+~P1(f324(f324(f232(x79781),f324(f324(f82(x79781),x79782),x79784)),f324(f324(f82(x79781),x79783),x79784)))
% 18.77/18.50 [7979]~P76(x79791)+P1(f324(f324(f231(x79791),x79792),x79793))+~P1(f324(f324(f231(x79791),f324(f324(f82(x79791),x79794),x79792)),f324(f324(f82(x79791),x79794),x79793)))
% 18.77/18.50 [7980]~P76(x79801)+P1(f324(f324(f231(x79801),x79802),x79803))+~P1(f324(f324(f231(x79801),f324(f324(f82(x79801),x79804),x79802)),f324(f324(f82(x79801),x79804),x79803)))
% 18.77/18.50 [7981]~P76(x79811)+P1(f324(f324(f231(x79811),x79812),x79813))+~P1(f324(f324(f231(x79811),f324(f324(f82(x79811),x79812),x79814)),f324(f324(f82(x79811),x79813),x79814)))
% 18.77/18.50 [7982]~P76(x79821)+P1(f324(f324(f231(x79821),x79822),x79823))+~P1(f324(f324(f231(x79821),f324(f324(f82(x79821),x79822),x79824)),f324(f324(f82(x79821),x79823),x79824)))
% 18.77/18.50 [8030]P1(f324(x80301,x80302))+~E(f324(f324(f128(x80303),f324(f180(f839(x80303)),f161(x80303,x80301,x80304))),x80304),f115(x80303))+~P1(f324(f324(f326(x80303),x80302),f324(f157(x80303),x80304)))
% 18.77/18.50 [8151]P1(f324(x81511,x81512))+~P1(f324(f324(f326(x81513),x81512),f324(f157(x81513),x81514)))+P1(f324(f324(f232(a838),f324(f180(f839(x81513)),f324(f126(x81513,x81511),x81514))),f324(f180(f839(x81513)),x81514)))
% 18.77/18.50 [8280]E(x82801,x82802)+P1(f324(f324(f186(x82803),x82801),f761(x82802,x82801,x82803,x82804)))+~P1(f324(f324(f186(f35(x82804,x82803)),x82801),x82802))
% 18.77/18.50 [8308]~P1(f324(x83084,x83082))+P1(f324(f324(f186(x83081),x83082),f761(x83083,x83082,x83081,x83084)))+~P1(f324(f324(f186(f35(x83084,x83081)),x83082),x83083))
% 18.77/18.50 [8634]~P29(x86344,x86343,x86341,f238(f845(x86344,a832)))+E(f324(x86341,f541(x86342,x86341,x86343,x86344)),x86342)+~P1(f324(f324(f326(x86343),x86342),f324(f304(x86344,x86343,x86341),f238(f845(x86344,a832)))))
% 18.77/18.50 [8755]~P84(x87554)+P1(f324(f324(f326(x87551),f691(x87552,x87553,x87551,x87554)),x87553))+P1(f324(f324(f232(x87554),f2(x87554)),f324(f324(f11(x87551,x87554),x87552),x87553)))
% 18.77/18.50 [8756]~P84(x87564)+P1(f324(f324(f326(x87561),f692(x87562,x87563,x87561,x87564)),x87563))+P1(f324(f324(f231(x87564),f2(x87564)),f324(f324(f11(x87561,x87564),x87562),x87563)))
% 18.77/18.50 [8775]~P1(f324(f64(x87751),x87754))+P1(f324(f324(f326(x87751),f585(x87752,x87753,x87754,x87751)),x87754))+P1(f324(f64(f844(x87751,x87753)),f324(f324(f249(x87751,x87753),x87754),x87752)))
% 18.77/18.50 [8819]E(x88191,x88192)+P1(f324(f324(f186(f35(x88193,x88194)),f761(x88191,x88192,x88194,x88193)),x88191))+~P1(f324(f324(f186(f35(x88193,x88194)),x88192),x88191))
% 18.77/18.50 [8839]~P1(f324(x88391,x88394))+P1(f324(f324(f186(f35(x88391,x88392)),f761(x88393,x88394,x88392,x88391)),x88393))+~P1(f324(f324(f186(f35(x88391,x88392)),x88394),x88393))
% 18.77/18.50 [9070]~P1(f324(f64(x90701),x90703))+~P1(f324(f64(x90702),f324(x90704,f585(x90704,x90702,x90703,x90701))))+P1(f324(f64(f844(x90701,x90702)),f324(f324(f249(x90701,x90702),x90703),x90704)))
% 18.77/18.50 [9081]~P84(x90811)+~P1(f324(f324(f232(x90811),f2(x90811)),f324(x90813,f691(x90813,x90814,x90812,x90811))))+P1(f324(f324(f232(x90811),f2(x90811)),f324(f324(f11(x90812,x90811),x90813),x90814)))
% 18.77/18.50 [9082]~P84(x90821)+~P1(f324(f324(f231(x90821),f2(x90821)),f324(x90823,f692(x90823,x90824,x90822,x90821))))+P1(f324(f324(f231(x90821),f2(x90821)),f324(f324(f11(x90822,x90821),x90823),x90824)))
% 18.77/18.50 [9086]~E(f324(f180(f839(x90864)),x90862),f324(f180(f839(x90864)),x90863))+P1(f324(f324(f326(f844(f839(x90864),f839(x90864))),f324(f324(f247(f839(x90864),f839(x90864)),x90863),x90862)),f145(x90864,x90861)))+P1(f324(f324(f232(a838),f721(x90861,x90862,x90863,x90864)),f324(f180(f839(x90864)),x90863)))
% 18.77/18.50 [9201]E(f324(f324(f158(x92011),f722(x92012,x92013,x92014,x92011)),x92013),f324(f324(f158(x92011),f722(x92012,x92013,x92014,x92011)),x92014))+~P1(f324(f324(f326(f844(f839(x92011),f839(x92011))),f324(f324(f247(f839(x92011),f839(x92011)),x92014),x92013)),f136(x92011,x92012)))+P1(f324(f324(f232(a838),f324(f180(f839(x92011)),x92014)),f324(f180(f839(x92011)),x92013)))
% 18.77/18.50 [9259]~P1(f324(f324(f232(a838),f2(a838)),x92593))+~P1(f324(f324(f232(a838),x92594),x92591))+P1(f324(f324(f232(a838),f324(f324(f82(a838),f324(f324(f83(a838),x92591),f51(a838,x92592,x92593))),x92594)),f324(f324(f83(a838),x92591),x92593)))
% 18.77/18.50 [9444]~P101(x94442)+~P1(f324(f324(f231(x94442),f324(x94443,f508(x94444,x94443,x94441,x94442))),f324(x94444,f508(x94444,x94443,x94441,x94442))))+P1(f324(f324(f231(f845(x94441,x94442)),x94443),x94444))
% 18.77/18.50 [9537]~P6(x95371)+E(f324(f324(f8(a838,x95371),f324(f324(f20(a838,x95371,x95371),f324(f324(f10(x95371,f845(x95371,x95371),a838),f3(x95371)),x95372)),f324(f324(f10(a838,x95371,a838),x95372),f324(f324(f9(a838,a838,a838),f82(a838)),f80(a838))))),f296(a838,x95373,x95374)),f324(f324(f3(x95371),f324(x95372,x95373)),f324(x95372,f324(f324(f82(a838),x95374),f80(a838)))))+~P1(f324(f324(f231(a838),x95373),x95374))
% 18.77/18.50 [6565]~P7(x65651)+E(f324(f324(f42(x65651),f324(f324(f83(x65651),x65652),x65653)),x65654),f324(f324(f83(x65651),x65652),f324(f324(f42(x65651),x65653),x65654)))+~P1(f324(f324(f280(x65651),x65654),x65653))
% 18.77/18.50 [6655]E(f324(f324(f125(x66551),x66552),x66553),x66554)+~E(x66553,f324(f324(f128(x66551),f324(f180(f839(x66551)),x66552)),x66554))+~E(f324(f324(f158(x66551),f324(f180(f839(x66551)),x66552)),x66554),x66552)
% 18.77/18.50 [6715]~P60(x67152)+E(x67151,f2(x67152))+E(f324(f324(f284(x67152),f324(f324(f240(x67152),x67153),x67154)),f324(f324(f240(x67152),x67151),x67154)),f324(f324(f240(x67152),f324(f324(f284(x67152),x67153),x67151)),x67154))
% 18.77/18.50 [6868]~P7(x68681)+E(f324(f324(f42(x68681),f324(f324(f83(x68681),x68682),x68683)),x68684),f324(f324(f83(x68681),f324(f324(f42(x68681),x68682),x68684)),x68683))+~P1(f324(f324(f280(x68681),x68684),x68682))
% 18.77/18.50 [6877]~P86(x68771)+~P1(f324(f324(f232(x68771),x68773),x68774))+P1(f324(f324(f232(x68771),f324(f324(f235(x68771),x68772),x68773)),x68774))
% 18.77/18.50 [6878]~P86(x68781)+~P1(f324(f324(f232(x68781),x68783),x68784))+P1(f324(f324(f232(x68781),f324(f324(f235(x68781),x68782),x68783)),x68784))
% 18.77/18.50 [6879]~P86(x68791)+~P1(f324(f324(f232(x68791),x68792),x68794))+P1(f324(f324(f232(x68791),f324(f324(f235(x68791),x68792),x68793)),x68794))
% 18.77/18.50 [6880]~P86(x68801)+~P1(f324(f324(f232(x68801),x68802),x68804))+P1(f324(f324(f232(x68801),f324(f324(f235(x68801),x68802),x68803)),x68804))
% 18.77/18.50 [6881]~P99(x68811)+~P1(f324(f324(f232(x68811),x68813),x68814))+P1(f324(f324(f232(x68811),f324(f324(f104(x68811),x68812),x68813)),x68814))
% 18.77/18.50 [6882]~P99(x68821)+~P1(f324(f324(f232(x68821),x68822),x68824))+P1(f324(f324(f232(x68821),f324(f324(f104(x68821),x68822),x68823)),x68824))
% 18.77/18.50 [6883]~P86(x68831)+~P1(f324(f324(f231(x68831),x68833),x68834))+P1(f324(f324(f231(x68831),f324(f324(f235(x68831),x68832),x68833)),x68834))
% 18.77/18.50 [6884]~P86(x68841)+~P1(f324(f324(f231(x68841),x68843),x68844))+P1(f324(f324(f231(x68841),f324(f324(f235(x68841),x68842),x68843)),x68844))
% 18.77/18.50 [6885]~P86(x68851)+~P1(f324(f324(f231(x68851),x68852),x68854))+P1(f324(f324(f231(x68851),f324(f324(f235(x68851),x68852),x68853)),x68854))
% 18.77/18.50 [6886]~P86(x68861)+~P1(f324(f324(f231(x68861),x68862),x68864))+P1(f324(f324(f231(x68861),f324(f324(f235(x68861),x68862),x68863)),x68864))
% 18.77/18.50 [6887]~P99(x68871)+~P1(f324(f324(f231(x68871),x68873),x68874))+P1(f324(f324(f231(x68871),f324(f324(f104(x68871),x68872),x68873)),x68874))
% 18.77/18.50 [6888]~P99(x68881)+~P1(f324(f324(f231(x68881),x68882),x68884))+P1(f324(f324(f231(x68881),f324(f324(f104(x68881),x68882),x68883)),x68884))
% 18.77/18.50 [6905]~P1(f324(x69053,x69054))+~P1(f324(x69052,x69054))+P1(f324(f324(f324(f104(f845(x69051,a832)),x69052),x69053),x69054))
% 18.77/18.50 [6937]~E(f324(f180(f839(x69371)),x69373),f324(f180(f839(x69372)),x69374))+~P1(f324(f127(x69371),x69373))+E(f168(x69371,x69372,f165(x69371,x69372,f324(f324(f166(x69371,x69372),x69373),x69374))),f324(f157(x69371),x69373))
% 18.77/18.50 [7031]P28(x70311,x70312,x70313)+~P28(x70311,x70314,x70313)+~P1(f324(f324(f231(f845(f837(x70311),a832)),x70314),x70312))
% 18.77/18.50 [7032]P28(x70321,x70322,x70323)+~P28(x70321,x70322,x70324)+~P1(f324(f324(f231(f845(f837(x70321),a832)),x70323),x70324))
% 18.77/18.50 [7169]~P7(x71691)+E(f324(f324(f42(x71691),f324(f324(f240(x71691),x71692),x71693)),f324(f324(f240(x71691),x71694),x71693)),f324(f324(f240(x71691),f324(f324(f42(x71691),x71692),x71694)),x71693))+~P1(f324(f324(f280(x71691),x71694),x71692))
% 18.77/18.50 [7427]~P67(x74271)+E(f324(f324(f82(x74271),f324(x74272,x74273)),f324(f324(f8(a838,x74271),x74272),f324(f295(a838,f324(a114,x74273)),x74274))),f324(f324(f8(a838,x74271),x74272),f324(f295(a838,x74273),x74274)))+~P1(f324(f324(f232(a838),x74273),x74274))
% 18.77/18.50 [7455]~P86(x74551)+P1(f324(f324(f232(x74551),x74552),x74553))+~P1(f324(f324(f232(x74551),f324(f324(f178(x74551),x74554),x74552)),x74553))
% 18.77/18.50 [7456]~P86(x74561)+P1(f324(f324(f232(x74561),x74562),x74563))+~P1(f324(f324(f232(x74561),f324(f324(f178(x74561),x74562),x74564)),x74563))
% 18.77/18.50 [7457]~P86(x74571)+P1(f324(f324(f231(x74571),x74572),x74573))+~P1(f324(f324(f231(x74571),f324(f324(f178(x74571),x74574),x74572)),x74573))
% 18.77/18.50 [7458]~P86(x74581)+P1(f324(f324(f231(x74581),x74582),x74583))+~P1(f324(f324(f231(x74581),f324(f324(f178(x74581),x74584),x74582)),x74583))
% 18.77/18.50 [7459]~P86(x74591)+P1(f324(f324(f231(x74591),x74592),x74593))+~P1(f324(f324(f231(x74591),f324(f324(f178(x74591),x74592),x74594)),x74593))
% 18.77/18.50 [7460]~P86(x74601)+P1(f324(f324(f231(x74601),x74602),x74603))+~P1(f324(f324(f231(x74601),f324(f324(f178(x74601),x74602),x74604)),x74603))
% 18.77/18.50 [7461]~P93(x74611)+P1(f324(f324(f231(x74611),x74612),x74613))+~P1(f324(f324(f231(x74611),f324(f324(f103(x74611),x74614),x74612)),x74613))
% 18.77/18.50 [7462]~P93(x74621)+P1(f324(f324(f231(x74621),x74622),x74623))+~P1(f324(f324(f231(x74621),f324(f324(f103(x74621),x74624),x74622)),x74623))
% 18.77/18.50 [7463]~P93(x74631)+P1(f324(f324(f231(x74631),x74632),x74633))+~P1(f324(f324(f231(x74631),f324(f324(f103(x74631),x74632),x74634)),x74633))
% 18.77/18.50 [7464]~P93(x74641)+P1(f324(f324(f231(x74641),x74642),x74643))+~P1(f324(f324(f231(x74641),f324(f324(f103(x74641),x74642),x74644)),x74643))
% 18.77/18.50 [7465]~P105(x74651)+P1(f324(f324(f280(x74651),x74652),x74653))+~P1(f324(f324(f280(x74651),f324(f324(f83(x74651),x74654),x74652)),x74653))
% 18.77/18.50 [7466]~P105(x74661)+P1(f324(f324(f280(x74661),x74662),x74663))+~P1(f324(f324(f280(x74661),f324(f324(f83(x74661),x74662),x74664)),x74663))
% 18.77/18.50 [7543]~P1(f324(f324(f326(x75431),x75432),x75434))+P1(f324(f324(f326(x75431),x75432),x75433))+P1(f324(f324(f326(x75431),x75432),f324(f324(f3(f845(x75431,a832)),x75434),x75433)))
% 18.77/18.50 [7544]~P1(f324(f324(f326(x75441),x75442),x75444))+P1(f324(f324(f326(x75441),x75442),x75443))+P1(f324(f324(f326(x75441),x75442),f324(f324(f3(f845(x75441,a832)),x75444),x75443)))
% 18.77/18.50 [7625]P1(f324(x76251,x76252))+P1(f324(x76253,x76252))+~P1(f324(f324(f324(f103(f845(x76254,a832)),x76253),x76251),x76252))
% 18.77/18.50 [7634]~P1(f324(f324(f326(x76341),x76342),x76344))+~P1(f324(f324(f326(x76341),x76342),x76343))+P1(f324(f324(f326(x76341),x76342),f324(f324(f104(f845(x76341,a832)),x76343),x76344)))
% 18.77/18.50 [7635]~P1(f324(f324(f326(x76351),x76352),x76354))+~P1(f324(f324(f326(x76351),x76352),x76353))+P1(f324(f324(f326(x76351),x76352),f324(f324(f104(f845(x76351,a832)),x76353),x76354)))
% 18.77/18.50 [7691]~P86(x76911)+~P1(f324(f64(x76911),x76914))+E(f324(f324(f67(x76911,x76911,f235(x76911)),x76912),f324(f324(f303(x76911),x76913),x76914)),f324(f324(f235(x76911),x76913),f324(f324(f67(x76911,x76911,f235(x76911)),x76912),x76914)))
% 18.77/18.50 [7692]~P86(x76921)+~P1(f324(f64(x76921),x76924))+E(f324(f324(f67(x76921,x76921,f178(x76921)),x76922),f324(f324(f303(x76921),x76923),x76924)),f324(f324(f178(x76921),x76923),f324(f324(f67(x76921,x76921,f178(x76921)),x76922),x76924)))
% 18.77/18.50 [7693]~P93(x76931)+~P1(f324(f64(x76931),x76934))+E(f324(f324(f67(x76931,x76931,f103(x76931)),x76932),f324(f324(f303(x76931),x76933),x76934)),f324(f324(f103(x76931),x76933),f324(f324(f67(x76931,x76931,f103(x76931)),x76932),x76934)))
% 18.77/18.50 [7694]~P99(x76941)+~P1(f324(f64(x76941),x76944))+E(f324(f324(f67(x76941,x76941,f104(x76941)),x76942),f324(f324(f303(x76941),x76943),x76944)),f324(f324(f104(x76941),x76943),f324(f324(f67(x76941,x76941,f104(x76941)),x76942),x76944)))
% 18.77/18.50 [7696]~P134(x76961)+~P90(x76961)+E(f324(f324(f82(x76961),f324(f324(f83(x76961),f324(f106(x76961),x76962)),x76963)),f324(f324(f83(x76961),f324(f106(x76961),x76962)),x76964)),f324(f324(f83(x76961),f324(f106(x76961),x76962)),f324(f324(f82(x76961),x76963),x76964)))
% 18.77/18.50 [7697]~P126(x76971)+~P90(x76971)+E(f324(f324(f3(x76971),f324(f324(f83(x76971),f324(f106(x76971),x76972)),x76973)),f324(f324(f83(x76971),f324(f106(x76971),x76972)),x76974)),f324(f324(f83(x76971),f324(f106(x76971),x76972)),f324(f324(f3(x76971),x76973),x76974)))
% 18.77/18.50 [7812]E(x78121,x78122)+P1(f324(f324(f326(x78123),x78121),f324(f157(x78123),x78124)))+~P1(f324(f324(f326(x78123),x78121),f324(f157(x78123),f324(f324(f139(x78123),x78122),x78124))))
% 18.77/18.50 [7986]P52(x79861,x79862,x79863)+~P52(x79861,x79862,x79864)+~P1(f324(f324(f231(f845(f844(x79861,x79862),a832)),x79863),x79864))
% 18.77/18.50 [8031]P1(f324(f324(f326(x80311),x80312),x80313))+P1(f324(f324(f326(x80311),x80312),x80314))+~P1(f324(f324(f326(x80311),x80312),f324(f324(f103(f845(x80311,a832)),x80314),x80313)))
% 18.77/18.50 [8032]P1(f324(f324(f326(x80321),x80322),x80323))+P1(f324(f324(f326(x80321),x80322),x80324))+~P1(f324(f324(f326(x80321),x80322),f324(f324(f103(f845(x80321,a832)),x80324),x80323)))
% 18.77/18.50 [8041]~P47(x80411,x80414,x80413)+~P1(f324(f324(f326(x80411),x80412),x80414))+P1(f324(f324(f326(f844(x80411,x80411)),f324(f324(f247(x80411,x80411),x80412),x80412)),x80413))
% 18.77/18.50 [8042]~P47(x80421,x80424,x80423)+~P1(f324(f324(f326(x80421),x80422),x80424))+P1(f324(f324(f326(f844(x80421,x80421)),f324(f324(f247(x80421,x80421),x80422),x80422)),x80423))
% 18.77/18.50 [8043]~P47(x80431,x80434,x80433)+~P1(f324(f324(f326(x80431),x80432),x80434))+P1(f324(f324(f326(f844(x80431,x80431)),f324(f324(f247(x80431,x80431),x80432),x80432)),x80433))
% 18.77/18.50 [8055]~P1(f324(f64(x80552),x80554))+~P1(f324(f64(x80551),x80553))+P1(f324(f64(f844(x80551,x80552)),f324(f324(f249(x80551,x80552),x80553),f324(f18(f845(x80552,a832),x80551),x80554))))
% 18.77/18.50 [8056]~P1(f324(f324(f326(x80561),x80562),x80564))+~P1(f324(f324(f231(f845(x80561,a832)),x80563),x80564))+P1(f324(f324(f231(f845(x80561,a832)),f324(f324(f303(x80561),x80562),x80563)),x80564))
% 18.77/18.50 [8064]~P2(x80642)+~P68(x80642)+E(f324(f324(f11(x80641,x80642),f324(f324(f10(a838,x80642,x80641),f102(x80642)),x80643)),x80644),f324(f102(x80642),f324(f324(f11(x80641,a838),x80643),x80644)))
% 18.77/18.50 [8065]~P119(x80652)+~P68(x80652)+E(f324(f324(f11(x80651,x80652),f324(f324(f10(a1,x80652,x80651),f105(x80652)),x80653)),x80654),f324(f105(x80652),f324(f324(f11(x80651,a1),x80653),x80654)))
% 18.77/18.50 [8091]E(f324(f324(f3(f845(x80911,a832)),x80912),f324(f324(f3(f845(x80911,a832)),x80913),x80914)),x80914)+~P1(f324(f324(f231(f845(x80911,a832)),x80912),x80913))+~P1(f324(f324(f231(f845(x80911,a832)),x80914),x80912))
% 18.77/18.50 [8185]~P1(f324(f64(x81851),x81854))+E(f324(f324(f3(a838),f324(f324(f8(x81851,a838),x81852),x81853)),f324(f324(f8(x81851,a838),x81852),x81854)),f324(f324(f8(x81851,a838),x81852),f324(f324(f3(f845(x81851,a832)),x81853),x81854)))+~P1(f324(f324(f231(f845(x81851,a832)),x81854),x81853))
% 18.77/18.50 [8342]~P12(x83421,x83424,x83423)+~P1(f324(f324(f326(x83421),x83422),x83424))+P1(f324(f324(f326(x83421),x83422),f324(f278(x83421,x83421,x83423),f324(f324(f303(x83421),x83422),f179(f845(x83421,a832))))))
% 18.77/18.50 [8405]~P1(f324(f324(f231(f845(x84051,a832)),x84052),x84053))+~P1(f324(f324(f231(f845(x84051,a832)),x84052),x84054))+P1(f324(f324(f231(f845(x84051,a832)),x84052),f324(f324(f104(f845(x84051,a832)),x84053),x84054)))
% 18.77/18.50 [8494]E(x84941,f179(f845(x84942,a832)))+P1(f324(f64(x84943),x84944))+~P1(f324(f64(f844(x84943,x84942)),f324(f324(f249(x84943,x84942),x84944),f324(f18(f845(x84942,a832),x84943),x84941))))
% 18.77/18.50 [8495]E(x84951,f179(f845(x84952,a832)))+P1(f324(f64(x84953),x84954))+~P1(f324(f64(f844(x84952,x84953)),f324(f324(f249(x84952,x84953),x84951),f324(f18(f845(x84953,a832),x84952),x84954))))
% 18.77/18.50 [8553]P1(f324(f324(f326(x85531),x85532),f314(x85531,x85533)))+~P1(f324(f324(f326(x85531),x85534),f314(x85531,x85533)))+~P1(f324(f324(f326(f844(x85531,x85531)),f324(f324(f247(x85531,x85531),x85532),x85534)),x85533))
% 18.77/18.50 [8554]P1(f324(f324(f326(x85541),x85542),f314(x85541,x85543)))+~P1(f324(f324(f326(x85541),x85544),f314(x85541,x85543)))+~P1(f324(f324(f326(f844(x85541,x85541)),f324(f324(f247(x85541,x85541),x85542),x85544)),x85543))
% 18.77/18.50 [8606]~P36(x86061,x86064)+P1(f324(f324(f326(f844(x86061,x86061)),f324(f324(f247(x86061,x86061),x86063),x86062)),f301(x86061,x86064)))+P36(x86061,f324(f324(f303(f844(x86061,x86061)),f324(f324(f247(x86061,x86061),x86062),x86063)),x86064))
% 18.77/18.50 [8607]~P55(x86071,x86074)+P1(f324(f324(f326(f844(x86071,x86071)),f324(f324(f247(x86071,x86071),x86073),x86072)),f301(x86071,x86074)))+P55(x86071,f324(f324(f303(f844(x86071,x86071)),f324(f324(f247(x86071,x86071),x86072),x86073)),x86074))
% 18.77/18.50 [8681]~E(x86812,x86813)+~P1(f324(f324(f326(x86811),x86812),f324(f157(x86811),x86814)))+P1(f324(f324(f326(f844(x86811,x86811)),f324(f324(f247(x86811,x86811),x86812),x86813)),f324(f157(f844(x86811,x86811)),f324(f324(f166(x86811,x86811),x86814),x86814))))
% 18.77/18.50 [8753]~E(x87533,x87534)+P1(f324(f324(f252(x87531,x87531,a832),a321),x87532))+~P1(f324(f324(f326(f844(x87531,x87531)),x87532),f324(f157(f844(x87531,x87531)),f324(f324(f166(x87531,x87531),x87533),x87534))))
% 18.77/18.50 [8791]P1(f324(f324(f326(f844(f839(x87911),f839(x87911))),f324(f324(f247(f839(x87911),f839(x87911)),x87912),x87913)),f136(x87911,x87914)))+~E(f324(f324(f158(x87911),f324(f180(f839(x87911)),x87912)),x87913),x87912)+~P1(f324(f324(f232(a838),f324(f180(f839(x87911)),x87912)),f324(f180(f839(x87911)),x87913)))
% 18.77/18.50 [8883]~P1(f324(f64(x88831),x88834))+P1(f324(f324(f326(x88831),f527(x88832,x88833,x88834,x88831)),x88834))+P1(f324(f64(x88833),f324(f324(f45(x88831,f845(x88833,a832)),x88834),x88832)))
% 18.77/18.50 [8884]~P1(f324(f64(x88841),x88844))+P1(f324(f324(f326(x88841),f618(x88842,x88843,x88844,x88841)),x88844))+P1(f324(f64(x88843),f324(f324(f45(x88841,f845(x88843,a832)),x88844),x88842)))
% 18.77/18.50 [8958]P1(f324(f324(f326(f844(x89581,x89581)),x89582),f324(f324(f282(x89581,x89581,x89581),x89583),f301(x89581,x89583))))+~P1(f324(f324(f232(a838),f2(a838)),x89584))+~P1(f324(f324(f326(f844(x89581,x89581)),x89582),f324(f324(f172(f844(x89581,x89581),a832),x89584),x89583)))
% 18.77/18.50 [8965]~P36(x89651,x89652)+~P1(f324(f324(f326(f844(x89651,x89651)),f324(f324(f247(x89651,x89651),x89654),x89653)),x89652))+~P1(f324(f324(f326(f844(x89651,x89651)),f324(f324(f247(x89651,x89651),x89653),x89654)),x89652))
% 18.77/18.50 [8966]~P36(x89661,x89662)+~P1(f324(f324(f326(f844(x89661,x89661)),f324(f324(f247(x89661,x89661),x89664),x89663)),x89662))+~P1(f324(f324(f326(f844(x89661,x89661)),f324(f324(f247(x89661,x89661),x89663),x89664)),x89662))
% 18.77/18.50 [9080]~P1(f324(f64(x90801),x90804))+E(f324(f324(f8(x90801,a838),f324(f324(f10(f845(x90802,a832),a838,x90801),f41(x90802)),x90803)),x90804),f324(f41(f844(x90801,x90802)),f324(f324(f249(x90801,x90802),x90804),x90803)))+P1(f324(f324(f326(x90801),f586(x90803,x90802,x90804,x90801)),x90804))
% 18.77/18.50 [9084]~P1(f324(f127(x90841),x90842))+P1(f324(f127(x90841),f324(f324(f146(x90841,x90842),x90843),x90844)))+P1(f324(f324(f326(x90841),x90844),f324(f324(f3(f845(x90841,a832)),f324(f157(x90841),x90842)),f324(f324(f303(x90841),f324(f324(f149(x90841),x90842),x90843)),f179(f845(x90841,a832))))))
% 18.77/18.50 [9093]~P1(f324(f64(x90932),x90933))+~P1(f324(f64(x90931),f324(x90934,f527(x90934,x90931,x90933,x90932))))+P1(f324(f64(x90931),f324(f324(f45(x90932,f845(x90931,a832)),x90933),x90934)))
% 18.77/18.50 [9094]~P1(f324(f64(x90942),x90943))+~P1(f324(f64(x90941),f324(x90944,f618(x90944,x90941,x90943,x90942))))+P1(f324(f64(x90941),f324(f324(f45(x90942,f845(x90941,a832)),x90943),x90944)))
% 18.77/18.50 [9161]~P1(f324(f324(f326(f844(x91611,x91611)),x91612),f324(f324(f282(x91611,x91611,x91611),x91614),f301(x91611,x91614))))+P1(f324(f324(f326(f844(x91611,x91611)),x91612),f324(f324(f282(x91611,x91611,x91611),x91613),f301(x91611,x91613))))+~P1(f324(f324(f231(f845(f844(x91611,x91611),a832)),x91614),x91613))
% 18.77/18.50 [9169]E(f324(f324(f158(x91691),f722(x91694,x91693,x91692,x91691)),x91693),f324(f324(f158(x91691),f722(x91694,x91693,x91692,x91691)),x91692))+~P1(f324(f324(f326(f844(f839(x91691),f839(x91691))),f324(f324(f247(f839(x91691),f839(x91691)),x91692),x91693)),f136(x91691,x91694)))+E(f324(f324(f158(x91691),f324(f180(f839(x91691)),x91692)),x91693),x91692)
% 18.77/18.50 [9185]~P1(f324(f64(x91851),x91854))+E(f324(f324(f8(x91851,a838),f324(f324(f10(f845(x91852,a832),a838,x91851),f41(x91852)),x91853)),x91854),f324(f41(f844(x91851,x91852)),f324(f324(f249(x91851,x91852),x91854),x91853)))+~P1(f324(f64(x91852),f324(x91853,f586(x91853,x91852,x91854,x91851))))
% 18.77/18.50 [9190]~E(f324(f180(f839(x91901)),x91903),f324(f180(f839(x91901)),x91902))+P1(f324(f324(f326(f844(f839(x91901),f839(x91901))),f324(f324(f247(f839(x91901),f839(x91901)),x91902),x91903)),f145(x91901,x91904)))+P1(f324(f324(f326(f844(x91901,x91901)),f704(x91904,x91903,x91902,x91901)),f324(f157(f844(x91901,x91901)),f324(f324(f166(x91901,x91901),x91902),x91903))))
% 18.77/18.50 [9272]~P1(f324(f324(f326(f844(f839(x92721),f839(x92721))),f324(f324(f247(f839(x92721),f839(x92721)),x92722),x92723)),f136(x92721,x92724)))+E(f324(f324(f158(x92721),f324(f180(f839(x92721)),x92722)),x92723),x92722)+P1(f324(f324(f232(a838),f722(x92724,x92723,x92722,x92721)),f324(f324(f235(a838),f324(f180(f839(x92721)),x92722)),f324(f180(f839(x92721)),x92723))))
% 18.77/18.50 [9291]~P1(f324(f324(f326(f844(f839(x92911),f839(x92911))),f324(f324(f247(f839(x92911),f839(x92911)),x92912),x92913)),f136(x92911,x92914)))+P1(f324(f324(f232(a838),f324(f180(f839(x92911)),x92912)),f324(f180(f839(x92911)),x92913)))+P1(f324(f324(f232(a838),f722(x92914,x92913,x92912,x92911)),f324(f324(f235(a838),f324(f180(f839(x92911)),x92912)),f324(f180(f839(x92911)),x92913))))
% 18.77/18.50 [9572]~P1(f324(f324(f324(x95721,f693(x95721,x95724,x95723,x95722)),f694(x95721,x95724,x95723,x95722)),f695(x95721,x95724,x95723,x95722)))+P1(f324(f324(f324(x95721,x95722),x95723),x95724))+~P1(f324(f313(f844(f845(a1,f842(f839(a831))),f844(a1,a1)),a311),f324(f324(f247(f845(a1,f842(f839(a831))),f844(a1,a1)),x95722),f324(f324(f247(a1,a1),x95723),x95724))))
% 18.77/18.50 [9637]P1(f324(f324(f324(x96371,x96372),x96373),x96374))+P1(f324(f313(f844(f845(a1,f842(f839(a831))),f844(a1,a1)),a311),f324(f324(f247(f845(a1,f842(f839(a831))),f844(a1,a1)),f693(x96371,x96374,x96373,x96372)),f324(f324(f247(a1,a1),f694(x96371,x96374,x96373,x96372)),f695(x96371,x96374,x96373,x96372)))))+~P1(f324(f313(f844(f845(a1,f842(f839(a831))),f844(a1,a1)),a311),f324(f324(f247(f845(a1,f842(f839(a831))),f844(a1,a1)),x96372),f324(f324(f247(a1,a1),x96373),x96374))))
% 18.77/18.50 [9676]~P1(f324(f324(f326(f844(f839(x96761),f839(x96761))),f324(f324(f247(f839(x96761),f839(x96761)),x96762),x96763)),f136(x96761,x96764)))+E(f324(f324(f158(x96761),f324(f180(f839(x96761)),x96762)),x96763),x96762)+P1(f324(f324(f326(f844(x96761,x96761)),f324(f324(f247(x96761,x96761),f324(f324(f149(x96761),x96762),f722(x96764,x96763,x96762,x96761))),f324(f324(f149(x96761),x96763),f722(x96764,x96763,x96762,x96761)))),x96764))
% 18.77/18.50 [9677]~P1(f324(f324(f326(f844(f839(x96771),f839(x96771))),f324(f324(f247(f839(x96771),f839(x96771)),x96772),x96773)),f136(x96771,x96774)))+P1(f324(f324(f232(a838),f324(f180(f839(x96771)),x96772)),f324(f180(f839(x96771)),x96773)))+P1(f324(f324(f326(f844(x96771,x96771)),f324(f324(f247(x96771,x96771),f324(f324(f149(x96771),x96772),f722(x96774,x96773,x96772,x96771))),f324(f324(f149(x96771),x96773),f722(x96774,x96773,x96772,x96771)))),x96774))
% 18.77/18.50 [9747]~E(f324(f180(f839(x97471)),x97472),f324(f180(f839(x97471)),x97473))+P1(f324(f324(f326(f844(f839(x97471),f839(x97471))),f324(f324(f247(f839(x97471),f839(x97471)),x97472),x97473)),f145(x97471,x97474)))+~P1(f324(f324(f326(f844(x97471,x97471)),f324(f324(f247(x97471,x97471),f324(f324(f149(x97471),x97472),f721(x97474,x97473,x97472,x97471))),f324(f324(f149(x97471),x97473),f721(x97474,x97473,x97472,x97471)))),x97474))
% 18.77/18.50 [9886]~P67(x98861)+~P1(f324(f64(x98862),x98864))+E(f324(f151(x98861),f324(f324(f141(x98862,x98861),x98863),f92(f839(x98862),f324(f324(f20(f839(x98862),a832,a832),f324(f324(f10(a832,f845(a832,a832),f839(x98862)),a322),f324(f324(f9(f839(x98862),f845(x98862,a832),a832),f324(f324(f10(f845(x98862,a832),f845(f845(x98862,a832),a832),f839(x98862)),a321),f157(x98862))),x98864))),f127(x98862))))),f224(x98862,x98861,x98863,x98864))
% 18.77/18.50 [7260]~P59(x72602)+E(x72601,f2(x72602))+E(f324(f324(f284(x72602),f324(f324(f82(x72602),x72603),f324(f324(f83(x72602),x72604),x72601))),x72601),f324(f324(f82(x72602),x72604),f324(f324(f284(x72602),x72603),x72601)))
% 18.77/18.50 [7261]~P7(x72612)+E(x72611,f2(x72612))+E(f324(f324(f42(x72612),f324(f324(f82(x72612),x72613),f324(f324(f83(x72612),x72614),x72611))),x72611),f324(f324(f82(x72612),x72614),f324(f324(f42(x72612),x72613),x72611)))
% 18.77/18.50 [7262]~P7(x72622)+E(x72621,f2(x72622))+E(f324(f324(f42(x72622),f324(f324(f82(x72622),x72623),f324(f324(f83(x72622),x72621),x72624))),x72621),f324(f324(f82(x72622),x72624),f324(f324(f42(x72622),x72623),x72621)))
% 18.77/18.50 [7506]~P59(x75062)+E(x75061,f2(x75062))+E(f324(f324(f284(x75062),f324(f324(f82(x75062),x75063),f324(f324(f83(x75062),x75064),x75061))),x75061),f324(f324(f82(x75062),f324(f324(f284(x75062),x75063),x75061)),x75064))
% 18.77/18.50 [7507]~P60(x75072)+E(x75071,f2(x75072))+E(f324(f324(f284(x75072),f324(f324(f82(x75072),x75073),f324(f324(f83(x75072),x75071),x75074))),x75071),f324(f324(f82(x75072),f324(f324(f284(x75072),x75073),x75071)),x75074))
% 18.77/18.50 [7508]~P60(x75082)+E(x75081,f2(x75082))+E(f324(f324(f284(x75082),f324(f324(f3(x75082),x75083),f324(f324(f83(x75082),x75081),x75084))),x75081),f324(f324(f3(x75082),f324(f324(f284(x75082),x75083),x75081)),x75084))
% 18.77/18.50 [8568]~E(f324(f324(f282(x85681,x85681,x85681),x85682),x85684),f179(f845(f844(x85681,x85681),a832)))+~E(f324(f324(f282(x85681,x85681,x85681),x85682),x85683),f179(f845(f844(x85681,x85681),a832)))+E(f324(f324(f282(x85681,x85681,x85681),x85682),f324(f324(f103(f845(f844(x85681,x85681),a832)),x85683),x85684)),f179(f845(f844(x85681,x85681),a832)))
% 18.77/18.50 [8682]~P1(f324(f324(f231(f845(x86821,a832)),x86823),x86824))+~P1(f324(f324(f231(f845(x86821,a832)),x86822),x86824))+P1(f324(f324(f231(f845(x86821,a832)),f324(f324(f103(f845(x86821,a832)),x86822),x86823)),x86824))
% 18.77/18.50 [9016]~P1(f324(f64(x90161),x90164))+~P1(f324(f64(x90161),x90163))+E(f324(f324(f3(a838),f324(f324(f82(a838),f324(f324(f8(x90161,a838),x90162),x90163)),f324(f324(f8(x90161,a838),x90162),x90164))),f324(f324(f8(x90161,a838),x90162),f324(f324(f104(f845(x90161,a832)),x90163),x90164))),f324(f324(f8(x90161,a838),x90162),f324(f324(f103(f845(x90161,a832)),x90163),x90164)))
% 18.77/18.50 [9091]~P1(f324(f324(f326(x90911),x90913),x90912))+~P1(f324(f324(f231(f845(x90911,a832)),x90912),f324(f324(f303(x90911),x90913),x90914)))+P1(f324(f324(f231(f845(x90911,a832)),f324(f324(f3(f845(x90911,a832)),x90912),f324(f324(f303(x90911),x90913),f179(f845(x90911,a832))))),x90914))
% 18.77/18.50 [9243]~P1(f324(f324(f326(x92431),x92433),x92432))+P1(f324(f324(f231(f845(x92431,a832)),x92432),f324(f324(f303(x92431),x92433),x92434)))+~P1(f324(f324(f231(f845(x92431,a832)),f324(f324(f3(f845(x92431,a832)),x92432),f324(f324(f303(x92431),x92433),f179(f845(x92431,a832))))),x92434))
% 18.77/18.50 [9244]~P1(f324(f324(f326(x92441),x92443),x92442))+P1(f324(f324(f231(f845(x92441,a832)),x92442),f324(f324(f303(x92441),x92443),x92444)))+~P1(f324(f324(f231(f845(x92441,a832)),f324(f324(f3(f845(x92441,a832)),x92442),f324(f324(f303(x92441),x92443),f179(f845(x92441,a832))))),x92444))
% 18.77/18.50 [9270]~P1(f324(f324(f231(f845(x92701,a832)),x92702),x92704))+P1(f324(f324(f231(f845(x92701,a832)),x92702),f324(f324(f303(x92701),x92703),x92704)))+~P1(f324(f324(f231(f845(x92701,a832)),f324(f324(f3(f845(x92701,a832)),x92702),f324(f324(f303(x92701),x92703),f179(f845(x92701,a832))))),x92704))
% 18.77/18.50 [9329]~P1(f324(f324(f232(a838),x93292),x93294))+~P1(f324(f324(f231(a838),x93291),x93293))+P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),f324(f324(f247(a838,a838),x93291),x93292)),f324(f324(f247(a838,a838),x93293),x93294))),a38))
% 18.77/18.50 [9330]~P1(f324(f324(f231(a838),x93302),x93304))+~P1(f324(f324(f231(a838),x93301),x93303))+P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),f324(f324(f247(a838,a838),x93301),x93302)),f324(f324(f247(a838,a838),x93303),x93304))),a72))
% 18.77/18.50 [9712]~P29(x97121,f845(f845(x97121,a832),a832),f324(f324(f9(x97121,f845(f844(x97121,x97121),a832),f845(f845(x97121,a832),a832)),f324(f324(f10(f845(x97121,a832),f845(f845(f844(x97121,x97121),a832),f845(f845(x97121,a832),a832)),x97121),f63(x97121)),f324(f324(f9(x97121,f845(x97121,a832),f845(x97121,a832)),f303(x97121)),f179(f845(x97121,a832))))),x97123),x97122)+~P1(f324(f324(f326(x97121),x97124),x97122))+E(f324(f324(f3(f845(f845(x97121,a832),a832)),f324(f324(f63(x97121),x97122),x97123)),f324(f324(f63(x97121),f324(f324(f303(x97121),x97124),f179(f845(x97121,a832)))),x97123)),f324(f324(f63(x97121),f324(f324(f3(f845(x97121,a832)),x97122),f324(f324(f303(x97121),x97124),f179(f845(x97121,a832))))),x97123))
% 18.77/18.50 [9850]~P47(x98501,x98502,x98504)+~P1(f324(f324(f326(f844(x98501,x98501)),x98503),x98504))+P1(f324(f324(f252(x98501,x98501,a832),f324(f324(f9(x98501,f845(x98501,a832),f845(x98501,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x98501,a832),f845(x98501,a832)),x98501),f10(a832,a832,x98501)),f324(f324(f10(a832,f845(a832,a832),x98501),a322),f324(f324(f9(x98501,f845(x98501,a832),a832),f326(x98501)),x98502)))),f324(f324(f9(x98501,f845(x98501,a832),a832),f326(x98501)),x98502))),x98503))
% 18.77/18.50 [9860]P1(f324(f64(x98601),x98602))+~P1(f324(f64(x98603),f324(f304(x98601,x98603,x98604),x98602)))+~P1(f324(f64(x98601),f324(f257(x98601),f324(f324(f20(x98601,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98601),a322),f324(f324(f9(x98601,f845(x98601,a832),a832),f326(x98601)),x98602))),f324(f324(f9(x98601,x98603,a832),f324(f324(f10(x98603,f845(x98603,a832),x98601),a321),x98604)),f324(x98604,f602(x98604,x98603,x98602,x98601)))))))
% 18.77/18.50 [7969]~P60(x79692)+E(x79691,f2(x79692))+E(f324(f324(f284(x79692),f324(f324(f82(x79692),f324(f324(f83(x79692),x79691),x79693)),x79694)),x79691),f324(f324(f82(x79692),x79693),f324(f324(f284(x79692),x79694),x79691)))
% 18.77/18.50 [7970]~P60(x79702)+E(x79701,f2(x79702))+E(f324(f324(f284(x79702),f324(f324(f3(x79702),f324(f324(f83(x79702),x79701),x79703)),x79704)),x79701),f324(f324(f3(x79702),x79703),f324(f324(f284(x79702),x79704),x79701)))
% 18.77/18.50 [8818]~E(f324(f324(f282(x88181,x88181,x88181),x88183),x88184),f179(f845(f844(x88181,x88181),a832)))+~E(f324(f324(f282(x88181,x88181,x88181),x88182),x88184),f179(f845(f844(x88181,x88181),a832)))+E(f324(f324(f282(x88181,x88181,x88181),f324(f324(f103(f845(f844(x88181,x88181),a832)),x88182),x88183)),x88184),f179(f845(f844(x88181,x88181),a832)))
% 18.77/18.50 [9794]~P138(x97941)+~P138(x97942)+E(f324(f324(f310(x97941),f324(f324(f9(x97941,a101,f842(f839(a831))),f324(f324(f10(f845(x97942,f842(f839(a831))),f845(a101,f842(f839(a831))),x97941),f310(x97942)),f324(f324(f10(f845(x97942,f844(x97941,x97942)),f845(x97942,f842(f839(a831))),x97941),f324(f10(f844(x97941,x97942),f842(f839(a831)),x97942),x97943)),f247(x97941,x97942)))),x97944)),x97944),f324(f324(f310(f844(x97941,x97942)),x97943),x97944))
% 18.77/18.50 [9786]P1(f324(x97861,f387(x97862,x97863,x97861,x97864)))+~P1(f324(f64(x97864),f324(f257(x97864),x97861)))+P1(f324(f64(x97863),f324(f257(x97863),f324(f324(f10(f845(x97864,a832),a832,x97863),f89(x97864)),f324(f324(f10(f845(x97864,a832),f845(x97864,a832),x97863),f324(f20(x97864,a832,a832),f324(f324(f10(a832,f845(a832,a832),x97864),a322),x97861))),x97862)))))
% 18.77/18.50 [9807]~P1(f324(f64(x98072),f324(f257(x98072),x98073)))+~P1(f324(f64(x98071),f324(f257(x98071),f324(f324(f9(x98071,x98072,a832),x98074),f387(x98074,x98071,x98073,x98072)))))+P1(f324(f64(x98071),f324(f257(x98071),f324(f324(f10(f845(x98072,a832),a832,x98071),f89(x98072)),f324(f324(f10(f845(x98072,a832),f845(x98072,a832),x98071),f324(f20(x98072,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98072),a322),x98073))),x98074)))))
% 18.77/18.50 [5640]~E(x56405,x56402)+P39(f35(x56401,x56403),x56402,x56404,x56405)+P1(f324(x56401,x56402))
% 18.77/18.50 [6211]E(x62111,x62112)+~P39(f35(x62113,x62114),x62111,x62115,x62112)+P1(f324(x62113,x62111))
% 18.77/18.50 [7772]~P39(x77722,x77723,x77724,x77725)+~P39(f35(x77721,x77722),x77725,x77724,x77723)+P39(f35(x77721,x77722),x77723,x77724,x77723)
% 18.77/18.50 [8936]E(x89361,x89362)+~P39(f35(x89365,x89363),x89361,x89364,x89362)+P39(x89363,x89361,x89364,f753(x89362,x89364,x89361,x89363,x89365))
% 18.77/18.50 [8938]E(x89381,x89382)+P39(f35(x89383,x89384),f753(x89381,x89385,x89382,x89384,x89383),x89385,x89381)+~P39(f35(x89383,x89384),x89382,x89385,x89381)
% 18.77/18.50 [8940]~P39(f35(x89405,x89401),x89402,x89403,x89404)+P39(x89401,x89402,x89403,f753(x89404,x89403,x89402,x89401,x89405))+~P1(f324(x89405,x89402))
% 18.77/18.50 [8944]~P39(f35(x89441,x89442),x89445,x89444,x89443)+P39(f35(x89441,x89442),f753(x89443,x89444,x89445,x89442,x89441),x89444,x89443)+~P1(f324(x89441,x89445))
% 18.77/18.50 [6360]E(x63601,x63602)+~E(f324(x63603,x63601),f324(x63603,x63602))+~P29(x63604,x63605,x63603,f238(f845(x63604,a832)))
% 18.77/18.50 [6361]E(x63611,x63612)+~E(f324(x63613,x63611),f324(x63613,x63612))+~P29(x63614,x63615,x63613,f238(f845(x63614,a832)))
% 18.77/18.50 [6525]~E(f324(x65253,x65255),f182(x65252))+~E(f324(x65254,x65255),f182(x65252))+E(f324(f169(x65251,x65252,x65253,x65254),x65255),f182(x65252))
% 18.77/18.50 [7301]E(x73011,x73012)+~P29(x73013,x73014,x73015,f238(f845(x73013,a832)))+~E(f324(f304(x73013,x73014,x73015),x73011),f324(f304(x73013,x73014,x73015),x73012))
% 18.77/18.50 [7562]P29(x75622,x75623,f519(x75624,x75623,x75622,x75621),x75621)+~E(f324(f304(x75623,x75622,x75625),x75624),x75621)+E(x75621,f179(f845(x75622,a832)))
% 18.77/18.50 [8102]~P1(f324(f324(x81023,x81022),x81025))+~P1(f324(f324(x81023,x81024),x81022))+P1(f324(f324(f326(x81021),x81022),f292(x81021,x81023,x81024,x81025)))
% 18.77/18.50 [8103]~P1(f324(f324(x81033,x81032),x81035))+~P1(f324(f324(x81033,x81034),x81032))+P1(f324(f324(f326(x81031),x81032),f283(x81031,x81033,x81034,x81035)))
% 18.77/18.50 [8643]~P29(x86431,x86433,x86435,f238(f845(x86431,a832)))+~P29(x86433,x86432,x86434,f238(f845(x86433,a832)))+P29(x86431,x86432,f324(f75(x86433,x86432,x86431,x86434),x86435),f238(f845(x86431,a832)))
% 18.77/18.50 [9139]P1(f324(f324(f326(f844(x91391,x91391)),f324(f324(f247(x91391,x91391),x91392),x91393)),f301(x91391,x91394)))+~P1(f324(f324(f326(f844(x91391,x91391)),f324(f324(f247(x91391,x91391),x91392),x91395)),f301(x91391,x91394)))+~P1(f324(f324(f326(f844(x91391,x91391)),f324(f324(f247(x91391,x91391),x91395),x91393)),f301(x91391,x91394)))
% 18.77/18.50 [9176]~P86(x91762)+~P1(f324(f127(x91761),x91765))+P1(f324(f127(x91761),f138(x91761,x91762,x91763,x91764,x91765)))
% 18.77/18.50 [5169]~E(x51692,f115(x51691))+E(f324(f324(f125(x51691),x51692),x51693),f324(f324(f139(x51691),x51694),x51695))+~E(x51693,f324(f324(f139(x51691),x51694),x51695))
% 18.77/18.50 [5170]~E(x51702,f115(x51701))+E(f324(f324(f125(x51701),x51702),x51703),f324(f324(f139(x51701),x51704),x51705))+~E(f324(f324(f139(x51701),x51704),x51705),x51703)
% 18.77/18.50 [6317]~E(f324(f180(f839(x63171)),x63175),f324(f180(f839(x63172)),x63174))+E(f324(f324(f141(f844(x63171,x63172),x63172),f251(x63171,x63172)),x63173),x63174)+~E(f324(f324(f166(x63171,x63172),x63175),x63174),x63173)
% 18.77/18.50 [6318]~E(f324(f180(f839(x63181)),x63184),f324(f180(f839(x63182)),x63185))+E(f324(f324(f141(f844(x63181,x63182),x63181),f246(x63181,x63182)),x63183),x63184)+~E(f324(f324(f166(x63181,x63182),x63184),x63185),x63183)
% 18.77/18.50 [6817]~P86(x68171)+~P18(x68171,f324(f324(f141(x68172,x68171),x68173),x68175))+P18(x68171,f324(f324(f141(x68172,x68171),x68173),f324(f126(x68172,x68174),x68175)))
% 18.77/18.50 [6863]~P1(f324(x68633,x68635))+~P1(f324(f324(x68632,x68634),x68635))+P1(f324(f324(f94(x68631,x68632,x68633),x68634),x68635))
% 18.77/18.50 [6960]~P86(x69601)+P18(x69601,f324(f324(f141(x69602,x69601),x69603),f155(x69602,x69604,x69605)))+~P18(x69601,f324(f324(f141(x69602,x69601),x69603),x69605))
% 18.77/18.50 [6983]~P52(x69833,x69832,x69835)+~P52(x69831,x69833,x69834)+P52(x69831,x69832,f324(f324(f282(x69831,x69833,x69832),x69834),x69835))
% 18.77/18.50 [7073]E(x70731,x70732)+~P29(x70733,x70734,x70735,f238(f845(x70733,a832)))+~E(f324(f324(f141(x70733,x70734),x70735),x70731),f324(f324(f141(x70733,x70734),x70735),x70732))
% 18.77/18.50 [7074]E(x70741,x70742)+~P29(x70743,x70744,x70745,f238(f845(x70743,a832)))+~E(f324(f324(f141(x70743,x70744),x70745),x70741),f324(f324(f141(x70743,x70744),x70745),x70742))
% 18.77/18.50 [7156]P39(x71561,x71562,x71563,x71564)+~P39(x71561,x71562,x71565,x71564)+~P1(f324(f324(f231(a838),x71565),x71563))
% 18.77/18.50 [7246]~P1(f324(f324(f232(a838),x72461),f324(x72463,x72465)))+P1(f324(f324(f232(a838),x72461),f142(x72462,x72463,x72464)))+~P1(f324(f324(f326(x72462),x72465),f324(f157(x72462),x72464)))
% 18.77/18.50 [7247]~P1(f324(f324(f231(a838),x72471),f324(x72473,x72475)))+P1(f324(f324(f231(a838),x72471),f142(x72472,x72473,x72474)))+~P1(f324(f324(f326(x72472),x72475),f324(f157(x72472),x72474)))
% 18.77/18.50 [7662]~P85(x76621)+P1(f324(f324(f231(f845(x76621,a832)),f296(x76621,x76622,x76623)),f296(x76621,x76624,x76625)))+P1(f324(f324(f231(x76621),x76622),x76623))
% 18.77/18.50 [7689]~P9(x76891)+P1(f324(f324(f231(x76891),f324(f324(f46(x76892,x76891),x76893),x76894)),f324(x76894,x76895)))+~P1(f324(f324(f326(x76892),x76895),x76893))
% 18.77/18.50 [7759]~P29(x77591,x77592,x77594,x77593)+E(f324(f79(x77591,x77592,x77593,x77594),f324(x77594,x77595)),x77595)+~P1(f324(f324(f326(x77591),x77595),x77593))
% 18.77/18.50 [7958]~P1(f324(x79581,x79585))+P1(f324(x79581,f356(x79581,x79582,x79583,x79584)))+~P1(f324(f324(f326(x79584),x79585),x79583))
% 18.77/18.50 [7959]~P1(f324(x79591,x79595))+P1(f324(x79591,f356(x79591,x79592,x79593,x79594)))+~P1(f324(f324(f326(x79594),x79595),x79592))
% 18.77/18.50 [8053]P1(f324(f64(x80531),x80532))+~P1(f324(f64(x80533),x80534))+~P1(f324(f324(f231(f845(x80531,a832)),x80532),f324(f304(x80533,x80531,x80535),x80534)))
% 18.77/18.50 [8063]~P29(x80634,x80631,x80632,f238(f845(x80634,a832)))+~P1(f324(f324(f326(x80634),x80633),x80635))+P1(f324(f324(f326(x80631),f324(x80632,x80633)),f324(f304(x80634,x80631,x80632),x80635)))
% 18.77/18.50 [8215]E(x82151,x82152)+~P29(x82153,x82154,x82155,f324(f324(f103(f845(x82153,a832)),f324(f157(x82153),x82151)),f324(f157(x82153),x82152)))+~E(f324(f324(f141(x82153,x82154),x82155),x82151),f324(f324(f141(x82153,x82154),x82155),x82152))
% 18.77/18.50 [8216]E(x82161,x82162)+~P29(x82163,x82164,x82165,f324(f324(f103(f845(x82163,a832)),f324(f157(x82163),x82161)),f324(f157(x82163),x82162)))+~E(f324(f324(f141(x82163,x82164),x82165),x82161),f324(f324(f141(x82163,x82164),x82165),x82162))
% 18.77/18.50 [8273]~P85(x82731)+~P1(f324(f324(f232(f845(x82731,a832)),f296(x82731,x82734,x82735)),f296(x82731,x82732,x82733)))+P1(f324(f324(f231(x82731),x82732),x82733))
% 18.77/18.50 [8341]~P29(x83411,x83414,x83415,f238(f845(x83411,a832)))+~P1(f324(f324(f326(x83414),f324(x83415,x83412)),f324(f304(x83411,x83414,x83415),x83413)))+P1(f324(f324(f326(x83411),x83412),x83413))
% 18.77/18.50 [8418]P1(f324(x84181,x84182))+~P1(f324(x84181,f361(x84181,x84183,x84184,x84185)))+~P1(f324(f324(f326(x84185),x84182),x84184))
% 18.77/18.50 [8419]P1(f324(x84191,x84192))+~P1(f324(x84191,f361(x84191,x84193,x84194,x84195)))+~P1(f324(f324(f326(x84195),x84192),x84193))
% 18.77/18.50 [8679]~P29(x86792,x86793,x86791,x86794)+E(f324(x86791,f324(f79(x86792,x86793,x86794,x86791),x86795)),x86795)+~P1(f324(f324(f326(x86793),x86795),f324(f304(x86792,x86793,x86791),x86794)))
% 18.77/18.50 [8765]E(x87651,f115(x87652))+E(f324(f324(f139(x87652),x87653),f724(x87654,x87653,x87655,x87651,x87652)),x87651)+~E(f324(f324(f125(x87652),x87651),x87655),f324(f324(f139(x87652),x87653),x87654))
% 18.77/18.50 [8766]E(x87661,f115(x87662))+E(f324(f324(f139(x87662),x87663),f725(x87664,x87661,x87665,x87663,x87662)),x87661)+~E(f324(f324(f125(x87662),x87661),x87664),f324(f324(f139(x87662),x87663),x87665))
% 18.77/18.50 [8781]E(f324(f324(f139(x87812),x87813),f724(x87814,x87813,x87811,x87815,x87812)),x87815)+~E(f324(f324(f125(x87812),x87815),x87811),f324(f324(f139(x87812),x87813),x87814))+E(x87811,f324(f324(f139(x87812),x87813),x87814))
% 18.77/18.50 [8782]E(f324(f324(f139(x87821),x87822),f725(x87824,x87825,x87823,x87822,x87821)),x87825)+~E(f324(f324(f125(x87821),x87825),x87824),f324(f324(f139(x87821),x87822),x87823))+E(f324(f324(f139(x87821),x87822),x87823),x87824)
% 18.77/18.50 [8856]~E(f324(f304(x88563,x88562,x88564),f238(f845(x88563,a832))),f238(f845(x88562,a832)))+~E(f324(f304(x88561,x88563,x88565),f238(f845(x88561,a832))),f238(f845(x88563,a832)))+E(f324(f304(x88561,x88562,f324(f75(x88563,x88562,x88561,x88564),x88565)),f238(f845(x88561,a832))),f238(f845(x88562,a832)))
% 18.77/18.50 [9182]E(x91821,f115(x91822))+~E(f324(f324(f125(x91822),x91821),x91823),f324(f324(f139(x91822),x91825),x91824))+E(f324(f324(f125(x91822),f725(x91823,x91821,x91824,x91825,x91822)),x91823),x91824)
% 18.77/18.50 [9183]E(x91831,f115(x91832))+~E(f324(f324(f125(x91832),x91831),x91835),f324(f324(f139(x91832),x91834),x91833))+E(f324(f324(f125(x91832),f724(x91833,x91834,x91835,x91831,x91832)),x91835),x91833)
% 18.77/18.50 [9191]E(f324(f324(f125(x91912),f724(x91914,x91913,x91911,x91915,x91912)),x91911),x91914)+~E(f324(f324(f125(x91912),x91915),x91911),f324(f324(f139(x91912),x91913),x91914))+E(x91911,f324(f324(f139(x91912),x91913),x91914))
% 18.77/18.50 [9192]~E(f324(f324(f125(x91921),x91925),x91924),f324(f324(f139(x91921),x91922),x91923))+E(f324(f324(f125(x91921),f725(x91924,x91925,x91923,x91922,x91921)),x91924),x91923)+E(f324(f324(f139(x91921),x91922),x91923),x91924)
% 18.77/18.50 [9193]E(f324(f324(f125(x91931),x91935),f728(x91933,x91932,x91934,x91935,x91931)),x91932)+E(f324(f324(f125(x91931),x91932),f727(x91933,x91932,x91934,x91935,x91931)),x91935)+~E(f324(f324(f125(x91931),x91935),x91934),f324(f324(f125(x91931),x91932),x91933))
% 18.77/18.50 [9224]~P86(x92241)+P18(x92241,f324(f324(f141(x92242,x92241),x92243),f138(x92242,x92241,x92243,x92244,x92245)))+~P18(x92241,f324(f324(f141(x92242,x92241),x92243),x92245))
% 18.77/18.50 [9240]~P56(x92405,x92401,x92404,x92403)+P1(f324(f324(x92401,x92402),f564(x92403,x92404,x92401,x92405,x92402)))+~P1(f324(f324(f326(x92405),x92402),x92404))
% 18.77/18.50 [9338]~P1(f324(f324(f326(f844(x93381,x93381)),f324(f324(f247(x93381,x93381),x93385),x93383)),f301(x93381,x93384)))+P1(f324(f324(f326(f844(x93381,x93381)),f324(f324(f247(x93381,x93381),x93382),x93383)),f324(f324(f282(x93381,x93381,x93381),x93384),f301(x93381,x93384))))+~P1(f324(f324(f326(f844(x93381,x93381)),f324(f324(f247(x93381,x93381),x93382),x93385)),f324(f324(f282(x93381,x93381,x93381),x93384),f301(x93381,x93384))))
% 18.77/18.50 [9339]~P1(f324(f324(f326(f844(x93391,x93391)),f324(f324(f247(x93391,x93391),x93392),x93395)),f301(x93391,x93394)))+P1(f324(f324(f326(f844(x93391,x93391)),f324(f324(f247(x93391,x93391),x93392),x93393)),f324(f324(f282(x93391,x93391,x93391),x93394),f301(x93391,x93394))))+~P1(f324(f324(f326(f844(x93391,x93391)),f324(f324(f247(x93391,x93391),x93395),x93393)),f324(f324(f282(x93391,x93391,x93391),x93394),f301(x93391,x93394))))
% 18.77/18.50 [9341]P1(f324(f324(f326(f844(f839(x93411),f839(x93411))),f324(f324(f247(f839(x93411),f839(x93411)),x93412),x93413)),f145(x93411,f301(x93411,x93414))))+~P1(f324(f324(f326(f844(f839(x93411),f839(x93411))),f324(f324(f247(f839(x93411),f839(x93411)),x93412),x93415)),f145(x93411,f301(x93411,x93414))))+~P1(f324(f324(f326(f844(f839(x93411),f839(x93411))),f324(f324(f247(f839(x93411),f839(x93411)),x93415),x93413)),f145(x93411,f301(x93411,x93414))))
% 18.77/18.50 [9345]E(f324(f324(f125(x93451),x93452),f727(x93453,x93452,x93454,x93455,x93451)),x93455)+E(f324(f324(f125(x93451),f728(x93453,x93452,x93454,x93455,x93451)),x93453),x93454)+~E(f324(f324(f125(x93451),x93452),x93453),f324(f324(f125(x93451),x93455),x93454))
% 18.77/18.50 [9346]E(f324(f324(f125(x93461),x93462),f728(x93463,x93464,x93465,x93462,x93461)),x93464)+E(f324(f324(f125(x93461),f727(x93463,x93464,x93465,x93462,x93461)),x93465),x93463)+~E(f324(f324(f125(x93461),x93462),x93465),f324(f324(f125(x93461),x93464),x93463))
% 18.77/18.50 [9404]P1(f324(f324(f326(f844(x94041,x94041)),f324(f324(f247(x94041,x94041),x94042),x94043)),f324(f324(f282(x94041,x94041,x94041),x94044),f301(x94041,x94044))))+~P1(f324(f324(f326(f844(x94041,x94041)),f324(f324(f247(x94041,x94041),x94042),x94045)),f324(f324(f282(x94041,x94041,x94041),x94044),f301(x94041,x94044))))+~P1(f324(f324(f326(f844(x94041,x94041)),f324(f324(f247(x94041,x94041),x94045),x94043)),f324(f324(f282(x94041,x94041,x94041),x94044),f301(x94041,x94044))))
% 18.77/18.50 [9437]E(f324(f324(f125(x94371),f727(x94372,x94373,x94374,x94375,x94371)),x94374),x94372)+~E(f324(f324(f125(x94371),x94373),x94372),f324(f324(f125(x94371),x94375),x94374))+E(f324(f324(f125(x94371),f728(x94372,x94373,x94374,x94375,x94371)),x94372),x94374)
% 18.77/18.50 [9454]~P56(x94541,x94544,x94543,x94542)+~P1(f324(f324(f326(x94541),x94545),x94543))+P1(f324(f324(f326(x94541),f564(x94542,x94543,x94544,x94541,x94545)),x94542))
% 18.77/18.50 [9565]~P1(f324(f324(f326(f844(f845(x95651,a832),f845(x95651,a832))),f324(f324(f247(f845(x95651,a832),f845(x95651,a832)),x95654),x95653)),f317(x95651,x95652)))+~P1(f324(f324(f326(x95651),x95655),x95654))+P1(f324(f324(f326(x95651),f648(x95652,x95653,x95654,x95651,x95655)),x95653))
% 18.77/18.50 [6393]~P21(x63932,x63935,x63931)+~P1(f324(f64(x63932),x63934))+E(f324(x63931,f324(f324(f303(x63932),x63933),x63934)),f324(f324(f67(x63932,x63932,x63935),x63933),x63934))
% 18.77/18.50 [6394]~E(x63943,x63944)+~E(x63942,x63945)+E(f324(f324(f303(x63941),x63942),f324(f324(f303(x63941),x63943),f179(f845(x63941,a832)))),f324(f324(f303(x63941),x63944),f324(f324(f303(x63941),x63945),f179(f845(x63941,a832)))))
% 18.77/18.50 [6405]P1(f324(x64052,x64055))+E(f161(x64051,x64052,f324(f324(f125(x64051),x64053),x64054)),f161(x64051,x64052,x64053))+~P1(f324(f324(f326(x64051),x64055),f324(f157(x64051),x64053)))
% 18.77/18.50 [6440]E(f324(x64401,x64402),f179(f845(x64403,a832)))+~E(f324(f324(f45(x64404,f845(x64403,a832)),x64405),x64401),f179(f845(x64403,a832)))+~P1(f324(f324(f326(x64404),x64402),x64405))
% 18.77/18.50 [6441]E(f324(x64411,x64412),f238(f845(x64413,a832)))+~E(f324(f324(f46(x64414,f845(x64413,a832)),x64415),x64411),f238(f845(x64413,a832)))+~P1(f324(f324(f326(x64414),x64412),x64415))
% 18.77/18.50 [6442]E(f324(x64421,x64422),f179(f845(x64423,a832)))+~E(f324(f324(f45(x64424,f845(x64423,a832)),x64425),x64421),f179(f845(x64423,a832)))+~P1(f324(f324(f326(x64424),x64422),x64425))
% 18.77/18.50 [6443]E(f324(x64431,x64432),f238(f845(x64433,a832)))+~E(f324(f324(f46(x64434,f845(x64433,a832)),x64435),x64431),f238(f845(x64433,a832)))+~P1(f324(f324(f326(x64434),x64432),x64435))
% 18.77/18.50 [6765]~P1(f324(f324(f186(x67651),x67653),x67655))+~P1(f324(f324(f186(x67652),x67655),x67654))+P1(f324(f324(f186(f36(x67651,x67652)),x67653),x67654))
% 18.77/18.50 [6766]~P1(f324(f324(f186(x67661),x67663),x67665))+~P1(f324(f324(f186(x67662),x67665),x67664))+P1(f324(f324(f186(f36(x67661,x67662)),x67663),x67664))
% 18.77/18.50 [6969]~E(x69692,x69694)+~P136(x69691)+E(f324(f324(f82(x69691),f324(f324(f83(x69691),x69692),x69693)),f324(f324(f83(x69691),x69694),x69695)),f324(f324(f82(x69691),f324(f324(f83(x69691),x69692),x69695)),f324(f324(f83(x69691),x69694),x69693)))
% 18.77/18.50 [6970]~E(x69702,x69704)+~P136(x69701)+E(f324(f324(f82(x69701),f324(f324(f83(x69701),x69702),x69703)),f324(f324(f83(x69701),x69704),x69705)),f324(f324(f82(x69701),f324(f324(f83(x69701),x69702),x69705)),f324(f324(f83(x69701),x69704),x69703)))
% 18.77/18.50 [7030]~P9(x70301)+~P1(f324(f324(f326(x70304),x70303),x70305))+P1(f324(f324(f231(x70301),f324(x70302,x70303)),f324(f324(f45(x70304,x70301),x70305),x70302)))
% 18.77/18.50 [7077]~P101(x70771)+P1(f324(f324(f231(x70771),f324(x70772,x70773)),f324(x70774,x70773)))+~P1(f324(f324(f231(f845(x70775,x70771)),x70772),x70774))
% 18.77/18.50 [7078]~P101(x70781)+P1(f324(f324(f231(x70781),f324(x70782,x70783)),f324(x70784,x70783)))+~P1(f324(f324(f231(f845(x70785,x70781)),x70782),x70784))
% 18.77/18.50 [7079]~P101(x70791)+P1(f324(f324(f231(x70791),f324(x70792,x70793)),f324(x70794,x70793)))+~P1(f324(f324(f231(f845(x70795,x70791)),x70792),x70794))
% 18.77/18.50 [7214]E(x72141,x72142)+E(x72143,x72141)+~E(f324(f324(f303(x72144),x72141),f324(f324(f303(x72144),x72145),f179(f845(x72144,a832)))),f324(f324(f303(x72144),x72142),f324(f324(f303(x72144),x72143),f179(f845(x72144,a832)))))
% 18.77/18.50 [7215]E(x72151,x72152)+E(x72153,x72151)+~E(f324(f324(f303(x72154),x72153),f324(f324(f303(x72154),x72152),f179(f845(x72154,a832)))),f324(f324(f303(x72154),x72155),f324(f324(f303(x72154),x72151),f179(f845(x72154,a832)))))
% 18.77/18.50 [7216]E(x72161,x72162)+E(x72161,x72163)+~E(f324(f324(f303(x72164),x72163),f324(f324(f303(x72164),x72162),f179(f845(x72164,a832)))),f324(f324(f303(x72164),x72165),f324(f324(f303(x72164),x72161),f179(f845(x72164,a832)))))
% 18.77/18.50 [7217]E(x72171,x72172)+E(x72171,x72173)+~E(f324(f324(f303(x72174),x72171),f324(f324(f303(x72174),x72175),f179(f845(x72174,a832)))),f324(f324(f303(x72174),x72172),f324(f324(f303(x72174),x72173),f179(f845(x72174,a832)))))
% 18.77/18.50 [7769]P29(x77691,x77692,x77693,x77694)+~P29(x77691,x77692,x77693,x77695)+~P1(f324(f324(f231(f845(x77691,a832)),x77694),x77695))
% 18.77/18.50 [7871]P1(f324(x78711,x78712))+~P1(f324(f324(f186(x78714),x78712),x78715))+P1(f324(f324(f186(f33(x78711,x78713,x78714)),x78712),x78715))
% 18.77/18.50 [7872]P1(f324(x78721,x78722))+~P1(f324(f324(f186(x78724),x78722),x78725))+P1(f324(f324(f186(f33(x78721,x78723,x78724)),x78722),x78725))
% 18.77/18.50 [7873]P1(f324(x78731,x78732))+~P1(f324(f324(f186(x78734),x78732),x78735))+P1(f324(f324(f186(f33(x78731,x78733,x78734)),x78732),x78735))
% 18.77/18.50 [7899]~P1(f324(x78991,x78994))+~P1(f324(f324(f186(x78992),x78994),x78995))+P1(f324(f324(f186(f33(x78991,x78992,x78993)),x78994),x78995))
% 18.77/18.50 [7900]~P1(f324(x79001,x79004))+~P1(f324(f324(f186(x79002),x79004),x79005))+P1(f324(f324(f186(f33(x79001,x79002,x79003)),x79004),x79005))
% 18.77/18.50 [7901]~P1(f324(x79011,x79014))+~P1(f324(f324(f186(x79012),x79014),x79015))+P1(f324(f324(f186(f33(x79011,x79012,x79013)),x79014),x79015))
% 18.77/18.50 [7948]E(x79481,x79482)+~E(f324(f304(x79483,x79484,x79485),x79481),f324(f304(x79483,x79484,x79485),x79482))+~P29(x79483,x79484,x79485,f324(f324(f103(f845(x79483,a832)),x79481),x79482))
% 18.77/18.50 [8022]P1(f324(x80222,x80224))+E(f324(f324(f128(x80221),f324(f180(f839(x80221)),f161(x80221,x80222,x80223))),x80223),f324(f324(f139(x80221),x80224),x80225))+~E(f324(f324(f125(x80221),f161(x80221,x80222,x80223)),f324(f324(f139(x80221),x80224),x80225)),x80223)
% 18.77/18.50 [8051]~P29(x80511,x80512,x80513,x80515)+~P29(x80511,x80512,x80513,x80514)+P29(x80511,x80512,x80513,f324(f324(f104(f845(x80511,a832)),x80514),x80515))
% 18.77/18.50 [8158]~P67(x81581)+E(f324(f324(f82(x81581),f324(x81582,x81583)),f324(f151(x81581),f324(f324(f141(x81584,x81581),x81582),f155(x81584,x81583,x81585)))),f324(f151(x81581),f324(f324(f141(x81584,x81581),x81582),x81585)))+~P1(f324(f324(f326(x81584),x81583),f324(f157(x81584),x81585)))
% 18.77/18.50 [8245]~P86(x82451)+~P18(x82451,f324(f324(f141(x82452,x82451),x82453),x82455))+P18(x82451,f324(f324(f141(x82452,x82451),x82453),f324(f324(f137(x82452,x82451,x82453),x82454),x82455)))
% 18.77/18.50 [8323]P1(f324(x83231,x83232))+P1(f324(f324(f186(x83233),x83232),x83234))+~P1(f324(f324(f186(f33(x83231,x83235,x83233)),x83232),x83234))
% 18.77/18.50 [8324]P1(f324(x83241,x83242))+P1(f324(f324(f186(x83243),x83242),x83244))+~P1(f324(f324(f186(f33(x83241,x83245,x83243)),x83242),x83244))
% 18.77/18.50 [8325]P1(f324(x83251,x83252))+P1(f324(f324(f186(x83253),x83252),x83254))+~P1(f324(f324(f186(f33(x83251,x83255,x83253)),x83252),x83254))
% 18.77/18.50 [8336]~P9(x83361)+P1(f324(f324(f231(x83361),f324(f324(f45(x83362,x83361),x83363),x83364)),f324(f324(f45(x83362,x83361),x83365),x83364)))+~P1(f324(f324(f231(f845(x83362,a832)),x83363),x83365))
% 18.77/18.50 [8337]~P9(x83371)+P1(f324(f324(f231(x83371),f324(f324(f46(x83372,x83371),x83373),x83374)),f324(f324(f46(x83372,x83371),x83375),x83374)))+~P1(f324(f324(f231(f845(x83372,a832)),x83375),x83373))
% 18.77/18.50 [8345]~P1(f324(x83454,x83452))+P1(f324(f324(f186(x83451),x83452),x83453))+~P1(f324(f324(f186(f33(x83454,x83451,x83455)),x83452),x83453))
% 18.77/18.50 [8346]~P1(f324(x83464,x83462))+P1(f324(f324(f186(x83461),x83462),x83463))+~P1(f324(f324(f186(f33(x83464,x83461,x83465)),x83462),x83463))
% 18.77/18.50 [8347]~P1(f324(x83474,x83472))+P1(f324(f324(f186(x83471),x83472),x83473))+~P1(f324(f324(f186(f33(x83474,x83471,x83475)),x83472),x83473))
% 18.77/18.50 [8371]~P86(x83713)+P1(f324(f127(x83711),x83712))+~P1(f324(f127(x83711),f324(f324(f137(x83711,x83713,x83714),x83715),x83712)))
% 18.77/18.50 [8379]P1(f324(f324(f186(x83791),x83792),x83793))+P1(f324(f324(f186(x83794),x83792),x83793))+~P1(f324(f324(f186(f33(x83795,x83791,x83794)),x83792),x83793))
% 18.77/18.50 [8380]P1(f324(f324(f186(x83801),x83802),x83803))+P1(f324(f324(f186(x83804),x83802),x83803))+~P1(f324(f324(f186(f33(x83805,x83801,x83804)),x83802),x83803))
% 18.77/18.50 [8381]P1(f324(f324(f186(x83811),x83812),x83813))+P1(f324(f324(f186(x83814),x83812),x83813))+~P1(f324(f324(f186(f33(x83815,x83811,x83814)),x83812),x83813))
% 18.77/18.50 [8502]~P86(x85021)+~P1(f324(f324(f326(x85022),x85023),f324(f157(x85022),x85024)))+~P1(f324(f127(x85022),f324(f324(f137(x85022,x85021,x85025),x85023),x85024)))
% 18.77/18.50 [8578]~P86(x85781)+P18(x85781,f324(f324(f141(x85782,x85781),x85783),x85784))+~P18(x85781,f324(f324(f141(x85782,x85781),x85783),f324(f324(f137(x85782,x85781,x85783),x85785),x85784)))
% 18.77/18.50 [8666]~P86(x86662)+E(f324(f324(f137(x86661,x86662,x86663),x86664),x86665),f138(x86661,x86662,x86663,x86664,x86665))+P1(f324(f324(f326(x86662),f324(x86663,x86664)),f324(f304(x86661,x86662,x86663),f324(f157(x86661),x86665))))
% 18.77/18.50 [8734]~P86(x87342)+E(f138(x87341,x87342,x87343,x87344,x87345),x87345)+~P1(f324(f324(f326(x87342),f324(x87343,x87344)),f324(f304(x87341,x87342,x87343),f324(f157(x87341),x87345))))
% 18.77/18.50 [8747]~P29(x87472,x87471,x87473,x87475)+P1(f324(f324(f232(f845(x87471,a832)),f324(f304(x87472,x87471,x87473),x87474)),f324(f304(x87472,x87471,x87473),x87475)))+~P1(f324(f324(f232(f845(x87472,a832)),x87474),x87475))
% 18.77/18.50 [8772]~P29(x87722,x87721,x87723,f238(f845(x87722,a832)))+P1(f324(f324(f231(f845(x87721,a832)),f324(f304(x87722,x87721,x87723),x87724)),f324(f304(x87722,x87721,x87723),x87725)))+~P1(f324(f324(f231(f845(x87722,a832)),x87724),x87725))
% 18.77/18.50 [8894]~P29(x88941,x88942,x88943,f238(f845(x88941,a832)))+~P1(f324(f324(f231(f845(x88942,a832)),x88944),f324(f304(x88941,x88942,x88943),x88945)))+P1(f324(f324(f231(f845(x88941,a832)),f324(f305(x88941,x88942,x88943),x88944)),x88945))
% 18.77/18.50 [8913]~E(f324(f304(x89133,x89131,x89134),f238(f845(x89133,a832))),f238(f845(x89131,a832)))+P1(f324(f324(f231(f845(x89131,a832)),x89132),f324(f304(x89133,x89131,x89134),x89135)))+~P1(f324(f324(f231(f845(x89133,a832)),f324(f305(x89133,x89131,x89134),x89132)),x89135))
% 18.77/18.50 [8945]~E(f324(f226(x89452),x89454),f324(f165(x89451,x89452,x89455),x89453))+~P1(f324(f127(x89451),f324(f324(f141(f844(x89451,x89452),x89451),f246(x89451,x89452)),x89455)))+P1(f324(f324(f326(f844(x89451,x89452)),f324(f324(f247(x89451,x89452),x89453),x89454)),f324(f157(f844(x89451,x89452)),x89455)))
% 18.77/18.50 [8946]~E(f324(f165(x89461,x89462,x89465),x89463),f324(f226(x89462),x89464))+~P1(f324(f127(x89461),f324(f324(f141(f844(x89461,x89462),x89461),f246(x89461,x89462)),x89465)))+P1(f324(f324(f326(f844(x89461,x89462)),f324(f324(f247(x89461,x89462),x89463),x89464)),f324(f157(f844(x89461,x89462)),x89465)))
% 18.77/18.50 [9009]~P29(x90091,x90094,x90095,f238(f845(x90091,a832)))+~P1(f324(f324(f231(f845(x90094,a832)),f324(f304(x90091,x90094,x90095),x90092)),f324(f304(x90091,x90094,x90095),x90093)))+P1(f324(f324(f231(f845(x90091,a832)),x90092),x90093))
% 18.77/18.50 [9073]E(f324(f226(x90731),x90732),f324(f165(x90733,x90731,x90734),x90735))+~P1(f324(f127(x90733),f324(f324(f141(f844(x90733,x90731),x90733),f246(x90733,x90731)),x90734)))+~P1(f324(f324(f326(f844(x90733,x90731)),f324(f324(f247(x90733,x90731),x90735),x90732)),f324(f157(f844(x90733,x90731)),x90734)))
% 18.77/18.50 [9074]E(f324(f165(x90741,x90742,x90743),x90744),f324(f226(x90742),x90745))+~P1(f324(f127(x90741),f324(f324(f141(f844(x90741,x90742),x90741),f246(x90741,x90742)),x90743)))+~P1(f324(f324(f326(f844(x90741,x90742)),f324(f324(f247(x90741,x90742),x90744),x90745)),f324(f157(f844(x90741,x90742)),x90743)))
% 18.77/18.50 [9075]E(f324(f165(x90751,x90752,x90753),x90754),f324(f226(x90752),x90755))+~P1(f324(f127(x90751),f324(f324(f141(f844(x90751,x90752),x90751),f246(x90751,x90752)),x90753)))+~P1(f324(f324(f326(f844(x90751,x90752)),f324(f324(f247(x90751,x90752),x90754),x90755)),f324(f157(f844(x90751,x90752)),x90753)))
% 18.77/18.50 [9112]~P72(x91121)+~E(f324(x91123,f765(x91123,x91124,x91125,x91122,x91121)),f2(x91121))+E(f324(f151(x91121),f324(f324(f141(x91122,x91121),x91123),f324(f126(x91122,x91124),x91125))),f324(f151(x91121),f324(f324(f141(x91122,x91121),x91123),x91125)))
% 18.77/18.50 [9286]~P20(x92861,x92862,x92863)+~P1(f324(f64(x92861),x92865))+P1(f324(f69(x92861,x92862,x92863,x92864,x92865),f324(f324(f67(x92861,x92862,x92863),x92864),x92865)))
% 18.77/18.50 [9360]P1(f324(x93601,f689(x93602,x93601,x93603,x93604,x93605)))+~P1(f324(f324(f231(f845(x93605,a832)),x93604),x93603))+P1(f324(f324(f231(f845(x93605,a832)),f324(f324(f104(f845(x93605,a832)),x93604),f324(f257(x93605),x93601))),f324(f324(f104(f845(x93605,a832)),x93603),f324(f257(x93605),x93602))))
% 18.77/18.50 [9374]~P72(x93741)+~P1(f324(x93744,f765(x93743,x93744,x93745,x93742,x93741)))+E(f324(f151(x93741),f324(f324(f141(x93742,x93741),x93743),f324(f126(x93742,x93744),x93745))),f324(f151(x93741),f324(f324(f141(x93742,x93741),x93743),x93745)))
% 18.77/18.50 [9452]~P9(x94525)+P1(f324(f324(f326(x94521),f665(x94522,x94523,x94521,x94524,x94525)),x94523))+P1(f324(f324(f231(x94525),x94524),f324(f324(f46(x94521,x94525),x94523),x94522)))
% 18.77/18.50 [9455]~P72(x94551)+E(f324(f151(x94551),f324(f324(f141(x94552,x94551),x94553),f324(f126(x94552,x94554),x94555))),f324(f151(x94551),f324(f324(f141(x94552,x94551),x94553),x94555)))+P1(f324(f324(f326(x94552),f765(x94553,x94554,x94555,x94552,x94551)),f324(f157(x94552),x94555)))
% 18.77/18.50 [9465]~P1(f324(x94655,f689(x94655,x94653,x94654,x94652,x94651)))+~P1(f324(f324(f231(f845(x94651,a832)),x94652),x94654))+P1(f324(f324(f231(f845(x94651,a832)),f324(f324(f104(f845(x94651,a832)),x94652),f324(f257(x94651),x94653))),f324(f324(f104(f845(x94651,a832)),x94654),f324(f257(x94651),x94655))))
% 18.77/18.50 [9529]P1(f324(f324(f326(x95291),f689(x95292,x95293,x95294,x95295,x95291)),x95295))+~P1(f324(f324(f231(f845(x95291,a832)),x95295),x95294))+P1(f324(f324(f231(f845(x95291,a832)),f324(f324(f104(f845(x95291,a832)),x95295),f324(f257(x95291),x95293))),f324(f324(f104(f845(x95291,a832)),x95294),f324(f257(x95291),x95292))))
% 18.77/18.50 [9575]~P9(x95751)+~P1(f324(f324(f231(x95751),x95752),f324(x95755,f665(x95755,x95754,x95753,x95752,x95751))))+P1(f324(f324(f231(x95751),x95752),f324(f324(f46(x95753,x95751),x95754),x95755)))
% 18.77/18.50 [9607]~P68(x96071)+~P1(f324(f64(x96072),x96075))+E(f324(f324(f324(f68(x96071,x96072,f83(x96071)),f324(f324(f20(x96072,x96071,x96071),f324(f324(f10(x96071,f845(x96071,x96071),x96072),f83(x96071)),x96073)),x96074)),f80(x96071)),x96075),f324(f324(f83(x96071),f324(f324(f324(f68(x96071,x96072,f83(x96071)),x96073),f80(x96071)),x96075)),f324(f324(f324(f68(x96071,x96072,f83(x96071)),x96074),f80(x96071)),x96075)))
% 18.77/18.50 [9658]~P1(f324(f324(f326(f844(f845(x96581,a832),f845(x96581,a832))),f324(f324(f247(f845(x96581,a832),f845(x96581,a832)),x96585),x96584)),f317(x96581,x96583)))+~P1(f324(f324(f326(x96581),x96582),x96585))+P1(f324(f324(f326(f844(x96581,x96581)),f324(f324(f247(x96581,x96581),x96582),f648(x96583,x96584,x96585,x96581,x96582))),x96583))
% 18.77/18.50 [9804]~P1(f324(f324(f326(f844(f839(x98041),f839(x98041))),f324(f324(f247(f839(x98041),f839(x98041)),f324(f324(f125(x98041),x98045),x98042)),f324(f324(f125(x98041),x98045),x98043))),f136(x98041,x98044)))+P1(f324(f324(f326(f844(f839(x98041),f839(x98041))),f324(f324(f247(f839(x98041),f839(x98041)),x98042),x98043)),f136(x98041,x98044)))+P1(f324(f324(f326(f844(x98041,x98041)),f324(f324(f247(x98041,x98041),f729(x98044,x98043,x98042,x98045,x98041)),f729(x98044,x98043,x98042,x98045,x98041))),x98044))
% 18.77/18.50 [7082]~E(x70823,x70825)+E(f324(f324(f149(x70821),f324(f324(f146(x70821,x70822),x70823),x70824)),x70825),x70824)+~P1(f324(f324(f232(a838),x70823),f324(f180(f839(x70821)),x70822)))
% 18.77/18.50 [7091]~E(f324(f180(f839(x70911)),x70913),f324(f180(f839(x70912)),x70914))+E(f324(f165(x70911,x70912,f324(f324(f166(x70911,x70912),x70913),x70914)),x70915),f182(x70912))+P1(f324(f324(f326(x70911),x70915),f324(f157(x70911),x70913)))
% 18.77/18.50 [7210]~E(f324(f324(f125(x72101),x72102),x72104),f324(f324(f125(x72101),x72103),x72105))+E(f324(f324(f158(x72101),f324(f180(f839(x72101)),x72102)),x72103),x72102)+P1(f324(f324(f231(a838),f324(f180(f839(x72101)),x72103)),f324(f180(f839(x72101)),x72102)))
% 18.77/18.50 [7211]E(x72111,x72112)+E(f324(f324(f149(x72113),f324(f324(f146(x72113,x72114),x72111),x72115)),x72112),f324(f324(f149(x72113),x72114),x72112))+~P1(f324(f324(f232(a838),x72111),f324(f180(f839(x72113)),x72114)))
% 18.77/18.50 [7730]~E(f324(f324(f125(x77301),x77302),x77304),f324(f324(f125(x77301),x77303),x77305))+E(f324(f324(f158(x77301),f324(f180(f839(x77301)),x77302)),x77303),x77302)+~P1(f324(f324(f231(a838),f324(f180(f839(x77301)),x77302)),f324(f180(f839(x77301)),x77303)))
% 18.77/18.50 [7754]~P1(f324(f64(x77541),f324(x77544,x77545)))+~P1(f324(f324(f326(x77542),x77545),x77543))+P1(f324(f64(x77541),f324(f324(f46(x77542,f845(x77541,a832)),x77543),x77544)))
% 18.77/18.50 [7867]~E(f324(f180(f839(x78671)),x78672),f324(f180(f839(x78673)),x78674))+~E(f324(f165(x78671,x78673,f324(f324(f166(x78671,x78673),x78672),x78674)),x78675),f182(x78673))+~P1(f324(f324(f326(x78671),x78675),f324(f157(x78671),x78672)))
% 18.77/18.50 [7934]~P47(x79341,x79343,x79345)+~P47(x79341,x79342,x79344)+P47(x79341,f324(f324(f103(f845(x79341,a832)),x79342),x79343),f324(f324(f103(f845(f844(x79341,x79341),a832)),x79344),x79345))
% 18.77/18.50 [7935]~P47(x79351,x79353,x79355)+~P47(x79351,x79352,x79354)+P47(x79351,f324(f324(f104(f845(x79351,a832)),x79352),x79353),f324(f324(f104(f845(f844(x79351,x79351),a832)),x79354),x79355))
% 18.77/18.50 [8288]E(f324(f324(f247(x82881,x82882),f324(f324(f149(x82881),x82883),x82884)),f324(f324(f149(x82882),x82885),x82884)),f324(f324(f149(f844(x82881,x82882)),f324(f324(f166(x82881,x82882),x82883),x82885)),x82884))+~P1(f324(f324(f232(a838),x82884),f324(f180(f839(x82881)),x82883)))+~P1(f324(f324(f232(a838),x82884),f324(f180(f839(x82882)),x82885)))
% 18.77/18.50 [8446]~P47(x84461,x84463,x84464)+P1(f324(f324(f326(x84461),x84462),x84463))+~P1(f324(f324(f326(f844(x84461,x84461)),f324(f324(f247(x84461,x84461),x84465),x84462)),x84464))
% 18.77/18.50 [8447]~P47(x84471,x84473,x84474)+P1(f324(f324(f326(x84471),x84472),x84473))+~P1(f324(f324(f326(f844(x84471,x84471)),f324(f324(f247(x84471,x84471),x84472),x84475)),x84474))
% 18.77/18.50 [8448]~P12(x84481,x84483,x84484)+P1(f324(f324(f326(x84481),x84482),x84483))+~P1(f324(f324(f326(f844(x84481,x84481)),f324(f324(f247(x84481,x84481),x84485),x84482)),x84484))
% 18.77/18.50 [8449]~P12(x84491,x84493,x84494)+P1(f324(f324(f326(x84491),x84492),x84493))+~P1(f324(f324(f326(f844(x84491,x84491)),f324(f324(f247(x84491,x84491),x84492),x84495)),x84494))
% 18.77/18.50 [8688]~P12(x86881,x86885,x86882)+E(f324(f278(x86881,x86881,x86882),f324(f324(f303(x86881),x86883),f179(f845(x86881,a832)))),f324(f278(x86881,x86881,x86882),f324(f324(f303(x86881),x86884),f179(f845(x86881,a832)))))+~P1(f324(f324(f326(f844(x86881,x86881)),f324(f324(f247(x86881,x86881),x86883),x86884)),x86882))
% 18.77/18.50 [8689]~P12(x86891,x86895,x86892)+E(f324(f278(x86891,x86891,x86892),f324(f324(f303(x86891),x86893),f179(f845(x86891,a832)))),f324(f278(x86891,x86891,x86892),f324(f324(f303(x86891),x86894),f179(f845(x86891,a832)))))+~P1(f324(f324(f326(f844(x86891,x86891)),f324(f324(f247(x86891,x86891),x86893),x86894)),x86892))
% 18.77/18.50 [8853]P1(f324(x88531,x88532))+~P1(f324(f324(f326(x88533),x88532),x88535))+P1(f324(f324(f326(x88533),f361(x88531,x88534,x88535,x88533)),f324(f324(f103(f845(x88533,a832)),x88535),x88534)))
% 18.77/18.50 [8854]P1(f324(x88541,x88542))+~P1(f324(f324(f326(x88543),x88542),x88544))+P1(f324(f324(f326(x88543),f361(x88541,x88544,x88545,x88543)),f324(f324(f103(f845(x88543,a832)),x88545),x88544)))
% 18.77/18.50 [8862]~P1(f324(x88622,x88625))+~P1(f324(f324(f326(x88621),x88625),x88624))+P1(f324(f324(f326(x88621),f356(x88622,x88623,x88624,x88621)),f324(f324(f103(f845(x88621,a832)),x88624),x88623)))
% 18.77/18.50 [8863]~P1(f324(x88632,x88635))+~P1(f324(f324(f326(x88631),x88635),x88633))+P1(f324(f324(f326(x88631),f356(x88632,x88633,x88634,x88631)),f324(f324(f103(f845(x88631,a832)),x88634),x88633)))
% 18.77/18.50 [8876]~P1(f324(f324(f231(f845(x88761,a832)),x88765),x88763))+~P1(f324(f324(f231(f845(x88761,a832)),x88762),x88764))+P1(f324(f324(f231(f845(x88761,a832)),f324(f324(f3(f845(x88761,a832)),x88762),x88763)),f324(f324(f3(f845(x88761,a832)),x88764),x88765)))
% 18.77/18.50 [8877]~P1(f324(f324(f231(f845(x88771,a832)),x88773),x88775))+~P1(f324(f324(f231(f845(x88771,a832)),x88772),x88774))+P1(f324(f324(f231(f845(x88771,a832)),f324(f324(f103(f845(x88771,a832)),x88772),x88773)),f324(f324(f103(f845(x88771,a832)),x88774),x88775)))
% 18.77/18.50 [8878]~P1(f324(f324(f231(f845(x88781,a832)),x88783),x88785))+~P1(f324(f324(f231(f845(x88781,a832)),x88782),x88784))+P1(f324(f324(f231(f845(x88781,a832)),f324(f324(f104(f845(x88781,a832)),x88782),x88783)),f324(f324(f104(f845(x88781,a832)),x88784),x88785)))
% 18.77/18.50 [8961]P1(f324(f324(f326(f844(x89611,x89611)),f324(f324(f247(x89611,x89611),x89612),x89613)),f319(x89611,x89614,x89615)))+~P1(f324(f324(f231(a838),f324(x89614,x89612)),f324(x89614,x89613)))+~P1(f324(f324(f326(f844(x89611,x89611)),f324(f324(f247(x89611,x89611),x89612),x89613)),x89615))
% 18.77/18.50 [8968]~E(f324(f180(f839(x89681)),x89683),f324(f180(f839(x89682)),x89684))+E(f324(f165(x89681,x89682,f324(f324(f166(x89681,x89682),x89683),x89684)),x89685),f324(f226(x89682),f703(x89685,x89684,x89682,x89683,x89681)))+~P1(f324(f324(f326(x89681),x89685),f324(f157(x89681),x89683)))
% 18.77/18.50 [9119]P1(f324(f324(f326(f844(x91191,x91191)),f324(f324(f247(x91191,x91191),x91192),x91193)),f301(x91191,x91194)))+~P1(f324(f324(f326(f844(x91191,x91191)),f324(f324(f247(x91191,x91191),x91192),x91195)),f301(x91191,x91194)))+~P1(f324(f324(f326(f844(x91191,x91191)),f324(f324(f247(x91191,x91191),x91195),x91193)),x91194))
% 18.77/18.50 [9120]P1(f324(f324(f326(f844(x91201,x91201)),f324(f324(f247(x91201,x91201),x91202),x91203)),f301(x91201,x91204)))+~P1(f324(f324(f326(f844(x91201,x91201)),f324(f324(f247(x91201,x91201),x91205),x91203)),f301(x91201,x91204)))+~P1(f324(f324(f326(f844(x91201,x91201)),f324(f324(f247(x91201,x91201),x91202),x91205)),x91204))
% 18.77/18.50 [9214]E(x92141,x92142)+E(f324(a114,f559(x92143,x92144,x92141,x92142,x92145)),x92144)+~P1(f324(f324(f326(f844(x92145,x92145)),f324(f324(f247(x92145,x92145),x92142),x92141)),f324(f324(f172(f844(x92145,x92145),a832),x92144),x92143)))
% 18.77/18.50 [9215]E(x92151,x92152)+E(f324(a114,f561(x92153,x92154,x92151,x92152,x92155)),x92154)+~P1(f324(f324(f326(f844(x92155,x92155)),f324(f324(f247(x92155,x92155),x92152),x92151)),f324(f324(f172(f844(x92155,x92155),a832),x92154),x92153)))
% 18.77/18.50 [9216]E(x92161,f2(a838))+E(f324(a114,f559(x92162,x92161,x92163,x92164,x92165)),x92161)+~P1(f324(f324(f326(f844(x92165,x92165)),f324(f324(f247(x92165,x92165),x92164),x92163)),f324(f324(f172(f844(x92165,x92165),a832),x92161),x92162)))
% 18.77/18.50 [9217]E(x92171,f2(a838))+E(f324(a114,f561(x92172,x92171,x92173,x92174,x92175)),x92171)+~P1(f324(f324(f326(f844(x92175,x92175)),f324(f324(f247(x92175,x92175),x92174),x92173)),f324(f324(f172(f844(x92175,x92175),a832),x92171),x92172)))
% 18.77/18.50 [9236]P1(f324(f324(f326(f844(x92361,x92361)),f324(f324(f247(x92361,x92361),x92362),x92363)),f324(f324(f282(x92361,x92361,x92361),x92364),f301(x92361,x92364))))+~P1(f324(f324(f326(f844(x92361,x92361)),f324(f324(f247(x92361,x92361),x92362),x92365)),x92364))+~P1(f324(f324(f326(f844(x92361,x92361)),f324(f324(f247(x92361,x92361),x92365),x92363)),x92364))
% 18.77/18.50 [9245]~P1(f324(f324(f326(f844(x92451,x92451)),f324(f324(f247(x92451,x92451),x92452),x92455)),f301(x92451,x92454)))+P1(f324(f324(f326(f844(x92451,x92451)),f324(f324(f247(x92451,x92451),x92452),x92453)),f324(f324(f282(x92451,x92451,x92451),x92454),f301(x92451,x92454))))+~P1(f324(f324(f326(f844(x92451,x92451)),f324(f324(f247(x92451,x92451),x92455),x92453)),x92454))
% 18.77/18.50 [9246]~P1(f324(f324(f326(f844(x92461,x92461)),f324(f324(f247(x92461,x92461),x92465),x92463)),f301(x92461,x92464)))+P1(f324(f324(f326(f844(x92461,x92461)),f324(f324(f247(x92461,x92461),x92462),x92463)),f324(f324(f282(x92461,x92461,x92461),x92464),f301(x92461,x92464))))+~P1(f324(f324(f326(f844(x92461,x92461)),f324(f324(f247(x92461,x92461),x92462),x92465)),x92464))
% 18.77/18.50 [9282]~P12(x92821,x92825,x92822)+~P1(f324(f324(f326(f844(x92821,x92821)),f324(f324(f247(x92821,x92821),x92823),x92824)),x92822))+P1(f324(f324(f231(f845(x92821,a832)),f324(f278(x92821,x92821,x92822),f324(f324(f303(x92821),x92823),f179(f845(x92821,a832))))),f324(f278(x92821,x92821,x92822),f324(f324(f303(x92821),x92824),f179(f845(x92821,a832))))))
% 18.77/18.50 [9334]P1(f324(f324(f326(f844(x93341,x93341)),f324(f324(f247(x93341,x93341),x93342),x93343)),f324(f324(f282(x93341,x93341,x93341),x93344),f301(x93341,x93344))))+~P1(f324(f324(f326(f844(x93341,x93341)),f324(f324(f247(x93341,x93341),x93342),x93345)),f324(f324(f282(x93341,x93341,x93341),x93344),f301(x93341,x93344))))+~P1(f324(f324(f326(f844(x93341,x93341)),f324(f324(f247(x93341,x93341),x93345),x93343)),x93344))
% 18.77/18.50 [9335]P1(f324(f324(f326(f844(x93351,x93351)),f324(f324(f247(x93351,x93351),x93352),x93353)),f324(f324(f282(x93351,x93351,x93351),x93354),f301(x93351,x93354))))+~P1(f324(f324(f326(f844(x93351,x93351)),f324(f324(f247(x93351,x93351),x93355),x93353)),f324(f324(f282(x93351,x93351,x93351),x93354),f301(x93351,x93354))))+~P1(f324(f324(f326(f844(x93351,x93351)),f324(f324(f247(x93351,x93351),x93352),x93355)),x93354))
% 18.77/18.50 [9383]~P1(f324(f69(x93831,x93831,x93834,x93832,x93833),x93835))+P1(f324(f324(f326(x93831),x93832),x93833))+P1(f324(f65(x93831,x93834,f324(f324(f303(x93831),x93832),x93833)),x93835))
% 18.77/18.50 [9426]~E(f324(f304(x94263,x94262,x94265),x94264),x94261)+E(x94261,f179(f845(x94262,a832)))+P1(f324(f324(f231(f845(x94263,a832)),f324(f304(x94262,x94263,f519(x94264,x94263,x94262,x94261)),x94261)),x94264))
% 18.77/18.50 [9468]~P9(x94685)+P1(f324(f324(f326(x94681),f535(x94682,x94683,x94684,x94681,x94685)),x94684))+P1(f324(f324(f231(x94685),f324(f324(f45(x94681,x94685),x94684),x94683)),x94682))
% 18.77/18.50 [9635]E(x96351,x96352)+P1(f324(f324(f326(f844(x96353,x96353)),f324(f324(f247(x96353,x96353),x96351),f562(x96354,x96355,x96352,x96351,x96353))),x96354))+~P1(f324(f324(f326(f844(x96353,x96353)),f324(f324(f247(x96353,x96353),x96351),x96352)),f324(f324(f172(f844(x96353,x96353),a832),x96355),x96354)))
% 18.77/18.50 [9636]E(x96361,f2(a838))+P1(f324(f324(f326(f844(x96362,x96362)),f324(f324(f247(x96362,x96362),x96363),f562(x96364,x96361,x96365,x96363,x96362))),x96364))+~P1(f324(f324(f326(f844(x96362,x96362)),f324(f324(f247(x96362,x96362),x96363),x96365)),f324(f324(f172(f844(x96362,x96362),a832),x96361),x96364)))
% 18.77/18.50 [9679]~P9(x96791)+~P1(f324(f324(f231(x96791),f324(x96794,f535(x96795,x96794,x96793,x96792,x96791))),x96795))+P1(f324(f324(f231(x96791),f324(f324(f45(x96792,x96791),x96793),x96794)),x96795))
% 18.77/18.50 [9734]E(x97341,x97342)+P1(f324(f324(f326(f844(x97343,x97343)),f324(f324(f247(x97343,x97343),f560(x97344,x97345,x97341,x97342,x97343)),x97341)),x97344))+~P1(f324(f324(f326(f844(x97343,x97343)),f324(f324(f247(x97343,x97343),x97342),x97341)),f324(f324(f172(f844(x97343,x97343),a832),x97345),x97344)))
% 18.77/18.50 [9735]E(x97351,f2(a838))+P1(f324(f324(f326(f844(x97352,x97352)),f324(f324(f247(x97352,x97352),f560(x97353,x97351,x97354,x97355,x97352)),x97354)),x97353))+~P1(f324(f324(f326(f844(x97352,x97352)),f324(f324(f247(x97352,x97352),x97355),x97354)),f324(f324(f172(f844(x97352,x97352),a832),x97351),x97353)))
% 18.77/18.50 [9739]E(x97391,x97392)+P1(f324(f324(f326(f844(x97393,x97393)),f324(f324(f247(x97393,x97393),x97391),f560(x97394,x97395,x97392,x97391,x97393))),f324(f324(f172(f844(x97393,x97393),a832),f559(x97394,x97395,x97392,x97391,x97393)),x97394)))+~P1(f324(f324(f326(f844(x97393,x97393)),f324(f324(f247(x97393,x97393),x97391),x97392)),f324(f324(f172(f844(x97393,x97393),a832),x97395),x97394)))
% 18.77/18.50 [9740]E(x97401,f2(a838))+P1(f324(f324(f326(f844(x97402,x97402)),f324(f324(f247(x97402,x97402),x97403),f560(x97404,x97401,x97405,x97403,x97402))),f324(f324(f172(f844(x97402,x97402),a832),f559(x97404,x97401,x97405,x97403,x97402)),x97404)))+~P1(f324(f324(f326(f844(x97402,x97402)),f324(f324(f247(x97402,x97402),x97403),x97405)),f324(f324(f172(f844(x97402,x97402),a832),x97401),x97404)))
% 18.77/18.50 [9795]E(x97951,x97952)+P1(f324(f324(f326(f844(x97953,x97953)),f324(f324(f247(x97953,x97953),f562(x97954,x97955,x97951,x97952,x97953)),x97951)),f324(f324(f172(f844(x97953,x97953),a832),f561(x97954,x97955,x97951,x97952,x97953)),x97954)))+~P1(f324(f324(f326(f844(x97953,x97953)),f324(f324(f247(x97953,x97953),x97952),x97951)),f324(f324(f172(f844(x97953,x97953),a832),x97955),x97954)))
% 18.77/18.50 [9796]E(x97961,f2(a838))+P1(f324(f324(f326(f844(x97962,x97962)),f324(f324(f247(x97962,x97962),f562(x97963,x97961,x97964,x97965,x97962)),x97964)),f324(f324(f172(f844(x97962,x97962),a832),f561(x97963,x97961,x97964,x97965,x97962)),x97963)))+~P1(f324(f324(f326(f844(x97962,x97962)),f324(f324(f247(x97962,x97962),x97965),x97964)),f324(f324(f172(f844(x97962,x97962),a832),x97961),x97963)))
% 18.77/18.50 [9829]~P67(x98292)+~P1(f324(f64(x98291),x98295))+E(f324(f324(f8(x98291,x98292),f324(f324(f9(x98291,x98292,x98292),f324(f324(f20(x98291,x98292,f845(x98292,x98292)),f324(f324(f10(a832,f845(x98292,f845(x98292,x98292)),x98291),f98(x98292)),f324(f324(f9(x98291,f845(x98291,a832),a832),f326(x98291)),x98293))),x98294)),f2(x98292))),x98295),f324(f324(f8(x98291,x98292),x98294),f324(f324(f104(f845(x98291,a832)),x98295),x98293)))
% 18.77/18.50 [8500]~P68(x85001)+~P1(f324(f64(x85004),x85005))+E(f324(f324(f83(x85001),f324(x85002,x85003)),f324(f324(f11(x85004,x85001),x85002),f324(f324(f3(f845(x85004,a832)),x85005),f324(f324(f303(x85004),x85003),f179(f845(x85004,a832)))))),f324(f324(f11(x85004,x85001),x85002),f324(f324(f303(x85004),x85003),x85005)))
% 18.77/18.50 [8501]~P67(x85011)+~P1(f324(f64(x85014),x85015))+E(f324(f324(f82(x85011),f324(x85012,x85013)),f324(f324(f8(x85014,x85011),x85012),f324(f324(f3(f845(x85014,a832)),x85015),f324(f324(f303(x85014),x85013),f179(f845(x85014,a832)))))),f324(f324(f8(x85014,x85011),x85012),f324(f324(f303(x85014),x85013),x85015)))
% 18.77/18.50 [8787]~P86(x87872)+~P18(x87872,f324(f154(x87872),f324(f324(f141(x87871,x87872),x87874),x87875)))+E(f324(f126(x87871,f324(f324(f10(x87872,a832,x87871),f324(f232(x87872),x87873)),x87874)),x87875),f161(x87871,f324(f324(f10(x87872,a832,x87871),f324(f232(x87872),x87873)),x87874),x87875))
% 18.77/18.50 [8808]~P67(x88081)+E(f324(f324(f82(x88081),f324(f324(f8(a838,x88081),x88082),f296(a838,x88083,x88084))),f324(f324(f8(a838,x88081),x88082),f296(a838,f324(f324(f82(a838),x88084),f80(a838)),f324(f324(f82(a838),x88084),x88085)))),f324(f324(f8(a838,x88081),x88082),f296(a838,x88083,f324(f324(f82(a838),x88084),x88085))))+~P1(f324(f324(f231(a838),x88083),f324(f324(f82(a838),x88084),f80(a838))))
% 18.77/18.50 [8809]~P1(f324(f324(f326(x88091),x88094),x88095))+~P1(f324(f324(f231(f845(x88091,a832)),f324(f157(x88091),x88092)),x88095))+P1(f324(f324(f231(f845(x88091,a832)),f324(f157(x88091),f324(f324(f146(x88091,x88092),x88093),x88094))),x88095))
% 18.77/18.50 [9018]~P9(x90182)+~P1(f324(f64(x90181),x90185))+E(f324(f324(f67(x90181,x90182,f324(f324(f10(x90182,f845(x90182,x90182),x90181),f103(x90182)),x90183)),x90184),x90185),f324(f324(f103(x90182),x90184),f324(f324(f45(x90181,x90182),x90185),x90183)))
% 18.77/18.50 [9019]~P9(x90192)+~P1(f324(f64(x90191),x90195))+E(f324(f324(f67(x90191,x90192,f324(f324(f10(x90192,f845(x90192,x90192),x90191),f104(x90192)),x90193)),x90194),x90195),f324(f324(f104(x90192),x90194),f324(f324(f46(x90191,x90192),x90195),x90193)))
% 18.77/18.50 [9104]~P29(x91041,x91042,x91043,x91045)+P29(x91041,x91042,x91043,f324(f324(f303(x91041),x91044),x91045))+P1(f324(f324(f326(x91042),f324(x91043,x91044)),f324(f304(x91041,x91042,x91043),f324(f324(f3(f845(x91041,a832)),x91045),f324(f324(f303(x91041),x91044),f179(f845(x91041,a832)))))))
% 18.77/18.50 [9107]P1(f324(x91072,x91075))+~P1(f324(f324(f326(x91071),x91075),f324(f157(x91071),x91073)))+E(f324(f324(f128(x91071),f324(f180(f839(x91071)),f161(x91071,x91072,f324(f324(f125(x91071),x91073),x91074)))),f324(f324(f125(x91071),x91073),x91074)),f324(f324(f125(x91071),f324(f324(f128(x91071),f324(f180(f839(x91071)),f161(x91071,x91072,x91073))),x91073)),x91074))
% 18.77/18.50 [9308]~P1(f324(f324(f326(f844(f839(x93081),f839(x93081))),f324(f324(f247(f839(x93081),f839(x93081)),x93082),x93084)),f145(x93081,x93085)))+~P1(f324(f324(f232(a838),x93083),f324(f180(f839(x93081)),x93082)))+P1(f324(f324(f326(f844(x93081,x93081)),f324(f324(f247(x93081,x93081),f324(f324(f149(x93081),x93082),x93083)),f324(f324(f149(x93081),x93084),x93083))),x93085))
% 18.77/18.50 [9539]E(x95391,f2(a1))+~P1(f324(f55(x95393,x95391),f324(f324(f247(a1,a1),x95394),x95395)))+P1(f324(f55(f324(f324(f83(a1),x95392),x95393),x95391),f324(f324(f247(a1,a1),f324(f324(f82(a1),f324(f324(f83(a1),x95392),x95394)),f324(f324(f42(a1),f324(f324(f83(a1),x95392),x95395)),x95391))),f51(a1,f324(f324(f83(a1),x95392),x95395),x95391))))
% 18.77/18.50 [9544]~P1(f324(f324(f232(a838),f2(a838)),x95443))+~P1(f324(f54(x95442,x95443),f324(f324(f247(a838,a838),x95444),x95445)))+P1(f324(f54(f324(f324(f83(a838),x95441),x95442),x95443),f324(f324(f247(a838,a838),f324(f324(f82(a838),f324(f324(f83(a838),x95441),x95444)),f324(f324(f42(a838),f324(f324(f83(a838),x95441),x95445)),x95443))),f51(a838,f324(f324(f83(a838),x95441),x95445),x95443))))
% 18.77/18.50 [9851]~P67(x98512)+~P1(f324(f64(x98511),x98514))+E(f324(f324(f8(x98511,x98512),x98513),f324(f257(x98511),f324(f324(f20(x98511,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98511),a322),f324(f324(f9(x98511,f845(x98511,a832),a832),f326(x98511)),x98514))),f324(f324(f9(x98511,f845(x98511,a832),a832),f326(x98511)),x98515)))),f324(f324(f8(x98511,x98512),f324(f324(f9(x98511,x98512,x98512),f324(f324(f20(x98511,x98512,f845(x98512,x98512)),f324(f324(f10(a832,f845(x98512,f845(x98512,x98512)),x98511),f98(x98512)),f324(f324(f9(x98511,f845(x98511,a832),a832),f326(x98511)),x98515))),x98513)),f2(x98512))),x98514))
% 18.77/18.50 [8140]~E(f324(f324(f125(x81401),x81402),x81405),f324(f324(f125(x81401),x81403),x81404))+E(f324(f324(f125(x81401),f324(f324(f128(x81401),f324(f180(f839(x81401)),x81402)),x81403)),x81404),x81405)+P1(f324(f324(f231(a838),f324(f180(f839(x81401)),x81403)),f324(f180(f839(x81401)),x81402)))
% 18.77/18.50 [8340]~E(f324(f324(f125(x83402),x83403),x83401),f324(f324(f125(x83402),x83404),x83405))+E(x83401,f324(f324(f125(x83402),f324(f324(f128(x83402),f324(f180(f839(x83402)),x83403)),x83404)),x83405))+~P1(f324(f324(f231(a838),f324(f180(f839(x83402)),x83403)),f324(f180(f839(x83402)),x83404)))
% 18.77/18.50 [8429]~E(f324(f324(f82(a838),f324(f324(f83(a838),x84293),x84294)),x84291),f324(f324(f82(a838),f324(f324(f83(a838),x84292),x84294)),x84295))+~P1(f324(f324(f231(a838),x84293),x84292))+E(x84291,f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x84292),x84293)),x84294)),x84295))
% 18.77/18.50 [8430]~E(f324(f324(f82(a838),f324(f324(f83(a838),x84301),x84303)),x84304),f324(f324(f82(a838),f324(f324(f83(a838),x84302),x84303)),x84305))+~P1(f324(f324(f231(a838),x84302),x84301))+E(f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x84301),x84302)),x84303)),x84304),x84305)
% 18.77/18.50 [8571]E(f324(f324(f82(a838),f324(f324(f83(a838),x85711),x85712)),x85713),f324(f324(f82(a838),f324(f324(f83(a838),x85714),x85712)),x85715))+~P1(f324(f324(f231(a838),x85714),x85711))+~E(x85715,f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x85711),x85714)),x85712)),x85713))
% 18.77/18.50 [8572]E(f324(f324(f82(a838),f324(f324(f83(a838),x85721),x85722)),x85723),f324(f324(f82(a838),f324(f324(f83(a838),x85724),x85722)),x85725))+~P1(f324(f324(f231(a838),x85724),x85721))+~E(f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x85721),x85724)),x85722)),x85723),x85725)
% 18.77/18.50 [8909]~P1(f324(f324(f280(a1),x89091),x89094))+~P1(f324(f324(f280(a1),x89091),f324(f324(f82(a1),x89092),x89095)))+P1(f324(f324(f280(a1),x89091),f324(f324(f82(a1),f324(f324(f82(a1),x89092),f324(f324(f83(a1),x89093),x89094))),x89095)))
% 18.77/18.50 [9105]~P1(f324(f324(f280(a1),x91051),x91054))+P1(f324(f324(f280(a1),x91051),f324(f324(f82(a1),x91052),x91053)))+~P1(f324(f324(f280(a1),x91051),f324(f324(f82(a1),f324(f324(f82(a1),x91052),f324(f324(f83(a1),x91055),x91054))),x91053)))
% 18.77/18.50 [9356]~P68(x93562)+~P1(f324(f64(x93561),x93565))+E(f324(f324(f11(x93561,x93562),f324(f324(f20(x93561,x93562,x93562),f324(f324(f10(x93562,f845(x93562,x93562),x93561),f83(x93562)),x93563)),x93564)),x93565),f324(f324(f83(x93562),f324(f324(f11(x93561,x93562),x93563),x93565)),f324(f324(f11(x93561,x93562),x93564),x93565)))
% 18.77/18.50 [9357]~P59(x93572)+~P1(f324(f64(x93571),x93575))+E(f324(f324(f11(x93571,x93572),f324(f324(f20(x93571,x93572,x93572),f324(f324(f10(x93572,f845(x93572,x93572),x93571),f284(x93572)),x93573)),x93574)),x93575),f324(f324(f284(x93572),f324(f324(f11(x93571,x93572),x93573),x93575)),f324(f324(f11(x93571,x93572),x93574),x93575)))
% 18.77/18.50 [9358]~P67(x93582)+~P1(f324(f64(x93581),x93585))+E(f324(f324(f8(x93581,x93582),f324(f324(f20(x93581,x93582,x93582),f324(f324(f10(x93582,f845(x93582,x93582),x93581),f82(x93582)),x93583)),x93584)),x93585),f324(f324(f82(x93582),f324(f324(f8(x93581,x93582),x93583),x93585)),f324(f324(f8(x93581,x93582),x93584),x93585)))
% 18.77/18.50 [9482]~E(f635(x94825,x94824,x94823,x94822,x94821),f636(x94825,x94824,x94823,x94822,x94821))+P1(f324(f324(f326(f844(x94821,x94821)),f324(f324(f247(x94821,x94821),x94822),x94823)),f301(x94821,x94824)))+~P1(f324(f324(f326(f844(x94821,x94821)),f324(f324(f247(x94821,x94821),x94822),x94823)),f301(x94821,f324(f324(f103(f845(f844(x94821,x94821),a832)),x94824),x94825))))
% 18.77/18.50 [9483]~E(f637(x94835,x94834,x94833,x94832,x94831),f638(x94835,x94834,x94833,x94832,x94831))+P1(f324(f324(f326(f844(x94831,x94831)),f324(f324(f247(x94831,x94831),x94832),x94833)),f301(x94831,x94834)))+~P1(f324(f324(f326(f844(x94831,x94831)),f324(f324(f247(x94831,x94831),x94832),x94833)),f301(x94831,f324(f324(f103(f845(f844(x94831,x94831),a832)),x94834),x94835))))
% 18.77/18.50 [9669]P1(f324(f324(f326(f844(x96691,x96691)),f324(f324(f247(x96691,x96691),x96692),f636(x96695,x96694,x96693,x96692,x96691))),f301(x96691,x96694)))+P1(f324(f324(f326(f844(x96691,x96691)),f324(f324(f247(x96691,x96691),x96692),x96693)),f301(x96691,x96694)))+~P1(f324(f324(f326(f844(x96691,x96691)),f324(f324(f247(x96691,x96691),x96692),x96693)),f301(x96691,f324(f324(f103(f845(f844(x96691,x96691),a832)),x96694),x96695))))
% 18.77/18.50 [9761]P1(f324(f324(f326(f844(x97611,x97611)),f324(f324(f247(x97611,x97611),f638(x97615,x97614,x97613,x97612,x97611)),x97613)),f301(x97611,x97614)))+P1(f324(f324(f326(f844(x97611,x97611)),f324(f324(f247(x97611,x97611),x97612),x97613)),f301(x97611,x97614)))+~P1(f324(f324(f326(f844(x97611,x97611)),f324(f324(f247(x97611,x97611),x97612),x97613)),f301(x97611,f324(f324(f103(f845(f844(x97611,x97611),a832)),x97614),x97615))))
% 18.77/18.50 [9802]P1(f324(f324(f326(f844(x98021,x98021)),f324(f324(f247(x98021,x98021),x98022),x98023)),f301(x98021,x98024)))+P1(f324(f324(f326(f844(x98021,x98021)),f324(f324(f247(x98021,x98021),f636(x98025,x98024,x98023,x98022,x98021)),f635(x98025,x98024,x98023,x98022,x98021))),x98025))+~P1(f324(f324(f326(f844(x98021,x98021)),f324(f324(f247(x98021,x98021),x98022),x98023)),f301(x98021,f324(f324(f103(f845(f844(x98021,x98021),a832)),x98024),x98025))))
% 18.77/18.50 [9803]P1(f324(f324(f326(f844(x98031,x98031)),f324(f324(f247(x98031,x98031),x98032),x98033)),f301(x98031,x98034)))+P1(f324(f324(f326(f844(x98031,x98031)),f324(f324(f247(x98031,x98031),f637(x98035,x98034,x98033,x98032,x98031)),f638(x98035,x98034,x98033,x98032,x98031))),x98035))+~P1(f324(f324(f326(f844(x98031,x98031)),f324(f324(f247(x98031,x98031),x98032),x98033)),f301(x98031,f324(f324(f103(f845(f844(x98031,x98031),a832)),x98034),x98035))))
% 18.77/18.50 [9926]~P1(f324(f324(f326(f844(f839(x99261),f839(x99261))),f324(f324(f247(f839(x99261),f839(x99261)),x99264),x99265)),f145(x99261,x99262)))+~P1(f324(f324(f326(f844(x99261,x99261)),x99263),f324(f157(f844(x99261,x99261)),f324(f324(f166(x99261,x99261),x99264),x99265))))+P1(f324(f324(f252(x99261,x99261,a832),f324(f324(f9(x99261,f845(f844(x99261,x99261),a832),f845(x99261,a832)),f324(f324(f10(f845(x99261,f845(f845(f844(x99261,x99261),a832),a832)),f845(f845(f844(x99261,x99261),a832),f845(x99261,a832)),x99261),f9(x99261,f845(f844(x99261,x99261),a832),a832)),f324(f324(f10(f845(x99261,f844(x99261,x99261)),f845(x99261,f845(f845(f844(x99261,x99261),a832),a832)),x99261),f324(f10(f844(x99261,x99261),f845(f845(f844(x99261,x99261),a832),a832),x99261),f326(f844(x99261,x99261)))),f247(x99261,x99261)))),x99262)),x99263))
% 18.77/18.50 [9387]~P1(f324(f324(f231(a838),x93873),x93872))+~P1(f324(f324(f232(a838),f324(f324(f82(a838),f324(f324(f83(a838),x93873),x93874)),x93871)),f324(f324(f82(a838),f324(f324(f83(a838),x93872),x93874)),x93875)))+P1(f324(f324(f232(a838),x93871),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x93872),x93873)),x93874)),x93875)))
% 18.77/18.50 [9388]~P1(f324(f324(f231(a838),x93883),x93882))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),f324(f324(f83(a838),x93883),x93884)),x93881)),f324(f324(f82(a838),f324(f324(f83(a838),x93882),x93884)),x93885)))+P1(f324(f324(f231(a838),x93881),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x93882),x93883)),x93884)),x93885)))
% 18.77/18.50 [9408]~P1(f324(f324(f231(a838),x94081),x94084))+P1(f324(f324(f232(a838),f324(f324(f82(a838),f324(f324(f83(a838),x94081),x94082)),x94083)),f324(f324(f82(a838),f324(f324(f83(a838),x94084),x94082)),x94085)))+~P1(f324(f324(f232(a838),x94083),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x94084),x94081)),x94082)),x94085)))
% 18.77/18.50 [9409]~P1(f324(f324(f231(a838),x94091),x94094))+P1(f324(f324(f231(a838),f324(f324(f82(a838),f324(f324(f83(a838),x94091),x94092)),x94093)),f324(f324(f82(a838),f324(f324(f83(a838),x94094),x94092)),x94095)))+~P1(f324(f324(f231(a838),x94093),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x94094),x94091)),x94092)),x94095)))
% 18.77/18.50 [9519]~P1(f324(f324(f231(a838),x95192),x95191))+~P1(f324(f324(f232(a838),f324(f324(f82(a838),f324(f324(f83(a838),x95191),x95193)),x95194)),f324(f324(f82(a838),f324(f324(f83(a838),x95192),x95193)),x95195)))+P1(f324(f324(f232(a838),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x95191),x95192)),x95193)),x95194)),x95195))
% 18.77/18.50 [9520]~P1(f324(f324(f231(a838),x95202),x95201))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),f324(f324(f83(a838),x95201),x95203)),x95204)),f324(f324(f82(a838),f324(f324(f83(a838),x95202),x95203)),x95205)))+P1(f324(f324(f231(a838),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x95201),x95202)),x95203)),x95204)),x95205))
% 18.77/18.50 [9562]~P1(f324(f324(f231(a838),x95624),x95621))+P1(f324(f324(f232(a838),f324(f324(f82(a838),f324(f324(f83(a838),x95621),x95622)),x95623)),f324(f324(f82(a838),f324(f324(f83(a838),x95624),x95622)),x95625)))+~P1(f324(f324(f232(a838),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x95621),x95624)),x95622)),x95623)),x95625))
% 18.77/18.50 [9563]~P1(f324(f324(f231(a838),x95634),x95631))+P1(f324(f324(f231(a838),f324(f324(f82(a838),f324(f324(f83(a838),x95631),x95632)),x95633)),f324(f324(f82(a838),f324(f324(f83(a838),x95634),x95632)),x95635)))+~P1(f324(f324(f231(a838),f324(f324(f82(a838),f324(f324(f83(a838),f324(f324(f3(a838),x95631),x95634)),x95632)),x95633)),x95635))
% 18.77/18.50 [9787]~P16(x97871,x97872,x97875,x97873)+~P1(f324(f324(f326(f844(x97871,x97871)),x97874),x97875))+P1(f324(f324(f252(x97871,x97871,a832),f324(f324(f9(x97871,f845(x97871,x97872),f845(x97871,a832)),f324(f324(f10(f845(x97872,a832),f845(f845(x97871,x97872),f845(x97871,a832)),x97871),f10(x97872,a832,x97871)),f324(f324(f10(x97872,f845(x97872,a832),x97871),a321),x97873))),x97873)),x97874))
% 18.77/18.50 [7096]~P39(x70964,x70962,x70965,x70966)+P39(f33(x70961,x70963,x70964),x70962,x70965,x70966)+P1(f324(x70961,x70962))
% 18.77/18.50 [7097]~P39(x70974,x70972,x70975,x70976)+P39(f33(x70971,x70973,x70974),x70972,x70975,x70976)+P1(f324(x70971,x70972))
% 18.77/18.50 [7098]~P39(x70984,x70982,x70985,x70986)+P39(f33(x70981,x70983,x70984),x70982,x70985,x70986)+P1(f324(x70981,x70982))
% 18.77/18.50 [7174]~P39(x71742,x71744,x71745,x71746)+P39(f33(x71741,x71742,x71743),x71744,x71745,x71746)+~P1(f324(x71741,x71744))
% 18.77/18.50 [7175]~P39(x71752,x71754,x71755,x71756)+P39(f33(x71751,x71752,x71753),x71754,x71755,x71756)+~P1(f324(x71751,x71754))
% 18.77/18.50 [7176]~P39(x71762,x71764,x71765,x71766)+P39(f33(x71761,x71762,x71763),x71764,x71765,x71766)+~P1(f324(x71761,x71764))
% 18.77/18.50 [7265]P39(x72653,x72652,x72654,x72655)+~P39(f33(x72651,x72656,x72653),x72652,x72654,x72655)+P1(f324(x72651,x72652))
% 18.77/18.50 [7266]P39(x72663,x72662,x72664,x72665)+~P39(f33(x72661,x72666,x72663),x72662,x72664,x72665)+P1(f324(x72661,x72662))
% 18.77/18.50 [7267]P39(x72673,x72672,x72674,x72675)+~P39(f33(x72671,x72676,x72673),x72672,x72674,x72675)+P1(f324(x72671,x72672))
% 18.77/18.50 [7298]P39(x72981,x72982,x72983,x72984)+~P39(f33(x72985,x72981,x72986),x72982,x72983,x72984)+~P1(f324(x72985,x72982))
% 18.77/18.50 [7299]P39(x72991,x72992,x72993,x72994)+~P39(f33(x72995,x72991,x72996),x72992,x72993,x72994)+~P1(f324(x72995,x72992))
% 18.77/18.50 [7300]P39(x73001,x73002,x73003,x73004)+~P39(f33(x73005,x73001,x73006),x73002,x73003,x73004)+~P1(f324(x73005,x73002))
% 18.77/18.50 [7675]~P39(x76751,x76753,x76754,x76756)+~P39(x76752,x76756,x76754,x76755)+P39(f36(x76751,x76752),x76753,x76754,x76755)
% 18.77/18.50 [7676]~P39(x76761,x76763,x76764,x76766)+~P39(x76762,x76766,x76764,x76765)+P39(f36(x76761,x76762),x76763,x76764,x76765)
% 18.77/18.50 [7677]P39(x76771,x76772,x76773,x76774)+P39(x76775,x76772,x76773,x76774)+~P39(f33(x76776,x76771,x76775),x76772,x76773,x76774)
% 18.77/18.50 [7678]P39(x76781,x76782,x76783,x76784)+P39(x76785,x76782,x76783,x76784)+~P39(f33(x76786,x76781,x76785),x76782,x76783,x76784)
% 18.77/18.50 [7679]P39(x76791,x76792,x76793,x76794)+P39(x76795,x76792,x76793,x76794)+~P39(f33(x76796,x76791,x76795),x76792,x76793,x76794)
% 18.77/18.50 [6645]~E(f324(x66454,x66455),f182(x66452))+E(f324(f169(x66451,x66452,x66453,x66454),x66455),f324(f226(x66452),x66456))+~E(f324(x66453,x66455),f324(f226(x66452),x66456))
% 18.77/18.50 [6754]~E(f324(x67543,x67546),f182(x67541))+E(f324(f228(f842(x67541),x67542,f182(x67541),x67543),f324(x67544,x67545)),f182(x67541))+~E(f324(x67544,x67545),f324(f226(x67542),x67546))
% 18.77/18.50 [7357]E(f324(x73571,x73572),f182(x73573))+~E(f324(f169(x73575,x73573,x73576,x73571),x73572),f324(f226(x73573),x73574))+E(f324(x73571,x73572),f324(f226(x73573),x73574))
% 18.77/18.50 [7358]E(f324(x73581,x73582),f182(x73583))+~E(f324(f169(x73585,x73583,x73586,x73581),x73582),f324(f226(x73583),x73584))+E(f324(x73581,x73582),f324(f226(x73583),x73584))
% 18.77/18.50 [7398]~E(f324(f169(x73986,x73983,x73985,x73981),x73982),f324(f226(x73983),x73984))+E(f324(x73981,x73982),f324(f226(x73983),x73984))+E(f324(x73985,x73982),f324(f226(x73983),x73984))
% 18.77/18.50 [7399]~E(f324(f169(x73996,x73993,x73995,x73991),x73992),f324(f226(x73993),x73994))+E(f324(x73991,x73992),f324(f226(x73993),x73994))+E(f324(x73995,x73992),f324(f226(x73993),x73994))
% 18.77/18.50 [8300]~P23(x83006,x83001,x83002,x83004)+E(f324(f75(x83001,x83001,x83001,f324(x83002,x83003)),f324(x83004,x83005)),f324(f75(x83001,x83001,x83001,f324(x83004,x83005)),f324(x83002,x83003)))+~P1(f324(f64(x83006),x83005))
% 18.77/18.50 [8698]~P29(x86981,x86983,x86985,x86986)+~P29(x86983,x86982,x86984,f324(f304(x86981,x86983,x86985),x86986))+P29(x86981,x86982,f324(f75(x86983,x86982,x86981,x86984),x86985),x86986)
% 18.77/18.50 [8699]~P29(x86991,x86993,x86995,x86996)+~P29(x86993,x86992,x86994,f324(f304(x86991,x86993,x86995),x86996))+P29(x86991,x86992,f324(f75(x86993,x86992,x86991,x86994),x86995),x86996)
% 18.77/18.50 [8858]~P29(x88584,x88581,x88585,x88586)+~P29(x88584,x88582,f324(f75(x88581,x88582,x88584,x88583),x88585),x88586)+P29(x88581,x88582,x88583,f324(f304(x88584,x88581,x88585),x88586))
% 18.77/18.50 [9199]~P1(f324(f324(x91993,x91992),x91996))+~P1(f324(f324(x91994,x91995),x91992))+P1(f324(f324(f326(x91991),x91992),f293(x91991,x91993,x91994,x91995,x91996)))
% 18.77/18.50 [9200]~P1(f324(f324(x92004,x92002),x92006))+~P1(f324(f324(x92003,x92005),x92002))+P1(f324(f324(f326(x92001),x92002),f290(x92001,x92003,x92004,x92005,x92006)))
% 18.77/18.50 [9309]E(x93091,x93092)+E(x93093,x93094)+~P1(f324(f324(f326(f844(f839(x93095),f839(x93095))),f324(f324(f247(f839(x93095),f839(x93095)),f324(f324(f139(x93095),x93093),x93091)),f324(f324(f139(x93095),x93094),x93092))),f144(x93095,x93096)))
% 18.77/18.50 [9318]~E(x93182,x93184)+P1(f324(f324(f326(f844(f839(x93181),f839(x93181))),f324(f324(f247(f839(x93181),f839(x93181)),f324(f324(f139(x93181),x93182),x93183)),f324(f324(f139(x93181),x93184),x93185))),f134(x93181,x93186)))+~P1(f324(f324(f326(f844(f839(x93181),f839(x93181))),f324(f324(f247(f839(x93181),f839(x93181)),x93183),x93185)),f134(x93181,x93186)))
% 18.77/18.51 [9319]~E(x93192,x93194)+P1(f324(f324(f326(f844(f839(x93191),f839(x93191))),f324(f324(f247(f839(x93191),f839(x93191)),f324(f324(f139(x93191),x93192),x93193)),f324(f324(f139(x93191),x93194),x93195))),f136(x93191,x93196)))+~P1(f324(f324(f326(f844(f839(x93191),f839(x93191))),f324(f324(f247(f839(x93191),f839(x93191)),x93193),x93195)),f136(x93191,x93196)))
% 18.77/18.51 [9320]~E(x93202,x93204)+P1(f324(f324(f326(f844(f839(x93201),f839(x93201))),f324(f324(f247(f839(x93201),f839(x93201)),f324(f324(f139(x93201),x93202),x93203)),f324(f324(f139(x93201),x93204),x93205))),f144(x93201,x93206)))+~P1(f324(f324(f326(f844(f839(x93201),f839(x93201))),f324(f324(f247(f839(x93201),f839(x93201)),x93203),x93205)),f144(x93201,x93206)))
% 18.77/18.51 [9321]~E(x93212,x93214)+P1(f324(f324(f326(f844(f839(x93211),f839(x93211))),f324(f324(f247(f839(x93211),f839(x93211)),f324(f324(f125(x93211),x93212),x93213)),f324(f324(f125(x93211),x93214),x93215))),f144(x93211,x93216)))+~P1(f324(f324(f326(f844(f839(x93211),f839(x93211))),f324(f324(f247(f839(x93211),f839(x93211)),x93213),x93215)),f144(x93211,x93216)))
% 18.77/18.51 [9322]~E(x93223,x93225)+P1(f324(f324(f326(f844(f839(x93221),f839(x93221))),f324(f324(f247(f839(x93221),f839(x93221)),f324(f324(f125(x93221),x93222),x93223)),f324(f324(f125(x93221),x93224),x93225))),f144(x93221,x93226)))+~P1(f324(f324(f326(f844(f839(x93221),f839(x93221))),f324(f324(f247(f839(x93221),f839(x93221)),x93222),x93224)),f144(x93221,x93226)))
% 18.77/18.51 [9375]E(x93751,x93752)+P1(f324(f324(f326(f844(f839(x93753),f839(x93753))),f324(f324(f247(f839(x93753),f839(x93753)),x93751),x93752)),f144(x93753,x93754)))+~P1(f324(f324(f326(f844(f839(x93753),f839(x93753))),f324(f324(f247(f839(x93753),f839(x93753)),f324(f324(f139(x93753),x93755),x93751)),f324(f324(f139(x93753),x93756),x93752))),f144(x93753,x93754)))
% 18.77/18.51 [9521]~E(x95213,x95215)+P1(f324(f324(f326(f844(f839(x95211),f839(x95211))),f324(f324(f247(f839(x95211),f839(x95211)),f324(f324(f125(x95211),x95212),f324(f324(f139(x95211),x95213),f115(x95211)))),f324(f324(f125(x95211),x95214),f324(f324(f139(x95211),x95215),f115(x95211))))),f144(x95211,x95216)))+~P1(f324(f324(f326(f844(f839(x95211),f839(x95211))),f324(f324(f247(f839(x95211),f839(x95211)),x95212),x95214)),f144(x95211,x95216)))
% 18.77/18.51 [9532]E(f324(x95321,x95322),f182(x95323))+~E(f324(f228(f842(x95326),x95323,f182(x95326),x95324),f324(x95321,x95322)),f182(x95326))+E(f324(x95324,f698(x95322,x95321,x95324,x95325,x95326,x95323)),f182(x95326))
% 18.77/18.51 [9533]E(f324(x95331,x95332),f182(x95333))+~E(f324(f228(f842(x95336),x95333,f182(x95336),x95334),f324(x95331,x95332)),f182(x95336))+E(f324(f226(x95333),f698(x95332,x95331,x95334,x95335,x95336,x95333)),f324(x95331,x95332))
% 18.77/18.51 [9566]E(x95661,x95662)+E(x95663,x95664)+~P1(f324(f324(f326(f844(f839(x95665),f839(x95665))),f324(f324(f247(f839(x95665),f839(x95665)),f324(f324(f125(x95665),x95663),f324(f324(f139(x95665),x95661),f115(x95665)))),f324(f324(f125(x95665),x95664),f324(f324(f139(x95665),x95662),f115(x95665))))),f144(x95665,x95666)))
% 18.77/18.51 [9588]E(x95881,x95882)+~P1(f324(f324(f326(f844(f839(x95883),f839(x95883))),f324(f324(f247(f839(x95883),f839(x95883)),f324(f324(f125(x95883),x95881),f324(f324(f139(x95883),x95885),f115(x95883)))),f324(f324(f125(x95883),x95882),f324(f324(f139(x95883),x95886),f115(x95883))))),f144(x95883,x95884)))+P1(f324(f324(f326(f844(f839(x95883),f839(x95883))),f324(f324(f247(f839(x95883),f839(x95883)),x95881),x95882)),f144(x95883,x95884)))
% 18.77/18.51 [9619]~P1(f324(f324(f326(f844(f845(x96191,a832),f845(x96191,a832))),f324(f324(f247(f845(x96191,a832),f845(x96191,a832)),x96192),x96194)),f317(x96191,x96196)))+~P1(f324(f324(f326(f844(f845(x96191,a832),f845(x96191,a832))),f324(f324(f247(f845(x96191,a832),f845(x96191,a832)),x96193),x96195)),f317(x96191,x96196)))+P1(f324(f324(f326(f844(f845(x96191,a832),f845(x96191,a832))),f324(f324(f247(f845(x96191,a832),f845(x96191,a832)),f324(f324(f103(f845(x96191,a832)),x96192),x96193)),f324(f324(f103(f845(x96191,a832)),x96194),x96195))),f317(x96191,x96196)))
% 18.77/18.51 [5062]~E(f324(x50623,x50626),x50625)+~E(x50624,f324(f226(x50621),x50626))+E(f324(f324(f195(x50621,x50622),x50623),x50624),f324(f226(x50622),x50625))
% 18.77/18.51 [5465]~E(f324(f324(f125(x54651),x54656),x54653),x54655)+E(f324(f324(f125(x54651),x54652),x54653),f324(f324(f139(x54651),x54654),x54655))+~E(x54652,f324(f324(f139(x54651),x54654),x54656))
% 18.77/18.51 [5466]~E(f324(f324(f125(x54661),x54666),x54663),x54665)+E(f324(f324(f125(x54661),x54662),x54663),f324(f324(f125(x54661),x54664),x54665))+~E(x54662,f324(f324(f125(x54661),x54664),x54666))
% 18.77/18.51 [5467]E(f324(f324(f125(x54671),x54672),x54673),f324(f324(f139(x54671),x54674),x54675))+~E(f324(f324(f139(x54671),x54674),x54676),x54672)+~E(x54675,f324(f324(f125(x54671),x54676),x54673))
% 18.77/18.51 [5468]E(f324(f324(f125(x54681),x54682),x54683),f324(f324(f139(x54681),x54684),x54685))+~E(f324(f324(f139(x54681),x54684),x54686),x54682)+~E(x54685,f324(f324(f125(x54681),x54686),x54683))
% 18.77/18.51 [5469]~E(f324(f324(f125(x54691),x54692),x54696),x54694)+E(f324(f324(f125(x54691),x54692),x54693),f324(f324(f125(x54691),x54694),x54695))+~E(x54693,f324(f324(f125(x54691),x54696),x54695))
% 18.77/18.51 [5470]~E(f324(f324(f125(x54701),x54702),x54706),x54704)+E(f324(f324(f125(x54701),x54702),x54703),f324(f324(f125(x54701),x54704),x54705))+~E(x54703,f324(f324(f125(x54701),x54706),x54705))
% 18.77/18.51 [6638]E(f324(x66381,x66382),f324(x66383,x66382))+~E(f324(f324(f141(x66384,x66385),x66381),x66386),f324(f324(f141(x66384,x66385),x66383),x66386))+~P1(f324(f324(f326(x66384),x66382),f324(f157(x66384),x66386)))
% 18.77/18.51 [7033]~P23(x70334,x70335,x70336,x70331)+E(f324(f324(x70331,x70332),x70333),f324(f324(f67(x70334,x70335,x70336),x70333),x70332))+~P1(f324(f64(x70334),x70332))
% 18.77/18.51 [7101]~E(x71012,f324(x71014,x71016))+~P1(f324(f324(f326(x71013),x71016),x71015))+P1(f324(f324(f326(x71011),x71012),f324(f304(x71013,x71011,x71014),x71015)))
% 18.77/18.51 [7102]~E(x71022,f324(x71024,x71026))+~P1(f324(f324(f326(x71023),x71026),x71025))+P1(f324(f324(f326(x71021),x71022),f324(f304(x71023,x71021,x71024),x71025)))
% 18.77/18.51 [7103]~E(x71032,f324(x71034,x71036))+~P1(f324(f324(f326(x71033),x71036),x71035))+P1(f324(f324(f326(x71031),x71032),f324(f304(x71033,x71031,x71034),x71035)))
% 18.77/18.51 [7104]~E(f324(x71044,x71042),x71046)+~P1(f324(f324(f326(x71043),x71046),x71045))+P1(f324(f324(f326(x71041),x71042),f324(f305(x71041,x71043,x71044),x71045)))
% 18.77/18.51 [7580]~P34(x75801,x75802,x75804,x75806)+P34(x75801,x75802,f324(f324(f139(x75801),x75803),x75804),f324(f324(f139(x75801),x75805),x75806))+~P1(f324(f324(x75802,x75803),x75805))
% 18.77/18.51 [7581]~P34(x75811,x75812,x75814,x75816)+P34(x75811,x75812,f324(f324(f139(x75811),x75813),x75814),f324(f324(f139(x75811),x75815),x75816))+~P1(f324(f324(x75812,x75813),x75815))
% 18.77/18.51 [8579]~P54(x85794,x85795,x85791,x85792,x85796)+E(f324(x85791,f324(x85792,x85793)),x85793)+~P1(f324(f324(f326(x85795),x85793),x85796))
% 18.77/18.51 [9311]E(x93111,x93112)+E(f324(f180(f839(x93113)),x93114),f324(f180(f839(x93113)),x93115))+~P1(f324(f324(f326(f844(f839(x93113),f839(x93113))),f324(f324(f247(f839(x93113),f839(x93113)),f324(f324(f139(x93113),x93111),x93114)),f324(f324(f139(x93113),x93112),x93115))),f134(x93113,x93116)))
% 18.77/18.51 [9371]~P20(x93711,x93712,x93713)+E(f324(f324(f67(x93711,x93712,x93713),x93714),x93715),x93716)+~P1(f324(f69(x93711,x93712,x93713,x93714,x93715),x93716))
% 18.77/18.51 [9378]E(f324(f180(f839(x93781)),x93782),f324(f180(f839(x93781)),x93783))+P1(f324(f324(f326(f844(f839(x93781),f839(x93781))),f324(f324(f247(f839(x93781),f839(x93781)),x93782),x93783)),f134(x93781,x93784)))+~P1(f324(f324(f326(f844(f839(x93781),f839(x93781))),f324(f324(f247(f839(x93781),f839(x93781)),f324(f324(f139(x93781),x93785),x93782)),f324(f324(f139(x93781),x93786),x93783))),f134(x93781,x93784)))
% 18.77/18.51 [9400]~P1(f324(f324(f326(f844(x94001,x94001)),f324(f324(f247(x94001,x94001),x94002),x94004)),f301(x94001,x94006)))+P1(f324(f324(f326(f844(f839(x94001),f839(x94001))),f324(f324(f247(f839(x94001),f839(x94001)),f324(f324(f139(x94001),x94002),x94003)),f324(f324(f139(x94001),x94004),x94005))),f301(f839(x94001),f144(x94001,x94006))))+~P1(f324(f324(f326(f844(f839(x94001),f839(x94001))),f324(f324(f247(f839(x94001),f839(x94001)),x94003),x94005)),f301(f839(x94001),f144(x94001,x94006))))
% 18.77/18.51 [9879]~P67(x98792)+E(f324(f324(f8(x98791,x98792),f324(f324(f10(f845(x98793,a832),x98792,x98791),f324(f8(x98793,x98792),x98794)),f324(f324(f10(f845(x98793,a832),f845(x98793,a832),x98791),f257(x98793)),f324(f324(f10(f845(x98793,a832),f845(x98793,a832),x98791),f324(f20(x98793,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98793),a322),f324(f324(f9(x98793,f845(x98793,a832),a832),f326(x98793)),x98795)))),f324(f9(x98793,x98791,a832),f324(f324(f10(x98791,f845(x98791,a832),x98793),a321),x98796)))))),f324(f304(x98793,x98791,x98796),x98795)),f324(f324(f8(x98793,x98792),x98794),x98795))+~P1(f324(f64(x98793),x98795))
% 18.77/18.51 [6698]~P86(x66983)+P1(f324(x66982,x66985))+E(f324(f126(x66981,x66982),f324(f324(f137(x66981,x66983,x66984),x66985),x66986)),f324(f126(x66981,x66982),x66986))
% 18.77/18.51 [6700]P1(f324(x67001,x67002))+~E(f152(x67003,x67001,x67004),f324(f324(f247(f839(x67003),f839(x67003)),x67005),x67006))+~P1(f324(f324(f326(x67003),x67002),f324(f157(x67003),x67005)))
% 18.77/18.51 [6751]~P1(f324(x67512,x67516))+~E(f152(x67511,x67512,x67513),f324(f324(f247(f839(x67511),f839(x67511)),x67514),x67515))+~P1(f324(f324(f326(x67511),x67516),f324(f157(x67511),x67515)))
% 18.77/18.51 [7444]~P19(x74441,x74442,x74443)+~P1(f324(f64(x74441),x74446))+E(f324(f324(f67(x74441,x74442,x74443),x74444),f324(f324(f303(x74441),x74445),x74446)),f324(f324(f67(x74441,x74442,x74443),f324(f324(x74443,x74445),x74444)),x74446))
% 18.77/18.51 [7496]~P86(x74962)+~P1(f324(f324(f231(x74962),f324(x74963,x74964)),f324(x74963,x74965)))+E(f324(f324(f137(x74961,x74962,x74963),x74964),f324(f324(f139(x74961),x74965),x74966)),f324(f324(f139(x74961),x74964),f324(f324(f139(x74961),x74965),x74966)))
% 18.77/18.51 [7612]E(x76121,x76122)+~E(f324(f324(f249(x76123,x76124),x76121),f324(f18(f845(x76124,a832),x76123),x76125)),f324(f324(f249(x76123,x76124),x76122),f324(f18(f845(x76124,a832),x76123),x76125)))+~P1(f324(f324(f326(x76124),x76126),x76125))
% 18.77/18.51 [7681]~P19(x76811,x76812,x76813)+~P1(f324(f64(x76811),x76816))+E(f324(f324(f67(x76811,x76812,x76813),x76814),f324(f324(f303(x76811),x76815),x76816)),f324(f324(x76813,x76815),f324(f324(f67(x76811,x76812,x76813),x76814),x76816)))
% 18.77/18.51 [7799]~P20(x77991,x77992,x77993)+~P1(f324(f64(x77991),x77996))+E(f324(f324(f67(x77991,x77992,x77993),f324(f324(x77993,x77994),x77995)),x77996),f324(f324(x77993,x77994),f324(f324(f67(x77991,x77992,x77993),x77995),x77996)))
% 18.77/18.51 [7868]~P24(x78682,x78685,x78686,x78681)+~P1(f324(f64(x78682),x78684))+E(f324(x78681,f324(f324(f303(x78682),x78683),x78684)),f324(f75(x78685,x78685,x78685,f324(x78681,x78684)),f324(x78686,x78683)))
% 18.77/18.51 [7907]~P86(x79072)+P1(f324(f324(f231(x79072),f324(x79073,x79074)),f324(x79073,x79075)))+E(f324(f324(f137(x79071,x79072,x79073),x79074),f324(f324(f139(x79071),x79075),x79076)),f324(f324(f139(x79071),x79075),f324(f324(f137(x79071,x79072,x79073),x79074),x79076)))
% 18.77/18.51 [8044]~E(f324(f180(f839(x80441)),x80445),f324(f180(f839(x80442)),x80446))+~E(f324(f180(f839(x80441)),x80443),f324(f180(f839(x80442)),x80444))+E(f324(f324(f125(f844(x80441,x80442)),f324(f324(f166(x80441,x80442),x80443),x80444)),f324(f324(f166(x80441,x80442),x80445),x80446)),f324(f324(f166(x80441,x80442),f324(f324(f125(x80441),x80443),x80445)),f324(f324(f125(x80442),x80444),x80446)))
% 18.77/18.51 [8155]~E(x81552,f324(f304(x81553,x81551,x81554),x81556))+P1(f324(f324(f231(f845(x81551,a832)),x81552),f324(f304(x81553,x81551,x81554),x81555)))+~P1(f324(f324(f231(f845(x81553,a832)),x81556),x81555))
% 18.77/18.51 [8257]~P86(x82575)+E(f324(x82571,x82572),f324(x82571,x82573))+E(f324(f324(f137(x82574,x82575,x82571),x82572),f324(f324(f137(x82574,x82575,x82571),x82573),x82576)),f324(f324(f137(x82574,x82575,x82571),x82573),f324(f324(f137(x82574,x82575,x82571),x82572),x82576)))
% 18.77/18.51 [8293]~P29(x82933,x82931,x82934,x82935)+P29(x82933,x82931,f324(f324(f324(f74(x82933,x82931),x82934),x82936),x82932),x82935)+P1(f324(f324(f326(x82931),x82932),f324(f304(x82933,x82931,x82934),x82935)))
% 18.77/18.51 [8437]~P1(f324(f324(f326(x84372),x84374),f324(x84376,x84373)))+~P1(f324(f324(f326(x84371),x84373),x84375))+P1(f324(f324(f326(f844(x84371,x84372)),f324(f324(f247(x84371,x84372),x84373),x84374)),f324(f324(f249(x84371,x84372),x84375),x84376)))
% 18.77/18.51 [8438]~P1(f324(f324(f326(x84382),x84384),f324(x84386,x84383)))+~P1(f324(f324(f326(x84381),x84383),x84385))+P1(f324(f324(f326(f844(x84381,x84382)),f324(f324(f247(x84381,x84382),x84383),x84384)),f324(f324(f249(x84381,x84382),x84385),x84386)))
% 18.77/18.51 [8851]~P68(x88512)+~P29(x88514,x88511,x88515,x88516)+E(f324(f324(f11(x88511,x88512),x88513),f324(f304(x88514,x88511,x88515),x88516)),f324(f324(f11(x88514,x88512),f324(f75(x88511,x88512,x88514,x88513),x88515)),x88516))
% 18.77/18.51 [8852]~P67(x88522)+~P29(x88524,x88521,x88525,x88526)+E(f324(f324(f8(x88521,x88522),x88523),f324(f304(x88524,x88521,x88525),x88526)),f324(f324(f8(x88524,x88522),f324(f75(x88521,x88522,x88524,x88523),x88525)),x88526))
% 18.77/18.51 [9085]~P23(x90853,x90851,x90856,x90852)+~P1(f324(f64(x90853),x90854))+E(f324(f75(x90851,x90851,x90851,f324(x90852,f324(f324(f3(f845(x90853,a832)),x90854),f324(f324(f303(x90853),x90855),f179(f845(x90853,a832)))))),f324(x90856,x90855)),f324(x90852,f324(f324(f303(x90853),x90855),x90854)))
% 18.77/18.51 [9649]~E(f324(f304(x96492,x96494,x96496),f238(f845(x96492,a832))),f238(f845(x96494,a832)))+~E(f324(f304(x96491,x96493,x96495),f238(f845(x96491,a832))),f238(f845(x96493,a832)))+E(f324(f304(f844(x96491,x96492),f844(x96493,x96494),f253(x96491,x96493,x96492,x96494,x96495,x96496)),f238(f845(f844(x96491,x96492),a832))),f238(f845(f844(x96493,x96494),a832)))
% 18.77/18.51 [9710]~P29(x97103,x97104,x97105,f324(x97106,f682(x97106,x97105,x97104,x97103,x97102,x97101)))+P29(x97103,x97104,x97105,f324(f324(f46(x97102,f845(x97103,a832)),x97101),x97106))+E(x97101,f179(f845(x97102,a832)))
% 18.77/18.51 [9766]P29(x97666,x97665,x97664,f324(f324(f46(x97662,f845(x97666,a832)),x97661),x97663))+E(x97661,f179(f845(x97662,a832)))+P1(f324(f324(f326(x97662),f682(x97663,x97664,x97665,x97666,x97662,x97661)),x97661))
% 18.77/18.51 [9772]P1(f324(f324(f326(x97721),f645(x97722,x97723,x97724,x97725,x97726,x97721)),x97726))+P1(f324(f324(f231(f845(f844(x97721,x97724),a832)),f324(f324(f249(x97721,x97724),x97726),x97723)),f324(f324(f249(x97721,x97724),x97725),x97722)))+~P1(f324(f324(f231(f845(x97721,a832)),x97726),x97725))
% 18.77/18.51 [9816]P28(x98166,x98165,f324(f324(f303(f837(x98166)),f324(f324(f324(f93(x98166),x98164),x98163),x98162)),f179(f845(f837(x98166),a832))))+~P28(x98166,x98165,f324(f324(f303(f837(x98166)),f324(f324(f324(f93(x98166),x98164),x98163),x98161)),f179(f845(f837(x98166),a832))))+P1(f324(f324(x98161,f567(x98162,x98161,x98163,x98164,x98165,x98166)),f568(x98162,x98161,x98163,x98164,x98165,x98166)))
% 18.77/18.51 [9817]P28(x98176,x98175,f324(f324(f303(f837(x98176)),f324(f324(f324(f93(x98176),x98171),x98173),x98172)),f179(f845(f837(x98176),a832))))+~P28(x98176,x98175,f324(f324(f303(f837(x98176)),f324(f324(f324(f93(x98176),x98174),x98173),x98172)),f179(f845(f837(x98176),a832))))+P1(f324(f324(x98171,f569(x98171,x98172,x98173,x98174,x98175,x98176)),f570(x98171,x98172,x98173,x98174,x98175,x98176)))
% 18.77/18.51 [9854]~P28(x98541,x98542,f324(f324(f303(f837(x98541)),f324(f324(f324(f93(x98541),x98543),x98544),x98546)),f179(f845(f837(x98541),a832))))+P28(x98541,x98542,f324(f324(f303(f837(x98541)),f324(f324(f324(f93(x98541),x98543),x98544),x98545)),f179(f845(f837(x98541),a832))))+~P1(f324(f324(x98545,f567(x98545,x98546,x98544,x98543,x98542,x98541)),f568(x98545,x98546,x98544,x98543,x98542,x98541)))
% 18.77/18.51 [9855]~P28(x98551,x98552,f324(f324(f303(f837(x98551)),f324(f324(f324(f93(x98551),x98556),x98554),x98555)),f179(f845(f837(x98551),a832))))+P28(x98551,x98552,f324(f324(f303(f837(x98551)),f324(f324(f324(f93(x98551),x98553),x98554),x98555)),f179(f845(f837(x98551),a832))))+~P1(f324(f324(x98556,f569(x98553,x98555,x98554,x98556,x98552,x98551)),f570(x98553,x98555,x98554,x98556,x98552,x98551)))
% 18.77/18.51 [9895]~P1(f324(f324(f231(f845(x98952,a832)),f324(x98954,f645(x98956,x98954,x98952,x98955,x98953,x98951))),f324(x98956,f645(x98956,x98954,x98952,x98955,x98953,x98951))))+~P1(f324(f324(f231(f845(x98951,a832)),x98953),x98955))+P1(f324(f324(f231(f845(f844(x98951,x98952),a832)),f324(f324(f249(x98951,x98952),x98953),x98954)),f324(f324(f249(x98951,x98952),x98955),x98956)))
% 18.77/18.51 [7630]~P1(f324(x76301,x76305))+~P1(f324(x76306,x76304))+P1(f324(x76301,f324(f251(x76302,x76303),f324(f324(f247(x76302,x76303),x76304),x76305))))
% 18.77/18.51 [7631]~P1(f324(x76311,x76314))+~P1(f324(x76316,x76315))+P1(f324(x76311,f324(f246(x76312,x76313),f324(f324(f247(x76312,x76313),x76314),x76315))))
% 18.77/18.51 [7685]~P1(f324(f324(x76854,x76856),x76855))+~P1(f324(f324(f326(x76851),x76856),x76853))+P1(f324(f324(f324(f45(x76851,f845(x76852,a832)),x76853),x76854),x76855))
% 18.77/18.51 [7686]~P1(f324(f324(x76864,x76866),x76865))+~P1(f324(f324(f326(x76861),x76866),x76863))+P1(f324(f324(f324(f45(x76861,f845(x76862,a832)),x76863),x76864),x76865))
% 18.77/18.51 [7720]~E(f324(f180(f839(x77201)),x77203),f324(f180(f839(x77204)),x77205))+~E(f324(f165(x77201,x77204,f324(f324(f166(x77201,x77204),x77203),x77205)),x77202),f324(f226(x77204),x77206))+P1(f324(f324(f326(x77201),x77202),f324(f157(x77201),x77203)))
% 18.77/18.51 [7994]~P1(f324(f324(f326(x79941),x79942),f324(x79945,x79946)))+~P1(f324(f324(f326(x79943),x79946),x79944))+P1(f324(f324(f326(x79941),x79942),f324(f324(f45(x79943,f845(x79941,a832)),x79944),x79945)))
% 18.77/18.51 [7995]~P1(f324(f324(f326(x79951),x79952),f324(x79955,x79956)))+~P1(f324(f324(f326(x79953),x79956),x79954))+P1(f324(f324(f326(x79951),x79952),f324(f324(f45(x79953,f845(x79951,a832)),x79954),x79955)))
% 18.77/18.51 [8036]P1(f324(f324(x80361,x80362),x80363))+~P1(f324(f324(x80364,x80362),x80363))+~P1(f324(f324(f231(f845(x80365,f845(x80366,a832))),x80364),x80361))
% 18.77/18.51 [8037]P1(f324(f324(x80371,x80372),x80373))+~P1(f324(f324(x80374,x80372),x80373))+~P1(f324(f324(f231(f845(x80375,f845(x80376,a832))),x80374),x80371))
% 18.77/18.51 [8177]P1(f324(f324(x81771,x81772),x81773))+~P1(f324(f324(f326(x81774),x81772),x81775))+~P1(f324(f324(f324(f46(x81774,f845(x81776,a832)),x81775),x81771),x81773))
% 18.77/18.51 [8178]P1(f324(f324(x81781,x81782),x81783))+~P1(f324(f324(f326(x81784),x81782),x81785))+~P1(f324(f324(f324(f46(x81784,f845(x81786,a832)),x81785),x81781),x81783))
% 18.77/18.51 [8179]P1(f324(f324(x81791,x81792),x81793))+~P1(f324(f324(f326(x81794),x81792),x81795))+~P1(f324(f324(f324(f46(x81794,f845(x81796,a832)),x81795),x81791),x81793))
% 18.77/18.51 [8313]P1(f324(f324(f326(x83131),x83132),f324(x83133,x83134)))+~P1(f324(f324(f326(x83135),x83134),x83136))+~P1(f324(f324(f326(x83131),x83132),f324(f324(f46(x83135,f845(x83131,a832)),x83136),x83133)))
% 18.77/18.51 [8314]P1(f324(f324(f326(x83141),x83142),f324(x83143,x83144)))+~P1(f324(f324(f326(x83145),x83144),x83146))+~P1(f324(f324(f326(x83141),x83142),f324(f324(f46(x83145,f845(x83141,a832)),x83146),x83143)))
% 18.77/18.51 [8315]P1(f324(f324(f326(x83151),x83152),f324(x83153,x83154)))+~P1(f324(f324(f326(x83155),x83154),x83156))+~P1(f324(f324(f326(x83151),x83152),f324(f324(f46(x83155,f845(x83151,a832)),x83156),x83153)))
% 18.77/18.51 [8561]~P16(x85614,x85615,x85616,x85611)+E(f324(x85611,x85612),f324(x85611,x85613))+~P1(f324(f324(f326(f844(x85614,x85614)),f324(f324(f247(x85614,x85614),x85612),x85613)),x85616))
% 18.77/18.51 [8592]P1(f324(f324(f231(f845(x85921,a832)),x85922),f324(x85923,x85924)))+~P1(f324(f324(f326(x85925),x85924),x85926))+~P1(f324(f324(f231(f845(x85921,a832)),x85922),f324(f324(f46(x85925,f845(x85921,a832)),x85926),x85923)))
% 18.77/18.51 [8619]~P52(x86193,x86194,f324(f279(x86194,x86193),x86195))+E(x86191,f179(f845(x86192,a832)))+E(f324(f324(f46(x86192,f845(x86193,a832)),x86191),f324(f324(f10(f845(x86194,a832),f845(x86193,a832),x86192),f278(x86194,x86193,x86195)),x86196)),f324(f278(x86194,x86193,x86195),f324(f324(f46(x86192,f845(x86194,a832)),x86191),x86196)))
% 18.77/18.51 [8691]P1(f324(f324(f326(x86911),x86912),f324(f278(x86913,x86911,x86914),x86915)))+~P1(f324(f324(f326(x86913),x86916),x86915))+~P1(f324(f324(f326(f844(x86913,x86911)),f324(f324(f247(x86913,x86911),x86916),x86912)),x86914))
% 18.77/18.51 [8692]P1(f324(f324(f326(x86921),x86922),f324(f278(x86923,x86921,x86924),x86925)))+~P1(f324(f324(f326(x86923),x86926),x86925))+~P1(f324(f324(f326(f844(x86923,x86921)),f324(f324(f247(x86923,x86921),x86926),x86922)),x86924))
% 18.77/18.51 [8963]P1(f324(f324(f231(f845(x89631,a832)),f324(f278(x89632,x89631,x89633),x89634)),f324(f278(x89632,x89631,x89635),x89636)))+~P1(f324(f324(f231(f845(x89632,a832)),x89634),x89636))+~P1(f324(f324(f231(f845(f844(x89632,x89631),a832)),x89633),x89635))
% 18.77/18.51 [9121]~P1(f324(f324(f326(x91212),x91216),x91214))+~P1(f324(f324(f231(f845(x91211,a832)),x91213),x91215))+P1(f324(f324(f231(f845(f844(x91211,x91212),a832)),f324(f324(f249(x91211,x91212),x91213),f324(f18(f845(x91212,a832),x91211),x91214))),f324(f324(f249(x91211,x91212),x91215),f324(f18(f845(x91212,a832),x91211),x91214))))
% 18.77/18.51 [9269]~E(x92693,x92695)+P1(f324(f324(f326(f844(f839(x92691),f839(x92691))),f324(f324(f247(f839(x92691),f839(x92691)),f324(f324(f139(x92691),x92692),x92693)),f324(f324(f139(x92691),x92694),x92695))),f144(x92691,x92696)))+~P1(f324(f324(f326(f844(x92691,x92691)),f324(f324(f247(x92691,x92691),x92692),x92694)),x92696))
% 18.77/18.51 [9275]~E(f324(f180(f839(x92751)),x92753),f324(f180(f839(x92751)),x92755))+P1(f324(f324(f326(f844(f839(x92751),f839(x92751))),f324(f324(f247(f839(x92751),f839(x92751)),f324(f324(f139(x92751),x92752),x92753)),f324(f324(f139(x92751),x92754),x92755))),f134(x92751,x92756)))+~P1(f324(f324(f326(f844(x92751,x92751)),f324(f324(f247(x92751,x92751),x92752),x92754)),x92756))
% 18.77/18.51 [9303]P1(f324(f324(f326(f844(x93031,x93031)),f324(f324(f247(x93031,x93031),x93032),x93033)),f324(f324(f172(f844(x93031,x93031),a832),f324(a114,x93034)),x93035)))+~P1(f324(f324(f326(f844(x93031,x93031)),f324(f324(f247(x93031,x93031),x93036),x93033)),x93035))+~P1(f324(f324(f326(f844(x93031,x93031)),f324(f324(f247(x93031,x93031),x93032),x93036)),f324(f324(f172(f844(x93031,x93031),a832),x93034),x93035)))
% 18.77/18.51 [9304]P1(f324(f324(f326(f844(x93041,x93041)),f324(f324(f247(x93041,x93041),x93042),x93043)),f324(f324(f172(f844(x93041,x93041),a832),f324(a114,x93044)),x93045)))+~P1(f324(f324(f326(f844(x93041,x93041)),f324(f324(f247(x93041,x93041),x93042),x93046)),x93045))+~P1(f324(f324(f326(f844(x93041,x93041)),f324(f324(f247(x93041,x93041),x93046),x93043)),f324(f324(f172(f844(x93041,x93041),a832),x93044),x93045)))
% 18.77/18.51 [9307]~P1(f324(f324(f326(x93074),x93075),x93076))+P1(f324(f324(f231(f845(x93071,a832)),x93072),x93073))+~P1(f324(f324(f231(f845(f844(x93071,x93074),a832)),f324(f324(f249(x93071,x93074),x93072),f324(f18(f845(x93074,a832),x93071),x93076))),f324(f324(f249(x93071,x93074),x93073),f324(f18(f845(x93074,a832),x93071),x93076))))
% 18.77/18.51 [9347]E(x93471,x93472)+~P1(f324(f324(f326(f844(f839(x93473),f839(x93473))),f324(f324(f247(f839(x93473),f839(x93473)),f324(f324(f139(x93473),x93471),x93475)),f324(f324(f139(x93473),x93472),x93476))),f134(x93473,x93474)))+P1(f324(f324(f326(f844(x93473,x93473)),f324(f324(f247(x93473,x93473),x93471),x93472)),x93474))
% 18.77/18.51 [9348]E(x93481,x93482)+~P1(f324(f324(f326(f844(f839(x93483),f839(x93483))),f324(f324(f247(f839(x93483),f839(x93483)),f324(f324(f139(x93483),x93481),x93485)),f324(f324(f139(x93483),x93482),x93486))),f136(x93483,x93484)))+P1(f324(f324(f326(f844(x93483,x93483)),f324(f324(f247(x93483,x93483),x93481),x93482)),x93484))
% 18.77/18.51 [9349]E(x93491,x93492)+~P1(f324(f324(f326(f844(f839(x93493),f839(x93493))),f324(f324(f247(f839(x93493),f839(x93493)),f324(f324(f139(x93493),x93491),x93495)),f324(f324(f139(x93493),x93492),x93496))),f144(x93493,x93494)))+P1(f324(f324(f326(f844(x93493,x93493)),f324(f324(f247(x93493,x93493),x93491),x93492)),x93494))
% 18.77/18.51 [9386]P1(f324(f324(f326(f844(f839(x93861),f839(x93861))),f324(f324(f247(f839(x93861),f839(x93861)),f324(f324(f139(x93861),x93862),x93863)),f324(f324(f139(x93861),x93864),x93865))),f145(x93861,x93866)))+~P1(f324(f324(f326(f844(f839(x93861),f839(x93861))),f324(f324(f247(f839(x93861),f839(x93861)),x93863),x93865)),f145(x93861,x93866)))+~P1(f324(f324(f326(f844(x93861,x93861)),f324(f324(f247(x93861,x93861),x93862),x93864)),x93866))
% 18.77/18.51 [9406]P1(f324(x94061,x94062))+~P1(f324(x94061,f532(x94061,x94063,x94064,x94065,x94066)))+~P1(f324(f324(f326(x94066),x94062),f324(f324(f45(x94065,f845(x94066,a832)),x94064),x94063)))
% 18.77/18.51 [9411]~P1(f324(f324(f326(f844(f839(x94111),f839(x94111))),f324(f324(f247(f839(x94111),f839(x94111)),f324(f324(f139(x94111),x94112),x94115)),f324(f324(f139(x94111),x94113),x94116))),f134(x94111,x94114)))+P1(f324(f324(f326(f844(f839(x94111),f839(x94111))),f324(f324(f247(f839(x94111),f839(x94111)),x94115),x94116)),f134(x94111,x94114)))+P1(f324(f324(f326(f844(x94111,x94111)),f324(f324(f247(x94111,x94111),x94112),x94113)),x94114))
% 18.77/18.51 [9412]~P1(f324(f324(f326(f844(f839(x94121),f839(x94121))),f324(f324(f247(f839(x94121),f839(x94121)),f324(f324(f139(x94121),x94122),x94125)),f324(f324(f139(x94121),x94123),x94126))),f136(x94121,x94124)))+P1(f324(f324(f326(f844(f839(x94121),f839(x94121))),f324(f324(f247(f839(x94121),f839(x94121)),x94125),x94126)),f136(x94121,x94124)))+P1(f324(f324(f326(f844(x94121,x94121)),f324(f324(f247(x94121,x94121),x94122),x94123)),x94124))
% 18.77/18.51 [9413]~P1(f324(f324(f326(f844(f839(x94131),f839(x94131))),f324(f324(f247(f839(x94131),f839(x94131)),f324(f324(f139(x94131),x94132),x94135)),f324(f324(f139(x94131),x94133),x94136))),f144(x94131,x94134)))+P1(f324(f324(f326(f844(f839(x94131),f839(x94131))),f324(f324(f247(f839(x94131),f839(x94131)),x94135),x94136)),f144(x94131,x94134)))+P1(f324(f324(f326(f844(x94131,x94131)),f324(f324(f247(x94131,x94131),x94132),x94133)),x94134))
% 18.77/18.51 [9492]P1(f324(x94921,x94922))+P1(f324(f324(f326(x94923),f533(x94921,x94924,x94925,x94923,x94926)),x94925))+~P1(f324(f324(f326(x94926),x94922),f324(f324(f45(x94923,f845(x94926,a832)),x94925),x94924)))
% 18.77/18.51 [9499]~E(x94992,x94994)+P1(f324(f324(f326(f844(f839(x94991),f839(x94991))),f324(f324(f247(f839(x94991),f839(x94991)),f324(f324(f125(x94991),x94992),f324(f324(f139(x94991),x94993),f115(x94991)))),f324(f324(f125(x94991),x94994),f324(f324(f139(x94991),x94995),f115(x94991))))),f144(x94991,x94996)))+~P1(f324(f324(f326(f844(x94991,x94991)),f324(f324(f247(x94991,x94991),x94993),x94995)),x94996))
% 18.77/18.51 [9579]E(x95791,x95792)+~P1(f324(f324(f326(f844(f839(x95793),f839(x95793))),f324(f324(f247(f839(x95793),f839(x95793)),f324(f324(f125(x95793),x95795),f324(f324(f139(x95793),x95791),f115(x95793)))),f324(f324(f125(x95793),x95796),f324(f324(f139(x95793),x95792),f115(x95793))))),f144(x95793,x95794)))+P1(f324(f324(f326(f844(x95793,x95793)),f324(f324(f247(x95793,x95793),x95791),x95792)),x95794))
% 18.77/18.51 [9606]~P1(f324(f324(f326(f844(f839(x96061),f839(x96061))),f324(f324(f247(f839(x96061),f839(x96061)),f324(f324(f125(x96061),x96065),f324(f324(f139(x96061),x96062),f115(x96061)))),f324(f324(f125(x96061),x96066),f324(f324(f139(x96061),x96063),f115(x96061))))),f144(x96061,x96064)))+P1(f324(f324(f326(f844(f839(x96061),f839(x96061))),f324(f324(f247(f839(x96061),f839(x96061)),x96065),x96066)),f144(x96061,x96064)))+P1(f324(f324(f326(f844(x96061,x96061)),f324(f324(f247(x96061,x96061),x96062),x96063)),x96064))
% 18.77/18.51 [9620]P1(f324(x96201,x96202))+P1(f324(f324(f326(x96203),f532(x96201,x96204,x96205,x96206,x96203)),f324(x96204,f533(x96201,x96204,x96205,x96206,x96203))))+~P1(f324(f324(f326(x96203),x96202),f324(f324(f45(x96206,f845(x96203,a832)),x96205),x96204)))
% 18.77/18.51 [8705]~P20(x87053,x87054,x87051)+~P1(f324(f64(x87053),x87056))+E(f324(f324(x87051,x87052),f324(f324(f67(x87053,x87054,x87051),x87055),f324(f324(f3(f845(x87053,a832)),x87056),f324(f324(f303(x87053),x87052),f179(f845(x87053,a832)))))),f324(f324(f67(x87053,x87054,x87051),x87055),f324(f324(f303(x87053),x87052),x87056)))
% 18.77/18.51 [8804]~E(f324(f165(x88041,x88042,x88044),x88045),f324(f226(x88042),x88046))+~P1(f324(f324(x88043,x88045),x88046))+E(f324(f165(x88041,x88042,f324(f126(f844(x88041,x88042),f324(f252(x88041,x88042,a832),x88043)),x88044)),x88045),f324(f226(x88042),x88046))
% 18.77/18.51 [8969]~P1(f324(f324(f326(x89695),x89693),x89696))+P1(f324(f324(f231(f845(x89691,a832)),f324(x89692,x89693)),x89694))+~P1(f324(f324(f231(f845(x89691,a832)),f324(f324(f45(x89695,f845(x89691,a832)),x89696),x89692)),x89694))
% 18.77/18.51 [9554]~P12(x95541,x95545,x95544)+P1(f324(f324(f326(f844(x95541,x95541)),f324(f324(f247(x95541,x95541),x95542),x95543)),x95544))+~P1(f324(f324(f326(x95541),x95546),f324(f324(f104(f845(x95541,a832)),f324(f278(x95541,x95541,x95544),f324(f324(f303(x95541),x95542),f179(f845(x95541,a832))))),f324(f278(x95541,x95541,x95544),f324(f324(f303(x95541),x95543),f179(f845(x95541,a832)))))))
% 18.77/18.51 [8471]~P126(x84712)+~E(f324(f324(f82(x84712),f324(f324(f83(x84712),x84714),x84715)),x84711),f324(f324(f82(x84712),f324(f324(f83(x84712),x84713),x84715)),x84716))+E(x84711,f324(f324(f82(x84712),f324(f324(f83(x84712),f324(f324(f3(x84712),x84713),x84714)),x84715)),x84716))
% 18.77/18.51 [8472]~P126(x84721)+~E(f324(f324(f82(x84721),f324(f324(f83(x84721),x84722),x84724)),x84725),f324(f324(f82(x84721),f324(f324(f83(x84721),x84723),x84724)),x84726))+E(f324(f324(f82(x84721),f324(f324(f83(x84721),f324(f324(f3(x84721),x84722),x84723)),x84724)),x84725),x84726)
% 18.77/18.51 [8622]~P126(x86221)+E(f324(f324(f82(x86221),f324(f324(f83(x86221),x86222),x86223)),x86224),f324(f324(f82(x86221),f324(f324(f83(x86221),x86225),x86223)),x86226))+~E(x86226,f324(f324(f82(x86221),f324(f324(f83(x86221),f324(f324(f3(x86221),x86222),x86225)),x86223)),x86224))
% 18.77/18.51 [8623]~P126(x86231)+E(f324(f324(f82(x86231),f324(f324(f83(x86231),x86232),x86233)),x86234),f324(f324(f82(x86231),f324(f324(f83(x86231),x86235),x86233)),x86236))+~E(f324(f324(f82(x86231),f324(f324(f83(x86231),f324(f324(f3(x86231),x86232),x86235)),x86233)),x86234),x86236)
% 18.77/18.51 [8915]~P1(f324(f324(x89154,x89155),x89156))+~P1(f324(f324(x89153,x89155),x89156))+P1(f324(f324(f324(f324(f104(f845(x89151,f845(x89152,a832))),x89153),x89154),x89155),x89156))
% 18.77/18.51 [9140]P1(f324(f324(x91401,x91402),x91403))+P1(f324(f324(x91404,x91402),x91403))+~P1(f324(f324(f324(f324(f103(f845(x91405,f845(x91406,a832))),x91404),x91401),x91402),x91403))
% 18.77/18.51 [9299]~E(f324(f180(f839(x92991)),x92995),f324(f180(f839(x92992)),x92996))+E(f169(x92991,x92992,f171(x92991,x92992,x92993,f324(f324(f3(f845(x92991,a832)),x92994),f324(f157(x92991),x92995))),f165(x92991,x92992,f324(f154(f844(x92991,x92992)),f324(f324(f166(x92991,x92992),x92995),x92996)))),f171(x92991,x92992,f169(x92991,x92992,x92993,f165(x92991,x92992,f324(f154(f844(x92991,x92992)),f324(f324(f166(x92991,x92992),x92995),x92996)))),x92994))+~P1(f324(f324(f231(f845(x92991,a832)),f324(f157(x92991),x92995)),x92994))
% 18.77/18.51 [9428]~P128(x94281)+~P1(f324(f324(f232(x94281),f324(f324(f82(x94281),f324(f324(f83(x94281),x94284),x94285)),x94282)),f324(f324(f82(x94281),f324(f324(f83(x94281),x94283),x94285)),x94286)))+P1(f324(f324(f232(x94281),x94282),f324(f324(f82(x94281),f324(f324(f83(x94281),f324(f324(f3(x94281),x94283),x94284)),x94285)),x94286)))
% 18.77/18.51 [9429]~P128(x94291)+~P1(f324(f324(f231(x94291),f324(f324(f82(x94291),f324(f324(f83(x94291),x94294),x94295)),x94292)),f324(f324(f82(x94291),f324(f324(f83(x94291),x94293),x94295)),x94296)))+P1(f324(f324(f231(x94291),x94292),f324(f324(f82(x94291),f324(f324(f83(x94291),f324(f324(f3(x94291),x94293),x94294)),x94295)),x94296)))
% 18.77/18.51 [9448]~P128(x94481)+P1(f324(f324(f232(x94481),f324(f324(f82(x94481),f324(f324(f83(x94481),x94482),x94483)),x94484)),f324(f324(f82(x94481),f324(f324(f83(x94481),x94485),x94483)),x94486)))+~P1(f324(f324(f232(x94481),x94484),f324(f324(f82(x94481),f324(f324(f83(x94481),f324(f324(f3(x94481),x94485),x94482)),x94483)),x94486)))
% 18.77/18.51 [9449]~P128(x94491)+P1(f324(f324(f231(x94491),f324(f324(f82(x94491),f324(f324(f83(x94491),x94492),x94493)),x94494)),f324(f324(f82(x94491),f324(f324(f83(x94491),x94495),x94493)),x94496)))+~P1(f324(f324(f231(x94491),x94494),f324(f324(f82(x94491),f324(f324(f83(x94491),f324(f324(f3(x94491),x94495),x94492)),x94493)),x94496)))
% 18.77/18.51 [9547]~P128(x95471)+~P1(f324(f324(f232(x95471),f324(f324(f82(x95471),f324(f324(f83(x95471),x95472),x95474)),x95475)),f324(f324(f82(x95471),f324(f324(f83(x95471),x95473),x95474)),x95476)))+P1(f324(f324(f232(x95471),f324(f324(f82(x95471),f324(f324(f83(x95471),f324(f324(f3(x95471),x95472),x95473)),x95474)),x95475)),x95476))
% 18.77/18.51 [9548]~P128(x95481)+~P1(f324(f324(f231(x95481),f324(f324(f82(x95481),f324(f324(f83(x95481),x95482),x95484)),x95485)),f324(f324(f82(x95481),f324(f324(f83(x95481),x95483),x95484)),x95486)))+P1(f324(f324(f231(x95481),f324(f324(f82(x95481),f324(f324(f83(x95481),f324(f324(f3(x95481),x95482),x95483)),x95484)),x95485)),x95486))
% 18.77/18.51 [9590]~P128(x95901)+P1(f324(f324(f232(x95901),f324(f324(f82(x95901),f324(f324(f83(x95901),x95902),x95903)),x95904)),f324(f324(f82(x95901),f324(f324(f83(x95901),x95905),x95903)),x95906)))+~P1(f324(f324(f232(x95901),f324(f324(f82(x95901),f324(f324(f83(x95901),f324(f324(f3(x95901),x95902),x95905)),x95903)),x95904)),x95906))
% 18.77/18.51 [9591]~P128(x95911)+P1(f324(f324(f231(x95911),f324(f324(f82(x95911),f324(f324(f83(x95911),x95912),x95913)),x95914)),f324(f324(f82(x95911),f324(f324(f83(x95911),x95915),x95913)),x95916)))+~P1(f324(f324(f231(x95911),f324(f324(f82(x95911),f324(f324(f83(x95911),f324(f324(f3(x95911),x95912),x95915)),x95913)),x95914)),x95916))
% 18.77/18.51 [9762]~P67(x97622)+~P1(f324(f64(x97621),x97626))+E(f324(f324(f8(x97621,x97622),f324(f324(f20(x97621,x97622,x97622),f324(f324(f20(x97621,x97622,f845(x97622,x97622)),f324(f324(f10(a832,f845(x97622,f845(x97622,x97622)),x97621),f98(x97622)),x97623)),x97624)),x97625)),x97626),f324(f324(f82(x97622),f324(f324(f8(x97621,x97622),x97624),f324(f324(f104(f845(x97621,a832)),x97626),f324(f257(x97621),x97623)))),f324(f324(f8(x97621,x97622),x97625),f324(f324(f104(f845(x97621,a832)),x97626),f324(f81(f845(x97621,a832)),f324(f257(x97621),x97623))))))
% 18.77/18.51 [9825]P1(f324(f324(f326(x98252),x98254),x98256))+P1(f324(f324(f326(x98252),x98255),x98256))+E(f324(f305(x98251,x98252,f324(f324(f9(x98251,x98252,x98252),f324(f324(f9(x98251,x98252,f845(x98252,x98252)),f324(f324(f10(a832,f845(x98252,f845(x98252,x98252)),x98251),f98(x98252)),f324(f324(f9(x98251,f845(x98251,a832),a832),f326(x98251)),x98253))),x98254)),x98255)),x98256),f179(f845(x98251,a832)))
% 18.77/18.51 [9826]P1(f324(f324(f326(x98262),x98265),x98266))+~P1(f324(f324(f326(x98262),x98264),x98266))+E(f324(f305(x98261,x98262,f324(f324(f9(x98261,x98262,x98262),f324(f324(f9(x98261,x98262,f845(x98262,x98262)),f324(f324(f10(a832,f845(x98262,f845(x98262,x98262)),x98261),f98(x98262)),f324(f324(f9(x98261,f845(x98261,a832),a832),f326(x98261)),x98263))),x98264)),x98265)),x98266),x98263)
% 18.77/18.51 [9827]P1(f324(f324(f326(x98272),x98274),x98276))+~P1(f324(f324(f326(x98272),x98275),x98276))+E(f324(f305(x98271,x98272,f324(f324(f9(x98271,x98272,x98272),f324(f324(f9(x98271,x98272,f845(x98272,x98272)),f324(f324(f10(a832,f845(x98272,f845(x98272,x98272)),x98271),f98(x98272)),f324(f324(f9(x98271,f845(x98271,a832),a832),f326(x98271)),x98273))),x98274)),x98275)),x98276),f324(f81(f845(x98271,a832)),x98273))
% 18.77/18.51 [9828]~P1(f324(f324(f326(x98282),x98284),x98286))+~P1(f324(f324(f326(x98282),x98285),x98286))+E(f324(f305(x98281,x98282,f324(f324(f9(x98281,x98282,x98282),f324(f324(f9(x98281,x98282,f845(x98282,x98282)),f324(f324(f10(a832,f845(x98282,f845(x98282,x98282)),x98281),f98(x98282)),f324(f324(f9(x98281,f845(x98281,a832),a832),f326(x98281)),x98283))),x98284)),x98285)),x98286),f238(f845(x98281,a832)))
% 18.77/18.51 [9960]P28(x99601,x99602,f324(f324(f303(f837(x99601)),f324(f324(f324(f93(x99601),f324(x99603,x99604)),f324(a27,x99604)),f324(x99605,x99604))),f179(f845(f837(x99601),a832))))+~P1(f324(f324(f326(a834),x99604),x99606))+~P28(x99601,f324(f324(f103(f845(f837(x99601),a832)),x99602),f324(f304(a834,f837(x99601),f324(f324(f20(a834,f845(x99601,f845(a835,a832)),f837(x99601)),f324(f324(f20(a834,a833,f845(f845(x99601,f845(a835,a832)),f837(x99601))),f324(f324(f10(f845(x99601,f845(a835,a832)),f845(a833,f845(f845(x99601,f845(a835,a832)),f837(x99601))),a834),f93(x99601)),x99603)),a27)),x99605)),x99606)),f324(f304(a834,f837(x99601),f324(f324(f20(a834,f845(x99601,f845(a835,a832)),f837(x99601)),f324(f324(f20(a834,a833,f845(f845(x99601,f845(a835,a832)),f837(x99601))),f324(f324(f10(f845(x99601,f845(a835,a832)),f845(a833,f845(f845(x99601,f845(a835,a832)),f837(x99601))),a834),f93(x99601)),x99603)),f324(f324(f10(f842(a833),a833,a834),f230(a833)),a30))),x99605)),x99606))
% 18.77/18.51 [8496]E(x84961,x84962)+~P54(x84964,x84965,x84963,x84966,x84967)+~E(f324(x84963,x84961),f324(x84963,x84962))
% 18.77/18.51 [6861]E(f324(f228(f842(x68611),x68612,f182(x68611),x68613),f324(x68614,x68615)),f324(f226(x68611),x68616))+~E(f324(x68614,x68615),f324(f226(x68612),x68617))+~E(f324(x68613,x68617),f324(f226(x68611),x68616))
% 18.77/18.51 [8517]~P15(x85176,x85175,x85177,x85174,x85171)+E(f324(f324(x85171,x85172),x85173),x85174)+P1(f324(f64(x85175),x85173))
% 18.77/18.51 [8518]~P15(x85186,x85185,x85187,x85184,x85181)+E(f324(f324(x85181,x85182),x85183),x85184)+P1(f324(f64(x85185),x85183))
% 18.77/18.51 [9294]P41(x92941,x92942,x92943,x92944,x92945,f324(f324(x92943,x92946),x92947))+~E(f324(f324(x92943,x92946),x92947),x92944)+~E(x92945,f179(f845(x92941,a832)))
% 18.77/18.51 [9469]~P1(f324(x94696,x94693))+~P1(f324(f324(f326(f844(x94692,x94692)),f324(f324(f247(x94692,x94692),x94694),x94695)),f324(x94697,x94693)))+P1(f324(f324(f326(f844(f844(x94691,x94692),f844(x94691,x94692))),f324(f324(f247(f844(x94691,x94692),f844(x94691,x94692)),f324(f324(f247(x94691,x94692),x94693),x94694)),f324(f324(f247(x94691,x94692),x94693),x94695))),f276(x94691,x94692,x94696,x94697)))
% 18.77/18.51 [9647]~P29(x96473,x96471,x96474,f238(f845(x96473,a832)))+E(f324(f165(x96471,x96472,f324(f324(f141(f844(x96473,x96472),f844(x96471,x96472)),f324(f252(x96473,x96472,f844(x96471,x96472)),f324(f324(f10(x96471,f845(x96472,f844(x96471,x96472)),x96473),f247(x96471,x96472)),x96474))),x96475)),f324(x96474,x96476)),f324(f226(x96472),x96477))+~E(f324(f165(x96473,x96472,x96475),x96476),f324(f226(x96472),x96477))
% 18.77/18.51 [9881]~P41(x98812,x98817,x98813,x98816,x98811,f324(f324(x98813,x98815),x98814))+E(f324(f324(x98813,f404(x98814,x98815,x98811,x98816,x98813,x98817,x98812)),f405(x98814,x98815,x98811,x98816,x98813,x98817,x98812)),f324(f324(x98813,x98815),x98814))+E(x98811,f179(f845(x98812,a832)))
% 18.77/18.51 [9882]~P41(x98827,x98826,x98821,x98824,x98825,f324(f324(x98821,x98822),x98823))+E(f324(f324(x98821,f404(x98823,x98822,x98825,x98824,x98821,x98826,x98827)),f405(x98823,x98822,x98825,x98824,x98821,x98826,x98827)),f324(f324(x98821,x98822),x98823))+E(f324(f324(x98821,x98822),x98823),x98824)
% 18.77/18.51 [9535]~P1(f324(f69(x95351,x95354,x95355,x95356,x95353),x95357))+P1(f324(f69(x95351,x95354,x95355,x95356,f324(f324(f303(x95351),x95352),x95353)),f324(f324(x95355,x95352),x95357)))+P1(f324(f324(f326(x95351),x95352),x95353))
% 18.77/18.51 [9905]~P41(x99052,x99057,x99056,x99055,x99051,f324(f324(x99056,x99054),x99053))+E(x99051,f179(f845(x99052,a832)))+P1(f324(f324(f326(x99052),f404(x99053,x99054,x99051,x99055,x99056,x99057,x99052)),x99051))
% 18.77/18.51 [9906]~P41(x99065,x99067,x99061,x99064,x99066,f324(f324(x99061,x99062),x99063))+E(f324(f324(x99061,x99062),x99063),x99064)+P1(f324(f324(f326(x99065),f404(x99063,x99062,x99066,x99064,x99061,x99067,x99065)),x99066))
% 18.77/18.51 [6637]~E(x66375,x66377)+~E(x66376,x66374)+E(f324(f324(f324(f324(f74(x66371,f842(x66372)),x66373),x66374),f324(f226(x66372),x66375)),x66376),f324(f226(x66372),x66377))
% 18.77/18.51 [6775]E(x67751,x67752)+~E(f324(x67755,x67751),f324(f226(x67754),x67757))+E(f324(f324(f324(f324(f74(x67753,f842(x67754)),x67755),x67752),f324(f226(x67754),x67756)),x67751),f324(f226(x67754),x67757))
% 18.77/18.51 [7522]E(x75221,x75222)+~E(x75223,x75224)+~E(f324(f324(f324(f324(f74(x75225,f842(x75226)),x75227),x75224),f324(f226(x75226),x75221)),x75223),f324(f226(x75226),x75222))
% 18.77/18.51 [7587]E(x75871,x75872)+E(f324(x75873,x75874),f324(f226(x75875),x75871))+~E(f324(f324(f324(f324(f74(x75876,f842(x75875)),x75873),x75877),f324(f226(x75875),x75872)),x75874),f324(f226(x75875),x75871))
% 18.77/18.51 [7588]E(x75881,x75882)+E(f324(x75883,x75881),f324(f226(x75884),x75885))+~E(f324(f324(f324(f324(f74(x75886,f842(x75884)),x75883),x75882),f324(f226(x75884),x75887)),x75881),f324(f226(x75884),x75885))
% 18.77/18.51 [8726]~P25(x87264,x87265,x87266,x87267,x87261)+~P1(f324(f64(x87265),x87263))+E(f324(f324(x87261,x87262),x87263),f324(f324(f324(f68(x87264,x87265,x87266),x87262),x87267),x87263))
% 18.77/18.51 [8727]~P15(x87274,x87275,x87276,x87277,x87271)+~P1(f324(f64(x87275),x87273))+E(f324(f324(x87271,x87272),x87273),f324(f324(f324(f68(x87274,x87275,x87276),x87272),x87277),x87273))
% 18.77/18.51 [9262]~P28(x92621,x92622,f324(f324(f303(f837(x92621)),f324(f324(f324(f93(x92621),x92623),x92624),x92627)),f179(f845(f837(x92621),a832))))+P28(x92621,x92622,f324(f324(f303(f837(x92621)),f324(f324(f324(f93(x92621),x92623),f36(x92624,x92625)),x92626)),f179(f845(f837(x92621),a832))))+~P28(x92621,x92622,f324(f324(f303(f837(x92621)),f324(f324(f324(f93(x92621),x92627),x92625),x92626)),f179(f845(f837(x92621),a832))))
% 18.77/18.51 [9443]~P27(x94433,x94434,x94435,x94437,x94436,x94431)+~P1(f324(f64(x94434),x94432))+E(f324(x94431,x94432),f324(f324(f324(f68(x94433,x94434,x94435),x94436),x94437),x94432))
% 18.77/18.51 [9585]P41(x95851,x95852,x95853,x95854,x95855,f324(f324(x95853,x95856),x95857))+~P41(x95851,x95852,x95853,x95854,f324(f324(f3(f845(x95851,a832)),x95855),f324(f324(f303(x95851),x95856),f179(f845(x95851,a832)))),x95857)+~P1(f324(f324(f326(x95851),x95856),x95855))
% 18.77/18.51 [9856]~P28(x98561,x98562,f324(f324(f303(f837(x98561)),f324(f324(f324(f93(x98561),f94(x98561,x98563,x98564)),x98565),x98567)),f179(f845(f837(x98561),a832))))+P28(x98561,x98562,f324(f324(f303(f837(x98561)),f324(f324(f324(f93(x98561),x98563),f33(x98564,x98565,x98566)),x98567)),f179(f845(f837(x98561),a832))))+~P28(x98561,x98562,f324(f324(f303(f837(x98561)),f324(f324(f324(f93(x98561),f94(x98561,x98563,f324(f75(a832,a832,a835,a320),x98564))),x98566),x98567)),f179(f845(f837(x98561),a832))))
% 18.77/18.51 [9922]P1(f324(f324(x99227,f825(x99224,x99225,x99221,x99226,x99223,x99222,x99227)),f826(x99224,x99225,x99221,x99226,x99223,x99222,x99227)))+~P1(f324(f324(x99227,f324(f251(x99222,x99223),x99226)),f324(f246(x99222,x99223),x99226)))+P1(f324(x99221,f324(f324(f252(x99222,x99223,x99224),x99225),x99226)))
% 18.77/18.51 [9931]~P41(x99312,x99313,x99314,x99315,x99311,f324(f324(x99314,x99317),x99316))+P41(x99312,x99313,x99314,x99315,f324(f324(f3(f845(x99312,a832)),x99311),f324(f324(f303(x99312),f404(x99316,x99317,x99311,x99315,x99314,x99313,x99312)),f179(f845(x99312,a832)))),f405(x99316,x99317,x99311,x99315,x99314,x99313,x99312))+E(x99311,f179(f845(x99312,a832)))
% 18.77/18.51 [9932]~P41(x99325,x99326,x99321,x99324,x99327,f324(f324(x99321,x99322),x99323))+P41(x99325,x99326,x99321,x99324,f324(f324(f3(f845(x99325,a832)),x99327),f324(f324(f303(x99325),f404(x99323,x99322,x99327,x99324,x99321,x99326,x99325)),f179(f845(x99325,a832)))),f405(x99323,x99322,x99327,x99324,x99321,x99326,x99325))+E(f324(f324(x99321,x99322),x99323),x99324)
% 18.77/18.51 [9953]~P1(f324(x99531,f324(f324(x99535,f826(x99534,x99535,x99531,x99536,x99533,x99532,x99537)),f825(x99534,x99535,x99531,x99536,x99533,x99532,x99537))))+~P1(f324(f324(x99537,f324(f251(x99532,x99533),x99536)),f324(f246(x99532,x99533),x99536)))+P1(f324(x99531,f324(f324(f252(x99532,x99533,x99534),x99535),x99536)))
% 18.77/18.51 [9283]P1(f324(f324(f231(f845(f844(x92831,x92832),a832)),f324(f324(f282(x92831,x92833,x92832),x92834),x92835)),f324(f324(f282(x92831,x92833,x92832),x92836),x92837)))+~P1(f324(f324(f231(f845(f844(x92833,x92832),a832)),x92835),x92837))+~P1(f324(f324(f231(f845(f844(x92831,x92833),a832)),x92834),x92836))
% 18.77/18.51 [9596]~P1(f324(f324(f326(x95961),x95966),x95965))+P1(f324(f69(x95961,x95962,x95963,x95964,x95965),f324(f324(x95963,x95966),x95967)))+~P1(f324(f69(x95961,x95962,x95963,x95964,f324(f324(f3(f845(x95961,a832)),x95965),f324(f324(f303(x95961),x95966),f179(f845(x95961,a832))))),x95967))
% 18.77/18.51 [9189]E(f169(x91891,x91892,x91893,f165(x91891,x91892,f324(f154(f844(x91891,x91892)),f324(f324(f166(x91891,x91892),x91894),f324(f324(f146(x91892,x91895),x91896),x91897))))),f169(x91891,x91892,x91893,f165(x91891,x91892,f324(f154(f844(x91891,x91892)),f324(f324(f166(x91891,x91892),x91894),x91895)))))+~P1(f324(f324(f232(a838),x91896),f324(f180(f839(x91892)),x91895)))+~P1(f324(f324(f231(a838),f324(f180(f839(x91891)),x91894)),x91896))
% 18.77/18.51 [9986]~P135(x99861)+~P29(f844(x99862,x99863),x99861,f324(f252(x99862,x99863,x99861),f324(f324(f9(x99862,f845(x99863,x99861),f845(x99863,x99861)),f324(f324(f10(f845(x99861,x99861),f845(f845(x99863,x99861),f845(x99863,x99861)),x99862),f10(x99861,x99861,x99863)),f324(f324(f10(x99861,f845(x99861,x99861),x99862),f83(x99861)),x99864))),x99865)),f324(f324(f249(x99862,x99863),x99866),f324(f18(f845(x99863,a832),x99862),x99867)))+E(f324(f324(f8(x99861,x99861),f37(x99861)),f324(f257(x99861),f324(f324(f10(f845(x99862,a832),a832,x99861),f89(x99862)),f324(f324(f10(f845(x99862,f845(x99863,a832)),f845(x99862,a832),x99861),f324(f10(f845(x99863,a832),a832,x99862),f89(x99863))),f324(f324(f9(x99861,f845(x99862,f845(x99863,a832)),f845(x99862,f845(x99863,a832))),f324(f324(f10(f845(x99862,f845(f845(x99863,a832),f845(x99863,a832))),f845(f845(x99862,f845(x99863,a832)),f845(x99862,f845(x99863,a832))),x99861),f20(x99862,f845(x99863,a832),f845(x99863,a832))),f324(f324(f10(f845(x99862,f845(x99863,f845(a832,a832))),f845(x99862,f845(f845(x99863,a832),f845(x99863,a832))),x99861),f324(f10(f845(x99863,f845(a832,a832)),f845(f845(x99863,a832),f845(x99863,a832)),x99862),f20(x99863,a832,a832))),f324(f324(f10(f845(x99862,f845(x99863,a832)),f845(x99862,f845(x99863,f845(a832,a832))),x99861),f324(f10(f845(x99863,a832),f845(x99863,f845(a832,a832)),x99862),f324(f10(a832,f845(a832,a832),x99863),a322))),f324(f324(f9(x99861,f845(x99862,f845(x99863,x99861)),f845(x99862,f845(x99863,a832))),f324(f324(f10(f845(f845(x99863,x99861),f845(x99863,a832)),f845(f845(x99862,f845(x99863,x99861)),f845(x99862,f845(x99863,a832))),x99861),f10(f845(x99863,x99861),f845(x99863,a832),x99862)),f324(f324(f10(f845(x99861,a832),f845(f845(x99863,x99861),f845(x99863,a832)),x99861),f10(x99861,a832,x99863)),a321))),f324(f324(f9(x99862,f845(x99863,x99861),f845(x99863,x99861)),f324(f324(f10(f845(x99861,x99861),f845(f845(x99863,x99861),f845(x99863,x99861)),x99862),f10(x99861,x99861,x99863)),f324(f324(f10(x99861,f845(x99861,x99861),x99862),f83(x99861)),x99864))),x99865)))))),f324(f324(f9(x99862,f845(x99863,a832),f845(x99863,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x99863,a832),f845(x99863,a832)),x99862),f10(a832,a832,x99863)),f324(f324(f10(a832,f845(a832,a832),x99862),a322),f324(f324(f9(x99862,f845(x99862,a832),a832),f326(x99862)),x99866)))),f324(f324(f9(x99863,f845(x99863,a832),a832),f326(x99863)),x99867))))))),f324(f324(f83(x99861),f324(f324(f8(x99862,x99861),x99864),x99866)),f324(f324(f8(x99863,x99861),x99865),x99867)))
% 18.77/18.51 [9440]~P1(f324(f324(x94404,x94406),x94408))+~P1(f324(f324(x94405,x94408),x94407))+P1(f324(f324(f248(x94401,x94402,x94403,x94404,x94405),x94406),x94407))
% 18.77/18.51 [9441]~P1(f324(f324(x94414,x94416),x94418))+~P1(f324(f324(x94415,x94418),x94417))+P1(f324(f324(f248(x94411,x94412,x94413,x94414,x94415),x94416),x94417))
% 18.77/18.51 [9065]~P23(x90658,x90651,x90653,x90655)+~P1(f324(f64(x90658),x90656))+E(f324(f75(x90651,x90651,x90652,f324(x90653,x90654)),f324(f75(x90651,x90651,x90652,f324(x90655,x90656)),x90657)),f324(f75(x90651,x90651,x90652,f324(x90655,x90656)),f324(f75(x90651,x90651,x90652,f324(x90653,x90654)),x90657)))
% 18.77/18.51 [9433]~P26(x94337,x94332,x94335,x94338,x94336,x94331)+~P1(f324(f64(x94332),x94334))+E(f324(x94331,f324(f324(f303(x94332),x94333),x94334)),f324(f324(x94335,f324(x94336,x94333)),f324(x94331,x94334)))
% 18.77/18.51 [9545]~P29(x95452,x95454,x95456,x95458)+~P29(x95451,x95453,x95455,x95457)+P29(f844(x95451,x95452),f844(x95453,x95454),f253(x95451,x95453,x95452,x95454,x95455,x95456),f324(f324(f249(x95451,x95452),x95457),f324(f18(f845(x95452,a832),x95451),x95458)))
% 18.77/18.51 [9225]P1(f324(f324(f326(f844(x92251,x92252)),f324(f324(f247(x92251,x92252),x92253),x92254)),f324(f324(f282(x92251,x92255,x92252),x92256),x92257)))+~P1(f324(f324(f326(f844(x92251,x92255)),f324(f324(f247(x92251,x92255),x92253),x92258)),x92256))+~P1(f324(f324(f326(f844(x92255,x92252)),f324(f324(f247(x92255,x92252),x92258),x92254)),x92257))
% 18.77/18.51 [9416]~P1(f324(f324(f231(f845(f844(x94163,x94162),a832)),x94165),f324(f324(f249(x94163,x94162),x94168),f324(f18(f845(x94162,a832),x94163),x94167))))+~P1(f324(f324(f231(f845(f844(x94161,x94163),a832)),x94164),f324(f324(f249(x94161,x94163),x94166),f324(f18(f845(x94163,a832),x94161),x94168))))+P1(f324(f324(f231(f845(f844(x94161,x94162),a832)),f324(f324(f282(x94161,x94163,x94162),x94164),x94165)),f324(f324(f249(x94161,x94162),x94166),f324(f18(f845(x94162,a832),x94161),x94167))))
% 18.77/18.51 [9464]~E(x94643,x94645)+P1(f324(f324(f326(f844(f844(x94641,x94642),f844(x94641,x94642))),f324(f324(f247(f844(x94641,x94642),f844(x94641,x94642)),f324(f324(f247(x94641,x94642),x94643),x94644)),f324(f324(f247(x94641,x94642),x94645),x94646))),f318(x94641,x94642,x94647,x94648)))+~P1(f324(f324(f326(f844(x94642,x94642)),f324(f324(f247(x94642,x94642),x94644),x94646)),x94648))
% 18.77/18.51 [9564]E(x95641,x95642)+~P1(f324(f324(f326(f844(f844(x95643,x95645),f844(x95643,x95645))),f324(f324(f247(f844(x95643,x95645),f844(x95643,x95645)),f324(f324(f247(x95643,x95645),x95641),x95646)),f324(f324(f247(x95643,x95645),x95642),x95647))),f318(x95643,x95645,x95644,x95648)))+P1(f324(f324(f326(f844(x95643,x95643)),f324(f324(f247(x95643,x95643),x95641),x95642)),x95644))
% 18.77/18.51 [9578]~P1(f324(f324(f326(f844(f844(x95781,x95785),f844(x95781,x95785))),f324(f324(f247(f844(x95781,x95785),f844(x95781,x95785)),f324(f324(f247(x95781,x95785),x95782),x95786)),f324(f324(f247(x95781,x95785),x95783),x95787))),f318(x95781,x95785,x95784,x95788)))+P1(f324(f324(f326(f844(x95781,x95781)),f324(f324(f247(x95781,x95781),x95782),x95783)),x95784))+P1(f324(f324(f326(f844(x95785,x95785)),f324(f324(f247(x95785,x95785),x95786),x95787)),x95788))
% 18.77/18.51 [9493]~P27(x94937,x94935,x94931,x94938,x94932,x94934)+~P1(f324(f64(x94935),x94936))+E(f324(f324(x94931,f324(x94932,x94933)),f324(x94934,f324(f324(f3(f845(x94935,a832)),x94936),f324(f324(f303(x94935),x94933),f179(f845(x94935,a832)))))),f324(x94934,f324(f324(f303(x94935),x94933),x94936)))
% 18.77/18.51 [9025]~P1(f324(f324(f324(x90255,x90258),x90256),x90257))+~P1(f324(f324(f326(x90251),x90258),x90254))+P1(f324(f324(f324(f324(f45(x90251,f845(x90252,f845(x90253,a832))),x90254),x90255),x90256),x90257))
% 18.77/18.51 [9026]~P1(f324(f324(f324(x90265,x90268),x90266),x90267))+~P1(f324(f324(f326(x90261),x90268),x90264))+P1(f324(f324(f324(f324(f45(x90261,f845(x90262,f845(x90263,a832))),x90264),x90265),x90266),x90267))
% 18.77/18.51 [9211]P1(f324(f324(f324(x92111,x92112),x92113),x92114))+~P1(f324(f324(f326(x92115),x92112),x92116))+~P1(f324(f324(f324(f324(f46(x92115,f845(x92117,f845(x92118,a832))),x92116),x92111),x92113),x92114))
% 18.77/18.51 [9212]P1(f324(f324(f324(x92121,x92122),x92123),x92124))+~P1(f324(f324(f326(x92125),x92122),x92126))+~P1(f324(f324(f324(f324(f46(x92125,f845(x92127,f845(x92128,a832))),x92126),x92121),x92123),x92124))
% 18.77/18.51 [9213]P1(f324(f324(f324(x92131,x92132),x92133),x92134))+~P1(f324(f324(f326(x92135),x92132),x92136))+~P1(f324(f324(f324(f324(f46(x92135,f845(x92137,f845(x92138,a832))),x92136),x92131),x92133),x92134))
% 18.77/18.51 [9407]~P25(x94073,x94072,x94074,x94078,x94071)+~P1(f324(f64(x94072),x94077))+E(f324(f324(x94071,f324(f324(f20(x94072,x94073,x94073),f324(f324(f10(x94073,f845(x94073,x94073),x94072),x94074),x94075)),x94076)),x94077),f324(f324(x94074,f324(f324(x94071,x94075),x94077)),f324(f324(x94071,x94076),x94077)))
% 18.77/18.51 [9655]~E(f324(f304(x96552,x96554,x96556),x96558),x965510)+~E(f324(f304(x96551,x96553,x96555),x96557),x96559)+E(f324(f304(f844(x96551,x96552),f844(x96553,x96554),f253(x96551,x96553,x96552,x96554,x96555,x96556)),f324(f324(f249(x96551,x96552),x96557),f324(f18(f845(x96552,a832),x96551),x96558))),f324(f324(f249(x96553,x96554),x96559),f324(f18(f845(x96554,a832),x96553),x965510)))
% 18.77/18.51 [4663]~P86(x46632)+~P18(x46632,x46631)+P18(x46632,f116(x46632,x46631))+E(x46631,f115(x46632))
% 18.77/18.51 [4894]~P9(x48942)+E(f12(x48942,x48941),f44(x48942,x48941))+E(x48941,f179(f845(x48942,a832)))+~P1(f324(f64(x48942),x48941))
% 18.77/18.51 [4895]~P9(x48952)+E(f15(x48952,x48951),f43(x48952,x48951))+E(x48951,f179(f845(x48952,a832)))+~P1(f324(f64(x48952),x48951))
% 18.77/18.51 [5840]~P94(x58402)+E(x58401,f179(f845(x58402,a832)))+P1(f324(f324(f231(x58402),f12(x58402,x58401)),f15(x58402,x58401)))+~P1(f324(f64(x58402),x58401))
% 18.77/18.51 [5854]~P38(x58542)+~P38(x58541)+E(x58541,x58542)+~E(f324(f304(a1,a838,a107),x58541),f324(f304(a1,a838,a107),x58542))
% 18.77/18.51 [8895]~P103(x88951)+~P1(f324(f324(f326(x88951),x88952),f112(x88951)))+P1(f324(f324(f232(x88951),f324(f324(f82(x88951),f324(f324(f82(x88951),f80(x88951)),x88952)),x88952)),f2(x88951)))+~P1(f324(f324(f232(x88951),x88952),f2(x88951)))
% 18.77/18.51 [9109]~P103(x91091)+~P1(f324(f324(f326(x91091),x91092),f112(x91091)))+~P1(f324(f324(f232(x91091),f324(f324(f82(x91091),f324(f324(f82(x91091),f80(x91091)),x91092)),x91092)),f2(x91091)))+P1(f324(f324(f232(x91091),x91092),f2(x91091)))
% 18.77/18.51 [4718]~P108(x47182)+~P135(x47182)+E(x47181,f2(a838))+E(f324(f324(f240(x47182),f2(x47182)),x47181),f2(x47182))
% 18.77/18.51 [4722]~P108(x47221)+~P135(x47221)+~E(x47222,f2(a838))+E(f324(f324(f240(x47221),f2(x47221)),x47222),f80(x47221))
% 18.77/18.51 [4881]~P133(x48812)+E(x48811,f80(x48812))+E(x48811,f324(f81(x48812),f80(x48812)))+~E(f324(f324(f83(x48812),x48811),x48811),f80(x48812))
% 18.77/18.51 [5125]~P82(x51252)+E(x51251,f2(x51252))+E(f84(x51252,x51251),f324(f81(x51252),f80(x51252)))+P1(f324(f324(f232(x51252),f2(x51252)),x51251))
% 18.77/18.51 [5317]~E(x53172,f80(a1))+~E(x53171,f80(a1))+E(f324(f324(f83(a1),x53171),x53172),f80(a1))+~P1(f324(f324(f232(a1),f2(a1)),x53171))
% 18.77/18.51 [5357]~P82(x53572)+E(f84(x53572,x53571),f80(x53572))+E(x53571,f2(x53572))+~P1(f324(f324(f232(x53572),f2(x53572)),x53571))
% 18.77/18.51 [5366]E(x53661,x53662)+~E(f324(f106(a838),x53661),f324(f106(a838),x53662))+P1(f324(a185,f324(f106(a1),x53662)))+P1(f324(a185,f324(f106(a1),x53661)))
% 18.77/18.51 [5415]~P88(x54151)+~E(x54152,f2(x54151))+E(f324(f324(f82(x54151),x54152),x54152),f2(x54151))+~P1(f324(f324(f326(x54151),x54152),f112(x54151)))
% 18.77/18.51 [5453]E(x54531,f2(a1))+~E(f324(f324(f42(a1),x54532),x54531),f2(a1))+P1(f324(f324(f232(a1),x54531),x54532))+P1(f324(f324(f232(a1),x54532),x54531))
% 18.77/18.51 [5483]E(x54831,f2(a1))+~E(f324(f324(f42(a1),x54832),x54831),f2(a1))+P1(f324(f324(f231(a1),x54832),f2(a1)))+P1(f324(f324(f232(a1),x54832),x54831))
% 18.77/18.51 [5515]E(x55151,f2(a1))+~E(f324(f324(f42(a1),x55152),x55151),f2(a1))+P1(f324(f324(f231(a1),f2(a1)),x55152))+P1(f324(f324(f232(a1),x55151),x55152))
% 18.77/18.51 [5551]E(x55511,f2(a1))+~E(f324(f324(f42(a1),x55512),x55511),f2(a1))+P1(f324(f324(f231(a1),x55512),f2(a1)))+P1(f324(f324(f231(a1),f2(a1)),x55512))
% 18.77/18.51 [5552]~P88(x55522)+E(x55521,f2(x55522))+~E(f324(f324(f82(x55522),x55521),x55521),f2(x55522))+~P1(f324(f324(f326(x55522),x55521),f112(x55522)))
% 18.77/18.51 [5619]E(f324(f106(a838),x56191),f324(f106(a838),x56192))+~E(f324(f106(a1),x56192),f2(a1))+P1(f324(a185,f324(f106(a1),x56192)))+~P1(f324(a185,f324(f106(a1),x56191)))
% 18.77/18.51 [5646]~E(f324(f106(a838),x56462),f324(f106(a838),x56461))+E(f324(f106(a1),x56461),f2(a1))+P1(f324(a185,f324(f106(a1),x56461)))+~P1(f324(a185,f324(f106(a1),x56462)))
% 18.77/18.51 [5655]~P86(x56552)+E(x56551,f179(f845(x56552,a832)))+~P1(f324(f64(x56552),x56551))+P1(f324(f324(f326(x56552),f16(x56552,x56551)),x56551))
% 18.77/18.51 [5656]~P86(x56562)+E(x56561,f179(f845(x56562,a832)))+~P1(f324(f64(x56562),x56561))+P1(f324(f324(f326(x56562),f17(x56562,x56561)),x56561))
% 18.77/18.51 [5820]~P103(x58201)+~P89(x58201)+P1(f324(f324(f232(x58201),f2(x58201)),f324(f106(x58201),x58202)))+~P1(f324(f324(f232(a1),a85),x58202))
% 18.77/18.51 [5821]~P103(x58211)+~P89(x58211)+P1(f324(f324(f231(x58211),f2(x58211)),f324(f106(x58211),x58212)))+~P1(f324(f324(f231(a1),a85),x58212))
% 18.77/18.51 [5839]~P103(x58391)+~P89(x58391)+E(f324(f77(x58391),f324(f106(x58391),x58392)),f324(f106(x58391),x58392))+P1(f324(f324(f232(x58391),f324(f106(x58391),x58392)),f2(x58391)))
% 18.77/18.51 [5880]E(x58801,x58802)+~E(f324(a107,x58801),f324(a107,x58802))+~P1(f324(f324(f231(a1),f2(a1)),x58802))+~P1(f324(f324(f231(a1),f2(a1)),x58801))
% 18.77/18.51 [5881]E(x58811,x58812)+~E(f324(a107,x58811),f324(a107,x58812))+~P1(f324(f324(f231(a1),f2(a1)),x58812))+~P1(f324(f324(f231(a1),f2(a1)),x58811))
% 18.77/18.51 [5909]~E(x59091,f2(a1))+E(f52(x59091,x59092),f324(f324(f247(a1,a1),f2(a1)),f2(a1)))+P1(f324(f324(f231(a1),f2(a1)),x59092))+~P1(f324(f324(f231(a1),f2(a1)),x59091))
% 18.77/18.51 [6080]~P89(x60802)+~P103(x60802)+~P1(f324(f324(f232(x60802),f2(x60802)),f324(f106(x60802),x60801)))+P1(f324(f324(f232(a1),a85),x60801))
% 18.77/18.51 [6081]~P89(x60812)+~P103(x60812)+~P1(f324(f324(f231(x60812),f2(x60812)),f324(f106(x60812),x60811)))+P1(f324(f324(f231(a1),a85),x60811))
% 18.77/18.51 [6086]~P103(x60861)+~P89(x60861)+P1(f324(f324(f232(x60861),f324(f106(x60861),x60862)),f2(x60861)))+~P1(f324(f324(f232(a1),x60862),a85))
% 18.77/18.51 [6087]~P103(x60871)+~P89(x60871)+P1(f324(f324(f231(x60871),f324(f106(x60871),x60872)),f2(x60871)))+~P1(f324(f324(f231(a1),x60872),a85))
% 18.77/18.51 [6416]~P89(x64162)+~P103(x64162)+~P1(f324(f324(f232(x64162),f324(f106(x64162),x64161)),f2(x64162)))+P1(f324(f324(f232(a1),x64161),a85))
% 18.77/18.51 [6417]~P89(x64172)+~P103(x64172)+~P1(f324(f324(f231(x64172),f324(f106(x64172),x64171)),f2(x64172)))+P1(f324(f324(f231(a1),x64171),a85))
% 18.77/18.51 [6509]~P103(x65091)+~P89(x65091)+E(f324(f77(x65091),f324(f106(x65091),x65092)),f324(f81(x65091),f324(f106(x65091),x65092)))+~P1(f324(f324(f232(x65091),f324(f106(x65091),x65092)),f2(x65091)))
% 18.77/18.51 [6526]E(f324(f106(a838),x65261),f324(f106(a838),x65262))+~E(f324(f106(a1),x65262),f2(a1))+~P1(f324(f324(f231(a1),f324(f106(a1),x65261)),f2(a1)))+~P1(f324(a185,f324(f106(a1),x65261)))
% 18.77/18.51 [6707]E(x67071,x67072)+~E(f324(a5,x67071),f324(a5,x67072))+~P1(f324(f324(f326(a838),x67072),f238(f845(a838,a832))))+~P1(f324(f324(f326(a838),x67071),f238(f845(a838,a832))))
% 18.77/18.51 [6939]P1(f324(f324(f232(a838),f324(a107,x69391)),f324(a107,x69392)))+~P1(f324(f324(f231(a1),f2(a1)),x69392))+~P1(f324(f324(f231(a1),f2(a1)),x69391))+~P1(f324(f324(f232(a1),x69391),x69392))
% 18.77/18.51 [6940]P1(f324(f324(f231(a838),f324(a107,x69401)),f324(a107,x69402)))+~P1(f324(f324(f231(a1),f2(a1)),x69402))+~P1(f324(f324(f231(a1),f2(a1)),x69401))+~P1(f324(f324(f231(a1),x69401),x69402))
% 18.77/18.51 [6941]P1(f324(f324(f280(a838),f324(a107,x69411)),f324(a107,x69412)))+~P1(f324(f324(f231(a1),f2(a1)),x69412))+~P1(f324(f324(f231(a1),f2(a1)),x69411))+~P1(f324(f324(f280(a1),x69411),x69412))
% 18.77/18.51 [7173]~P10(x71731)+~P38(x71732)+~P1(f324(f324(f326(a1),x71731),x71732))+P1(f324(f324(f326(a838),f324(a107,x71731)),f324(f304(a1,a838,a107),x71732)))
% 18.77/18.51 [7181]~P1(f324(f324(f232(a838),f324(a107,x71811)),f324(a107,x71812)))+~P1(f324(f324(f231(a1),f2(a1)),x71812))+~P1(f324(f324(f231(a1),f2(a1)),x71811))+P1(f324(f324(f232(a1),x71811),x71812))
% 18.77/18.51 [7182]~P1(f324(f324(f231(a838),f324(a107,x71821)),f324(a107,x71822)))+~P1(f324(f324(f231(a1),f2(a1)),x71822))+~P1(f324(f324(f231(a1),f2(a1)),x71821))+P1(f324(f324(f231(a1),x71821),x71822))
% 18.77/18.51 [7183]~P1(f324(f324(f280(a838),f324(a107,x71831)),f324(a107,x71832)))+~P1(f324(f324(f231(a1),f2(a1)),x71832))+~P1(f324(f324(f231(a1),f2(a1)),x71831))+P1(f324(f324(f280(a1),x71831),x71832))
% 18.77/18.51 [7450]~P86(x74502)+E(x74501,f179(f845(x74502,a832)))+~P1(f324(f64(x74502),x74501))+P1(f324(f324(f231(x74502),f14(x74502,f235(x74502),x74501)),f13(x74502,f178(x74502),x74501)))
% 18.77/18.51 [7778]~P10(x77781)+~P38(x77782)+P1(f324(f324(f326(a1),x77781),x77782))+~P1(f324(f324(f326(a838),f324(a107,x77781)),f324(f304(a1,a838,a107),x77782)))
% 18.77/18.51 [5652]~P119(x56522)+E(x56521,f2(a1))+E(f324(f81(x56522),f324(f105(x56522),f324(f81(a1),x56521))),f324(f105(x56522),x56521))+~P1(f324(f324(f232(a1),x56521),f2(a1)))
% 18.77/18.51 [5728]~P88(x57281)+~P89(x57281)+~P33(x57281,f324(f106(x57281),x57282))+P33(x57281,f324(f106(x57281),f324(f324(f82(a1),x57282),x57282)))
% 18.77/18.51 [6070]~P69(x60702)+E(x60701,f179(f845(x60702,a832)))+E(f17(x60702,f324(f304(x60702,x60702,f81(x60702)),x60701)),f324(f81(x60702),f16(x60702,x60701)))+~P1(f324(f64(x60702),x60701))
% 18.77/18.51 [6071]~P69(x60712)+E(x60711,f179(f845(x60712,a832)))+E(f16(x60712,f324(f304(x60712,x60712,f81(x60712)),x60711)),f324(f81(x60712),f17(x60712,x60711)))+~P1(f324(f64(x60712),x60711))
% 18.77/18.51 [6101]~P88(x61011)+~P89(x61011)+P33(x61011,f324(f106(x61011),x61012))+~P33(x61011,f324(f106(x61011),f324(f324(f82(a1),x61012),x61012)))
% 18.77/18.51 [6196]E(x61961,f2(a1))+E(f324(a57,f56(f324(f81(a1),x61961),f324(f81(a1),x61962))),f52(x61961,x61962))+P1(f324(f324(f231(a1),f2(a1)),x61962))+~P1(f324(f324(f231(a1),f2(a1)),x61961))
% 18.77/18.51 [7084]~P1(f324(f324(f232(a1),f2(a1)),x70842))+~P1(f324(f324(f231(a1),f2(a1)),x70841))+~P1(f324(f324(f231(a1),x70842),x70841))+P1(f324(f324(f232(a1),f2(a1)),f324(f324(f42(a1),x70841),x70842)))
% 18.77/18.51 [7527]~E(x75272,f2(a1))+E(f209(x75271,x75272),f324(f324(f247(a1,a1),f2(a1)),f80(a1)))+P1(f324(f324(f232(a1),x75272),f2(a1)))+~P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),x75271),x75272)))
% 18.77/18.51 [7528]~E(x75281,f2(a1))+E(f209(x75281,x75282),f324(f324(f247(a1,a1),f2(a1)),f80(a1)))+P1(f324(f324(f232(a1),x75282),f2(a1)))+~P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),x75281),x75282)))
% 18.77/18.51 [8540]~P38(x85402)+~P38(x85401)+P1(f324(f324(f232(f845(a838,a832)),f324(f304(a1,a838,a107),x85401)),f324(f304(a1,a838,a107),x85402)))+~P1(f324(f324(f232(f845(a1,a832)),x85401),x85402))
% 18.77/18.51 [8541]~P38(x85412)+~P38(x85411)+P1(f324(f324(f231(f845(a838,a832)),f324(f304(a1,a838,a107),x85411)),f324(f304(a1,a838,a107),x85412)))+~P1(f324(f324(f231(f845(a1,a832)),x85411),x85412))
% 18.77/18.51 [8820]~P38(x88202)+~P38(x88201)+~P1(f324(f324(f232(f845(a838,a832)),f324(f304(a1,a838,a107),x88201)),f324(f304(a1,a838,a107),x88202)))+P1(f324(f324(f232(f845(a1,a832)),x88201),x88202))
% 18.77/18.51 [8821]~P38(x88212)+~P38(x88211)+~P1(f324(f324(f231(f845(a838,a832)),f324(f304(a1,a838,a107),x88211)),f324(f304(a1,a838,a107),x88212)))+P1(f324(f324(f231(f845(a1,a832)),x88211),x88212))
% 18.77/18.51 [9254]E(x92541,f2(a1))+E(x92542,f2(a1))+E(f324(f324(f88(a1,f844(a1,a1)),f324(f324(a211,x92542),x92541)),f324(f324(f20(a1,a1,f844(a1,a1)),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f324(f42(a1),x92542))),f324(f42(a1),x92541))),f209(x92542,x92541))+P1(f324(f324(f232(a1),x92541),f2(a1)))
% 18.77/18.51 [8106]~P89(x81062)+~P103(x81062)+~P1(f324(f324(f232(x81062),f324(f106(x81062),x81061)),f80(x81062)))+P1(f324(f324(f232(a1),x81061),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))
% 18.77/18.51 [8107]~P89(x81072)+~P103(x81072)+~P1(f324(f324(f231(x81072),f324(f106(x81072),x81071)),f80(x81072)))+P1(f324(f324(f231(a1),x81071),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))
% 18.77/18.51 [8383]~P103(x83831)+~P89(x83831)+P1(f324(f324(f232(x83831),f324(f106(x83831),x83832)),f80(x83831)))+~P1(f324(f324(f232(a1),x83832),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))
% 18.77/18.51 [8384]~P103(x83841)+~P89(x83841)+P1(f324(f324(f231(x83841),f324(f106(x83841),x83842)),f80(x83841)))+~P1(f324(f324(f231(a1),x83842),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))
% 18.77/18.51 [8566]~P89(x85662)+~P103(x85662)+~P1(f324(f324(f232(x85662),f80(x85662)),f324(f106(x85662),x85661)))+P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),x85661))
% 18.77/18.51 [8567]~P89(x85672)+~P103(x85672)+~P1(f324(f324(f231(x85672),f80(x85672)),f324(f106(x85672),x85671)))+P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),x85671))
% 18.77/18.51 [8902]~P103(x89021)+~P89(x89021)+P1(f324(f324(f232(x89021),f80(x89021)),f324(f106(x89021),x89022)))+~P1(f324(f324(f232(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),x89022))
% 18.77/18.51 [8903]~P103(x89031)+~P89(x89031)+P1(f324(f324(f231(x89031),f80(x89031)),f324(f106(x89031),x89032)))+~P1(f324(f324(f231(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),x89032))
% 18.77/18.51 [9377]~P133(x93772)+E(x93771,f80(x93772))+E(x93771,f324(f81(x93772),f80(x93772)))+~E(f324(f324(f240(x93772),x93771),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f80(x93772))
% 18.77/18.51 [9629]~P89(x96291)+~P61(x96291)+~P1(f324(f324(f232(x96291),f2(x96291)),x96292))+P1(f324(f324(f232(x96291),f2(x96291)),f324(f324(f284(x96291),x96292),f324(f106(x96291),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.77/18.51 [9630]~P89(x96301)+~P61(x96301)+~P1(f324(f324(f232(x96301),f2(x96301)),x96302))+P1(f324(f324(f232(x96301),f2(x96301)),f324(f324(f284(x96301),x96302),f324(f106(x96301),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.77/18.51 [9685]~P89(x96851)+~P61(x96851)+P1(f324(f324(f232(x96851),f2(x96851)),x96852))+~P1(f324(f324(f232(x96851),f2(x96851)),f324(f324(f284(x96851),x96852),f324(f106(x96851),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.77/18.51 [9959]~P119(x99592)+E(x99591,f2(a1))+P1(f324(f324(f232(a1),x99591),f2(a1)))+E(f324(f324(f252(a1,a1,x99592),f324(f324(f9(a1,f845(a1,f845(x99592,x99592)),f845(a1,x99592)),f324(f324(f10(f845(f845(x99592,x99592),x99592),f845(f845(a1,f845(x99592,x99592)),f845(a1,x99592)),a1),f10(f845(x99592,x99592),x99592,a1)),f324(f324(f10(x99592,f845(f845(x99592,x99592),x99592),a1),f88(x99592,x99592)),f105(x99592)))),f324(f324(f9(a1,f845(x99592,x99592),f845(x99592,x99592)),f324(f324(f10(f845(x99592,f845(x99592,x99592)),f845(f845(x99592,x99592),f845(x99592,x99592)),a1),f20(x99592,x99592,x99592)),f324(f324(f9(a1,f845(x99592,x99592),f845(x99592,f845(x99592,x99592))),f324(f324(f10(f845(x99592,f845(x99592,x99592)),f845(f845(x99592,x99592),f845(x99592,f845(x99592,x99592))),a1),f10(x99592,f845(x99592,x99592),x99592)),f324(f324(f10(a832,f845(x99592,f845(x99592,x99592)),a1),f98(x99592)),f324(f324(f9(a1,a1,a832),a321),f2(a1))))),f324(f324(f20(x99592,x99592,x99592),f82(x99592)),f7(x99592))))),f324(f324(f9(x99592,x99592,x99592),f324(f324(f10(x99592,f845(x99592,x99592),x99592),f82(x99592)),f324(f324(f20(x99592,x99592,x99592),f82(x99592)),f7(x99592)))),f80(x99592))))),f52(x99591,f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f105(x99592),x99591))
% 18.77/18.51 [9732]P1(f324(f324(f231(a1),x97321),f2(a1)))+P1(f324(f324(f232(a1),x97322),x97321))+~P1(f324(f313(f844(a1,a1),a62),f324(f324(f247(a1,a1),x97322),x97321)))+E(f324(f49(x97321),f53(x97322,f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97321))),f53(x97322,x97321))
% 18.77/18.51 [9736]P1(f324(f324(f231(a1),x97361),f2(a1)))+~P1(f324(f313(f844(a1,a1),a58),f324(f324(f247(a1,a1),x97362),x97361)))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),x97362),x97361)))+E(f324(f49(x97361),f56(x97362,f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),x97361))),f56(x97362,x97361))
% 18.77/18.51 [4689]~P88(x46893)+~P89(x46893)+E(x46891,x46892)+~E(f324(f106(x46893),x46891),f324(f106(x46893),x46892))
% 18.77/18.51 [5829]~P1(f324(x58291,x58292))+~P1(f324(x58291,x58293))+~P1(f324(f324(f231(a838),x58293),f632(x58292,x58291)))+P1(f324(x58291,f2(a838)))
% 18.77/18.51 [6262]P139(x62622,x62623,x62621)+E(x62621,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f768(x62621,x62623,x62622)))+P1(f324(f324(f232(a1),x62621),f2(a1)))
% 18.77/18.51 [6263]P140(x62632,x62633,x62631)+E(x62631,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f772(x62631,x62633,x62632)))+P1(f324(f324(f232(a1),x62631),f2(a1)))
% 18.77/18.51 [6395]P139(x63951,x63952,x63953)+~P1(f324(x63951,x63952))+P1(f324(f324(f231(a1),f2(a1)),f768(x63953,x63952,x63951)))+P1(f324(f324(f232(a1),x63953),f2(a1)))
% 18.77/18.51 [6419]P140(x64191,x64192,x64193)+P1(f324(f324(f231(a1),f2(a1)),f772(x64193,x64192,x64191)))+~P1(f324(x64191,f2(a1)))+P1(f324(f324(f232(a1),x64193),f2(a1)))
% 18.77/18.51 [6451]P139(x64512,x64513,x64511)+E(x64511,f2(a1))+~P1(f324(x64512,f768(x64511,x64513,x64512)))+P1(f324(f324(f232(a1),x64511),f2(a1)))
% 18.77/18.51 [6452]P140(x64522,x64523,x64521)+E(x64521,f2(a1))+~P1(f324(x64522,f773(x64521,x64523,x64522)))+P1(f324(f324(f232(a1),x64521),f2(a1)))
% 18.77/18.51 [6556]~P86(x65561)+~P9(x65561)+~P1(f324(f324(f232(x65561),x65562),f43(x65561,x65563)))+P1(f324(f324(f232(x65561),x65562),f652(x65563,x65562,x65561)))
% 18.77/18.51 [6566]P139(x65661,x65662,x65663)+~P1(f324(x65661,x65662))+~P1(f324(x65661,f768(x65663,x65662,x65661)))+P1(f324(f324(f232(a1),x65663),f2(a1)))
% 18.77/18.51 [6599]P140(x65991,x65992,x65993)+~P1(f324(x65991,f773(x65993,x65992,x65991)))+~P1(f324(x65991,f2(a1)))+P1(f324(f324(f232(a1),x65993),f2(a1)))
% 18.77/18.51 [6864]P139(x68642,x68643,x68641)+E(x68641,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f768(x68641,x68643,x68642)))+P1(f324(f324(f232(a1),x68641),f767(x68641,x68643,x68642)))
% 18.77/18.51 [6865]P140(x68652,x68653,x68651)+E(x68651,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f772(x68651,x68653,x68652)))+P1(f324(f324(f232(a1),x68651),f771(x68651,x68653,x68652)))
% 18.77/18.51 [6982]P139(x69821,x69822,x69823)+~P1(f324(x69821,x69822))+P1(f324(f324(f231(a1),f2(a1)),f768(x69823,x69822,x69821)))+P1(f324(f324(f232(a1),x69823),f767(x69823,x69822,x69821)))
% 18.77/18.51 [7003]P140(x70031,x70032,x70033)+P1(f324(f324(f231(a1),f2(a1)),f772(x70033,x70032,x70031)))+P1(f324(f324(f232(a1),x70033),f771(x70033,x70032,x70031)))+~P1(f324(x70031,f2(a1)))
% 18.77/18.51 [7034]P139(x70342,x70343,x70341)+E(x70341,f2(a1))+~P1(f324(x70342,f768(x70341,x70343,x70342)))+P1(f324(f324(f232(a1),x70341),f767(x70341,x70343,x70342)))
% 18.77/18.51 [7035]P140(x70352,x70353,x70351)+E(x70351,f2(a1))+~P1(f324(x70352,f773(x70351,x70353,x70352)))+P1(f324(f324(f232(a1),x70351),f771(x70351,x70353,x70352)))
% 18.77/18.51 [7075]P139(x70752,x70753,x70751)+E(x70751,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f768(x70751,x70753,x70752)))+~P1(f324(x70752,f767(x70751,x70753,x70752)))
% 18.77/18.51 [7076]P140(x70762,x70763,x70761)+E(x70761,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f772(x70761,x70763,x70762)))+~P1(f324(x70762,f776(x70761,x70763,x70762)))
% 18.77/18.51 [7180]P139(x71801,x71802,x71803)+~P1(f324(x71801,x71802))+~P1(f324(x71801,f768(x71803,x71802,x71801)))+P1(f324(f324(f232(a1),x71803),f767(x71803,x71802,x71801)))
% 18.77/18.51 [7196]P140(x71961,x71962,x71963)+~P1(f324(x71961,f773(x71963,x71962,x71961)))+P1(f324(f324(f232(a1),x71963),f771(x71963,x71962,x71961)))+~P1(f324(x71961,f2(a1)))
% 18.77/18.51 [7202]P139(x72021,x72022,x72023)+~P1(f324(x72021,x72022))+P1(f324(f324(f231(a1),f2(a1)),f768(x72023,x72022,x72021)))+~P1(f324(x72021,f767(x72023,x72022,x72021)))
% 18.77/18.51 [7220]P140(x72201,x72202,x72203)+P1(f324(f324(f231(a1),f2(a1)),f772(x72203,x72202,x72201)))+~P1(f324(x72201,f776(x72203,x72202,x72201)))+~P1(f324(x72201,f2(a1)))
% 18.77/18.51 [7244]P139(x72442,x72443,x72441)+E(x72441,f2(a1))+~P1(f324(x72442,f768(x72441,x72443,x72442)))+~P1(f324(x72442,f767(x72441,x72443,x72442)))
% 18.77/18.51 [7245]P140(x72452,x72453,x72451)+E(x72451,f2(a1))+~P1(f324(x72452,f773(x72451,x72453,x72452)))+~P1(f324(x72452,f776(x72451,x72453,x72452)))
% 18.77/18.51 [7341]P139(x73411,x73412,x73413)+~P1(f324(x73411,x73412))+~P1(f324(x73411,f768(x73413,x73412,x73411)))+~P1(f324(x73411,f767(x73413,x73412,x73411)))
% 18.77/18.51 [7356]P140(x73561,x73562,x73563)+~P1(f324(x73561,f773(x73563,x73562,x73561)))+~P1(f324(x73561,f776(x73563,x73562,x73561)))+~P1(f324(x73561,f2(a1)))
% 18.77/18.51 [7410]P139(x74102,x74103,x74101)+E(x74101,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f768(x74101,x74103,x74102)))+P1(f324(f324(f231(a1),f767(x74101,x74103,x74102)),f2(a1)))
% 18.77/18.51 [7411]P140(x74112,x74113,x74111)+E(x74111,f2(a1))+P1(f324(f324(f231(a1),f2(a1)),f772(x74111,x74113,x74112)))+P1(f324(f324(f231(a1),f771(x74111,x74113,x74112)),f2(a1)))
% 18.77/18.51 [7412]~P2(x74121)+~P1(f324(f324(f326(x74121),x74123),f175(x74121)))+~P1(f324(f324(f326(x74121),x74122),f175(x74121)))+P1(f324(f324(f326(x74121),f324(f324(f83(x74121),x74122),x74123)),f175(x74121)))
% 18.77/18.51 [7413]~P119(x74131)+~P1(f324(f324(f326(x74131),x74133),f112(x74131)))+~P1(f324(f324(f326(x74131),x74132),f112(x74131)))+P1(f324(f324(f326(x74131),f324(f324(f83(x74131),x74132),x74133)),f112(x74131)))
% 18.77/18.51 [7414]~P2(x74141)+~P1(f324(f324(f326(x74141),x74143),f175(x74141)))+~P1(f324(f324(f326(x74141),x74142),f175(x74141)))+P1(f324(f324(f326(x74141),f324(f324(f82(x74141),x74142),x74143)),f175(x74141)))
% 18.77/18.51 [7415]~P119(x74151)+~P1(f324(f324(f326(x74151),x74153),f112(x74151)))+~P1(f324(f324(f326(x74151),x74152),f112(x74151)))+P1(f324(f324(f326(x74151),f324(f324(f82(x74151),x74152),x74153)),f112(x74151)))
% 18.77/18.51 [7416]~P119(x74161)+~P1(f324(f324(f326(x74161),x74163),f112(x74161)))+~P1(f324(f324(f326(x74161),x74162),f112(x74161)))+P1(f324(f324(f326(x74161),f324(f324(f3(x74161),x74162),x74163)),f112(x74161)))
% 18.77/18.51 [7417]~P80(x74171)+~P1(f324(f324(f232(x74171),x74173),f2(x74171)))+~P1(f324(f324(f232(x74171),x74172),f2(x74171)))+P1(f324(f324(f232(x74171),f324(f324(f82(x74171),x74172),x74173)),f2(x74171)))
% 18.77/18.51 [7418]~P80(x74181)+~P1(f324(f324(f231(x74181),x74182),f2(x74181)))+~P1(f324(f324(f232(x74181),x74183),f2(x74181)))+P1(f324(f324(f232(x74181),f324(f324(f82(x74181),x74182),x74183)),f2(x74181)))
% 18.77/18.51 [7419]~P80(x74191)+~P1(f324(f324(f231(x74191),x74193),f2(x74191)))+~P1(f324(f324(f232(x74191),x74192),f2(x74191)))+P1(f324(f324(f232(x74191),f324(f324(f82(x74191),x74192),x74193)),f2(x74191)))
% 18.77/18.51 [7420]~P80(x74201)+~P1(f324(f324(f231(x74201),x74203),f2(x74201)))+~P1(f324(f324(f231(x74201),x74202),f2(x74201)))+P1(f324(f324(f231(x74201),f324(f324(f82(x74201),x74202),x74203)),f2(x74201)))
% 18.77/18.51 [7446]P139(x74463,x74462,x74461)+E(x74461,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x74461),f769(x74461,x74462,x74463))),f768(x74461,x74462,x74463)),x74462)+P1(f324(f324(f232(a1),x74461),f2(a1)))
% 18.77/18.51 [7447]P140(x74473,x74472,x74471)+E(x74471,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x74471),f773(x74471,x74472,x74473))),f772(x74471,x74472,x74473)),x74472)+P1(f324(f324(f232(a1),x74471),f2(a1)))
% 18.77/18.51 [7532]P139(x75321,x75322,x75323)+~P1(f324(x75321,x75322))+P1(f324(f324(f231(a1),f2(a1)),f768(x75323,x75322,x75321)))+P1(f324(f324(f231(a1),f767(x75323,x75322,x75321)),f2(a1)))
% 18.77/18.51 [7563]P140(x75631,x75632,x75633)+P1(f324(f324(f231(a1),f2(a1)),f772(x75633,x75632,x75631)))+~P1(f324(x75631,f2(a1)))+P1(f324(f324(f231(a1),f771(x75633,x75632,x75631)),f2(a1)))
% 18.77/18.51 [7571]P139(x75713,x75712,x75711)+~P1(f324(x75713,x75712))+E(f324(f324(f82(a1),f324(f324(f83(a1),x75711),f769(x75711,x75712,x75713))),f768(x75711,x75712,x75713)),x75712)+P1(f324(f324(f232(a1),x75711),f2(a1)))
% 18.77/18.51 [7576]P139(x75762,x75763,x75761)+E(x75761,f2(a1))+~P1(f324(x75762,f768(x75761,x75763,x75762)))+P1(f324(f324(f231(a1),f767(x75761,x75763,x75762)),f2(a1)))
% 18.77/18.51 [7577]P140(x75772,x75773,x75771)+E(x75771,f2(a1))+~P1(f324(x75772,f773(x75771,x75773,x75772)))+P1(f324(f324(f231(a1),f771(x75771,x75773,x75772)),f2(a1)))
% 18.77/18.51 [7582]P140(x75823,x75822,x75821)+E(f324(f324(f82(a1),f324(f324(f83(a1),x75821),f773(x75821,x75822,x75823))),f772(x75821,x75822,x75823)),x75822)+~P1(f324(x75823,f2(a1)))+P1(f324(f324(f232(a1),x75821),f2(a1)))
% 18.77/18.51 [7636]P139(x76361,x76362,x76363)+~P1(f324(x76361,x76362))+~P1(f324(x76361,f768(x76363,x76362,x76361)))+P1(f324(f324(f231(a1),f767(x76363,x76362,x76361)),f2(a1)))
% 18.77/18.51 [7641]P140(x76411,x76412,x76413)+~P1(f324(x76411,f773(x76413,x76412,x76411)))+~P1(f324(x76411,f2(a1)))+P1(f324(f324(f231(a1),f771(x76413,x76412,x76411)),f2(a1)))
% 18.77/18.51 [7716]~P61(x77161)+~P1(f324(f324(f232(x77161),f324(f324(f284(x77161),x77163),x77162)),f2(x77161)))+P1(f324(f324(f232(x77161),x77162),f2(x77161)))+P1(f324(f324(f232(x77161),x77163),f2(x77161)))
% 18.77/18.51 [7717]~P117(x77171)+~P1(f324(f324(f231(x77171),f324(f324(f83(x77171),x77173),x77172)),f2(x77171)))+P1(f324(f324(f231(x77171),x77172),f2(x77171)))+P1(f324(f324(f231(x77171),x77173),f2(x77171)))
% 18.77/18.51 [7718]~P61(x77181)+~P1(f324(f324(f231(x77181),f324(f324(f284(x77181),x77183),x77182)),f2(x77181)))+P1(f324(f324(f231(x77181),x77182),f2(x77181)))+P1(f324(f324(f231(x77181),x77183),f2(x77181)))
% 18.77/18.51 [7831]P139(x78313,x78312,x78311)+E(x78311,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x78311),f769(x78311,x78312,x78313))),f768(x78311,x78312,x78313)),x78312)+P1(f324(f324(f232(a1),x78311),f767(x78311,x78312,x78313)))
% 18.77/18.51 [7832]P140(x78323,x78322,x78321)+E(x78321,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x78321),f773(x78321,x78322,x78323))),f772(x78321,x78322,x78323)),x78322)+P1(f324(f324(f232(a1),x78321),f771(x78321,x78322,x78323)))
% 18.77/18.51 [7843]P139(x78433,x78432,x78431)+E(x78431,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x78431),f770(x78431,x78432,x78433))),f767(x78431,x78432,x78433)),x78432)+P1(f324(f324(f231(a1),f2(a1)),f768(x78431,x78432,x78433)))
% 18.77/18.51 [7844]P140(x78443,x78442,x78441)+E(x78441,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x78441),f776(x78441,x78442,x78443))),f771(x78441,x78442,x78443)),x78442)+P1(f324(f324(f231(a1),f2(a1)),f772(x78441,x78442,x78443)))
% 18.77/18.51 [7892]P139(x78923,x78922,x78921)+~P1(f324(x78923,x78922))+E(f324(f324(f82(a1),f324(f324(f83(a1),x78921),f769(x78921,x78922,x78923))),f768(x78921,x78922,x78923)),x78922)+P1(f324(f324(f232(a1),x78921),f767(x78921,x78922,x78923)))
% 18.77/18.51 [7904]P140(x79043,x79042,x79041)+E(f324(f324(f82(a1),f324(f324(f83(a1),x79041),f773(x79041,x79042,x79043))),f772(x79041,x79042,x79043)),x79042)+P1(f324(f324(f232(a1),x79041),f771(x79041,x79042,x79043)))+~P1(f324(x79043,f2(a1)))
% 18.77/18.51 [7910]P139(x79103,x79102,x79101)+~P1(f324(x79103,x79102))+E(f324(f324(f82(a1),f324(f324(f83(a1),x79101),f770(x79101,x79102,x79103))),f767(x79101,x79102,x79103)),x79102)+P1(f324(f324(f231(a1),f2(a1)),f768(x79101,x79102,x79103)))
% 18.77/18.51 [7917]P140(x79173,x79172,x79171)+E(f324(f324(f82(a1),f324(f324(f83(a1),x79171),f776(x79171,x79172,x79173))),f771(x79171,x79172,x79173)),x79172)+P1(f324(f324(f231(a1),f2(a1)),f772(x79171,x79172,x79173)))+~P1(f324(x79173,f2(a1)))
% 18.77/18.51 [7927]P139(x79273,x79272,x79271)+E(x79271,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x79271),f769(x79271,x79272,x79273))),f768(x79271,x79272,x79273)),x79272)+~P1(f324(x79273,f767(x79271,x79272,x79273)))
% 18.77/18.51 [7928]P140(x79283,x79282,x79281)+E(x79281,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x79281),f773(x79281,x79282,x79283))),f772(x79281,x79282,x79283)),x79282)+~P1(f324(x79283,f776(x79281,x79282,x79283)))
% 18.77/18.51 [7929]P139(x79293,x79292,x79291)+E(x79291,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x79291),f770(x79291,x79292,x79293))),f767(x79291,x79292,x79293)),x79292)+~P1(f324(x79293,f768(x79291,x79292,x79293)))
% 18.77/18.51 [7930]P140(x79303,x79302,x79301)+E(x79301,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x79301),f776(x79301,x79302,x79303))),f771(x79301,x79302,x79303)),x79302)+~P1(f324(x79303,f773(x79301,x79302,x79303)))
% 18.77/18.51 [7984]P139(x79843,x79842,x79841)+~P1(f324(x79843,x79842))+E(f324(f324(f82(a1),f324(f324(f83(a1),x79841),f769(x79841,x79842,x79843))),f768(x79841,x79842,x79843)),x79842)+~P1(f324(x79843,f767(x79841,x79842,x79843)))
% 18.77/18.51 [7985]P139(x79853,x79852,x79851)+~P1(f324(x79853,x79852))+E(f324(f324(f82(a1),f324(f324(f83(a1),x79851),f770(x79851,x79852,x79853))),f767(x79851,x79852,x79853)),x79852)+~P1(f324(x79853,f768(x79851,x79852,x79853)))
% 18.77/18.51 [7998]P140(x79983,x79982,x79981)+E(f324(f324(f82(a1),f324(f324(f83(a1),x79981),f773(x79981,x79982,x79983))),f772(x79981,x79982,x79983)),x79982)+~P1(f324(x79983,f776(x79981,x79982,x79983)))+~P1(f324(x79983,f2(a1)))
% 18.77/18.51 [7999]P140(x79993,x79992,x79991)+E(f324(f324(f82(a1),f324(f324(f83(a1),x79991),f776(x79991,x79992,x79993))),f771(x79991,x79992,x79993)),x79992)+~P1(f324(x79993,f773(x79991,x79992,x79993)))+~P1(f324(x79993,f2(a1)))
% 18.77/18.51 [8099]P139(x80993,x80992,x80991)+E(x80991,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x80991),f769(x80991,x80992,x80993))),f768(x80991,x80992,x80993)),x80992)+P1(f324(f324(f231(a1),f767(x80991,x80992,x80993)),f2(a1)))
% 18.77/18.51 [8100]P140(x81003,x81002,x81001)+E(x81001,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x81001),f773(x81001,x81002,x81003))),f772(x81001,x81002,x81003)),x81002)+P1(f324(f324(f231(a1),f771(x81001,x81002,x81003)),f2(a1)))
% 18.77/18.51 [8139]P139(x81393,x81392,x81391)+~P1(f324(x81393,x81392))+E(f324(f324(f82(a1),f324(f324(f83(a1),x81391),f769(x81391,x81392,x81393))),f768(x81391,x81392,x81393)),x81392)+P1(f324(f324(f231(a1),f767(x81391,x81392,x81393)),f2(a1)))
% 18.77/18.51 [8145]P140(x81453,x81452,x81451)+E(f324(f324(f82(a1),f324(f324(f83(a1),x81451),f773(x81451,x81452,x81453))),f772(x81451,x81452,x81453)),x81452)+~P1(f324(x81453,f2(a1)))+P1(f324(f324(f231(a1),f771(x81451,x81452,x81453)),f2(a1)))
% 18.77/18.51 [8276]P139(x82763,x82762,x82761)+E(x82761,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x82761),f770(x82761,x82762,x82763))),f767(x82761,x82762,x82763)),x82762)+E(f324(f324(f82(a1),f324(f324(f83(a1),x82761),f769(x82761,x82762,x82763))),f768(x82761,x82762,x82763)),x82762)
% 18.77/18.51 [8277]P140(x82773,x82772,x82771)+E(x82771,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x82771),f776(x82771,x82772,x82773))),f771(x82771,x82772,x82773)),x82772)+E(f324(f324(f82(a1),f324(f324(f83(a1),x82771),f773(x82771,x82772,x82773))),f772(x82771,x82772,x82773)),x82772)
% 18.77/18.51 [8299]P139(x82993,x82992,x82991)+~P1(f324(x82993,x82992))+E(f324(f324(f82(a1),f324(f324(f83(a1),x82991),f770(x82991,x82992,x82993))),f767(x82991,x82992,x82993)),x82992)+E(f324(f324(f82(a1),f324(f324(f83(a1),x82991),f769(x82991,x82992,x82993))),f768(x82991,x82992,x82993)),x82992)
% 18.77/18.51 [8310]P140(x83103,x83102,x83101)+E(f324(f324(f82(a1),f324(f324(f83(a1),x83101),f776(x83101,x83102,x83103))),f771(x83101,x83102,x83103)),x83102)+E(f324(f324(f82(a1),f324(f324(f83(a1),x83101),f773(x83101,x83102,x83103))),f772(x83101,x83102,x83103)),x83102)+~P1(f324(x83103,f2(a1)))
% 18.77/18.51 [8907]~P117(x89071)+~E(x89073,f2(x89071))+~E(x89072,f2(x89071))+P1(f324(f324(f231(x89071),f324(f324(f82(x89071),f324(f324(f83(x89071),x89072),x89072)),f324(f324(f83(x89071),x89073),x89073))),f2(x89071)))
% 18.77/18.51 [9908]~P103(x99081)+~E(x99083,f2(x99081))+~E(x99082,f2(x99081))+P1(f324(f324(f231(x99081),f324(f324(f82(x99081),f324(f324(f240(x99081),x99082),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x99081),x99083),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))),f2(x99081)))
% 18.77/18.51 [4639]~E(x46393,x46391)+~P114(x46392)+E(x46391,f2(x46392))+E(f324(f324(f284(x46392),x46393),x46391),f80(x46392))
% 18.77/18.51 [4690]~P95(x46901)+~E(x46903,f179(x46901))+~E(x46902,f179(x46901))+E(f324(f324(f103(x46901),x46902),x46903),f179(x46901))
% 18.77/18.51 [4691]~P98(x46911)+~E(x46913,f238(x46911))+~E(x46912,f238(x46911))+E(f324(f324(f104(x46911),x46912),x46913),f238(x46911))
% 18.77/18.51 [4779]~P114(x47793)+E(x47791,x47792)+E(x47792,f2(x47793))+~E(f324(f324(f284(x47793),x47791),x47792),f80(x47793))
% 18.77/18.51 [4795]~P120(x47952)+E(x47951,f2(x47952))+E(x47953,f2(x47952))+~E(f324(f324(f83(x47952),x47953),x47951),f2(x47952))
% 18.77/18.51 [4796]~P120(x47962)+E(x47961,f2(x47962))+E(x47963,f2(x47962))+~E(f324(f324(f83(x47962),x47963),x47961),f2(x47962))
% 18.77/18.51 [4797]~P132(x47972)+E(x47971,f2(x47972))+E(x47973,f2(x47972))+~E(f324(f324(f83(x47972),x47973),x47971),f2(x47972))
% 18.77/18.51 [5162]~P112(x51623)+E(x51621,x51622)+E(x51621,f324(f81(x51623),x51622))+~E(f324(f324(f83(x51623),x51621),x51621),f324(f324(f83(x51623),x51622),x51622))
% 18.77/18.51 [5198]~P91(x51981)+E(f324(f81(x51981),x51982),x51983)+~E(f324(f324(f103(x51981),x51982),x51983),f238(x51981))+~E(f324(f324(f104(x51981),x51982),x51983),f179(x51981))
% 18.77/18.51 [5273]~P86(x52733)+E(x52731,x52732)+P1(f324(f324(f232(x52733),x52732),x52731))+P1(f324(f324(f232(x52733),x52731),x52732))
% 18.77/18.51 [5274]~P86(x52743)+E(x52741,x52742)+P1(f324(f324(f232(x52743),x52742),x52741))+P1(f324(f324(f232(x52743),x52741),x52742))
% 18.77/18.51 [5275]~P86(x52753)+E(x52751,x52752)+P1(f324(f324(f232(x52753),x52752),x52751))+P1(f324(f324(f232(x52753),x52751),x52752))
% 18.77/18.51 [5276]~P86(x52763)+E(x52761,x52762)+P1(f324(f324(f232(x52763),x52762),x52761))+P1(f324(f324(f232(x52763),x52761),x52762))
% 18.77/18.51 [5277]~P86(x52773)+E(x52771,x52772)+P1(f324(f324(f232(x52773),x52772),x52771))+P1(f324(f324(f232(x52773),x52771),x52772))
% 18.77/18.51 [5278]~P103(x52783)+E(x52781,x52782)+P1(f324(f324(f232(x52783),x52782),x52781))+P1(f324(f324(f232(x52783),x52781),x52782))
% 18.77/18.51 [5279]~P86(x52793)+E(x52791,x52792)+P1(f324(f324(f232(x52793),x52792),x52791))+P1(f324(f324(f232(x52793),x52791),x52792))
% 18.77/18.51 [5280]~E(x52802,x52803)+~P86(x52801)+P1(f324(f324(f231(x52801),x52802),x52803))+P1(f324(f324(f232(x52801),x52802),x52803))
% 18.77/18.51 [5444]P139(x54442,x54443,x54441)+E(x54441,f2(a1))+P1(f324(f324(f232(a1),x54441),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x54441))
% 18.77/18.51 [5445]P140(x54452,x54453,x54451)+E(x54451,f2(a1))+P1(f324(f324(f232(a1),x54451),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x54451))
% 18.77/18.51 [5472]E(x54721,x54722)+P1(f324(f324(x54723,x54721),x54722))+P1(f324(f324(f232(a838),x54722),x54721))+P1(f324(f324(f232(a838),x54721),x54722))
% 18.77/18.51 [5531]~P85(x55313)+E(x55311,x55312)+~P1(f324(f324(f231(x55313),x55312),x55311))+P1(f324(f324(f232(x55313),x55312),x55311))
% 18.77/18.51 [5532]~P85(x55323)+E(x55321,x55322)+~P1(f324(f324(f231(x55323),x55321),x55322))+P1(f324(f324(f232(x55323),x55321),x55322))
% 18.77/18.51 [5533]~P85(x55333)+E(x55331,x55332)+~P1(f324(f324(f231(x55333),x55331),x55332))+P1(f324(f324(f232(x55333),x55331),x55332))
% 18.77/18.51 [5534]~P85(x55343)+E(x55341,x55342)+~P1(f324(f324(f231(x55343),x55341),x55342))+P1(f324(f324(f232(x55343),x55341),x55342))
% 18.77/18.51 [5535]~P85(x55353)+E(x55351,x55352)+~P1(f324(f324(f231(x55353),x55351),x55352))+P1(f324(f324(f232(x55353),x55351),x55352))
% 18.77/18.51 [5536]~P85(x55363)+E(x55361,x55362)+~P1(f324(f324(f231(x55363),x55361),x55362))+P1(f324(f324(f232(x55363),x55361),x55362))
% 18.77/18.51 [5537]~P85(x55373)+E(x55371,x55372)+~P1(f324(f324(f231(x55373),x55371),x55372))+P1(f324(f324(f232(x55373),x55371),x55372))
% 18.77/18.51 [5538]~P86(x55383)+E(x55381,x55382)+~P1(f324(f324(f231(x55383),x55381),x55382))+P1(f324(f324(f232(x55383),x55381),x55382))
% 18.77/18.51 [5539]~P86(x55393)+E(x55391,x55392)+~P1(f324(f324(f231(x55393),x55391),x55392))+P1(f324(f324(f232(x55393),x55391),x55392))
% 18.77/18.51 [5649]P139(x56491,x56492,x56493)+~P1(f324(x56491,x56492))+P1(f324(f324(f232(a1),x56493),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x56493))
% 18.77/18.51 [5700]P140(x57001,x57002,x57003)+~P1(f324(x57001,f2(a1)))+P1(f324(f324(f232(a1),x57003),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x57003))
% 18.77/18.51 [5704]~P94(x57041)+E(f324(f324(f103(x57041),x57042),f12(x57041,x57043)),x57042)+~P1(f324(f64(x57041),x57043))+~P1(f324(f324(f326(x57041),x57042),x57043))
% 18.77/18.51 [5705]~P94(x57051)+E(f324(f324(f104(x57051),x57052),f15(x57051,x57053)),x57052)+~P1(f324(f64(x57051),x57053))+~P1(f324(f324(f326(x57051),x57052),x57053))
% 18.77/18.51 [5738]~P86(x57381)+E(f324(f324(f235(x57381),x57382),f17(x57381,x57383)),f17(x57381,x57383))+~P1(f324(f64(x57381),x57383))+~P1(f324(f324(f326(x57381),x57382),x57383))
% 18.77/18.51 [5739]~P86(x57391)+E(f324(f324(f178(x57391),x57392),f16(x57391,x57393)),f16(x57391,x57393))+~P1(f324(f64(x57391),x57393))+~P1(f324(f324(f326(x57391),x57392),x57393))
% 18.77/18.51 [5740]~P94(x57401)+E(f324(f324(f103(x57401),x57402),f15(x57401,x57403)),f15(x57401,x57403))+~P1(f324(f64(x57401),x57403))+~P1(f324(f324(f326(x57401),x57402),x57403))
% 18.77/18.51 [5741]~P94(x57411)+E(f324(f324(f104(x57411),x57412),f12(x57411,x57413)),f12(x57411,x57413))+~P1(f324(f64(x57411),x57413))+~P1(f324(f324(f326(x57411),x57412),x57413))
% 18.77/18.51 [5779]E(x57791,x57792)+~P85(x57793)+~P1(f324(f324(f231(x57793),x57792),x57791))+~P1(f324(f324(f231(x57793),x57791),x57792))
% 18.77/18.51 [5780]E(x57801,x57802)+~P85(x57803)+~P1(f324(f324(f231(x57803),x57802),x57801))+~P1(f324(f324(f231(x57803),x57801),x57802))
% 18.77/18.51 [5781]E(x57811,x57812)+~P85(x57813)+~P1(f324(f324(f231(x57813),x57812),x57811))+~P1(f324(f324(f231(x57813),x57811),x57812))
% 18.77/18.51 [5782]E(x57821,x57822)+~P85(x57823)+~P1(f324(f324(f231(x57823),x57822),x57821))+~P1(f324(f324(f231(x57823),x57821),x57822))
% 18.77/18.51 [5784]~E(x57841,x57842)+~P86(x57843)+~P1(f324(f324(f232(x57843),x57841),x57842))+~P1(f324(f324(f231(x57843),x57841),x57842))
% 18.77/18.51 [5926]~P102(x59261)+P1(f324(f324(f231(x59261),x59263),x59262))+~P1(f324(f324(f231(x59261),x59262),x59263))+P1(f324(f324(f232(x59261),x59262),x59263))
% 18.77/18.51 [5950]~P86(x59501)+~P1(f324(f64(x59501),x59503))+P1(f324(f324(f231(x59501),x59502),f16(x59501,x59503)))+~P1(f324(f324(f326(x59501),x59502),x59503))
% 18.77/18.51 [6004]~P86(x60041)+E(f324(f324(f235(x60041),x60042),f13(x60041,f178(x60041),x60043)),x60042)+~P1(f324(f64(x60041),x60043))+~P1(f324(f324(f326(x60041),x60042),x60043))
% 18.77/18.51 [6005]~P86(x60051)+E(f324(f324(f178(x60051),x60052),f14(x60051,f235(x60051),x60053)),x60052)+~P1(f324(f64(x60051),x60053))+~P1(f324(f324(f326(x60051),x60052),x60053))
% 18.77/18.51 [6147]E(x61471,x61472)+~E(f324(f324(f3(a838),x61471),x61473),f324(f324(f3(a838),x61472),x61473))+~P1(f324(f324(f231(a838),x61473),x61471))+~P1(f324(f324(f231(a838),x61473),x61472))
% 18.77/18.51 [6175]~P86(x61751)+~P1(f324(f64(x61751),x61752))+~P1(f324(f324(f326(x61751),x61753),x61752))+P1(f324(f324(f231(x61751),f17(x61751,x61752)),x61753))
% 18.77/18.51 [6218]E(x62181,f2(a838))+~P1(f324(f54(x62183,x62181),x62182))+P1(f324(f324(f232(a838),f2(a838)),x62181))+P1(f324(f324(f232(a838),x62181),f324(f251(a838,a838),x62182)))
% 18.77/18.51 [6241]P139(x62412,x62413,x62411)+E(x62411,f2(a1))+P1(f324(f324(f232(a1),x62411),f767(x62411,x62413,x62412)))+P1(f324(f324(f232(a1),f2(a1)),x62411))
% 18.77/18.51 [6242]P140(x62422,x62423,x62421)+E(x62421,f2(a1))+P1(f324(f324(f232(a1),x62421),f771(x62421,x62423,x62422)))+P1(f324(f324(f232(a1),f2(a1)),x62421))
% 18.77/18.51 [6243]~P86(x62431)+E(f324(f324(f235(x62431),x62432),f14(x62431,f235(x62431),x62433)),f14(x62431,f235(x62431),x62433))+~P1(f324(f64(x62431),x62433))+~P1(f324(f324(f326(x62431),x62432),x62433))
% 18.77/18.51 [6244]~P86(x62441)+E(f324(f324(f178(x62441),x62442),f13(x62441,f178(x62441),x62443)),f13(x62441,f178(x62441),x62443))+~P1(f324(f64(x62441),x62443))+~P1(f324(f324(f326(x62441),x62442),x62443))
% 18.77/18.51 [6251]~P1(f324(x62511,x62512))+P1(f324(x62511,f784(x62512,x62511,x62513)))+P1(f324(x62511,f2(a838)))+~P1(f324(f324(f232(a838),x62512),x62513))
% 18.77/18.51 [6289]~P1(f324(f324(f280(a838),x62892),x62891))+~P1(f324(f324(f280(a838),x62891),x62893))+P1(f324(f324(f280(a838),x62891),x62892))+P1(f324(f324(f280(a838),x62892),x62893))
% 18.77/18.51 [6290]~P1(f324(f324(f280(a838),x62903),x62902))+~P1(f324(f324(f280(a838),x62902),x62901))+P1(f324(f324(f280(a838),x62901),x62902))+P1(f324(f324(f280(a838),x62903),x62901))
% 18.77/18.51 [6310]~P1(f324(x63101,x63102))+~P1(f324(f64(x63103),x63102))+P1(f324(x63101,f430(x63101,x63102,x63103)))+P1(f324(x63101,f179(f845(x63103,a832))))
% 18.77/18.51 [6325]~P103(x63251)+~P89(x63251)+P1(f324(f324(f232(x63251),f324(f106(x63251),x63252)),f324(f106(x63251),x63253)))+~P1(f324(f324(f232(a1),x63252),x63253))
% 18.77/18.51 [6326]~P103(x63261)+~P89(x63261)+P1(f324(f324(f231(x63261),f324(f106(x63261),x63262)),f324(f106(x63261),x63263)))+~P1(f324(f324(f231(a1),x63262),x63263))
% 18.77/18.51 [6329]~P1(f324(x63291,x63293))+~P1(f324(f64(x63292),x63293))+P1(f324(f64(x63292),f430(x63291,x63293,x63292)))+P1(f324(x63291,f179(f845(x63292,a832))))
% 18.77/18.51 [6363]P139(x63631,x63632,x63633)+~P1(f324(x63631,x63632))+P1(f324(f324(f232(a1),x63633),f767(x63633,x63632,x63631)))+P1(f324(f324(f232(a1),f2(a1)),x63633))
% 18.77/18.51 [6402]P140(x64021,x64022,x64023)+P1(f324(f324(f232(a1),x64023),f771(x64023,x64022,x64021)))+~P1(f324(x64021,f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x64023))
% 18.77/18.51 [6430]~P101(x64301)+~P90(x64301)+E(f324(f324(f235(x64301),f324(f106(x64301),x64302)),f324(f106(x64301),x64303)),f324(f106(x64301),x64303))+P1(f324(f324(f231(x64301),f324(f106(x64301),x64302)),f324(f106(x64301),x64303)))
% 18.77/18.51 [6431]~P101(x64311)+~P90(x64311)+E(f324(f324(f178(x64311),f324(f106(x64311),x64312)),f324(f106(x64311),x64313)),f324(f106(x64311),x64312))+P1(f324(f324(f231(x64311),f324(f106(x64311),x64312)),f324(f106(x64311),x64313)))
% 18.77/18.51 [6438]E(x64381,f2(a838))+~P1(f324(f54(x64383,x64381),x64382))+~P1(f324(f324(f232(a838),f2(a838)),x64381))+P1(f324(f324(f231(a838),f2(a838)),f324(f251(a838,a838),x64382)))
% 18.77/18.51 [6444]~P1(f324(f324(f280(a838),x64441),x64443))+~P1(f324(f324(f280(a838),x64442),x64441))+~P1(f324(f324(f280(a838),x64443),x64442))+P1(f324(f324(f280(a838),x64441),x64442))
% 18.77/18.51 [6445]~P1(f324(f324(f280(a838),x64451),x64453))+~P1(f324(f324(f280(a838),x64452),x64451))+P1(f324(f324(f280(a838),x64451),x64452))+~P1(f324(f324(f280(a838),x64453),x64452))
% 18.77/18.51 [6493]P139(x64932,x64933,x64931)+E(x64931,f2(a1))+~P1(f324(x64932,f767(x64931,x64933,x64932)))+P1(f324(f324(f232(a1),f2(a1)),x64931))
% 18.77/18.51 [6494]P140(x64942,x64943,x64941)+E(x64941,f2(a1))+~P1(f324(x64942,f776(x64941,x64943,x64942)))+P1(f324(f324(f232(a1),f2(a1)),x64941))
% 18.77/18.51 [6515]~P7(x65151)+~P90(x65151)+~E(f51(x65151,f324(f106(x65151),x65153),f324(f106(x65151),x65152)),f2(x65151))+P1(f324(f324(f280(x65151),f324(f106(x65151),x65152)),f324(f106(x65151),x65153)))
% 18.77/18.51 [6589]P139(x65891,x65892,x65893)+~P1(f324(x65891,x65892))+~P1(f324(x65891,f767(x65893,x65892,x65891)))+P1(f324(f324(f232(a1),f2(a1)),x65893))
% 18.77/18.51 [6619]P140(x66191,x66192,x66193)+~P1(f324(x66191,f776(x66193,x66192,x66191)))+~P1(f324(x66191,f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x66193))
% 18.77/18.51 [6630]E(x66301,f2(a838))+~P1(f324(f54(x66303,x66301),x66302))+P1(f324(f324(f231(a838),f324(f251(a838,a838),x66302)),f2(a838)))+P1(f324(f324(f232(a838),f2(a838)),x66301))
% 18.77/18.51 [6735]~P89(x67353)+~P103(x67353)+~P1(f324(f324(f232(x67353),f324(f106(x67353),x67351)),f324(f106(x67353),x67352)))+P1(f324(f324(f232(a1),x67351),x67352))
% 18.77/18.51 [6736]~P89(x67363)+~P103(x67363)+~P1(f324(f324(f231(x67363),f324(f106(x67363),x67361)),f324(f106(x67363),x67362)))+P1(f324(f324(f231(a1),x67361),x67362))
% 18.77/18.51 [6768]~P86(x67681)+~P18(x67681,x67683)+P18(x67681,f324(f324(f139(x67681),x67682),x67683))+~P1(f324(f324(f231(x67681),x67682),f751(x67683,x67682,x67681)))
% 18.77/18.51 [6769]~P86(x67691)+~P18(x67691,x67693)+P18(x67691,f324(f324(f139(x67691),x67692),x67693))+~P1(f324(f324(f231(x67691),x67692),f755(x67693,x67692,x67691)))
% 18.77/18.51 [6842]~P7(x68421)+~P90(x68421)+E(f51(x68421,f324(f106(x68421),x68422),f324(f106(x68421),x68423)),f2(x68421))+~P1(f324(f324(f280(x68421),f324(f106(x68421),x68423)),f324(f106(x68421),x68422)))
% 18.77/18.51 [6856]P139(x68562,x68563,x68561)+E(x68561,f2(a1))+P1(f324(f324(f232(a1),x68561),f2(a1)))+P1(f324(f324(f232(a1),f768(x68561,x68563,x68562)),x68561))
% 18.77/18.51 [6857]P140(x68572,x68573,x68571)+E(x68571,f2(a1))+P1(f324(f324(f232(a1),x68571),f2(a1)))+P1(f324(f324(f232(a1),f772(x68571,x68573,x68572)),x68571))
% 18.77/18.51 [6862]~P86(x68621)+~P90(x68621)+P1(f324(f324(f232(x68621),f324(f106(x68621),x68622)),f324(f106(x68621),x68623)))+P1(f324(f324(f231(x68621),f324(f106(x68621),x68623)),f324(f106(x68621),x68622)))
% 18.77/18.51 [6896]P139(x68962,x68963,x68961)+E(x68961,f2(a1))+P1(f324(f324(f231(a1),f767(x68961,x68963,x68962)),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x68961))
% 18.77/18.51 [6897]P140(x68972,x68973,x68971)+E(x68971,f2(a1))+P1(f324(f324(f231(a1),f771(x68971,x68973,x68972)),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x68971))
% 18.77/18.51 [6915]~P86(x69151)+~P18(x69151,x69153)+E(f324(f324(f137(x69151,x69151,f7(x69151)),x69152),f155(x69151,x69152,x69153)),x69153)+~P1(f324(f324(f326(x69151),x69152),f324(f157(x69151),x69153)))
% 18.77/18.51 [6965]P139(x69651,x69652,x69653)+~P1(f324(x69651,x69652))+P1(f324(f324(f232(a1),x69653),f2(a1)))+P1(f324(f324(f232(a1),f768(x69653,x69652,x69651)),x69653))
% 18.77/18.51 [6971]~P101(x69711)+~P90(x69711)+E(f324(f324(f235(x69711),f324(f106(x69711),x69712)),f324(f106(x69711),x69713)),f324(f106(x69711),x69712))+~P1(f324(f324(f231(x69711),f324(f106(x69711),x69712)),f324(f106(x69711),x69713)))
% 18.77/18.51 [6972]~P101(x69721)+~P90(x69721)+E(f324(f324(f178(x69721),f324(f106(x69721),x69722)),f324(f106(x69721),x69723)),f324(f106(x69721),x69723))+~P1(f324(f324(f231(x69721),f324(f106(x69721),x69722)),f324(f106(x69721),x69723)))
% 18.77/18.51 [6985]P140(x69851,x69852,x69853)+~P1(f324(x69851,f2(a1)))+P1(f324(f324(f232(a1),x69853),f2(a1)))+P1(f324(f324(f232(a1),f772(x69853,x69852,x69851)),x69853))
% 18.77/18.51 [6995]P139(x69951,x69952,x69953)+~P1(f324(x69951,x69952))+P1(f324(f324(f231(a1),f767(x69953,x69952,x69951)),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x69953))
% 18.77/18.51 [7019]P140(x70191,x70192,x70193)+~P1(f324(x70191,f2(a1)))+P1(f324(f324(f231(a1),f771(x70193,x70192,x70191)),f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x70193))
% 18.77/18.51 [7046]~P1(f324(x70461,x70462))+P1(f324(x70461,f2(a838)))+~P1(f324(f324(f232(a838),x70462),x70463))+P1(f324(f324(f232(a838),f784(x70462,x70461,x70463)),x70463))
% 18.77/18.51 [7063]~P86(x70631)+~P18(x70631,x70633)+P18(x70631,f324(f324(f139(x70631),x70632),x70633))+P1(f324(f324(f326(x70631),f751(x70633,x70632,x70631)),f324(f157(x70631),x70633)))
% 18.77/18.51 [7064]~P86(x70641)+~P18(x70641,x70643)+P18(x70641,f324(f324(f139(x70641),x70642),x70643))+P1(f324(f324(f326(x70641),f755(x70643,x70642,x70641)),f324(f157(x70641),x70643)))
% 18.77/18.51 [7185]~P86(x71851)+~P9(x71851)+~P1(f324(f324(f232(x71851),x71853),f43(x71851,x71852)))+P1(f324(f324(f326(x71851),f652(x71852,x71853,x71851)),x71852))
% 18.77/18.51 [7354]~P86(x73541)+~P9(x73541)+~P1(f324(f324(f232(x73541),f44(x73541,x73543)),x73542))+P1(f324(f324(f326(x73541),f670(x73542,x73543,x73541)),x73543))
% 18.77/18.51 [7355]~P86(x73551)+~P9(x73551)+~P1(f324(f324(f232(x73551),f44(x73551,x73553)),x73552))+P1(f324(f324(f232(x73551),f670(x73552,x73553,x73551)),x73552))
% 18.77/18.51 [7372]P139(x73722,x73723,x73721)+E(x73721,f2(a1))+P1(f324(f324(f232(a1),x73721),f767(x73721,x73723,x73722)))+P1(f324(f324(f232(a1),f768(x73721,x73723,x73722)),x73721))
% 18.77/18.51 [7373]P140(x73732,x73733,x73731)+E(x73731,f2(a1))+P1(f324(f324(f232(a1),x73731),f771(x73731,x73733,x73732)))+P1(f324(f324(f232(a1),f772(x73731,x73733,x73732)),x73731))
% 18.77/18.51 [7469]P139(x74693,x74692,x74691)+E(x74691,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x74691),f770(x74691,x74692,x74693))),f767(x74691,x74692,x74693)),x74692)+P1(f324(f324(f232(a1),f2(a1)),x74691))
% 18.77/18.51 [7470]P140(x74703,x74702,x74701)+E(x74701,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x74701),f776(x74701,x74702,x74703))),f771(x74701,x74702,x74703)),x74702)+P1(f324(f324(f232(a1),f2(a1)),x74701))
% 18.77/18.51 [7471]~P122(x74711)+~P1(f324(f324(f232(x74711),x74712),f2(x74711)))+P1(f324(f324(f232(x74711),f324(f324(f83(x74711),x74712),x74713)),f2(x74711)))+~P1(f324(f324(f232(x74711),f2(x74711)),x74713))
% 18.77/18.51 [7472]~P122(x74721)+~P1(f324(f324(f232(x74721),x74723),f2(x74721)))+P1(f324(f324(f232(x74721),f324(f324(f83(x74721),x74722),x74723)),f2(x74721)))+~P1(f324(f324(f232(x74721),f2(x74721)),x74722))
% 18.77/18.51 [7473]~P122(x74731)+~P1(f324(f324(f232(x74731),x74732),f2(x74731)))+P1(f324(f324(f232(x74731),f324(f324(f83(x74731),x74732),x74733)),f2(x74731)))+~P1(f324(f324(f232(x74731),f2(x74731)),x74733))
% 18.77/18.51 [7474]~P61(x74741)+~P1(f324(f324(f232(x74741),x74743),f2(x74741)))+P1(f324(f324(f232(x74741),f324(f324(f284(x74741),x74742),x74743)),f2(x74741)))+~P1(f324(f324(f232(x74741),f2(x74741)),x74742))
% 18.77/18.51 [7475]~P61(x74751)+~P1(f324(f324(f232(x74751),x74752),f2(x74751)))+P1(f324(f324(f232(x74751),f324(f324(f284(x74751),x74752),x74753)),f2(x74751)))+~P1(f324(f324(f232(x74751),f2(x74751)),x74753))
% 18.77/18.51 [7476]~P62(x74761)+~P1(f324(f324(f232(x74761),x74763),f2(x74761)))+P1(f324(f324(f232(x74761),f324(f324(f284(x74761),x74762),x74763)),f2(x74761)))+~P1(f324(f324(f232(x74761),f2(x74761)),x74762))
% 18.77/18.51 [7477]~P62(x74771)+~P1(f324(f324(f232(x74771),x74772),f2(x74771)))+P1(f324(f324(f232(x74771),f324(f324(f284(x74771),x74772),x74773)),f2(x74771)))+~P1(f324(f324(f232(x74771),f2(x74771)),x74773))
% 18.77/18.51 [7478]~P127(x74781)+~P1(f324(f324(f231(x74781),x74782),f2(x74781)))+P1(f324(f324(f231(x74781),f324(f324(f83(x74781),x74782),x74783)),f2(x74781)))+~P1(f324(f324(f231(x74781),f2(x74781)),x74783))
% 18.77/18.51 [7479]~P117(x74791)+~P1(f324(f324(f231(x74791),x74793),f2(x74791)))+P1(f324(f324(f231(x74791),f324(f324(f83(x74791),x74792),x74793)),f2(x74791)))+~P1(f324(f324(f231(x74791),f2(x74791)),x74792))
% 18.77/18.51 [7480]~P117(x74801)+~P1(f324(f324(f231(x74801),x74802),f2(x74801)))+P1(f324(f324(f231(x74801),f324(f324(f83(x74801),x74802),x74803)),f2(x74801)))+~P1(f324(f324(f231(x74801),f2(x74801)),x74803))
% 18.77/18.51 [7481]~P127(x74811)+~P1(f324(f324(f231(x74811),x74813),f2(x74811)))+P1(f324(f324(f231(x74811),f324(f324(f83(x74811),x74812),x74813)),f2(x74811)))+~P1(f324(f324(f231(x74811),f2(x74811)),x74812))
% 18.77/18.51 [7482]~P127(x74821)+~P1(f324(f324(f231(x74821),x74823),f2(x74821)))+P1(f324(f324(f231(x74821),f324(f324(f83(x74821),x74822),x74823)),f2(x74821)))+~P1(f324(f324(f231(x74821),f2(x74821)),x74822))
% 18.77/18.51 [7483]~P127(x74831)+~P1(f324(f324(f231(x74831),x74832),f2(x74831)))+P1(f324(f324(f231(x74831),f324(f324(f83(x74831),x74832),x74833)),f2(x74831)))+~P1(f324(f324(f231(x74831),f2(x74831)),x74833))
% 18.77/18.51 [7484]~P127(x74841)+~P1(f324(f324(f231(x74841),x74842),f2(x74841)))+P1(f324(f324(f231(x74841),f324(f324(f83(x74841),x74842),x74843)),f2(x74841)))+~P1(f324(f324(f231(x74841),f2(x74841)),x74843))
% 18.77/18.51 [7485]~P61(x74851)+~P1(f324(f324(f231(x74851),x74853),f2(x74851)))+P1(f324(f324(f231(x74851),f324(f324(f284(x74851),x74852),x74853)),f2(x74851)))+~P1(f324(f324(f231(x74851),f2(x74851)),x74852))
% 18.77/18.51 [7486]~P61(x74861)+~P1(f324(f324(f231(x74861),x74862),f2(x74861)))+P1(f324(f324(f231(x74861),f324(f324(f284(x74861),x74862),x74863)),f2(x74861)))+~P1(f324(f324(f231(x74861),f2(x74861)),x74863))
% 18.77/18.51 [7487]~P62(x74871)+~P1(f324(f324(f232(x74871),x74873),f2(x74871)))+P1(f324(f324(f231(x74871),f324(f324(f284(x74871),x74872),x74873)),f2(x74871)))+~P1(f324(f324(f231(x74871),f2(x74871)),x74872))
% 18.77/18.51 [7488]~P62(x74881)+~P1(f324(f324(f231(x74881),x74882),f2(x74881)))+P1(f324(f324(f231(x74881),f324(f324(f284(x74881),x74882),x74883)),f2(x74881)))+~P1(f324(f324(f232(x74881),f2(x74881)),x74883))
% 18.77/18.51 [7504]P139(x75041,x75042,x75043)+~P1(f324(x75041,x75042))+P1(f324(f324(f232(a1),x75043),f767(x75043,x75042,x75041)))+P1(f324(f324(f232(a1),f768(x75043,x75042,x75041)),x75043))
% 18.77/18.51 [7517]P140(x75171,x75172,x75173)+P1(f324(f324(f232(a1),x75173),f771(x75173,x75172,x75171)))+~P1(f324(x75171,f2(a1)))+P1(f324(f324(f232(a1),f772(x75173,x75172,x75171)),x75173))
% 18.77/18.51 [7569]P139(x75692,x75693,x75691)+E(x75691,f2(a1))+~P1(f324(x75692,f767(x75691,x75693,x75692)))+P1(f324(f324(f232(a1),f768(x75691,x75693,x75692)),x75691))
% 18.77/18.51 [7570]P140(x75702,x75703,x75701)+E(x75701,f2(a1))+~P1(f324(x75702,f776(x75701,x75703,x75702)))+P1(f324(f324(f232(a1),f772(x75701,x75703,x75702)),x75701))
% 18.77/18.51 [7579]P139(x75793,x75792,x75791)+~P1(f324(x75793,x75792))+E(f324(f324(f82(a1),f324(f324(f83(a1),x75791),f770(x75791,x75792,x75793))),f767(x75791,x75792,x75793)),x75792)+P1(f324(f324(f232(a1),f2(a1)),x75791))
% 18.77/18.51 [7597]P140(x75973,x75972,x75971)+E(f324(f324(f82(a1),f324(f324(f83(a1),x75971),f776(x75971,x75972,x75973))),f771(x75971,x75972,x75973)),x75972)+~P1(f324(x75973,f2(a1)))+P1(f324(f324(f232(a1),f2(a1)),x75971))
% 18.77/18.51 [7622]~P1(f324(x76221,x76223))+~P1(f324(f64(x76222),x76223))+P1(f324(f324(f326(x76222),f431(x76221,x76223,x76222)),f430(x76221,x76223,x76222)))+P1(f324(x76221,f179(f845(x76222,a832))))
% 18.77/18.51 [7632]P139(x76321,x76322,x76323)+~P1(f324(x76321,x76322))+~P1(f324(x76321,f767(x76323,x76322,x76321)))+P1(f324(f324(f232(a1),f768(x76323,x76322,x76321)),x76323))
% 18.77/18.51 [7638]P140(x76381,x76382,x76383)+~P1(f324(x76381,f776(x76383,x76382,x76381)))+~P1(f324(x76381,f2(a1)))+P1(f324(f324(f232(a1),f772(x76383,x76382,x76381)),x76383))
% 18.77/18.51 [7709]~P2(x77093)+P1(f324(x77091,x77092))+~P1(f324(f324(f326(x77093),x77092),f175(x77093)))+~P1(f324(x77091,f324(f102(x77093),f396(x77091,x77092,x77093))))
% 18.77/18.51 [7711]~P90(x77111)+~P86(x77111)+~P1(f324(f324(f232(x77111),f324(f106(x77111),x77112)),f324(f106(x77111),x77113)))+~P1(f324(f324(f231(x77111),f324(f106(x77111),x77113)),f324(f106(x77111),x77112)))
% 18.77/18.51 [7748]~P61(x77481)+~P1(f324(f324(f232(x77481),f324(f324(f284(x77481),x77483),x77482)),f2(x77481)))+P1(f324(f324(f232(x77481),x77482),f2(x77481)))+P1(f324(f324(f232(x77481),f2(x77481)),x77482))
% 18.77/18.51 [7749]~P61(x77491)+~P1(f324(f324(f232(x77491),f324(f324(f284(x77491),x77492),x77493)),f2(x77491)))+P1(f324(f324(f232(x77491),x77492),f2(x77491)))+P1(f324(f324(f232(x77491),f2(x77491)),x77492))
% 18.77/18.51 [7750]~P117(x77501)+~P1(f324(f324(f231(x77501),f324(f324(f83(x77501),x77503),x77502)),f2(x77501)))+P1(f324(f324(f231(x77501),x77502),f2(x77501)))+P1(f324(f324(f231(x77501),f2(x77501)),x77502))
% 18.77/18.51 [7751]~P117(x77511)+~P1(f324(f324(f231(x77511),f324(f324(f83(x77511),x77512),x77513)),f2(x77511)))+P1(f324(f324(f231(x77511),x77512),f2(x77511)))+P1(f324(f324(f231(x77511),f2(x77511)),x77512))
% 18.77/18.51 [7752]~P61(x77521)+~P1(f324(f324(f231(x77521),f324(f324(f284(x77521),x77523),x77522)),f2(x77521)))+P1(f324(f324(f231(x77521),x77522),f2(x77521)))+P1(f324(f324(f231(x77521),f2(x77521)),x77522))
% 18.77/18.51 [7753]~P61(x77531)+~P1(f324(f324(f231(x77531),f324(f324(f284(x77531),x77532),x77533)),f2(x77531)))+P1(f324(f324(f231(x77531),x77532),f2(x77531)))+P1(f324(f324(f231(x77531),f2(x77531)),x77532))
% 18.77/18.51 [7779]~P61(x77791)+~P1(f324(f324(f232(x77791),f324(f324(f284(x77791),x77792),x77793)),f2(x77791)))+P1(f324(f324(f232(x77791),f2(x77791)),x77792))+P1(f324(f324(f232(x77791),f2(x77791)),x77793))
% 18.77/18.51 [7780]~P117(x77801)+~P1(f324(f324(f231(x77801),f324(f324(f83(x77801),x77802),x77803)),f2(x77801)))+P1(f324(f324(f231(x77801),f2(x77801)),x77802))+P1(f324(f324(f231(x77801),f2(x77801)),x77803))
% 18.77/18.51 [7781]~P61(x77811)+~P1(f324(f324(f231(x77811),f324(f324(f284(x77811),x77812),x77813)),f2(x77811)))+P1(f324(f324(f231(x77811),f2(x77811)),x77812))+P1(f324(f324(f231(x77811),f2(x77811)),x77813))
% 18.77/18.51 [7800]P139(x78002,x78003,x78001)+E(x78001,f2(a1))+P1(f324(f324(f231(a1),f767(x78001,x78003,x78002)),f2(a1)))+P1(f324(f324(f232(a1),f768(x78001,x78003,x78002)),x78001))
% 18.77/18.51 [7801]P140(x78012,x78013,x78011)+E(x78011,f2(a1))+P1(f324(f324(f231(a1),f771(x78011,x78013,x78012)),f2(a1)))+P1(f324(f324(f232(a1),f772(x78011,x78013,x78012)),x78011))
% 18.77/18.51 [7807]~P84(x78071)+~P1(f324(f324(f232(x78071),x78072),f80(x78071)))+P1(f324(f324(f232(x78071),f324(f324(f240(x78071),x78072),f324(a114,x78073))),f80(x78071)))+~P1(f324(f324(f232(x78071),f2(x78071)),x78072))
% 18.77/18.51 [7862]~P86(x78621)+~E(x78623,f115(x78621))+~P18(x78621,f324(f154(x78621),x78623))+E(f324(f131(x78621,x78621,f324(f9(x78621,x78621,x78621),f178(x78621)),x78622),f324(f154(x78621),x78623)),x78622)
% 18.77/18.51 [7864]P139(x78641,x78642,x78643)+~P1(f324(x78641,x78642))+P1(f324(f324(f231(a1),f767(x78643,x78642,x78641)),f2(a1)))+P1(f324(f324(f232(a1),f768(x78643,x78642,x78641)),x78643))
% 18.77/18.51 [7876]P140(x78761,x78762,x78763)+~P1(f324(x78761,f2(a1)))+P1(f324(f324(f231(a1),f771(x78763,x78762,x78761)),f2(a1)))+P1(f324(f324(f232(a1),f772(x78763,x78762,x78761)),x78763))
% 18.77/18.51 [8094]P139(x80943,x80942,x80941)+E(x80941,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x80941),f770(x80941,x80942,x80943))),f767(x80941,x80942,x80943)),x80942)+P1(f324(f324(f232(a1),f768(x80941,x80942,x80943)),x80941))
% 18.77/18.51 [8095]P140(x80953,x80952,x80951)+E(x80951,f2(a1))+E(f324(f324(f82(a1),f324(f324(f83(a1),x80951),f776(x80951,x80952,x80953))),f771(x80951,x80952,x80953)),x80952)+P1(f324(f324(f232(a1),f772(x80951,x80952,x80953)),x80951))
% 18.77/18.51 [8130]P139(x81303,x81302,x81301)+~P1(f324(x81303,x81302))+E(f324(f324(f82(a1),f324(f324(f83(a1),x81301),f770(x81301,x81302,x81303))),f767(x81301,x81302,x81303)),x81302)+P1(f324(f324(f232(a1),f768(x81301,x81302,x81303)),x81301))
% 18.77/18.51 [8131]~P67(x81311)+~P68(x81311)+~P38(x81313)+E(f324(f324(f11(a838,x81311),f324(f324(f10(a1,x81311,a838),x81312),f102(a1))),f324(f304(a1,a838,a107),x81313)),f324(f324(f11(a1,x81311),x81312),x81313))
% 18.77/18.51 [8132]~P67(x81321)+~P68(x81321)+~P38(x81323)+E(f324(f324(f8(a838,x81321),f324(f324(f10(a1,x81321,a838),x81322),f102(a1))),f324(f304(a1,a838,a107),x81323)),f324(f324(f8(a1,x81321),x81322),x81323))
% 18.77/18.51 [8141]P140(x81413,x81412,x81411)+E(f324(f324(f82(a1),f324(f324(f83(a1),x81411),f776(x81411,x81412,x81413))),f771(x81411,x81412,x81413)),x81412)+~P1(f324(x81413,f2(a1)))+P1(f324(f324(f232(a1),f772(x81411,x81412,x81413)),x81411))
% 18.77/18.51 [8160]~E(x81602,f2(a838))+~E(f324(f246(a838,a838),x81603),f2(a838))+~E(x81601,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x81603)),x81602)),f324(f251(a838,a838),x81603)))+P1(f324(f54(x81601,x81602),x81603))
% 18.77/18.51 [9003]P1(f324(f324(f231(a1),x90031),f2(a1)))+~P1(f324(f324(f232(a1),f324(f324(f82(a1),f324(f324(f83(a1),x90032),x90031)),x90033)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x90032))+~P1(f324(f324(f231(a1),f2(a1)),x90033))
% 18.77/18.51 [5600]~P94(x56002)+E(x56001,f179(f845(x56002,a832)))+~P1(f324(f64(x56002),x56001))+E(f12(x56002,f324(f324(f303(x56002),x56003),x56001)),f324(f324(f104(x56002),x56003),f12(x56002,x56001)))
% 18.77/18.51 [5601]~P86(x56012)+E(x56011,f179(f845(x56012,a832)))+~P1(f324(f64(x56012),x56011))+E(f16(x56012,f324(f324(f303(x56012),x56013),x56011)),f324(f324(f178(x56012),x56013),f16(x56012,x56011)))
% 18.77/18.51 [5602]~P86(x56022)+E(x56021,f179(f845(x56022,a832)))+~P1(f324(f64(x56022),x56021))+E(f17(x56022,f324(f324(f303(x56022),x56023),x56021)),f324(f324(f235(x56022),x56023),f17(x56022,x56021)))
% 18.77/18.51 [5603]~P94(x56032)+E(x56031,f179(f845(x56032,a832)))+~P1(f324(f64(x56032),x56031))+E(f15(x56032,f324(f324(f303(x56032),x56033),x56031)),f324(f324(f103(x56032),x56033),f15(x56032,x56031)))
% 18.77/18.51 [5923]~P117(x59231)+~E(x59233,f2(x59231))+~E(x59232,f2(x59231))+E(f324(f324(f82(x59231),f324(f324(f83(x59231),x59232),x59232)),f324(f324(f83(x59231),x59233),x59233)),f2(x59231))
% 18.77/18.51 [5998]~P92(x59982)+E(x59981,f179(f845(x59982,a832)))+~P1(f324(f64(x59982),x59981))+E(f324(f66(x59982,f83(x59982)),f324(f324(f303(x59982),x59983),x59981)),f324(f324(f83(x59982),x59983),f324(f66(x59982,f83(x59982)),x59981)))
% 18.77/18.51 [6125]~P86(x61252)+E(x61251,f179(f845(x61252,a832)))+~P1(f324(f64(x61252),x61251))+E(f13(x61252,f178(x61252),f324(f324(f303(x61252),x61253),x61251)),f324(f324(f178(x61252),x61253),f13(x61252,f178(x61252),x61251)))
% 18.77/18.51 [6126]~P86(x61262)+E(x61261,f179(f845(x61262,a832)))+~P1(f324(f64(x61262),x61261))+E(f14(x61262,f235(x61262),f324(f324(f303(x61262),x61263),x61261)),f324(f324(f235(x61262),x61263),f14(x61262,f235(x61262),x61261)))
% 18.77/18.51 [6536]~P94(x65361)+~P1(f324(f64(x65361),x65363))+E(f324(f324(f67(x65361,x65361,f104(x65361)),x65362),x65363),f12(x65361,f324(f324(f303(x65361),x65362),x65363)))+P1(f324(f324(f326(x65361),x65362),x65363))
% 18.77/18.51 [6537]~P86(x65371)+~P1(f324(f64(x65371),x65373))+E(f324(f324(f67(x65371,x65371,f178(x65371)),x65372),x65373),f16(x65371,f324(f324(f303(x65371),x65372),x65373)))+P1(f324(f324(f326(x65371),x65372),x65373))
% 18.77/18.51 [6538]~P86(x65381)+~P1(f324(f64(x65381),x65383))+E(f324(f324(f67(x65381,x65381,f235(x65381)),x65382),x65383),f17(x65381,f324(f324(f303(x65381),x65382),x65383)))+P1(f324(f324(f326(x65381),x65382),x65383))
% 18.77/18.51 [6539]~P94(x65391)+~P1(f324(f64(x65391),x65393))+E(f324(f324(f67(x65391,x65391,f103(x65391)),x65392),x65393),f15(x65391,f324(f324(f303(x65391),x65392),x65393)))+P1(f324(f324(f326(x65391),x65392),x65393))
% 18.77/18.51 [6654]~P4(x66541)+~P1(f324(f64(x66541),x66543))+E(f324(f66(x66541,f83(x66541)),f324(f324(f303(x66541),x66542),x66543)),f324(f324(f67(x66541,x66541,f83(x66541)),x66542),x66543))+P1(f324(f324(f326(x66541),x66542),x66543))
% 18.77/18.51 [6672]~P86(x66721)+~P1(f324(f64(x66721),x66723))+E(f13(x66721,f178(x66721),f324(f324(f303(x66721),x66722),x66723)),f324(f324(f67(x66721,x66721,f178(x66721)),x66722),x66723))+P1(f324(f324(f326(x66721),x66722),x66723))
% 18.77/18.51 [6673]~P86(x66731)+~P1(f324(f64(x66731),x66733))+E(f14(x66731,f235(x66731),f324(f324(f303(x66731),x66732),x66733)),f324(f324(f67(x66731,x66731,f235(x66731)),x66732),x66733))+P1(f324(f324(f326(x66731),x66732),x66733))
% 18.77/18.51 [6743]~E(f324(f324(f82(a1),x67432),f324(f324(f83(a1),x67433),x67431)),x67433)+~P1(f324(f324(f232(a1),f2(a1)),x67433))+P1(f324(f324(f231(a1),f80(a1)),x67431))+~P1(f324(f324(f232(a1),x67432),x67433))
% 18.77/18.51 [6774]~E(f324(f324(f82(a1),x67742),f324(f324(f83(a1),x67743),x67741)),x67743)+P1(f324(f324(f231(a1),x67741),f80(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x67743))+~P1(f324(f324(f231(a1),f2(a1)),x67742))
% 18.77/18.51 [6792]E(x67921,f2(a838))+~P1(f324(f54(x67923,x67921),x67922))+~P1(f324(f324(f232(a838),f2(a838)),x67921))+P1(f324(f324(f232(a838),f324(f251(a838,a838),x67922)),x67921))
% 18.77/18.51 [6821]~P131(x68211)+~P1(f324(f324(f231(x68211),x68212),f2(x68211)))+~P1(f324(f324(f231(x68211),x68213),f2(x68211)))+E(f324(f324(f83(x68211),f324(f77(x68211),x68212)),f324(f77(x68211),x68213)),f324(f77(x68211),f324(f324(f83(x68211),x68212),x68213)))
% 18.77/18.51 [6873]~P131(x68731)+~P1(f324(f324(f231(x68731),x68732),f2(x68731)))+E(f324(f324(f83(x68731),f324(f77(x68731),x68732)),f324(f77(x68731),x68733)),f324(f77(x68731),f324(f324(f83(x68731),x68732),x68733)))+~P1(f324(f324(f231(x68731),f2(x68731)),x68733))
% 18.77/18.51 [6874]~P131(x68741)+~P1(f324(f324(f231(x68741),x68743),f2(x68741)))+E(f324(f324(f83(x68741),f324(f77(x68741),x68742)),f324(f77(x68741),x68743)),f324(f77(x68741),f324(f324(f83(x68741),x68742),x68743)))+~P1(f324(f324(f231(x68741),f2(x68741)),x68742))
% 18.77/18.51 [6924]~P131(x69241)+E(f324(f324(f83(x69241),f324(f77(x69241),x69242)),f324(f77(x69241),x69243)),f324(f77(x69241),f324(f324(f83(x69241),x69242),x69243)))+~P1(f324(f324(f231(x69241),f2(x69241)),x69242))+~P1(f324(f324(f231(x69241),f2(x69241)),x69243))
% 18.77/18.51 [6942]~P117(x69421)+~P1(f324(f324(f232(x69421),x69423),f2(x69421)))+~P1(f324(f324(f232(x69421),x69422),f2(x69421)))+P1(f324(f324(f232(x69421),f2(x69421)),f324(f324(f83(x69421),x69422),x69423)))
% 18.77/18.51 [6943]~P61(x69431)+~P1(f324(f324(f232(x69431),x69433),f2(x69431)))+~P1(f324(f324(f232(x69431),x69432),f2(x69431)))+P1(f324(f324(f232(x69431),f2(x69431)),f324(f324(f284(x69431),x69432),x69433)))
% 18.77/18.51 [6944]~P62(x69441)+~P1(f324(f324(f232(x69441),x69443),f2(x69441)))+~P1(f324(f324(f232(x69441),x69442),f2(x69441)))+P1(f324(f324(f232(x69441),f2(x69441)),f324(f324(f284(x69441),x69442),x69443)))
% 18.77/18.51 [6945]~P117(x69451)+~P1(f324(f324(f231(x69451),x69453),f2(x69451)))+~P1(f324(f324(f231(x69451),x69452),f2(x69451)))+P1(f324(f324(f231(x69451),f2(x69451)),f324(f324(f83(x69451),x69452),x69453)))
% 18.77/18.51 [6946]~P128(x69461)+~P1(f324(f324(f231(x69461),x69463),f2(x69461)))+~P1(f324(f324(f231(x69461),x69462),f2(x69461)))+P1(f324(f324(f231(x69461),f2(x69461)),f324(f324(f83(x69461),x69462),x69463)))
% 18.77/18.51 [6947]~P128(x69471)+~P1(f324(f324(f231(x69471),x69473),f2(x69471)))+~P1(f324(f324(f231(x69471),x69472),f2(x69471)))+P1(f324(f324(f231(x69471),f2(x69471)),f324(f324(f83(x69471),x69472),x69473)))
% 18.77/18.51 [6948]~P61(x69481)+~P1(f324(f324(f231(x69481),x69483),f2(x69481)))+~P1(f324(f324(f231(x69481),x69482),f2(x69481)))+P1(f324(f324(f231(x69481),f2(x69481)),f324(f324(f284(x69481),x69482),x69483)))
% 18.77/18.51 [6949]~P62(x69491)+~P1(f324(f324(f232(x69491),x69493),f2(x69491)))+~P1(f324(f324(f231(x69491),x69492),f2(x69491)))+P1(f324(f324(f231(x69491),f2(x69491)),f324(f324(f284(x69491),x69492),x69493)))
% 18.77/18.51 [6950]~P84(x69501)+~P1(f324(f324(f232(a838),f2(a838)),x69503))+~P1(f324(f324(f232(x69501),f80(x69501)),x69502))+P1(f324(f324(f232(x69501),f80(x69501)),f324(f324(f240(x69501),x69502),x69503)))
% 18.77/18.51 [7047]~P122(x70471)+~P1(f324(f324(f232(x70471),f2(x70471)),x70473))+~P1(f324(f324(f232(x70471),f2(x70471)),x70472))+P1(f324(f324(f232(x70471),f2(x70471)),f324(f324(f83(x70471),x70472),x70473)))
% 18.77/18.51 [7048]~P80(x70481)+~P1(f324(f324(f232(x70481),f2(x70481)),x70483))+~P1(f324(f324(f232(x70481),f2(x70481)),x70482))+P1(f324(f324(f232(x70481),f2(x70481)),f324(f324(f82(x70481),x70482),x70483)))
% 18.77/18.51 [7049]~P80(x70491)+~P1(f324(f324(f231(x70491),f2(x70491)),x70492))+~P1(f324(f324(f232(x70491),f2(x70491)),x70493))+P1(f324(f324(f232(x70491),f2(x70491)),f324(f324(f82(x70491),x70492),x70493)))
% 18.77/18.51 [7050]~P80(x70501)+~P1(f324(f324(f231(x70501),f2(x70501)),x70503))+~P1(f324(f324(f232(x70501),f2(x70501)),x70502))+P1(f324(f324(f232(x70501),f2(x70501)),f324(f324(f82(x70501),x70502),x70503)))
% 18.77/18.51 [7051]~P61(x70511)+~P1(f324(f324(f232(x70511),f2(x70511)),x70513))+~P1(f324(f324(f232(x70511),f2(x70511)),x70512))+P1(f324(f324(f232(x70511),f2(x70511)),f324(f324(f284(x70511),x70512),x70513)))
% 18.77/18.51 [7052]~P62(x70521)+~P1(f324(f324(f232(x70521),f2(x70521)),x70523))+~P1(f324(f324(f232(x70521),f2(x70521)),x70522))+P1(f324(f324(f232(x70521),f2(x70521)),f324(f324(f284(x70521),x70522),x70523)))
% 18.77/18.51 [7053]~P84(x70531)+~P1(f324(f324(f232(x70531),f80(x70531)),x70533))+~P1(f324(f324(f232(x70531),f80(x70531)),x70532))+P1(f324(f324(f232(x70531),f80(x70531)),f324(f324(f83(x70531),x70532),x70533)))
% 18.77/18.51 [7054]~P117(x70541)+~P1(f324(f324(f231(x70541),f2(x70541)),x70543))+~P1(f324(f324(f231(x70541),f2(x70541)),x70542))+P1(f324(f324(f231(x70541),f2(x70541)),f324(f324(f83(x70541),x70542),x70543)))
% 18.77/18.51 [7055]~P127(x70551)+~P1(f324(f324(f231(x70551),f2(x70551)),x70553))+~P1(f324(f324(f231(x70551),f2(x70551)),x70552))+P1(f324(f324(f231(x70551),f2(x70551)),f324(f324(f83(x70551),x70552),x70553)))
% 18.77/18.51 [7056]~P128(x70561)+~P1(f324(f324(f231(x70561),f2(x70561)),x70563))+~P1(f324(f324(f231(x70561),f2(x70561)),x70562))+P1(f324(f324(f231(x70561),f2(x70561)),f324(f324(f83(x70561),x70562),x70563)))
% 18.77/18.51 [7057]~P80(x70571)+~P1(f324(f324(f231(x70571),f2(x70571)),x70573))+~P1(f324(f324(f231(x70571),f2(x70571)),x70572))+P1(f324(f324(f231(x70571),f2(x70571)),f324(f324(f82(x70571),x70572),x70573)))
% 18.77/18.51 [7058]~P61(x70581)+~P1(f324(f324(f231(x70581),f2(x70581)),x70583))+~P1(f324(f324(f231(x70581),f2(x70581)),x70582))+P1(f324(f324(f231(x70581),f2(x70581)),f324(f324(f284(x70581),x70582),x70583)))
% 18.77/18.51 [7059]~P62(x70591)+~P1(f324(f324(f232(x70591),f2(x70591)),x70593))+~P1(f324(f324(f231(x70591),f2(x70591)),x70592))+P1(f324(f324(f231(x70591),f2(x70591)),f324(f324(f284(x70591),x70592),x70593)))
% 18.77/18.51 [7136]~P94(x71361)+~P1(f324(f64(x71361),x71363))+E(f12(x71361,f324(f324(f303(x71361),x71362),x71363)),x71362)+~E(f324(f324(f3(f845(x71361,a832)),x71363),f324(f324(f303(x71361),x71362),f179(f845(x71361,a832)))),f179(f845(x71361,a832)))
% 18.77/18.51 [7137]~P86(x71371)+~P1(f324(f64(x71371),x71373))+E(f16(x71371,f324(f324(f303(x71371),x71372),x71373)),x71372)+~E(f324(f324(f3(f845(x71371,a832)),x71373),f324(f324(f303(x71371),x71372),f179(f845(x71371,a832)))),f179(f845(x71371,a832)))
% 18.77/18.51 [7138]~P86(x71381)+~P1(f324(f64(x71381),x71383))+E(f17(x71381,f324(f324(f303(x71381),x71382),x71383)),x71382)+~E(f324(f324(f3(f845(x71381,a832)),x71383),f324(f324(f303(x71381),x71382),f179(f845(x71381,a832)))),f179(f845(x71381,a832)))
% 18.77/18.51 [7139]~P94(x71391)+~P1(f324(f64(x71391),x71393))+E(f15(x71391,f324(f324(f303(x71391),x71392),x71393)),x71392)+~E(f324(f324(f3(f845(x71391,a832)),x71393),f324(f324(f303(x71391),x71392),f179(f845(x71391,a832)))),f179(f845(x71391,a832)))
% 18.77/18.51 [7140]~P61(x71401)+P1(f324(f324(f232(x71401),x71402),f2(x71401)))+P1(f324(f324(f232(x71401),f2(x71401)),x71403))+~P1(f324(f324(f232(x71401),f2(x71401)),f324(f324(f284(x71401),x71403),x71402)))
% 18.77/18.51 [7141]~P61(x71411)+P1(f324(f324(f232(x71411),x71412),f2(x71411)))+P1(f324(f324(f232(x71411),f2(x71411)),x71413))+~P1(f324(f324(f232(x71411),f2(x71411)),f324(f324(f284(x71411),x71412),x71413)))
% 18.77/18.51 [7142]~P61(x71421)+P1(f324(f324(f232(x71421),x71422),f2(x71421)))+P1(f324(f324(f232(x71421),f2(x71421)),x71422))+~P1(f324(f324(f232(x71421),f2(x71421)),f324(f324(f284(x71421),x71423),x71422)))
% 18.77/18.51 [7143]~P61(x71431)+P1(f324(f324(f232(x71431),x71432),f2(x71431)))+P1(f324(f324(f232(x71431),f2(x71431)),x71432))+~P1(f324(f324(f232(x71431),f2(x71431)),f324(f324(f284(x71431),x71432),x71433)))
% 18.77/18.51 [7144]~P117(x71441)+P1(f324(f324(f231(x71441),x71442),f2(x71441)))+P1(f324(f324(f231(x71441),f2(x71441)),x71443))+~P1(f324(f324(f231(x71441),f2(x71441)),f324(f324(f83(x71441),x71443),x71442)))
% 18.77/18.51 [7145]~P117(x71451)+P1(f324(f324(f231(x71451),x71452),f2(x71451)))+P1(f324(f324(f231(x71451),f2(x71451)),x71453))+~P1(f324(f324(f231(x71451),f2(x71451)),f324(f324(f83(x71451),x71452),x71453)))
% 18.77/18.51 [7146]~P61(x71461)+P1(f324(f324(f231(x71461),x71462),f2(x71461)))+P1(f324(f324(f231(x71461),f2(x71461)),x71463))+~P1(f324(f324(f231(x71461),f2(x71461)),f324(f324(f284(x71461),x71463),x71462)))
% 18.77/18.51 [7147]~P61(x71471)+P1(f324(f324(f231(x71471),x71472),f2(x71471)))+P1(f324(f324(f231(x71471),f2(x71471)),x71473))+~P1(f324(f324(f231(x71471),f2(x71471)),f324(f324(f284(x71471),x71472),x71473)))
% 18.77/18.51 [7148]~P117(x71481)+P1(f324(f324(f231(x71481),x71482),f2(x71481)))+P1(f324(f324(f231(x71481),f2(x71481)),x71482))+~P1(f324(f324(f231(x71481),f2(x71481)),f324(f324(f83(x71481),x71483),x71482)))
% 18.77/18.51 [7149]~P117(x71491)+P1(f324(f324(f231(x71491),x71492),f2(x71491)))+P1(f324(f324(f231(x71491),f2(x71491)),x71492))+~P1(f324(f324(f231(x71491),f2(x71491)),f324(f324(f83(x71491),x71492),x71493)))
% 18.77/18.51 [7150]~P61(x71501)+P1(f324(f324(f231(x71501),x71502),f2(x71501)))+P1(f324(f324(f231(x71501),f2(x71501)),x71502))+~P1(f324(f324(f231(x71501),f2(x71501)),f324(f324(f284(x71501),x71503),x71502)))
% 18.77/18.51 [7151]~P61(x71511)+P1(f324(f324(f231(x71511),x71512),f2(x71511)))+P1(f324(f324(f231(x71511),f2(x71511)),x71512))+~P1(f324(f324(f231(x71511),f2(x71511)),f324(f324(f284(x71511),x71512),x71513)))
% 18.77/18.51 [7236]~P1(f324(f324(f280(a838),x72361),x72363))+P1(f324(f324(f280(a838),x72361),x72362))+~P1(f324(f324(f231(a838),x72362),x72363))+~P1(f324(f324(f280(a838),x72361),f324(f324(f3(a838),x72363),x72362)))
% 18.77/18.51 [7237]~P1(f324(f324(f280(a838),x72371),x72373))+P1(f324(f324(f280(a838),x72371),x72372))+~P1(f324(f324(f231(a838),x72373),x72372))+~P1(f324(f324(f280(a838),x72371),f324(f324(f3(a838),x72372),x72373)))
% 18.77/18.51 [7252]~E(f324(f324(f104(f845(x72521,a832)),f324(f157(x72521),x72522)),f324(f157(x72521),x72523)),f179(f845(x72521,a832)))+~P1(f324(f127(x72521),x72523))+~P1(f324(f127(x72521),x72522))+P1(f324(f127(x72521),f324(f324(f125(x72521),x72522),x72523)))
% 18.77/18.51 [7253]~P86(x72531)+~P1(f324(f64(x72531),x72533))+E(f13(x72531,f178(x72531),f324(f324(f303(x72531),x72532),x72533)),x72532)+~E(f324(f324(f3(f845(x72531,a832)),x72533),f324(f324(f303(x72531),x72532),f179(f845(x72531,a832)))),f179(f845(x72531,a832)))
% 18.77/18.51 [7254]~P86(x72541)+~P1(f324(f64(x72541),x72543))+E(f14(x72541,f235(x72541),f324(f324(f303(x72541),x72542),x72543)),x72542)+~E(f324(f324(f3(f845(x72541,a832)),x72543),f324(f324(f303(x72541),x72542),f179(f845(x72541,a832)))),f179(f845(x72541,a832)))
% 18.77/18.51 [7272]~P103(x72721)+~P1(f324(f324(f232(x72721),x72722),x72723))+~P1(f324(f324(f232(x72721),f324(f81(x72721),x72722)),x72723))+P1(f324(f324(f232(x72721),f324(f77(x72721),x72722)),x72723))
% 18.77/18.51 [7273]~P78(x72731)+~P1(f324(f324(f231(x72731),x72732),x72733))+~P1(f324(f324(f231(x72731),f324(f81(x72731),x72732)),x72733))+P1(f324(f324(f231(x72731),f324(f77(x72731),x72732)),x72733))
% 18.77/18.51 [7274]~P78(x72741)+~P1(f324(f324(f231(x72741),x72742),x72743))+~P1(f324(f324(f231(x72741),f324(f81(x72741),x72742)),x72743))+P1(f324(f324(f231(x72741),f324(f77(x72741),x72742)),x72743))
% 18.77/18.51 [7343]~P122(x73431)+P1(f324(f324(f232(x73431),f2(x73431)),x73432))+~P1(f324(f324(f232(x73431),f2(x73431)),x73433))+~P1(f324(f324(f232(x73431),f2(x73431)),f324(f324(f83(x73431),x73433),x73432)))
% 18.77/18.51 [7344]~P122(x73441)+P1(f324(f324(f232(x73441),f2(x73441)),x73442))+~P1(f324(f324(f232(x73441),f2(x73441)),x73443))+~P1(f324(f324(f232(x73441),f2(x73441)),f324(f324(f83(x73441),x73442),x73443)))
% 18.77/18.51 [7655]E(x76551,x76552)+~P1(f324(f64(x76553),x76551))+~P1(f324(f324(f231(a838),f324(f41(x76553),x76551)),f324(f41(x76553),x76552)))+~P1(f324(f324(f231(f845(x76553,a832)),x76552),x76551))
% 18.77/18.51 [7728]~P1(f324(f324(f231(a838),x77282),x77281))+~P1(f324(f324(f232(a838),x77281),x77283))+~P1(f324(f324(f231(a838),x77282),x77283))+P1(f324(f324(f232(a838),f324(f324(f3(a838),x77281),x77282)),f324(f324(f3(a838),x77283),x77282)))
% 18.77/18.51 [7729]~P1(f324(f324(f231(a838),x77292),x77291))+~P1(f324(f324(f231(a838),x77292),x77293))+~P1(f324(f324(f231(a838),x77291),x77293))+P1(f324(f324(f231(a838),f324(f324(f3(a838),x77291),x77292)),f324(f324(f3(a838),x77293),x77292)))
% 18.77/18.51 [7804]~P1(f324(f324(f232(a1),x78041),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x78042))+~P1(f324(f324(f231(a1),x78042),x78043))+P1(f324(f324(f231(a1),f324(f324(f42(a1),x78041),x78042)),f324(f324(f42(a1),x78041),x78043)))
% 18.77/18.51 [7815]~P1(f324(f324(f232(a1),f2(a1)),x78153))+~P1(f324(f324(f231(a1),f2(a1)),x78151))+~P1(f324(f324(f231(a1),x78153),x78152))+P1(f324(f324(f231(a1),f324(f324(f42(a1),x78151),x78152)),f324(f324(f42(a1),x78151),x78153)))
% 18.77/18.51 [7953]E(f324(x79531,f793(x79532,x79531,x79533)),x79532)+~P1(f324(f324(f231(a1),x79532),f324(x79531,x79533)))+P1(f324(f324(f232(a838),f794(x79532,x79531,x79533)),x79533))+~P1(f324(f324(f231(a1),f324(x79531,f2(a838))),x79532))
% 18.77/18.51 [7954]E(f324(x79541,f797(x79542,x79541,x79543)),x79542)+~P1(f324(f324(f231(a1),x79542),f324(x79541,x79543)))+P1(f324(f324(f232(a838),f798(x79542,x79541,x79543)),x79543))+~P1(f324(f324(f231(a1),f324(x79541,f2(a838))),x79542))
% 18.77/18.51 [8054]~P1(f324(f64(x80541),x80543))+~P1(f324(f324(f232(a838),f324(f41(x80541),x80542)),f324(f41(x80541),x80543)))+~P1(f324(f324(f231(f845(x80541,a832)),x80542),x80543))+P1(f324(f324(f232(f845(x80541,a832)),x80542),x80543))
% 18.77/18.51 [8083]E(f324(f324(f3(a1),f454(x80833,x80831,x80832)),f455(x80833,x80831,x80832)),x80831)+E(f324(f324(f82(a1),x80831),x80832),x80831)+~P1(f324(f324(f232(a1),f2(a1)),x80832))+~P1(f324(f324(f326(a1),f324(f324(f82(a1),x80831),f80(a1))),x80833))
% 18.77/18.51 [8084]E(f324(f324(f82(a1),f443(x80843,x80841,x80842)),f444(x80843,x80841,x80842)),x80841)+E(f324(f324(f3(a1),x80841),x80842),x80841)+~P1(f324(f324(f232(a1),f2(a1)),x80842))+~P1(f324(f324(f326(a1),f324(f324(f3(a1),x80841),f80(a1))),x80843))
% 18.77/18.51 [8136]~P1(f324(f324(f231(a838),x81363),x81361))+P1(f324(f324(f232(a838),x81361),x81362))+~P1(f324(f324(f231(a838),x81363),x81362))+~P1(f324(f324(f232(a838),f324(f324(f3(a838),x81361),x81363)),f324(f324(f3(a838),x81362),x81363)))
% 18.77/18.51 [8137]~P1(f324(f324(f231(a838),x81373),x81371))+P1(f324(f324(f231(a838),x81371),x81372))+~P1(f324(f324(f231(a838),x81373),x81372))+~P1(f324(f324(f231(a838),f324(f324(f3(a838),x81371),x81373)),f324(f324(f3(a838),x81372),x81373)))
% 18.77/18.51 [8153]~P86(x81532)+E(x81531,f115(x81532))+~P18(x81532,f324(f154(x81532),x81531))+E(f324(f131(x81532,x81532,f324(f9(x81532,x81532,x81532),f178(x81532)),x81533),f324(f154(x81532),x81531)),f324(f324(f178(x81532),f324(f324(f149(x81532),x81531),f2(a838))),x81533))
% 18.77/18.51 [8218]E(f324(f324(f82(a1),x82181),x82182),x82181)+~P1(f324(f324(f232(a1),f2(a1)),x82182))+P1(f324(f324(f326(a1),f454(x82183,x82181,x82182)),x82183))+~P1(f324(f324(f326(a1),f324(f324(f82(a1),x82181),f80(a1))),x82183))
% 18.77/18.51 [8219]E(f324(f324(f3(a1),x82191),x82192),x82191)+~P1(f324(f324(f232(a1),f2(a1)),x82192))+P1(f324(f324(f326(a1),f443(x82193,x82191,x82192)),x82193))+~P1(f324(f324(f326(a1),f324(f324(f3(a1),x82191),f80(a1))),x82193))
% 18.77/18.51 [8297]~P1(f324(f324(f231(a1),x82971),f324(x82972,x82973)))+P1(f324(f324(f231(a838),f793(x82971,x82972,x82973)),x82973))+P1(f324(f324(f232(a838),f794(x82971,x82972,x82973)),x82973))+~P1(f324(f324(f231(a1),f324(x82972,f2(a838))),x82971))
% 18.77/18.51 [8298]~P1(f324(f324(f231(a1),x82981),f324(x82982,x82983)))+P1(f324(f324(f231(a838),f797(x82981,x82982,x82983)),x82983))+P1(f324(f324(f232(a838),f798(x82981,x82982,x82983)),x82983))+~P1(f324(f324(f231(a1),f324(x82982,f2(a838))),x82981))
% 18.77/18.51 [8374]E(f324(f324(f82(a1),x83741),x83742),x83741)+~P1(f324(f324(f232(a1),f2(a1)),x83742))+P1(f324(f324(f326(a1),f455(x83743,x83741,x83742)),f296(a1,f80(a1),x83742)))+~P1(f324(f324(f326(a1),f324(f324(f82(a1),x83741),f80(a1))),x83743))
% 18.77/18.51 [8375]E(f324(f324(f3(a1),x83751),x83752),x83751)+~P1(f324(f324(f232(a1),f2(a1)),x83752))+P1(f324(f324(f326(a1),f444(x83753,x83751,x83752)),f296(a1,f80(a1),x83752)))+~P1(f324(f324(f326(a1),f324(f324(f3(a1),x83751),f80(a1))),x83753))
% 18.77/18.51 [8497]~P84(x84971)+~P1(f324(f324(f232(x84971),x84972),f80(x84971)))+~P1(f324(f324(f232(x84971),f2(x84971)),x84972))+P1(f324(f324(f232(x84971),f324(f324(f83(x84971),x84972),f324(f324(f240(x84971),x84972),x84973))),f324(f324(f240(x84971),x84972),x84973)))
% 18.77/18.51 [8573]~P1(f324(x85731,x85732))+P1(f324(x85731,f2(a838)))+~P1(f324(f324(f232(a838),x85732),x85733))+~P1(f324(x85731,f51(a838,f324(a114,f784(x85732,x85731,x85733)),x85733)))
% 18.77/18.51 [8706]E(f811(x87061,x87062,x87063),f2(a838))+P1(f324(f324(x87061,x87063),x87062))+P1(f324(f324(x87061,f811(x87061,x87062,x87063)),f51(a838,f810(x87061,x87062,x87063),f811(x87061,x87062,x87063))))+~P1(f324(f313(f844(a838,a838),a213),f324(f324(f247(a838,a838),x87063),x87062)))
% 18.77/18.51 [8739]~P29(x87391,x87391,x87392,x87393)+E(f324(f304(x87391,x87391,x87392),x87393),x87393)+~P1(f324(f64(x87391),x87393))+~P1(f324(f324(f231(f845(x87391,a832)),f324(f304(x87391,x87391,x87392),x87393)),x87393))
% 18.77/18.51 [8952]P1(f324(f324(x89521,x89522),x89523))+~P1(f324(f324(f232(a1),f808(x89521,x89523,x89522)),f2(a1)))+P1(f324(f324(x89521,f324(f81(a1),f806(x89521,x89523,x89522))),f324(f81(a1),f808(x89521,x89523,x89522))))+~P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),x89522),x89523)))
% 18.77/18.51 [9111]P1(f324(f324(x91111,x91112),x91113))+P1(f324(f324(x91111,f324(f324(f82(a1),f720(x91111,x91113,x91112)),f80(a1))),f723(x91111,x91113,x91112)))+~P1(f324(f324(f231(a1),f720(x91111,x91113,x91112)),f723(x91111,x91113,x91112)))+~P1(f324(f313(f844(a1,a1),a167),f324(f324(f247(a1,a1),x91112),x91113)))
% 18.77/18.51 [9792]E(f324(x97921,f793(x97922,x97921,x97923)),x97922)+~P1(f324(f324(f231(a1),x97922),f324(x97921,x97923)))+~P1(f324(f324(f231(a1),f324(f77(a1),f324(f324(f3(a1),f324(x97921,f324(f324(f82(a838),f794(x97922,x97921,x97923)),f80(a838)))),f324(x97921,f794(x97922,x97921,x97923))))),f80(a1)))+~P1(f324(f324(f231(a1),f324(x97921,f2(a838))),x97922))
% 18.77/18.51 [9793]E(f324(x97931,f797(x97932,x97931,x97933)),x97932)+~P1(f324(f324(f231(a1),x97932),f324(x97931,x97933)))+~P1(f324(f324(f231(a1),f324(f77(a1),f324(f324(f3(a1),f324(x97931,f324(f324(f82(a838),f798(x97932,x97931,x97933)),f80(a838)))),f324(x97931,f798(x97932,x97931,x97933))))),f80(a1)))+~P1(f324(f324(f231(a1),f324(x97931,f2(a838))),x97932))
% 18.77/18.51 [9797]~P1(f324(f324(f231(a1),x97971),f324(x97972,x97973)))+~P1(f324(f324(f231(a1),f324(f77(a1),f324(f324(f3(a1),f324(x97972,f324(f324(f82(a838),f794(x97971,x97972,x97973)),f80(a838)))),f324(x97972,f794(x97971,x97972,x97973))))),f80(a1)))+P1(f324(f324(f231(a838),f793(x97971,x97972,x97973)),x97973))+~P1(f324(f324(f231(a1),f324(x97972,f2(a838))),x97971))
% 18.77/18.51 [9798]~P1(f324(f324(f231(a1),x97981),f324(x97982,x97983)))+~P1(f324(f324(f231(a1),f324(f77(a1),f324(f324(f3(a1),f324(x97982,f324(f324(f82(a838),f798(x97981,x97982,x97983)),f80(a838)))),f324(x97982,f798(x97981,x97982,x97983))))),f80(a1)))+P1(f324(f324(f231(a838),f797(x97981,x97982,x97983)),x97983))+~P1(f324(f324(f231(a1),f324(x97982,f2(a838))),x97981))
% 18.77/18.51 [9852]E(x98521,x98522)+~E(f324(f131(f839(x98523),f839(x98523),f125(x98523),f115(x98523)),x98521),f324(f131(f839(x98523),f839(x98523),f125(x98523),f115(x98523)),x98522))+~E(f324(f180(f839(f839(x98523))),x98521),f324(f180(f839(f839(x98523))),x98522))+~P1(f324(f324(f252(f839(x98523),f839(x98523),a832),f324(f324(f9(f839(x98523),f845(f839(x98523),a838),f845(f839(x98523),a832)),f324(f324(f10(f845(a838,a832),f845(f845(f839(x98523),a838),f845(f839(x98523),a832)),f839(x98523)),f10(a838,a832,f839(x98523))),f324(f324(f10(a838,f845(a838,a832),f839(x98523)),a321),f180(f839(x98523))))),f180(f839(x98523)))),f762(x98521,x98522,x98523)))
% 18.77/18.51 [9853]E(x98531,x98532)+~E(f324(f131(f839(x98533),f839(x98533),f125(x98533),f115(x98533)),x98531),f324(f131(f839(x98533),f839(x98533),f125(x98533),f115(x98533)),x98532))+~E(f324(f180(f839(f839(x98533))),x98531),f324(f180(f839(f839(x98533))),x98532))+~P1(f324(f324(f252(f839(x98533),f839(x98533),a832),f324(f324(f9(f839(x98533),f845(f839(x98533),a838),f845(f839(x98533),a832)),f324(f324(f10(f845(a838,a832),f845(f845(f839(x98533),a838),f845(f839(x98533),a832)),f839(x98533)),f10(a838,a832,f839(x98533))),f324(f324(f10(a838,f845(a838,a832),f839(x98533)),a321),f180(f839(x98533))))),f180(f839(x98533)))),f763(x98532,x98531,x98533)))
% 18.77/18.51 [6643]~E(f80(a838),f2(a838))+~P1(f324(f64(x66431),x66433))+~P1(f324(f64(x66431),x66432))+E(f324(f324(f82(a838),f324(f41(x66431),x66432)),f324(f41(x66431),x66433)),f324(f41(x66431),f324(f324(f103(f845(x66431,a832)),x66432),x66433)))
% 18.77/18.51 [7065]~P86(x70651)+~P1(f324(f64(x70651),x70652))+~P1(f324(f324(f326(x70651),x70653),x70652))+P1(f324(f324(f231(x70651),f324(f66(x70651,f235(x70651)),x70652)),x70653))
% 18.77/18.51 [7066]~P99(x70661)+~P1(f324(f64(x70661),x70662))+~P1(f324(f324(f326(x70661),x70663),x70662))+P1(f324(f324(f231(x70661),f324(f66(x70661,f104(x70661)),x70662)),x70663))
% 18.77/18.51 [7340]~P1(f324(f64(x73401),x73403))+~P1(f324(f64(x73401),x73402))+~E(f324(f324(f104(f845(x73401,a832)),x73402),x73403),f179(f845(x73401,a832)))+E(f324(f324(f82(a838),f324(f41(x73401),x73402)),f324(f41(x73401),x73403)),f324(f41(x73401),f324(f324(f103(f845(x73401,a832)),x73402),x73403)))
% 18.77/18.51 [8142]~P36(x81421,x81423)+~P36(x81421,x81422)+~E(f324(f324(f104(f845(x81421,a832)),f324(f262(x81421,x81421),x81422)),f324(f260(x81421,x81421),x81423)),f179(f845(x81421,a832)))+P36(x81421,f324(f324(f103(f845(f844(x81421,x81421),a832)),x81422),x81423))
% 18.77/18.51 [8231]E(x82311,f324(f324(f42(a838),x82312),x82313))+~P1(f324(f324(f232(a838),f2(a838)),x82313))+~P1(f324(f324(f232(a838),x82312),f324(f324(f83(a838),x82313),f324(a114,x82311))))+~P1(f324(f324(f231(a838),f324(f324(f83(a838),x82313),x82311)),x82312))
% 18.77/18.51 [8372]~P1(f324(f64(x83721),x83722))+~P1(f324(f64(x83721),x83723))+E(f324(f324(f82(a838),f324(f41(x83721),x83722)),f324(f41(x83721),x83723)),f324(f41(x83721),f324(f324(f103(f845(x83721,a832)),x83722),x83723)))+P1(f324(f324(f326(x83721),f424(x83723,x83722,x83721)),f324(f324(f104(f845(x83721,a832)),x83722),x83723)))
% 18.77/18.51 [8717]~P117(x87172)+~E(x87171,f2(x87172))+~E(x87173,f2(x87172))+~P1(f324(f324(f232(x87172),f2(x87172)),f324(f324(f82(x87172),f324(f324(f83(x87172),x87173),x87173)),f324(f324(f83(x87172),x87171),x87171))))
% 18.77/18.51 [9184]~P36(x91841,x91843)+~P36(x91841,x91842)+P36(x91841,f324(f324(f103(f845(f844(x91841,x91841),a832)),x91842),x91843))+~P1(f324(f324(f231(f845(f844(x91841,x91841),a832)),f324(f324(f282(x91841,x91841,x91841),x91842),x91843)),x91842))
% 18.77/18.51 [9310]~P1(f324(x93101,x93103))+~P1(f324(f64(x93102),x93103))+P1(f324(x93101,f179(f845(x93102,a832))))+~P1(f324(x93101,f324(f324(f3(f845(x93102,a832)),f430(x93101,x93103,x93102)),f324(f324(f303(x93102),f431(x93101,x93103,x93102)),f179(f845(x93102,a832))))))
% 18.77/18.51 [8526]~P1(f324(f324(f232(a1),f2(a1)),x85263))+P1(f324(f324(f231(a1),f2(a1)),x85261))+~P1(f324(f324(f232(a1),x85262),x85263))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f324(f324(f83(a1),x85263),x85261)),x85262)))
% 18.77/18.51 [8547]~P94(x85471)+~P1(f324(f64(x85471),x85472))+E(f324(f324(f3(f845(x85471,a832)),x85472),f324(f324(f303(x85471),x85473),f179(f845(x85471,a832)))),f179(f845(x85471,a832)))+E(f324(f324(f104(x85471),x85473),f12(x85471,f324(f324(f3(f845(x85471,a832)),x85472),f324(f324(f303(x85471),x85473),f179(f845(x85471,a832)))))),f12(x85471,f324(f324(f303(x85471),x85473),x85472)))
% 18.77/18.51 [8548]~P86(x85481)+~P1(f324(f64(x85481),x85482))+E(f324(f324(f3(f845(x85481,a832)),x85482),f324(f324(f303(x85481),x85483),f179(f845(x85481,a832)))),f179(f845(x85481,a832)))+E(f324(f324(f178(x85481),x85483),f16(x85481,f324(f324(f3(f845(x85481,a832)),x85482),f324(f324(f303(x85481),x85483),f179(f845(x85481,a832)))))),f16(x85481,f324(f324(f303(x85481),x85483),x85482)))
% 18.77/18.51 [8549]~P86(x85491)+~P1(f324(f64(x85491),x85492))+E(f324(f324(f3(f845(x85491,a832)),x85492),f324(f324(f303(x85491),x85493),f179(f845(x85491,a832)))),f179(f845(x85491,a832)))+E(f324(f324(f235(x85491),x85493),f17(x85491,f324(f324(f3(f845(x85491,a832)),x85492),f324(f324(f303(x85491),x85493),f179(f845(x85491,a832)))))),f17(x85491,f324(f324(f303(x85491),x85493),x85492)))
% 18.77/18.51 [8550]~P94(x85501)+~P1(f324(f64(x85501),x85502))+E(f324(f324(f3(f845(x85501,a832)),x85502),f324(f324(f303(x85501),x85503),f179(f845(x85501,a832)))),f179(f845(x85501,a832)))+E(f324(f324(f103(x85501),x85503),f15(x85501,f324(f324(f3(f845(x85501,a832)),x85502),f324(f324(f303(x85501),x85503),f179(f845(x85501,a832)))))),f15(x85501,f324(f324(f303(x85501),x85503),x85502)))
% 18.77/18.51 [8613]~P86(x86131)+~P1(f324(f64(x86131),x86132))+E(f324(f324(f3(f845(x86131,a832)),x86132),f324(f324(f303(x86131),x86133),f179(f845(x86131,a832)))),f179(f845(x86131,a832)))+E(f324(f324(f178(x86131),x86133),f13(x86131,f178(x86131),f324(f324(f3(f845(x86131,a832)),x86132),f324(f324(f303(x86131),x86133),f179(f845(x86131,a832)))))),f13(x86131,f178(x86131),f324(f324(f303(x86131),x86133),x86132)))
% 18.77/18.51 [8614]~P86(x86141)+~P1(f324(f64(x86141),x86142))+E(f324(f324(f3(f845(x86141,a832)),x86142),f324(f324(f303(x86141),x86143),f179(f845(x86141,a832)))),f179(f845(x86141,a832)))+E(f324(f324(f235(x86141),x86143),f14(x86141,f235(x86141),f324(f324(f3(f845(x86141,a832)),x86142),f324(f324(f303(x86141),x86143),f179(f845(x86141,a832)))))),f14(x86141,f235(x86141),f324(f324(f303(x86141),x86143),x86142)))
% 18.77/18.51 [9126]E(x91261,x91262)+~E(f324(f131(f839(x91263),f839(x91263),f125(x91263),f115(x91263)),x91261),f324(f131(f839(x91263),f839(x91263),f125(x91263),f115(x91263)),x91262))+~E(f324(f180(f839(f839(x91263))),x91261),f324(f180(f839(f839(x91263))),x91262))+P1(f324(f324(f326(f844(f839(x91263),f839(x91263))),f762(x91261,x91262,x91263)),f324(f157(f844(f839(x91263),f839(x91263))),f324(f324(f166(f839(x91263),f839(x91263)),x91262),x91261))))
% 18.77/18.51 [9127]E(x91271,x91272)+~E(f324(f131(f839(x91273),f839(x91273),f125(x91273),f115(x91273)),x91271),f324(f131(f839(x91273),f839(x91273),f125(x91273),f115(x91273)),x91272))+~E(f324(f180(f839(f839(x91273))),x91271),f324(f180(f839(f839(x91273))),x91272))+P1(f324(f324(f326(f844(f839(x91273),f839(x91273))),f763(x91272,x91271,x91273)),f324(f157(f844(f839(x91273),f839(x91273))),f324(f324(f166(f839(x91273),f839(x91273)),x91271),x91272))))
% 18.77/18.51 [9941]~P74(x99412)+E(x99411,f179(f845(x99412,a832)))+~P1(f324(f64(x99412),x99411))+E(f16(x99412,f324(f257(x99412),f324(f324(f10(f845(x99412,a832),a832,x99412),f89(x99412)),f324(f324(f9(x99412,f845(x99412,a832),f845(x99412,a832)),f324(f324(f10(f845(x99412,f845(a832,a832)),f845(f845(x99412,a832),f845(x99412,a832)),x99412),f20(x99412,a832,a832)),f324(f324(f10(f845(x99412,a832),f845(x99412,f845(a832,a832)),x99412),f324(f10(a832,f845(a832,a832),x99412),a322)),f324(f324(f9(x99412,f845(x99412,x99412),f845(x99412,a832)),f324(f324(f10(f845(x99412,a832),f845(f845(x99412,x99412),f845(x99412,a832)),x99412),f10(x99412,a832,x99412)),a321)),f324(f82(x99412),x99413))))),f324(f324(f9(x99412,f845(x99412,a832),a832),f326(x99412)),x99411))))),f324(f324(f82(x99412),x99413),f16(x99412,x99411)))
% 18.77/18.51 [9942]~P74(x99422)+E(x99421,f179(f845(x99422,a832)))+~P1(f324(f64(x99422),x99421))+E(f17(x99422,f324(f257(x99422),f324(f324(f10(f845(x99422,a832),a832,x99422),f89(x99422)),f324(f324(f9(x99422,f845(x99422,a832),f845(x99422,a832)),f324(f324(f10(f845(x99422,f845(a832,a832)),f845(f845(x99422,a832),f845(x99422,a832)),x99422),f20(x99422,a832,a832)),f324(f324(f10(f845(x99422,a832),f845(x99422,f845(a832,a832)),x99422),f324(f10(a832,f845(a832,a832),x99422),a322)),f324(f324(f9(x99422,f845(x99422,x99422),f845(x99422,a832)),f324(f324(f10(f845(x99422,a832),f845(f845(x99422,x99422),f845(x99422,a832)),x99422),f10(x99422,a832,x99422)),a321)),f324(f82(x99422),x99423))))),f324(f324(f9(x99422,f845(x99422,a832),a832),f326(x99422)),x99421))))),f324(f324(f82(x99422),x99423),f17(x99422,x99421)))
% 18.77/18.51 [9943]~P97(x99432)+E(x99431,f179(f845(x99432,a832)))+~P1(f324(f64(x99432),x99431))+E(f12(x99432,f324(f257(x99432),f324(f324(f10(f845(x99432,a832),a832,x99432),f89(x99432)),f324(f324(f9(x99432,f845(x99432,a832),f845(x99432,a832)),f324(f324(f10(f845(x99432,f845(a832,a832)),f845(f845(x99432,a832),f845(x99432,a832)),x99432),f20(x99432,a832,a832)),f324(f324(f10(f845(x99432,a832),f845(x99432,f845(a832,a832)),x99432),f324(f10(a832,f845(a832,a832),x99432),a322)),f324(f324(f9(x99432,f845(x99432,x99432),f845(x99432,a832)),f324(f324(f10(f845(x99432,a832),f845(f845(x99432,x99432),f845(x99432,a832)),x99432),f10(x99432,a832,x99432)),a321)),f324(f103(x99432),x99433))))),f324(f324(f9(x99432,f845(x99432,a832),a832),f326(x99432)),x99431))))),f324(f324(f103(x99432),x99433),f12(x99432,x99431)))
% 18.77/18.51 [9944]~P97(x99442)+E(x99441,f179(f845(x99442,a832)))+~P1(f324(f64(x99442),x99441))+E(f15(x99442,f324(f257(x99442),f324(f324(f10(f845(x99442,a832),a832,x99442),f89(x99442)),f324(f324(f9(x99442,f845(x99442,a832),f845(x99442,a832)),f324(f324(f10(f845(x99442,f845(a832,a832)),f845(f845(x99442,a832),f845(x99442,a832)),x99442),f20(x99442,a832,a832)),f324(f324(f10(f845(x99442,a832),f845(x99442,f845(a832,a832)),x99442),f324(f10(a832,f845(a832,a832),x99442),a322)),f324(f324(f9(x99442,f845(x99442,x99442),f845(x99442,a832)),f324(f324(f10(f845(x99442,a832),f845(f845(x99442,x99442),f845(x99442,a832)),x99442),f10(x99442,a832,x99442)),a321)),f324(f104(x99442),x99443))))),f324(f324(f9(x99442,f845(x99442,a832),a832),f326(x99442)),x99441))))),f324(f324(f104(x99442),x99443),f15(x99442,x99441)))
% 18.77/18.51 [9945]~P86(x99452)+E(x99451,f179(f845(x99452,a832)))+~P1(f324(f64(x99452),x99451))+E(f13(x99452,f178(x99452),f324(f257(x99452),f324(f324(f10(f845(x99452,a832),a832,x99452),f89(x99452)),f324(f324(f9(x99452,f845(x99452,a832),f845(x99452,a832)),f324(f324(f10(f845(x99452,f845(a832,a832)),f845(f845(x99452,a832),f845(x99452,a832)),x99452),f20(x99452,a832,a832)),f324(f324(f10(f845(x99452,a832),f845(x99452,f845(a832,a832)),x99452),f324(f10(a832,f845(a832,a832),x99452),a322)),f324(f324(f9(x99452,f845(x99452,x99452),f845(x99452,a832)),f324(f324(f10(f845(x99452,a832),f845(f845(x99452,x99452),f845(x99452,a832)),x99452),f10(x99452,a832,x99452)),a321)),f324(f235(x99452),x99453))))),f324(f324(f9(x99452,f845(x99452,a832),a832),f326(x99452)),x99451))))),f324(f324(f235(x99452),x99453),f13(x99452,f178(x99452),x99451)))
% 18.77/18.51 [9946]~P86(x99462)+E(x99461,f179(f845(x99462,a832)))+~P1(f324(f64(x99462),x99461))+E(f14(x99462,f235(x99462),f324(f257(x99462),f324(f324(f10(f845(x99462,a832),a832,x99462),f89(x99462)),f324(f324(f9(x99462,f845(x99462,a832),f845(x99462,a832)),f324(f324(f10(f845(x99462,f845(a832,a832)),f845(f845(x99462,a832),f845(x99462,a832)),x99462),f20(x99462,a832,a832)),f324(f324(f10(f845(x99462,a832),f845(x99462,f845(a832,a832)),x99462),f324(f10(a832,f845(a832,a832),x99462),a322)),f324(f324(f9(x99462,f845(x99462,x99462),f845(x99462,a832)),f324(f324(f10(f845(x99462,a832),f845(f845(x99462,x99462),f845(x99462,a832)),x99462),f10(x99462,a832,x99462)),a321)),f324(f178(x99462),x99463))))),f324(f324(f9(x99462,f845(x99462,a832),a832),f326(x99462)),x99461))))),f324(f324(f178(x99462),x99463),f14(x99462,f235(x99462),x99461)))
% 18.77/18.51 [9678]~P103(x96781)+~E(x96783,f2(x96781))+~E(x96782,f2(x96781))+E(f324(f324(f82(x96781),f324(f324(f240(x96781),x96782),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x96781),x96783),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f2(x96781))
% 18.77/18.51 [9836]~P84(x98361)+~P1(f324(f324(f231(x98361),f2(x98361)),x98363))+P1(f324(f324(f232(x98361),x98362),x98363))+~P1(f324(f324(f232(x98361),f324(f324(f240(x98361),x98362),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98361),x98363),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.77/18.51 [9837]~P84(x98371)+~P1(f324(f324(f231(x98371),f2(x98371)),x98373))+P1(f324(f324(f231(x98371),x98372),x98373))+~P1(f324(f324(f231(x98371),f324(f324(f240(x98371),x98372),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98371),x98373),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))))
% 18.77/18.51 [9883]~P103(x98832)+~E(x98831,f2(x98832))+~E(x98833,f2(x98832))+~P1(f324(f324(f232(x98832),f2(x98832)),f324(f324(f82(x98832),f324(f324(f240(x98832),x98833),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99))))),f324(f324(f240(x98832),x98831),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))))
% 18.77/18.51 [9098]E(x90981,x90982)+~E(f741(x90981,x90982,x90984,x90983),f742(x90981,x90982,x90984,x90983))+P1(f324(f324(f326(f844(f839(x90983),f839(x90983))),f324(f324(f247(f839(x90983),f839(x90983)),x90982),x90981)),f136(x90983,x90984)))+P1(f324(f324(f326(f844(f839(x90983),f839(x90983))),f324(f324(f247(f839(x90983),f839(x90983)),x90981),x90982)),f136(x90983,x90984)))
% 18.77/18.51 [4676]~P59(x46762)+~E(x46764,f2(x46762))+~E(x46761,f2(x46762))+E(x46761,f324(f324(f284(x46762),x46763),x46764))
% 18.77/18.51 [4677]~P59(x46771)+~E(x46773,f2(x46771))+~E(x46774,f2(x46771))+E(f324(f324(f284(x46771),x46772),x46773),x46774)
% 18.77/18.51 [4786]~P59(x47862)+E(x47861,f2(x47862))+~E(x47863,f2(x47862))+~E(x47861,f324(f324(f284(x47862),x47864),x47863))
% 18.77/18.51 [4787]~P59(x47872)+E(x47871,f2(x47872))+~E(x47873,f2(x47872))+~E(f324(f324(f284(x47872),x47874),x47873),x47871)
% 18.77/18.51 [4962]~P114(x49622)+E(x49621,f2(x49622))+~E(f324(f324(f284(x49622),x49623),x49621),x49624)+E(x49623,f324(f324(f83(x49622),x49624),x49621))
% 18.77/18.51 [4963]~P114(x49632)+E(x49631,f2(x49632))+~E(f324(f324(f83(x49632),x49633),x49631),x49634)+E(x49633,f324(f324(f284(x49632),x49634),x49631))
% 18.77/18.51 [4964]~P114(x49642)+E(x49641,f2(x49642))+~E(f324(f324(f83(x49642),x49643),x49641),x49644)+E(x49643,f324(f324(f284(x49642),x49644),x49641))
% 18.77/18.51 [4965]~P59(x49652)+E(x49651,f2(x49652))+~E(f324(f324(f284(x49652),x49653),x49651),x49654)+E(x49653,f324(f324(f83(x49652),x49654),x49651))
% 18.77/18.51 [4966]~P59(x49662)+E(x49661,f2(x49662))+~E(f324(f324(f83(x49662),x49663),x49661),x49664)+E(x49663,f324(f324(f284(x49662),x49664),x49661))
% 18.77/18.51 [4967]~P114(x49672)+E(x49671,f2(x49672))+~E(x49673,f324(f324(f284(x49672),x49674),x49671))+E(f324(f324(f83(x49672),x49673),x49671),x49674)
% 18.77/18.51 [4968]~P114(x49682)+E(x49681,f2(x49682))+~E(x49683,f324(f324(f83(x49682),x49684),x49681))+E(f324(f324(f284(x49682),x49683),x49681),x49684)
% 18.77/18.51 [4969]~P114(x49692)+E(x49691,f2(x49692))+~E(x49693,f324(f324(f83(x49692),x49694),x49691))+E(f324(f324(f284(x49692),x49693),x49691),x49694)
% 18.77/18.51 [4970]~P59(x49702)+E(x49701,f2(x49702))+~E(x49703,f324(f324(f284(x49702),x49704),x49701))+E(f324(f324(f83(x49702),x49703),x49701),x49704)
% 18.77/18.51 [4971]~P59(x49712)+E(x49711,f2(x49712))+~E(x49713,f324(f324(f83(x49712),x49714),x49711))+E(f324(f324(f284(x49712),x49713),x49711),x49714)
% 18.77/18.51 [5004]~P59(x50042)+~E(x50041,f2(x50042))+~E(f324(f324(f83(x50042),x50041),x50044),x50043)+E(x50041,f324(f324(f284(x50042),x50043),x50044))
% 18.77/18.51 [5005]~P59(x50051)+~E(x50054,f2(x50051))+~E(x50052,f324(f324(f83(x50051),x50054),x50053))+E(f324(f324(f284(x50051),x50052),x50053),x50054)
% 18.77/18.51 [5072]~E(x50723,x50724)+~E(x50722,x50723)+~P85(x50721)+E(f296(x50721,x50722,x50723),f324(f324(f303(x50721),x50724),f179(f845(x50721,a832))))
% 18.77/18.51 [5268]~E(f133(x52682,x52681),x52684)+~E(f116(x52682,x52681),x52683)+E(x52681,f115(x52682))+E(f324(f324(f125(x52682),x52683),f324(f324(f139(x52682),x52684),f115(x52682))),x52681)
% 18.77/18.51 [5891]~P84(x58913)+E(x58911,x58912)+~E(f324(f324(f240(x58913),x58914),x58911),f324(f324(f240(x58913),x58914),x58912))+~P1(f324(f324(f232(x58913),f80(x58913)),x58914))
% 18.77/18.51 [5892]E(x58921,x58922)+~E(f324(f324(f303(x58923),x58924),x58921),f324(f324(f303(x58923),x58924),x58922))+P1(f324(f324(f326(x58923),x58924),x58922))+P1(f324(f324(f326(x58923),x58924),x58921))
% 18.77/18.51 [5930]E(f324(x59301,x59302),f2(a838))+~E(f324(f324(f8(x59303,a838),x59301),x59304),f2(a838))+~P1(f324(f64(x59303),x59304))+~P1(f324(f324(f326(x59303),x59302),x59304))
% 18.77/18.51 [5931]E(f324(x59311,x59312),f80(a838))+~E(f324(f324(f11(x59313,a838),x59311),x59314),f80(a838))+~P1(f324(f64(x59313),x59314))+~P1(f324(f324(f326(x59313),x59312),x59314))
% 18.77/18.51 [6157]~P85(x61571)+~P1(f324(f324(f232(x61571),x61574),x61573))+P1(f324(f324(f232(x61571),x61572),x61573))+~P1(f324(f324(f232(x61571),x61572),x61574))
% 18.77/18.51 [6158]~P85(x61581)+~P1(f324(f324(f231(x61581),x61584),x61583))+P1(f324(f324(f232(x61581),x61582),x61583))+~P1(f324(f324(f232(x61581),x61582),x61584))
% 18.77/18.51 [6159]~P85(x61591)+~P1(f324(f324(f231(x61591),x61592),x61594))+P1(f324(f324(f232(x61591),x61592),x61593))+~P1(f324(f324(f232(x61591),x61594),x61593))
% 18.77/18.51 [6160]~P102(x61601)+~P1(f324(f324(f232(x61601),x61602),x61604))+P1(f324(f324(f232(x61601),x61602),x61603))+~P1(f324(f324(f232(x61601),x61604),x61603))
% 18.77/18.51 [6161]~P102(x61611)+~P1(f324(f324(f231(x61611),x61612),x61614))+P1(f324(f324(f232(x61611),x61612),x61613))+~P1(f324(f324(f232(x61611),x61614),x61613))
% 18.77/18.51 [6162]~P102(x61621)+~P1(f324(f324(f231(x61621),x61624),x61623))+P1(f324(f324(f232(x61621),x61622),x61623))+~P1(f324(f324(f232(x61621),x61622),x61624))
% 18.77/18.51 [6163]~P85(x61631)+~P1(f324(f324(f231(x61631),x61634),x61633))+P1(f324(f324(f231(x61631),x61632),x61633))+~P1(f324(f324(f231(x61631),x61632),x61634))
% 18.77/18.51 [6164]~P102(x61641)+~P1(f324(f324(f231(x61641),x61642),x61644))+P1(f324(f324(f231(x61641),x61642),x61643))+~P1(f324(f324(f231(x61641),x61644),x61643))
% 18.77/18.51 [6165]~P105(x61651)+~P1(f324(f324(f280(x61651),x61652),x61654))+P1(f324(f324(f280(x61651),x61652),x61653))+~P1(f324(f324(f280(x61651),x61654),x61653))
% 18.77/18.51 [6408]~P9(x64081)+~P1(f324(f324(f231(x64081),x64082),f44(x64081,x64084)))+P1(f324(f324(f231(x64081),x64082),x64083))+~P1(f324(f324(f326(x64081),x64083),x64084))
% 18.77/18.51 [6558]~P86(x65581)+~P18(x65581,f324(f324(f139(x65581),x65582),x65584))+~P1(f324(f324(f326(x65581),x65583),f324(f157(x65581),x65584)))+P1(f324(f324(f231(x65581),x65582),x65583))
% 18.77/18.51 [6559]~P86(x65591)+~P18(x65591,f324(f324(f139(x65591),x65592),x65594))+~P1(f324(f324(f326(x65591),x65593),f324(f157(x65591),x65594)))+P1(f324(f324(f231(x65591),x65592),x65593))
% 18.77/18.51 [6652]~P9(x66521)+~P1(f324(f324(f231(x66521),f43(x66521,x66524)),x66523))+P1(f324(f324(f231(x66521),x66522),x66523))+~P1(f324(f324(f326(x66521),x66522),x66524))
% 18.77/18.51 [6806]~P7(x68061)+P1(f324(f324(f280(x68061),x68062),f51(x68061,x68063,x68064)))+~P1(f324(f324(f280(x68061),x68062),x68064))+~P1(f324(f324(f280(x68061),x68062),x68063))
% 18.77/18.51 [6807]~P7(x68071)+P1(f324(f324(f280(x68071),x68072),f51(x68071,x68073,x68074)))+~P1(f324(f324(f280(x68071),x68072),x68074))+~P1(f324(f324(f280(x68071),x68072),x68073))
% 18.77/18.51 [7068]~P86(x70681)+E(f324(f324(f103(f845(x70681,a832)),f324(f295(x70681,x70682),x70683)),f324(f295(x70681,x70683),x70684)),f324(f295(x70681,x70682),x70684))+~P1(f324(f324(f231(x70681),x70683),x70684))+~P1(f324(f324(f231(x70681),x70682),x70683))
% 18.77/18.51 [7153]~P7(x71531)+~P1(f324(f324(f280(x71531),x71532),f51(x71531,x71533,x71534)))+P1(f324(f324(f280(x71531),x71532),x71533))+~P1(f324(f324(f280(x71531),x71532),x71534))
% 18.77/18.51 [7154]~P7(x71541)+~P1(f324(f324(f280(x71541),x71542),f51(x71541,x71543,x71544)))+P1(f324(f324(f280(x71541),x71542),x71543))+~P1(f324(f324(f280(x71541),x71542),x71544))
% 18.77/18.51 [7195]~P86(x71951)+E(f324(f324(f103(f845(x71951,a832)),f324(f295(x71951,x71952),x71953)),f296(x71951,x71953,x71954)),f296(x71951,x71952,x71954))+~P1(f324(f324(f231(x71951),x71953),x71954))+~P1(f324(f324(f231(x71951),x71952),x71953))
% 18.77/18.51 [7209]~P85(x72091)+~P50(a838,x72091,f280(a838),x72092)+P1(f324(f324(f231(x72091),f324(x72092,x72093)),f324(x72092,x72094)))+~P1(f324(f324(f280(a838),x72093),x72094))
% 18.77/18.51 [7263]~P86(x72631)+E(f324(f324(f103(f845(x72631,a832)),f299(x72631,x72632,x72633)),f324(f295(x72631,x72633),x72634)),f299(x72631,x72632,x72634))+~P1(f324(f324(f232(x72631),x72632),x72633))+~P1(f324(f324(f231(x72631),x72633),x72634))
% 18.77/18.51 [7286]~P86(x72861)+E(f324(f324(f103(f845(x72861,a832)),f296(x72861,x72862,x72863)),f299(x72861,x72863,x72864)),f324(f295(x72861,x72862),x72864))+~P1(f324(f324(f232(x72861),x72863),x72864))+~P1(f324(f324(f231(x72861),x72862),x72863))
% 18.77/18.51 [7321]~P86(x73211)+E(f324(f324(f103(f845(x73211,a832)),f299(x73211,x73212,x73213)),f296(x73211,x73213,x73214)),f298(x73211,x73212,x73214))+~P1(f324(f324(f232(x73211),x73212),x73213))+~P1(f324(f324(f231(x73211),x73213),x73214))
% 18.77/18.51 [7322]~P86(x73221)+E(f324(f324(f103(f845(x73221,a832)),f298(x73221,x73222,x73223)),f299(x73221,x73223,x73224)),f299(x73221,x73222,x73224))+~P1(f324(f324(f232(x73221),x73223),x73224))+~P1(f324(f324(f231(x73221),x73222),x73223))
% 18.77/18.51 [7323]~P86(x73231)+E(f324(f324(f103(f845(x73231,a832)),f298(x73231,x73232,x73233)),f298(x73231,x73233,x73234)),f298(x73231,x73232,x73234))+~P1(f324(f324(f231(x73231),x73233),x73234))+~P1(f324(f324(f231(x73231),x73232),x73233))
% 18.77/18.51 [7324]~P86(x73241)+E(f324(f324(f103(f845(x73241,a832)),f296(x73241,x73242,x73243)),f298(x73241,x73243,x73244)),f296(x73241,x73242,x73244))+~P1(f324(f324(f231(x73241),x73243),x73244))+~P1(f324(f324(f231(x73241),x73242),x73243))
% 18.77/18.51 [8126]P29(x81261,x81262,f526(x81263,x81262,x81264,x81261),x81264)+~P1(f324(f64(x81262),x81263))+~P1(f324(f64(x81261),x81264))+~P1(f324(f324(f231(a838),f324(f41(x81261),x81264)),f324(f41(x81262),x81263)))
% 18.77/18.51 [8198]~P68(x81981)+~E(f324(x81983,f642(x81983,x81984,x81982,x81981)),f80(x81981))+E(f324(f324(f324(f68(x81981,x81982,f83(x81981)),x81983),f80(x81981)),x81984),f80(x81981))+~P1(f324(f64(x81982),x81984))
% 18.77/18.51 [8469]~P84(x84691)+~P1(f324(f324(f231(x84691),f2(x84691)),x84693))+P1(f324(f324(f231(x84691),x84692),x84693))+~P1(f324(f324(f231(x84691),f324(f324(f240(x84691),x84692),f324(a114,x84694))),f324(f324(f240(x84691),x84693),f324(a114,x84694))))
% 18.77/18.51 [8805]~P68(x88051)+E(f324(f324(f324(f68(x88051,x88052,f83(x88051)),x88053),f80(x88051)),x88054),f80(x88051))+~P1(f324(f64(x88052),x88054))+P1(f324(f324(f326(x88052),f642(x88053,x88054,x88052,x88051)),x88054))
% 18.77/18.51 [9049]~P12(x90492,x90493,x90494)+~P1(f324(f64(x90492),x90493))+~P1(f324(f324(f280(a838),x90491),f324(f41(x90492),f522(x90491,x90494,x90493,x90492))))+P1(f324(f324(f280(a838),x90491),f324(f41(x90492),x90493)))
% 18.77/18.51 [9237]~P1(f324(f324(f280(a838),x92372),x92373))+P1(f324(f324(f280(a838),x92371),x92372))+P1(f324(f324(f280(a838),x92373),x92374))+~P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x92372,x92373)),f283(a838,f280(a838),x92371,x92374)))
% 18.77/18.51 [9241]P1(f324(f324(f280(a838),x92411),x92412))+~P1(f324(f324(f280(a838),x92412),x92413))+~P1(f324(f324(f280(a838),x92414),x92413))+~P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x92412,x92413)),f283(a838,f280(a838),x92411,x92414)))
% 18.77/18.51 [9242]~P1(f324(f324(f280(a838),x92423),x92421))+P1(f324(f324(f280(a838),x92421),x92422))+~P1(f324(f324(f280(a838),x92423),x92424))+~P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x92423,x92421)),f283(a838,f280(a838),x92424,x92422)))
% 18.77/18.51 [9249]~P1(f324(f324(f280(a838),x92491),x92493))+~P1(f324(f324(f280(a838),x92491),x92492))+~P1(f324(f324(f280(a838),x92494),x92493))+~P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x92491,x92493)),f283(a838,f280(a838),x92492,x92494)))
% 18.77/18.51 [9255]~P1(f324(f324(f231(a1),x92554),f2(a1)))+P1(f324(f324(f231(a1),f324(f324(f82(a1),f324(f324(f83(a1),x92551),f51(a1,x92552,x92553))),x92554)),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x92553))+~P1(f324(f324(f232(a1),x92551),x92554))
% 18.77/18.51 [9671]~P1(f324(f64(x96711),x96712))+~P1(f324(f324(f326(x96711),x96714),x96712))+~P1(f324(f324(f326(x96711),x96713),x96712))+P1(f324(f324(f232(a838),f324(f41(x96711),f324(f324(f3(f845(x96711,a832)),f324(f324(f3(f845(x96711,a832)),x96712),f324(f324(f303(x96711),x96713),f179(f845(x96711,a832))))),f324(f324(f303(x96711),x96714),f179(f845(x96711,a832)))))),f324(f41(x96711),x96712)))
% 18.77/18.51 [6714]~P135(x67143)+~P113(x67143)+P1(f324(x67141,f824(x67142,x67141,x67143)))+~P1(f324(x67141,f324(f324(f83(x67143),x67142),x67144)))
% 18.77/18.51 [6777]~P86(x67771)+~P1(f324(f324(f232(x67771),x67772),x67774))+~P1(f324(f324(f232(x67771),x67772),x67773))+P1(f324(f324(f232(x67771),x67772),f324(f324(f235(x67771),x67773),x67774)))
% 18.77/18.51 [6778]~P86(x67781)+~P1(f324(f324(f231(x67781),x67782),x67784))+~P1(f324(f324(f231(x67781),x67782),x67783))+P1(f324(f324(f231(x67781),x67782),f324(f324(f235(x67781),x67783),x67784)))
% 18.77/18.51 [6779]~P86(x67791)+~P1(f324(f324(f231(x67791),x67792),x67794))+~P1(f324(f324(f231(x67791),x67792),x67793))+P1(f324(f324(f231(x67791),x67792),f324(f324(f235(x67791),x67793),x67794)))
% 18.77/18.51 [6780]~P86(x67801)+~P1(f324(f324(f231(x67801),x67802),x67804))+~P1(f324(f324(f231(x67801),x67802),x67803))+P1(f324(f324(f231(x67801),x67802),f324(f324(f235(x67801),x67803),x67804)))
% 18.77/18.51 [6781]~P99(x67811)+~P1(f324(f324(f231(x67811),x67812),x67814))+~P1(f324(f324(f231(x67811),x67812),x67813))+P1(f324(f324(f231(x67811),x67812),f324(f324(f104(x67811),x67813),x67814)))
% 18.77/18.51 [6782]~P99(x67821)+~P1(f324(f324(f231(x67821),x67822),x67824))+~P1(f324(f324(f231(x67821),x67822),x67823))+P1(f324(f324(f231(x67821),x67822),f324(f324(f104(x67821),x67823),x67824)))
% 18.77/18.51 [6783]~P99(x67831)+~P1(f324(f324(f231(x67831),x67832),x67834))+~P1(f324(f324(f231(x67831),x67832),x67833))+P1(f324(f324(f231(x67831),x67832),f324(f324(f104(x67831),x67833),x67834)))
% 18.77/18.51 [6784]~P105(x67841)+~P1(f324(f324(f280(x67841),x67842),x67844))+~P1(f324(f324(f280(x67841),x67842),x67843))+P1(f324(f324(f280(x67841),x67842),f324(f324(f82(x67841),x67843),x67844)))
% 18.77/18.51 [6785]~P107(x67851)+~P1(f324(f324(f280(x67851),x67852),x67854))+~P1(f324(f324(f280(x67851),x67852),x67853))+P1(f324(f324(f280(x67851),x67852),f324(f324(f3(x67851),x67853),x67854)))
% 18.77/18.51 [6805]~P60(x68052)+E(x68051,f2(x68052))+E(f324(f324(f284(x68052),f324(f324(f240(x68052),x68051),x68053)),f324(f324(f240(x68052),x68051),x68054)),f324(f324(f240(x68052),x68051),f324(f324(f3(a838),x68053),x68054)))+~P1(f324(f324(f231(a838),x68054),x68053))
% 18.77/18.51 [6849]~P86(x68491)+~P18(x68491,f324(f324(f139(x68491),x68493),x68494))+P18(x68491,f324(f324(f139(x68491),x68492),f324(f324(f139(x68491),x68493),x68494)))+~P1(f324(f324(f231(x68491),x68492),x68493))
% 18.77/18.51 [6850]~P86(x68501)+~P18(x68501,f324(f324(f139(x68501),x68503),x68504))+P18(x68501,f324(f324(f139(x68501),x68502),f324(f324(f139(x68501),x68503),x68504)))+~P1(f324(f324(f231(x68501),x68502),x68503))
% 18.77/18.51 [6890]~P84(x68901)+~P1(f324(f324(f232(x68901),f2(x68901)),x68903))+~P1(f324(f324(f232(x68901),x68902),x68904))+P1(f324(f324(f232(x68901),x68902),f324(f324(f82(x68901),x68903),x68904)))
% 18.77/18.51 [6891]~P80(x68911)+~P1(f324(f324(f231(x68911),f2(x68911)),x68913))+~P1(f324(f324(f232(x68911),x68912),x68914))+P1(f324(f324(f232(x68911),x68912),f324(f324(f82(x68911),x68913),x68914)))
% 18.77/18.51 [6892]~P80(x68921)+~P1(f324(f324(f231(x68921),x68922),x68924))+~P1(f324(f324(f232(x68921),f2(x68921)),x68923))+P1(f324(f324(f232(x68921),x68922),f324(f324(f82(x68921),x68923),x68924)))
% 18.77/18.51 [6893]~P80(x68931)+~P1(f324(f324(f231(x68931),f2(x68931)),x68934))+~P1(f324(f324(f231(x68931),x68932),x68933))+P1(f324(f324(f231(x68931),x68932),f324(f324(f82(x68931),x68933),x68934)))
% 18.77/18.51 [6894]~P80(x68941)+~P1(f324(f324(f231(x68941),f2(x68941)),x68943))+~P1(f324(f324(f231(x68941),x68942),x68944))+P1(f324(f324(f231(x68941),x68942),f324(f324(f82(x68941),x68943),x68944)))
% 18.77/18.51 [6928]~P86(x69281)+P1(f324(f324(f232(x69281),x69282),x69283))+P1(f324(f324(f232(x69281),x69282),x69284))+~P1(f324(f324(f232(x69281),x69282),f324(f324(f178(x69281),x69284),x69283)))
% 18.77/18.51 [6929]~P86(x69291)+P1(f324(f324(f231(x69291),x69292),x69293))+P1(f324(f324(f231(x69291),x69292),x69294))+~P1(f324(f324(f231(x69291),x69292),f324(f324(f178(x69291),x69294),x69293)))
% 18.77/18.51 [7616]~P62(x76161)+~P1(f324(f324(f232(x76161),x76164),f2(x76161)))+~P1(f324(f324(f232(x76161),x76163),f324(f324(f284(x76161),x76162),x76164)))+P1(f324(f324(f232(x76161),x76162),f324(f324(f83(x76161),x76163),x76164)))
% 18.77/18.51 [7617]~P62(x76171)+~P1(f324(f324(f232(x76171),x76174),f2(x76171)))+~P1(f324(f324(f232(x76171),x76173),f324(f324(f83(x76171),x76172),x76174)))+P1(f324(f324(f232(x76171),x76172),f324(f324(f284(x76171),x76173),x76174)))
% 18.77/18.51 [7618]~P62(x76181)+~P1(f324(f324(f232(x76181),x76184),f2(x76181)))+~P1(f324(f324(f231(x76181),x76183),f324(f324(f284(x76181),x76182),x76184)))+P1(f324(f324(f231(x76181),x76182),f324(f324(f83(x76181),x76183),x76184)))
% 18.77/18.51 [7619]~P62(x76191)+~P1(f324(f324(f232(x76191),x76194),f2(x76191)))+~P1(f324(f324(f231(x76191),x76193),f324(f324(f83(x76191),x76192),x76194)))+P1(f324(f324(f231(x76191),x76192),f324(f324(f284(x76191),x76193),x76194)))
% 18.77/18.51 [7731]~P117(x77311)+~P1(f324(f324(f232(x77311),x77312),f2(x77311)))+~P1(f324(f324(f232(x77311),x77314),x77313))+P1(f324(f324(f232(x77311),f324(f324(f83(x77311),x77312),x77313)),f324(f324(f83(x77311),x77312),x77314)))
% 18.77/18.51 [7732]~P117(x77321)+~P1(f324(f324(f232(x77321),x77322),f2(x77321)))+~P1(f324(f324(f232(x77321),x77324),x77323))+P1(f324(f324(f232(x77321),f324(f324(f83(x77321),x77322),x77323)),f324(f324(f83(x77321),x77322),x77324)))
% 18.77/18.51 [7733]~P117(x77331)+~P1(f324(f324(f232(x77331),x77333),f2(x77331)))+~P1(f324(f324(f232(x77331),x77334),x77332))+P1(f324(f324(f232(x77331),f324(f324(f83(x77331),x77332),x77333)),f324(f324(f83(x77331),x77334),x77333)))
% 18.77/18.51 [7734]~P117(x77341)+~P1(f324(f324(f232(x77341),x77343),f2(x77341)))+~P1(f324(f324(f232(x77341),x77344),x77342))+P1(f324(f324(f232(x77341),f324(f324(f83(x77341),x77342),x77343)),f324(f324(f83(x77341),x77344),x77343)))
% 18.77/18.51 [7735]~P117(x77351)+~P1(f324(f324(f232(x77351),x77352),f2(x77351)))+~P1(f324(f324(f232(x77351),x77354),x77353))+P1(f324(f324(f232(x77351),f324(f324(f83(x77351),x77352),x77353)),f324(f324(f83(x77351),x77352),x77354)))
% 18.77/18.51 [7736]~P62(x77361)+~P1(f324(f324(f232(x77361),x77363),f2(x77361)))+~P1(f324(f324(f232(x77361),x77364),x77362))+P1(f324(f324(f232(x77361),f324(f324(f284(x77361),x77362),x77363)),f324(f324(f284(x77361),x77364),x77363)))
% 18.77/18.51 [7737]~P117(x77371)+~P1(f324(f324(f232(x77371),x77372),f2(x77371)))+~P1(f324(f324(f231(x77371),x77374),x77373))+P1(f324(f324(f231(x77371),f324(f324(f83(x77371),x77372),x77373)),f324(f324(f83(x77371),x77372),x77374)))
% 18.77/18.51 [7738]~P128(x77381)+~P1(f324(f324(f231(x77381),x77382),f2(x77381)))+~P1(f324(f324(f231(x77381),x77384),x77383))+P1(f324(f324(f231(x77381),f324(f324(f83(x77381),x77382),x77383)),f324(f324(f83(x77381),x77382),x77384)))
% 18.77/18.51 [7739]~P128(x77391)+~P1(f324(f324(f231(x77391),x77393),f2(x77391)))+~P1(f324(f324(f231(x77391),x77394),x77392))+P1(f324(f324(f231(x77391),f324(f324(f83(x77391),x77392),x77393)),f324(f324(f83(x77391),x77394),x77393)))
% 18.77/18.51 [7740]~P61(x77401)+~P1(f324(f324(f231(x77401),x77403),f2(x77401)))+~P1(f324(f324(f231(x77401),x77404),x77402))+P1(f324(f324(f231(x77401),f324(f324(f284(x77401),x77402),x77403)),f324(f324(f284(x77401),x77404),x77403)))
% 18.77/18.51 [7741]~P84(x77411)+~P1(f324(f324(f232(x77411),f80(x77411)),x77412))+~P1(f324(f324(f232(a838),x77413),x77414))+P1(f324(f324(f232(x77411),f324(f324(f240(x77411),x77412),x77413)),f324(f324(f240(x77411),x77412),x77414)))
% 18.77/18.51 [7742]~P84(x77421)+~P1(f324(f324(f232(x77421),f80(x77421)),x77422))+~P1(f324(f324(f232(a838),x77423),x77424))+P1(f324(f324(f232(x77421),f324(f324(f240(x77421),x77422),x77423)),f324(f324(f240(x77421),x77422),x77424)))
% 18.77/18.51 [7743]~P84(x77431)+~P1(f324(f324(f232(x77431),f80(x77431)),x77432))+~P1(f324(f324(f231(a838),x77433),x77434))+P1(f324(f324(f231(x77431),f324(f324(f240(x77431),x77432),x77433)),f324(f324(f240(x77431),x77432),x77434)))
% 18.77/18.51 [7744]~P84(x77441)+~P1(f324(f324(f231(x77441),f80(x77441)),x77442))+~P1(f324(f324(f231(a838),x77443),x77444))+P1(f324(f324(f231(x77441),f324(f324(f240(x77441),x77442),x77443)),f324(f324(f240(x77441),x77442),x77444)))
% 18.77/18.51 [7771]P1(f324(f324(f232(a838),f2(a838)),f324(x77711,x77712)))+~P1(f324(f64(x77713),x77714))+~P1(f324(f324(f326(x77713),x77712),x77714))+~P1(f324(f324(f232(a838),f2(a838)),f324(f324(f11(x77713,a838),x77711),x77714)))
% 18.77/18.51 [7782]~P117(x77821)+~P1(f324(f324(f232(x77821),x77823),x77824))+~P1(f324(f324(f232(x77821),f2(x77821)),x77822))+P1(f324(f324(f232(x77821),f324(f324(f83(x77821),x77822),x77823)),f324(f324(f83(x77821),x77822),x77824)))
% 18.77/18.51 [7783]~P104(x77831)+~P1(f324(f324(f232(x77831),x77833),x77834))+~P1(f324(f324(f232(x77831),f2(x77831)),x77832))+P1(f324(f324(f232(x77831),f324(f324(f83(x77831),x77832),x77833)),f324(f324(f83(x77831),x77832),x77834)))
% 18.77/18.51 [7784]~P122(x77841)+~P1(f324(f324(f232(x77841),x77843),x77844))+~P1(f324(f324(f232(x77841),f2(x77841)),x77842))+P1(f324(f324(f232(x77841),f324(f324(f83(x77841),x77842),x77843)),f324(f324(f83(x77841),x77842),x77844)))
% 18.77/18.51 [7785]~P117(x77851)+~P1(f324(f324(f232(x77851),x77852),x77854))+~P1(f324(f324(f232(x77851),f2(x77851)),x77853))+P1(f324(f324(f232(x77851),f324(f324(f83(x77851),x77852),x77853)),f324(f324(f83(x77851),x77854),x77853)))
% 18.77/18.51 [7786]~P122(x77861)+~P1(f324(f324(f232(x77861),x77862),x77864))+~P1(f324(f324(f232(x77861),f2(x77861)),x77863))+P1(f324(f324(f232(x77861),f324(f324(f83(x77861),x77862),x77863)),f324(f324(f83(x77861),x77864),x77863)))
% 18.77/18.51 [7787]~P117(x77871)+~P1(f324(f324(f232(x77871),x77873),x77874))+~P1(f324(f324(f232(x77871),f2(x77871)),x77872))+P1(f324(f324(f232(x77871),f324(f324(f83(x77871),x77872),x77873)),f324(f324(f83(x77871),x77872),x77874)))
% 18.77/18.51 [7788]~P62(x77881)+~P1(f324(f324(f232(x77881),x77882),x77884))+~P1(f324(f324(f232(x77881),f2(x77881)),x77883))+P1(f324(f324(f232(x77881),f324(f324(f284(x77881),x77882),x77883)),f324(f324(f284(x77881),x77884),x77883)))
% 18.77/18.51 [7789]~P117(x77891)+~P1(f324(f324(f232(x77891),f2(x77891)),x77892))+~P1(f324(f324(f231(x77891),x77893),x77894))+P1(f324(f324(f231(x77891),f324(f324(f83(x77891),x77892),x77893)),f324(f324(f83(x77891),x77892),x77894)))
% 18.77/18.51 [7790]~P130(x77901)+~P1(f324(f324(f231(x77901),x77903),x77904))+~P1(f324(f324(f231(x77901),f2(x77901)),x77902))+P1(f324(f324(f231(x77901),f324(f324(f83(x77901),x77902),x77903)),f324(f324(f83(x77901),x77902),x77904)))
% 18.77/18.51 [7791]~P129(x77911)+~P1(f324(f324(f231(x77911),x77913),x77914))+~P1(f324(f324(f231(x77911),f2(x77911)),x77912))+P1(f324(f324(f231(x77911),f324(f324(f83(x77911),x77912),x77913)),f324(f324(f83(x77911),x77912),x77914)))
% 18.77/18.51 [7792]~P130(x77921)+~P1(f324(f324(f231(x77921),x77922),x77924))+~P1(f324(f324(f231(x77921),f2(x77921)),x77923))+P1(f324(f324(f231(x77921),f324(f324(f83(x77921),x77922),x77923)),f324(f324(f83(x77921),x77924),x77923)))
% 18.77/18.51 [7793]~P84(x77931)+~P1(f324(f324(f231(x77931),x77932),x77934))+~P1(f324(f324(f231(x77931),f2(x77931)),x77932))+P1(f324(f324(f231(x77931),f324(f324(f240(x77931),x77932),x77933)),f324(f324(f240(x77931),x77934),x77933)))
% 18.77/18.51 [7794]~P61(x77941)+~P1(f324(f324(f231(x77941),x77942),x77944))+~P1(f324(f324(f231(x77941),f2(x77941)),x77943))+P1(f324(f324(f231(x77941),f324(f324(f284(x77941),x77942),x77943)),f324(f324(f284(x77941),x77944),x77943)))
% 18.77/18.51 [7833]~P101(x78332)+P1(f324(f324(f231(f845(x78331,x78332)),x78334),x78333))+~P1(f324(f324(f231(f845(x78331,x78332)),x78333),x78334))+P1(f324(f324(f232(f845(x78331,x78332)),x78333),x78334))
% 18.77/18.51 [7878]P1(f324(f324(f326(x78781),x78782),x78783))+P1(f324(f324(f326(x78781),x78782),x78784))+~P1(f324(f324(f231(f845(x78781,a832)),x78784),x78783))+P1(f324(f324(f232(f845(x78781,a832)),x78784),f324(f324(f303(x78781),x78782),x78783)))
% 18.77/18.51 [7987]~P112(x79872)+E(x79871,f2(x79872))+P1(f324(f324(f280(x79872),x79873),x79874))+~P1(f324(f324(f280(x79872),f324(f324(f83(x79872),x79873),x79871)),f324(f324(f83(x79872),x79874),x79871)))
% 18.77/18.51 [7988]~P112(x79882)+E(x79881,f2(x79882))+P1(f324(f324(f280(x79882),x79883),x79884))+~P1(f324(f324(f280(x79882),f324(f324(f83(x79882),x79881),x79883)),f324(f324(f83(x79882),x79881),x79884)))
% 18.77/18.51 [8035]P1(f324(f324(f326(x80351),x80352),x80353))+P1(f324(f324(f326(x80351),x80352),x80354))+~P1(f324(f324(f232(f845(x80351,a832)),x80354),f324(f324(f303(x80351),x80352),x80353)))+P1(f324(f324(f231(f845(x80351,a832)),x80354),x80353))
% 18.77/18.51 [8104]~P117(x81041)+P1(f324(f324(f232(x81041),x81043),x81042))+P1(f324(f324(f232(x81041),x81042),x81043))+~P1(f324(f324(f232(x81041),f324(f324(f83(x81041),x81044),x81042)),f324(f324(f83(x81041),x81044),x81043)))
% 18.77/18.51 [8105]~P117(x81051)+P1(f324(f324(f232(x81051),x81053),x81052))+P1(f324(f324(f232(x81051),x81052),x81053))+~P1(f324(f324(f232(x81051),f324(f324(f83(x81051),x81052),x81054)),f324(f324(f83(x81051),x81053),x81054)))
% 18.77/18.51 [8116]~P117(x81161)+P1(f324(f324(f232(x81161),x81164),f2(x81161)))+P1(f324(f324(f232(x81161),x81162),x81163))+~P1(f324(f324(f232(x81161),f324(f324(f83(x81161),x81162),x81164)),f324(f324(f83(x81161),x81163),x81164)))
% 18.77/18.51 [8117]~P117(x81171)+P1(f324(f324(f232(x81171),x81174),f2(x81171)))+P1(f324(f324(f232(x81171),x81172),x81173))+~P1(f324(f324(f232(x81171),f324(f324(f83(x81171),x81174),x81172)),f324(f324(f83(x81171),x81174),x81173)))
% 18.77/18.51 [8120]~P117(x81201)+P1(f324(f324(f232(x81201),x81202),x81203))+P1(f324(f324(f232(x81201),f2(x81201)),x81204))+~P1(f324(f324(f232(x81201),f324(f324(f83(x81201),x81204),x81203)),f324(f324(f83(x81201),x81204),x81202)))
% 18.77/18.51 [8121]~P117(x81211)+P1(f324(f324(f232(x81211),x81212),x81213))+P1(f324(f324(f232(x81211),f2(x81211)),x81214))+~P1(f324(f324(f232(x81211),f324(f324(f83(x81211),x81213),x81214)),f324(f324(f83(x81211),x81212),x81214)))
% 18.77/18.51 [8134]~P117(x81341)+P1(f324(f324(f232(x81341),x81342),f2(x81341)))+P1(f324(f324(f232(x81341),f2(x81341)),x81342))+~P1(f324(f324(f232(x81341),f324(f324(f83(x81341),x81343),x81342)),f324(f324(f83(x81341),x81344),x81342)))
% 18.77/18.51 [8135]~P117(x81351)+P1(f324(f324(f232(x81351),x81352),f2(x81351)))+P1(f324(f324(f232(x81351),f2(x81351)),x81352))+~P1(f324(f324(f232(x81351),f324(f324(f83(x81351),x81352),x81353)),f324(f324(f83(x81351),x81352),x81354)))
% 18.77/18.51 [8161]~P117(x81611)+~P1(f324(f324(f232(x81611),x81614),f2(x81611)))+P1(f324(f324(f232(x81611),x81612),x81613))+~P1(f324(f324(f232(x81611),f324(f324(f83(x81611),x81614),x81613)),f324(f324(f83(x81611),x81614),x81612)))
% 18.77/18.51 [8162]~P117(x81621)+~P1(f324(f324(f232(x81621),x81624),f2(x81621)))+P1(f324(f324(f231(x81621),x81622),x81623))+~P1(f324(f324(f231(x81621),f324(f324(f83(x81621),x81624),x81623)),f324(f324(f83(x81621),x81624),x81622)))
% 18.77/18.51 [8173]~P84(x81733)+~P1(f324(f324(f232(x81733),f80(x81733)),x81734))+P1(f324(f324(f232(a838),x81731),x81732))+~P1(f324(f324(f232(x81733),f324(f324(f240(x81733),x81734),x81731)),f324(f324(f240(x81733),x81734),x81732)))
% 18.77/18.51 [8174]~P84(x81743)+~P1(f324(f324(f232(x81743),f80(x81743)),x81744))+P1(f324(f324(f232(a838),x81741),x81742))+~P1(f324(f324(f232(x81743),f324(f324(f240(x81743),x81744),x81741)),f324(f324(f240(x81743),x81744),x81742)))
% 18.77/18.51 [8175]~P84(x81753)+~P1(f324(f324(f232(x81753),f80(x81753)),x81754))+P1(f324(f324(f231(a838),x81751),x81752))+~P1(f324(f324(f231(x81753),f324(f324(f240(x81753),x81754),x81751)),f324(f324(f240(x81753),x81754),x81752)))
% 18.77/18.51 [8176]~P84(x81763)+~P1(f324(f324(f232(x81763),f80(x81763)),x81764))+P1(f324(f324(f231(a838),x81761),x81762))+~P1(f324(f324(f231(x81763),f324(f324(f240(x81763),x81764),x81761)),f324(f324(f240(x81763),x81764),x81762)))
% 18.77/18.51 [8186]~P117(x81861)+P1(f324(f324(f232(x81861),x81862),x81863))+~P1(f324(f324(f232(x81861),f2(x81861)),x81864))+~P1(f324(f324(f232(x81861),f324(f324(f83(x81861),x81864),x81862)),f324(f324(f83(x81861),x81864),x81863)))
% 18.77/18.51 [8187]~P122(x81871)+P1(f324(f324(f232(x81871),x81872),x81873))+~P1(f324(f324(f231(x81871),f2(x81871)),x81874))+~P1(f324(f324(f232(x81871),f324(f324(f83(x81871),x81874),x81872)),f324(f324(f83(x81871),x81874),x81873)))
% 18.77/18.51 [8188]~P123(x81881)+P1(f324(f324(f232(x81881),x81882),x81883))+~P1(f324(f324(f231(x81881),f2(x81881)),x81884))+~P1(f324(f324(f232(x81881),f324(f324(f83(x81881),x81884),x81882)),f324(f324(f83(x81881),x81884),x81883)))
% 18.77/18.51 [8189]~P84(x81891)+~P1(f324(f324(f231(x81891),f2(x81891)),x81893))+P1(f324(f324(f232(x81891),x81892),x81893))+~P1(f324(f324(f232(x81891),f324(f324(f240(x81891),x81892),x81894)),f324(f324(f240(x81891),x81893),x81894)))
% 18.77/18.51 [8190]~P122(x81901)+P1(f324(f324(f232(x81901),x81902),x81903))+~P1(f324(f324(f231(x81901),f2(x81901)),x81904))+~P1(f324(f324(f232(x81901),f324(f324(f83(x81901),x81902),x81904)),f324(f324(f83(x81901),x81903),x81904)))
% 18.77/18.51 [8191]~P123(x81911)+P1(f324(f324(f232(x81911),x81912),x81913))+~P1(f324(f324(f231(x81911),f2(x81911)),x81914))+~P1(f324(f324(f232(x81911),f324(f324(f83(x81911),x81912),x81914)),f324(f324(f83(x81911),x81913),x81914)))
% 18.77/18.51 [8192]~P117(x81921)+P1(f324(f324(f231(x81921),x81922),x81923))+~P1(f324(f324(f232(x81921),f2(x81921)),x81924))+~P1(f324(f324(f231(x81921),f324(f324(f83(x81921),x81924),x81922)),f324(f324(f83(x81921),x81924),x81923)))
% 18.77/18.51 [8193]~P122(x81931)+P1(f324(f324(f231(x81931),x81932),x81933))+~P1(f324(f324(f232(x81931),f2(x81931)),x81934))+~P1(f324(f324(f231(x81931),f324(f324(f83(x81931),x81934),x81932)),f324(f324(f83(x81931),x81934),x81933)))
% 18.77/18.51 [8194]~P122(x81941)+P1(f324(f324(f231(x81941),x81942),x81943))+~P1(f324(f324(f232(x81941),f2(x81941)),x81944))+~P1(f324(f324(f231(x81941),f324(f324(f83(x81941),x81942),x81944)),f324(f324(f83(x81941),x81943),x81944)))
% 18.77/18.51 [8234]P1(f324(f324(f326(x82341),x82342),x82343))+~P1(f324(f324(f231(f845(x82341,a832)),x82343),x82344))+~P1(f324(f324(f232(f845(x82341,a832)),x82343),x82344))+P1(f324(f324(f232(f845(x82341,a832)),x82343),f324(f324(f303(x82341),x82342),x82344)))
% 18.77/18.51 [8269]~P135(x82691)+~P113(x82691)+P1(f324(f324(f280(x82691),x82692),f324(f324(f82(x82691),f824(x82692,x82693,x82691)),f2(x82691))))+~P1(f324(x82693,f324(f324(f83(x82691),x82692),x82694)))
% 18.77/18.51 [8593]E(f324(f324(f3(a1),f466(x85931,x85932,x85933,x85934)),f467(x85931,x85932,x85933,x85934)),x85934)+~P1(f324(f324(f232(a1),f2(a1)),x85933))+~P1(f324(f324(f231(a1),x85931),x85934))+P1(f324(f324(f231(a1),x85931),f324(f324(f82(a1),x85934),x85933)))
% 18.77/18.51 [8594]E(f324(f324(f3(a1),f471(x85941,x85942,x85943,x85944)),f472(x85941,x85942,x85943,x85944)),x85944)+~P1(f324(f324(f232(a1),f2(a1)),x85943))+~P1(f324(f324(f232(a1),x85941),x85944))+P1(f324(f324(f232(a1),x85941),f324(f324(f82(a1),x85944),x85943)))
% 18.77/18.51 [8723]~E(f324(f324(f149(x87231),x87233),f745(x87234,x87233,x87231,x87232)),f324(f324(f149(x87231),x87234),f745(x87234,x87233,x87231,x87232)))+E(f324(f324(f158(x87231),x87232),x87233),f324(f324(f158(x87231),x87232),x87234))+~P1(f324(f324(f231(a838),x87232),f324(f180(f839(x87231)),x87233)))+~P1(f324(f324(f231(a838),x87232),f324(f180(f839(x87231)),x87234)))
% 18.77/18.51 [8776]~P1(f324(f324(f232(a1),f2(a1)),x87763))+~P1(f324(f324(f231(a1),x87761),x87764))+P1(f324(f324(f326(a1),f466(x87761,x87762,x87763,x87764)),x87762))+P1(f324(f324(f231(a1),x87761),f324(f324(f82(a1),x87764),x87763)))
% 18.77/18.51 [8777]~P1(f324(f324(f232(a1),f2(a1)),x87773))+~P1(f324(f324(f232(a1),x87771),x87774))+P1(f324(f324(f326(a1),f471(x87771,x87772,x87773,x87774)),x87772))+P1(f324(f324(f232(a1),x87771),f324(f324(f82(a1),x87774),x87773)))
% 18.77/18.51 [8814]~P86(x88141)+~P1(f324(f64(x88141),x88143))+~P1(f324(f324(f326(x88141),x88144),x88143))+P1(f324(f324(f231(x88141),f324(f324(f67(x88141,x88141,f235(x88141)),x88142),x88143)),f324(f324(f235(x88141),x88144),x88142)))
% 18.77/18.51 [8815]~P99(x88151)+~P1(f324(f64(x88151),x88153))+~P1(f324(f324(f326(x88151),x88154),x88153))+P1(f324(f324(f231(x88151),f324(f324(f67(x88151,x88151,f104(x88151)),x88152),x88153)),f324(f324(f104(x88151),x88154),x88152)))
% 18.77/18.51 [8823]~P12(x88232,x88233,x88234)+~P1(f324(f64(x88232),x88233))+P1(f324(f324(f280(a838),x88231),f324(f41(x88232),x88233)))+P1(f324(f324(f326(f845(x88232,a832)),f522(x88231,x88234,x88233,x88232)),f324(f324(f63(x88232),x88233),x88234)))
% 18.77/18.51 [8861]E(f324(f324(f158(x88611),x88612),x88613),f324(f324(f158(x88611),x88612),x88614))+P1(f324(f324(f232(a838),f745(x88613,x88614,x88611,x88612)),x88612))+~P1(f324(f324(f231(a838),x88612),f324(f180(f839(x88611)),x88613)))+~P1(f324(f324(f231(a838),x88612),f324(f180(f839(x88611)),x88614)))
% 18.77/18.51 [8866]~P1(f324(f324(f232(a1),f2(a1)),x88663))+~P1(f324(f324(f232(a1),x88661),x88662))+P1(f324(f324(f326(a1),f472(x88661,x88664,x88663,x88662)),f296(a1,f80(a1),x88663)))+P1(f324(f324(f232(a1),x88661),f324(f324(f82(a1),x88662),x88663)))
% 18.77/18.51 [8867]~P1(f324(f324(f232(a1),f2(a1)),x88673))+~P1(f324(f324(f231(a1),x88671),x88672))+P1(f324(f324(f326(a1),f467(x88671,x88674,x88673,x88672)),f296(a1,f80(a1),x88673)))+P1(f324(f324(f231(a1),x88671),f324(f324(f82(a1),x88672),x88673)))
% 18.77/18.51 [9024]~E(f165(x90241,x90242,x90243),f165(x90241,x90242,x90244))+E(f324(f157(f844(x90241,x90242)),x90243),f324(f157(f844(x90241,x90242)),x90244))+~P1(f324(f127(x90241),f324(f324(f141(f844(x90241,x90242),x90241),f246(x90241,x90242)),x90244)))+~P1(f324(f127(x90241),f324(f324(f141(f844(x90241,x90242),x90241),f246(x90241,x90242)),x90243)))
% 18.77/18.51 [9027]E(f165(x90271,x90272,x90273),f165(x90271,x90272,x90274))+~E(f324(f157(f844(x90271,x90272)),x90273),f324(f157(f844(x90271,x90272)),x90274))+~P1(f324(f127(x90271),f324(f324(f141(f844(x90271,x90272),x90271),f246(x90271,x90272)),x90274)))+~P1(f324(f127(x90271),f324(f324(f141(f844(x90271,x90272),x90271),f246(x90271,x90272)),x90273)))
% 18.77/18.51 [9146]~P86(x91461)+~P1(f324(f64(x91461),x91464))+P1(f324(f324(f326(x91461),f681(x91462,x91463,x91464,x91461)),x91464))+P1(f324(f324(f231(x91461),f324(f324(f67(x91461,x91461,f178(x91461)),x91462),x91464)),f324(f324(f178(x91461),x91463),x91462)))
% 18.77/18.51 [9147]~P93(x91471)+~P1(f324(f64(x91471),x91474))+P1(f324(f324(f326(x91471),f688(x91472,x91473,x91474,x91471)),x91474))+P1(f324(f324(f231(x91471),f324(f324(f67(x91471,x91471,f103(x91471)),x91472),x91474)),f324(f324(f103(x91471),x91473),x91472)))
% 18.77/18.51 [9273]~P86(x92731)+~P1(f324(f64(x92731),x92733))+~P1(f324(f324(f231(x92731),f681(x92732,x92734,x92733,x92731)),x92734))+P1(f324(f324(f231(x92731),f324(f324(f67(x92731,x92731,f178(x92731)),x92732),x92733)),f324(f324(f178(x92731),x92734),x92732)))
% 18.77/18.51 [9274]~P93(x92741)+~P1(f324(f64(x92741),x92743))+~P1(f324(f324(f231(x92741),f688(x92742,x92744,x92743,x92741)),x92744))+P1(f324(f324(f231(x92741),f324(f324(f67(x92741,x92741,f103(x92741)),x92742),x92743)),f324(f324(f103(x92741),x92744),x92742)))
% 18.77/18.51 [9276]~P1(f324(f324(f232(a1),f2(a1)),x92763))+~P1(f324(f324(f231(a1),f2(a1)),x92764))+~P1(f324(f324(f232(a1),x92764),x92761))+P1(f324(f324(f232(a1),f324(f324(f82(a1),f324(f324(f83(a1),x92761),f51(a1,x92762,x92763))),x92764)),f324(f324(f83(a1),x92761),x92763)))
% 18.77/18.51 [9541]~P85(x95411)+P1(f324(f324(f232(x95411),f324(x95412,x95413)),f324(x95412,x95414)))+~P1(f324(f324(f232(a838),x95413),x95414))+~P1(f324(f324(f232(x95411),f324(x95412,f386(x95414,x95413,x95412,x95411))),f324(x95412,f324(a114,f386(x95414,x95413,x95412,x95411)))))
% 18.77/18.51 [9542]~P85(x95421)+P1(f324(f324(f232(x95421),f324(x95422,x95423)),f324(x95422,x95424)))+~P1(f324(f324(f232(a838),x95423),x95424))+~P1(f324(f324(f232(x95421),f324(x95422,f373(x95424,x95423,x95422,x95421))),f324(x95422,f324(a114,f373(x95424,x95423,x95422,x95421)))))
% 18.77/18.51 [9543]~P85(x95433)+~P1(f324(f324(f232(x95433),f324(x95434,x95431)),f324(x95434,x95432)))+P1(f324(f324(f232(a838),x95431),x95432))+~P1(f324(f324(f232(x95433),f324(x95434,f386(x95432,x95431,x95434,x95433))),f324(x95434,f324(a114,f386(x95432,x95431,x95434,x95433)))))
% 18.77/18.51 [9640]E(x96401,x96402)+P1(f324(f324(f326(f844(f839(x96403),f839(x96403))),f324(f324(f247(f839(x96403),f839(x96403)),x96402),x96401)),f136(x96403,x96404)))+P1(f324(f324(f326(f844(f839(x96403),f839(x96403))),f324(f324(f247(f839(x96403),f839(x96403)),x96401),x96402)),f136(x96403,x96404)))+~P1(f324(f324(f326(f844(x96403,x96403)),f324(f324(f247(x96403,x96403),f741(x96401,x96402,x96404,x96403)),f742(x96401,x96402,x96404,x96403))),x96404))
% 18.77/18.51 [9641]E(x96411,x96412)+P1(f324(f324(f326(f844(f839(x96413),f839(x96413))),f324(f324(f247(f839(x96413),f839(x96413)),x96412),x96411)),f136(x96413,x96414)))+P1(f324(f324(f326(f844(f839(x96413),f839(x96413))),f324(f324(f247(f839(x96413),f839(x96413)),x96411),x96412)),f136(x96413,x96414)))+~P1(f324(f324(f326(f844(x96413,x96413)),f324(f324(f247(x96413,x96413),f742(x96411,x96412,x96414,x96413)),f741(x96411,x96412,x96414,x96413))),x96414))
% 18.77/18.51 [7310]~P86(x73101)+~P1(f324(f324(f232(x73101),x73103),x73104))+~P1(f324(f324(f232(x73101),x73102),x73104))+P1(f324(f324(f232(x73101),f324(f324(f178(x73101),x73102),x73103)),x73104))
% 18.77/18.51 [7311]~P86(x73111)+~P1(f324(f324(f231(x73111),x73113),x73114))+~P1(f324(f324(f231(x73111),x73112),x73114))+P1(f324(f324(f231(x73111),f324(f324(f178(x73111),x73112),x73113)),x73114))
% 18.77/18.51 [7312]~P86(x73121)+~P1(f324(f324(f231(x73121),x73123),x73124))+~P1(f324(f324(f231(x73121),x73122),x73124))+P1(f324(f324(f231(x73121),f324(f324(f178(x73121),x73122),x73123)),x73124))
% 18.77/18.51 [7313]~P86(x73131)+~P1(f324(f324(f231(x73131),x73133),x73134))+~P1(f324(f324(f231(x73131),x73132),x73134))+P1(f324(f324(f231(x73131),f324(f324(f178(x73131),x73132),x73133)),x73134))
% 18.77/18.51 [7314]~P93(x73141)+~P1(f324(f324(f231(x73141),x73143),x73144))+~P1(f324(f324(f231(x73141),x73142),x73144))+P1(f324(f324(f231(x73141),f324(f324(f103(x73141),x73142),x73143)),x73144))
% 18.77/18.51 [7315]~P93(x73151)+~P1(f324(f324(f231(x73151),x73153),x73154))+~P1(f324(f324(f231(x73151),x73152),x73154))+P1(f324(f324(f231(x73151),f324(f324(f103(x73151),x73152),x73153)),x73154))
% 18.77/18.51 [7316]~P93(x73161)+~P1(f324(f324(f231(x73161),x73163),x73164))+~P1(f324(f324(f231(x73161),x73162),x73164))+P1(f324(f324(f231(x73161),f324(f324(f103(x73161),x73162),x73163)),x73164))
% 18.77/18.51 [7560]~P7(x75601)+E(f324(f324(f82(x75601),f324(f324(f42(x75601),x75602),x75603)),f324(f324(f42(x75601),x75604),x75603)),f324(f324(f42(x75601),f324(f324(f82(x75601),x75602),x75604)),x75603))+~P1(f324(f324(f280(x75601),x75603),x75604))+~P1(f324(f324(f280(x75601),x75603),x75602))
% 18.77/18.51 [7639]~E(x76391,x76393)+E(f129(a838,f324(f295(a838,x76391),x76392)),f324(f324(f139(a838),x76393),x76394))+~E(f129(a838,f324(f295(a838,f324(f324(f82(a838),x76391),f80(a838))),x76392)),x76394)+~P1(f324(f324(f232(a838),x76391),x76392))
% 18.77/18.51 [7650]~P86(x76501)+P1(f324(f324(f232(x76501),x76502),x76503))+P1(f324(f324(f232(x76501),x76504),x76503))+~P1(f324(f324(f232(x76501),f324(f324(f235(x76501),x76504),x76502)),x76503))
% 18.77/18.51 [7651]~P86(x76511)+P1(f324(f324(f231(x76511),x76512),x76513))+P1(f324(f324(f231(x76511),x76514),x76513))+~P1(f324(f324(f231(x76511),f324(f324(f235(x76511),x76514),x76512)),x76513))
% 18.77/18.51 [7936]~P61(x79361)+~P1(f324(f324(f232(x79361),f2(x79361)),x79363))+~P1(f324(f324(f232(x79361),x79362),f324(f324(f284(x79361),x79364),x79363)))+P1(f324(f324(f232(x79361),f324(f324(f83(x79361),x79362),x79363)),x79364))
% 18.77/18.51 [7937]~P62(x79371)+~P1(f324(f324(f232(x79371),f2(x79371)),x79373))+~P1(f324(f324(f232(x79371),x79372),f324(f324(f284(x79371),x79374),x79373)))+P1(f324(f324(f232(x79371),f324(f324(f83(x79371),x79372),x79373)),x79374))
% 18.77/18.51 [7938]~P61(x79381)+~P1(f324(f324(f232(x79381),f2(x79381)),x79383))+~P1(f324(f324(f232(x79381),x79382),f324(f324(f83(x79381),x79384),x79383)))+P1(f324(f324(f232(x79381),f324(f324(f284(x79381),x79382),x79383)),x79384))
% 18.77/18.51 [7939]~P62(x79391)+~P1(f324(f324(f232(x79391),f2(x79391)),x79393))+~P1(f324(f324(f232(x79391),x79392),f324(f324(f83(x79391),x79394),x79393)))+P1(f324(f324(f232(x79391),f324(f324(f284(x79391),x79392),x79393)),x79394))
% 18.77/18.51 [7940]~P62(x79401)+~P1(f324(f324(f232(x79401),f2(x79401)),x79403))+~P1(f324(f324(f232(x79401),x79402),f324(f324(f83(x79401),x79404),x79403)))+P1(f324(f324(f232(x79401),f324(f324(f284(x79401),x79402),x79403)),x79404))
% 18.77/18.51 [7941]~P61(x79411)+~P1(f324(f324(f232(x79411),f2(x79411)),x79413))+~P1(f324(f324(f231(x79411),x79412),f324(f324(f284(x79411),x79414),x79413)))+P1(f324(f324(f231(x79411),f324(f324(f83(x79411),x79412),x79413)),x79414))
% 18.77/18.51 [7942]~P62(x79421)+~P1(f324(f324(f232(x79421),f2(x79421)),x79423))+~P1(f324(f324(f231(x79421),x79422),f324(f324(f284(x79421),x79424),x79423)))+P1(f324(f324(f231(x79421),f324(f324(f83(x79421),x79422),x79423)),x79424))
% 18.77/18.51 [7943]~P61(x79431)+~P1(f324(f324(f232(x79431),f2(x79431)),x79433))+~P1(f324(f324(f231(x79431),x79432),f324(f324(f83(x79431),x79434),x79433)))+P1(f324(f324(f231(x79431),f324(f324(f284(x79431),x79432),x79433)),x79434))
% 18.77/18.51 [7944]~P62(x79441)+~P1(f324(f324(f232(x79441),f2(x79441)),x79443))+~P1(f324(f324(f231(x79441),x79442),f324(f324(f83(x79441),x79444),x79443)))+P1(f324(f324(f231(x79441),f324(f324(f284(x79441),x79442),x79443)),x79444))
% 18.77/18.51 [7945]~P62(x79451)+~P1(f324(f324(f232(x79451),f2(x79451)),x79453))+~P1(f324(f324(f231(x79451),x79452),f324(f324(f83(x79451),x79454),x79453)))+P1(f324(f324(f231(x79451),f324(f324(f284(x79451),x79452),x79453)),x79454))
% 18.77/18.51 [8073]~P61(x80731)+~P1(f324(f324(f232(x80731),f2(x80731)),x80734))+P1(f324(f324(f232(x80731),x80732),f324(f324(f83(x80731),x80733),x80734)))+~P1(f324(f324(f232(x80731),f324(f324(f284(x80731),x80732),x80734)),x80733))
% 18.77/18.51 [8074]~P61(x80741)+~P1(f324(f324(f232(x80741),f2(x80741)),x80744))+P1(f324(f324(f232(x80741),x80742),f324(f324(f284(x80741),x80743),x80744)))+~P1(f324(f324(f232(x80741),f324(f324(f83(x80741),x80742),x80744)),x80743))
% 18.77/18.51 [8075]~P62(x80751)+~P1(f324(f324(f232(x80751),f2(x80751)),x80754))+P1(f324(f324(f232(x80751),x80752),f324(f324(f284(x80751),x80753),x80754)))+~P1(f324(f324(f232(x80751),f324(f324(f83(x80751),x80752),x80754)),x80753))
% 18.77/18.51 [8076]~P62(x80761)+~P1(f324(f324(f232(x80761),f2(x80761)),x80764))+P1(f324(f324(f232(x80761),x80762),f324(f324(f83(x80761),x80763),x80764)))+~P1(f324(f324(f232(x80761),f324(f324(f284(x80761),x80762),x80764)),x80763))
% 18.77/18.51 [8077]~P62(x80771)+~P1(f324(f324(f232(x80771),f2(x80771)),x80774))+P1(f324(f324(f232(x80771),x80772),f324(f324(f284(x80771),x80773),x80774)))+~P1(f324(f324(f232(x80771),f324(f324(f83(x80771),x80772),x80774)),x80773))
% 18.77/18.51 [8078]~P61(x80781)+~P1(f324(f324(f232(x80781),f2(x80781)),x80784))+P1(f324(f324(f231(x80781),x80782),f324(f324(f83(x80781),x80783),x80784)))+~P1(f324(f324(f231(x80781),f324(f324(f284(x80781),x80782),x80784)),x80783))
% 18.77/18.51 [8079]~P61(x80791)+~P1(f324(f324(f232(x80791),f2(x80791)),x80794))+P1(f324(f324(f231(x80791),x80792),f324(f324(f284(x80791),x80793),x80794)))+~P1(f324(f324(f231(x80791),f324(f324(f83(x80791),x80792),x80794)),x80793))
% 18.77/18.51 [8080]~P62(x80801)+~P1(f324(f324(f232(x80801),f2(x80801)),x80804))+P1(f324(f324(f231(x80801),x80802),f324(f324(f284(x80801),x80803),x80804)))+~P1(f324(f324(f231(x80801),f324(f324(f83(x80801),x80802),x80804)),x80803))
% 18.77/18.51 [8081]~P62(x80811)+~P1(f324(f324(f232(x80811),f2(x80811)),x80814))+P1(f324(f324(f231(x80811),x80812),f324(f324(f83(x80811),x80813),x80814)))+~P1(f324(f324(f231(x80811),f324(f324(f284(x80811),x80812),x80814)),x80813))
% 18.77/18.51 [8082]~P62(x80821)+~P1(f324(f324(f232(x80821),f2(x80821)),x80824))+P1(f324(f324(f231(x80821),x80822),f324(f324(f284(x80821),x80823),x80824)))+~P1(f324(f324(f231(x80821),f324(f324(f83(x80821),x80822),x80824)),x80823))
% 18.77/18.51 [8239]~P62(x82391)+~P1(f324(f324(f232(x82391),x82393),f2(x82391)))+~P1(f324(f324(f232(x82391),f324(f324(f284(x82391),x82394),x82393)),x82392))+P1(f324(f324(f232(x82391),f324(f324(f83(x82391),x82392),x82393)),x82394))
% 18.77/18.51 [8240]~P62(x82401)+~P1(f324(f324(f232(x82401),x82403),f2(x82401)))+~P1(f324(f324(f232(x82401),f324(f324(f83(x82401),x82404),x82403)),x82402))+P1(f324(f324(f232(x82401),f324(f324(f284(x82401),x82402),x82403)),x82404))
% 18.77/18.51 [8241]~P62(x82411)+~P1(f324(f324(f232(x82411),x82413),f2(x82411)))+~P1(f324(f324(f231(x82411),f324(f324(f284(x82411),x82414),x82413)),x82412))+P1(f324(f324(f231(x82411),f324(f324(f83(x82411),x82412),x82413)),x82414))
% 18.77/18.51 [8242]~P62(x82421)+~P1(f324(f324(f232(x82421),x82423),f2(x82421)))+~P1(f324(f324(f231(x82421),f324(f324(f83(x82421),x82424),x82423)),x82422))+P1(f324(f324(f231(x82421),f324(f324(f284(x82421),x82422),x82423)),x82424))
% 18.77/18.51 [8255]~P1(f324(x82551,x82554))+~P1(f324(f324(f232(a838),x82552),f324(f324(f83(a838),x82553),f324(a114,x82554))))+P1(f324(x82551,f324(f324(f42(a838),x82552),x82553)))+~P1(f324(f324(f231(a838),f324(f324(f83(a838),x82553),x82554)),x82552))
% 18.77/18.51 [8467]~P86(x84671)+~P1(f324(f64(x84671),x84674))+~P1(f324(f324(f326(x84671),x84672),x84674))+P1(f324(f324(f231(x84671),f324(f324(f178(x84671),x84672),x84673)),f324(f324(f67(x84671,x84671,f178(x84671)),x84673),x84674)))
% 18.77/18.51 [8468]~P93(x84681)+~P1(f324(f64(x84681),x84684))+~P1(f324(f324(f326(x84681),x84682),x84684))+P1(f324(f324(f231(x84681),f324(f324(f103(x84681),x84682),x84683)),f324(f324(f67(x84681,x84681,f103(x84681)),x84683),x84684)))
% 18.77/18.51 [8595]~P1(f324(f64(x85951),x85952))+E(f324(f41(x85951),f324(f324(f3(f845(x85951,a832)),x85952),f324(f324(f303(x85951),x85953),x85954))),f324(f324(f3(a838),f324(f41(x85951),f324(f324(f3(f845(x85951,a832)),x85952),x85954))),f80(a838)))+P1(f324(f324(f326(x85951),x85953),x85954))+~P1(f324(f324(f326(x85951),x85953),x85952))
% 18.77/18.51 [8662]E(f324(f324(f82(a1),f462(x86621,x86622,x86623,x86624)),f463(x86621,x86622,x86623,x86624)),x86624)+~P1(f324(f324(f232(a1),f2(a1)),x86623))+~P1(f324(f324(f231(a1),x86624),x86621))+P1(f324(f324(f231(a1),f324(f324(f3(a1),x86624),x86623)),x86621))
% 18.77/18.51 [8663]E(f324(f324(f82(a1),f473(x86631,x86632,x86633,x86634)),f474(x86631,x86632,x86633,x86634)),x86634)+~P1(f324(f324(f232(a1),f2(a1)),x86633))+~P1(f324(f324(f232(a1),x86634),x86631))+P1(f324(f324(f232(a1),f324(f324(f3(a1),x86634),x86633)),x86631))
% 18.77/18.51 [8846]~P1(f324(f324(f232(a1),f2(a1)),x88463))+~P1(f324(f324(f231(a1),x88464),x88461))+P1(f324(f324(f326(a1),f462(x88461,x88462,x88463,x88464)),x88462))+P1(f324(f324(f231(a1),f324(f324(f3(a1),x88464),x88463)),x88461))
% 18.77/18.51 [8847]~P1(f324(f324(f232(a1),f2(a1)),x88473))+~P1(f324(f324(f232(a1),x88474),x88471))+P1(f324(f324(f326(a1),f473(x88471,x88472,x88473,x88474)),x88472))+P1(f324(f324(f232(a1),f324(f324(f3(a1),x88474),x88473)),x88471))
% 18.77/18.51 [8926]~P1(f324(f324(f232(a1),f2(a1)),x89262))+~P1(f324(f324(f232(a1),x89261),x89263))+P1(f324(f324(f326(a1),f474(x89263,x89264,x89262,x89261)),f296(a1,f80(a1),x89262)))+P1(f324(f324(f232(a1),f324(f324(f3(a1),x89261),x89262)),x89263))
% 18.77/18.51 [8927]~P1(f324(f324(f232(a1),f2(a1)),x89272))+~P1(f324(f324(f231(a1),x89271),x89273))+P1(f324(f324(f326(a1),f463(x89273,x89274,x89272,x89271)),f296(a1,f80(a1),x89272)))+P1(f324(f324(f231(a1),f324(f324(f3(a1),x89271),x89272)),x89273))
% 18.77/18.51 [8943]~P1(f324(f324(f232(a1),f2(a1)),x89433))+~P1(f324(f324(f231(a1),f2(a1)),x89434))+~P1(f324(f324(f232(a1),x89434),x89431))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f324(f324(f83(a1),x89431),f51(a1,x89432,x89433))),x89434)))
% 18.77/18.51 [9000]~P86(x90001)+~P1(f324(f64(x90001),x90004))+~P1(f324(f324(f231(x90001),x90002),f680(x90003,x90002,x90004,x90001)))+P1(f324(f324(f231(x90001),f324(f324(f235(x90001),x90002),x90003)),f324(f324(f67(x90001,x90001,f235(x90001)),x90003),x90004)))
% 18.77/18.51 [9001]~P99(x90011)+~P1(f324(f64(x90011),x90014))+~P1(f324(f324(f231(x90011),x90012),f687(x90013,x90012,x90014,x90011)))+P1(f324(f324(f231(x90011),f324(f324(f104(x90011),x90012),x90013)),f324(f324(f67(x90011,x90011,f104(x90011)),x90013),x90014)))
% 18.77/18.51 [9014]~P1(f324(f324(f231(a1),x90144),f2(a1)))+~P1(f324(f324(f232(a1),f2(a1)),x90142))+~P1(f324(f324(f232(a1),x90141),x90144))+P1(f324(f324(f232(a1),f324(f324(f83(a1),x90141),x90142)),f324(f324(f82(a1),f324(f324(f83(a1),x90141),f51(a1,x90143,x90142))),x90144)))
% 18.77/18.51 [9036]P1(f324(f64(x90361),x90362))+~P1(f324(f64(x90361),x90363))+~P1(f324(f324(f326(f845(x90361,a832)),x90362),f324(f324(f63(x90361),x90363),x90364)))+~P1(f324(f324(f231(f845(f844(x90361,x90361),a832)),x90364),f324(f324(f249(x90361,x90361),x90363),f324(f18(f845(x90361,a832),x90361),x90363))))
% 18.77/18.51 [9059]~P86(x90591)+~P1(f324(f64(x90591),x90594))+P1(f324(f324(f326(x90591),f680(x90592,x90593,x90594,x90591)),x90594))+P1(f324(f324(f231(x90591),f324(f324(f235(x90591),x90593),x90592)),f324(f324(f67(x90591,x90591,f235(x90591)),x90592),x90594)))
% 18.77/18.51 [9060]~P99(x90601)+~P1(f324(f64(x90601),x90604))+P1(f324(f324(f326(x90601),f687(x90602,x90603,x90604,x90601)),x90604))+P1(f324(f324(f231(x90601),f324(f324(f104(x90601),x90603),x90602)),f324(f324(f67(x90601,x90601,f104(x90601)),x90602),x90604)))
% 18.77/18.51 [9435]~P1(f324(f64(x94352),x94354))+~P1(f324(f64(x94351),x94353))+~P1(f324(f324(f231(a838),f324(f41(x94352),x94354)),f324(f41(x94351),x94353)))+P1(f324(f324(f231(f845(x94351,a832)),f324(f304(x94352,x94351,f526(x94353,x94351,x94354,x94352)),x94354)),x94353))
% 18.77/18.51 [9097]~P1(f324(f324(f326(x90971),x90972),x90974))+P1(f324(f324(f326(x90971),x90972),x90973))+~P1(f324(f324(f232(f845(x90971,a832)),x90974),f324(f324(f303(x90971),x90972),x90973)))+P1(f324(f324(f232(f845(x90971,a832)),f324(f324(f3(f845(x90971,a832)),x90974),f324(f324(f303(x90971),x90972),f179(f845(x90971,a832))))),x90973))
% 18.77/18.51 [9251]~P1(f324(f324(f326(x92511),x92512),x92514))+P1(f324(f324(f326(x92511),x92512),x92513))+P1(f324(f324(f232(f845(x92511,a832)),x92514),f324(f324(f303(x92511),x92512),x92513)))+~P1(f324(f324(f232(f845(x92511,a832)),f324(f324(f3(f845(x92511,a832)),x92514),f324(f324(f303(x92511),x92512),f179(f845(x92511,a832))))),x92513))
% 18.77/18.51 [9279]P1(f324(f324(f326(x92791),x92792),x92793))+~P1(f324(f324(f231(f845(x92791,a832)),x92794),x92793))+P1(f324(f324(f232(f845(x92791,a832)),x92794),f324(f324(f303(x92791),x92792),x92793)))+~P1(f324(f324(f232(f845(x92791,a832)),f324(f324(f3(f845(x92791,a832)),x92794),f324(f324(f303(x92791),x92792),f179(f845(x92791,a832))))),x92793))
% 18.77/18.51 [9284]~P1(f324(f324(f326(x92841),x92843),x92842))+~P1(f324(f324(f232(f845(x92841,a832)),x92842),x92844))+P1(f324(f324(f232(f845(x92841,a832)),x92842),f324(f324(f303(x92841),x92843),x92844)))+~P1(f324(f324(f232(f845(x92841,a832)),f324(f324(f3(f845(x92841,a832)),x92842),f324(f324(f303(x92841),x92843),f179(f845(x92841,a832))))),x92844))
% 18.77/18.51 [9296]~P1(f324(f324(f231(f845(x92961,a832)),x92962),x92964))+~P1(f324(f324(f232(f845(x92961,a832)),x92962),x92964))+P1(f324(f324(f232(f845(x92961,a832)),x92962),f324(f324(f303(x92961),x92963),x92964)))+~P1(f324(f324(f232(f845(x92961,a832)),f324(f324(f3(f845(x92961,a832)),x92962),f324(f324(f303(x92961),x92963),f179(f845(x92961,a832))))),x92964))
% 18.77/18.51 [9631]E(f324(f324(f149(x96311),f324(f324(f149(f839(x96311)),f163(x96311,x96312)),x96313)),x96314),f324(f324(f149(x96311),f324(f324(f149(f839(x96311)),x96312),x96314)),x96313))+~P1(f324(f324(f232(a838),x96313),f324(f180(f839(f839(x96311))),f163(x96311,x96312))))+~P18(a838,f324(f154(a838),f324(f324(f141(f839(x96311),a838),f180(f839(x96311))),x96312)))+~P1(f324(f324(f232(a838),x96314),f324(f180(f839(f839(x96311))),f324(f126(f839(x96311),f324(f324(f10(a838,a832,f839(x96311)),f324(f232(a838),x96313)),f180(f839(x96311)))),x96312))))
% 18.77/18.51 [9653]~P1(f324(f324(f326(f844(a838,a838)),x96534),x96531))+~P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),x96534),x96532)),a72))+~P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x96531),x96533)),a73))+P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x96531),f324(f324(f303(f844(a838,a838)),x96532),x96533))),a73))
% 18.77/18.51 [9654]~P1(f324(f324(f326(f844(a838,a838)),x96544),x96541))+~P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),x96544),x96542)),a38))+~P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x96541),x96543)),a39))+P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x96541),f324(f324(f303(f844(a838,a838)),x96542),x96543))),a39))
% 18.77/18.51 [9667]~P1(f324(f324(f326(f844(a838,a838)),x96674),x96673))+~P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),x96671),x96674)),a72))+~P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x96672),x96673)),a71))+P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),f324(f324(f303(f844(a838,a838)),x96671),x96672)),x96673)),a71))
% 18.77/18.51 [9668]~P1(f324(f324(f326(f844(a838,a838)),x96684),x96683))+~P1(f324(f324(f326(f844(f844(a838,a838),f844(a838,a838))),f324(f324(f247(f844(a838,a838),f844(a838,a838)),x96681),x96684)),a38))+~P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),x96682),x96683)),a40))+P1(f324(f324(f326(f844(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832))),f324(f324(f247(f845(f844(a838,a838),a832),f845(f844(a838,a838),a832)),f324(f324(f303(f844(a838,a838)),x96681),x96682)),x96683)),a40))
% 18.77/18.51 [5838]~P11(x58384,x58381)+~P1(f324(f324(x58381,x58382),x58385))+P1(f324(f324(x58381,x58382),x58383))+~P1(f324(f324(x58381,x58385),x58383))
% 18.77/18.51 [5099]~P6(x50995)+E(x50991,x50992)+~E(x50993,x50994)+~E(f324(f324(f3(x50995),x50993),x50994),f324(f324(f3(x50995),x50991),x50992))
% 18.77/18.51 [5100]~P6(x51005)+E(x51001,x51002)+~E(x51003,x51004)+~E(f324(f324(f3(x51005),x51003),x51004),f324(f324(f3(x51005),x51001),x51002))
% 18.77/18.51 [5951]~P21(x59515,x59511,x59513)+E(f324(f324(x59511,x59512),f324(x59513,x59514)),f324(x59513,x59514))+~P1(f324(f64(x59515),x59514))+~P1(f324(f324(f326(x59515),x59512),x59514))
% 18.77/18.51 [6148]~P70(x61481)+~E(f324(f324(f3(x61481),x61484),x61485),f324(f324(f3(x61481),x61482),x61483))+~P1(f324(f324(f232(x61481),x61484),x61485))+P1(f324(f324(f232(x61481),x61482),x61483))
% 18.77/18.51 [6149]~P70(x61491)+~E(f324(f324(f3(x61491),x61494),x61495),f324(f324(f3(x61491),x61492),x61493))+~P1(f324(f324(f232(x61491),x61494),x61495))+P1(f324(f324(f232(x61491),x61492),x61493))
% 18.77/18.51 [6150]~P70(x61501)+~E(f324(f324(f3(x61501),x61504),x61505),f324(f324(f3(x61501),x61502),x61503))+~P1(f324(f324(f231(x61501),x61504),x61505))+P1(f324(f324(f231(x61501),x61502),x61503))
% 18.77/18.51 [6151]~P70(x61511)+~E(f324(f324(f3(x61511),x61514),x61515),f324(f324(f3(x61511),x61512),x61513))+~P1(f324(f324(f231(x61511),x61514),x61515))+P1(f324(f324(f231(x61511),x61512),x61513))
% 18.77/18.51 [7155]~E(x71552,f324(f324(f139(x71551),x71554),x71555))+P1(f324(f324(f326(f839(x71551)),x71552),f147(x71551,x71553)))+~P1(f324(f324(f326(f839(x71551)),x71555),f147(x71551,x71553)))+~P1(f324(f324(f326(x71551),x71554),x71553))
% 18.77/18.51 [7592]~E(f324(f180(f839(x75921)),x75923),f324(f180(f839(x75922)),x75924))+~E(f324(f324(f141(f844(x75921,x75922),x75922),f251(x75921,x75922)),x75925),x75924)+~E(f324(f324(f141(f844(x75921,x75922),x75921),f246(x75921,x75922)),x75925),x75923)+E(f324(f324(f166(x75921,x75922),x75923),x75924),x75925)
% 18.77/18.51 [7933]~P85(x79331)+P1(f324(f324(f232(f845(x79331,a832)),f296(x79331,x79332,x79333)),f296(x79331,x79334,x79335)))+~P1(f324(f324(f231(x79331),x79334),x79335))+P1(f324(f324(f231(x79331),x79332),x79333))
% 18.77/18.51 [8028]~P85(x80281)+P1(f324(f324(f231(f845(x80281,a832)),f296(x80281,x80282,x80283)),f296(x80281,x80284,x80285)))+~P1(f324(f324(f231(x80281),x80283),x80285))+~P1(f324(f324(f231(x80281),x80284),x80282))
% 18.77/18.51 [8149]~P86(x81491)+P1(f324(f324(f231(x81491),x81492),x81493))+P1(f324(f324(f231(x81491),x81494),x81493))+~P1(f324(f324(f231(f845(x81491,a832)),f324(f295(x81491,x81493),x81492)),f324(f295(x81491,x81494),x81495)))
% 18.77/18.51 [8150]~P86(x81501)+P1(f324(f324(f231(x81501),x81502),x81503))+P1(f324(f324(f231(x81501),x81502),x81504))+~P1(f324(f324(f231(f845(x81501,a832)),f324(f295(x81501,x81503),x81502)),f324(f295(x81501,x81505),x81504)))
% 18.77/18.51 [8390]~P85(x83901)+~P1(f324(f324(f232(f845(x83901,a832)),f296(x83901,x83904,x83902)),f296(x83901,x83905,x83903)))+P1(f324(f324(f231(x83901),x83902),x83903))+~P1(f324(f324(f231(x83901),x83904),x83902))
% 18.77/18.51 [8391]~P85(x83911)+~P1(f324(f324(f231(f845(x83911,a832)),f296(x83911,x83914,x83912)),f296(x83911,x83915,x83913)))+P1(f324(f324(f231(x83911),x83912),x83913))+~P1(f324(f324(f231(x83911),x83914),x83912))
% 18.77/18.51 [8392]~P85(x83921)+~P1(f324(f324(f232(f845(x83921,a832)),f296(x83921,x83923,x83924)),f296(x83921,x83922,x83925)))+P1(f324(f324(f231(x83921),x83922),x83923))+~P1(f324(f324(f231(x83921),x83923),x83924))
% 18.77/18.51 [8393]~P85(x83931)+~P1(f324(f324(f231(f845(x83931,a832)),f296(x83931,x83933,x83934)),f296(x83931,x83932,x83935)))+P1(f324(f324(f231(x83931),x83932),x83933))+~P1(f324(f324(f231(x83931),x83933),x83934))
% 18.77/18.51 [5837]~P21(x58372,x58375,x58373)+E(x58371,f179(f845(x58372,a832)))+~P1(f324(f64(x58372),x58371))+E(f324(x58373,f324(f324(f303(x58372),x58374),x58371)),f324(f324(x58375,x58374),f324(x58373,x58371)))
% 18.77/18.51 [6641]~E(x66411,x66412)+~E(f324(f324(f104(f845(x66413,a832)),x66414),x66415),f179(f845(x66413,a832)))+~P1(f324(f324(f326(x66413),x66412),x66415))+~P1(f324(f324(f326(x66413),x66411),x66414))
% 18.77/18.51 [6727]~P22(x67272,x67275,x67271)+~P1(f324(f64(x67272),x67274))+E(f324(x67271,f324(f324(f303(x67272),x67273),x67274)),f324(f324(f67(x67272,x67272,x67275),x67273),x67274))+P1(f324(f324(f326(x67272),x67273),x67274))
% 18.77/18.51 [6800]~P68(x68002)+~P1(f324(f64(x68001),x68005))+E(f324(f324(f11(x68001,x68002),x68003),f324(f324(f303(x68001),x68004),x68005)),f324(f324(f83(x68002),f324(x68003,x68004)),f324(f324(f11(x68001,x68002),x68003),x68005)))+P1(f324(f324(f326(x68001),x68004),x68005))
% 18.77/18.51 [6801]~P68(x68012)+~P1(f324(f64(x68011),x68015))+E(f324(f324(f11(x68011,x68012),x68013),f324(f324(f303(x68011),x68014),x68015)),f324(f324(f83(x68012),f324(x68013,x68014)),f324(f324(f11(x68011,x68012),x68013),x68015)))+P1(f324(f324(f326(x68011),x68014),x68015))
% 18.77/18.51 [6802]~P67(x68022)+~P1(f324(f64(x68021),x68025))+E(f324(f324(f8(x68021,x68022),x68023),f324(f324(f303(x68021),x68024),x68025)),f324(f324(f82(x68022),f324(x68023,x68024)),f324(f324(f8(x68021,x68022),x68023),x68025)))+P1(f324(f324(f326(x68021),x68024),x68025))
% 18.77/18.51 [6803]~P67(x68032)+~P1(f324(f64(x68031),x68035))+E(f324(f324(f8(x68031,x68032),x68033),f324(f324(f303(x68031),x68034),x68035)),f324(f324(f82(x68032),f324(x68033,x68034)),f324(f324(f8(x68031,x68032),x68033),x68035)))+P1(f324(f324(f326(x68031),x68034),x68035))
% 18.77/18.51 [7213]~P105(x72131)+~P1(f324(f64(x72134),x72135))+~P1(f324(f324(f326(x72134),x72133),x72135))+P1(f324(f324(f280(x72131),f324(x72132,x72133)),f324(f324(f11(x72134,x72131),x72132),x72135)))
% 18.77/18.51 [7326]~P22(x73262,x73265,x73261)+~P1(f324(f64(x73262),x73264))+E(f324(x73261,f324(f324(f303(x73262),x73263),x73264)),x73263)+~E(f324(f324(f3(f845(x73262,a832)),x73264),f324(f324(f303(x73262),x73263),f179(f845(x73262,a832)))),f179(f845(x73262,a832)))
% 18.77/18.51 [7642]~P1(f324(x76421,x76423))+~P1(f324(f324(f186(x76422),x76423),x76425))+~P1(f324(f324(f186(f35(x76421,x76422)),x76425),x76424))+P1(f324(f324(f186(f35(x76421,x76422)),x76423),x76424))
% 18.77/18.51 [7643]~P1(f324(x76431,x76433))+~P1(f324(f324(f186(x76432),x76433),x76435))+~P1(f324(f324(f186(f35(x76431,x76432)),x76435),x76434))+P1(f324(f324(f186(f35(x76431,x76432)),x76433),x76434))
% 18.77/18.51 [7661]~P105(x76611)+~P1(f324(f324(f280(x76611),x76612),x76614))+~P1(f324(f324(f231(a838),x76613),x76615))+P1(f324(f324(f280(x76611),f324(f324(f240(x76611),x76612),x76613)),f324(f324(f240(x76611),x76614),x76615)))
% 18.77/18.51 [7695]~P7(x76951)+E(f324(f324(f42(x76951),f324(f324(f83(x76951),x76952),x76953)),f324(f324(f83(x76951),x76954),x76955)),f324(f324(f83(x76951),f324(f324(f42(x76951),x76952),x76954)),f324(f324(f42(x76951),x76953),x76955)))+~P1(f324(f324(f280(x76951),x76955),x76953))+~P1(f324(f324(f280(x76951),x76954),x76952))
% 18.77/18.51 [7699]~P79(x76991)+~P1(f324(f324(f232(x76991),x76993),x76995))+~P1(f324(f324(f232(x76991),x76992),x76994))+P1(f324(f324(f232(x76991),f324(f324(f82(x76991),x76992),x76993)),f324(f324(f82(x76991),x76994),x76995)))
% 18.77/18.51 [7700]~P79(x77001)+~P1(f324(f324(f231(x77001),x77002),x77004))+~P1(f324(f324(f232(x77001),x77003),x77005))+P1(f324(f324(f232(x77001),f324(f324(f82(x77001),x77002),x77003)),f324(f324(f82(x77001),x77004),x77005)))
% 18.77/18.51 [7701]~P79(x77011)+~P1(f324(f324(f231(x77011),x77013),x77015))+~P1(f324(f324(f232(x77011),x77012),x77014))+P1(f324(f324(f232(x77011),f324(f324(f82(x77011),x77012),x77013)),f324(f324(f82(x77011),x77014),x77015)))
% 18.77/18.51 [7702]~P77(x77021)+~P1(f324(f324(f231(x77021),x77023),x77025))+~P1(f324(f324(f231(x77021),x77022),x77024))+P1(f324(f324(f231(x77021),f324(f324(f82(x77021),x77022),x77023)),f324(f324(f82(x77021),x77024),x77025)))
% 18.77/18.51 [7703]~P86(x77031)+~P1(f324(f324(f231(x77031),x77033),x77035))+~P1(f324(f324(f231(x77031),x77032),x77034))+P1(f324(f324(f231(x77031),f324(f324(f235(x77031),x77032),x77033)),f324(f324(f235(x77031),x77034),x77035)))
% 18.77/18.51 [7704]~P86(x77041)+~P1(f324(f324(f231(x77041),x77043),x77045))+~P1(f324(f324(f231(x77041),x77042),x77044))+P1(f324(f324(f231(x77041),f324(f324(f178(x77041),x77042),x77043)),f324(f324(f178(x77041),x77044),x77045)))
% 18.77/18.51 [7705]~P93(x77051)+~P1(f324(f324(f231(x77051),x77053),x77055))+~P1(f324(f324(f231(x77051),x77052),x77054))+P1(f324(f324(f231(x77051),f324(f324(f103(x77051),x77052),x77053)),f324(f324(f103(x77051),x77054),x77055)))
% 18.77/18.51 [7706]~P99(x77061)+~P1(f324(f324(f231(x77061),x77063),x77065))+~P1(f324(f324(f231(x77061),x77062),x77064))+P1(f324(f324(f231(x77061),f324(f324(f104(x77061),x77062),x77063)),f324(f324(f104(x77061),x77064),x77065)))
% 18.77/18.51 [7707]~P105(x77071)+~P1(f324(f324(f280(x77071),x77073),x77075))+~P1(f324(f324(f280(x77071),x77072),x77074))+P1(f324(f324(f280(x77071),f324(f324(f83(x77071),x77072),x77073)),f324(f324(f83(x77071),x77074),x77075)))
% 18.77/18.51 [7841]~P136(x78415)+E(x78411,x78412)+E(x78413,x78414)+~E(f324(f324(f82(x78415),f324(f324(f83(x78415),x78413),x78411)),f324(f324(f83(x78415),x78414),x78412)),f324(f324(f82(x78415),f324(f324(f83(x78415),x78413),x78412)),f324(f324(f83(x78415),x78414),x78411)))
% 18.77/18.51 [7842]~P136(x78425)+E(x78421,x78422)+E(x78423,x78424)+~E(f324(f324(f82(x78425),f324(f324(f83(x78425),x78423),x78421)),f324(f324(f83(x78425),x78424),x78422)),f324(f324(f82(x78425),f324(f324(f83(x78425),x78423),x78422)),f324(f324(f83(x78425),x78424),x78421)))
% 18.77/18.51 [7983]P31(x79831,x79832,x79833)+~P32(x79831,x79834,x79835)+~P31(x79831,x79832,f621(x79835,x79834,x79831,x79832))+~P1(f324(f324(f326(f837(x79831)),x79833),x79835))
% 18.77/18.51 [8049]~P86(x80494)+~P1(f324(f127(x80491),x80493))+P1(f324(f324(f326(x80491),x80492),f324(f157(x80491),x80493)))+P1(f324(f127(x80491),f324(f324(f137(x80491,x80494,x80495),x80492),x80493)))
% 18.77/18.51 [8195]~P67(x81951)+E(f324(f324(f82(x81951),f324(f324(f8(a838,x81951),x81952),f324(f295(a838,x81953),x81954))),f324(f324(f8(a838,x81951),x81952),f324(f295(a838,x81954),x81955))),f324(f324(f8(a838,x81951),x81952),f324(f295(a838,x81953),x81955)))+~P1(f324(f324(f231(a838),x81954),x81955))+~P1(f324(f324(f231(a838),x81953),x81954))
% 18.77/18.51 [8196]~P6(x81961)+E(f324(f324(f3(x81961),f324(f324(f8(a838,x81961),x81962),f324(f295(a838,x81963),x81964))),f324(f324(f8(a838,x81961),x81962),f324(f295(a838,x81963),x81965))),f324(f324(f8(a838,x81961),x81962),f324(f295(a838,x81965),x81964)))+~P1(f324(f324(f231(a838),x81965),x81964))+~P1(f324(f324(f231(a838),x81963),x81965))
% 18.77/18.51 [8512]~P60(x85122)+E(x85121,f2(x85122))+E(x85123,f2(x85122))+E(f324(f324(f284(x85122),f324(f324(f82(x85122),f324(f324(f83(x85122),x85124),x85121)),f324(f324(f83(x85122),x85125),x85123))),f324(f324(f83(x85122),x85123),x85121)),f324(f324(f82(x85122),f324(f324(f284(x85122),x85124),x85123)),f324(f324(f284(x85122),x85125),x85121)))
% 18.77/18.51 [8513]~P60(x85132)+E(x85131,f2(x85132))+E(x85133,f2(x85132))+E(f324(f324(f284(x85132),f324(f324(f3(x85132),f324(f324(f83(x85132),x85134),x85131)),f324(f324(f83(x85132),x85135),x85133))),f324(f324(f83(x85132),x85133),x85131)),f324(f324(f3(x85132),f324(f324(f284(x85132),x85134),x85133)),f324(f324(f284(x85132),x85135),x85131)))
% 18.77/18.51 [8522]~E(x85222,f324(x85223,x85221))+E(x85221,f541(x85222,x85223,x85224,x85225))+~P29(x85225,x85224,x85223,f238(f845(x85225,a832)))+~P1(f324(f324(f326(x85224),x85222),f324(f304(x85225,x85224,x85223),f238(f845(x85225,a832)))))
% 18.77/18.51 [8710]~P103(x87101)+~P1(f324(f324(f232(x87101),f324(f77(x87101),x87102)),x87104))+P1(f324(f324(f232(x87101),f324(f324(f83(x87101),f324(f77(x87101),x87102)),f324(f77(x87101),x87103))),f324(f324(f83(x87101),x87104),x87105)))+~P1(f324(f324(f232(x87101),f324(f77(x87101),x87103)),x87105))
% 18.77/18.51 [8724]~P32(x87241,x87245,x87244)+P31(x87241,x87242,x87243)+P1(f324(f324(f326(f837(x87241)),f621(x87244,x87245,x87241,x87242)),x87245))+~P1(f324(f324(f326(f837(x87241)),x87243),x87244))
% 18.77/18.51 [8806]~P29(x88061,x88063,x88065,x88062)+~P1(f324(f64(x88063),x88064))+P1(f324(f324(f231(a838),f324(f41(x88061),x88062)),f324(f41(x88063),x88064)))+~P1(f324(f324(f231(f845(x88063,a832)),f324(f304(x88061,x88063,x88065),x88062)),x88064))
% 18.77/18.51 [8873]~P68(x88732)+~P29(x88731,x88731,x88734,x88735)+~P1(f324(f64(x88731),x88735))+E(f324(f324(f11(x88731,x88732),f324(f75(x88731,x88732,x88731,x88733),x88734)),x88735),f324(f324(f11(x88731,x88732),x88733),f324(f304(x88731,x88731,x88734),x88735)))
% 18.77/18.51 [8874]~P67(x88742)+~P29(x88741,x88741,x88744,x88745)+~P1(f324(f64(x88741),x88745))+E(f324(f324(f8(x88741,x88742),f324(f75(x88741,x88742,x88741,x88743),x88744)),x88745),f324(f324(f8(x88741,x88742),x88743),f324(f304(x88741,x88741,x88744),x88745)))
% 18.77/18.51 [8949]~E(f548(x89492,x89494,x89491,x89493,x89495),x89495)+~E(x89492,f324(x89494,x89495))+~P29(x89493,x89491,x89494,f238(f845(x89493,a832)))+P1(f324(f324(f326(x89491),x89492),f324(f304(x89493,x89491,x89494),f238(f845(x89493,a832)))))
% 18.77/18.51 [8980]~P36(x89801,x89802)+~P1(f324(f324(f326(x89801),x89803),x89804))+~P1(f324(f324(f326(x89801),x89805),x89804))+~P1(f324(f324(f326(f844(x89801,x89801)),f324(f324(f247(x89801,x89801),x89805),f369(x89802,x89801,x89804))),x89802))
% 18.77/18.51 [9013]~P29(x90132,x90133,x90135,x90131)+E(x90131,f179(f845(x90132,a832)))+E(f324(f304(x90133,x90132,f525(x90134,x90133,x90132,x90131)),x90134),x90131)+~P1(f324(f324(f231(f845(x90133,a832)),f324(f304(x90132,x90133,x90135),x90131)),x90134))
% 18.77/18.51 [9052]~E(x90522,f324(x90521,x90525))+~P29(x90524,x90523,x90521,f238(f845(x90524,a832)))+E(f324(x90521,f548(x90522,x90521,x90523,x90524,x90525)),x90522)+P1(f324(f324(f326(x90523),x90522),f324(f304(x90524,x90523,x90521),f238(f845(x90524,a832)))))
% 18.77/18.51 [9461]~P86(x94615)+~P9(x94615)+P1(f324(f324(f326(x94611),f534(x94612,x94613,x94611,x94614,x94615)),x94613))+~P1(f324(f324(f232(x94615),x94614),f324(f324(f45(x94611,x94615),x94613),x94612)))
% 18.77/18.51 [9466]~P86(x94661)+~P9(x94661)+P1(f324(f324(f232(x94661),x94662),f324(x94663,f534(x94663,x94664,x94665,x94662,x94661))))+~P1(f324(f324(f232(x94661),x94662),f324(f324(f45(x94665,x94661),x94664),x94663)))
% 18.77/18.51 [9536]~P4(x95361)+~P1(f324(f69(x95361,x95361,f83(x95361),x95362,x95363),x95365))+P1(f324(f324(f326(x95361),x95362),x95363))+P1(f324(f69(x95361,x95361,f83(x95361),x95364,f324(f324(f303(x95361),x95362),x95363)),f324(f324(f83(x95361),x95364),x95365)))
% 18.77/18.51 [9748]~P68(x97482)+~P1(f324(f64(x97481),x97485))+E(f324(f324(f11(x97481,x97482),f324(f324(f9(x97481,x97482,x97482),f324(f324(f20(x97481,x97482,f845(x97482,x97482)),f324(f324(f10(a832,f845(x97482,f845(x97482,x97482)),x97481),f98(x97482)),f324(a321,x97483))),x97484)),f80(x97482))),x97485),f80(x97482))+P1(f324(f324(f326(x97481),x97483),x97485))
% 18.77/18.51 [9749]~P67(x97492)+~P1(f324(f64(x97491),x97495))+E(f324(f324(f8(x97491,x97492),f324(f324(f9(x97491,x97492,x97492),f324(f324(f20(x97491,x97492,f845(x97492,x97492)),f324(f324(f10(a832,f845(x97492,f845(x97492,x97492)),x97491),f98(x97492)),f324(a321,x97493))),x97494)),f2(x97492))),x97495),f2(x97492))+P1(f324(f324(f326(x97491),x97493),x97495))
% 18.77/18.51 [9750]~P68(x97502)+~P1(f324(f64(x97501),x97505))+E(f324(f324(f11(x97501,x97502),f324(f324(f9(x97501,x97502,x97502),f324(f324(f20(x97501,x97502,f845(x97502,x97502)),f324(f324(f10(a832,f845(x97502,f845(x97502,x97502)),x97501),f98(x97502)),f324(a321,x97503))),x97504)),f80(x97502))),x97505),f324(x97504,x97503))+~P1(f324(f324(f326(x97501),x97503),x97505))
% 18.77/18.51 [9751]~P67(x97512)+~P1(f324(f64(x97511),x97515))+E(f324(f324(f8(x97511,x97512),f324(f324(f9(x97511,x97512,x97512),f324(f324(f20(x97511,x97512,f845(x97512,x97512)),f324(f324(f10(a832,f845(x97512,f845(x97512,x97512)),x97511),f98(x97512)),f324(a321,x97513))),x97514)),f2(x97512))),x97515),f324(x97514,x97513))+~P1(f324(f324(f326(x97511),x97513),x97515))
% 18.77/18.51 [9811]~P68(x98112)+~P1(f324(f64(x98111),x98115))+E(f324(f324(f11(x98111,x98112),f324(f324(f9(x98111,x98112,x98112),f324(f324(f20(x98111,x98112,f845(x98112,x98112)),f324(f324(f10(a832,f845(x98112,f845(x98112,x98112)),x98111),f98(x98112)),f324(f324(f9(x98111,x98111,a832),a321),x98113))),x98114)),f80(x98112))),x98115),f80(x98112))+P1(f324(f324(f326(x98111),x98113),x98115))
% 18.77/18.51 [9812]~P67(x98122)+~P1(f324(f64(x98121),x98125))+E(f324(f324(f8(x98121,x98122),f324(f324(f9(x98121,x98122,x98122),f324(f324(f20(x98121,x98122,f845(x98122,x98122)),f324(f324(f10(a832,f845(x98122,f845(x98122,x98122)),x98121),f98(x98122)),f324(f324(f9(x98121,x98121,a832),a321),x98123))),x98124)),f2(x98122))),x98125),f2(x98122))+P1(f324(f324(f326(x98121),x98123),x98125))
% 18.77/18.51 [9814]~P68(x98142)+~P1(f324(f64(x98141),x98145))+E(f324(f324(f11(x98141,x98142),f324(f324(f9(x98141,x98142,x98142),f324(f324(f20(x98141,x98142,f845(x98142,x98142)),f324(f324(f10(a832,f845(x98142,f845(x98142,x98142)),x98141),f98(x98142)),f324(f324(f9(x98141,x98141,a832),a321),x98143))),x98144)),f80(x98142))),x98145),f324(x98144,x98143))+~P1(f324(f324(f326(x98141),x98143),x98145))
% 18.77/18.51 [9815]~P67(x98152)+~P1(f324(f64(x98151),x98155))+E(f324(f324(f8(x98151,x98152),f324(f324(f9(x98151,x98152,x98152),f324(f324(f20(x98151,x98152,f845(x98152,x98152)),f324(f324(f10(a832,f845(x98152,f845(x98152,x98152)),x98151),f98(x98152)),f324(f324(f9(x98151,x98151,a832),a321),x98153))),x98154)),f2(x98152))),x98155),f324(x98154,x98153))+~P1(f324(f324(f326(x98151),x98153),x98155))
% 18.77/18.51 [7698]~P6(x76982)+~P1(f324(f64(x76981),x76984))+E(f324(f324(f8(x76981,x76982),x76983),f324(f324(f3(f845(x76981,a832)),x76984),f324(f324(f303(x76981),x76985),f179(f845(x76981,a832))))),f324(f324(f8(x76981,x76982),x76983),x76984))+P1(f324(f324(f326(x76981),x76985),x76984))
% 18.77/18.51 [8201]~P126(x82012)+~P1(f324(f64(x82011),x82014))+E(f324(f324(f8(x82011,x82012),x82013),f324(f324(f3(f845(x82011,a832)),x82014),f324(f324(f303(x82011),x82015),f179(f845(x82011,a832))))),f324(f324(f3(x82012),f324(f324(f8(x82011,x82012),x82013),x82014)),f324(x82013,x82015)))+~P1(f324(f324(f326(x82011),x82015),x82014))
% 18.77/18.51 [8202]~P6(x82022)+~P1(f324(f64(x82021),x82024))+E(f324(f324(f8(x82021,x82022),x82023),f324(f324(f3(f845(x82021,a832)),x82024),f324(f324(f303(x82021),x82025),f179(f845(x82021,a832))))),f324(f324(f3(x82022),f324(f324(f8(x82021,x82022),x82023),x82024)),f324(x82023,x82025)))+~P1(f324(f324(f326(x82021),x82025),x82024))
% 18.77/18.51 [8213]~P105(x82131)+~P1(f324(f324(f231(a838),x82133),x82135))+~P1(f324(f324(f280(x82131),f324(f324(f240(x82131),x82132),x82135)),x82134))+P1(f324(f324(f280(x82131),f324(f324(f240(x82131),x82132),x82133)),x82134))
% 18.77/18.51 [8230]~P6(x82301)+~P1(f324(f64(x82302),x82304))+E(f324(f324(f3(x82301),f324(f324(f8(x82302,x82301),x82303),x82304)),f324(f324(f8(x82302,x82301),x82303),x82305)),f324(f324(f8(x82302,x82301),x82303),f324(f324(f3(f845(x82302,a832)),x82304),x82305)))+~P1(f324(f324(f231(f845(x82302,a832)),x82305),x82304))
% 18.77/18.51 [8251]P1(f324(f64(x82511),f324(x82512,x82513)))+~P1(f324(f64(x82514),x82515))+~P1(f324(f324(f326(x82514),x82513),x82515))+~P1(f324(f64(x82511),f324(f324(f45(x82514,f845(x82511,a832)),x82515),x82512)))
% 18.77/18.51 [8675]~P12(x86751,x86755,x86754)+~E(f324(f278(x86751,x86751,x86754),f324(f324(f303(x86751),x86752),f179(f845(x86751,a832)))),f324(f278(x86751,x86751,x86754),f324(f324(f303(x86751),x86753),f179(f845(x86751,a832)))))+~P1(f324(f324(f326(x86751),x86753),x86755))+P1(f324(f324(f326(f844(x86751,x86751)),f324(f324(f247(x86751,x86751),x86752),x86753)),x86754))
% 18.77/18.51 [8941]~P1(f324(x89411,x89415))+P1(f324(x89411,f359(x89411,x89412,x89413,x89414)))+P1(f324(x89411,f358(x89411,x89412,x89413,x89414)))+~P1(f324(f324(f326(x89414),x89415),f324(f324(f103(f845(x89414,a832)),x89413),x89412)))
% 18.77/18.51 [9101]~P1(f324(x91011,x91015))+P1(f324(x91011,f358(x91011,x91012,x91013,x91014)))+P1(f324(f324(f326(x91014),f359(x91011,x91012,x91013,x91014)),x91012))+~P1(f324(f324(f326(x91014),x91015),f324(f324(f103(f845(x91014,a832)),x91013),x91012)))
% 18.77/18.51 [9102]~P1(f324(x91021,x91025))+P1(f324(x91021,f359(x91021,x91022,x91023,x91024)))+P1(f324(f324(f326(x91024),f358(x91021,x91022,x91023,x91024)),x91023))+~P1(f324(f324(f326(x91024),x91025),f324(f324(f103(f845(x91024,a832)),x91023),x91022)))
% 18.77/18.51 [9106]P1(f324(x91061,x91062))+~P1(f324(x91061,f363(x91061,x91063,x91064,x91065)))+~P1(f324(x91061,f362(x91061,x91063,x91064,x91065)))+~P1(f324(f324(f326(x91065),x91062),f324(f324(f103(f845(x91065,a832)),x91064),x91063)))
% 18.77/18.51 [9141]E(x91411,x91412)+~P1(f324(f324(f326(f844(x91413,x91413)),f324(f324(f247(x91413,x91413),x91411),x91412)),f301(x91413,x91415)))+P1(f324(f324(f326(x91413),x91411),x91414))+~P1(f324(f324(f231(f845(f844(x91413,x91413),a832)),x91415),f324(f324(f249(x91413,x91413),x91414),f324(f18(f845(x91413,a832),x91413),x91414))))
% 18.77/18.51 [9158]P1(f324(x91581,x91582))+~P1(f324(x91581,f362(x91581,x91584,x91585,x91583)))+P1(f324(f324(f326(x91583),f363(x91581,x91584,x91585,x91583)),x91584))+~P1(f324(f324(f326(x91583),x91582),f324(f324(f103(f845(x91583,a832)),x91585),x91584)))
% 18.77/18.51 [9159]P1(f324(x91591,x91592))+~P1(f324(x91591,f363(x91591,x91594,x91595,x91593)))+P1(f324(f324(f326(x91593),f362(x91591,x91594,x91595,x91593)),x91595))+~P1(f324(f324(f326(x91593),x91592),f324(f324(f103(f845(x91593,a832)),x91595),x91594)))
% 18.77/18.51 [9221]P1(f324(x92211,x92212))+P1(f324(f324(f326(x92213),f363(x92211,x92214,x92215,x92213)),x92214))+P1(f324(f324(f326(x92213),f362(x92211,x92214,x92215,x92213)),x92215))+~P1(f324(f324(f326(x92213),x92212),f324(f324(f103(f845(x92213,a832)),x92215),x92214)))
% 18.77/18.51 [9223]~P1(f324(x92232,x92235))+P1(f324(f324(f326(x92231),f359(x92232,x92233,x92234,x92231)),x92233))+P1(f324(f324(f326(x92231),f358(x92232,x92233,x92234,x92231)),x92234))+~P1(f324(f324(f326(x92231),x92235),f324(f324(f103(f845(x92231,a832)),x92234),x92233)))
% 18.77/18.51 [9369]~P12(x93691,x93695,x93694)+~P1(f324(f324(f326(x93691),x93693),x93695))+P1(f324(f324(f326(f844(x93691,x93691)),f324(f324(f247(x93691,x93691),x93692),x93693)),x93694))+~P1(f324(f324(f231(f845(x93691,a832)),f324(f278(x93691,x93691,x93694),f324(f324(f303(x93691),x93693),f179(f845(x93691,a832))))),f324(f278(x93691,x93691,x93694),f324(f324(f303(x93691),x93692),f179(f845(x93691,a832))))))
% 18.77/18.51 [9490]~P86(x94905)+~P9(x94905)+P1(f324(f324(f326(x94901),f666(x94902,x94903,x94904,x94901,x94905)),x94904))+~P1(f324(f324(f232(x94905),f324(f324(f46(x94901,x94905),x94904),x94903)),x94902))
% 18.77/18.51 [9523]~P77(x95235)+~P72(x95235)+P1(f324(f324(f326(x95231),f740(x95232,x95233,x95234,x95231,x95235)),f324(f157(x95231),x95234)))+P1(f324(f324(f231(x95235),f324(f151(x95235),f324(f324(f141(x95231,x95235),x95233),x95234))),f324(f151(x95235),f324(f324(f141(x95231,x95235),x95232),x95234))))
% 18.77/18.51 [9621]~P86(x96211)+~P9(x96211)+P1(f324(f324(f232(x96211),f324(x96212,f666(x96213,x96212,x96214,x96215,x96211))),x96213))+~P1(f324(f324(f232(x96211),f324(f324(f46(x96215,x96211),x96214),x96212)),x96213))
% 18.77/18.51 [9764]~P77(x97641)+~P72(x97641)+~P1(f324(f324(f231(x97641),f324(x97643,f740(x97645,x97643,x97644,x97642,x97641))),f324(x97645,f740(x97645,x97643,x97644,x97642,x97641))))+P1(f324(f324(f231(x97641),f324(f151(x97641),f324(f324(f141(x97642,x97641),x97643),x97644))),f324(f151(x97641),f324(f324(f141(x97642,x97641),x97645),x97644))))
% 18.77/18.51 [8529]~P68(x85291)+~P1(f324(f64(x85294),x85295))+~P1(f324(f324(f326(x85294),x85293),x85295))+E(f324(f324(f83(x85291),f324(x85292,x85293)),f324(f324(f11(x85294,x85291),x85292),f324(f324(f3(f845(x85294,a832)),x85295),f324(f324(f303(x85294),x85293),f179(f845(x85294,a832)))))),f324(f324(f11(x85294,x85291),x85292),x85295))
% 18.77/18.51 [8530]~P67(x85301)+~P1(f324(f64(x85304),x85305))+~P1(f324(f324(f326(x85304),x85303),x85305))+E(f324(f324(f82(x85301),f324(x85302,x85303)),f324(f324(f8(x85304,x85301),x85302),f324(f324(f3(f845(x85304,a832)),x85305),f324(f324(f303(x85304),x85303),f179(f845(x85304,a832)))))),f324(f324(f8(x85304,x85301),x85302),x85305))
% 18.77/18.51 [8531]~P67(x85311)+~P1(f324(f64(x85314),x85315))+~P1(f324(f324(f326(x85314),x85313),x85315))+E(f324(f324(f82(x85311),f324(x85312,x85313)),f324(f324(f8(x85314,x85311),x85312),f324(f324(f3(f845(x85314,a832)),x85315),f324(f324(f303(x85314),x85313),f179(f845(x85314,a832)))))),f324(f324(f8(x85314,x85311),x85312),x85315))
% 18.77/18.51 [8585]~P22(x85851,x85854,x85855)+~P1(f324(f64(x85851),x85852))+E(f324(f324(f3(f845(x85851,a832)),x85852),f324(f324(f303(x85851),x85853),f179(f845(x85851,a832)))),f179(f845(x85851,a832)))+E(f324(f324(x85854,x85853),f324(x85855,f324(f324(f3(f845(x85851,a832)),x85852),f324(f324(f303(x85851),x85853),f179(f845(x85851,a832)))))),f324(x85855,f324(f324(f303(x85851),x85853),x85852)))
% 18.77/18.51 [8921]~P68(x89211)+~P1(f324(f64(x89212),x89215))+~P1(f324(f64(x89212),x89214))+E(f324(f324(f83(x89211),f324(f324(f11(x89212,x89211),x89213),f324(f324(f103(f845(x89212,a832)),x89214),x89215))),f324(f324(f11(x89212,x89211),x89213),f324(f324(f104(f845(x89212,a832)),x89214),x89215))),f324(f324(f83(x89211),f324(f324(f11(x89212,x89211),x89213),x89214)),f324(f324(f11(x89212,x89211),x89213),x89215)))
% 18.77/18.51 [8922]~P68(x89221)+~P1(f324(f64(x89222),x89225))+~P1(f324(f64(x89222),x89224))+E(f324(f324(f83(x89221),f324(f324(f11(x89222,x89221),x89223),f324(f324(f103(f845(x89222,a832)),x89224),x89225))),f324(f324(f11(x89222,x89221),x89223),f324(f324(f104(f845(x89222,a832)),x89224),x89225))),f324(f324(f83(x89221),f324(f324(f11(x89222,x89221),x89223),x89224)),f324(f324(f11(x89222,x89221),x89223),x89225)))
% 18.77/18.51 [8923]~P67(x89231)+~P1(f324(f64(x89232),x89235))+~P1(f324(f64(x89232),x89234))+E(f324(f324(f82(x89231),f324(f324(f8(x89232,x89231),x89233),f324(f324(f103(f845(x89232,a832)),x89234),x89235))),f324(f324(f8(x89232,x89231),x89233),f324(f324(f104(f845(x89232,a832)),x89234),x89235))),f324(f324(f82(x89231),f324(f324(f8(x89232,x89231),x89233),x89234)),f324(f324(f8(x89232,x89231),x89233),x89235)))
% 18.77/18.51 [9051]~P6(x90511)+~P1(f324(f64(x90512),x90515))+~P1(f324(f64(x90512),x90514))+E(f324(f324(f3(x90511),f324(f324(f82(x90511),f324(f324(f8(x90512,x90511),x90513),x90514)),f324(f324(f8(x90512,x90511),x90513),x90515))),f324(f324(f8(x90512,x90511),x90513),f324(f324(f104(f845(x90512,a832)),x90514),x90515))),f324(f324(f8(x90512,x90511),x90513),f324(f324(f103(f845(x90512,a832)),x90514),x90515)))
% 18.77/18.51 [9235]~P29(x92351,x92352,x92353,x92355)+~P29(x92351,x92352,x92353,x92354)+P29(x92351,x92352,x92353,f324(f324(f103(f845(x92351,a832)),x92354),x92355))+~E(f324(f324(f104(f845(x92352,a832)),f324(f304(x92351,x92352,x92353),f324(f324(f3(f845(x92351,a832)),x92354),x92355))),f324(f304(x92351,x92352,x92353),f324(f324(f3(f845(x92351,a832)),x92355),x92354))),f179(f845(x92352,a832)))
% 18.77/18.51 [9342]E(x93421,f2(a1))+~P1(f324(f324(f232(a1),f2(a1)),x93423))+~P1(f324(f55(x93422,x93421),f324(f324(f247(a1,a1),x93424),x93425)))+P1(f324(f55(x93422,f324(f324(f83(a1),x93421),x93423)),f324(f324(f247(a1,a1),f324(f324(f42(a1),x93424),x93423)),f324(f324(f82(a1),f324(f324(f83(a1),x93421),f51(a1,x93424,x93423))),x93425))))
% 18.77/18.51 [9350]~P1(f324(f324(f232(a838),f2(a838)),x93503))+~P1(f324(f324(f232(a838),f2(a838)),x93502))+~P1(f324(f54(x93501,x93502),f324(f324(f247(a838,a838),x93504),x93505)))+P1(f324(f54(x93501,f324(f324(f83(a838),x93502),x93503)),f324(f324(f247(a838,a838),f324(f324(f42(a838),x93504),x93503)),f324(f324(f82(a838),f324(f324(f83(a838),x93502),f51(a838,x93504,x93503))),x93505))))
% 18.77/18.51 [9401]E(f324(f324(f82(a1),f479(x94011,x94012,x94013,x94014,x94015)),f480(x94011,x94012,x94013,x94014,x94015)),x94015)+~P1(f324(f324(f280(a1),x94014),x94013))+~P1(f324(f324(f280(a1),x94014),f324(f324(f82(a1),x94015),x94011)))+P1(f324(f324(f280(a1),x94014),f324(f324(f82(a1),f324(f324(f3(a1),x94015),x94013)),x94011)))
% 18.77/18.51 [9402]E(f324(f324(f3(a1),f481(x94021,x94022,x94023,x94024,x94025)),f482(x94021,x94022,x94023,x94024,x94025)),x94025)+~P1(f324(f324(f280(a1),x94024),x94023))+~P1(f324(f324(f280(a1),x94024),f324(f324(f82(a1),x94025),x94021)))+P1(f324(f324(f280(a1),x94024),f324(f324(f82(a1),f324(f324(f82(a1),x94025),x94023)),x94021)))
% 18.77/18.51 [9403]~P68(x94031)+~P1(f324(f64(x94032),x94035))+~P1(f324(f64(x94032),x94034))+E(f324(f324(f83(x94031),f324(f324(f324(f68(x94031,x94032,f83(x94031)),x94033),f80(x94031)),f324(f324(f103(f845(x94032,a832)),x94034),x94035))),f324(f324(f324(f68(x94031,x94032,f83(x94031)),x94033),f80(x94031)),f324(f324(f104(f845(x94032,a832)),x94034),x94035))),f324(f324(f83(x94031),f324(f324(f324(f68(x94031,x94032,f83(x94031)),x94033),f80(x94031)),x94034)),f324(f324(f324(f68(x94031,x94032,f83(x94031)),x94033),f80(x94031)),x94035)))
% 18.77/18.51 [9405]~E(f324(f324(f158(x94051),x94055),x94052),f324(f324(f158(x94051),x94055),x94053))+P1(f324(f324(f326(f844(f839(x94051),f839(x94051))),f324(f324(f247(f839(x94051),f839(x94051)),x94052),x94053)),f136(x94051,x94054)))+~P1(f324(f324(f232(a838),x94055),f324(f324(f235(a838),f324(f180(f839(x94051)),x94052)),f324(f180(f839(x94051)),x94053))))+~P1(f324(f324(f326(f844(x94051,x94051)),f324(f324(f247(x94051,x94051),f324(f324(f149(x94051),x94052),x94055)),f324(f324(f149(x94051),x94053),x94055))),x94054))
% 18.77/18.51 [9414]E(f324(f324(f82(a1),f487(x94141,x94142,x94143,x94144,x94145)),f488(x94141,x94142,x94143,x94144,x94145)),x94145)+~P1(f324(f324(f280(a1),x94144),x94143))+P1(f324(f324(f280(a1),x94144),f324(f324(f82(a1),x94145),x94141)))+~P1(f324(f324(f280(a1),x94144),f324(f324(f82(a1),f324(f324(f3(a1),x94145),x94143)),x94141)))
% 18.77/18.51 [9415]E(f324(f324(f3(a1),f483(x94151,x94152,x94153,x94154,x94155)),f484(x94151,x94152,x94153,x94154,x94155)),x94155)+~P1(f324(f324(f280(a1),x94154),x94153))+P1(f324(f324(f280(a1),x94154),f324(f324(f82(a1),x94155),x94151)))+~P1(f324(f324(f280(a1),x94154),f324(f324(f82(a1),f324(f324(f82(a1),x94155),x94153)),x94151)))
% 18.77/18.51 [9500]~P1(f324(f324(f280(a1),x95004),x95003))+P1(f324(f324(f326(a1),f479(x95001,x95002,x95003,x95004,x95005)),x95002))+~P1(f324(f324(f280(a1),x95004),f324(f324(f82(a1),x95005),x95001)))+P1(f324(f324(f280(a1),x95004),f324(f324(f82(a1),f324(f324(f3(a1),x95005),x95003)),x95001)))
% 18.77/18.51 [9501]~P1(f324(f324(f280(a1),x95014),x95013))+P1(f324(f324(f326(a1),f481(x95011,x95012,x95013,x95014,x95015)),x95012))+~P1(f324(f324(f280(a1),x95014),f324(f324(f82(a1),x95015),x95011)))+P1(f324(f324(f280(a1),x95014),f324(f324(f82(a1),f324(f324(f82(a1),x95015),x95013)),x95011)))
% 18.77/18.51 [9508]~P1(f324(f324(f280(a1),x95084),x95083))+P1(f324(f324(f326(a1),f480(x95081,x95082,x95083,x95084,x95085)),f296(a1,f80(a1),x95083)))+~P1(f324(f324(f280(a1),x95084),f324(f324(f82(a1),x95085),x95081)))+P1(f324(f324(f280(a1),x95084),f324(f324(f82(a1),f324(f324(f3(a1),x95085),x95083)),x95081)))
% 18.77/18.51 [9509]~P1(f324(f324(f280(a1),x95094),x95093))+P1(f324(f324(f326(a1),f482(x95091,x95092,x95093,x95094,x95095)),f296(a1,f80(a1),x95093)))+~P1(f324(f324(f280(a1),x95094),f324(f324(f82(a1),x95095),x95091)))+P1(f324(f324(f280(a1),x95094),f324(f324(f82(a1),f324(f324(f82(a1),x95095),x95093)),x95091)))
% 18.77/18.51 [9510]~P2(x95105)+~P77(x95105)+P1(f324(f324(f326(x95101),f500(x95102,x95103,x95104,x95101,x95105)),x95104))+P1(f324(f324(f231(x95105),f324(f324(f8(x95101,x95105),x95103),x95104)),f324(f324(f83(x95105),f324(f102(x95105),f324(f41(x95101),x95104))),x95102)))
% 18.77/18.51 [9511]~P1(f324(f324(f280(a1),x95114),x95113))+P1(f324(f324(f326(a1),f483(x95111,x95112,x95113,x95114,x95115)),x95112))+P1(f324(f324(f280(a1),x95114),f324(f324(f82(a1),x95115),x95111)))+~P1(f324(f324(f280(a1),x95114),f324(f324(f82(a1),f324(f324(f82(a1),x95115),x95113)),x95111)))
% 18.77/18.51 [9512]~P1(f324(f324(f280(a1),x95124),x95123))+P1(f324(f324(f326(a1),f487(x95121,x95122,x95123,x95124,x95125)),x95122))+P1(f324(f324(f280(a1),x95124),f324(f324(f82(a1),x95125),x95121)))+~P1(f324(f324(f280(a1),x95124),f324(f324(f82(a1),f324(f324(f3(a1),x95125),x95123)),x95121)))
% 18.77/18.51 [9513]~P1(f324(f324(f280(a1),x95131),x95135))+P1(f324(f324(f326(a1),f484(x95133,x95134,x95135,x95131,x95132)),f296(a1,f80(a1),x95135)))+P1(f324(f324(f280(a1),x95131),f324(f324(f82(a1),x95132),x95133)))+~P1(f324(f324(f280(a1),x95131),f324(f324(f82(a1),f324(f324(f82(a1),x95132),x95135)),x95133)))
% 18.77/18.51 [9514]~P1(f324(f324(f280(a1),x95141),x95145))+P1(f324(f324(f326(a1),f488(x95143,x95144,x95145,x95141,x95142)),f296(a1,f80(a1),x95145)))+P1(f324(f324(f280(a1),x95141),f324(f324(f82(a1),x95142),x95143)))+~P1(f324(f324(f280(a1),x95141),f324(f324(f82(a1),f324(f324(f3(a1),x95142),x95145)),x95143)))
% 18.77/18.51 [9681]~P2(x96811)+~P77(x96811)+~P1(f324(f324(f231(x96811),f324(x96813,f500(x96815,x96813,x96814,x96812,x96811))),x96815))+P1(f324(f324(f231(x96811),f324(f324(f8(x96812,x96811),x96813),x96814)),f324(f324(f83(x96811),f324(f102(x96811),f324(f41(x96812),x96814))),x96815)))
% 18.77/18.51 [8557]E(f324(f324(f125(x85571),x85572),x85573),f324(f324(f125(x85571),x85574),x85575))+~E(f324(f324(f158(x85571),f324(f180(f839(x85571)),x85572)),x85574),x85572)+~E(f324(f324(f125(x85571),f324(f324(f128(x85571),f324(f180(f839(x85571)),x85572)),x85574)),x85575),x85573)+P1(f324(f324(f231(a838),f324(f180(f839(x85571)),x85574)),f324(f180(f839(x85571)),x85572)))
% 18.77/18.51 [8673]E(f324(f324(f125(x86731),x86732),x86733),f324(f324(f125(x86731),x86734),x86735))+~E(f324(f324(f158(x86731),f324(f180(f839(x86731)),x86732)),x86734),x86732)+~E(x86733,f324(f324(f125(x86731),f324(f324(f128(x86731),f324(f180(f839(x86731)),x86732)),x86734)),x86735))+~P1(f324(f324(f231(a838),f324(f180(f839(x86731)),x86732)),f324(f180(f839(x86731)),x86734)))
% 18.77/18.51 [9832]~P1(f324(x98325,x98324))+~P1(f324(f64(x98322),f324(f257(x98322),x98325)))+P1(f324(f64(x98321),f324(f257(x98321),f324(f324(f9(x98321,x98322,a832),x98323),x98324))))+~P1(f324(f64(x98321),f324(f257(x98321),f324(f324(f10(f845(x98322,a832),a832,x98321),f89(x98322)),f324(f324(f10(f845(x98322,a832),f845(x98322,a832),x98321),f324(f20(x98322,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98322),a322),x98325))),x98323)))))
% 18.77/18.51 [7845]~P39(x78452,x78453,x78454,x78456)+~P39(f35(x78451,x78452),x78456,x78454,x78455)+P39(f35(x78451,x78452),x78453,x78454,x78455)+~P1(f324(x78451,x78453))
% 18.77/18.51 [7846]~P39(x78462,x78463,x78464,x78466)+~P39(f35(x78461,x78462),x78466,x78464,x78465)+P39(f35(x78461,x78462),x78463,x78464,x78465)+~P1(f324(x78461,x78463))
% 18.77/18.51 [8366]~P23(x83665,x83661,x83666,x83662)+E(f324(f75(x83661,x83661,x83661,f324(x83662,x83663)),f324(x83662,x83664)),f324(f75(x83661,x83661,x83661,f324(x83662,x83664)),f324(x83662,x83663)))+~P1(f324(f64(x83665),x83664))+~P1(f324(f64(x83665),x83663))
% 18.77/18.51 [7756]~P29(x77561,x77562,x77564,x77563)+~E(f324(x77564,x77566),x77565)+E(f324(f79(x77561,x77562,x77563,x77564),x77565),x77566)+~P1(f324(f324(f326(x77561),x77566),x77563))
% 18.77/18.51 [7952]~P24(x79526,x79521,x79524,x79522)+E(f324(f75(x79521,x79521,x79521,f324(x79522,x79523)),f324(x79524,x79525)),f324(x79522,x79523))+~P1(f324(f64(x79526),x79523))+~P1(f324(f324(f326(x79526),x79525),x79523))
% 18.77/18.51 [9089]~P23(x90893,x90891,x90896,x90892)+E(f324(f75(x90891,x90891,x90891,f324(x90892,f324(f324(f3(f845(x90893,a832)),x90894),f324(f324(f303(x90893),x90895),f179(f845(x90893,a832)))))),f324(x90896,x90895)),f324(x90892,x90894))+~P1(f324(f64(x90893),x90894))+~P1(f324(f324(f326(x90893),x90895),x90894))
% 18.77/18.51 [6808]~P7(x68081)+~E(f51(x68081,x68083,x68084),f51(x68081,x68086,x68084))+~E(f51(x68081,x68082,x68084),f51(x68081,x68085,x68084))+E(f51(x68081,f324(f324(f83(x68081),x68082),x68083),x68084),f51(x68081,f324(f324(f83(x68081),x68085),x68086),x68084))
% 18.77/18.51 [6809]~P7(x68091)+~E(f51(x68091,x68093,x68094),f51(x68091,x68096,x68094))+~E(f51(x68091,x68092,x68094),f51(x68091,x68095,x68094))+E(f51(x68091,f324(f324(f82(x68091),x68092),x68093),x68094),f51(x68091,f324(f324(f82(x68091),x68095),x68096),x68094))
% 18.77/18.51 [6810]~P8(x68101)+~E(f51(x68101,x68103,x68104),f51(x68101,x68106,x68104))+~E(f51(x68101,x68102,x68104),f51(x68101,x68105,x68104))+E(f51(x68101,f324(f324(f3(x68101),x68102),x68103),x68104),f51(x68101,f324(f324(f3(x68101),x68105),x68106),x68104))
% 18.77/18.51 [7645]~P20(x76451,x76452,x76453)+~P1(f324(f64(x76451),x76456))+E(f324(f324(f67(x76451,x76452,x76453),x76454),f324(f324(f303(x76451),x76455),x76456)),f324(f324(f67(x76451,x76452,x76453),f324(f324(x76453,x76455),x76454)),x76456))+P1(f324(f324(f326(x76451),x76455),x76456))
% 18.77/18.51 [7713]~P9(x77131)+P1(f324(f324(f231(x77131),x77132),f324(x77133,x77134)))+~P1(f324(f324(f326(x77135),x77134),x77136))+~P1(f324(f324(f231(x77131),x77132),f324(f324(f46(x77135,x77131),x77136),x77133)))
% 18.77/18.51 [7875]~P20(x78751,x78752,x78753)+~P1(f324(f64(x78751),x78756))+E(f324(f324(f67(x78751,x78752,x78753),x78754),f324(f324(f303(x78751),x78755),x78756)),f324(f324(x78753,x78755),f324(f324(f67(x78751,x78752,x78753),x78754),x78756)))+P1(f324(f324(f326(x78751),x78755),x78756))
% 18.77/18.51 [7968]~P86(x79683)+~P1(f324(x79682,x79685))+~P18(x79683,f324(f324(f141(x79681,x79683),x79684),x79686))+E(f324(f126(x79681,x79682),f324(f324(f137(x79681,x79683,x79684),x79685),x79686)),f324(f324(f137(x79681,x79683,x79684),x79685),f324(f126(x79681,x79682),x79686)))
% 18.77/18.51 [7992]E(x79921,x79922)+E(x79923,f2(a1))+~P1(f324(f55(x79924,x79923),f324(f324(f247(a1,a1),x79925),x79922)))+~P1(f324(f55(x79924,x79923),f324(f324(f247(a1,a1),x79926),x79921)))
% 18.77/18.51 [7993]E(x79931,x79932)+E(x79933,f2(a1))+~P1(f324(f55(x79934,x79933),f324(f324(f247(a1,a1),x79932),x79935)))+~P1(f324(f55(x79934,x79933),f324(f324(f247(a1,a1),x79931),x79936)))
% 18.77/18.51 [8015]~P23(x80152,x80155,x80156,x80151)+~P1(f324(f64(x80152),x80154))+E(f324(x80151,f324(f324(f303(x80152),x80153),x80154)),f324(f75(x80155,x80155,x80155,f324(x80151,x80154)),f324(x80156,x80153)))+P1(f324(f324(f326(x80152),x80153),x80154))
% 18.77/18.51 [8233]~P24(x82335,x82331,x82336,x82332)+E(f324(f75(x82331,x82331,x82331,f324(x82332,x82333)),f324(x82332,x82334)),f324(x82332,x82333))+~P1(f324(f64(x82335),x82333))+~P1(f324(f324(f231(f845(x82335,a832)),x82334),x82333))
% 18.77/18.51 [9281]~P29(x92811,x92812,x92814,x92813)+~P1(f324(f324(f326(x92812),x92815),f324(f304(x92811,x92812,x92814),x92813)))+P1(f324(f324(f326(x92811),f324(f79(x92811,x92812,x92813,x92814),x92815)),x92816))+~P1(f324(f324(f231(f845(x92811,a832)),x92813),x92816))
% 18.77/18.51 [9632]~P67(x96322)+~E(f629(x96321,x96323,x96325,x96326,x96324,x96322),f628(x96321,x96323,x96325,x96326,x96324,x96322))+~P1(f324(f64(x96324),x96326))+E(f324(f324(f8(x96321,x96322),x96323),f324(f304(x96324,x96321,x96325),x96326)),f324(f324(f8(x96324,x96322),f324(f75(x96321,x96322,x96324,x96323),x96325)),x96326))
% 18.77/18.51 [9663]~P67(x96636)+E(f324(x96631,f629(x96632,x96633,x96631,x96634,x96635,x96636)),f324(x96631,f628(x96632,x96633,x96631,x96634,x96635,x96636)))+E(f324(f324(f8(x96632,x96636),x96633),f324(f304(x96635,x96632,x96631),x96634)),f324(f324(f8(x96635,x96636),f324(f75(x96632,x96636,x96635,x96633),x96631)),x96634))+~P1(f324(f64(x96635),x96634))
% 18.77/18.51 [9715]~P67(x97152)+~E(f324(x97153,f324(x97155,f628(x97151,x97153,x97155,x97156,x97154,x97152))),f2(x97152))+~P1(f324(f64(x97154),x97156))+E(f324(f324(f8(x97151,x97152),x97153),f324(f304(x97154,x97151,x97155),x97156)),f324(f324(f8(x97154,x97152),f324(f75(x97151,x97152,x97154,x97153),x97155)),x97156))
% 18.77/18.51 [9773]~P67(x97732)+~P1(f324(f64(x97734),x97736))+E(f324(f324(f8(x97731,x97732),x97733),f324(f304(x97734,x97731,x97735),x97736)),f324(f324(f8(x97734,x97732),f324(f75(x97731,x97732,x97734,x97733),x97735)),x97736))+P1(f324(f324(f326(x97734),f628(x97731,x97733,x97735,x97736,x97734,x97732)),x97736))
% 18.77/18.51 [9774]~P67(x97742)+~P1(f324(f64(x97744),x97746))+E(f324(f324(f8(x97741,x97742),x97743),f324(f304(x97744,x97741,x97745),x97746)),f324(f324(f8(x97744,x97742),f324(f75(x97741,x97742,x97744,x97743),x97745)),x97746))+P1(f324(f324(f326(x97744),f629(x97741,x97743,x97745,x97746,x97744,x97742)),x97746))
% 18.77/18.51 [9896]~P68(x98961)+~P1(f324(f64(x98962),x98966))+E(f324(f324(f324(f68(x98961,x98962,f83(x98961)),f324(f324(f20(x98962,f845(x98963,a832),x98961),f324(f324(f9(x98962,x98961,f845(f845(x98963,a832),x98961)),f324(f324(f10(f845(x98963,x98961),f845(x98961,f845(f845(x98963,a832),x98961)),x98962),f68(x98961,x98963,f83(x98961))),x98964)),f80(x98961))),x98965)),f80(x98961)),x98966),f324(f324(f324(f68(x98961,f844(x98962,x98963),f83(x98961)),f324(f252(x98962,x98963,x98961),x98964)),f80(x98961)),f324(f324(f249(x98962,x98963),x98966),x98965)))+P1(f324(f324(f326(x98962),f582(x98964,x98965,x98963,x98966,x98962,x98961)),x98966))
% 18.77/18.51 [9912]~P68(x99121)+~P1(f324(f64(x99122),x99126))+E(f324(f324(f324(f68(x99121,x99122,f83(x99121)),f324(f324(f20(x99122,f845(x99123,a832),x99121),f324(f324(f9(x99122,x99121,f845(f845(x99123,a832),x99121)),f324(f324(f10(f845(x99123,x99121),f845(x99121,f845(f845(x99123,a832),x99121)),x99122),f68(x99121,x99123,f83(x99121))),x99124)),f80(x99121))),x99125)),f80(x99121)),x99126),f324(f324(f324(f68(x99121,f844(x99122,x99123),f83(x99121)),f324(f252(x99122,x99123,x99121),x99124)),f80(x99121)),f324(f324(f249(x99122,x99123),x99126),x99125)))+~P1(f324(f64(x99123),f324(x99125,f582(x99124,x99125,x99123,x99126,x99122,x99121))))
% 18.77/18.51 [8148]~P24(x81482,x81485,x81486,x81481)+~P1(f324(f64(x81482),x81484))+~P1(f324(f64(x81482),x81483))+E(f324(x81481,f324(f324(f103(f845(x81482,a832)),x81483),x81484)),f324(f75(x81485,x81485,x81485,f324(x81481,x81483)),f324(x81481,x81484)))
% 18.77/18.51 [8368]~P9(x83681)+P1(f324(f324(f231(x83681),f324(x83682,x83683)),x83684))+~P1(f324(f324(f326(x83685),x83683),x83686))+~P1(f324(f324(f231(x83681),f324(f324(f45(x83685,x83681),x83686),x83682)),x83684))
% 18.77/18.51 [8744]~P29(x87442,x87441,x87443,x87446)+E(f324(f324(f3(f845(x87441,a832)),f324(f304(x87442,x87441,x87443),x87444)),f324(f304(x87442,x87441,x87443),x87445)),f324(f304(x87442,x87441,x87443),f324(f324(f3(f845(x87442,a832)),x87444),x87445)))+~P1(f324(f324(f231(f845(x87442,a832)),x87445),x87446))+~P1(f324(f324(f231(f845(x87442,a832)),x87444),x87446))
% 18.77/18.51 [8745]~P29(x87452,x87451,x87453,x87456)+E(f324(f324(f104(f845(x87451,a832)),f324(f304(x87452,x87451,x87453),x87454)),f324(f304(x87452,x87451,x87453),x87455)),f324(f304(x87452,x87451,x87453),f324(f324(f104(f845(x87452,a832)),x87454),x87455)))+~P1(f324(f324(f231(f845(x87452,a832)),x87455),x87456))+~P1(f324(f324(f231(f845(x87452,a832)),x87454),x87456))
% 18.77/18.51 [8981]E(x89811,x89812)+~P52(x89813,x89814,x89815)+~P1(f324(f324(f326(f844(x89813,x89814)),f324(f324(f247(x89813,x89814),x89816),x89812)),x89815))+~P1(f324(f324(f326(f844(x89813,x89814)),f324(f324(f247(x89813,x89814),x89816),x89811)),x89815))
% 18.77/18.51 [8982]E(x89821,x89822)+~P52(x89823,x89824,x89825)+~P1(f324(f324(f326(f844(x89823,x89824)),f324(f324(f247(x89823,x89824),x89826),x89822)),x89825))+~P1(f324(f324(f326(f844(x89823,x89824)),f324(f324(f247(x89823,x89824),x89826),x89821)),x89825))
% 18.77/18.51 [9711]~P4(x97111)+~E(f324(x97113,f649(x97114,x97116,x97113,x97115,x97112,x97111)),f324(x97116,f649(x97114,x97116,x97113,x97115,x97112,x97111)))+~P1(f324(f64(x97112),x97115))+E(f324(f324(f324(f68(x97111,x97112,f83(x97111)),x97113),x97114),x97115),f324(f324(f324(f68(x97111,x97112,f83(x97111)),x97116),x97114),x97115))
% 18.77/18.51 [9770]~P4(x97701)+~P1(f324(f64(x97702),x97705))+E(f324(f324(f324(f68(x97701,x97702,f83(x97701)),x97703),x97704),x97705),f324(f324(f324(f68(x97701,x97702,f83(x97701)),x97706),x97704),x97705))+P1(f324(f324(f326(x97702),f649(x97704,x97703,x97706,x97705,x97702,x97701)),x97705))
% 18.77/18.51 [8570]~P4(x85701)+~P1(f324(f64(x85702),x85706))+P1(f324(f324(f326(x85702),x85705),x85706))+E(f324(f324(f324(f68(x85701,x85702,f83(x85701)),x85703),x85704),f324(f324(f303(x85702),x85705),x85706)),f324(f324(f83(x85701),f324(x85703,x85705)),f324(f324(f324(f68(x85701,x85702,f83(x85701)),x85703),x85704),x85706)))
% 18.77/18.51 [8615]~P12(x86151,x86156,x86153)+~P16(x86151,f845(x86152,a832),x86153,x86155)+~P1(f324(f324(f326(x86151),x86154),x86156))+E(f324(f324(f45(x86151,f845(x86152,a832)),f324(f278(x86151,x86151,x86153),f324(f324(f303(x86151),x86154),f179(f845(x86151,a832))))),x86155),f324(x86155,x86154))
% 18.77/18.51 [8725]~P20(x87253,x87254,x87251)+~P1(f324(f64(x87253),x87256))+~P1(f324(f324(f326(x87253),x87252),x87256))+E(f324(f324(x87251,x87252),f324(f324(f67(x87253,x87254,x87251),x87255),f324(f324(f3(f845(x87253,a832)),x87256),f324(f324(f303(x87253),x87252),f179(f845(x87253,a832)))))),f324(f324(f67(x87253,x87254,x87251),x87255),x87256))
% 18.77/18.51 [8992]~P23(x89923,x89921,x89926,x89922)+~P1(f324(f64(x89923),x89925))+~P1(f324(f64(x89923),x89924))+E(f324(f75(x89921,x89921,x89921,f324(x89922,f324(f324(f103(f845(x89923,a832)),x89924),x89925))),f324(x89922,f324(f324(f104(f845(x89923,a832)),x89924),x89925))),f324(f75(x89921,x89921,x89921,f324(x89922,x89924)),f324(x89922,x89925)))
% 18.77/18.51 [9301]~E(x93013,f324(f324(f146(x93011,x93012),x93015),x93016))+P1(f324(f324(f326(f844(f839(x93011),f839(x93011))),f324(f324(f247(f839(x93011),f839(x93011)),x93012),x93013)),f144(x93011,x93014)))+~P1(f324(f324(f232(a838),x93015),f324(f180(f839(x93011)),x93012)))+~P1(f324(f324(f326(f844(x93011,x93011)),f324(f324(f247(x93011,x93011),f324(f324(f149(x93011),x93012),x93015)),x93016)),x93014))
% 18.77/18.51 [9790]~P68(x97902)+~P1(f324(f64(x97901),x97906))+P1(f324(f324(f326(x97901),f580(x97904,x97905,x97903,x97906,x97901,x97902)),x97906))+E(f324(f324(f11(x97901,x97902),f324(f324(f20(x97901,f845(x97903,a832),x97902),f324(f324(f10(f845(x97903,x97902),f845(f845(x97903,a832),x97902),x97901),f11(x97903,x97902)),x97904)),x97905)),x97906),f324(f324(f11(f844(x97901,x97903),x97902),f324(f252(x97901,x97903,x97902),x97904)),f324(f324(f249(x97901,x97903),x97906),x97905)))
% 18.77/18.51 [9791]~P67(x97912)+~P1(f324(f64(x97911),x97916))+P1(f324(f324(f326(x97911),f581(x97914,x97915,x97913,x97916,x97911,x97912)),x97916))+E(f324(f324(f8(x97911,x97912),f324(f324(f20(x97911,f845(x97913,a832),x97912),f324(f324(f10(f845(x97913,x97912),f845(f845(x97913,a832),x97912),x97911),f8(x97913,x97912)),x97914)),x97915)),x97916),f324(f324(f8(f844(x97911,x97913),x97912),f324(f252(x97911,x97913,x97912),x97914)),f324(f324(f249(x97911,x97913),x97916),x97915)))
% 18.77/18.51 [9830]~P68(x98302)+~P1(f324(f64(x98301),x98306))+~P1(f324(f64(x98303),f324(x98305,f580(x98304,x98305,x98303,x98306,x98301,x98302))))+E(f324(f324(f11(x98301,x98302),f324(f324(f20(x98301,f845(x98303,a832),x98302),f324(f324(f10(f845(x98303,x98302),f845(f845(x98303,a832),x98302),x98301),f11(x98303,x98302)),x98304)),x98305)),x98306),f324(f324(f11(f844(x98301,x98303),x98302),f324(f252(x98301,x98303,x98302),x98304)),f324(f324(f249(x98301,x98303),x98306),x98305)))
% 18.77/18.51 [9831]~P67(x98312)+~P1(f324(f64(x98311),x98316))+~P1(f324(f64(x98313),f324(x98315,f581(x98314,x98315,x98313,x98316,x98311,x98312))))+E(f324(f324(f8(x98311,x98312),f324(f324(f20(x98311,f845(x98313,a832),x98312),f324(f324(f10(f845(x98313,x98312),f845(f845(x98313,a832),x98312),x98311),f8(x98313,x98312)),x98314)),x98315)),x98316),f324(f324(f8(f844(x98311,x98313),x98312),f324(f252(x98311,x98313,x98312),x98314)),f324(f324(f249(x98311,x98313),x98316),x98315)))
% 18.77/18.51 [9813]~P68(x98132)+~P1(f324(f64(x98131),x98136))+P1(f324(f324(f326(x98131),x98133),x98136))+E(f324(f324(f11(x98131,x98132),f324(f324(f9(x98131,x98132,x98132),f324(f324(f20(x98131,x98132,f845(x98132,x98132)),f324(f324(f10(a832,f845(x98132,f845(x98132,x98132)),x98131),f98(x98132)),f324(f324(f9(x98131,x98131,a832),a321),x98133))),x98134)),x98135)),x98136),f324(f324(f240(x98132),x98135),f324(f41(x98131),x98136)))
% 18.77/18.51 [9818]~P68(x98182)+~P1(f324(f64(x98181),x98186))+~P1(f324(f324(f326(x98181),x98183),x98186))+E(f324(f324(f11(x98181,x98182),f324(f324(f9(x98181,x98182,x98182),f324(f324(f20(x98181,x98182,f845(x98182,x98182)),f324(f324(f10(a832,f845(x98182,f845(x98182,x98182)),x98181),f98(x98182)),f324(f324(f9(x98181,x98181,a832),a321),x98183))),x98184)),x98185)),x98186),f324(f324(f83(x98182),f324(x98184,x98183)),f324(f324(f240(x98182),x98185),f324(f324(f3(a838),f324(f41(x98181),x98186)),f80(a838)))))
% 18.77/18.51 [9884]~P1(f324(f64(x98841),x98845))+~P1(f324(f64(x98842),x98843))+P1(f324(f324(f326(x98842),f495(x98846,x98844,x98843,x98842,x98845,x98841)),x98843))+E(f324(f324(f8(x98841,a838),f324(f324(f10(f845(x98842,a832),a838,x98841),f41(x98842)),f324(f324(f10(f845(x98842,a832),f845(x98842,a832),x98841),f257(x98842)),f324(f324(f10(f845(x98842,a832),f845(x98842,a832),x98841),f324(f20(x98842,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98842),a322),f324(f324(f9(x98842,f845(x98842,a832),a832),f326(x98842)),x98843)))),x98844)))),x98845),f324(f324(f83(a838),x98846),f324(f41(x98842),x98843)))
% 18.77/18.51 [9885]~P1(f324(f64(x98851),x98855))+~P1(f324(f64(x98852),x98853))+P1(f324(f324(f326(x98852),f506(x98856,x98854,x98853,x98852,x98855,x98851)),x98853))+E(f324(f324(f8(x98851,a838),f324(f324(f10(f845(x98852,a832),a838,x98851),f41(x98852)),f324(f324(f10(f845(x98852,a832),f845(x98852,a832),x98851),f257(x98852)),f324(f324(f10(f845(x98852,a832),f845(x98852,a832),x98851),f324(f20(x98852,a832,a832),f324(f324(f10(a832,f845(a832,a832),x98852),a322),f324(f324(f9(x98852,f845(x98852,a832),a832),f326(x98852)),x98853)))),x98854)))),x98855),f324(f324(f8(x98852,a838),x98856),x98853))
% 18.77/18.51 [9918]~P1(f324(f64(x99182),x99183))+~P1(f324(f64(x99181),x99185))+~E(f324(f41(x99181),f324(f257(x99181),f324(f324(f20(x99181,a832,a832),f324(f324(f10(a832,f845(a832,a832),x99181),a322),f324(f324(f9(x99181,f845(x99181,a832),a832),f326(x99181)),x99185))),f324(f324(f9(x99181,x99182,a832),x99184),f495(x99186,x99184,x99183,x99182,x99185,x99181))))),x99186)+E(f324(f324(f8(x99181,a838),f324(f324(f10(f845(x99182,a832),a838,x99181),f41(x99182)),f324(f324(f10(f845(x99182,a832),f845(x99182,a832),x99181),f257(x99182)),f324(f324(f10(f845(x99182,a832),f845(x99182,a832),x99181),f324(f20(x99182,a832,a832),f324(f324(f10(a832,f845(a832,a832),x99182),a322),f324(f324(f9(x99182,f845(x99182,a832),a832),f326(x99182)),x99183)))),x99184)))),x99185),f324(f324(f83(a838),x99186),f324(f41(x99182),x99183)))
% 18.77/18.51 [9920]~P1(f324(f64(x99202),x99203))+~P1(f324(f64(x99201),x99205))+~E(f324(f41(x99201),f324(f257(x99201),f324(f324(f20(x99201,a832,a832),f324(f324(f10(a832,f845(a832,a832),x99201),a322),f324(f324(f9(x99201,f845(x99201,a832),a832),f326(x99201)),x99205))),f324(f324(f9(x99201,x99202,a832),x99204),f506(x99206,x99204,x99203,x99202,x99205,x99201))))),f324(x99206,f506(x99206,x99204,x99203,x99202,x99205,x99201)))+E(f324(f324(f8(x99201,a838),f324(f324(f10(f845(x99202,a832),a838,x99201),f41(x99202)),f324(f324(f10(f845(x99202,a832),f845(x99202,a832),x99201),f257(x99202)),f324(f324(f10(f845(x99202,a832),f845(x99202,a832),x99201),f324(f20(x99202,a832,a832),f324(f324(f10(a832,f845(a832,a832),x99202),a322),f324(f324(f9(x99202,f845(x99202,a832),a832),f326(x99202)),x99203)))),x99204)))),x99205),f324(f324(f8(x99202,a838),x99206),x99203))
% 18.77/18.51 [9569]E(x95691,x95692)+~P20(x95693,x95694,x95695)+~P1(f324(f69(x95693,x95694,x95695,x95696,x95697),x95692))+~P1(f324(f69(x95693,x95694,x95695,x95696,x95697),x95691))
% 18.77/18.51 [9372]P1(f324(x93721,x93722))+~P1(f324(f324(f326(x93727),x93722),f324(x93726,x93724)))+~P1(f324(x93721,f531(x93721,x93726,x93725,x93723,x93727)))+~P1(f324(f324(f326(x93723),x93724),x93725))
% 18.77/18.51 [9805]~P20(x98057,x98056,x98051)+E(f324(f324(x98051,x98052),f659(x98052,x98053,x98054,x98055,x98051,x98056,x98057)),x98053)+~P1(f324(f69(x98057,x98056,x98051,x98055,x98054),x98053))+~P1(f324(f324(f326(x98057),x98052),x98054))
% 18.77/18.51 [9869]~P20(x98691,x98692,x98693)+~P1(f324(f69(x98691,x98692,x98693,x98694,x98695),x98697))+P1(f324(f69(x98691,x98692,x98693,x98694,f324(f324(f3(f845(x98691,a832)),x98695),f324(f324(f303(x98691),x98696),f179(f845(x98691,a832))))),f659(x98696,x98697,x98695,x98694,x98693,x98692,x98691)))+~P1(f324(f324(f326(x98691),x98696),x98695))
% 18.77/18.51 [9277]~P4(x92771)+~P29(x92775,x92772,x92776,x92777)+~P1(f324(f64(x92775),x92777))+E(f324(f324(f324(f68(x92771,x92772,f83(x92771)),x92773),x92774),f324(f304(x92775,x92772,x92776),x92777)),f324(f324(f324(f68(x92771,x92775,f83(x92771)),f324(f75(x92772,x92771,x92775,x92773),x92776)),x92774),x92777))
% 18.77/18.51 [9396]~E(f324(f324(f303(x93961),x93965),x93966),f324(f324(f303(x93961),x93962),x93963))+~P1(f324(f69(x93961,x93961,x93964,x93962,x93963),x93967))+P1(f324(f324(f326(x93961),x93962),x93963))+P1(f324(f65(x93961,x93964,f324(f324(f303(x93961),x93965),x93966)),x93967))
% 18.77/18.51 [9478]P1(f324(x94781,x94782))+~P1(f324(f324(f326(x94783),x94782),f324(x94784,x94787)))+~P1(f324(f324(f326(x94786),x94787),x94785))+P1(f324(f324(f326(x94783),f531(x94781,x94784,x94785,x94786,x94783)),f324(f324(f45(x94786,f845(x94783,a832)),x94785),x94784)))
% 18.77/18.51 [9491]~P29(x94912,x94911,x94915,x94914)+~P29(x94911,x94913,x94916,f324(f304(x94912,x94911,x94915),x94914))+E(f324(f324(f75(x94911,x94912,x94913,f79(x94912,x94911,x94914,x94915)),f79(x94911,x94913,f324(f304(x94912,x94911,x94915),x94914),x94916)),x94917),f324(f79(x94912,x94913,x94914,f324(f75(x94911,x94913,x94912,x94916),x94915)),x94917))+~P1(f324(f324(f326(x94913),x94917),f324(f304(x94911,x94913,x94916),f324(f304(x94912,x94911,x94915),x94914))))
% 18.77/18.51 [9806]~P20(x98067,x98066,x98061)+E(f324(f324(x98061,x98062),f683(x98063,x98064,x98062,x98065,x98061,x98066,x98067)),x98063)+P1(f324(f324(f326(x98067),x98062),x98064))+~P1(f324(f69(x98067,x98066,x98061,x98065,f324(f324(f303(x98067),x98062),x98064)),x98063))
% 18.77/18.51 [9868]~P20(x98681,x98684,x98685)+P1(f324(f69(x98681,x98684,x98685,x98686,x98683),f683(x98687,x98683,x98682,x98686,x98685,x98684,x98681)))+P1(f324(f324(f326(x98681),x98682),x98683))+~P1(f324(f69(x98681,x98684,x98685,x98686,f324(f324(f303(x98681),x98682),x98683)),x98687))
% 18.77/18.51 [9551]E(x95511,f2(a1))+~P1(f324(f55(x95513,x95511),f324(f324(f247(a1,a1),x95515),x95517)))+~P1(f324(f55(x95512,x95511),f324(f324(f247(a1,a1),x95514),x95516)))+P1(f324(f55(f324(f324(f82(a1),x95512),x95513),x95511),f324(f324(f247(a1,a1),f324(f324(f82(a1),f324(f324(f82(a1),x95514),x95515)),f324(f324(f42(a1),f324(f324(f82(a1),x95516),x95517)),x95511))),f51(a1,f324(f324(f82(a1),x95516),x95517),x95511))))
% 18.77/18.51 [9553]~P1(f324(f324(f232(a838),f2(a838)),x95533))+~P1(f324(f54(x95532,x95533),f324(f324(f247(a838,a838),x95535),x95537)))+~P1(f324(f54(x95531,x95533),f324(f324(f247(a838,a838),x95534),x95536)))+P1(f324(f54(f324(f324(f82(a838),x95531),x95532),x95533),f324(f324(f247(a838,a838),f324(f324(f82(a838),f324(f324(f82(a838),x95534),x95535)),f324(f324(f42(a838),f324(f324(f82(a838),x95536),x95537)),x95533))),f51(a838,f324(f324(f82(a838),x95536),x95537),x95533))))
% 18.77/18.51 [9917]~P67(x99172)+~P1(f324(f64(x99173),x99175))+~P1(f324(f64(x99171),x99177))+E(f324(f324(f8(x99171,x99172),f324(f324(f20(x99171,f845(x99173,a832),x99172),f324(f324(f10(f845(x99173,x99172),f845(f845(x99173,a832),x99172),x99171),f8(x99173,x99172)),x99174)),f324(f324(f10(f845(x99173,a832),f845(x99173,a832),x99171),f257(x99173)),f324(f324(f10(f845(x99173,a832),f845(x99173,a832),x99171),f324(f20(x99173,a832,a832),f324(f324(f10(a832,f845(a832,a832),x99173),a322),f324(f324(f9(x99173,f845(x99173,a832),a832),f326(x99173)),x99175)))),x99176)))),x99177),f324(f324(f8(x99173,x99172),f324(f324(f20(x99173,f845(x99171,a832),x99172),f324(f324(f10(f845(x99171,x99172),f845(f845(x99171,a832),x99172),x99173),f8(x99171,x99172)),f324(f9(x99171,x99173,x99172),x99174))),f324(f324(f10(f845(x99171,a832),f845(x99171,a832),x99173),f257(x99171)),f324(f324(f10(f845(x99171,a832),f845(x99171,a832),x99173),f324(f20(x99171,a832,a832),f324(f324(f10(a832,f845(a832,a832),x99171),a322),f324(f324(f9(x99171,f845(x99171,a832),a832),f326(x99171)),x99177)))),f324(f9(x99171,x99173,a832),x99176))))),x99175))
% 18.77/18.51 [9434]~P26(x94347,x94346,x94341,x94348,x94342,x94344)+E(f324(f324(x94341,f324(x94342,x94343)),f324(x94344,x94345)),f324(x94344,x94345))+~P1(f324(f64(x94346),x94345))+~P1(f324(f324(f326(x94346),x94343),x94345))
% 18.77/18.51 [9438]~P17(x94386,x94381,x94382,x94388,x94383,x94384)+~P12(x94386,x94387,x94388)+P16(x94381,x94382,x94383,f324(x94384,x94385))+~P1(f324(f324(f326(x94386),x94385),x94387))
% 18.77/18.51 [7672]~P39(x76724,x76725,x76726,x76723)+~P31(x76728,x76726,f324(f324(f324(f93(x76728),x76727),x76724),x76721))+P1(f324(f324(x76721,x76722),x76723))+~P1(f324(f324(x76727,x76722),x76725))
% 18.77/18.51 [9077]~P23(x90777,x90771,x90778,x90773)+~P1(f324(f64(x90777),x90775))+~P1(f324(f64(x90777),x90774))+E(f324(f75(x90771,x90771,x90772,f324(x90773,x90774)),f324(f75(x90771,x90771,x90772,f324(x90773,x90775)),x90776)),f324(f75(x90771,x90771,x90772,f324(x90773,x90775)),f324(f75(x90771,x90771,x90772,f324(x90773,x90774)),x90776)))
% 18.77/18.51 [9148]~P29(x91482,x91482,x91485,x91486)+~P25(x91483,x91482,x91487,x91488,x91481)+~P1(f324(f64(x91482),x91486))+E(f324(f324(x91481,f324(f75(x91482,x91483,x91482,x91484),x91485)),x91486),f324(f324(x91481,x91484),f324(f304(x91482,x91482,x91485),x91486)))
% 18.77/18.51 [9436]~P27(x94367,x94362,x94365,x94368,x94366,x94361)+~P1(f324(f64(x94362),x94364))+E(f324(x94361,f324(f324(f303(x94362),x94363),x94364)),f324(f324(x94365,f324(x94366,x94363)),f324(x94361,x94364)))+P1(f324(f324(f326(x94362),x94363),x94364))
% 18.77/18.51 [9445]~P26(x94456,x94455,x94451,x94457,x94458,x94452)+E(f324(f324(x94451,f324(x94452,x94453)),f324(x94452,x94454)),f324(x94452,x94454))+~P1(f324(f64(x94455),x94454))+~P1(f324(f324(f231(f845(x94455,a832)),x94453),x94454))
% 18.77/18.51 [9064]P1(f324(f324(f326(f844(f839(x90641),f839(x90641))),f324(f324(f247(f839(x90641),f839(x90641)),x90642),x90643)),f144(x90641,x90644)))+~E(x90643,f324(f324(f125(x90641),x90645),f324(f324(f139(x90641),x90646),x90647)))+~E(x90642,f324(f324(f125(x90641),x90645),f324(f324(f139(x90641),x90648),x90647)))+~P1(f324(f324(f326(f844(x90641,x90641)),f324(f324(f247(x90641,x90641),x90648),x90646)),x90644))
% 18.77/18.51 [9439]~P26(x94396,x94392,x94395,x94397,x94398,x94391)+~P1(f324(f64(x94392),x94394))+~P1(f324(f64(x94392),x94393))+E(f324(x94391,f324(f324(f103(f845(x94392,a832)),x94393),x94394)),f324(f324(x94395,f324(x94391,x94393)),f324(x94391,x94394)))
% 18.77/18.51 [9957]~P29(x99574,x99572,x99575,x99578)+E(f324(f324(f46(x99571,f845(x99572,a832)),x99573),f324(f324(f10(f845(x99574,a832),f845(x99572,a832),x99571),f304(x99574,x99572,x99575)),x99576)),f324(f304(x99574,x99572,x99575),f324(f324(f46(x99571,f845(x99574,a832)),x99573),x99576)))+~P1(f324(f324(f326(x99571),x99577),x99573))+P1(f324(f324(f326(x99571),f674(x99577,x99576,x99573,x99571,x99578,x99575,x99572,x99574)),x99573))
% 18.77/18.51 [9978]~P29(x99784,x99782,x99785,x99787)+E(f324(f324(f46(x99781,f845(x99782,a832)),x99783),f324(f324(f10(f845(x99784,a832),f845(x99782,a832),x99781),f304(x99784,x99782,x99785)),x99786)),f324(f304(x99784,x99782,x99785),f324(f324(f46(x99781,f845(x99784,a832)),x99783),x99786)))+~P1(f324(f324(f326(x99781),x99788),x99783))+~P1(f324(f324(f231(f845(x99784,a832)),f324(x99786,f674(x99788,x99786,x99783,x99781,x99787,x99785,x99782,x99784))),x99787))
% 18.77/18.51 [9497]~P27(x94977,x94975,x94971,x94978,x94972,x94974)+~P1(f324(f64(x94975),x94976))+~P1(f324(f324(f326(x94975),x94973),x94976))+E(f324(f324(x94971,f324(x94972,x94973)),f324(x94974,f324(f324(f3(f845(x94975,a832)),x94976),f324(f324(f303(x94975),x94973),f179(f845(x94975,a832)))))),f324(x94974,x94976))
% 18.77/18.51 [9506]~P27(x95066,x95063,x95061,x95067,x95068,x95062)+~P1(f324(f64(x95063),x95065))+~P1(f324(f64(x95063),x95064))+E(f324(f324(x95061,f324(x95062,f324(f324(f103(f845(x95063,a832)),x95064),x95065))),f324(x95062,f324(f324(f104(f845(x95063,a832)),x95064),x95065))),f324(f324(x95061,f324(x95062,x95064)),f324(x95062,x95065)))
% 18.77/18.51 [9589]P41(x95891,x95892,x95893,x95894,x95895,f324(f324(x95893,x95896),x95897))+~P41(x95891,x95892,x95893,x95894,f324(f324(f3(f845(x95891,a832)),x95895),f324(f324(f303(x95891),x95898),f179(f845(x95891,a832)))),x95899)+~E(f324(f324(x95893,x95896),x95897),f324(f324(x95893,x95898),x95899))+~P1(f324(f324(f326(x95891),x95898),x95895))
% 18.77/18.51 [9989]P28(x99891,x99892,f324(f324(f303(f837(x99891)),f324(f324(f324(f93(x99891),f324(x99893,f388(x99894,x99895,x99896,x99897,x99893,x99892,x99891,x99898,x99899))),f324(x99897,f388(x99894,x99895,x99896,x99897,x99893,x99892,x99891,x99898,x99899))),f324(x99896,f388(x99894,x99895,x99896,x99897,x99893,x99892,x99891,x99898,x99899)))),f179(f845(f837(x99891),a832))))+~P1(f324(f64(x99899),x99898))+~P28(x99891,x99892,f324(f304(x99899,f837(x99891),f324(f324(f20(x99899,f845(x99891,f845(a835,a832)),f837(x99891)),f324(f324(f20(x99899,a833,f845(f845(x99891,f845(a835,a832)),f837(x99891))),f324(f324(f10(f845(x99891,f845(a835,a832)),f845(a833,f845(f845(x99891,f845(a835,a832)),f837(x99891))),x99899),f93(x99891)),x99893)),x99897)),x99896)),x99898))+P28(x99891,x99892,f324(f304(x99899,f837(x99891),f324(f324(f20(x99899,f845(x99891,f845(a835,a832)),f837(x99891)),f324(f324(f20(x99899,a833,f845(f845(x99891,f845(a835,a832)),f837(x99891))),f324(f324(f10(f845(x99891,f845(a835,a832)),f845(a833,f845(f845(x99891,f845(a835,a832)),f837(x99891))),x99899),f93(x99891)),x99895)),x99897)),x99894)),x99898))
% 18.77/18.51 [9990]~P28(x99901,x99902,f324(f324(f303(f837(x99901)),f324(f324(f324(f93(x99901),f324(x99904,f388(x99906,x99904,x99908,x99905,x99909,x99902,x99901,x99907,x99903))),f324(x99905,f388(x99906,x99904,x99908,x99905,x99909,x99902,x99901,x99907,x99903))),f324(x99906,f388(x99906,x99904,x99908,x99905,x99909,x99902,x99901,x99907,x99903)))),f179(f845(f837(x99901),a832))))+~P1(f324(f64(x99903),x99907))+~P28(x99901,x99902,f324(f304(x99903,f837(x99901),f324(f324(f20(x99903,f845(x99901,f845(a835,a832)),f837(x99901)),f324(f324(f20(x99903,a833,f845(f845(x99901,f845(a835,a832)),f837(x99901))),f324(f324(f10(f845(x99901,f845(a835,a832)),f845(a833,f845(f845(x99901,f845(a835,a832)),f837(x99901))),x99903),f93(x99901)),x99909)),x99905)),x99908)),x99907))+P28(x99901,x99902,f324(f304(x99903,f837(x99901),f324(f324(f20(x99903,f845(x99901,f845(a835,a832)),f837(x99901)),f324(f324(f20(x99903,a833,f845(f845(x99901,f845(a835,a832)),f837(x99901))),f324(f324(f10(f845(x99901,f845(a835,a832)),f845(a833,f845(f845(x99901,f845(a835,a832)),f837(x99901))),x99903),f93(x99901)),x99904)),x99905)),x99906)),x99907))
% 18.77/18.51 [9530]~P17(x95306,x95307,x95308,x95309,x953010,x95301)+E(f324(f324(x95301,x95302),x95303),f324(f324(x95301,x95304),x95305))+~P1(f324(f324(f326(f844(x95307,x95307)),f324(f324(f247(x95307,x95307),x95303),x95305)),x953010))+~P1(f324(f324(f326(f844(x95306,x95306)),f324(f324(f247(x95306,x95306),x95302),x95304)),x95309))
% 18.77/18.51 [6734]E(x67341,x67342)+~P1(f324(f324(f231(a1),f2(a1)),x67342))+~P1(f324(f324(f231(a1),f2(a1)),x67341))+~P1(f324(f324(f280(a1),x67342),x67341))+~P1(f324(f324(f280(a1),x67341),x67342))
% 18.77/18.51 [9300]E(x93001,f2(a1))+E(x93002,f2(a1))+E(f324(f324(f88(a1,f844(a1,a1)),f324(f324(a211,x93002),x93001)),f324(f324(f20(a1,a1,f844(a1,a1)),f324(f324(f10(a1,f845(a1,f844(a1,a1)),a1),f247(a1,a1)),f324(f42(a1),x93002))),f324(f42(a1),x93001))),f209(x93002,x93001))+P1(f324(f324(f232(a1),x93001),f2(a1)))+~P1(f324(f313(f844(a1,a1),a215),f324(f324(f247(a1,a1),x93002),x93001)))
% 18.77/18.51 [9150]~P94(x91502)+E(x91501,f179(f845(x91502,a832)))+~P1(f324(f64(x91502),x91501))+P1(f324(f324(f326(x91502),f12(x91502,x91501)),x91501))+~P1(f324(f324(f326(x91502),f324(f324(f104(x91502),f425(x91501,x91502)),f427(x91501,x91502))),f324(f324(f303(x91502),f425(x91501,x91502)),f324(f324(f303(x91502),f427(x91501,x91502)),f179(f845(x91502,a832))))))
% 18.77/18.51 [9151]~P86(x91512)+E(x91511,f179(f845(x91512,a832)))+~P1(f324(f64(x91512),x91511))+P1(f324(f324(f326(x91512),f16(x91512,x91511)),x91511))+~P1(f324(f324(f326(x91512),f324(f324(f178(x91512),f397(x91511,x91512)),f398(x91511,x91512))),f324(f324(f303(x91512),f397(x91511,x91512)),f324(f324(f303(x91512),f398(x91511,x91512)),f179(f845(x91512,a832))))))
% 18.77/18.51 [9152]~P86(x91522)+E(x91521,f179(f845(x91522,a832)))+~P1(f324(f64(x91522),x91521))+P1(f324(f324(f326(x91522),f17(x91522,x91521)),x91521))+~P1(f324(f324(f326(x91522),f324(f324(f235(x91522),f399(x91521,x91522)),f400(x91521,x91522))),f324(f324(f303(x91522),f399(x91521,x91522)),f324(f324(f303(x91522),f400(x91521,x91522)),f179(f845(x91522,a832))))))
% 18.77/18.51 [9153]~P94(x91532)+E(x91531,f179(f845(x91532,a832)))+~P1(f324(f64(x91532),x91531))+P1(f324(f324(f326(x91532),f15(x91532,x91531)),x91531))+~P1(f324(f324(f326(x91532),f324(f324(f103(x91532),f401(x91531,x91532)),f402(x91531,x91532))),f324(f324(f303(x91532),f401(x91531,x91532)),f324(f324(f303(x91532),f402(x91531,x91532)),f179(f845(x91532,a832))))))
% 18.77/18.51 [9181]~P4(x91812)+E(x91811,f179(f845(x91812,a832)))+~P1(f324(f64(x91812),x91811))+P1(f324(f324(f326(x91812),f324(f66(x91812,f83(x91812)),x91811)),x91811))+~P1(f324(f324(f326(x91812),f324(f324(f83(x91812),f587(x91811,x91812)),f588(x91811,x91812))),f324(f324(f303(x91812),f587(x91811,x91812)),f324(f324(f303(x91812),f588(x91811,x91812)),f179(f845(x91812,a832))))))
% 18.77/18.51 [9187]~P86(x91872)+E(x91871,f179(f845(x91872,a832)))+~P1(f324(f64(x91872),x91871))+P1(f324(f324(f326(x91872),f13(x91872,f178(x91872),x91871)),x91871))+~P1(f324(f324(f326(x91872),f324(f324(f178(x91872),f385(x91871,x91872)),f389(x91871,x91872))),f324(f324(f303(x91872),f385(x91871,x91872)),f324(f324(f303(x91872),f389(x91871,x91872)),f179(f845(x91872,a832))))))
% 18.77/18.51 [9188]~P86(x91882)+E(x91881,f179(f845(x91882,a832)))+~P1(f324(f64(x91882),x91881))+P1(f324(f324(f326(x91882),f14(x91882,f235(x91882),x91881)),x91881))+~P1(f324(f324(f326(x91882),f324(f324(f235(x91882),f390(x91881,x91882)),f391(x91881,x91882))),f324(f324(f303(x91882),f390(x91881,x91882)),f324(f324(f303(x91882),f391(x91881,x91882)),f179(f845(x91882,a832))))))
% 18.77/18.51 [6348]~P80(x63482)+E(x63481,f2(x63482))+~E(f324(f324(f82(x63482),x63483),x63481),f2(x63482))+~P1(f324(f324(f231(x63482),f2(x63482)),x63483))+~P1(f324(f324(f231(x63482),f2(x63482)),x63481))
% 18.77/18.51 [6349]~P80(x63492)+E(x63491,f2(x63492))+~E(f324(f324(f82(x63492),x63491),x63493),f2(x63492))+~P1(f324(f324(f231(x63492),f2(x63492)),x63493))+~P1(f324(f324(f231(x63492),f2(x63492)),x63491))
% 18.77/18.51 [6551]~P1(f324(f324(f280(a838),x65512),x65511))+~P1(f324(f324(f280(a838),x65511),x65513))+P1(f324(f324(f280(a838),x65512),x65513))+P1(f324(f324(f280(a838),x65511),x65512))+P1(f324(f324(f280(a838),x65513),x65511))
% 18.77/18.51 [6733]~P1(f324(f324(f280(a838),x67331),x67333))+~P1(f324(f324(f280(a838),x67333),x67332))+~P1(f324(f324(f280(a838),x67332),x67331))+P1(f324(f324(f280(a838),x67331),x67332))+P1(f324(f324(f280(a838),x67333),x67331))
% 18.77/18.51 [7070]~P86(x70701)+E(f17(x70701,x70702),x70703)+~P1(f324(f64(x70701),x70702))+~P1(f324(f324(f231(x70701),x70703),f655(x70703,x70702,x70701)))+~P1(f324(f324(f326(x70701),x70703),x70702))
% 18.77/18.51 [7106]~P86(x71061)+~P18(x71061,x71062)+~P18(x71061,x71063)+P18(x71061,f324(f324(f125(x71061),x71062),x71063))+P1(f324(f324(f326(x71061),f752(x71063,x71062,x71061)),f324(f157(x71061),x71062)))
% 18.77/18.51 [7107]~P86(x71071)+~P18(x71071,x71072)+~P18(x71071,x71073)+P18(x71071,f324(f324(f125(x71071),x71072),x71073))+P1(f324(f324(f326(x71071),f754(x71073,x71072,x71071)),f324(f157(x71071),x71073)))
% 18.77/18.51 [7171]~P86(x71711)+E(f16(x71711,x71712),x71713)+~P1(f324(f64(x71711),x71712))+P1(f324(f324(f326(x71711),f646(x71713,x71712,x71711)),x71712))+~P1(f324(f324(f326(x71711),x71713),x71712))
% 18.77/18.51 [7172]~P86(x71721)+E(f17(x71721,x71722),x71723)+~P1(f324(f64(x71721),x71722))+P1(f324(f324(f326(x71721),f655(x71723,x71722,x71721)),x71722))+~P1(f324(f324(f326(x71721),x71723),x71722))
% 18.77/18.51 [7777]~P86(x77771)+E(f16(x77771,x77772),x77773)+~P1(f324(f64(x77771),x77772))+~P1(f324(f324(f326(x77771),x77773),x77772))+~P1(f324(f324(f231(x77771),f646(x77773,x77772,x77771)),x77773))
% 18.77/18.51 [8097]~P86(x80971)+~P18(x80971,x80972)+~P18(x80971,x80973)+P18(x80971,f324(f324(f125(x80971),x80972),x80973))+~P1(f324(f324(f231(x80971),f752(x80973,x80972,x80971)),f754(x80973,x80972,x80971)))
% 18.77/18.51 [8830]~P94(x88302)+E(x88301,f179(f845(x88302,a832)))+~E(f324(f324(f104(x88302),f324(x88303,f432(x88301,x88303,x88302))),f324(x88303,f434(x88301,x88303,x88302))),f324(x88303,f324(f324(f104(x88302),f432(x88301,x88303,x88302)),f434(x88301,x88303,x88302))))+E(f12(x88302,f324(f304(x88302,x88302,x88303),x88301)),f324(x88303,f12(x88302,x88301)))+~P1(f324(f64(x88302),x88301))
% 18.77/18.51 [8831]~P86(x88312)+E(x88311,f179(f845(x88312,a832)))+~E(f324(f324(f178(x88312),f324(x88313,f409(x88311,x88313,x88312))),f324(x88313,f414(x88311,x88313,x88312))),f324(x88313,f324(f324(f178(x88312),f409(x88311,x88313,x88312)),f414(x88311,x88313,x88312))))+E(f16(x88312,f324(f304(x88312,x88312,x88313),x88311)),f324(x88313,f16(x88312,x88311)))+~P1(f324(f64(x88312),x88311))
% 18.77/18.51 [8832]~P86(x88322)+E(x88321,f179(f845(x88322,a832)))+~E(f324(f324(f235(x88322),f324(x88323,f415(x88321,x88323,x88322))),f324(x88323,f416(x88321,x88323,x88322))),f324(x88323,f324(f324(f235(x88322),f415(x88321,x88323,x88322)),f416(x88321,x88323,x88322))))+E(f17(x88322,f324(f304(x88322,x88322,x88323),x88321)),f324(x88323,f17(x88322,x88321)))+~P1(f324(f64(x88322),x88321))
% 18.77/18.51 [8833]~P94(x88332)+E(x88331,f179(f845(x88332,a832)))+~E(f324(f324(f103(x88332),f324(x88333,f417(x88331,x88333,x88332))),f324(x88333,f418(x88331,x88333,x88332))),f324(x88333,f324(f324(f103(x88332),f417(x88331,x88333,x88332)),f418(x88331,x88333,x88332))))+E(f15(x88332,f324(f304(x88332,x88332,x88333),x88331)),f324(x88333,f15(x88332,x88331)))+~P1(f324(f64(x88332),x88331))
% 18.77/18.51 [8896]~P86(x88962)+E(x88961,f179(f845(x88962,a832)))+~E(f324(f324(f178(x88962),f324(x88963,f410(x88961,x88963,x88962))),f324(x88963,f411(x88961,x88963,x88962))),f324(x88963,f324(f324(f178(x88962),f410(x88961,x88963,x88962)),f411(x88961,x88963,x88962))))+E(f13(x88962,f178(x88962),f324(f304(x88962,x88962,x88963),x88961)),f324(x88963,f13(x88962,f178(x88962),x88961)))+~P1(f324(f64(x88962),x88961))
% 18.77/18.51 [8897]~P86(x88972)+E(x88971,f179(f845(x88972,a832)))+~E(f324(f324(f235(x88972),f324(x88973,f412(x88971,x88973,x88972))),f324(x88973,f413(x88971,x88973,x88972))),f324(x88973,f324(f324(f235(x88972),f412(x88971,x88973,x88972)),f413(x88971,x88973,x88972))))+E(f14(x88972,f235(x88972),f324(f304(x88972,x88972,x88973),x88971)),f324(x88973,f14(x88972,f235(x88972),x88971)))+~P1(f324(f64(x88972),x88971))
% 18.77/18.51 [5965]~P94(x59652)+E(x59651,f179(f845(x59652,a832)))+~P1(f324(f64(x59652),x59651))+E(f12(x59652,f324(f324(f303(x59652),x59653),x59651)),f324(f324(f104(x59652),x59653),f12(x59652,x59651)))+P1(f324(f324(f326(x59652),x59653),x59651))
% 18.77/18.51 [5966]~P86(x59662)+E(x59661,f179(f845(x59662,a832)))+~P1(f324(f64(x59662),x59661))+E(f16(x59662,f324(f324(f303(x59662),x59663),x59661)),f324(f324(f178(x59662),x59663),f16(x59662,x59661)))+P1(f324(f324(f326(x59662),x59663),x59661))
% 18.77/18.51 [5967]~P86(x59672)+E(x59671,f179(f845(x59672,a832)))+~P1(f324(f64(x59672),x59671))+E(f17(x59672,f324(f324(f303(x59672),x59673),x59671)),f324(f324(f235(x59672),x59673),f17(x59672,x59671)))+P1(f324(f324(f326(x59672),x59673),x59671))
% 18.77/18.51 [5968]~P94(x59682)+E(x59681,f179(f845(x59682,a832)))+~P1(f324(f64(x59682),x59681))+E(f15(x59682,f324(f324(f303(x59682),x59683),x59681)),f324(f324(f103(x59682),x59683),f15(x59682,x59681)))+P1(f324(f324(f326(x59682),x59683),x59681))
% 18.77/18.51 [6365]~P4(x63652)+E(x63651,f179(f845(x63652,a832)))+~P1(f324(f64(x63652),x63651))+E(f324(f66(x63652,f83(x63652)),f324(f324(f303(x63652),x63653),x63651)),f324(f324(f83(x63652),x63653),f324(f66(x63652,f83(x63652)),x63651)))+P1(f324(f324(f326(x63652),x63653),x63651))
% 18.77/18.51 [6454]~P86(x64542)+E(x64541,f179(f845(x64542,a832)))+~P1(f324(f64(x64542),x64541))+E(f13(x64542,f178(x64542),f324(f324(f303(x64542),x64543),x64541)),f324(f324(f178(x64542),x64543),f13(x64542,f178(x64542),x64541)))+P1(f324(f324(f326(x64542),x64543),x64541))
% 18.77/18.51 [6455]~P86(x64552)+E(x64551,f179(f845(x64552,a832)))+~P1(f324(f64(x64552),x64551))+E(f14(x64552,f235(x64552),f324(f324(f303(x64552),x64553),x64551)),f324(f324(f235(x64552),x64553),f14(x64552,f235(x64552),x64551)))+P1(f324(f324(f326(x64552),x64553),x64551))
% 18.77/18.51 [6908]~P86(x69082)+E(f324(f324(f235(x69082),f17(x69082,x69081)),f17(x69082,x69083)),f17(x69082,x69083))+E(x69081,f179(f845(x69082,a832)))+~P1(f324(f64(x69082),x69083))+~P1(f324(f324(f231(f845(x69082,a832)),x69081),x69083))
% 18.77/18.51 [6909]~P86(x69092)+E(f324(f324(f178(x69092),f16(x69092,x69091)),f16(x69092,x69093)),f16(x69092,x69093))+E(x69091,f179(f845(x69092,a832)))+~P1(f324(f64(x69092),x69093))+~P1(f324(f324(f231(f845(x69092,a832)),x69091),x69093))
% 18.77/18.51 [6910]~P94(x69102)+E(f324(f324(f103(x69102),f15(x69102,x69101)),f15(x69102,x69103)),f15(x69102,x69103))+E(x69101,f179(f845(x69102,a832)))+~P1(f324(f64(x69102),x69103))+~P1(f324(f324(f231(f845(x69102,a832)),x69101),x69103))
% 18.77/18.51 [6911]~P94(x69112)+E(f324(f324(f104(x69112),f12(x69112,x69111)),f12(x69112,x69113)),f12(x69112,x69113))+E(x69111,f179(f845(x69112,a832)))+~P1(f324(f64(x69112),x69113))+~P1(f324(f324(f231(f845(x69112,a832)),x69111),x69113))
% 18.77/18.51 [7227]~P86(x72272)+E(x72271,f179(f845(x72272,a832)))+~P1(f324(f64(x72272),x72273))+P1(f324(f324(f231(x72272),f16(x72272,x72271)),f16(x72272,x72273)))+~P1(f324(f324(f231(f845(x72272,a832)),x72271),x72273))
% 18.77/18.51 [7228]~P86(x72282)+E(x72281,f179(f845(x72282,a832)))+~P1(f324(f64(x72282),x72283))+P1(f324(f324(f231(x72282),f17(x72282,x72283)),f17(x72282,x72281)))+~P1(f324(f324(f231(f845(x72282,a832)),x72281),x72283))
% 18.77/18.51 [7290]~P94(x72901)+E(f12(x72901,x72902),x72903)+~P1(f324(f64(x72901),x72902))+~E(f324(f324(f3(f845(x72901,a832)),x72902),f324(f324(f303(x72901),x72903),f179(f845(x72901,a832)))),f179(f845(x72901,a832)))+~P1(f324(f324(f326(x72901),x72903),x72902))
% 18.77/18.51 [7291]~P86(x72911)+E(f16(x72911,x72912),x72913)+~P1(f324(f64(x72911),x72912))+~E(f324(f324(f3(f845(x72911,a832)),x72912),f324(f324(f303(x72911),x72913),f179(f845(x72911,a832)))),f179(f845(x72911,a832)))+~P1(f324(f324(f326(x72911),x72913),x72912))
% 18.77/18.51 [7292]~P86(x72921)+E(f17(x72921,x72922),x72923)+~P1(f324(f64(x72921),x72922))+~E(f324(f324(f3(f845(x72921,a832)),x72922),f324(f324(f303(x72921),x72923),f179(f845(x72921,a832)))),f179(f845(x72921,a832)))+~P1(f324(f324(f326(x72921),x72923),x72922))
% 18.77/18.51 [7293]~P94(x72931)+E(f15(x72931,x72932),x72933)+~P1(f324(f64(x72931),x72932))+~E(f324(f324(f3(f845(x72931,a832)),x72932),f324(f324(f303(x72931),x72933),f179(f845(x72931,a832)))),f179(f845(x72931,a832)))+~P1(f324(f324(f326(x72931),x72933),x72932))
% 18.77/18.51 [7396]~P86(x73961)+E(f13(x73961,f178(x73961),x73962),x73963)+~P1(f324(f64(x73961),x73962))+~E(f324(f324(f3(f845(x73961,a832)),x73962),f324(f324(f303(x73961),x73963),f179(f845(x73961,a832)))),f179(f845(x73961,a832)))+~P1(f324(f324(f326(x73961),x73963),x73962))
% 18.77/18.51 [7397]~P86(x73971)+E(f14(x73971,f235(x73971),x73972),x73973)+~P1(f324(f64(x73971),x73972))+~E(f324(f324(f3(f845(x73971,a832)),x73972),f324(f324(f303(x73971),x73973),f179(f845(x73971,a832)))),f179(f845(x73971,a832)))+~P1(f324(f324(f326(x73971),x73973),x73972))
% 18.77/18.51 [7434]~P86(x74342)+E(x74341,f179(f845(x74342,a832)))+~P1(f324(f64(x74342),x74341))+~P1(f324(f324(f232(x74342),x74343),f573(x74343,x74341,x74342)))+P1(f324(f324(f232(x74342),x74343),f324(f66(x74342,f235(x74342)),x74341)))
% 18.77/18.51 [7435]~P86(x74352)+E(x74351,f179(f845(x74352,a832)))+~P1(f324(f64(x74352),x74351))+~P1(f324(f324(f231(x74352),x74353),f574(x74353,x74351,x74352)))+P1(f324(f324(f231(x74352),x74353),f324(f66(x74352,f235(x74352)),x74351)))
% 18.77/18.51 [7436]~P99(x74362)+E(x74361,f179(f845(x74362,a832)))+~P1(f324(f64(x74362),x74361))+~P1(f324(f324(f231(x74362),x74363),f575(x74363,x74361,x74362)))+P1(f324(f324(f231(x74362),x74363),f324(f66(x74362,f104(x74362)),x74361)))
% 18.77/18.51 [7524]~P99(x75242)+E(x75241,f179(f845(x75242,a832)))+~P1(f324(f64(x75242),x75241))+P1(f324(f324(f326(x75242),f575(x75243,x75241,x75242)),x75241))+P1(f324(f324(f231(x75242),x75243),f324(f66(x75242,f104(x75242)),x75241)))
% 18.77/18.51 [7525]~P86(x75252)+E(x75251,f179(f845(x75252,a832)))+~P1(f324(f64(x75252),x75251))+P1(f324(f324(f326(x75252),f574(x75253,x75251,x75252)),x75251))+P1(f324(f324(f231(x75252),x75253),f324(f66(x75252,f235(x75252)),x75251)))
% 18.77/18.51 [7526]~P86(x75262)+E(x75261,f179(f845(x75262,a832)))+~P1(f324(f64(x75262),x75261))+P1(f324(f324(f326(x75262),f573(x75263,x75261,x75262)),x75261))+P1(f324(f324(f232(x75262),x75263),f324(f66(x75262,f235(x75262)),x75261)))
% 18.77/18.51 [7647]~P86(x76472)+E(x76471,f179(f845(x76472,a832)))+E(f324(f324(f235(x76472),f14(x76472,f235(x76472),x76471)),f14(x76472,f235(x76472),x76473)),f14(x76472,f235(x76472),x76473))+~P1(f324(f64(x76472),x76473))+~P1(f324(f324(f231(f845(x76472,a832)),x76471),x76473))
% 18.77/18.51 [7648]~P86(x76482)+E(x76481,f179(f845(x76482,a832)))+E(f324(f324(f178(x76482),f13(x76482,f178(x76482),x76481)),f13(x76482,f178(x76482),x76483)),f13(x76482,f178(x76482),x76483))+~P1(f324(f64(x76482),x76483))+~P1(f324(f324(f231(f845(x76482,a832)),x76481),x76483))
% 18.77/18.51 [7852]~E(f671(x78521,x78523,x78522),f672(x78521,x78523,x78522))+~E(f324(f41(x78522),f673(x78521,x78523,x78522)),x78521)+E(f324(f324(f83(a838),x78521),f324(f41(f845(x78522,a832)),x78523)),f324(f41(x78522),f43(f845(x78522,a832),x78523)))+~P1(f324(f64(x78522),f43(f845(x78522,a832),x78523)))+~P1(f324(f64(f845(x78522,a832)),x78523))
% 18.77/18.51 [8033]~P86(x80332)+E(x80331,f179(f845(x80332,a832)))+~P1(f324(f64(x80332),x80333))+P1(f324(f324(f231(x80332),f324(f66(x80332,f235(x80332)),x80333)),f324(f66(x80332,f235(x80332)),x80331)))+~P1(f324(f324(f231(f845(x80332,a832)),x80331),x80333))
% 18.77/18.51 [8338]~E(f671(x83381,x83383,x83382),f672(x83381,x83383,x83382))+E(f324(f324(f83(a838),x83381),f324(f41(f845(x83382,a832)),x83383)),f324(f41(x83382),f43(f845(x83382,a832),x83383)))+P1(f324(f324(f326(f845(x83382,a832)),f673(x83381,x83383,x83382)),x83383))+~P1(f324(f64(x83382),f43(f845(x83382,a832),x83383)))+~P1(f324(f64(f845(x83382,a832)),x83383))
% 18.77/18.51 [8363]~E(f324(f41(x83632),f673(x83631,x83633,x83632)),x83631)+E(f324(f324(f83(a838),x83631),f324(f41(f845(x83632,a832)),x83633)),f324(f41(x83632),f43(f845(x83632,a832),x83633)))+P1(f324(f324(f326(f845(x83632,a832)),f672(x83631,x83633,x83632)),x83633))+~P1(f324(f64(x83632),f43(f845(x83632,a832),x83633)))+~P1(f324(f64(f845(x83632,a832)),x83633))
% 18.77/18.51 [8364]~E(f324(f41(x83642),f673(x83641,x83643,x83642)),x83641)+E(f324(f324(f83(a838),x83641),f324(f41(f845(x83642,a832)),x83643)),f324(f41(x83642),f43(f845(x83642,a832),x83643)))+P1(f324(f324(f326(f845(x83642,a832)),f671(x83641,x83643,x83642)),x83643))+~P1(f324(f64(x83642),f43(f845(x83642,a832),x83643)))+~P1(f324(f64(f845(x83642,a832)),x83643))
% 18.77/18.51 [8394]~E(f324(f41(x83942),f673(x83941,x83943,x83942)),x83941)+~E(f324(f324(f104(f845(x83942,a832)),f672(x83941,x83943,x83942)),f671(x83941,x83943,x83942)),f179(f845(x83942,a832)))+E(f324(f324(f83(a838),x83941),f324(f41(f845(x83942,a832)),x83943)),f324(f41(x83942),f43(f845(x83942,a832),x83943)))+~P1(f324(f64(f845(x83942,a832)),x83943))+~P1(f324(f64(x83942),f43(f845(x83942,a832),x83943)))
% 18.77/18.51 [8620]E(f324(f324(f83(a838),x86201),f324(f41(f845(x86202,a832)),x86203)),f324(f41(x86202),f43(f845(x86202,a832),x86203)))+P1(f324(f324(f326(f845(x86202,a832)),f673(x86201,x86203,x86202)),x86203))+P1(f324(f324(f326(f845(x86202,a832)),f672(x86201,x86203,x86202)),x86203))+~P1(f324(f64(f845(x86202,a832)),x86203))+~P1(f324(f64(x86202),f43(f845(x86202,a832),x86203)))
% 18.77/18.51 [8621]E(f324(f324(f83(a838),x86211),f324(f41(f845(x86212,a832)),x86213)),f324(f41(x86212),f43(f845(x86212,a832),x86213)))+P1(f324(f324(f326(f845(x86212,a832)),f673(x86211,x86213,x86212)),x86213))+P1(f324(f324(f326(f845(x86212,a832)),f671(x86211,x86213,x86212)),x86213))+~P1(f324(f64(f845(x86212,a832)),x86213))+~P1(f324(f64(x86212),f43(f845(x86212,a832),x86213)))
% 18.77/18.51 [8646]~E(f324(f324(f104(f845(x86462,a832)),f672(x86461,x86463,x86462)),f671(x86461,x86463,x86462)),f179(f845(x86462,a832)))+E(f324(f324(f83(a838),x86461),f324(f41(f845(x86462,a832)),x86463)),f324(f41(x86462),f43(f845(x86462,a832),x86463)))+~P1(f324(f64(f845(x86462,a832)),x86463))+P1(f324(f324(f326(f845(x86462,a832)),f673(x86461,x86463,x86462)),x86463))+~P1(f324(f64(x86462),f43(f845(x86462,a832),x86463)))
% 18.77/18.51 [8875]~P92(x88752)+E(x88751,f179(f845(x88752,a832)))+~E(f324(f324(f83(x88752),f324(x88753,f589(x88751,x88753,x88752))),f324(x88753,f590(x88751,x88753,x88752))),f324(x88753,f324(f324(f83(x88752),f589(x88751,x88753,x88752)),f590(x88751,x88753,x88752))))+~P1(f324(f64(x88752),x88751))+E(f324(f66(x88752,f83(x88752)),f324(f304(x88752,x88752,x88753),x88751)),f324(x88753,f324(f66(x88752,f83(x88752)),x88751)))
% 18.77/18.51 [9746]P1(f324(f324(x97461,x97462),x97463))+P1(f324(f324(f232(a1),f802(x97461,x97463,x97462)),f803(x97461,x97463,x97462)))+P1(f324(f324(f231(a1),f803(x97461,x97463,x97462)),f2(a1)))+P1(f324(f324(x97461,f802(x97461,x97463,x97462)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f803(x97461,x97463,x97462))))+~P1(f324(f313(f844(a1,a1),a62),f324(f324(f247(a1,a1),x97462),x97463)))
% 18.77/18.51 [9752]P1(f324(f324(x97521,x97522),x97523))+P1(f324(f324(f231(a1),f801(x97521,x97523,x97522)),f2(a1)))+P1(f324(f324(x97521,f800(x97521,x97523,x97522)),f324(f324(f83(a1),f324(f106(a1),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f801(x97521,x97523,x97522))))+P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f800(x97521,x97523,x97522)),f801(x97521,x97523,x97522))))+~P1(f324(f313(f844(a1,a1),a58),f324(f324(f247(a1,a1),x97522),x97523)))
% 18.77/18.51 [7822]~P103(x78221)+~P1(f324(f324(f231(x78221),x78222),f80(x78221)))+~P1(f324(f324(f231(x78221),f2(x78221)),x78222))+~P1(f324(f324(f231(x78221),f2(x78221)),x78223))+P1(f324(f324(f231(x78221),f324(f324(f83(x78221),x78222),x78223)),x78223))
% 18.77/18.51 [7823]~P103(x78231)+~P1(f324(f324(f231(x78231),x78233),f80(x78231)))+~P1(f324(f324(f231(x78231),f2(x78231)),x78233))+~P1(f324(f324(f231(x78231),f2(x78231)),x78232))+P1(f324(f324(f231(x78231),f324(f324(f83(x78231),x78232),x78233)),x78232))
% 18.77/18.51 [8180]~P86(x81802)+E(x81801,f179(f845(x81802,a832)))+~P1(f324(f64(x81802),x81801))+P1(f324(f324(f326(x81802),f577(x81803,x81801,x81802)),x81801))+~P1(f324(f324(f231(x81802),f324(f66(x81802,f235(x81802)),x81801)),x81803))
% 18.77/18.51 [8181]~P86(x81812)+E(x81811,f179(f845(x81812,a832)))+~P1(f324(f64(x81812),x81811))+P1(f324(f324(f326(x81812),f578(x81813,x81811,x81812)),x81811))+~P1(f324(f324(f232(x81812),f324(f66(x81812,f235(x81812)),x81811)),x81813))
% 18.77/18.51 [8182]~P86(x81822)+E(x81821,f179(f845(x81822,a832)))+~P1(f324(f64(x81822),x81821))+P1(f324(f324(f232(x81822),f578(x81823,x81821,x81822)),x81823))+~P1(f324(f324(f232(x81822),f324(f66(x81822,f235(x81822)),x81821)),x81823))
% 18.77/18.51 [8183]~P86(x81832)+E(x81831,f179(f845(x81832,a832)))+~P1(f324(f64(x81832),x81831))+P1(f324(f324(f231(x81832),f577(x81833,x81831,x81832)),x81833))+~P1(f324(f324(f231(x81832),f324(f66(x81832,f235(x81832)),x81831)),x81833))
% 18.77/18.51 [8268]~P1(f324(x82681,x82683))+P1(f324(x82681,f468(x82681,x82682)))+P1(f324(x82681,f465(x82681,x82682)))+~P1(f324(f324(f232(a1),f2(a1)),x82682))+P1(f324(x82681,f324(f324(f3(a1),f465(x82681,x82682)),f324(f324(f83(a1),f469(x82681,x82682)),x82682))))
% 18.77/18.51 [8483]~P1(f324(x84831,x84833))+P1(f324(x84831,f465(x84831,x84832)))+~P1(f324(f324(f232(a1),f2(a1)),x84832))+P1(f324(f324(f326(a1),f468(x84831,x84832)),f296(a1,f80(a1),x84832)))+P1(f324(x84831,f324(f324(f3(a1),f465(x84831,x84832)),f324(f324(f83(a1),f469(x84831,x84832)),x84832))))
% 18.77/18.51 [8665]~P1(f324(x86651,x86653))+~P1(f324(x86651,f465(x86651,x86652)))+P1(f324(x86651,f468(x86651,x86652)))+~P1(f324(f324(f232(a1),f2(a1)),x86652))+~P1(f324(x86651,f324(f324(f3(a1),f465(x86651,x86652)),f324(f324(f83(a1),f469(x86651,x86652)),x86652))))
% 18.77/18.51 [8770]~P1(f324(x87701,x87703))+~P1(f324(x87701,f465(x87701,x87702)))+~P1(f324(f324(f232(a1),f2(a1)),x87702))+P1(f324(f324(f326(a1),f468(x87701,x87702)),f296(a1,f80(a1),x87702)))+~P1(f324(x87701,f324(f324(f3(a1),f465(x87701,x87702)),f324(f324(f83(a1),f469(x87701,x87702)),x87702))))
% 18.77/18.51 [8581]~P94(x85811)+~P1(f324(f64(x85811),x85812))+E(f324(f324(f3(f845(x85811,a832)),x85812),f324(f324(f303(x85811),x85813),f179(f845(x85811,a832)))),f179(f845(x85811,a832)))+~P1(f324(f324(f326(x85811),x85813),x85812))+E(f324(f324(f104(x85811),x85813),f12(x85811,f324(f324(f3(f845(x85811,a832)),x85812),f324(f324(f303(x85811),x85813),f179(f845(x85811,a832)))))),f12(x85811,x85812))
% 18.77/18.51 [8582]~P86(x85821)+~P1(f324(f64(x85821),x85822))+E(f324(f324(f3(f845(x85821,a832)),x85822),f324(f324(f303(x85821),x85823),f179(f845(x85821,a832)))),f179(f845(x85821,a832)))+~P1(f324(f324(f326(x85821),x85823),x85822))+E(f324(f324(f178(x85821),x85823),f16(x85821,f324(f324(f3(f845(x85821,a832)),x85822),f324(f324(f303(x85821),x85823),f179(f845(x85821,a832)))))),f16(x85821,x85822))
% 18.77/18.51 [8583]~P86(x85831)+~P1(f324(f64(x85831),x85832))+E(f324(f324(f3(f845(x85831,a832)),x85832),f324(f324(f303(x85831),x85833),f179(f845(x85831,a832)))),f179(f845(x85831,a832)))+~P1(f324(f324(f326(x85831),x85833),x85832))+E(f324(f324(f235(x85831),x85833),f17(x85831,f324(f324(f3(f845(x85831,a832)),x85832),f324(f324(f303(x85831),x85833),f179(f845(x85831,a832)))))),f17(x85831,x85832))
% 18.77/18.51 [8584]~P94(x85841)+~P1(f324(f64(x85841),x85842))+E(f324(f324(f3(f845(x85841,a832)),x85842),f324(f324(f303(x85841),x85843),f179(f845(x85841,a832)))),f179(f845(x85841,a832)))+~P1(f324(f324(f326(x85841),x85843),x85842))+E(f324(f324(f103(x85841),x85843),f15(x85841,f324(f324(f3(f845(x85841,a832)),x85842),f324(f324(f303(x85841),x85843),f179(f845(x85841,a832)))))),f15(x85841,x85842))
% 18.77/18.51 [8641]~P86(x86411)+~P1(f324(f64(x86411),x86412))+E(f324(f324(f3(f845(x86411,a832)),x86412),f324(f324(f303(x86411),x86413),f179(f845(x86411,a832)))),f179(f845(x86411,a832)))+~P1(f324(f324(f326(x86411),x86413),x86412))+E(f324(f324(f178(x86411),x86413),f13(x86411,f178(x86411),f324(f324(f3(f845(x86411,a832)),x86412),f324(f324(f303(x86411),x86413),f179(f845(x86411,a832)))))),f13(x86411,f178(x86411),x86412))
% 18.77/18.51 [8642]~P86(x86421)+~P1(f324(f64(x86421),x86422))+E(f324(f324(f3(f845(x86421,a832)),x86422),f324(f324(f303(x86421),x86423),f179(f845(x86421,a832)))),f179(f845(x86421,a832)))+~P1(f324(f324(f326(x86421),x86423),x86422))+E(f324(f324(f235(x86421),x86423),f14(x86421,f235(x86421),f324(f324(f3(f845(x86421,a832)),x86422),f324(f324(f303(x86421),x86423),f179(f845(x86421,a832)))))),f14(x86421,f235(x86421),x86422))
% 18.77/18.51 [8653]~P86(x86531)+~P1(f324(f64(x86531),x86533))+~P1(f324(f64(x86531),x86532))+E(f324(f324(f104(f845(x86531,a832)),x86532),x86533),f179(f845(x86531,a832)))+E(f324(f324(f235(x86531),f17(x86531,f324(f324(f103(f845(x86531,a832)),x86532),x86533))),f17(x86531,f324(f324(f104(f845(x86531,a832)),x86532),x86533))),f324(f324(f235(x86531),f17(x86531,x86532)),f17(x86531,x86533)))
% 18.77/18.51 [8654]~P86(x86541)+~P1(f324(f64(x86541),x86543))+~P1(f324(f64(x86541),x86542))+E(f324(f324(f104(f845(x86541,a832)),x86542),x86543),f179(f845(x86541,a832)))+E(f324(f324(f178(x86541),f16(x86541,f324(f324(f103(f845(x86541,a832)),x86542),x86543))),f16(x86541,f324(f324(f104(f845(x86541,a832)),x86542),x86543))),f324(f324(f178(x86541),f16(x86541,x86542)),f16(x86541,x86543)))
% 18.77/18.51 [8655]~P94(x86551)+~P1(f324(f64(x86551),x86553))+~P1(f324(f64(x86551),x86552))+E(f324(f324(f104(f845(x86551,a832)),x86552),x86553),f179(f845(x86551,a832)))+E(f324(f324(f103(x86551),f15(x86551,f324(f324(f103(f845(x86551,a832)),x86552),x86553))),f15(x86551,f324(f324(f104(f845(x86551,a832)),x86552),x86553))),f324(f324(f103(x86551),f15(x86551,x86552)),f15(x86551,x86553)))
% 18.77/18.51 [8656]~P94(x86561)+~P1(f324(f64(x86561),x86563))+~P1(f324(f64(x86561),x86562))+E(f324(f324(f104(f845(x86561,a832)),x86562),x86563),f179(f845(x86561,a832)))+E(f324(f324(f104(x86561),f12(x86561,f324(f324(f103(f845(x86561,a832)),x86562),x86563))),f12(x86561,f324(f324(f104(f845(x86561,a832)),x86562),x86563))),f324(f324(f104(x86561),f12(x86561,x86562)),f12(x86561,x86563)))
% 18.77/18.51 [8849]~P86(x88491)+~P1(f324(f64(x88491),x88493))+~P1(f324(f64(x88491),x88492))+E(f324(f324(f104(f845(x88491,a832)),x88492),x88493),f179(f845(x88491,a832)))+E(f324(f324(f235(x88491),f14(x88491,f235(x88491),f324(f324(f103(f845(x88491,a832)),x88492),x88493))),f14(x88491,f235(x88491),f324(f324(f104(f845(x88491,a832)),x88492),x88493))),f324(f324(f235(x88491),f14(x88491,f235(x88491),x88492)),f14(x88491,f235(x88491),x88493)))
% 18.77/18.51 [8850]~P86(x88501)+~P1(f324(f64(x88501),x88503))+~P1(f324(f64(x88501),x88502))+E(f324(f324(f104(f845(x88501,a832)),x88502),x88503),f179(f845(x88501,a832)))+E(f324(f324(f178(x88501),f13(x88501,f178(x88501),f324(f324(f103(f845(x88501,a832)),x88502),x88503))),f13(x88501,f178(x88501),f324(f324(f104(f845(x88501,a832)),x88502),x88503))),f324(f324(f178(x88501),f13(x88501,f178(x88501),x88502)),f13(x88501,f178(x88501),x88503)))
% 18.77/18.51 [9586]~P84(x95863)+E(x95861,x95862)+~P1(f324(f324(f231(x95863),f2(x95863)),x95862))+~P1(f324(f324(f231(x95863),f2(x95863)),x95861))+~E(f324(f324(f240(x95863),x95861),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))),f324(f324(f240(x95863),x95862),f324(f106(a838),f324(f324(f82(a1),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)),f324(f324(f3(a1),f324(f324(f82(a1),a85),a85)),a99)))))
% 18.77/18.51 [4905]~P90(x49051)+~P59(x49051)+~E(x49054,f2(x49051))+~E(f324(f106(x49051),x49052),f2(x49051))+E(f324(f106(x49051),x49052),f324(f324(f284(x49051),x49053),x49054))
% 18.77/18.51 [4906]~P90(x49061)+~P59(x49061)+~E(x49063,f2(x49061))+~E(f324(f106(x49061),x49064),f2(x49061))+E(f324(f324(f284(x49061),x49062),x49063),f324(f106(x49061),x49064))
% 18.77/18.51 [5001]~P90(x50012)+~P59(x50012)+~E(x50011,f2(x50012))+~E(f324(f106(x50012),x50014),f2(x50012))+E(x50011,f324(f324(f284(x50012),x50013),f324(f106(x50012),x50014)))
% 18.77/18.51 [5002]~P90(x50021)+~P59(x50021)+~E(x50024,f2(x50021))+~E(f324(f106(x50021),x50023),f2(x50021))+E(f324(f324(f284(x50021),x50022),f324(f106(x50021),x50023)),x50024)
% 18.77/18.51 [5027]~P90(x50271)+~P59(x50271)+~E(x50273,f2(x50271))+E(f324(f106(x50271),x50272),f2(x50271))+~E(f324(f106(x50271),x50272),f324(f324(f284(x50271),x50274),x50273))
% 18.77/18.51 [5028]~P90(x50281)+~P59(x50281)+~E(x50283,f2(x50281))+E(f324(f106(x50281),x50282),f2(x50281))+~E(f324(f324(f284(x50281),x50284),x50283),f324(f106(x50281),x50282))
% 18.77/18.51 [5187]~P90(x51872)+~P59(x51872)+E(x51871,f2(x51872))+~E(f324(f106(x51872),x51873),f2(x51872))+~E(x51871,f324(f324(f284(x51872),x51874),f324(f106(x51872),x51873)))
% 18.77/18.51 [5188]~P90(x51882)+~P59(x51882)+E(x51881,f2(x51882))+~E(f324(f106(x51882),x51883),f2(x51882))+~E(f324(f324(f284(x51882),x51884),f324(f106(x51882),x51883)),x51881)
% 18.77/18.51 [5410]~P90(x54102)+~P59(x54102)+~E(x54101,f2(x54102))+E(x54101,f324(f324(f284(x54102),x54103),f324(f106(x54102),x54104)))+~E(f324(f324(f83(x54102),x54101),f324(f106(x54102),x54104)),x54103)
% 18.77/18.51 [5411]~P90(x54111)+~P59(x54111)+~E(x54114,f2(x54111))+~E(x54112,f324(f324(f83(x54111),x54114),f324(f106(x54111),x54113)))+E(f324(f324(f284(x54111),x54112),f324(f106(x54111),x54113)),x54114)
% 18.77/18.51 [5475]~P90(x54751)+~P59(x54751)+E(f324(f106(x54751),x54752),f2(x54751))+~E(f324(f324(f284(x54751),x54753),f324(f106(x54751),x54752)),x54754)+E(x54753,f324(f324(f83(x54751),x54754),f324(f106(x54751),x54752)))
% 18.77/18.51 [5476]~P90(x54761)+~P59(x54761)+E(f324(f106(x54761),x54762),f2(x54761))+~E(f324(f324(f83(x54761),x54763),f324(f106(x54761),x54762)),x54764)+E(x54763,f324(f324(f284(x54761),x54764),f324(f106(x54761),x54762)))
% 18.77/18.51 [5477]~P90(x54771)+~P59(x54771)+E(f324(f106(x54771),x54772),f2(x54771))+~E(x54773,f324(f324(f284(x54771),x54774),f324(f106(x54771),x54772)))+E(f324(f324(f83(x54771),x54773),f324(f106(x54771),x54772)),x54774)
% 18.77/18.51 [5478]~P90(x54781)+~P59(x54781)+E(f324(f106(x54781),x54782),f2(x54781))+~E(x54783,f324(f324(f83(x54781),x54784),f324(f106(x54781),x54782)))+E(f324(f324(f284(x54781),x54783),f324(f106(x54781),x54782)),x54784)
% 18.77/18.51 [5684]~P7(x56842)+E(x56841,f2(x56842))+~E(f324(f324(f42(x56842),x56843),x56841),x56844)+E(x56843,f324(f324(f83(x56842),x56844),x56841))+~P1(f324(f324(f280(x56842),x56841),x56843))
% 18.77/18.51 [5685]~P7(x56852)+E(x56851,f2(x56852))+~E(x56853,f324(f324(f83(x56852),x56854),x56851))+E(f324(f324(f42(x56852),x56853),x56851),x56854)+~P1(f324(f324(f280(x56852),x56851),x56853))
% 18.77/18.51 [6153]E(f485(x61531,x61532,x61533),x61534)+E(f324(x61531,x61534),f2(a838))+~E(f324(f324(f8(x61533,a838),x61531),x61532),f80(a838))+~P1(f324(f64(x61533),x61532))+~P1(f324(f324(f326(x61533),x61534),x61532))
% 18.77/18.51 [6220]E(f489(x62201,x62202,x62203),x62204)+E(f324(x62201,x62204),f2(a838))+~E(f324(f324(f8(x62203,a838),x62201),x62202),f324(a114,f2(a838)))+~P1(f324(f64(x62203),x62202))+~P1(f324(f324(f326(x62203),x62204),x62202))
% 18.77/18.51 [6334]~P86(x63341)+~P9(x63341)+P1(f324(f324(f232(x63341),x63342),f43(x63341,x63343)))+~P1(f324(f324(f232(x63341),x63342),x63344))+~P1(f324(f324(f326(x63341),x63344),x63343))
% 18.77/18.51 [6512]~P86(x65121)+~P9(x65121)+~P1(f324(f324(f232(x65121),x65124),x65123))+P1(f324(f324(f232(x65121),f44(x65121,x65122)),x65123))+~P1(f324(f324(f326(x65121),x65124),x65122))
% 18.77/18.51 [6791]~P84(x67913)+E(x67911,x67912)+~E(f324(f324(f240(x67913),x67911),f324(a114,x67914)),f324(f324(f240(x67913),x67912),f324(a114,x67914)))+~P1(f324(f324(f231(x67913),f2(x67913)),x67912))+~P1(f324(f324(f231(x67913),f2(x67913)),x67911))
% 18.77/18.51 [7002]~E(f491(x70022,x70023,x70021,x70024),x70024)+~E(f324(x70022,x70024),f80(a838))+E(f324(f324(f8(x70021,a838),x70022),x70023),f80(a838))+~P1(f324(f64(x70021),x70023))+~P1(f324(f324(f326(x70021),x70024),x70023))
% 18.77/18.51 [7009]~P120(x70094)+~P105(x70094)+E(f324(x70091,f395(x70091,x70092,x70093,x70094)),f2(x70094))+~E(f324(f324(f11(x70093,x70094),x70091),x70092),f2(x70094))+~P1(f324(f64(x70093),x70092))
% 18.77/18.51 [7093]~E(f490(x70932,x70933,x70931,x70934),x70934)+~E(f324(x70932,x70934),f324(a114,f2(a838)))+E(f324(f324(f8(x70931,a838),x70932),x70933),f324(a114,f2(a838)))+~P1(f324(f64(x70931),x70933))+~P1(f324(f324(f326(x70931),x70934),x70933))
% 18.77/18.51 [7863]~E(f324(x78632,x78634),f80(a838))+~E(f324(x78632,f491(x78632,x78633,x78631,x78634)),f2(a838))+E(f324(f324(f8(x78631,a838),x78632),x78633),f80(a838))+~P1(f324(f64(x78631),x78633))+~P1(f324(f324(f326(x78631),x78634),x78633))
% 18.77/18.51 [7909]~E(f324(x79092,x79094),f324(a114,f2(a838)))+~E(f324(x79092,f490(x79092,x79093,x79091,x79094)),f2(a838))+E(f324(f324(f8(x79091,a838),x79092),x79093),f324(a114,f2(a838)))+~P1(f324(f64(x79091),x79093))+~P1(f324(f324(f326(x79091),x79094),x79093))
% 18.77/18.51 [7990]~P135(x79902)+~P113(x79902)+~P1(f324(x79901,x79904))+~P1(f324(f324(f280(x79902),x79903),f324(f324(f82(x79902),x79904),f2(x79902))))+P1(f324(x79901,f324(f324(f83(x79902),x79903),f827(x79903,x79901,x79902))))
% 18.77/18.51 [8486]E(x84861,x84862)+E(f324(f324(f82(a1),f456(x84863,x84862,x84864,x84861)),f457(x84863,x84862,x84864,x84861)),x84861)+~E(f324(f324(f3(a1),x84861),x84864),x84862)+~P1(f324(f324(f232(a1),f2(a1)),x84864))+~P1(f324(f324(f326(a1),x84862),x84863))
% 18.77/18.51 [8487]E(x84871,x84872)+E(f324(f324(f3(a1),f450(x84873,x84872,x84874,x84871)),f451(x84873,x84872,x84874,x84871)),x84871)+~E(f324(f324(f82(a1),x84871),x84874),x84872)+~P1(f324(f324(f232(a1),f2(a1)),x84874))+~P1(f324(f324(f326(a1),x84872),x84873))
% 18.77/18.51 [8652]E(f324(x86521,f817(x86522,x86521,x86523,x86524)),x86522)+P1(f324(f324(f231(a838),x86524),f818(x86522,x86521,x86523,x86524)))+~P1(f324(f324(f231(a1),x86522),f324(x86521,x86523)))+~P1(f324(f324(f232(a838),x86524),x86523))+~P1(f324(f324(f231(a1),f324(x86521,x86524)),x86522))
% 18.77/18.51 [8669]~P120(x86694)+~P105(x86694)+~E(f324(f324(f11(x86691,x86694),x86692),x86693),f2(x86694))+~P1(f324(f64(x86691),x86693))+P1(f324(f324(f326(x86691),f395(x86692,x86693,x86691,x86694)),x86693))
% 18.77/18.51 [8702]~E(f324(x87022,x87024),f80(a838))+E(f324(f324(f8(x87021,a838),x87022),x87023),f80(a838))+~P1(f324(f64(x87021),x87023))+~P1(f324(f324(f326(x87021),x87024),x87023))+P1(f324(f324(f326(x87021),f491(x87022,x87023,x87021,x87024)),x87023))
% 18.77/18.51 [8711]E(x87111,x87112)+~E(f324(f324(f82(a1),x87112),x87114),x87111)+~P1(f324(f324(f232(a1),f2(a1)),x87114))+~P1(f324(f324(f326(a1),x87111),x87113))+P1(f324(f324(f326(a1),f450(x87113,x87111,x87114,x87112)),x87113))
% 18.77/18.51 [8712]E(x87121,x87122)+~E(f324(f324(f3(a1),x87122),x87124),x87121)+~P1(f324(f324(f232(a1),f2(a1)),x87124))+~P1(f324(f324(f326(a1),x87121),x87123))+P1(f324(f324(f326(a1),f456(x87123,x87121,x87124,x87122)),x87123))
% 18.77/18.51 [8714]~E(f324(x87142,x87144),f324(a114,f2(a838)))+E(f324(f324(f8(x87141,a838),x87142),x87143),f324(a114,f2(a838)))+~P1(f324(f64(x87141),x87143))+~P1(f324(f324(f326(x87141),x87144),x87143))+P1(f324(f324(f326(x87141),f490(x87142,x87143,x87141,x87144)),x87143))
% 18.77/18.51 [8718]P56(x87182,x87183,x87184,x87181)+E(x87181,f179(f845(x87182,a832)))+~P1(f324(f64(x87182),x87184))+~P1(f324(f64(x87182),x87181))+P1(f324(f324(f326(x87182),f563(x87181,x87184,x87183,x87182)),x87184))
% 18.77/18.51 [8783]E(x87831,x87832)+~E(f324(f324(f82(a1),x87832),x87834),x87831)+~P1(f324(f324(f232(a1),f2(a1)),x87834))+~P1(f324(f324(f326(a1),x87831),x87833))+P1(f324(f324(f326(a1),f451(x87833,x87831,x87834,x87832)),f296(a1,f80(a1),x87834)))
% 18.77/18.51 [8784]E(x87841,x87842)+~E(f324(f324(f3(a1),x87842),x87844),x87841)+~P1(f324(f324(f232(a1),f2(a1)),x87844))+~P1(f324(f324(f326(a1),x87841),x87843))+P1(f324(f324(f326(a1),f457(x87843,x87841,x87844,x87842)),f296(a1,f80(a1),x87844)))
% 18.77/18.51 [8855]P1(f324(f324(f231(a838),x88551),f817(x88552,x88553,x88554,x88551)))+~P1(f324(f324(f231(a1),x88552),f324(x88553,x88554)))+P1(f324(f324(f231(a838),x88551),f818(x88552,x88553,x88554,x88551)))+~P1(f324(f324(f232(a838),x88551),x88554))+~P1(f324(f324(f231(a1),f324(x88553,x88551)),x88552))
% 18.77/18.51 [8956]E(f324(x89561,f817(x89562,x89561,x89563,x89564)),x89562)+~P1(f324(f324(f231(a1),x89562),f324(x89561,x89563)))+P1(f324(f324(f232(a838),f818(x89562,x89561,x89563,x89564)),x89563))+~P1(f324(f324(f232(a838),x89564),x89563))+~P1(f324(f324(f231(a1),f324(x89561,x89564)),x89562))
% 18.77/18.51 [9061]~P1(f324(f324(f280(a838),x90614),x90611))+~P1(f324(f324(f280(a838),x90614),x90613))+~P1(f324(f324(f280(a838),x90612),x90611))+P1(f324(f324(f280(a838),x90611),x90612))+P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x90613,x90612)),f283(a838,f280(a838),x90614,x90611)))
% 18.77/18.51 [9062]~P1(f324(f324(f280(a838),x90622),x90621))+~P1(f324(f324(f280(a838),x90623),x90624))+~P1(f324(f324(f280(a838),x90622),x90624))+P1(f324(f324(f280(a838),x90621),x90622))+P1(f324(f324(f232(f845(a838,a832)),f283(a838,f280(a838),x90621,x90623)),f283(a838,f280(a838),x90622,x90624)))
% 18.77/18.51 [9071]~P1(f324(f324(f231(a1),x90712),f324(x90713,x90714)))+P1(f324(f324(f231(a838),x90711),f818(x90712,x90713,x90714,x90711)))+P1(f324(f324(f231(a838),f817(x90712,x90713,x90714,x90711)),x90714))+~P1(f324(f324(f232(a838),x90711),x90714))+~P1(f324(f324(f231(a1),f324(x90713,x90711)),x90712))
% 18.77/18.51 [9072]~P1(f324(f324(f231(a1),x90722),f324(x90723,x90724)))+P1(f324(f324(f231(a838),x90721),f817(x90722,x90723,x90724,x90721)))+P1(f324(f324(f232(a838),f818(x90722,x90723,x90724,x90721)),x90724))+~P1(f324(f324(f232(a838),x90721),x90724))+~P1(f324(f324(f231(a1),f324(x90723,x90721)),x90722))
% 18.77/18.51 [9163]~P1(f324(f324(f231(a1),x91631),f324(x91632,x91633)))+P1(f324(f324(f231(a838),f817(x91631,x91632,x91633,x91634)),x91633))+~P1(f324(f324(f232(a838),x91634),x91633))+~P1(f324(f324(f231(a1),f324(x91632,x91634)),x91631))+P1(f324(f324(f232(a838),f818(x91631,x91632,x91633,x91634)),x91633))
% 18.77/18.51 [9247]E(x92471,f179(f845(x92472,a832)))+~P1(f324(f64(x92472),x92474))+~P1(f324(f64(x92472),x92471))+P1(f324(f324(f326(f844(f845(x92472,a832),f845(x92472,a832))),f324(f324(f247(f845(x92472,a832),f845(x92472,a832)),x92474),x92471)),f317(x92472,x92473)))+P1(f324(f324(f326(x92472),f565(x92473,x92471,x92474,x92472)),x92474))
% 18.77/18.51 [9248]E(x92481,f179(f845(x92482,a832)))+~P1(f324(f64(x92482),x92484))+~P1(f324(f64(x92482),x92481))+P1(f324(f324(f326(f844(f845(x92482,a832),f845(x92482,a832))),f324(f324(f247(f845(x92482,a832),f845(x92482,a832)),x92484),x92481)),f317(x92482,x92483)))+P1(f324(f324(f326(x92482),f647(x92483,x92481,x92484,x92482)),x92484))
% 18.77/18.51 [9897]E(f324(x98971,f817(x98972,x98971,x98973,x98974)),x98972)+~P1(f324(f324(f231(a1),x98972),f324(x98971,x98973)))+~P1(f324(f324(f231(a1),f324(f77(a1),f324(f324(f3(a1),f324(x98971,f324(f324(f82(a838),f818(x98972,x98971,x98973,x98974)),f80(a838)))),f324(x98971,f818(x98972,x98971,x98973,x98974))))),f80(a1)))+~P1(f324(f324(f232(a838),x98974),x98973))+~P1(f324(f324(f231(a1),f324(x98971,x98974)),x98972))
% 18.77/18.51 [9898]~P1(f324(f324(f231(a1),x98982),f324(x98983,x98984)))+P1(f324(f324(f231(a838),x98981),f817(x98982,x98983,x98984,x98981)))+~P1(f324(f324(f231(a1),f324(f77(a1),f324(f324(f3(a1),f324(x98983,f324(f324(f82(a838),f818(x98982,x98983,x98984,x98981)),f80(a838)))),f324(x98983,f818(x98982,x98983,x98984,x98981))))),f80(a1)))+~P1(f324(f324(f232(a838),x98981),x98984))+~P1(f324(f324(f231(a1),f324(x98983,x98981)),x98982))
% 18.77/18.51 [9899]~P1(f324(f324(f231(a1),x98991),f324(x98992,x98993)))+~P1(f324(f324(f231(a1),f324(f77(a1),f324(f324(f3(a1),f324(x98992,f324(f324(f82(a838),f818(x98991,x98992,x98993,x98994)),f80(a838)))),f324(x98992,f818(x98991,x98992,x98993,x98994))))),f80(a1)))+~P1(f324(f324(f232(a838),x98994),x98993))+~P1(f324(f324(f231(a1),f324(x98992,x98994)),x98991))+P1(f324(f324(f231(a838),f817(x98991,x98992,x98993,x98994)),x98993))
% 18.77/18.51 [5432]~P90(x54322)+~P59(x54322)+E(x54321,f2(x54322))+~E(f324(f324(f284(x54322),x54323),x54321),f324(f106(x54322),x54324))+E(x54323,f324(f324(f83(x54322),f324(f106(x54322),x54324)),x54321))
% 18.77/18.51 [5433]~P90(x54332)+~P59(x54332)+E(x54331,f2(x54332))+~E(f324(f106(x54332),x54333),f324(f324(f284(x54332),x54334),x54331))+E(f324(f324(f83(x54332),f324(f106(x54332),x54333)),x54331),x54334)
% 18.77/18.51 [5586]~P90(x55862)+~P59(x55862)+E(x55861,f2(x55862))+E(f324(f106(x55862),x55863),f324(f324(f284(x55862),x55864),x55861))+~E(f324(f324(f83(x55862),f324(f106(x55862),x55863)),x55861),x55864)
% 18.77/18.51 [5587]~P90(x55872)+~P59(x55872)+E(x55871,f2(x55872))+E(f324(f324(f284(x55872),x55873),x55871),f324(f106(x55872),x55874))+~E(x55873,f324(f324(f83(x55872),f324(f106(x55872),x55874)),x55871))
% 18.77/18.51 [5722]~P90(x57221)+~P59(x57221)+~E(f324(f106(x57221),x57222),f2(x57221))+E(f324(f106(x57221),x57222),f324(f324(f284(x57221),x57223),x57224))+~E(f324(f324(f83(x57221),f324(f106(x57221),x57222)),x57224),x57223)
% 18.77/18.51 [5723]~P90(x57231)+~P59(x57231)+~E(f324(f106(x57231),x57234),f2(x57231))+E(f324(f324(f284(x57231),x57232),x57233),f324(f106(x57231),x57234))+~E(x57232,f324(f324(f83(x57231),f324(f106(x57231),x57234)),x57233))
% 18.77/18.51 [7060]~P61(x70601)+P1(f324(f324(f232(x70601),x70602),f2(x70601)))+~P1(f324(f324(f232(x70601),x70603),f2(x70601)))+P1(f324(f324(f232(x70601),f2(x70601)),x70602))+P1(f324(f324(f232(x70601),x70603),f324(f324(f284(x70601),x70604),x70602)))
% 18.77/18.51 [7061]~P61(x70611)+P1(f324(f324(f232(x70611),x70612),f2(x70611)))+~P1(f324(f324(f231(x70611),x70613),f2(x70611)))+P1(f324(f324(f232(x70611),f2(x70611)),x70612))+P1(f324(f324(f231(x70611),x70613),f324(f324(f284(x70611),x70614),x70612)))
% 18.77/18.51 [7331]~P61(x73311)+P1(f324(f324(f232(x73311),x73312),f2(x73311)))+P1(f324(f324(f232(x73311),x73313),f2(x73311)))+P1(f324(f324(f232(x73311),f2(x73311)),x73313))+~P1(f324(f324(f232(x73311),x73312),f324(f324(f284(x73311),x73314),x73313)))
% 18.77/18.51 [7332]~P61(x73321)+P1(f324(f324(f232(x73321),x73322),f2(x73321)))+P1(f324(f324(f231(x73321),x73323),f2(x73321)))+P1(f324(f324(f232(x73321),f2(x73321)),x73322))+~P1(f324(f324(f231(x73321),x73323),f324(f324(f284(x73321),x73324),x73322)))
% 18.77/18.51 [7453]E(x74531,x74532)+~E(f324(f324(f149(x74533),x74534),x74531),f324(f324(f149(x74533),x74534),x74532))+~P1(f324(f127(x74533),x74534))+~P1(f324(f324(f232(a838),x74532),f324(f180(f839(x74533)),x74534)))+~P1(f324(f324(f232(a838),x74531),f324(f180(f839(x74533)),x74534)))
% 18.77/18.51 [7454]E(x74541,x74542)+~E(f324(f324(f149(x74543),x74544),x74541),f324(f324(f149(x74543),x74544),x74542))+~P1(f324(f127(x74543),x74544))+~P1(f324(f324(f232(a838),x74542),f324(f180(f839(x74543)),x74544)))+~P1(f324(f324(f232(a838),x74541),f324(f180(f839(x74543)),x74544)))
% 18.77/18.51 [7824]~P61(x78241)+~P1(f324(f324(f232(x78241),x78243),f2(x78241)))+P1(f324(f324(f232(x78241),f2(x78241)),x78242))+~P1(f324(f324(f232(x78241),x78244),f324(f324(f83(x78241),x78243),x78242)))+P1(f324(f324(f232(x78241),x78243),f324(f324(f284(x78241),x78244),x78242)))
% 18.77/18.51 [7825]~P61(x78251)+~P1(f324(f324(f231(x78251),x78253),f2(x78251)))+P1(f324(f324(f232(x78251),f2(x78251)),x78252))+~P1(f324(f324(f231(x78251),x78254),f324(f324(f83(x78251),x78253),x78252)))+P1(f324(f324(f231(x78251),x78253),f324(f324(f284(x78251),x78254),x78252)))
% 18.77/18.51 [7826]~P61(x78261)+~P1(f324(f324(f232(x78261),x78262),f2(x78261)))+P1(f324(f324(f232(x78261),f2(x78261)),x78262))+~P1(f324(f324(f232(x78261),x78264),f324(f324(f83(x78261),x78263),x78262)))+P1(f324(f324(f232(x78261),x78263),f324(f324(f284(x78261),x78264),x78262)))
% 18.77/18.51 [7827]~P61(x78271)+~P1(f324(f324(f232(x78271),x78272),f2(x78271)))+P1(f324(f324(f232(x78271),f2(x78271)),x78272))+~P1(f324(f324(f232(x78271),x78274),f324(f324(f284(x78271),x78273),x78272)))+P1(f324(f324(f232(x78271),x78273),f324(f324(f83(x78271),x78274),x78272)))
% 18.77/18.51 [7828]~P61(x78281)+~P1(f324(f324(f232(x78281),x78282),f2(x78281)))+P1(f324(f324(f232(x78281),f2(x78281)),x78282))+~P1(f324(f324(f231(x78281),x78284),f324(f324(f83(x78281),x78283),x78282)))+P1(f324(f324(f231(x78281),x78283),f324(f324(f284(x78281),x78284),x78282)))
% 18.77/18.51 [7829]~P61(x78291)+~P1(f324(f324(f232(x78291),x78292),f2(x78291)))+P1(f324(f324(f232(x78291),f2(x78291)),x78292))+~P1(f324(f324(f231(x78291),x78294),f324(f324(f284(x78291),x78293),x78292)))+P1(f324(f324(f231(x78291),x78293),f324(f324(f83(x78291),x78294),x78292)))
% 18.77/18.51 [7957]~P7(x79571)+~P1(f324(f324(f280(x79571),x79573),x79574))+~P1(f324(f324(f280(x79571),x79573),x79572))+~P1(f324(f324(f280(x79571),x79572),x79574))+P1(f324(f324(f280(x79571),f324(f324(f42(x79571),x79572),x79573)),f324(f324(f42(x79571),x79574),x79573)))
% 18.77/18.51 [7971]~P86(x79711)+~P18(x79711,x79712)+~P1(f324(f324(f231(a838),x79713),x79714))+P1(f324(f324(f231(x79711),f324(f324(f149(x79711),x79712),x79713)),f324(f324(f149(x79711),x79712),x79714)))+~P1(f324(f324(f232(a838),x79714),f324(f180(f839(x79711)),x79712)))
% 18.77/18.51 [7972]~P86(x79721)+~P18(x79721,x79722)+~P1(f324(f324(f231(a838),x79723),x79724))+P1(f324(f324(f231(x79721),f324(f324(f149(x79721),x79722),x79723)),f324(f324(f149(x79721),x79722),x79724)))+~P1(f324(f324(f232(a838),x79724),f324(f180(f839(x79721)),x79722)))
% 18.77/18.51 [8024]~P84(x80241)+~P1(f324(f324(f232(x80241),x80242),f80(x80241)))+~P1(f324(f324(f232(x80241),f2(x80241)),x80242))+~P1(f324(f324(f232(a838),x80244),x80243))+P1(f324(f324(f232(x80241),f324(f324(f240(x80241),x80242),x80243)),f324(f324(f240(x80241),x80242),x80244)))
% 18.77/18.51 [8025]~P84(x80251)+~P1(f324(f324(f231(x80251),x80252),f80(x80251)))+~P1(f324(f324(f231(x80251),f2(x80251)),x80252))+~P1(f324(f324(f231(a838),x80254),x80253))+P1(f324(f324(f231(x80251),f324(f324(f240(x80251),x80252),x80253)),f324(f324(f240(x80251),x80252),x80254)))
% 18.77/18.51 [8026]~P84(x80261)+~P1(f324(f324(f231(x80261),f2(x80261)),x80262))+~P1(f324(f324(f232(a838),f2(a838)),x80263))+~P1(f324(f324(f232(x80261),x80262),x80264))+P1(f324(f324(f232(x80261),f324(f324(f240(x80261),x80262),x80263)),f324(f324(f240(x80261),x80264),x80263)))
% 18.77/18.51 [8045]~P86(x80451)+~P18(x80451,f324(f154(x80451),x80452))+~P1(f324(f324(f231(a838),x80454),x80453))+P1(f324(f324(f231(x80451),f324(f324(f149(x80451),x80452),x80453)),f324(f324(f149(x80451),x80452),x80454)))+~P1(f324(f324(f232(a838),x80453),f324(f180(f839(x80451)),x80452)))
% 18.77/18.51 [8275]~P7(x82751)+P1(f324(f324(f280(x82751),x82752),x82753))+~P1(f324(f324(f280(x82751),x82754),x82753))+~P1(f324(f324(f280(x82751),x82754),x82752))+~P1(f324(f324(f280(x82751),f324(f324(f42(x82751),x82752),x82754)),f324(f324(f42(x82751),x82753),x82754)))
% 18.77/18.51 [8291]~P62(x82911)+~P1(f324(f324(f232(x82911),x82912),f2(x82911)))+~P1(f324(f324(f232(x82911),x82913),x82914))+~P1(f324(f324(f232(x82911),f2(x82911)),f324(f324(f83(x82911),x82913),x82914)))+P1(f324(f324(f232(x82911),f324(f324(f284(x82911),x82912),x82913)),f324(f324(f284(x82911),x82912),x82914)))
% 18.77/18.51 [8292]~P61(x82921)+~P1(f324(f324(f231(x82921),x82922),f2(x82921)))+~P1(f324(f324(f231(x82921),x82923),x82924))+~P1(f324(f324(f232(x82921),f2(x82921)),f324(f324(f83(x82921),x82923),x82924)))+P1(f324(f324(f231(x82921),f324(f324(f284(x82921),x82922),x82923)),f324(f324(f284(x82921),x82922),x82924)))
% 18.77/18.51 [8302]~P62(x83021)+~P1(f324(f324(f232(x83021),x83024),x83023))+~P1(f324(f324(f232(x83021),f2(x83021)),x83022))+~P1(f324(f324(f232(x83021),f2(x83021)),f324(f324(f83(x83021),x83023),x83024)))+P1(f324(f324(f232(x83021),f324(f324(f284(x83021),x83022),x83023)),f324(f324(f284(x83021),x83022),x83024)))
% 18.77/18.51 [8303]~P62(x83031)+~P1(f324(f324(f231(x83031),x83034),x83033))+~P1(f324(f324(f231(x83031),f2(x83031)),x83032))+~P1(f324(f324(f232(x83031),f2(x83031)),f324(f324(f83(x83031),x83033),x83034)))+P1(f324(f324(f231(x83031),f324(f324(f284(x83031),x83032),x83033)),f324(f324(f284(x83031),x83032),x83034)))
% 18.77/18.51 [8409]P1(f324(x84091,x84092))+~P1(f324(f64(x84094),x84092))+P1(f324(x84091,f496(x84091,x84093,x84092,x84094)))+~P1(f324(x84091,f179(f845(x84094,a832))))+~P1(f324(f324(f231(f845(x84094,a832)),x84092),x84093))
% 18.77/18.51 [8417]P1(f324(x84171,x84172))+P1(f324(f64(x84173),f496(x84171,x84174,x84172,x84173)))+~P1(f324(f64(x84173),x84172))+~P1(f324(x84171,f179(f845(x84173,a832))))+~P1(f324(f324(f231(f845(x84173,a832)),x84172),x84174))
% 18.77/18.51 [8648]E(f324(f324(f82(a1),f458(x86481,x86482,x86483,x86484)),f459(x86481,x86482,x86483,x86484)),x86484)+~P1(f324(f324(f232(a1),f2(a1)),x86483))+~P1(f324(f324(f232(a1),x86482),x86484))+~P1(f324(f324(f326(a1),x86482),x86481))+P1(f324(f324(f232(a1),x86482),f324(f324(f3(a1),x86484),x86483)))
% 18.77/18.51 [8836]~P1(f324(f324(f232(a1),f2(a1)),x88363))+~P1(f324(f324(f232(a1),x88362),x88364))+~P1(f324(f324(f326(a1),x88362),x88361))+P1(f324(f324(f326(a1),f458(x88361,x88362,x88363,x88364)),x88361))+P1(f324(f324(f232(a1),x88362),f324(f324(f3(a1),x88364),x88363)))
% 18.77/18.51 [8848]P1(f324(x88481,x88482))+~P1(f324(f64(x88483),x88482))+P1(f324(f324(f326(x88483),f497(x88481,x88484,x88482,x88483)),x88484))+~P1(f324(x88481,f179(f845(x88483,a832))))+~P1(f324(f324(f231(f845(x88483,a832)),x88482),x88484))
% 18.77/18.51 [8865]E(f324(f324(f82(a1),f438(x88651,x88652,x88653,x88654)),f439(x88651,x88652,x88653,x88654)),x88654)+~P1(f324(f324(f232(a1),f2(a1)),x88653))+~P1(f324(f324(f231(a1),x88652),x88654))+P1(f324(f324(f231(a1),x88652),f324(f324(f3(a1),x88654),x88653)))+~P1(f324(f324(f326(a1),f324(f324(f3(a1),x88652),f80(a1))),x88651))
% 18.77/18.51 [8912]~P1(f324(f324(f232(a1),f2(a1)),x89123))+~P1(f324(f324(f232(a1),x89121),x89122))+~P1(f324(f324(f326(a1),x89121),x89124))+P1(f324(f324(f326(a1),f459(x89124,x89121,x89123,x89122)),f296(a1,f80(a1),x89123)))+P1(f324(f324(f232(a1),x89121),f324(f324(f3(a1),x89122),x89123)))
% 18.77/18.51 [8999]~P1(f324(f324(f232(a1),f2(a1)),x89993))+~P1(f324(f324(f231(a1),x89992),x89994))+P1(f324(f324(f326(a1),f438(x89991,x89992,x89993,x89994)),x89991))+P1(f324(f324(f231(a1),x89992),f324(f324(f3(a1),x89994),x89993)))+~P1(f324(f324(f326(a1),f324(f324(f3(a1),x89992),f80(a1))),x89991))
% 18.77/18.51 [9037]~P1(f324(f324(f232(a1),f2(a1)),x90373))+~P1(f324(f324(f231(a1),x90371),x90372))+P1(f324(f324(f326(a1),f439(x90374,x90371,x90373,x90372)),f296(a1,f80(a1),x90373)))+P1(f324(f324(f231(a1),x90371),f324(f324(f3(a1),x90372),x90373)))+~P1(f324(f324(f326(a1),f324(f324(f3(a1),x90371),f80(a1))),x90374))
% 18.77/18.51 [9250]P1(f324(x92501,x92502))+~P1(f324(f324(f326(x92503),f497(x92501,x92504,x92502,x92503)),f496(x92501,x92504,x92502,x92503)))+~P1(f324(f64(x92503),x92502))+~P1(f324(x92501,f179(f845(x92503,a832))))+~P1(f324(f324(f231(f845(x92503,a832)),x92502),x92504))
% 18.77/18.51 [9458]P1(f324(x94581,x94582))+~P1(f324(f64(x94583),x94582))+~P1(f324(x94581,f324(f324(f303(x94583),f497(x94581,x94584,x94582,x94583)),f496(x94581,x94584,x94582,x94583))))+~P1(f324(x94581,f179(f845(x94583,a832))))+~P1(f324(f324(f231(f845(x94583,a832)),x94582),x94584))
% 18.77/18.51 [9780]~P85(x97803)+~P51(a838,x97803,f324(f324(f20(a838,f845(a838,a832),f845(a838,a832)),f324(f324(f10(f845(a838,f845(a832,a832)),f845(f845(a838,a832),f845(a838,a832)),a838),f20(a838,a832,a832)),f324(f324(f10(f845(a838,a832),f845(a838,f845(a832,a832)),a838),f324(f10(a832,f845(a832,a832),a838),a322)),f280(a838)))),f324(f324(f10(f845(a838,a832),f845(a838,a832),a838),f324(f10(a832,a832,a838),a320)),f324(f9(a838,a838,a832),f280(a838)))),x97804)+P1(f324(f324(f232(x97803),f324(x97804,x97802)),f324(x97804,x97801)))+~P1(f324(f324(f280(a838),x97802),x97801))+P1(f324(f324(f280(a838),x97801),x97802))
% 18.77/18.51 [7593]~P61(x75931)+P1(f324(f324(f232(x75931),x75932),f2(x75931)))+P1(f324(f324(f232(x75931),f2(x75931)),x75932))+~P1(f324(f324(f232(x75931),f2(x75931)),x75934))+P1(f324(f324(f232(x75931),f324(f324(f284(x75931),x75933),x75932)),x75934))
% 18.77/18.51 [7594]~P61(x75941)+P1(f324(f324(f232(x75941),x75942),f2(x75941)))+~P1(f324(f324(f231(x75941),f2(x75941)),x75944))+P1(f324(f324(f232(x75941),f2(x75941)),x75942))+P1(f324(f324(f231(x75941),f324(f324(f284(x75941),x75943),x75942)),x75944))
% 18.77/18.51 [7881]~P1(f324(f324(f231(a1),x78814),f2(a1)))+~E(x78812,f324(f324(f82(a1),f324(f324(f83(a1),x78811),x78813)),x78814))+P1(f324(f324(f232(a1),f2(a1)),x78811))+~P1(f324(f324(f232(a1),x78811),x78814))+P1(f324(f55(x78812,x78811),f324(f324(f247(a1,a1),x78813),x78814)))
% 18.77/18.51 [7919]~P1(f324(x79191,x79194))+P1(f324(x79191,f781(x79192,x79191,x79193)))+~P1(f324(f324(f232(a1),f2(a1)),x79193))+~P1(f324(f324(f231(a1),f2(a1)),x79192))+P1(f324(x79191,f324(f324(f82(a1),x79194),f324(f324(f83(a1),x79192),x79193))))
% 18.77/18.51 [7920]~P1(f324(x79201,x79204))+P1(f324(x79201,f789(x79202,x79201,x79203)))+~P1(f324(f324(f232(a1),f2(a1)),x79203))+~P1(f324(f324(f231(a1),f2(a1)),x79202))+P1(f324(x79201,f324(f324(f3(a1),x79204),f324(f324(f83(a1),x79202),x79203))))
% 18.77/18.51 [7921]~P61(x79211)+P1(f324(f324(f232(x79211),x79212),f2(x79211)))+P1(f324(f324(f232(x79211),f2(x79211)),x79212))+P1(f324(f324(f232(x79211),f2(x79211)),x79213))+~P1(f324(f324(f232(x79211),f324(f324(f284(x79211),x79214),x79212)),x79213))
% 18.77/18.51 [7922]~P61(x79221)+P1(f324(f324(f232(x79221),x79222),f2(x79221)))+P1(f324(f324(f232(x79221),f2(x79221)),x79222))+P1(f324(f324(f231(x79221),f2(x79221)),x79223))+~P1(f324(f324(f231(x79221),f324(f324(f284(x79221),x79224),x79222)),x79223))
% 18.77/18.51 [7967]~E(x79671,f324(f324(f82(a1),f324(f324(f83(a1),x79672),x79673)),x79674))+~P1(f324(f324(f232(a1),f2(a1)),x79672))+~P1(f324(f324(f231(a1),f2(a1)),x79674))+~P1(f324(f324(f232(a1),x79674),x79672))+P1(f324(f55(x79671,x79672),f324(f324(f247(a1,a1),x79673),x79674)))
% 18.77/18.51 [8087]~P61(x80871)+P1(f324(f324(f232(x80871),x80872),f2(x80871)))+~P1(f324(f324(f232(x80871),f2(x80871)),x80874))+~P1(f324(f324(f232(x80871),x80873),f324(f324(f83(x80871),x80874),x80872)))+P1(f324(f324(f232(x80871),f324(f324(f284(x80871),x80873),x80872)),x80874))
% 18.77/18.51 [8088]~P61(x80881)+P1(f324(f324(f232(x80881),x80882),f2(x80881)))+~P1(f324(f324(f231(x80881),f2(x80881)),x80884))+~P1(f324(f324(f231(x80881),x80883),f324(f324(f83(x80881),x80884),x80882)))+P1(f324(f324(f231(x80881),f324(f324(f284(x80881),x80883),x80882)),x80884))
% 18.77/18.51 [8168]~P61(x81681)+P1(f324(f324(f232(x81681),x81682),f2(x81681)))+~P1(f324(f324(f232(x81681),x81683),f2(x81681)))+P1(f324(f324(f232(x81681),x81683),f324(f324(f284(x81681),x81684),x81682)))+~P1(f324(f324(f232(x81681),f324(f324(f83(x81681),x81683),x81682)),x81684))
% 18.77/18.51 [8169]~P61(x81691)+P1(f324(f324(f232(x81691),x81692),f2(x81691)))+~P1(f324(f324(f231(x81691),x81693),f2(x81691)))+P1(f324(f324(f231(x81691),x81693),f324(f324(f284(x81691),x81694),x81692)))+~P1(f324(f324(f231(x81691),f324(f324(f83(x81691),x81693),x81692)),x81694))
% 18.77/18.51 [8327]~P61(x83271)+~P1(f324(f324(f232(x83271),x83272),f2(x83271)))+P1(f324(f324(f232(x83271),f2(x83271)),x83272))+~P1(f324(f324(f232(x83271),f324(f324(f284(x83271),x83274),x83272)),x83273))+P1(f324(f324(f232(x83271),f324(f324(f83(x83271),x83273),x83272)),x83274))
% 18.77/18.51 [8328]~P61(x83281)+~P1(f324(f324(f232(x83281),x83282),f2(x83281)))+P1(f324(f324(f232(x83281),f2(x83281)),x83282))+~P1(f324(f324(f232(x83281),f324(f324(f83(x83281),x83284),x83282)),x83283))+P1(f324(f324(f232(x83281),f324(f324(f284(x83281),x83283),x83282)),x83284))
% 18.77/18.51 [8329]~P61(x83291)+~P1(f324(f324(f232(x83291),x83292),f2(x83291)))+P1(f324(f324(f232(x83291),f2(x83291)),x83292))+~P1(f324(f324(f231(x83291),f324(f324(f284(x83291),x83294),x83292)),x83293))+P1(f324(f324(f231(x83291),f324(f324(f83(x83291),x83293),x83292)),x83294))
% 18.77/18.51 [8330]~P61(x83301)+~P1(f324(f324(f232(x83301),x83302),f2(x83301)))+P1(f324(f324(f232(x83301),f2(x83301)),x83302))+~P1(f324(f324(f231(x83301),f324(f324(f83(x83301),x83304),x83302)),x83303))+P1(f324(f324(f231(x83301),f324(f324(f284(x83301),x83303),x83302)),x83304))
% 18.77/18.51 [8350]~P61(x83501)+~P1(f324(f324(f232(x83501),f2(x83501)),x83504))+P1(f324(f324(f232(x83501),f2(x83501)),x83502))+~P1(f324(f324(f232(x83501),f324(f324(f83(x83501),x83504),x83502)),x83503))+P1(f324(f324(f232(x83501),f324(f324(f284(x83501),x83503),x83502)),x83504))
% 18.77/18.51 [8351]~P61(x83511)+~P1(f324(f324(f231(x83511),f2(x83511)),x83514))+P1(f324(f324(f232(x83511),f2(x83511)),x83512))+~P1(f324(f324(f231(x83511),f324(f324(f83(x83511),x83514),x83512)),x83513))+P1(f324(f324(f231(x83511),f324(f324(f284(x83511),x83513),x83512)),x83514))
% 18.77/18.51 [8403]~P90(x84031)+~P61(x84031)+~P1(f324(f324(f232(x84031),f2(x84031)),x84034))+~P1(f324(f324(f232(x84031),f324(f324(f284(x84031),x84032),x84034)),f324(f106(x84031),x84033)))+P1(f324(f324(f232(x84031),x84032),f324(f324(f83(x84031),f324(f106(x84031),x84033)),x84034)))
% 18.77/18.51 [8404]~P90(x84041)+~P61(x84041)+~P1(f324(f324(f232(x84041),f2(x84041)),x84044))+~P1(f324(f324(f231(x84041),f324(f324(f284(x84041),x84042),x84044)),f324(f106(x84041),x84043)))+P1(f324(f324(f231(x84041),x84042),f324(f324(f83(x84041),f324(f106(x84041),x84043)),x84044)))
% 18.77/18.51 [8410]~P90(x84101)+~P61(x84101)+~P1(f324(f324(f232(x84101),f2(x84101)),x84103))+P1(f324(f324(f232(x84101),f324(f324(f284(x84101),x84102),x84103)),f324(f106(x84101),x84104)))+~P1(f324(f324(f232(x84101),x84102),f324(f324(f83(x84101),f324(f106(x84101),x84104)),x84103)))
% 18.77/18.51 [8411]~P90(x84111)+~P61(x84111)+~P1(f324(f324(f232(x84111),f2(x84111)),x84113))+P1(f324(f324(f231(x84111),f324(f324(f284(x84111),x84112),x84113)),f324(f106(x84111),x84114)))+~P1(f324(f324(f231(x84111),x84112),f324(f324(f83(x84111),f324(f106(x84111),x84114)),x84113)))
% 18.77/18.51 [8425]~P61(x84251)+~P1(f324(f324(f232(x84251),x84254),f2(x84251)))+~P1(f324(f324(f232(x84251),x84253),f324(f324(f83(x84251),x84252),x84254)))+P1(f324(f324(f232(x84251),x84252),f324(f324(f284(x84251),x84253),x84254)))+~P1(f324(f324(f232(x84251),f324(f324(f83(x84251),x84252),x84254)),x84253))
% 18.77/18.51 [8426]~P61(x84261)+~P1(f324(f324(f232(x84261),x84262),f2(x84261)))+~P1(f324(f324(f232(x84261),x84263),f324(f324(f83(x84261),x84262),x84264)))+P1(f324(f324(f232(x84261),x84262),f324(f324(f284(x84261),x84263),x84264)))+~P1(f324(f324(f232(x84261),f324(f324(f83(x84261),x84262),x84264)),x84263))
% 18.77/18.51 [8427]~P61(x84271)+~P1(f324(f324(f232(x84271),x84274),f2(x84271)))+~P1(f324(f324(f231(x84271),x84273),f324(f324(f83(x84271),x84272),x84274)))+P1(f324(f324(f231(x84271),x84272),f324(f324(f284(x84271),x84273),x84274)))+~P1(f324(f324(f231(x84271),f324(f324(f83(x84271),x84272),x84274)),x84273))
% 18.77/18.51 [8428]~P61(x84281)+~P1(f324(f324(f231(x84281),x84282),f2(x84281)))+~P1(f324(f324(f231(x84281),x84283),f324(f324(f83(x84281),x84282),x84284)))+P1(f324(f324(f231(x84281),x84282),f324(f324(f284(x84281),x84283),x84284)))+~P1(f324(f324(f231(x84281),f324(f324(f83(x84281),x84282),x84284)),x84283))
% 18.77/18.51 [8473]~P90(x84731)+~P61(x84731)+~P1(f324(f324(f232(x84731),f2(x84731)),f324(f106(x84731),x84733)))+~P1(f324(f324(f232(x84731),x84732),f324(f324(f284(x84731),x84734),f324(f106(x84731),x84733))))+P1(f324(f324(f232(x84731),f324(f324(f83(x84731),x84732),f324(f106(x84731),x84733))),x84734))
% 18.77/18.51 [8474]~P90(x84741)+~P61(x84741)+~P1(f324(f324(f232(x84741),f2(x84741)),f324(f106(x84741),x84743)))+~P1(f324(f324(f232(x84741),x84742),f324(f324(f83(x84741),x84744),f324(f106(x84741),x84743))))+P1(f324(f324(f232(x84741),f324(f324(f284(x84741),x84742),f324(f106(x84741),x84743))),x84744))
% 18.77/18.51 [8475]~P90(x84751)+~P61(x84751)+~P1(f324(f324(f232(x84751),f2(x84751)),f324(f106(x84751),x84753)))+~P1(f324(f324(f231(x84751),x84752),f324(f324(f284(x84751),x84754),f324(f106(x84751),x84753))))+P1(f324(f324(f231(x84751),f324(f324(f83(x84751),x84752),f324(f106(x84751),x84753))),x84754))
% 18.77/18.51 [8476]~P90(x84761)+~P61(x84761)+~P1(f324(f324(f232(x84761),f2(x84761)),f324(f106(x84761),x84763)))+~P1(f324(f324(f231(x84761),x84762),f324(f324(f83(x84761),x84764),f324(f106(x84761),x84763))))+P1(f324(f324(f231(x84761),f324(f324(f284(x84761),x84762),f324(f106(x84761),x84763))),x84764))
% 18.77/18.51 [8527]~P61(x85271)+~P1(f324(f324(f232(x85271),x85273),f2(x85271)))+~P1(f324(f324(f232(x85271),x85272),f324(f324(f83(x85271),x85274),x85273)))+~P1(f324(f324(f232(x85271),f324(f324(f83(x85271),x85274),x85273)),x85272))+P1(f324(f324(f232(x85271),f324(f324(f284(x85271),x85272),x85273)),x85274))
% 18.77/18.51 [8528]~P61(x85281)+~P1(f324(f324(f232(x85281),x85283),f2(x85281)))+~P1(f324(f324(f231(x85281),x85282),f324(f324(f83(x85281),x85284),x85283)))+~P1(f324(f324(f231(x85281),f324(f324(f83(x85281),x85284),x85283)),x85282))+P1(f324(f324(f231(x85281),f324(f324(f284(x85281),x85282),x85283)),x85284))
% 18.77/18.51 [8542]~P61(x85421)+~P1(f324(f324(f232(x85421),f2(x85421)),x85424))+~P1(f324(f324(f232(x85421),x85422),f324(f324(f83(x85421),x85424),x85423)))+~P1(f324(f324(f232(x85421),f324(f324(f83(x85421),x85424),x85423)),x85422))+P1(f324(f324(f232(x85421),f324(f324(f284(x85421),x85422),x85423)),x85424))
% 18.77/18.51 [8543]~P61(x85431)+~P1(f324(f324(f231(x85431),f2(x85431)),x85434))+~P1(f324(f324(f231(x85431),x85432),f324(f324(f83(x85431),x85434),x85433)))+~P1(f324(f324(f231(x85431),f324(f324(f83(x85431),x85434),x85433)),x85432))+P1(f324(f324(f231(x85431),f324(f324(f284(x85431),x85432),x85433)),x85434))
% 18.77/18.51 [8574]~P90(x85741)+~P61(x85741)+~P1(f324(f324(f232(x85741),f2(x85741)),f324(f106(x85741),x85744)))+P1(f324(f324(f232(x85741),x85742),f324(f324(f83(x85741),x85743),f324(f106(x85741),x85744))))+~P1(f324(f324(f232(x85741),f324(f324(f284(x85741),x85742),f324(f106(x85741),x85744))),x85743))
% 18.77/18.51 [8575]~P90(x85751)+~P61(x85751)+~P1(f324(f324(f232(x85751),f2(x85751)),f324(f106(x85751),x85754)))+P1(f324(f324(f232(x85751),x85752),f324(f324(f284(x85751),x85753),f324(f106(x85751),x85754))))+~P1(f324(f324(f232(x85751),f324(f324(f83(x85751),x85752),f324(f106(x85751),x85754))),x85753))
% 18.77/18.51 [8576]~P90(x85761)+~P61(x85761)+~P1(f324(f324(f232(x85761),f2(x85761)),f324(f106(x85761),x85764)))+P1(f324(f324(f231(x85761),x85762),f324(f324(f83(x85761),x85763),f324(f106(x85761),x85764))))+~P1(f324(f324(f231(x85761),f324(f324(f284(x85761),x85762),f324(f106(x85761),x85764))),x85763))
% 18.77/18.51 [8577]~P90(x85771)+~P61(x85771)+~P1(f324(f324(f232(x85771),f2(x85771)),f324(f106(x85771),x85774)))+P1(f324(f324(f231(x85771),x85772),f324(f324(f284(x85771),x85773),f324(f106(x85771),x85774))))+~P1(f324(f324(f231(x85771),f324(f324(f83(x85771),x85772),f324(f106(x85771),x85774))),x85773))
% 18.77/18.51 [8704]E(f324(f324(f3(a1),f460(x87041,x87042,x87043,x87044)),f461(x87041,x87042,x87043,x87044)),x87044)+~P1(f324(f324(f232(a1),f2(a1)),x87043))+~P1(f324(f324(f326(a1),x87042),x87041))+~P1(f324(f324(f232(a1),x87044),x87042))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x87044),x87043)),x87042))
% 18.77/18.51 [8767]~P1(f324(x87671,x87672))+~P1(f324(f324(f232(a1),f2(a1)),x87674))+~P1(f324(f324(f231(a1),f2(a1)),x87673))+~P1(f324(x87671,f324(f324(f82(a1),f781(x87673,x87671,x87674)),x87674)))+P1(f324(x87671,f324(f324(f82(a1),x87672),f324(f324(f83(a1),x87673),x87674))))
% 18.77/18.51 [8768]~P1(f324(x87681,x87682))+~P1(f324(f324(f232(a1),f2(a1)),x87684))+~P1(f324(f324(f231(a1),f2(a1)),x87683))+~P1(f324(x87681,f324(f324(f3(a1),f789(x87683,x87681,x87684)),x87684)))+P1(f324(x87681,f324(f324(f3(a1),x87682),f324(f324(f83(a1),x87683),x87684))))
% 18.77/18.51 [8905]~P1(f324(f324(f232(a1),f2(a1)),x89053))+~P1(f324(f324(f326(a1),x89052),x89051))+~P1(f324(f324(f232(a1),x89054),x89052))+P1(f324(f324(f326(a1),f460(x89051,x89052,x89053,x89054)),x89051))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x89054),x89053)),x89052))
% 18.77/18.51 [8925]E(f324(f324(f3(a1),f445(x89251,x89252,x89253,x89254)),f446(x89251,x89252,x89253,x89254)),x89254)+~P1(f324(f324(f232(a1),f2(a1)),x89253))+~P1(f324(f324(f231(a1),x89254),x89252))+~P1(f324(f324(f326(a1),f324(f324(f82(a1),x89252),f80(a1))),x89251))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x89254),x89253)),x89252))
% 18.77/18.51 [8951]~P1(f324(f324(f232(a1),f2(a1)),x89512))+~P1(f324(f324(f326(a1),x89513),x89514))+~P1(f324(f324(f232(a1),x89511),x89513))+P1(f324(f324(f326(a1),f461(x89514,x89513,x89512,x89511)),f296(a1,f80(a1),x89512)))+P1(f324(f324(f232(a1),f324(f324(f82(a1),x89511),x89512)),x89513))
% 18.77/18.51 [9030]~P1(f324(f324(f232(a1),f2(a1)),x90303))+~P1(f324(f324(f231(a1),x90304),x90302))+P1(f324(f324(f326(a1),f445(x90301,x90302,x90303,x90304)),x90301))+~P1(f324(f324(f326(a1),f324(f324(f82(a1),x90302),f80(a1))),x90301))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x90304),x90303)),x90302))
% 18.77/18.51 [9067]~P1(f324(f324(f232(a1),f2(a1)),x90672))+~P1(f324(f324(f231(a1),x90671),x90673))+P1(f324(f324(f326(a1),f446(x90674,x90673,x90672,x90671)),f296(a1,f80(a1),x90672)))+~P1(f324(f324(f326(a1),f324(f324(f82(a1),x90673),f80(a1))),x90674))+P1(f324(f324(f231(a1),f324(f324(f82(a1),x90671),x90672)),x90673))
% 18.77/18.51 [9337]~P36(x93371,x93373)+~P30(x93371,x93374)+P36(x93371,f324(f324(f103(f845(f844(x93371,x93371),a832)),x93372),x93373))+~P1(f324(f324(f231(f845(f844(x93371,x93371),a832)),x93372),f324(f246(f845(f844(x93371,x93371),a832),f845(f844(x93371,x93371),a832)),x93374)))+~P1(f324(f324(f231(f845(f844(x93371,x93371),a832)),x93373),f324(f251(f845(f844(x93371,x93371),a832),f845(f844(x93371,x93371),a832)),x93374)))
% 18.77/18.51 [9613]~E(f324(f693(x96131,x96134,x96133,x96132),f695(x96131,x96134,x96133,x96132)),f182(f839(a831)))+P1(f324(f324(f232(a1),f694(x96131,x96134,x96133,x96132)),f695(x96131,x96134,x96133,x96132)))+P1(f324(f324(f324(x96131,x96132),x96133),x96134))+P1(f324(f324(f324(x96131,f693(x96131,x96134,x96133,x96132)),f694(x96131,x96134,x96133,x96132)),f324(f324(f82(a1),f695(x96131,x96134,x96133,x96132)),f80(a1))))+~P1(f324(f313(f844(f845(a1,f842(f839(a831))),f844(a1,a1)),a311),f324(f324(f247(f845(a1,f842(f839(a831))),f844(a1,a1)),x96132),f324(f324(f247(a1,a1),x96133),x96134))))
% 18.77/18.51 [9714]~P22(x97142,x97144,x97143)+E(x97141,f179(f845(x97142,a832)))+~P1(f324(f64(x97142),x97141))+P1(f324(f324(f326(x97142),f324(x97143,x97141)),x97141))+~P1(f324(f324(f326(x97142),f324(f324(x97144,f403(x97141,x97143,x97144,x97142)),f406(x97141,x97143,x97144,x97142))),f324(f324(f303(x97142),f403(x97141,x97143,x97144,x97142)),f324(f324(f303(x97142),f406(x97141,x97143,x97144,x97142)),f179(f845(x97142,a832))))))
% 18.77/18.51 [8564]~P90(x85641)+~P61(x85641)+~P1(f324(f324(f232(x85641),f2(x85641)),x85643))+~P1(f324(f324(f232(x85641),f324(f106(x85641),x85642)),f324(f324(f284(x85641),x85644),x85643)))+P1(f324(f324(f232(x85641),f324(f324(f83(x85641),f324(f106(x85641),x85642)),x85643)),x85644))
% 18.77/18.51 [8565]~P90(x85651)+~P61(x85651)+~P1(f324(f324(f232(x85651),f2(x85651)),x85653))+~P1(f324(f324(f231(x85651),f324(f106(x85651),x85652)),f324(f324(f284(x85651),x85654),x85653)))+P1(f324(f324(f231(x85651),f324(f324(f83(x85651),f324(f106(x85651),x85652)),x85653)),x85654))
% 18.77/18.51 [8707]~P90(x87071)+~P61(x87071)+~P1(f324(f324(f232(x87071),f2(x87071)),x87074))+P1(f324(f324(f232(x87071),f324(f106(x87071),x87072)),f324(f324(f284(x87071),x87073),x87074)))+~P1(f324(f324(f232(x87071),f324(f324(f83(x87071),f324(f106(x87071),x87072)),x87074)),x87073))
% 18.77/18.51 [8708]~P90(x87081)+~P61(x87081)+~P1(f324(f324(f232(x87081),f2(x87081)),x87084))+P1(f324(f324(f231(x87081),f324(f106(x87081),x87082)),f324(f324(f284(x87081),x87083),x87084)))+~P1(f324(f324(f231(x87081),f324(f324(f83(x87081),f324(f106(x87081),x87082)),x87084)),x87083))
% 18.77/18.51 [9257]~P52(x92571,x92571,x92574)+P1(f324(f324(f326(f844(x92571,x92571)),f324(f324(f247(x92571,x92571),x92572),x92573)),f301(x92571,x92574)))+P1(f324(f324(f326(f844(x92571,x92571)),f324(f324(f247(x92571,x92571),x92573),x92572)),f301(x92571,x92574)))+~P1(f324(f324(f326(f844(x92571,x92571)),f324(f324(f247(x92571,x92571),x92575),x92572)),f301(x92571,x92574)))+~P1(f324(f324(f326(f844(x92571,x92571)),f324(f324(f247(x92571,x92571),x92575),x92573)),f301(x92571,x92574)))
% 18.77/18.51 [5422]E(x54221,f2(a838))+~E(f324(f41(x54222),x54225),x54221)+E(f324(f41(x54222),x54223),f324(a114,x54221))+~E(x54223,f324(f324(f303(x54222),x54224),x54225))+P1(f324(f324(f326(x54222),x54224),x54225))
% 18.77/18.51 [5546]~P60(x55462)+E(x55461,f2(x55462))+E(x55463,f2(x55462))+~E(f324(f324(f284(x55462),x55464),x55463),f324(f324(f284(x55462),x55465),x55461))+E(f324(f324(f83(x55462),x55464),x55461),f324(f324(f83(x55462),x55465),x55463))
% 18.77/18.51 [5547]~P60(x55472)+E(x55471,f2(x55472))+E(x55473,f2(x55472))+~E(f324(f324(f83(x55472),x55474),x55473),f324(f324(f83(x55472),x55475),x55471))+E(f324(f324(f284(x55472),x55474),x55471),f324(f324(f284(x55472),x55475),x55473))
% 18.77/18.51 [5620]~E(f324(f41(x56201),x56205),x56203)+~E(x56205,f179(f845(x56201,a832)))+E(f324(f41(x56201),x56202),f324(a114,x56203))+~E(x56202,f324(f324(f303(x56201),x56204),x56205))+P1(f324(f324(f326(x56201),x56204),x56205))
% 18.77/18.51 [5847]~P105(x58472)+~E(f324(x58473,x58475),f2(x58472))+E(f324(f324(f11(x58471,x58472),x58473),x58474),f2(x58472))+~P1(f324(f64(x58471),x58474))+~P1(f324(f324(f326(x58471),x58475),x58474))
% 18.77/18.51 [6231]~P86(x62313)+E(x62311,x62312)+~E(f324(f295(x62313,x62314),x62311),f324(f295(x62313,x62315),x62312))+~P1(f324(f324(f232(x62313),x62315),x62312))+~P1(f324(f324(f232(x62313),x62314),x62311))
% 18.77/18.51 [6232]~P86(x62323)+E(x62321,x62322)+~E(f324(f295(x62323,x62321),x62324),f324(f295(x62323,x62322),x62325))+~P1(f324(f324(f232(x62323),x62322),x62325))+~P1(f324(f324(f232(x62323),x62321),x62324))
% 18.77/18.51 [6233]~P86(x62333)+E(x62331,x62332)+~E(f324(f295(x62333,x62334),x62331),f324(f295(x62333,x62335),x62332))+~P1(f324(f324(f232(x62333),x62335),x62332))+~P1(f324(f324(f232(x62333),x62334),x62331))
% 18.77/18.51 [6234]~P86(x62343)+E(x62341,x62342)+~E(f324(f295(x62343,x62341),x62344),f324(f295(x62343,x62342),x62345))+~P1(f324(f324(f232(x62343),x62342),x62345))+~P1(f324(f324(f232(x62343),x62341),x62344))
% 18.77/18.51 [7345]~P86(x73451)+~P18(x73451,f324(f324(f125(x73451),x73454),x73455))+~P1(f324(f324(f326(x73451),x73453),f324(f157(x73451),x73455)))+~P1(f324(f324(f326(x73451),x73452),f324(f157(x73451),x73454)))+P1(f324(f324(f231(x73451),x73452),x73453))
% 18.77/18.51 [8459]~P85(x84591)+~P1(f324(f324(f232(f845(x84591,a832)),f296(x84591,x84595,x84592)),f296(x84591,x84594,x84593)))+~P1(f324(f324(f231(x84591),x84595),x84592))+P1(f324(f324(f232(x84591),x84592),x84593))+P1(f324(f324(f232(x84591),x84594),x84595))
% 18.77/18.51 [9758]~P21(x97582,x97585,x97583)+E(x97581,f179(f845(x97582,a832)))+~E(f324(f324(x97585,f324(x97584,f600(x97581,x97584,x97583,x97585,x97582))),f324(x97584,f601(x97581,x97584,x97583,x97585,x97582))),f324(x97584,f324(f324(x97585,f600(x97581,x97584,x97583,x97585,x97582)),f601(x97581,x97584,x97583,x97585,x97582))))+E(f324(x97583,f324(f304(x97582,x97582,x97584),x97581)),f324(x97584,f324(x97583,x97581)))+~P1(f324(f64(x97582),x97581))
% 18.77/18.51 [6230]~P22(x62302,x62305,x62303)+E(x62301,f179(f845(x62302,a832)))+~P1(f324(f64(x62302),x62301))+E(f324(x62303,f324(f324(f303(x62302),x62304),x62301)),f324(f324(x62305,x62304),f324(x62303,x62301)))+P1(f324(f324(f326(x62302),x62304),x62301))
% 18.77/18.51 [7083]~P21(x70832,x70833,x70834)+E(f324(f324(x70833,f324(x70834,x70831)),f324(x70834,x70835)),f324(x70834,x70835))+E(x70831,f179(f845(x70832,a832)))+~P1(f324(f64(x70832),x70835))+~P1(f324(f324(f231(f845(x70832,a832)),x70831),x70835))
% 18.77/18.51 [7489]~P22(x74894,x74895,x74891)+E(f324(x74891,x74892),x74893)+~P1(f324(f64(x74894),x74892))+~E(f324(f324(f3(f845(x74894,a832)),x74892),f324(f324(f303(x74894),x74893),f179(f845(x74894,a832)))),f179(f845(x74894,a832)))+~P1(f324(f324(f326(x74894),x74893),x74892))
% 18.77/18.51 [7637]E(x76371,x76372)+~E(f324(f180(f839(x76373)),x76372),f324(f180(f839(x76374)),x76375))+~E(f324(f180(f839(x76373)),x76371),f324(f180(f839(x76374)),x76375))+~E(f165(x76374,x76373,f324(f324(f166(x76374,x76373),x76375),x76371)),f165(x76374,x76373,f324(f324(f166(x76374,x76373),x76375),x76372)))+~P1(f324(f127(x76374),x76375))
% 18.77/18.51 [8385]~P68(x83851)+~P113(x83851)+~P1(f324(f64(x83852),x83855))+P1(f324(f324(f280(x83851),f324(f324(f11(x83852,x83851),x83853),x83854)),f324(f324(f11(x83852,x83851),x83853),x83855)))+~P1(f324(f324(f231(f845(x83852,a832)),x83854),x83855))
% 18.77/18.51 [8432]E(x84321,x84322)+~P12(x84323,x84324,x84325)+E(f324(f324(f104(f845(x84323,a832)),x84321),x84322),f179(f845(x84323,a832)))+~P1(f324(f324(f326(f845(x84323,a832)),x84322),f324(f324(f63(x84323),x84324),x84325)))+~P1(f324(f324(f326(f845(x84323,a832)),x84321),f324(f324(f63(x84323),x84324),x84325)))
% 18.77/18.51 [8838]~P29(x88381,x88383,x88385,x88382)+~P1(f324(f64(x88383),x88384))+~P1(f324(f64(x88381),x88382))+P1(f324(f324(f231(a838),f324(f41(x88381),x88382)),f324(f41(x88383),x88384)))+~P1(f324(f324(f231(f845(x88383,a832)),f324(f304(x88381,x88383,x88385),x88382)),x88384))
% 18.77/18.51 [9135]~P68(x91352)+~E(f324(x91353,f421(x91353,x91354,x91355,x91351,x91352)),f80(x91352))+E(f324(f324(f11(x91351,x91352),x91353),x91354),f324(f324(f11(x91351,x91352),x91353),x91355))+~P1(f324(f64(x91351),x91355))+~P1(f324(f324(f231(f845(x91351,a832)),x91354),x91355))
% 18.77/18.51 [9136]~P68(x91362)+~E(f324(x91363,f422(x91363,x91364,x91365,x91361,x91362)),f80(x91362))+E(f324(f324(f11(x91361,x91362),x91363),x91364),f324(f324(f11(x91361,x91362),x91363),x91365))+~P1(f324(f64(x91361),x91365))+~P1(f324(f324(f231(f845(x91361,a832)),x91364),x91365))
% 18.77/18.51 [9137]~P67(x91372)+~E(f324(x91373,f498(x91373,x91374,x91375,x91371,x91372)),f2(x91372))+E(f324(f324(f8(x91371,x91372),x91373),x91374),f324(f324(f8(x91371,x91372),x91373),x91375))+~P1(f324(f64(x91371),x91375))+~P1(f324(f324(f231(f845(x91371,a832)),x91374),x91375))
% 18.77/18.51 [9138]~P67(x91382)+~E(f324(x91383,f507(x91383,x91384,x91385,x91381,x91382)),f2(x91382))+E(f324(f324(f8(x91381,x91382),x91383),x91384),f324(f324(f8(x91381,x91382),x91383),x91385))+~P1(f324(f64(x91381),x91385))+~P1(f324(f324(f231(f845(x91381,a832)),x91384),x91385))
% 18.77/18.51 [9594]~P80(x95941)+~P1(f324(f64(x95942),x95945))+~P1(f324(f324(f231(x95941),f2(x95941)),f324(x95943,f494(x95943,x95944,x95945,x95942,x95941))))+P1(f324(f324(f231(x95941),f324(f324(f8(x95942,x95941),x95943),x95944)),f324(f324(f8(x95942,x95941),x95943),x95945)))+~P1(f324(f324(f231(f845(x95942,a832)),x95944),x95945))
% 18.77/18.51 [7342]E(x73421,f2(a838))+P1(f324(x73422,x73423))+~E(x73424,f324(f324(f82(a838),f324(f324(f83(a838),x73421),x73423)),x73425))+~P1(f324(f324(f232(a838),x73425),x73421))+~P1(f324(x73422,f324(f324(f42(a838),x73424),x73421)))
% 18.77/18.51 [7428]E(x74281,f2(a838))+P1(f324(x74282,x74283))+~P1(f324(x74282,f51(a838,x74284,x74281)))+~E(x74284,f324(f324(f82(a838),f324(f324(f83(a838),x74281),x74285)),x74283))+~P1(f324(f324(f232(a838),x74283),x74281))
% 18.77/18.51 [7727]~P60(x77273)+E(f324(x77271,x77272),f2(x77273))+~P1(f324(f64(x77274),x77275))+E(f324(f324(f11(x77274,x77273),x77271),f324(f324(f3(f845(x77274,a832)),x77275),f324(f324(f303(x77274),x77272),f179(f845(x77274,a832))))),f324(f324(f11(x77274,x77273),x77271),x77275))+P1(f324(f324(f326(x77274),x77272),x77275))
% 18.77/18.51 [8127]~P68(x81271)+~P1(f324(f64(x81272),x81275))+~P1(f324(f64(x81272),x81274))+~E(f324(f324(f104(f845(x81272,a832)),x81274),x81275),f179(f845(x81272,a832)))+E(f324(f324(f83(x81271),f324(f324(f11(x81272,x81271),x81273),x81274)),f324(f324(f11(x81272,x81271),x81273),x81275)),f324(f324(f11(x81272,x81271),x81273),f324(f324(f103(f845(x81272,a832)),x81274),x81275)))
% 18.77/18.51 [8128]~P68(x81281)+~P1(f324(f64(x81282),x81285))+~P1(f324(f64(x81282),x81284))+~E(f324(f324(f104(f845(x81282,a832)),x81284),x81285),f179(f845(x81282,a832)))+E(f324(f324(f83(x81281),f324(f324(f11(x81282,x81281),x81283),x81284)),f324(f324(f11(x81282,x81281),x81283),x81285)),f324(f324(f11(x81282,x81281),x81283),f324(f324(f103(f845(x81282,a832)),x81284),x81285)))
% 18.77/18.51 [8129]~P67(x81291)+~P1(f324(f64(x81292),x81295))+~P1(f324(f64(x81292),x81294))+~E(f324(f324(f104(f845(x81292,a832)),x81294),x81295),f179(f845(x81292,a832)))+E(f324(f324(f82(x81291),f324(f324(f8(x81292,x81291),x81293),x81294)),f324(f324(f8(x81292,x81291),x81293),x81295)),f324(f324(f8(x81292,x81291),x81293),f324(f324(f103(f845(x81292,a832)),x81294),x81295)))
% 18.77/18.51 [8221]~P60(x82213)+E(f324(x82211,x82212),f2(x82213))+~P1(f324(f64(x82214),x82215))+E(f324(f324(f11(x82214,x82213),x82211),f324(f324(f3(f845(x82214,a832)),x82215),f324(f324(f303(x82214),x82212),f179(f845(x82214,a832))))),f324(f324(f284(x82213),f324(f324(f11(x82214,x82213),x82211),x82215)),f324(x82211,x82212)))+~P1(f324(f324(f326(x82214),x82212),x82215))
% 18.77/18.51 [8719]~P12(x87191,x87195,x87194)+~E(f324(f278(x87191,x87191,x87194),f324(f324(f303(x87191),x87192),f179(f845(x87191,a832)))),f324(f278(x87191,x87191,x87194),f324(f324(f303(x87191),x87193),f179(f845(x87191,a832)))))+~P1(f324(f324(f326(x87191),x87193),x87195))+~P1(f324(f324(f326(x87191),x87192),x87195))+P1(f324(f324(f326(f844(x87191,x87191)),f324(f324(f247(x87191,x87191),x87192),x87193)),x87194))
% 18.77/18.51 [8720]~P12(x87201,x87205,x87204)+~E(f324(f278(x87201,x87201,x87204),f324(f324(f303(x87201),x87202),f179(f845(x87201,a832)))),f324(f278(x87201,x87201,x87204),f324(f324(f303(x87201),x87203),f179(f845(x87201,a832)))))+~P1(f324(f324(f326(x87201),x87203),x87205))+~P1(f324(f324(f326(x87201),x87202),x87205))+P1(f324(f324(f326(f844(x87201,x87201)),f324(f324(f247(x87201,x87201),x87202),x87203)),x87204))
% 18.77/18.51 [8800]~P12(x88001,x88005,x88002)+E(f324(f278(x88001,x88001,x88002),f324(f324(f303(x88001),x88003),f179(f845(x88001,a832)))),f324(f278(x88001,x88001,x88002),f324(f324(f303(x88001),x88004),f179(f845(x88001,a832)))))+~P1(f324(f324(f326(x88001),x88004),x88005))+~P1(f324(f324(f326(x88001),x88003),x88005))+~P1(f324(f324(f326(f844(x88001,x88001)),f324(f324(f247(x88001,x88001),x88003),x88004)),x88002))
% 18.77/18.51 [8887]~P12(x88871,x88875,x88874)+~E(f324(f324(f63(x88871),f324(f324(f303(x88871),x88872),f179(f845(x88871,a832)))),x88874),f324(f324(f63(x88871),f324(f324(f303(x88871),x88873),f179(f845(x88871,a832)))),x88874))+~P1(f324(f324(f326(x88871),x88873),x88875))+~P1(f324(f324(f326(x88871),x88872),x88875))+P1(f324(f324(f326(f844(x88871,x88871)),f324(f324(f247(x88871,x88871),x88872),x88873)),x88874))
% 18.77/18.51 [8904]~P12(x89041,x89045,x89043)+E(f324(f324(f63(x89041),f324(f324(f303(x89041),x89042),f179(f845(x89041,a832)))),x89043),f324(f324(f63(x89041),f324(f324(f303(x89041),x89044),f179(f845(x89041,a832)))),x89043))+~P1(f324(f324(f326(x89041),x89044),x89045))+~P1(f324(f324(f326(x89041),x89042),x89045))+~P1(f324(f324(f326(f844(x89041,x89041)),f324(f324(f247(x89041,x89041),x89042),x89044)),x89043))
% 18.77/18.51 [9162]~P68(x91621)+~P1(f324(f64(x91622),x91625))+~P1(f324(f64(x91622),x91624))+~E(f324(f324(f104(f845(x91622,a832)),x91624),x91625),f179(f845(x91622,a832)))+E(f324(f324(f83(x91621),f324(f324(f324(f68(x91621,x91622,f83(x91621)),x91623),f80(x91621)),x91624)),f324(f324(f324(f68(x91621,x91622,f83(x91621)),x91623),f80(x91621)),x91625)),f324(f324(f324(f68(x91621,x91622,f83(x91621)),x91623),f80(x91621)),f324(f324(f103(f845(x91622,a832)),x91624),x91625)))
% 18.77/18.51 [9172]~P68(x91721)+~E(f324(x91723,f428(x91723,x91725,x91724,x91722,x91721)),f80(x91721))+~P1(f324(f64(x91722),x91724))+~P1(f324(f64(x91722),x91725))+E(f324(f324(f83(x91721),f324(f324(f11(x91722,x91721),x91723),x91724)),f324(f324(f11(x91722,x91721),x91723),x91725)),f324(f324(f11(x91722,x91721),x91723),f324(f324(f103(f845(x91722,a832)),x91724),x91725)))
% 18.77/18.51 [9173]~P68(x91731)+~E(f324(x91733,f429(x91733,x91735,x91734,x91732,x91731)),f80(x91731))+~P1(f324(f64(x91732),x91734))+~P1(f324(f64(x91732),x91735))+E(f324(f324(f83(x91731),f324(f324(f11(x91732,x91731),x91733),x91734)),f324(f324(f11(x91732,x91731),x91733),x91735)),f324(f324(f11(x91732,x91731),x91733),f324(f324(f103(f845(x91732,a832)),x91734),x91735)))
% 18.77/18.51 [9174]~P67(x91741)+~E(f324(x91743,f499(x91743,x91745,x91744,x91742,x91741)),f2(x91741))+~P1(f324(f64(x91742),x91744))+~P1(f324(f64(x91742),x91745))+E(f324(f324(f82(x91741),f324(f324(f8(x91742,x91741),x91743),x91744)),f324(f324(f8(x91742,x91741),x91743),x91745)),f324(f324(f8(x91742,x91741),x91743),f324(f324(f103(f845(x91742,a832)),x91744),x91745)))
% 18.77/18.51 [9175]~P67(x91751)+~E(f324(x91753,f501(x91753,x91755,x91754,x91752,x91751)),f2(x91751))+~P1(f324(f64(x91752),x91754))+~P1(f324(f64(x91752),x91755))+E(f324(f324(f82(x91751),f324(f324(f8(x91752,x91751),x91753),x91754)),f324(f324(f8(x91752,x91751),x91753),x91755)),f324(f324(f8(x91752,x91751),x91753),f324(f324(f103(f845(x91752,a832)),x91754),x91755)))
% 18.77/18.51 [9379]~P68(x93791)+~E(f324(x93793,f433(x93793,x93795,x93794,x93792,x93791)),f80(x93791))+~P1(f324(f64(x93792),x93794))+~P1(f324(f64(x93792),x93795))+E(f324(f324(f83(x93791),f324(f324(f324(f68(x93791,x93792,f83(x93791)),x93793),f80(x93791)),x93794)),f324(f324(f324(f68(x93791,x93792,f83(x93791)),x93793),f80(x93791)),x93795)),f324(f324(f324(f68(x93791,x93792,f83(x93791)),x93793),f80(x93791)),f324(f324(f103(f845(x93792,a832)),x93794),x93795)))
% 18.77/18.51 [9484]~P68(x94842)+E(f324(f324(f11(x94841,x94842),x94843),x94844),f324(f324(f11(x94841,x94842),x94843),x94845))+~P1(f324(f64(x94841),x94845))+~P1(f324(f324(f231(f845(x94841,a832)),x94844),x94845))+P1(f324(f324(f326(x94841),f421(x94843,x94844,x94845,x94841,x94842)),f324(f324(f3(f845(x94841,a832)),x94845),x94844)))
% 18.77/18.51 [9485]~P68(x94852)+E(f324(f324(f11(x94851,x94852),x94853),x94854),f324(f324(f11(x94851,x94852),x94853),x94855))+~P1(f324(f64(x94851),x94855))+~P1(f324(f324(f231(f845(x94851,a832)),x94854),x94855))+P1(f324(f324(f326(x94851),f422(x94853,x94854,x94855,x94851,x94852)),f324(f324(f3(f845(x94851,a832)),x94855),x94854)))
% 18.77/18.51 [9486]~P67(x94862)+E(f324(f324(f8(x94861,x94862),x94863),x94864),f324(f324(f8(x94861,x94862),x94863),x94865))+~P1(f324(f64(x94861),x94865))+~P1(f324(f324(f231(f845(x94861,a832)),x94864),x94865))+P1(f324(f324(f326(x94861),f498(x94863,x94864,x94865,x94861,x94862)),f324(f324(f3(f845(x94861,a832)),x94865),x94864)))
% 18.77/18.51 [9487]~P67(x94872)+E(f324(f324(f8(x94871,x94872),x94873),x94874),f324(f324(f8(x94871,x94872),x94873),x94875))+~P1(f324(f64(x94871),x94875))+~P1(f324(f324(f231(f845(x94871,a832)),x94874),x94875))+P1(f324(f324(f326(x94871),f507(x94873,x94874,x94875,x94871,x94872)),f324(f324(f3(f845(x94871,a832)),x94875),x94874)))
% 18.77/18.51 [9502]~P68(x95021)+~P1(f324(f64(x95022),x95024))+~P1(f324(f64(x95022),x95025))+E(f324(f324(f83(x95021),f324(f324(f11(x95022,x95021),x95023),x95024)),f324(f324(f11(x95022,x95021),x95023),x95025)),f324(f324(f11(x95022,x95021),x95023),f324(f324(f103(f845(x95022,a832)),x95024),x95025)))+P1(f324(f324(f326(x95022),f428(x95023,x95025,x95024,x95022,x95021)),f324(f324(f104(f845(x95022,a832)),x95024),x95025)))
% 18.77/18.51 [9503]~P68(x95031)+~P1(f324(f64(x95032),x95034))+~P1(f324(f64(x95032),x95035))+E(f324(f324(f83(x95031),f324(f324(f11(x95032,x95031),x95033),x95034)),f324(f324(f11(x95032,x95031),x95033),x95035)),f324(f324(f11(x95032,x95031),x95033),f324(f324(f103(f845(x95032,a832)),x95034),x95035)))+P1(f324(f324(f326(x95032),f429(x95033,x95035,x95034,x95032,x95031)),f324(f324(f104(f845(x95032,a832)),x95034),x95035)))
% 18.77/18.51 [9504]~P67(x95041)+~P1(f324(f64(x95042),x95044))+~P1(f324(f64(x95042),x95045))+E(f324(f324(f82(x95041),f324(f324(f8(x95042,x95041),x95043),x95044)),f324(f324(f8(x95042,x95041),x95043),x95045)),f324(f324(f8(x95042,x95041),x95043),f324(f324(f103(f845(x95042,a832)),x95044),x95045)))+P1(f324(f324(f326(x95042),f499(x95043,x95045,x95044,x95042,x95041)),f324(f324(f104(f845(x95042,a832)),x95044),x95045)))
% 18.77/18.51 [9505]~P67(x95051)+~P1(f324(f64(x95052),x95054))+~P1(f324(f64(x95052),x95055))+E(f324(f324(f82(x95051),f324(f324(f8(x95052,x95051),x95053),x95054)),f324(f324(f8(x95052,x95051),x95053),x95055)),f324(f324(f8(x95052,x95051),x95053),f324(f324(f103(f845(x95052,a832)),x95054),x95055)))+P1(f324(f324(f326(x95052),f501(x95053,x95055,x95054,x95052,x95051)),f324(f324(f104(f845(x95052,a832)),x95054),x95055)))
% 18.77/18.51 [9517]~P80(x95175)+~P1(f324(f64(x95171),x95174))+P1(f324(f324(f231(x95175),f324(f324(f8(x95171,x95175),x95172),x95173)),f324(f324(f8(x95171,x95175),x95172),x95174)))+~P1(f324(f324(f231(f845(x95171,a832)),x95173),x95174))+P1(f324(f324(f326(x95171),f494(x95172,x95173,x95174,x95171,x95175)),f324(f324(f3(f845(x95171,a832)),x95174),x95173)))
% 18.77/18.51 [9560]~P68(x95601)+~P1(f324(f64(x95602),x95604))+~P1(f324(f64(x95602),x95605))+E(f324(f324(f83(x95601),f324(f324(f324(f68(x95601,x95602,f83(x95601)),x95603),f80(x95601)),x95604)),f324(f324(f324(f68(x95601,x95602,f83(x95601)),x95603),f80(x95601)),x95605)),f324(f324(f324(f68(x95601,x95602,f83(x95601)),x95603),f80(x95601)),f324(f324(f103(f845(x95602,a832)),x95604),x95605)))+P1(f324(f324(f326(x95602),f433(x95603,x95605,x95604,x95602,x95601)),f324(f324(f104(f845(x95602,a832)),x95604),x95605)))
% 18.77/18.51 [8610]~P22(x86101,x86104,x86105)+~P1(f324(f64(x86101),x86102))+E(f324(f324(f3(f845(x86101,a832)),x86102),f324(f324(f303(x86101),x86103),f179(f845(x86101,a832)))),f179(f845(x86101,a832)))+~P1(f324(f324(f326(x86101),x86103),x86102))+E(f324(f324(x86104,x86103),f324(x86105,f324(f324(f3(f845(x86101,a832)),x86102),f324(f324(f303(x86101),x86103),f179(f845(x86101,a832)))))),f324(x86105,x86102))
% 18.77/18.51 [8680]~P22(x86801,x86804,x86805)+~P1(f324(f64(x86801),x86803))+~P1(f324(f64(x86801),x86802))+E(f324(f324(f104(f845(x86801,a832)),x86802),x86803),f179(f845(x86801,a832)))+E(f324(f324(x86804,f324(x86805,f324(f324(f103(f845(x86801,a832)),x86802),x86803))),f324(x86805,f324(f324(f104(f845(x86801,a832)),x86802),x86803))),f324(f324(x86804,f324(x86805,x86802)),f324(x86805,x86803)))
% 18.77/18.51 [9177]~P1(f324(f324(f231(a1),x91774),f2(a1)))+~P1(f324(f324(f232(a1),x91773),x91775))+P1(f324(f324(f231(a1),x91771),x91772))+~P1(f324(f324(f232(a1),x91773),x91774))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),f324(f324(f83(a1),x91773),x91772)),x91775)),f324(f324(f82(a1),f324(f324(f83(a1),x91773),x91771)),x91774)))
% 18.77/18.51 [9179]~P1(f324(f324(f231(a1),f2(a1)),x91795))+P1(f324(f324(f231(a1),x91791),x91792))+~P1(f324(f324(f232(a1),x91793),x91794))+~P1(f324(f324(f232(a1),x91795),x91794))+~P1(f324(f324(f231(a1),f324(f324(f82(a1),f324(f324(f83(a1),x91794),x91791)),x91795)),f324(f324(f82(a1),f324(f324(f83(a1),x91794),x91792)),x91793)))
% 18.77/18.51 [9292]~P60(x92925)+E(f324(x92921,f426(x92921,x92922,x92923,x92924,x92925)),f2(x92925))+~P1(f324(f64(x92924),x92923))+~P1(f324(f64(x92924),x92922))+E(f324(f324(f284(x92925),f324(f324(f83(x92925),f324(f324(f11(x92924,x92925),x92921),x92923)),f324(f324(f11(x92924,x92925),x92921),x92922))),f324(f324(f11(x92924,x92925),x92921),f324(f324(f104(f845(x92924,a832)),x92923),x92922))),f324(f324(f11(x92924,x92925),x92921),f324(f324(f103(f845(x92924,a832)),x92923),x92922)))
% 18.77/18.51 [9552]~P60(x95521)+~P1(f324(f64(x95522),x95524))+~P1(f324(f64(x95522),x95525))+E(f324(f324(f284(x95521),f324(f324(f83(x95521),f324(f324(f11(x95522,x95521),x95523),x95524)),f324(f324(f11(x95522,x95521),x95523),x95525))),f324(f324(f11(x95522,x95521),x95523),f324(f324(f104(f845(x95522,a832)),x95524),x95525))),f324(f324(f11(x95522,x95521),x95523),f324(f324(f103(f845(x95522,a832)),x95524),x95525)))+P1(f324(f324(f326(x95522),f426(x95523,x95525,x95524,x95522,x95521)),f324(f324(f104(f845(x95522,a832)),x95524),x95525)))
% 18.77/18.51 [8924]E(f324(f324(f125(x89241),x89242),x89243),f324(f324(f125(x89241),x89244),x89245))+~E(f324(f324(f158(x89241),f324(f180(f839(x89241)),x89244)),x89242),x89244)+~E(f324(f324(f158(x89241),f324(f180(f839(x89241)),x89242)),x89244),x89242)+~E(x89245,f324(f324(f125(x89241),f324(f324(f128(x89241),f324(f180(f839(x89241)),x89244)),x89242)),x89243))+~E(f324(f324(f125(x89241),f324(f324(f128(x89241),f324(f180(f839(x89241)),x89242)),x89244)),x89245),x89243)
% 18.77/18.51 [9290]~P86(x92902)+E(f324(f324(f137(x92901,x92902,x92903),x92904),f155(x92901,x92904,x92905)),x92905)+~P18(x92902,f324(f324(f141(x92901,x92902),x92903),x92905))+~P1(f324(f324(f326(x92901),x92904),f324(f157(x92901),x92905)))+~E(f324(f130(x92901),f324(f126(x92901,f324(f324(f10(x92902,a832,x92901),f324(a321,f324(x92903,x92904))),x92903)),x92905)),x92904)
% 18.77/18.51 [9609]~P4(x96091)+~P1(f324(f69(x96091,x96091,f83(x96091),x96092,x96093),x96095))+~P1(f324(f324(f326(x96091),x96094),x96093))+P1(f324(f324(f326(x96091),x96092),x96093))+P1(f324(f69(x96091,x96091,f83(x96091),x96094,f324(f324(f303(x96091),x96092),f324(f324(f3(f845(x96091,a832)),x96093),f324(f324(f303(x96091),x96094),f179(f845(x96091,a832)))))),x96095))
% 18.77/18.51 [7087]E(x70871,x70872)+~P29(x70874,x70875,x70873,x70876)+~E(f324(x70873,x70871),f324(x70873,x70872))+~P1(f324(f324(f326(x70874),x70872),x70876))+~P1(f324(f324(f326(x70874),x70871),x70876))
% 18.77/18.51 [7088]E(x70881,x70882)+~P29(x70884,x70885,x70883,x70886)+~E(f324(x70883,x70881),f324(x70883,x70882))+~P1(f324(f324(f326(x70884),x70882),x70886))+~P1(f324(f324(f326(x70884),x70881),x70886))
% 18.77/18.51 [7089]E(x70891,x70892)+~P29(x70894,x70895,x70893,x70896)+~E(f324(x70893,x70891),f324(x70893,x70892))+~P1(f324(f324(f326(x70894),x70892),x70896))+~P1(f324(f324(f326(x70894),x70891),x70896))
% 18.77/18.51 [7090]E(x70901,x70902)+~P29(x70904,x70905,x70903,x70906)+~E(f324(x70903,x70901),f324(x70903,x70902))+~P1(f324(f324(f326(x70904),x70902),x70906))+~P1(f324(f324(f326(x70904),x70901),x70906))
% 18.77/18.51 [6328]~P136(x63284)+E(x63281,x63282)+~E(x63285,x63286)+E(x63283,f2(x63284))+~E(f324(f324(f82(x63284),x63285),f324(f324(f83(x63284),x63283),x63281)),f324(f324(f82(x63284),x63286),f324(f324(f83(x63284),x63283),x63282)))
% 18.77/18.51 [7408]~P86(x74081)+~P9(x74081)+~P1(f324(f324(f232(x74081),x74082),f324(x74085,x74086)))+~P1(f324(f324(f326(x74083),x74086),x74084))+P1(f324(f324(f232(x74081),x74082),f324(f324(f45(x74083,x74081),x74084),x74085)))
% 18.77/18.51 [9771]~P105(x97716)+~P1(f324(f64(x97711),x97715))+P1(f324(f324(f326(x97711),f650(x97712,x97713,x97714,x97715,x97711,x97716)),x97714))+P1(f324(f324(f280(x97716),f324(f324(f11(x97711,x97716),x97713),x97714)),f324(f324(f11(x97711,x97716),x97712),x97715)))+~P1(f324(f324(f231(f845(x97711,a832)),x97714),x97715))
% 18.77/18.51 [9894]~P105(x98941)+~P1(f324(f64(x98942),x98946))+~P1(f324(f324(f280(x98941),f324(x98943,f650(x98945,x98943,x98944,x98946,x98942,x98941))),f324(x98945,f650(x98945,x98943,x98944,x98946,x98942,x98941))))+P1(f324(f324(f280(x98941),f324(f324(f11(x98942,x98941),x98943),x98944)),f324(f324(f11(x98942,x98941),x98945),x98946)))+~P1(f324(f324(f231(f845(x98942,a832)),x98944),x98946))
% 18.77/18.51 [8098]~P86(x80981)+~P9(x80981)+~P1(f324(f324(f232(x80981),f324(x80984,x80986)),x80985))+~P1(f324(f324(f326(x80982),x80986),x80983))+P1(f324(f324(f232(x80981),f324(f324(f46(x80982,x80981),x80983),x80984)),x80985))
% 18.77/18.51 [8357]~P23(x83572,x83575,x83576,x83571)+~P1(f324(f64(x83572),x83574))+~P1(f324(f64(x83572),x83573))+~E(f324(f324(f104(f845(x83572,a832)),x83573),x83574),f179(f845(x83572,a832)))+E(f324(x83571,f324(f324(f103(f845(x83572,a832)),x83573),x83574)),f324(f75(x83575,x83575,x83575,f324(x83571,x83573)),f324(x83571,x83574)))
% 18.77/18.51 [9004]~P113(x90041)+~P111(x90041)+~P1(f324(f324(f280(x90041),x90042),x90045))+~P1(f324(f324(f280(x90041),x90042),f324(f324(f82(x90041),x90043),x90046)))+P1(f324(f324(f280(x90041),x90042),f324(f324(f82(x90041),f324(f324(f3(x90041),x90043),f324(f324(f83(x90041),x90044),x90045))),x90046)))
% 18.77/18.51 [9005]~P113(x90051)+~P111(x90051)+~P1(f324(f324(f280(x90051),x90052),x90055))+~P1(f324(f324(f280(x90051),x90052),f324(f324(f82(x90051),x90053),x90056)))+P1(f324(f324(f280(x90051),x90052),f324(f324(f82(x90051),f324(f324(f3(x90051),x90053),f324(f324(f83(x90051),x90054),x90055))),x90056)))
% 18.77/18.51 [9166]~P113(x91661)+~P111(x91661)+~P1(f324(f324(f280(x91661),x91662),x91665))+P1(f324(f324(f280(x91661),x91662),f324(f324(f82(x91661),x91663),x91664)))+~P1(f324(f324(f280(x91661),x91662),f324(f324(f82(x91661),f324(f324(f3(x91661),x91663),f324(f324(f83(x91661),x91666),x91665))),x91664)))
% 18.77/18.51 [9167]~P113(x91671)+~P111(x91671)+~P1(f324(f324(f280(x91671),x91672),x91675))+P1(f324(f324(f280(x91671),x91672),f324(f324(f82(x91671),x91673),x91674)))+~P1(f324(f324(f280(x91671),x91672),f324(f324(f82(x91671),f324(f324(f3(x91671),x91673),f324(f324(f83(x91671),x91676),x91675))),x91674)))
% 18.77/18.51 [8651]E(x86511,x86512)+~P54(x86514,x86515,x86516,x86513,x86517)+~E(f324(x86513,x86511),f324(x86513,x86512))+~P1(f324(f324(f326(x86515),x86512),x86517))+~P1(f324(f324(f326(x86515),x86511),x86517))
% 18.77/18.51 [9902]~P12(x99021,x99027,x99026)+~P16(x99021,f845(x99025,a832),x99026,x99024)+P1(f324(f324(f326(x99021),f544(x99022,x99023,x99024,x99025,x99026,x99027,x99021)),x99027))+~P1(f324(f324(f326(f845(x99021,a832)),x99023),f324(f324(f63(x99021),x99027),x99026)))+P1(f324(f324(f326(f845(x99025,a832)),f324(f324(f45(x99021,f845(x99025,a832)),x99023),x99024)),x99022))
% 18.77/18.51 [9948]~P12(x99482,x99486,x99487)+~P16(x99482,f845(x99481,a832),x99487,x99484)+~P1(f324(f324(f326(f845(x99482,a832)),x99483),f324(f324(f63(x99482),x99486),x99487)))+~P1(f324(f324(f326(f845(x99481,a832)),f324(x99484,f544(x99485,x99483,x99484,x99481,x99487,x99486,x99482))),x99485))+P1(f324(f324(f326(f845(x99481,a832)),f324(f324(f45(x99482,f845(x99481,a832)),x99483),x99484)),x99485))
% 18.77/18.51 [8267]~P68(x82672)+~P29(x82671,x82675,x82678,x82674)+~E(x82673,f324(f75(x82675,x82672,x82671,x82676),x82678))+~E(x82677,f324(f304(x82671,x82675,x82678),x82674))+E(f324(f324(f11(x82671,x82672),x82673),x82674),f324(f324(f11(x82675,x82672),x82676),x82677))
% 18.77/18.51 [9952]~P68(x99522)+~P29(x99525,x99521,x99528,x99527)+~E(f324(x99526,f630(x99523,x99526,x99524,x99527,x99528,x99521,x99525,x99522)),f324(f324(f75(x99521,x99522,x99525,x99523),x99528),f630(x99523,x99526,x99524,x99527,x99528,x99521,x99525,x99522)))+~E(x99524,f324(f304(x99525,x99521,x99528),x99527))+E(f324(f324(f11(x99521,x99522),x99523),x99524),f324(f324(f11(x99525,x99522),x99526),x99527))
% 18.77/18.51 [9955]~P68(x99552)+~P29(x99551,x99555,x99558,x99554)+~E(x99557,f324(f304(x99551,x99555,x99558),x99554))+E(f324(f324(f11(x99551,x99552),x99553),x99554),f324(f324(f11(x99555,x99552),x99556),x99557))+P1(f324(f324(f326(x99551),f630(x99556,x99553,x99557,x99554,x99558,x99555,x99551,x99552)),x99554))
% 18.77/18.51 [9956]~P67(x99562)+~P29(x99561,x99565,x99568,x99564)+~E(x99567,f324(f304(x99561,x99565,x99568),x99564))+E(f324(f324(f8(x99561,x99562),x99563),x99564),f324(f324(f8(x99565,x99562),x99566),x99567))+P1(f324(f324(f326(x99561),f661(x99566,x99563,x99567,x99564,x99568,x99565,x99561,x99562)),x99564))
% 18.77/18.51 [9961]~P67(x99612)+~P29(x99615,x99611,x99618,x99617)+~E(x99614,f324(f304(x99615,x99611,x99618),x99617))+~E(f324(x99616,f661(x99613,x99616,x99614,x99617,x99618,x99611,x99615,x99612)),f324(x99613,f324(x99618,f661(x99613,x99616,x99614,x99617,x99618,x99611,x99615,x99612))))+E(f324(f324(f8(x99611,x99612),x99613),x99614),f324(f324(f8(x99615,x99612),x99616),x99617))
% 18.77/18.51 [9355]~E(f324(f180(f839(x93552)),x93555),f324(f180(f839(x93551)),x93553))+~E(f324(f180(f839(x93552)),x93554),f324(f180(f839(x93551)),x93553))+~E(f324(f324(f324(f74(x93551,f842(x93552)),f165(x93551,x93552,f324(f324(f166(x93551,x93552),x93553),x93554))),x93556),f324(f226(x93552),x93557)),f324(f324(f324(f74(x93551,f842(x93552)),f165(x93551,x93552,f324(f324(f166(x93551,x93552),x93553),x93555))),x93556),f324(f226(x93552),x93558)))+E(f165(x93551,x93552,f324(f324(f166(x93551,x93552),x93553),x93554)),f165(x93551,x93552,f324(f324(f166(x93551,x93552),x93553),x93555)))+P1(f324(f324(f326(x93551),x93556),f324(f157(x93551),x93553)))
% 18.77/18.51 [9453]~P27(x94536,x94532,x94535,x94537,x94538,x94531)+~P1(f324(f64(x94532),x94534))+~P1(f324(f64(x94532),x94533))+~E(f324(f324(f104(f845(x94532,a832)),x94533),x94534),f179(f845(x94532,a832)))+E(f324(x94531,f324(f324(f103(f845(x94532,a832)),x94533),x94534)),f324(f324(x94535,f324(x94531,x94533)),f324(x94531,x94534)))
% 18.77/18.51 [9847]~P27(x98478,x98472,x98475,x98477,x98476,x98471)+~E(f324(x98476,f603(x98474,x98473,x98471,x98476,x98477,x98475,x98472)),x98477)+~P1(f324(f64(x98472),x98473))+~P1(f324(f64(x98472),x98474))+E(f324(x98471,f324(f324(f103(f845(x98472,a832)),x98473),x98474)),f324(f324(x98475,f324(x98471,x98473)),f324(x98471,x98474)))
% 18.77/18.51 [9907]~P27(x99078,x99072,x99075,x99077,x99076,x99071)+~P1(f324(f64(x99072),x99073))+~P1(f324(f64(x99072),x99074))+E(f324(x99071,f324(f324(f103(f845(x99072,a832)),x99073),x99074)),f324(f324(x99075,f324(x99071,x99073)),f324(x99071,x99074)))+P1(f324(f324(f326(x99072),f603(x99074,x99073,x99071,x99076,x99077,x99075,x99072)),f324(f324(f104(f845(x99072,a832)),x99073),x99074)))
% 18.77/18.51 [9599]~P12(x95994,x95998,x95995)+~P12(x95991,x95999,x95993)+~P17(x95991,x95994,f845(x95992,a832),x95993,x95995,x95997)+P16(x95991,f845(x95992,a832),x95993,f324(f324(f10(f845(x95994,f845(x95992,a832)),f845(x95992,a832),x95991),f324(f45(x95994,f845(x95992,a832)),f324(f278(x95994,x95994,x95995),f324(f324(f303(x95994),x95996),f179(f845(x95994,a832)))))),x95997))+~P1(f324(f324(f326(x95994),x95996),x95998))
% 18.77/18.51 [4865]~P120(x48652)+~P121(x48652)+~P137(x48652)+~P108(x48652)+E(x48651,f2(x48652))+~E(f324(f324(f240(x48652),x48651),x48653),f2(x48652))
% 18.77/18.51 [4866]~P120(x48662)+~P121(x48662)+~P137(x48662)+~P108(x48662)+~E(x48661,f2(a838))+~E(f324(f324(f240(x48662),x48663),x48661),f2(x48662))
% 18.77/18.51 [6308]~P80(x63081)+~E(x63083,f2(x63081))+~E(x63082,f2(x63081))+E(f324(f324(f82(x63081),x63082),x63083),f2(x63081))+~P1(f324(f324(f231(x63081),f2(x63081)),x63083))+~P1(f324(f324(f231(x63081),f2(x63081)),x63082))
% 18.77/18.51 [8697]E(x86971,f2(a838))+~E(x86972,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x86973)),x86971)),f324(f251(a838,a838),x86973)))+P1(f324(f54(x86972,x86971),x86973))+~P1(f324(f324(f231(a838),f324(f251(a838,a838),x86973)),f2(a838)))+P1(f324(f324(f232(a838),f2(a838)),x86971))+~P1(f324(f324(f232(a838),x86971),f324(f251(a838,a838),x86973)))
% 18.77/18.51 [8709]~E(f324(f246(a838,a838),x87093),f2(a838))+~E(x87091,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x87093)),x87092)),f324(f251(a838,a838),x87093)))+P1(f324(f54(x87091,x87092),x87093))+~P1(f324(f324(f231(a838),f324(f251(a838,a838),x87093)),f2(a838)))+P1(f324(f324(f232(a838),f2(a838)),x87092))+~P1(f324(f324(f232(a838),x87092),f324(f251(a838,a838),x87093)))
% 18.77/18.51 [8716]E(x87161,f2(a838))+~E(x87162,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x87163)),x87161)),f324(f251(a838,a838),x87163)))+P1(f324(f54(x87162,x87161),x87163))+~P1(f324(f324(f232(a838),f2(a838)),x87161))+~P1(f324(f324(f231(a838),f2(a838)),f324(f251(a838,a838),x87163)))+~P1(f324(f324(f232(a838),f324(f251(a838,a838),x87163)),x87161))
% 18.77/18.51 [8731]~E(f324(f246(a838,a838),x87313),f2(a838))+~E(x87311,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x87313)),x87312)),f324(f251(a838,a838),x87313)))+P1(f324(f54(x87311,x87312),x87313))+~P1(f324(f324(f232(a838),f2(a838)),x87312))+~P1(f324(f324(f231(a838),f2(a838)),f324(f251(a838,a838),x87313)))+~P1(f324(f324(f232(a838),f324(f251(a838,a838),x87313)),x87312))
% 18.77/18.51 [6708]~P94(x67082)+E(x67081,f179(f845(x67082,a832)))+E(x67083,f179(f845(x67082,a832)))+~P1(f324(f64(x67082),x67081))+~P1(f324(f64(x67082),x67083))+E(f12(x67082,f324(f324(f103(f845(x67082,a832)),x67083),x67081)),f324(f324(f104(x67082),f12(x67082,x67083)),f12(x67082,x67081)))
% 18.77/18.51 [6709]~P86(x67092)+E(x67091,f179(f845(x67092,a832)))+E(x67093,f179(f845(x67092,a832)))+~P1(f324(f64(x67092),x67091))+~P1(f324(f64(x67092),x67093))+E(f16(x67092,f324(f324(f103(f845(x67092,a832)),x67093),x67091)),f324(f324(f178(x67092),f16(x67092,x67093)),f16(x67092,x67091)))
% 18.77/18.51 [6710]~P86(x67102)+E(x67101,f179(f845(x67102,a832)))+E(x67103,f179(f845(x67102,a832)))+~P1(f324(f64(x67102),x67101))+~P1(f324(f64(x67102),x67103))+E(f17(x67102,f324(f324(f103(f845(x67102,a832)),x67103),x67101)),f324(f324(f235(x67102),f17(x67102,x67103)),f17(x67102,x67101)))
% 18.77/18.51 [6711]~P94(x67112)+E(x67111,f179(f845(x67112,a832)))+E(x67113,f179(f845(x67112,a832)))+~P1(f324(f64(x67112),x67111))+~P1(f324(f64(x67112),x67113))+E(f15(x67112,f324(f324(f103(f845(x67112,a832)),x67113),x67111)),f324(f324(f103(x67112),f15(x67112,x67113)),f15(x67112,x67111)))
% 18.77/18.51 [7380]~P92(x73802)+E(x73801,f179(f845(x73802,a832)))+E(x73803,f179(f845(x73802,a832)))+~P1(f324(f64(x73802),x73801))+~P1(f324(f64(x73802),x73803))+E(f324(f324(f83(x73802),f324(f66(x73802,f83(x73802)),x73803)),f324(f66(x73802,f83(x73802)),x73801)),f324(f66(x73802,f83(x73802)),f324(f324(f103(f845(x73802,a832)),x73803),x73801)))
% 18.77/18.51 [7545]~P86(x75452)+E(x75451,f179(f845(x75452,a832)))+E(x75453,f179(f845(x75452,a832)))+~P1(f324(f64(x75452),x75451))+~P1(f324(f64(x75452),x75453))+E(f324(f324(f178(x75452),f13(x75452,f178(x75452),x75453)),f13(x75452,f178(x75452),x75451)),f13(x75452,f178(x75452),f324(f324(f103(f845(x75452,a832)),x75453),x75451)))
% 18.77/18.51 [7546]~P86(x75462)+E(x75461,f179(f845(x75462,a832)))+E(x75463,f179(f845(x75462,a832)))+~P1(f324(f64(x75462),x75461))+~P1(f324(f64(x75462),x75463))+E(f324(f324(f235(x75462),f14(x75462,f235(x75462),x75463)),f14(x75462,f235(x75462),x75461)),f14(x75462,f235(x75462),f324(f324(f103(f845(x75462,a832)),x75463),x75461)))
% 18.77/18.51 [8563]~P1(f324(x85631,x85633))+P1(f324(x85631,f470(x85631,x85632)))+P1(f324(x85631,f465(x85631,x85632)))+~P1(f324(f324(f232(a1),f2(a1)),x85632))+~P1(f324(f324(f326(a1),x85633),f296(a1,f80(a1),x85632)))+P1(f324(x85631,f324(f324(f3(a1),f465(x85631,x85632)),f324(f324(f83(a1),f469(x85631,x85632)),x85632))))
% 18.77/18.51 [8829]~P1(f324(x88291,x88293))+~P1(f324(x88291,f465(x88291,x88292)))+P1(f324(x88291,f470(x88291,x88292)))+~P1(f324(f324(f232(a1),f2(a1)),x88292))+~P1(f324(f324(f326(a1),x88293),f296(a1,f80(a1),x88292)))+~P1(f324(x88291,f324(f324(f3(a1),f465(x88291,x88292)),f324(f324(f83(a1),f469(x88291,x88292)),x88292))))
% 18.77/18.51 [9982]~P97(x99822)+E(x99821,f179(f845(x99822,a832)))+E(x99823,f179(f845(x99822,a832)))+~P1(f324(f64(x99822),x99821))+~P1(f324(f64(x99822),x99823))+E(f12(x99822,f324(f257(x99822),f324(f324(f10(f845(x99822,a832),a832,x99822),f89(x99822)),f324(f324(f10(f845(x99822,f845(x99822,a832)),f845(x99822,a832),x99822),f324(f10(f845(x99822,a832),a832,x99822),f89(x99822))),f324(f324(f9(x99822,f845(x99822,f845(x99822,a832)),f845(x99822,f845(x99822,a832))),f324(f324(f10(f845(x99822,f845(f845(x99822,a832),f845(x99822,a832))),f845(f845(x99822,f845(x99822,a832)),f845(x99822,f845(x99822,a832))),x99822),f20(x99822,f845(x99822,a832),f845(x99822,a832))),f324(f324(f10(f845(x99822,f845(x99822,f845(a832,a832))),f845(x99822,f845(f845(x99822,a832),f845(x99822,a832))),x99822),f324(f10(f845(x99822,f845(a832,a832)),f845(f845(x99822,a832),f845(x99822,a832)),x99822),f20(x99822,a832,a832))),f324(f324(f10(f845(x99822,f845(x99822,a832)),f845(x99822,f845(x99822,f845(a832,a832))),x99822),f324(f10(f845(x99822,a832),f845(x99822,f845(a832,a832)),x99822),f324(f10(a832,f845(a832,a832),x99822),a322))),f324(f324(f9(x99822,f845(x99822,f845(x99822,x99822)),f845(x99822,f845(x99822,a832))),f324(f324(f10(f845(f845(x99822,x99822),f845(x99822,a832)),f845(f845(x99822,f845(x99822,x99822)),f845(x99822,f845(x99822,a832))),x99822),f10(f845(x99822,x99822),f845(x99822,a832),x99822)),f324(f324(f10(f845(x99822,a832),f845(f845(x99822,x99822),f845(x99822,a832)),x99822),f10(x99822,a832,x99822)),a321))),f103(x99822)))))),f324(f324(f9(x99822,f845(x99822,a832),f845(x99822,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x99822,a832),f845(x99822,a832)),x99822),f10(a832,a832,x99822)),f324(f324(f10(a832,f845(a832,a832),x99822),a322),f324(f324(f9(x99822,f845(x99822,a832),a832),f326(x99822)),x99823)))),f324(f324(f9(x99822,f845(x99822,a832),a832),f326(x99822)),x99821))))))),f324(f324(f103(x99822),f12(x99822,x99823)),f12(x99822,x99821)))
% 18.77/18.51 [9983]~P97(x99832)+E(x99831,f179(f845(x99832,a832)))+E(x99833,f179(f845(x99832,a832)))+~P1(f324(f64(x99832),x99831))+~P1(f324(f64(x99832),x99833))+E(f15(x99832,f324(f257(x99832),f324(f324(f10(f845(x99832,a832),a832,x99832),f89(x99832)),f324(f324(f10(f845(x99832,f845(x99832,a832)),f845(x99832,a832),x99832),f324(f10(f845(x99832,a832),a832,x99832),f89(x99832))),f324(f324(f9(x99832,f845(x99832,f845(x99832,a832)),f845(x99832,f845(x99832,a832))),f324(f324(f10(f845(x99832,f845(f845(x99832,a832),f845(x99832,a832))),f845(f845(x99832,f845(x99832,a832)),f845(x99832,f845(x99832,a832))),x99832),f20(x99832,f845(x99832,a832),f845(x99832,a832))),f324(f324(f10(f845(x99832,f845(x99832,f845(a832,a832))),f845(x99832,f845(f845(x99832,a832),f845(x99832,a832))),x99832),f324(f10(f845(x99832,f845(a832,a832)),f845(f845(x99832,a832),f845(x99832,a832)),x99832),f20(x99832,a832,a832))),f324(f324(f10(f845(x99832,f845(x99832,a832)),f845(x99832,f845(x99832,f845(a832,a832))),x99832),f324(f10(f845(x99832,a832),f845(x99832,f845(a832,a832)),x99832),f324(f10(a832,f845(a832,a832),x99832),a322))),f324(f324(f9(x99832,f845(x99832,f845(x99832,x99832)),f845(x99832,f845(x99832,a832))),f324(f324(f10(f845(f845(x99832,x99832),f845(x99832,a832)),f845(f845(x99832,f845(x99832,x99832)),f845(x99832,f845(x99832,a832))),x99832),f10(f845(x99832,x99832),f845(x99832,a832),x99832)),f324(f324(f10(f845(x99832,a832),f845(f845(x99832,x99832),f845(x99832,a832)),x99832),f10(x99832,a832,x99832)),a321))),f104(x99832)))))),f324(f324(f9(x99832,f845(x99832,a832),f845(x99832,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x99832,a832),f845(x99832,a832)),x99832),f10(a832,a832,x99832)),f324(f324(f10(a832,f845(a832,a832),x99832),a322),f324(f324(f9(x99832,f845(x99832,a832),a832),f326(x99832)),x99833)))),f324(f324(f9(x99832,f845(x99832,a832),a832),f326(x99832)),x99831))))))),f324(f324(f104(x99832),f15(x99832,x99833)),f15(x99832,x99831)))
% 18.77/18.51 [9984]~P86(x99842)+E(x99841,f179(f845(x99842,a832)))+E(x99843,f179(f845(x99842,a832)))+~P1(f324(f64(x99842),x99841))+~P1(f324(f64(x99842),x99843))+E(f13(x99842,f178(x99842),f324(f257(x99842),f324(f324(f10(f845(x99842,a832),a832,x99842),f89(x99842)),f324(f324(f10(f845(x99842,f845(x99842,a832)),f845(x99842,a832),x99842),f324(f10(f845(x99842,a832),a832,x99842),f89(x99842))),f324(f324(f9(x99842,f845(x99842,f845(x99842,a832)),f845(x99842,f845(x99842,a832))),f324(f324(f10(f845(x99842,f845(f845(x99842,a832),f845(x99842,a832))),f845(f845(x99842,f845(x99842,a832)),f845(x99842,f845(x99842,a832))),x99842),f20(x99842,f845(x99842,a832),f845(x99842,a832))),f324(f324(f10(f845(x99842,f845(x99842,f845(a832,a832))),f845(x99842,f845(f845(x99842,a832),f845(x99842,a832))),x99842),f324(f10(f845(x99842,f845(a832,a832)),f845(f845(x99842,a832),f845(x99842,a832)),x99842),f20(x99842,a832,a832))),f324(f324(f10(f845(x99842,f845(x99842,a832)),f845(x99842,f845(x99842,f845(a832,a832))),x99842),f324(f10(f845(x99842,a832),f845(x99842,f845(a832,a832)),x99842),f324(f10(a832,f845(a832,a832),x99842),a322))),f324(f324(f9(x99842,f845(x99842,f845(x99842,x99842)),f845(x99842,f845(x99842,a832))),f324(f324(f10(f845(f845(x99842,x99842),f845(x99842,a832)),f845(f845(x99842,f845(x99842,x99842)),f845(x99842,f845(x99842,a832))),x99842),f10(f845(x99842,x99842),f845(x99842,a832),x99842)),f324(f324(f10(f845(x99842,a832),f845(f845(x99842,x99842),f845(x99842,a832)),x99842),f10(x99842,a832,x99842)),a321))),f235(x99842)))))),f324(f324(f9(x99842,f845(x99842,a832),f845(x99842,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x99842,a832),f845(x99842,a832)),x99842),f10(a832,a832,x99842)),f324(f324(f10(a832,f845(a832,a832),x99842),a322),f324(f324(f9(x99842,f845(x99842,a832),a832),f326(x99842)),x99843)))),f324(f324(f9(x99842,f845(x99842,a832),a832),f326(x99842)),x99841))))))),f324(f324(f235(x99842),f13(x99842,f178(x99842),x99843)),f13(x99842,f178(x99842),x99841)))
% 18.77/18.51 [9985]~P86(x99852)+E(x99851,f179(f845(x99852,a832)))+E(x99853,f179(f845(x99852,a832)))+~P1(f324(f64(x99852),x99851))+~P1(f324(f64(x99852),x99853))+E(f14(x99852,f235(x99852),f324(f257(x99852),f324(f324(f10(f845(x99852,a832),a832,x99852),f89(x99852)),f324(f324(f10(f845(x99852,f845(x99852,a832)),f845(x99852,a832),x99852),f324(f10(f845(x99852,a832),a832,x99852),f89(x99852))),f324(f324(f9(x99852,f845(x99852,f845(x99852,a832)),f845(x99852,f845(x99852,a832))),f324(f324(f10(f845(x99852,f845(f845(x99852,a832),f845(x99852,a832))),f845(f845(x99852,f845(x99852,a832)),f845(x99852,f845(x99852,a832))),x99852),f20(x99852,f845(x99852,a832),f845(x99852,a832))),f324(f324(f10(f845(x99852,f845(x99852,f845(a832,a832))),f845(x99852,f845(f845(x99852,a832),f845(x99852,a832))),x99852),f324(f10(f845(x99852,f845(a832,a832)),f845(f845(x99852,a832),f845(x99852,a832)),x99852),f20(x99852,a832,a832))),f324(f324(f10(f845(x99852,f845(x99852,a832)),f845(x99852,f845(x99852,f845(a832,a832))),x99852),f324(f10(f845(x99852,a832),f845(x99852,f845(a832,a832)),x99852),f324(f10(a832,f845(a832,a832),x99852),a322))),f324(f324(f9(x99852,f845(x99852,f845(x99852,x99852)),f845(x99852,f845(x99852,a832))),f324(f324(f10(f845(f845(x99852,x99852),f845(x99852,a832)),f845(f845(x99852,f845(x99852,x99852)),f845(x99852,f845(x99852,a832))),x99852),f10(f845(x99852,x99852),f845(x99852,a832),x99852)),f324(f324(f10(f845(x99852,a832),f845(f845(x99852,x99852),f845(x99852,a832)),x99852),f10(x99852,a832,x99852)),a321))),f178(x99852)))))),f324(f324(f9(x99852,f845(x99852,a832),f845(x99852,a832)),f324(f324(f10(f845(a832,a832),f845(f845(x99852,a832),f845(x99852,a832)),x99852),f10(a832,a832,x99852)),f324(f324(f10(a832,f845(a832,a832),x99852),a322),f324(f324(f9(x99852,f845(x99852,a832),a832),f326(x99852)),x99853)))),f324(f324(f9(x99852,f845(x99852,a832),a832),f326(x99852)),x99851))))))),f324(f324(f178(x99852),f14(x99852,f235(x99852),x99853)),f14(x99852,f235(x99852),x99851)))
% 18.77/18.51 [7043]~P84(x70433)+E(x70431,x70432)+~E(f324(f324(f240(x70433),x70431),x70434),f324(f324(f240(x70433),x70432),x70434))+~P1(f324(f324(f231(x70433),f2(x70433)),x70432))+~P1(f324(f324(f231(x70433),f2(x70433)),x70431))+~P1(f324(f324(f232(a838),f2(a838)),x70434))
% 18.77/18.51 [7905]~P90(x79051)+~P61(x79051)+P1(f324(f324(f232(x79051),x79052),f2(x79051)))+P1(f324(f324(f232(x79051),f2(x79051)),x79052))+P1(f324(f324(f232(x79051),f324(f324(f284(x79051),x79053),x79052)),f324(f106(x79051),x79054)))+~P1(f324(f324(f232(x79051),f2(x79051)),f324(f106(x79051),x79054)))
% 18.77/18.51 [7906]~P90(x79061)+~P61(x79061)+P1(f324(f324(f232(x79061),x79062),f2(x79061)))+P1(f324(f324(f232(x79061),f2(x79061)),x79062))+P1(f324(f324(f231(x79061),f324(f324(f284(x79061),x79063),x79062)),f324(f106(x79061),x79064)))+~P1(f324(f324(f231(x79061),f2(x79061)),f324(f106(x79061),x79064)))
% 18.77/18.51 [8146]~P90(x81461)+~P61(x81461)+P1(f324(f324(f232(x81461),x81462),f2(x81461)))+P1(f324(f324(f232(x81461),f2(x81461)),x81462))+~P1(f324(f324(f232(x81461),f324(f324(f284(x81461),x81464),x81462)),f324(f106(x81461),x81463)))+P1(f324(f324(f232(x81461),f2(x81461)),f324(f106(x81461),x81463)))
% 18.77/18.51 [8147]~P90(x81471)+~P61(x81471)+P1(f324(f324(f232(x81471),x81472),f2(x81471)))+P1(f324(f324(f232(x81471),f2(x81471)),x81472))+~P1(f324(f324(f231(x81471),f324(f324(f284(x81471),x81474),x81472)),f324(f106(x81471),x81473)))+P1(f324(f324(f231(x81471),f2(x81471)),f324(f106(x81471),x81473)))
% 18.77/18.51 [7337]~P86(x73372)+E(x73371,f179(f845(x73372,a832)))+~P1(f324(f64(x73372),x73371))+~P1(f324(f324(f326(x73372),x73374),x73371))+P1(f324(f324(f232(x73372),x73373),x73374))+~P1(f324(f324(f232(x73372),x73373),f324(f66(x73372,f235(x73372)),x73371)))
% 18.77/18.51 [7338]~P86(x73382)+E(x73381,f179(f845(x73382,a832)))+~P1(f324(f64(x73382),x73381))+~P1(f324(f324(f326(x73382),x73384),x73381))+P1(f324(f324(f231(x73382),x73383),x73384))+~P1(f324(f324(f231(x73382),x73383),f324(f66(x73382,f235(x73382)),x73381)))
% 18.77/18.51 [7339]~P99(x73392)+E(x73391,f179(f845(x73392,a832)))+~P1(f324(f64(x73392),x73391))+~P1(f324(f324(f326(x73392),x73394),x73391))+P1(f324(f324(f231(x73392),x73393),x73394))+~P1(f324(f324(f231(x73392),x73393),f324(f66(x73392,f104(x73392)),x73391)))
% 18.77/18.51 [7853]~P90(x78531)+~P61(x78531)+P1(f324(f324(f232(x78531),f324(f106(x78531),x78532)),f2(x78531)))+~P1(f324(f324(f232(x78531),x78533),f2(x78531)))+P1(f324(f324(f232(x78531),f2(x78531)),f324(f106(x78531),x78532)))+P1(f324(f324(f232(x78531),x78533),f324(f324(f284(x78531),x78534),f324(f106(x78531),x78532))))
% 18.77/18.51 [7854]~P90(x78541)+~P61(x78541)+P1(f324(f324(f232(x78541),f324(f106(x78541),x78542)),f2(x78541)))+~P1(f324(f324(f231(x78541),x78543),f2(x78541)))+P1(f324(f324(f232(x78541),f2(x78541)),f324(f106(x78541),x78542)))+P1(f324(f324(f231(x78541),x78543),f324(f324(f284(x78541),x78544),f324(f106(x78541),x78542))))
% 18.77/18.51 [7865]~P90(x78651)+~P61(x78651)+P1(f324(f324(f232(x78651),x78652),f2(x78651)))+~P1(f324(f324(f232(x78651),f324(f106(x78651),x78653)),f2(x78651)))+P1(f324(f324(f232(x78651),f2(x78651)),x78652))+P1(f324(f324(f232(x78651),f324(f106(x78651),x78653)),f324(f324(f284(x78651),x78654),x78652)))
% 18.77/18.51 [7866]~P90(x78661)+~P61(x78661)+P1(f324(f324(f232(x78661),x78662),f2(x78661)))+~P1(f324(f324(f231(x78661),f324(f106(x78661),x78663)),f2(x78661)))+P1(f324(f324(f232(x78661),f2(x78661)),x78662))+P1(f324(f324(f231(x78661),f324(f106(x78661),x78663)),f324(f324(f284(x78661),x78664),x78662)))
% 18.77/18.51 [8016]~P90(x80161)+~P61(x80161)+P1(f324(f324(f232(x80161),x80162),f2(x80161)))+P1(f324(f324(f232(x80161),f324(f106(x80161),x80163)),f2(x80161)))+P1(f324(f324(f232(x80161),f2(x80161)),x80162))+~P1(f324(f324(f232(x80161),f324(f106(x80161),x80163)),f324(f324(f284(x80161),x80164),x80162)))
% 18.77/18.51 [8017]~P90(x80171)+~P61(x80171)+P1(f324(f324(f232(x80171),x80172),f2(x80171)))+P1(f324(f324(f231(x80171),f324(f106(x80171),x80173)),f2(x80171)))+P1(f324(f324(f232(x80171),f2(x80171)),x80172))+~P1(f324(f324(f231(x80171),f324(f106(x80171),x80173)),f324(f324(f284(x80171),x80174),x80172)))
% 18.77/18.51 [8092]~P90(x80921)+~P61(x80921)+P1(f324(f324(f232(x80921),x80922),f2(x80921)))+P1(f324(f324(f232(x80921),f324(f106(x80921),x80923)),f2(x80921)))+P1(f324(f324(f232(x80921),f2(x80921)),f324(f106(x80921),x80923)))+~P1(f324(f324(f232(x80921),x80922),f324(f324(f284(x80921),x80924),f324(f106(x80921),x80923))))
% 18.77/18.51 [8093]~P90(x80931)+~P61(x80931)+P1(f324(f324(f231(x80931),x80932),f2(x80931)))+P1(f324(f324(f232(x80931),f324(f106(x80931),x80933)),f2(x80931)))+P1(f324(f324(f232(x80931),f2(x80931)),f324(f106(x80931),x80933)))+~P1(f324(f324(f231(x80931),x80932),f324(f324(f284(x80931),x80934),f324(f106(x80931),x80933))))
% 18.77/18.51 [8284]~P90(x82841)+~P61(x82841)+~P1(f324(f324(f232(x82841),x82843),f2(x82841)))+P1(f324(f324(f232(x82841),f2(x82841)),f324(f106(x82841),x82842)))+~P1(f324(f324(f232(x82841),x82844),f324(f324(f83(x82841),x82843),f324(f106(x82841),x82842))))+P1(f324(f324(f232(x82841),x82843),f324(f324(f284(x82841),x82844),f324(f106(x82841),x82842))))
% 18.77/18.51 [8285]~P90(x82851)+~P61(x82851)+~P1(f324(f324(f231(x82851),x82853),f2(x82851)))+P1(f324(f324(f232(x82851),f2(x82851)),f324(f106(x82851),x82852)))+~P1(f324(f324(f231(x82851),x82854),f324(f324(f83(x82851),x82853),f324(f106(x82851),x82852))))+P1(f324(f324(f231(x82851),x82853),f324(f324(f284(x82851),x82854),f324(f106(x82851),x82852))))
% 18.77/18.51 [8453]~P90(x84531)+~P61(x84531)+~P1(f324(f324(f232(x84531),f324(f106(x84531),x84532)),f2(x84531)))+P1(f324(f324(f232(x84531),f2(x84531)),f324(f106(x84531),x84532)))+~P1(f324(f324(f232(x84531),x84534),f324(f324(f83(x84531),x84533),f324(f106(x84531),x84532))))+P1(f324(f324(f232(x84531),x84533),f324(f324(f284(x84531),x84534),f324(f106(x84531),x84532))))
% 18.77/18.51 [8454]~P90(x84541)+~P61(x84541)+~P1(f324(f324(f232(x84541),f324(f106(x84541),x84542)),f2(x84541)))+P1(f324(f324(f232(x84541),f2(x84541)),f324(f106(x84541),x84542)))+~P1(f324(f324(f232(x84541),x84544),f324(f324(f284(x84541),x84543),f324(f106(x84541),x84542))))+P1(f324(f324(f232(x84541),x84543),f324(f324(f83(x84541),x84544),f324(f106(x84541),x84542))))
% 18.77/18.51 [8455]~P90(x84551)+~P61(x84551)+~P1(f324(f324(f232(x84551),f324(f106(x84551),x84552)),f2(x84551)))+P1(f324(f324(f232(x84551),f2(x84551)),f324(f106(x84551),x84552)))+~P1(f324(f324(f231(x84551),x84554),f324(f324(f83(x84551),x84553),f324(f106(x84551),x84552))))+P1(f324(f324(f231(x84551),x84553),f324(f324(f284(x84551),x84554),f324(f106(x84551),x84552))))
% 18.77/18.51 [8456]~P90(x84561)+~P61(x84561)+~P1(f324(f324(f232(x84561),f324(f106(x84561),x84562)),f2(x84561)))+P1(f324(f324(f232(x84561),f2(x84561)),f324(f106(x84561),x84562)))+~P1(f324(f324(f231(x84561),x84564),f324(f324(f284(x84561),x84563),f324(f106(x84561),x84562))))+P1(f324(f324(f231(x84561),x84563),f324(f324(f83(x84561),x84564),f324(f106(x84561),x84562))))
% 18.77/18.51 [7233]E(x72331,f2(a1))+E(f324(f324(f42(a1),x72332),x72331),x72333)+~P1(f324(f324(f231(a1),x72334),f2(a1)))+~E(x72332,f324(f324(f82(a1),f324(f324(f83(a1),x72331),x72333)),x72334))+P1(f324(f324(f232(a1),f2(a1)),x72331))+~P1(f324(f324(f232(a1),x72331),x72334))
% 18.77/18.51 [7249]E(f51(a1,x72492,x72491),x72493)+E(x72491,f2(a1))+~P1(f324(f324(f231(a1),x72493),f2(a1)))+~E(x72492,f324(f324(f82(a1),f324(f324(f83(a1),x72491),x72494)),x72493))+P1(f324(f324(f232(a1),f2(a1)),x72491))+~P1(f324(f324(f232(a1),x72491),x72493))
% 18.77/18.51 [7379]E(x73791,f2(a1))+E(f324(f324(f42(a1),x73792),x73791),x73793)+~E(x73792,f324(f324(f82(a1),f324(f324(f83(a1),x73791),x73793)),x73794))+~P1(f324(f324(f232(a1),f2(a1)),x73791))+~P1(f324(f324(f231(a1),f2(a1)),x73794))+~P1(f324(f324(f232(a1),x73794),x73791))
% 18.77/18.51 [7404]E(f51(a1,x74042,x74041),x74043)+E(x74041,f2(a1))+~E(x74042,f324(f324(f82(a1),f324(f324(f83(a1),x74041),x74044)),x74043))+~P1(f324(f324(f232(a1),f2(a1)),x74041))+~P1(f324(f324(f231(a1),f2(a1)),x74043))+~P1(f324(f324(f232(a1),x74043),x74041))
% 18.77/18.51 [7549]~P86(x75492)+E(x75491,f179(f845(x75492,a832)))+~P1(f324(f64(x75492),x75491))+~P1(f324(f324(f232(x75492),x75494),x75493))+~P1(f324(f324(f326(x75492),x75494),x75491))+P1(f324(f324(f232(x75492),f324(f66(x75492,f235(x75492)),x75491)),x75493))
% 18.77/18.51 [7550]~P86(x75502)+E(x75501,f179(f845(x75502,a832)))+~P1(f324(f64(x75502),x75501))+~P1(f324(f324(f231(x75502),x75504),x75503))+~P1(f324(f324(f326(x75502),x75504),x75501))+P1(f324(f324(f231(x75502),f324(f66(x75502,f235(x75502)),x75501)),x75503))
% 18.77/18.51 [8122]~P1(f324(f324(f231(a1),x81224),f2(a1)))+~E(x81221,f324(f324(f82(a1),f324(f324(f83(a1),x81222),x81223)),x81224))+~P1(f324(f324(f231(a1),f2(a1)),x81224))+~P1(f324(f324(f232(a1),x81224),x81222))+~P1(f324(f324(f232(a1),x81222),x81224))+P1(f324(f55(x81221,x81222),f324(f324(f247(a1,a1),x81223),x81224)))
% 18.77/18.51 [8243]~P90(x82431)+~P61(x82431)+P1(f324(f324(f232(x82431),f324(f106(x82431),x82432)),f2(x82431)))+~P1(f324(f324(f232(x82431),f2(x82431)),x82434))+P1(f324(f324(f232(x82431),f2(x82431)),f324(f106(x82431),x82432)))+P1(f324(f324(f232(x82431),f324(f324(f284(x82431),x82433),f324(f106(x82431),x82432))),x82434))
% 18.77/18.51 [8244]~P90(x82441)+~P61(x82441)+P1(f324(f324(f232(x82441),f324(f106(x82441),x82442)),f2(x82441)))+~P1(f324(f324(f231(x82441),f2(x82441)),x82444))+P1(f324(f324(f232(x82441),f2(x82441)),f324(f106(x82441),x82442)))+P1(f324(f324(f231(x82441),f324(f324(f284(x82441),x82443),f324(f106(x82441),x82442))),x82444))
% 18.77/18.51 [8360]~P90(x83601)+~P61(x83601)+~P1(f324(f324(f232(x83601),x83602),f2(x83601)))+P1(f324(f324(f232(x83601),f2(x83601)),x83602))+~P1(f324(f324(f232(x83601),f324(f106(x83601),x83604)),f324(f324(f284(x83601),x83603),x83602)))+P1(f324(f324(f232(x83601),x83603),f324(f324(f83(x83601),f324(f106(x83601),x83604)),x83602)))
% 18.77/18.51 [8361]~P90(x83611)+~P61(x83611)+~P1(f324(f324(f232(x83611),x83612),f2(x83611)))+P1(f324(f324(f232(x83611),f2(x83611)),x83612))+~P1(f324(f324(f231(x83611),f324(f106(x83611),x83614)),f324(f324(f284(x83611),x83613),x83612)))+P1(f324(f324(f231(x83611),x83613),f324(f324(f83(x83611),f324(f106(x83611),x83614)),x83612)))
% 18.77/18.51 [8401]~P90(x84011)+~P61(x84011)+~P1(f324(f324(f232(x84011),x84012),f2(x84011)))+P1(f324(f324(f232(x84011),f2(x84011)),x84012))+P1(f324(f324(f232(x84011),f324(f106(x84011),x84013)),f324(f324(f284(x84011),x84014),x84012)))+~P1(f324(f324(f232(x84011),x84014),f324(f324(f83(x84011),f324(f106(x84011),x84013)),x84012)))
% 18.77/18.51 [8402]~P90(x84021)+~P61(x84021)+~P1(f324(f324(f232(x84021),x84022),f2(x84021)))+P1(f324(f324(f232(x84021),f2(x84021)),x84022))+P1(f324(f324(f231(x84021),f324(f106(x84021),x84023)),f324(f324(f284(x84021),x84024),x84022)))+~P1(f324(f324(f231(x84021),x84024),f324(f324(f83(x84021),f324(f106(x84021),x84023)),x84022)))
% 18.77/18.51 [8484]~P90(x84841)+~P61(x84841)+P1(f324(f324(f232(x84841),f324(f106(x84841),x84843)),f2(x84841)))+P1(f324(f324(f232(x84841),f2(x84841)),x84842))+P1(f324(f324(f232(x84841),f2(x84841)),f324(f106(x84841),x84843)))+~P1(f324(f324(f232(x84841),f324(f324(f284(x84841),x84844),f324(f106(x84841),x84843))),x84842))
% 18.77/18.51 [8485]~P90(x84851)+~P61(x84851)+P1(f324(f324(f232(x84851),f324(f106(x84851),x84853)),f2(x84851)))+P1(f324(f324(f231(x84851),f2(x84851)),x84852))+P1(f324(f324(f232(x84851),f2(x84851)),f324(f106(x84851),x84853)))+~P1(f324(f324(f231(x84851),f324(f324(f284(x84851),x84854),f324(f106(x84851),x84853))),x84852))
% 18.77/18.51 [8524]~P90(x85241)+~P61(x85241)+~P1(f324(f324(f232(x85241),f324(f106(x85241),x85243)),f2(x85241)))+P1(f324(f324(f232(x85241),f2(x85241)),x85242))+P1(f324(f324(f232(x85241),f324(f106(x85241),x85243)),f324(f324(f284(x85241),x85244),x85242)))+~P1(f324(f324(f232(x85241),x85244),f324(f324(f83(x85241),f324(f106(x85241),x85243)),x85242)))
% 18.77/18.51 [8525]~P90(x85251)+~P61(x85251)+~P1(f324(f324(f231(x85251),f324(f106(x85251),x85253)),f2(x85251)))+P1(f324(f324(f232(x85251),f2(x85251)),x85252))+P1(f324(f324(f231(x85251),f324(f106(x85251),x85253)),f324(f324(f284(x85251),x85254),x85252)))+~P1(f324(f324(f231(x85251),x85254),f324(f324(f83(x85251),f324(f106(x85251),x85253)),x85252)))
% 18.77/18.51 [8532]~P90(x85321)+~P61(x85321)+P1(f324(f324(f232(x85321),x85322),f2(x85321)))+P1(f324(f324(f232(x85321),f324(f324(f284(x85321),x85323),x85322)),f324(f106(x85321),x85324)))+~P1(f324(f324(f232(x85321),f2(x85321)),f324(f106(x85321),x85324)))+~P1(f324(f324(f232(x85321),x85323),f324(f324(f83(x85321),f324(f106(x85321),x85324)),x85322)))
% 18.77/18.51 [8533]~P90(x85331)+~P61(x85331)+P1(f324(f324(f232(x85331),x85332),f2(x85331)))+P1(f324(f324(f231(x85331),f324(f324(f284(x85331),x85333),x85332)),f324(f106(x85331),x85334)))+~P1(f324(f324(f231(x85331),f2(x85331)),f324(f106(x85331),x85334)))+~P1(f324(f324(f231(x85331),x85333),f324(f324(f83(x85331),f324(f106(x85331),x85334)),x85332)))
% 18.77/18.51 [8551]~P90(x85511)+~P61(x85511)+P1(f324(f324(f232(x85511),f324(f106(x85511),x85512)),f2(x85511)))+~P1(f324(f324(f232(x85511),f2(x85511)),x85514))+~P1(f324(f324(f232(x85511),x85513),f324(f324(f83(x85511),x85514),f324(f106(x85511),x85512))))+P1(f324(f324(f232(x85511),f324(f324(f284(x85511),x85513),f324(f106(x85511),x85512))),x85514))
% 18.77/18.51 [8552]~P90(x85521)+~P61(x85521)+P1(f324(f324(f232(x85521),f324(f106(x85521),x85522)),f2(x85521)))+~P1(f324(f324(f231(x85521),f2(x85521)),x85524))+~P1(f324(f324(f231(x85521),x85523),f324(f324(f83(x85521),x85524),f324(f106(x85521),x85522))))+P1(f324(f324(f231(x85521),f324(f324(f284(x85521),x85523),f324(f106(x85521),x85522))),x85524))
% 18.77/18.51 [8635]~P90(x86351)+~P61(x86351)+P1(f324(f324(f232(x86351),f324(f106(x86351),x86352)),f2(x86351)))+~P1(f324(f324(f232(x86351),x86353),f2(x86351)))+P1(f324(f324(f232(x86351),x86353),f324(f324(f284(x86351),x86354),f324(f106(x86351),x86352))))+~P1(f324(f324(f232(x86351),f324(f324(f83(x86351),x86353),f324(f106(x86351),x86352))),x86354))
% 18.77/18.51 [8636]~P90(x86361)+~P61(x86361)+P1(f324(f324(f232(x86361),f324(f106(x86361),x86362)),f2(x86361)))+~P1(f324(f324(f231(x86361),x86363),f2(x86361)))+P1(f324(f324(f231(x86361),x86363),f324(f324(f284(x86361),x86364),f324(f106(x86361),x86362))))+~P1(f324(f324(f231(x86361),f324(f324(f83(x86361),x86363),f324(f106(x86361),x86362))),x86364))
% 18.77/18.51 [8735]~P90(x87351)+~P61(x87351)+~P1(f324(f324(f232(x87351),f2(x87351)),x87354))+P1(f324(f324(f232(x87351),f2(x87351)),f324(f106(x87351),x87352)))+~P1(f324(f324(f232(x87351),f324(f324(f83(x87351),x87354),f324(f106(x87351),x87352))),x87353))+P1(f324(f324(f232(x87351),f324(f324(f284(x87351),x87353),f324(f106(x87351),x87352))),x87354))
% 18.77/18.51 [8736]~P90(x87361)+~P61(x87361)+~P1(f324(f324(f231(x87361),f2(x87361)),x87364))+P1(f324(f324(f232(x87361),f2(x87361)),f324(f106(x87361),x87362)))+~P1(f324(f324(f231(x87361),f324(f324(f83(x87361),x87364),f324(f106(x87361),x87362))),x87363))+P1(f324(f324(f231(x87361),f324(f324(f284(x87361),x87363),f324(f106(x87361),x87362))),x87364))
% 18.77/18.51 [8785]~P90(x87851)+~P61(x87851)+~P1(f324(f324(f232(x87851),x87852),f2(x87851)))+P1(f324(f324(f232(x87851),x87852),f324(f324(f284(x87851),x87853),f324(f106(x87851),x87854))))+~P1(f324(f324(f232(x87851),x87853),f324(f324(f83(x87851),x87852),f324(f106(x87851),x87854))))+~P1(f324(f324(f232(x87851),f324(f324(f83(x87851),x87852),f324(f106(x87851),x87854))),x87853))
% 18.77/18.51 [8786]~P90(x87861)+~P61(x87861)+~P1(f324(f324(f231(x87861),x87862),f2(x87861)))+P1(f324(f324(f231(x87861),x87862),f324(f324(f284(x87861),x87863),f324(f106(x87861),x87864))))+~P1(f324(f324(f231(x87861),x87863),f324(f324(f83(x87861),x87862),f324(f106(x87861),x87864))))+~P1(f324(f324(f231(x87861),f324(f324(f83(x87861),x87862),f324(f106(x87861),x87864))),x87863))
% 18.77/18.51 [8810]~P90(x88101)+~P61(x88101)+~P1(f324(f324(f232(x88101),f324(f106(x88101),x88102)),f2(x88101)))+P1(f324(f324(f232(x88101),f2(x88101)),f324(f106(x88101),x88102)))+~P1(f324(f324(f232(x88101),f324(f324(f284(x88101),x88104),f324(f106(x88101),x88102))),x88103))+P1(f324(f324(f232(x88101),f324(f324(f83(x88101),x88103),f324(f106(x88101),x88102))),x88104))
% 18.77/18.51 [8811]~P90(x88111)+~P61(x88111)+~P1(f324(f324(f232(x88111),f324(f106(x88111),x88112)),f2(x88111)))+P1(f324(f324(f232(x88111),f2(x88111)),f324(f106(x88111),x88112)))+~P1(f324(f324(f232(x88111),f324(f324(f83(x88111),x88114),f324(f106(x88111),x88112))),x88113))+P1(f324(f324(f232(x88111),f324(f324(f284(x88111),x88113),f324(f106(x88111),x88112))),x88114))
% 18.77/18.51 [8812]~P90(x88121)+~P61(x88121)+~P1(f324(f324(f232(x88121),f324(f106(x88121),x88122)),f2(x88121)))+P1(f324(f324(f232(x88121),f2(x88121)),f324(f106(x88121),x88122)))+~P1(f324(f324(f231(x88121),f324(f324(f284(x88121),x88124),f324(f106(x88121),x88122))),x88123))+P1(f324(f324(f231(x88121),f324(f324(f83(x88121),x88123),f324(f106(x88121),x88122))),x88124))
% 18.77/18.51 [8813]~P90(x88131)+~P61(x88131)+~P1(f324(f324(f232(x88131),f324(f106(x88131),x88132)),f2(x88131)))+P1(f324(f324(f232(x88131),f2(x88131)),f324(f106(x88131),x88132)))+~P1(f324(f324(f231(x88131),f324(f324(f83(x88131),x88134),f324(f106(x88131),x88132))),x88133))+P1(f324(f324(f231(x88131),f324(f324(f284(x88131),x88133),f324(f106(x88131),x88132))),x88134))
% 18.77/18.51 [8888]~P90(x88881)+~P61(x88881)+~P1(f324(f324(f232(x88881),f324(f106(x88881),x88884)),f2(x88881)))+P1(f324(f324(f232(x88881),x88882),f324(f324(f284(x88881),x88883),f324(f106(x88881),x88884))))+~P1(f324(f324(f232(x88881),x88883),f324(f324(f83(x88881),x88882),f324(f106(x88881),x88884))))+~P1(f324(f324(f232(x88881),f324(f324(f83(x88881),x88882),f324(f106(x88881),x88884))),x88883))
% 18.77/18.51 [8889]~P90(x88891)+~P61(x88891)+~P1(f324(f324(f232(x88891),f324(f106(x88891),x88894)),f2(x88891)))+P1(f324(f324(f231(x88891),x88892),f324(f324(f284(x88891),x88893),f324(f106(x88891),x88894))))+~P1(f324(f324(f231(x88891),x88893),f324(f324(f83(x88891),x88892),f324(f106(x88891),x88894))))+~P1(f324(f324(f231(x88891),f324(f324(f83(x88891),x88892),f324(f106(x88891),x88894))),x88893))
% 18.77/18.51 [8928]~P90(x89281)+~P61(x89281)+~P1(f324(f324(f232(x89281),f2(x89281)),x89284))+~P1(f324(f324(f232(x89281),x89282),f324(f324(f83(x89281),x89284),f324(f106(x89281),x89283))))+~P1(f324(f324(f232(x89281),f324(f324(f83(x89281),x89284),f324(f106(x89281),x89283))),x89282))+P1(f324(f324(f232(x89281),f324(f324(f284(x89281),x89282),f324(f106(x89281),x89283))),x89284))
% 18.77/18.51 [8929]~P90(x89291)+~P61(x89291)+~P1(f324(f324(f231(x89291),f2(x89291)),x89294))+~P1(f324(f324(f231(x89291),x89292),f324(f324(f83(x89291),x89294),f324(f106(x89291),x89293))))+~P1(f324(f324(f231(x89291),f324(f324(f83(x89291),x89294),f324(f106(x89291),x89293))),x89292))+P1(f324(f324(f231(x89291),f324(f324(f284(x89291),x89292),f324(f106(x89291),x89293))),x89294))
% 18.77/18.51 [8959]~P90(x89591)+~P61(x89591)+~P1(f324(f324(f232(x89591),f324(f106(x89591),x89593)),f2(x89591)))+~P1(f324(f324(f232(x89591),x89592),f324(f324(f83(x89591),x89594),f324(f106(x89591),x89593))))+~P1(f324(f324(f232(x89591),f324(f324(f83(x89591),x89594),f324(f106(x89591),x89593))),x89592))+P1(f324(f324(f232(x89591),f324(f324(f284(x89591),x89592),f324(f106(x89591),x89593))),x89594))
% 18.77/18.51 [8960]~P90(x89601)+~P61(x89601)+~P1(f324(f324(f232(x89601),f324(f106(x89601),x89603)),f2(x89601)))+~P1(f324(f324(f231(x89601),x89602),f324(f324(f83(x89601),x89604),f324(f106(x89601),x89603))))+~P1(f324(f324(f231(x89601),f324(f324(f83(x89601),x89604),f324(f106(x89601),x89603))),x89602))+P1(f324(f324(f231(x89601),f324(f324(f284(x89601),x89602),f324(f106(x89601),x89603))),x89604))
% 18.77/18.51 [8693]~P90(x86931)+~P61(x86931)+~P1(f324(f324(f232(x86931),x86932),f2(x86931)))+~P1(f324(f324(f232(x86931),f324(f324(f284(x86931),x86934),x86932)),f324(f106(x86931),x86933)))+P1(f324(f324(f232(x86931),f2(x86931)),x86932))+P1(f324(f324(f232(x86931),f324(f324(f83(x86931),f324(f106(x86931),x86933)),x86932)),x86934))
% 18.77/18.51 [8694]~P90(x86941)+~P61(x86941)+~P1(f324(f324(f232(x86941),x86942),f2(x86941)))+~P1(f324(f324(f231(x86941),f324(f324(f284(x86941),x86944),x86942)),f324(f106(x86941),x86943)))+P1(f324(f324(f232(x86941),f2(x86941)),x86942))+P1(f324(f324(f231(x86941),f324(f324(f83(x86941),f324(f106(x86941),x86943)),x86942)),x86944))
% 18.77/18.51 [8788]~P90(x87881)+~P61(x87881)+~P1(f324(f324(f232(x87881),x87882),f2(x87881)))+P1(f324(f324(f232(x87881),f2(x87881)),x87882))+P1(f324(f324(f232(x87881),f324(f324(f284(x87881),x87883),x87882)),f324(f106(x87881),x87884)))+~P1(f324(f324(f232(x87881),f324(f324(f83(x87881),f324(f106(x87881),x87884)),x87882)),x87883))
% 18.77/18.51 [8789]~P90(x87891)+~P61(x87891)+~P1(f324(f324(f232(x87891),x87892),f2(x87891)))+P1(f324(f324(f232(x87891),f2(x87891)),x87892))+P1(f324(f324(f231(x87891),f324(f324(f284(x87891),x87893),x87892)),f324(f106(x87891),x87894)))+~P1(f324(f324(f231(x87891),f324(f324(f83(x87891),f324(f106(x87891),x87894)),x87892)),x87893))
% 18.77/18.51 [8826]~P90(x88261)+~P61(x88261)+P1(f324(f324(f232(x88261),x88262),f2(x88261)))+~P1(f324(f324(f232(x88261),f324(f106(x88261),x88263)),f2(x88261)))+P1(f324(f324(f232(x88261),f324(f106(x88261),x88263)),f324(f324(f284(x88261),x88264),x88262)))+~P1(f324(f324(f232(x88261),f324(f324(f83(x88261),f324(f106(x88261),x88263)),x88262)),x88264))
% 18.77/18.51 [8827]~P90(x88271)+~P61(x88271)+P1(f324(f324(f232(x88271),x88272),f2(x88271)))+~P1(f324(f324(f231(x88271),f324(f106(x88271),x88273)),f2(x88271)))+P1(f324(f324(f231(x88271),f324(f106(x88271),x88273)),f324(f324(f284(x88271),x88274),x88272)))+~P1(f324(f324(f231(x88271),f324(f324(f83(x88271),f324(f106(x88271),x88273)),x88272)),x88274))
% 18.77/18.51 [8842]~P90(x88421)+~P61(x88421)+P1(f324(f324(f232(x88421),f2(x88421)),x88422))+P1(f324(f324(f232(x88421),f324(f324(f284(x88421),x88423),x88422)),f324(f106(x88421),x88424)))+~P1(f324(f324(f232(x88421),f2(x88421)),f324(f106(x88421),x88424)))+~P1(f324(f324(f232(x88421),f324(f324(f83(x88421),f324(f106(x88421),x88424)),x88422)),x88423))
% 18.77/18.51 [8843]~P90(x88431)+~P61(x88431)+P1(f324(f324(f232(x88431),f2(x88431)),x88432))+P1(f324(f324(f231(x88431),f324(f324(f284(x88431),x88433),x88432)),f324(f106(x88431),x88434)))+~P1(f324(f324(f231(x88431),f2(x88431)),f324(f106(x88431),x88434)))+~P1(f324(f324(f231(x88431),f324(f324(f83(x88431),f324(f106(x88431),x88434)),x88432)),x88433))
% 18.77/18.51 [8990]~P90(x89901)+~P61(x89901)+~P1(f324(f324(f232(x89901),x89904),f2(x89901)))+P1(f324(f324(f232(x89901),f324(f106(x89901),x89902)),f324(f324(f284(x89901),x89903),x89904)))+~P1(f324(f324(f232(x89901),x89903),f324(f324(f83(x89901),f324(f106(x89901),x89902)),x89904)))+~P1(f324(f324(f232(x89901),f324(f324(f83(x89901),f324(f106(x89901),x89902)),x89904)),x89903))
% 18.77/18.51 [8991]~P90(x89911)+~P61(x89911)+~P1(f324(f324(f232(x89911),x89914),f2(x89911)))+P1(f324(f324(f231(x89911),f324(f106(x89911),x89912)),f324(f324(f284(x89911),x89913),x89914)))+~P1(f324(f324(f231(x89911),x89913),f324(f324(f83(x89911),f324(f106(x89911),x89912)),x89914)))+~P1(f324(f324(f231(x89911),f324(f324(f83(x89911),f324(f106(x89911),x89912)),x89914)),x89913))
% 18.77/18.51 [9020]~P90(x90201)+~P61(x90201)+~P1(f324(f324(f232(x90201),x90203),f2(x90201)))+P1(f324(f324(f232(x90201),f324(f324(f284(x90201),x90202),x90203)),f324(f106(x90201),x90204)))+~P1(f324(f324(f232(x90201),x90202),f324(f324(f83(x90201),f324(f106(x90201),x90204)),x90203)))+~P1(f324(f324(f232(x90201),f324(f324(f83(x90201),f324(f106(x90201),x90204)),x90203)),x90202))
% 18.77/18.51 [9021]~P90(x90211)+~P61(x90211)+~P1(f324(f324(f232(x90211),x90213),f2(x90211)))+P1(f324(f324(f231(x90211),f324(f324(f284(x90211),x90212),x90213)),f324(f106(x90211),x90214)))+~P1(f324(f324(f231(x90211),x90212),f324(f324(f83(x90211),f324(f106(x90211),x90214)),x90213)))+~P1(f324(f324(f231(x90211),f324(f324(f83(x90211),f324(f106(x90211),x90214)),x90213)),x90212))
% 18.77/18.51 [9039]~P90(x90391)+~P61(x90391)+~P1(f324(f324(f232(x90391),f324(f106(x90391),x90392)),f2(x90391)))+P1(f324(f324(f232(x90391),f324(f106(x90391),x90392)),f324(f324(f284(x90391),x90393),x90394)))+~P1(f324(f324(f232(x90391),x90393),f324(f324(f83(x90391),f324(f106(x90391),x90392)),x90394)))+~P1(f324(f324(f232(x90391),f324(f324(f83(x90391),f324(f106(x90391),x90392)),x90394)),x90393))
% 18.77/18.51 [9040]~P90(x90401)+~P61(x90401)+~P1(f324(f324(f231(x90401),f324(f106(x90401),x90402)),f2(x90401)))+P1(f324(f324(f231(x90401),f324(f106(x90401),x90402)),f324(f324(f284(x90401),x90403),x90404)))+~P1(f324(f324(f231(x90401),x90403),f324(f324(f83(x90401),f324(f106(x90401),x90402)),x90404)))+~P1(f324(f324(f231(x90401),f324(f324(f83(x90401),f324(f106(x90401),x90402)),x90404)),x90403))
% 18.77/18.51 [9045]~P90(x90451)+~P61(x90451)+P1(f324(f324(f232(x90451),f324(f324(f284(x90451),x90452),x90453)),f324(f106(x90451),x90454)))+~P1(f324(f324(f232(x90451),f2(x90451)),f324(f106(x90451),x90454)))+~P1(f324(f324(f232(x90451),x90452),f324(f324(f83(x90451),f324(f106(x90451),x90454)),x90453)))+~P1(f324(f324(f232(x90451),f324(f324(f83(x90451),f324(f106(x90451),x90454)),x90453)),x90452))
% 18.77/18.51 [9046]~P90(x90461)+~P61(x90461)+P1(f324(f324(f231(x90461),f324(f324(f284(x90461),x90462),x90463)),f324(f106(x90461),x90464)))+~P1(f324(f324(f231(x90461),f2(x90461)),f324(f106(x90461),x90464)))+~P1(f324(f324(f231(x90461),x90462),f324(f324(f83(x90461),f324(f106(x90461),x90464)),x90463)))+~P1(f324(f324(f231(x90461),f324(f324(f83(x90461),f324(f106(x90461),x90464)),x90463)),x90462))
% 18.77/18.51 [5870]~P120(x58702)+~P105(x58702)+~E(f324(x58703,x58705),f2(x58702))+E(f324(f324(f11(x58701,x58702),x58703),x58704),f2(x58702))+~P1(f324(f64(x58701),x58704))+~P1(f324(f324(f326(x58701),x58705),x58704))
% 18.77/18.51 [8289]~P85(x82891)+P1(f324(f324(f232(f845(x82891,a832)),f296(x82891,x82892,x82893)),f296(x82891,x82894,x82895)))+~P1(f324(f324(f232(x82891),x82893),x82895))+~P1(f324(f324(f231(x82891),x82894),x82892))+~P1(f324(f324(f231(x82891),x82894),x82895))+~P1(f324(f324(f231(x82891),x82893),x82895))
% 18.77/18.51 [8290]~P85(x82901)+P1(f324(f324(f232(f845(x82901,a832)),f296(x82901,x82902,x82903)),f296(x82901,x82904,x82905)))+~P1(f324(f324(f232(x82901),x82904),x82902))+~P1(f324(f324(f231(x82901),x82903),x82905))+~P1(f324(f324(f231(x82901),x82904),x82905))+~P1(f324(f324(f231(x82901),x82904),x82902))
% 18.77/18.51 [9066]P56(x90662,x90663,x90664,x90661)+E(x90661,f179(f845(x90662,a832)))+~P1(f324(f64(x90662),x90664))+~P1(f324(f64(x90662),x90661))+~P1(f324(f324(x90663,f563(x90661,x90664,x90663,x90662)),x90665))+~P1(f324(f324(f326(x90662),x90665),x90661))
% 18.77/18.51 [9196]~E(x91963,x91965)+~P67(x91961)+~P68(x91961)+~P38(x91963)+E(f324(f324(f11(a1,x91961),x91962),x91963),f324(f324(f11(a1,x91961),x91964),x91965))+P1(f324(f324(f231(a1),f2(a1)),f509(x91962,x91964,x91963,x91965,x91961)))
% 18.77/18.51 [9197]~E(x91973,x91975)+~P67(x91971)+~P68(x91971)+~P38(x91973)+E(f324(f324(f8(a1,x91971),x91972),x91973),f324(f324(f8(a1,x91971),x91974),x91975))+P1(f324(f324(f231(a1),f2(a1)),f558(x91972,x91974,x91973,x91975,x91971)))
% 18.77/18.51 [9362]~E(x93625,x93623)+~P67(x93621)+~P68(x93621)+~P38(x93625)+~E(f324(x93622,f509(x93624,x93622,x93625,x93623,x93621)),f324(x93624,f509(x93624,x93622,x93625,x93623,x93621)))+E(f324(f324(f11(a1,x93621),x93622),x93623),f324(f324(f11(a1,x93621),x93624),x93625))
% 18.77/18.51 [9363]~E(x93635,x93633)+~P67(x93631)+~P68(x93631)+~P38(x93635)+~E(f324(x93632,f558(x93634,x93632,x93635,x93633,x93631)),f324(x93634,f558(x93634,x93632,x93635,x93633,x93631)))+E(f324(f324(f8(a1,x93631),x93632),x93633),f324(f324(f8(a1,x93631),x93634),x93635))
% 18.77/18.51 [9450]~P70(x94503)+E(f324(x94501,x94502),f2(x94503))+~E(f324(f324(f8(x94504,x94503),x94501),x94505),f2(x94503))+~P1(f324(f64(x94504),x94505))+P1(f324(f324(f326(x94504),f503(x94502,x94501,x94505,x94504,x94503)),x94505))+~P1(f324(f324(f326(x94504),x94502),x94505))
% 18.77/18.51 [9574]~P70(x95743)+E(f324(x95741,x95742),f2(x95743))+~E(f324(f324(f8(x95744,x95743),x95741),x95745),f2(x95743))+~P1(f324(f64(x95744),x95745))+~P1(f324(f324(f326(x95744),x95742),x95745))+~P1(f324(f324(f231(x95743),f2(x95743)),f324(x95741,f503(x95742,x95741,x95745,x95744,x95743))))
% 18.77/18.51 [8203]~P122(x82031)+~P1(f324(f324(f231(x82031),f2(x82031)),x82033))+~P1(f324(f324(f232(x82031),x82033),x82035))+~P1(f324(f324(f232(x82031),x82032),x82034))+~P1(f324(f324(f232(x82031),f2(x82031)),x82034))+P1(f324(f324(f232(x82031),f324(f324(f83(x82031),x82032),x82033)),f324(f324(f83(x82031),x82034),x82035)))
% 18.77/18.51 [8204]~P122(x82041)+~P1(f324(f324(f231(x82041),f2(x82041)),x82043))+~P1(f324(f324(f231(x82041),f2(x82041)),x82042))+~P1(f324(f324(f232(x82041),x82043),x82045))+~P1(f324(f324(f232(x82041),x82042),x82044))+P1(f324(f324(f232(x82041),f324(f324(f83(x82041),x82042),x82043)),f324(f324(f83(x82041),x82044),x82045)))
% 18.77/18.51 [8205]~P122(x82051)+~P1(f324(f324(f231(x82051),x82052),x82054))+~P1(f324(f324(f231(x82051),f2(x82051)),x82053))+~P1(f324(f324(f232(x82051),x82053),x82055))+~P1(f324(f324(f232(x82051),f2(x82051)),x82052))+P1(f324(f324(f232(x82051),f324(f324(f83(x82051),x82052),x82053)),f324(f324(f83(x82051),x82054),x82055)))
% 18.77/18.51 [8206]~P122(x82061)+~P1(f324(f324(f231(x82061),x82063),x82065))+~P1(f324(f324(f231(x82061),f2(x82061)),x82062))+~P1(f324(f324(f232(x82061),x82062),x82064))+~P1(f324(f324(f232(x82061),f2(x82061)),x82063))+P1(f324(f324(f232(x82061),f324(f324(f83(x82061),x82062),x82063)),f324(f324(f83(x82061),x82064),x82065)))
% 18.77/18.51 [8207]~P62(x82071)+~P1(f324(f324(f231(x82071),x82072),x82074))+~P1(f324(f324(f232(x82071),x82075),x82073))+~P1(f324(f324(f232(x82071),f2(x82071)),x82075))+~P1(f324(f324(f232(x82071),f2(x82071)),x82072))+P1(f324(f324(f232(x82071),f324(f324(f284(x82071),x82072),x82073)),f324(f324(f284(x82071),x82074),x82075)))
% 18.77/18.51 [8208]~P62(x82081)+~P1(f324(f324(f231(x82081),x82085),x82083))+~P1(f324(f324(f231(x82081),f2(x82081)),x82082))+~P1(f324(f324(f232(x82081),x82082),x82084))+~P1(f324(f324(f232(x82081),f2(x82081)),x82085))+P1(f324(f324(f232(x82081),f324(f324(f284(x82081),x82082),x82083)),f324(f324(f284(x82081),x82084),x82085)))
% 18.77/18.51 [8209]~P130(x82091)+~P1(f324(f324(f231(x82091),x82093),x82095))+~P1(f324(f324(f231(x82091),x82092),x82094))+~P1(f324(f324(f231(x82091),f2(x82091)),x82093))+~P1(f324(f324(f231(x82091),f2(x82091)),x82094))+P1(f324(f324(f231(x82091),f324(f324(f83(x82091),x82092),x82093)),f324(f324(f83(x82091),x82094),x82095)))
% 18.77/18.51 [8210]~P130(x82101)+~P1(f324(f324(f231(x82101),x82103),x82105))+~P1(f324(f324(f231(x82101),x82102),x82104))+~P1(f324(f324(f231(x82101),f2(x82101)),x82103))+~P1(f324(f324(f231(x82101),f2(x82101)),x82102))+P1(f324(f324(f231(x82101),f324(f324(f83(x82101),x82102),x82103)),f324(f324(f83(x82101),x82104),x82105)))
% 18.77/18.51 [8211]~P62(x82111)+~P1(f324(f324(f232(x82111),f2(x82111)),x82115))+~P1(f324(f324(f231(x82111),x82115),x82113))+~P1(f324(f324(f231(x82111),x82112),x82114))+~P1(f324(f324(f231(x82111),f2(x82111)),x82112))+P1(f324(f324(f231(x82111),f324(f324(f284(x82111),x82112),x82113)),f324(f324(f284(x82111),x82114),x82115)))
% 18.77/18.51 [9488]~P67(x94885)+~P79(x94885)+E(x94881,f179(f845(x94882,a832)))+~P1(f324(f64(x94882),x94881))+P1(f324(f324(f326(x94882),f510(x94883,x94884,x94881,x94882,x94885)),x94881))+P1(f324(f324(f232(x94885),f324(f324(f8(x94882,x94885),x94884),x94881)),f324(f324(f8(x94882,x94885),x94883),x94881)))
% 18.77/18.51 [9595]~P77(x95951)+~P67(x95951)+~P1(f324(f64(x95952),x95955))+~P1(f324(f324(f231(x95951),f2(x95951)),f324(x95953,f504(x95953,x95954,x95955,x95952,x95951))))+P1(f324(f324(f231(x95951),f324(f324(f8(x95952,x95951),x95953),x95954)),f324(f324(f8(x95952,x95951),x95953),x95955)))+~P1(f324(f324(f231(f845(x95952,a832)),x95954),x95955))
% 18.77/18.51 [9763]~P67(x97633)+~P79(x97633)+E(x97631,f179(f845(x97632,a832)))+~P1(f324(f64(x97632),x97631))+~P1(f324(f324(f232(x97633),f324(x97634,f510(x97635,x97634,x97631,x97632,x97633))),f324(x97635,f510(x97635,x97634,x97631,x97632,x97633))))+P1(f324(f324(f232(x97633),f324(f324(f8(x97632,x97633),x97634),x97631)),f324(f324(f8(x97632,x97633),x97635),x97631)))
% 18.77/18.51 [6903]~P21(x69032,x69035,x69034)+E(x69031,f179(f845(x69032,a832)))+E(x69033,f179(f845(x69032,a832)))+~P1(f324(f64(x69032),x69031))+~P1(f324(f64(x69032),x69033))+E(f324(x69034,f324(f324(f103(f845(x69032,a832)),x69033),x69031)),f324(f324(x69035,f324(x69034,x69033)),f324(x69034,x69031)))
% 18.77/18.51 [7514]~P140(x75141,x75143,x75144)+P1(f324(x75141,x75142))+~P1(f324(f324(f232(a1),x75144),f2(a1)))+~P1(f324(f324(f231(a1),x75145),f2(a1)))+~E(x75143,f324(f324(f82(a1),f324(f324(f83(a1),x75144),x75142)),x75145))+~P1(f324(f324(f232(a1),x75144),x75145))
% 18.77/18.51 [7515]~P139(x75151,x75153,x75154)+P1(f324(x75151,x75152))+~P1(f324(f324(f232(a1),x75154),f2(a1)))+~P1(f324(f324(f231(a1),x75152),f2(a1)))+~E(x75153,f324(f324(f82(a1),f324(f324(f83(a1),x75154),x75155)),x75152))+~P1(f324(f324(f232(a1),x75154),x75152))
% 18.77/18.51 [7558]~P140(x75581,x75583,x75584)+P1(f324(x75581,x75582))+~E(x75583,f324(f324(f82(a1),f324(f324(f83(a1),x75584),x75582)),x75585))+~P1(f324(f324(f232(a1),f2(a1)),x75584))+~P1(f324(f324(f231(a1),f2(a1)),x75585))+~P1(f324(f324(f232(a1),x75585),x75584))
% 18.77/18.51 [7559]~P139(x75591,x75593,x75594)+P1(f324(x75591,x75592))+~E(x75593,f324(f324(f82(a1),f324(f324(f83(a1),x75594),x75595)),x75592))+~P1(f324(f324(f232(a1),f2(a1)),x75594))+~P1(f324(f324(f231(a1),f2(a1)),x75592))+~P1(f324(f324(f232(a1),x75592),x75594))
% 18.77/18.51 [8492]P1(f324(f324(x84921,x84922),x84923))+~P1(f324(f324(x84921,f324(f324(f42(a1),x84924),x84925)),f51(a1,x84924,x84925)))+~P1(f324(f324(f232(a1),x84925),f2(a1)))+~P1(f324(f324(f231(a1),x84923),f2(a1)))+~E(x84924,f324(f324(f82(a1),f324(f324(f83(a1),x84925),x84922)),x84923))+~P1(f324(f324(f232(a1),x84925),x84923))
% 18.77/18.51 [8499]P1(f324(f324(x84991,x84992),x84993))+~P1(f324(f324(x84991,f324(f324(f42(a1),x84994),x84995)),f51(a1,x84994,x84995)))+~E(x84994,f324(f324(f82(a1),f324(f324(f83(a1),x84995),x84992)),x84993))+~P1(f324(f324(f232(a1),f2(a1)),x84995))+~P1(f324(f324(f231(a1),f2(a1)),x84993))+~P1(f324(f324(f232(a1),x84993),x84995))
% 18.77/18.51 [8722]E(x87221,x87222)+~P53(x87223,x87225,x87224)+~P1(f324(f324(f326(x87223),x87222),x87225))+~P1(f324(f324(f326(x87223),x87221),x87225))+P1(f324(f324(f326(f844(x87223,x87223)),f324(f324(f247(x87223,x87223),x87221),x87222)),x87224))+P1(f324(f324(f326(f844(x87223,x87223)),f324(f324(f247(x87223,x87223),x87222),x87221)),x87224))
% 18.77/18.51 [9518]~P77(x95185)+~P67(x95185)+~P1(f324(f64(x95181),x95184))+P1(f324(f324(f231(x95185),f324(f324(f8(x95181,x95185),x95182),x95183)),f324(f324(f8(x95181,x95185),x95182),x95184)))+~P1(f324(f324(f231(f845(x95181,a832)),x95183),x95184))+P1(f324(f324(f326(x95181),f504(x95182,x95183,x95184,x95181,x95185)),f324(f324(f3(f845(x95181,a832)),x95184),x95183)))
% 18.77/18.51 [9603]E(x96031,f179(f845(x96032,a832)))+~P1(f324(f64(x96032),x96033))+~P1(f324(f64(x96032),x96031))+P1(f324(f324(f326(f844(f845(x96032,a832),f845(x96032,a832))),f324(f324(f247(f845(x96032,a832),f845(x96032,a832)),x96033),x96031)),f317(x96032,x96034)))+~P1(f324(f324(f326(x96032),x96035),x96031))+~P1(f324(f324(f326(f844(x96032,x96032)),f324(f324(f247(x96032,x96032),f565(x96034,x96031,x96033,x96032)),x96035)),x96034))
% 18.77/18.51 [9604]E(x96041,f179(f845(x96042,a832)))+~P1(f324(f64(x96042),x96043))+~P1(f324(f64(x96042),x96041))+P1(f324(f324(f326(f844(f845(x96042,a832),f845(x96042,a832))),f324(f324(f247(f845(x96042,a832),f845(x96042,a832)),x96043),x96041)),f317(x96042,x96044)))+~P1(f324(f324(f326(x96042),x96045),x96041))+~P1(f324(f324(f326(f844(x96042,x96042)),f324(f324(f247(x96042,x96042),f647(x96044,x96041,x96043,x96042)),x96045)),x96044))
% 18.77/18.51 [9765]~P70(x97651)+~E(f324(f324(f8(x97655,x97651),x97652),x97656),x97654)+~P1(f324(f64(x97655),x97656))+P1(f324(f324(f326(x97655),f505(x97653,x97654,x97652,x97656,x97655,x97651)),x97656))+P1(f324(f324(f231(x97651),f324(x97652,x97653)),x97654))+~P1(f324(f324(f326(x97655),x97653),x97656))
% 18.77/18.51 [9819]~P70(x98191)+~E(f324(f324(f8(x98195,x98191),x98192),x98196),x98194)+~P1(f324(f64(x98195),x98196))+~P1(f324(f324(f326(x98195),x98193),x98196))+~P1(f324(f324(f231(x98191),f2(x98191)),f324(x98192,f505(x98193,x98194,x98192,x98196,x98195,x98191))))+P1(f324(f324(f231(x98191),f324(x98192,x98193)),x98194))
% 18.77/18.51 [9934]~E(x99345,x99348)+~E(x99344,x99347)+~P101(x99341)+~P67(x99342)+E(f324(f324(f8(x99341,x99342),x99343),f324(f295(x99341,x99344),x99345)),f324(f324(f8(x99341,x99342),x99346),f324(f295(x99341,x99347),x99348)))+P1(f324(f324(f231(x99341),x99344),f660(x99343,x99346,x99345,x99348,x99344,x99347,x99341,x99342)))
% 18.77/18.51 [9951]~E(x99517,x99514)+~E(x99518,x99515)+~P101(x99511)+~P67(x99512)+~E(f324(x99513,f660(x99516,x99513,x99518,x99515,x99517,x99514,x99511,x99512)),f324(x99516,f660(x99516,x99513,x99518,x99515,x99517,x99514,x99511,x99512)))+E(f324(f324(f8(x99511,x99512),x99513),f324(f295(x99511,x99514),x99515)),f324(f324(f8(x99511,x99512),x99516),f324(f295(x99511,x99517),x99518)))
% 18.77/18.51 [9954]~E(x99544,x99547)+~E(x99545,x99548)+~P101(x99541)+~P67(x99542)+E(f324(f324(f8(x99541,x99542),x99543),f324(f295(x99541,x99544),x99545)),f324(f324(f8(x99541,x99542),x99546),f324(f295(x99541,x99547),x99548)))+P1(f324(f324(f232(x99541),f660(x99543,x99546,x99545,x99548,x99544,x99547,x99541,x99542)),x99545))
% 18.77/18.51 [9608]~P12(x96085,x96089,x96086)+~P12(x96081,x960810,x96083)+~P17(x96081,x96085,f845(x96082,a832),x96083,x96086,x96088)+~P1(f324(f324(f326(x96085),x96087),x96089))+~P1(f324(f324(f326(x96081),x96084),x960810))+E(f324(f324(f45(x96081,f845(x96082,a832)),f324(f278(x96081,x96081,x96083),f324(f324(f303(x96081),x96084),f179(f845(x96081,a832))))),f324(f324(f10(f845(x96085,f845(x96082,a832)),f845(x96082,a832),x96081),f324(f45(x96085,f845(x96082,a832)),f324(f278(x96085,x96085,x96086),f324(f324(f303(x96085),x96087),f179(f845(x96085,a832)))))),x96088)),f324(f324(x96088,x96084),x96087))
% 18.77/18.51 [5393]~P86(x53933)+~P18(x53933,x53932)+~P18(x53933,x53931)+E(x53931,x53932)+~E(f324(f157(x53933),x53931),f324(f157(x53933),x53932))+~P1(f324(f127(x53933),x53932))+~P1(f324(f127(x53933),x53931))
% 18.77/18.51 [4749]~P120(x47492)+~P121(x47492)+~P137(x47492)+~P108(x47492)+~E(x47493,f2(x47492))+E(x47491,f2(a838))+E(f324(f324(f240(x47492),x47493),x47491),f2(x47492))
% 18.77/18.51 [8954]E(x89541,f2(a838))+~E(x89542,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x89543)),x89541)),f324(f251(a838,a838),x89543)))+P1(f324(f54(x89542,x89541),x89543))+~P1(f324(f324(f231(a838),f324(f251(a838,a838),x89543)),f2(a838)))+~P1(f324(f324(f231(a838),f2(a838)),f324(f251(a838,a838),x89543)))+~P1(f324(f324(f232(a838),x89541),f324(f251(a838,a838),x89543)))+~P1(f324(f324(f232(a838),f324(f251(a838,a838),x89543)),x89541))
% 18.77/18.51 [8962]~E(f324(f246(a838,a838),x89623),f2(a838))+~E(x89621,f324(f324(f82(a838),f324(f324(f83(a838),f324(f246(a838,a838),x89623)),x89622)),f324(f251(a838,a838),x89623)))+P1(f324(f54(x89621,x89622),x89623))+~P1(f324(f324(f231(a838),f324(f251(a838,a838),x89623)),f2(a838)))+~P1(f324(f324(f231(a838),f2(a838)),f324(f251(a838,a838),x89623)))+~P1(f324(f324(f232(a838),x89622),f324(f251(a838,a838),x89623)))+~P1(f324(f324(f232(a838),f324(f251(a838,a838),x89623)),x89622))
% 18.77/18.51 [7392]~P94(x73922)+E(x73921,f179(f845(x73922,a832)))+E(x73923,f179(f845(x73922,a832)))+~P1(f324(f64(x73922),x73921))+~P1(f324(f64(x73922),x73923))+~E(f324(f324(f104(f845(x73922,a832)),x73923),x73921),f179(f845(x73922,a832)))+E(f12(x73922,f324(f324(f103(f845(x73922,a832)),x73923),x73921)),f324(f324(f104(x73922),f12(x73922,x73923)),f12(x73922,x73921)))
% 18.77/18.51 [7393]~P86(x73932)+E(x73931,f179(f845(x73932,a832)))+E(x73933,f179(f845(x73932,a832)))+~P1(f324(f64(x73932),x73931))+~P1(f324(f64(x73932),x73933))+~E(f324(f324(f104(f845(x73932,a832)),x73933),x73931),f179(f845(x73932,a832)))+E(f16(x73932,f324(f324(f103(f845(x73932,a832)),x73933),x73931)),f324(f324(f178(x73932),f16(x73932,x73933)),f16(x73932,x73931)))
% 18.77/18.51 [7394]~P86(x73942)+E(x73941,f179(f845(x73942,a832)))+E(x73943,f179(f845(x73942,a832)))+~P1(f324(f64(x73942),x73941))+~P1(f324(f64(x73942),x73943))+~E(f324(f324(f104(f845(x73942,a832)),x73943),x73941),f179(f845(x73942,a832)))+E(f17(x73942,f324(f324(f103(f845(x73942,a832)),x73943),x73941)),f324(f324(f235(x73942),f17(x73942,x73943)),f17(x73942,x73941)))
% 18.77/18.51 [7395]~P94(x73952)+E(x73951,f179(f845(x73952,a832)))+E(x73953,f179(f845(x73952,a832)))+~P1(f324(f64(x73952),x73951))+~P1(f324(f64(x73952),x73953))+~E(f324(f324(f104(f845(x73952,a832)),x73953),x73951),f179(f845(x73952,a832)))+E(f15(x73952,f324(f324(f103(f845(x73952,a832)),x73953),x73951)),f324(f324(f103(x73952),f15(x73952,x73953)),f15(x73952,x73951)))
% 18.77/18.51 [7877]~P4(x78772)+E(x78771,f179(f845(x78772,a832)))+E(x78773,f179(f845(x78772,a832)))+~P1(f324(f64(x78772),x78771))+~P1(f324(f64(x78772),x78773))+~E(f324(f324(f104(f845(x78772,a832)),x78773),x78771),f179(f845(x78772,a832)))+E(f324(f324(f83(x78772),f324(f66(x78772,f83(x78772)),x78773)),f324(f66(x78772,f83(x78772)),x78771)),f324(f66(x78772,f83(x78772)),f324(f324(f103(f845(x78772,a832)),x78773),x78771)))
% 18.77/18.51 [7949]~P86(x79492)+E(x79491,f179(f845(x79492,a832)))+E(x79493,f179(f845(x79492,a832)))+~P1(f324(f64(x79492),x79491))+~P1(f324(f64(x79492),x79493))+~E(f324(f324(f104(f845(x79492,a832)),x79493),x79491),f179(f845(x79492,a832)))+E(f324(f324(f178(x79492),f13(x79492,f178(x79492),x79493)),f13(x79492,f178(x79492),x79491)),f13(x79492,f178(x79492),f324(f324(f103(f845(x79492,a832)),x79493),x79491)))
% 18.77/18.51 [7950]~P86(x79502)+E(x79501,f179(f845(x79502,a832)))+E(x79503,f179(f845(x79502,a832)))+~P1(f324(f64(x79502),x79501))+~P1(f324(f64(x79502),x79503))+~E(f324(f324(f104(f845(x79502,a832)),x79503),x79501),f179(f845(x79502,a832)))+E(f324(f324(f235(x79502),f14(x79502,f235(x79502),x79503)),f14(x79502,f235(x79502),x79501)),f14(x79502,f235(x79502),f324(f324(f103(f845(x79502,a832)),x79503),x79501)))
% 18.77/18.51 [7653]E(x76531,f2(a1))+E(f324(f324(f42(a1),x76532),x76531),x76533)+~P1(f324(f324(f231(a1),x76534),f2(a1)))+~E(x76532,f324(f324(f82(a1),f324(f324(f83(a1),x76531),x76533)),x76534))+~P1(f324(f324(f231(a1),f2(a1)),x76534))+~P1(f324(f324(f232(a1),x76534),x76531))+~P1(f324(f324(f232(a1),x76531),x76534))
% 18.77/18.51 [7659]E(f51(a1,x76592,x76591),x76593)+E(x76591,f2(a1))+~P1(f324(f324(f231(a1),x76593),f2(a1)))+~E(x76592,f324(f324(f82(a1),f324(f324(f83(a1),x76591),x76594)),x76593))+~P1(f324(f324(f231(a1),f2(a1)),x76593))+~P1(f324(f324(f232(a1),x76593),x76591))+~P1(f324(f324(f232(a1),x76591),x76593))
% 18.77/18.51 [6674]~P7(x66742)+E(x66741,f2(x66742))+E(x66743,f2(x66742))+~E(f324(f324(f42(x66742),x66744),x66743),f324(f324(f42(x66742),x66745),x66741))+E(f324(f324(f83(x66742),x66744),x66741),f324(f324(f83(x66742),x66743),x66745))+~P1(f324(f324(f280(x66742),x66741),x66745))+~P1(f324(f324(f280(x66742),x66743),x66744))
% 18.77/18.51 [6675]~P7(x66752)+E(x66751,f2(x66752))+E(x66753,f2(x66752))+~E(f324(f324(f83(x66752),x66754),x66753),f324(f324(f83(x66752),x66751),x66755))+E(f324(f324(f42(x66752),x66754),x66751),f324(f324(f42(x66752),x66755),x66753))+~P1(f324(f324(f280(x66752),x66751),x66754))+~P1(f324(f324(f280(x66752),x66753),x66755))
% 18.77/18.51 [7567]~P22(x75672,x75675,x75674)+E(x75671,f179(f845(x75672,a832)))+E(x75673,f179(f845(x75672,a832)))+~P1(f324(f64(x75672),x75671))+~P1(f324(f64(x75672),x75673))+~E(f324(f324(f104(f845(x75672,a832)),x75673),x75671),f179(f845(x75672,a832)))+E(f324(x75674,f324(f324(f103(f845(x75672,a832)),x75673),x75671)),f324(f324(x75675,f324(x75674,x75673)),f324(x75674,x75671)))
% 18.77/18.51 [9168]~P29(x91683,x91681,x91685,x91684)+~P29(x91681,x91683,x91686,x91682)+E(f324(f41(x91681),x91682),f324(f41(x91683),x91684))+~P1(f324(f64(x91683),x91684))+~P1(f324(f64(x91681),x91682))+~P1(f324(f324(f231(f845(x91683,a832)),f324(f304(x91681,x91683,x91686),x91682)),x91684))+~P1(f324(f324(f231(f845(x91681,a832)),f324(f304(x91683,x91681,x91685),x91684)),x91682))
% 18.77/18.51 [9116]~P1(f324(f324(f232(a1),f324(f324(f82(a1),f324(f324(f83(a1),x91165),x91161)),x91166)),f2(a1)))+~E(f324(f324(f82(a1),f324(f324(f83(a1),x91163),x91162)),x91164),f324(f324(f82(a1),f324(f324(f83(a1),x91165),x91161)),x91166))+~P1(f324(f324(f232(a1),f2(a1)),x91165))+~P1(f324(f324(f231(a1),f2(a1)),x91166))+~P1(f324(f324(f232(a1),x91164),x91163))+~P1(f324(f324(f231(a1),x91165),x91163))+P1(f324(f324(f231(a1),x91161),x91162))
% 18.77/18.51 [8911]~E(f324(f324(f82(a1),f324(f324(f83(a1),x89113),x89111)),x89114),f324(f324(f82(a1),f324(f324(f83(a1),x89115),x89112)),x89116))+~P1(f324(f324(f232(a1),f2(a1)),x89115))+~P1(f324(f324(f231(a1),f2(a1)),x89114))+~P1(f324(f324(f232(a1),x89116),x89115))+~P1(f324(f324(f231(a1),x89115),x89113))+P1(f324(f324(f231(a1),x89111),x89112))+~P1(f324(f324(f231(a1),f2(a1)),f324(f324(f82(a1),f324(f324(f83(a1),x89115),x89112)),x89116)))
% 18.77/18.51 [9068]~P125(x90681)+~E(f324(f324(f82(x90681),x90682),x90684),f80(x90681))+~P1(f324(f324(f231(x90681),f2(x90681)),x90684))+~P1(f324(f324(f231(x90681),f2(x90681)),x90682))+~P1(f324(f324(f232(x90681),x90685),x90686))+~P1(f324(f324(f232(x90681),x90683),x90686))+P1(f324(f324(f232(x90681),f324(f324(f82(x90681),f324(f324(f83(x90681),x90682),x90683)),f324(f324(f83(x90681),x90684),x90685))),x90686))
% 18.77/18.51 [9069]~P124(x90691)+~E(f324(f324(f82(x90691),x90692),x90694),f80(x90691))+~P1(f324(f324(f231(x90691),x90695),x90696))+~P1(f324(f324(f231(x90691),x90693),x90696))+~P1(f324(f324(f231(x90691),f2(x90691)),x90694))+~P1(f324(f324(f231(x90691),f2(x90691)),x90692))+P1(f324(f324(f231(x90691),f324(f324(f82(x90691),f324(f324(f83(x90691),x90692),x90693)),f324(f324(f83(x90691),x90694),x90695))),x90696))
% 18.77/18.51 [9861]~P12(x98617,x98616,x98615)+E(x98611,x98612)+~P16(x98617,f845(x98614,a832),x98615,x98613)+E(f324(x98613,f543(x98611,x98612,x98613,x98614,x98615,x98616,x98617)),f324(x98613,f538(x98611,x98612,x98613,x98614,x98615,x98616,x98617)))+~E(f324(f324(f45(x98617,f845(x98614,a832)),x98611),x98613),f324(f324(f45(x98617,f845(x98614,a832)),x98612),x98613))+~P1(f324(f324(f326(f845(x98617,a832)),x98612),f324(f324(f63(x98617),x98616),x98615)))+~P1(f324(f324(f326(f845(x98617,a832)),x98611),f324(f324(f63(x98617),x98616),x98615)))
% 18.77/18.51 [9900]~P12(x99003,x99007,x99006)+E(x99001,x99002)+~P16(x99003,f845(x99005,a832),x99006,x99004)+~E(f324(f324(f45(x99003,f845(x99005,a832)),x99001),x99004),f324(f324(f45(x99003,f845(x99005,a832)),x99002),x99004))+P1(f324(f324(f326(x99003),f538(x99001,x99002,x99004,x99005,x99006,x99007,x99003)),x99007))+~P1(f324(f324(f326(f845(x99003,a832)),x99002),f324(f324(f63(x99003),x99007),x99006)))+~P1(f324(f324(f326(f845(x99003,a832)),x99001),f324(f324(f63(x99003),x99007),x99006)))
% 18.77/18.51 [9901]~P12(x99013,x99017,x99016)+E(x99011,x99012)+~P16(x99013,f845(x99015,a832),x99016,x99014)+~E(f324(f324(f45(x99013,f845(x99015,a832)),x99011),x99014),f324(f324(f45(x99013,f845(x99015,a832)),x99012),x99014))+P1(f324(f324(f326(x99013),f543(x99011,x99012,x99014,x99015,x99016,x99017,x99013)),x99017))+~P1(f324(f324(f326(f845(x99013,a832)),x99012),f324(f324(f63(x99013),x99017),x99016)))+~P1(f324(f324(f326(f845(x99013,a832)),x99011),f324(f324(f63(x99013),x99017),x99016)))
% 18.77/18.51 [9969]E(x99691,x99692)+~P12(x99693,x99696,x99697)+~P16(x99693,f845(x99694,a832),x99697,x99695)+~E(f324(f324(f45(x99693,f845(x99694,a832)),x99691),x99695),f324(f324(f45(x99693,f845(x99694,a832)),x99692),x99695))+~P1(f324(f324(f326(f844(x99693,x99693)),f324(f324(f247(x99693,x99693),f538(x99691,x99692,x99695,x99694,x99697,x99696,x99693)),f543(x99691,x99692,x99695,x99694,x99697,x99696,x99693))),x99697))+~P1(f324(f324(f326(f845(x99693,a832)),x99692),f324(f324(f63(x99693),x99696),x99697)))+~P1(f324(f324(f326(f845(x99693,a832)),x99691),f324(f324(f63(x99693),x99696),x99697)))
% 18.77/18.51 [8910]~P12(x89101,x89107,x89104)+~E(x89105,x89106)+~P1(f324(f324(f326(x89101),x89103),x89106))+~P1(f324(f324(f326(x89101),x89102),x89105))+~P1(f324(f324(f326(f845(x89101,a832)),x89106),f324(f324(f63(x89101),x89107),x89104)))+~P1(f324(f324(f326(f845(x89101,a832)),x89105),f324(f324(f63(x89101),x89107),x89104)))+P1(f324(f324(f326(f844(x89101,x89101)),f324(f324(f247(x89101,x89101),x89102),x89103)),x89104))
% 18.77/18.51 [9034]E(x90341,x90342)+~P12(x90343,x90344,x90345)+~P1(f324(f324(f326(x90343),x90346),x90342))+~P1(f324(f324(f326(x90343),x90347),x90341))+~P1(f324(f324(f326(f845(x90343,a832)),x90342),f324(f324(f63(x90343),x90344),x90345)))+~P1(f324(f324(f326(f845(x90343,a832)),x90341),f324(f324(f63(x90343),x90344),x90345)))+~P1(f324(f324(f326(f844(x90343,x90343)),f324(f324(f247(x90343,x90343),x90347),x90346)),x90345))
% 18.77/18.51 [9035]E(x90351,x90352)+~P12(x90353,x90354,x90355)+~P1(f324(f324(f326(x90353),x90356),x90352))+~P1(f324(f324(f326(x90353),x90357),x90351))+~P1(f324(f324(f326(f845(x90353,a832)),x90352),f324(f324(f63(x90353),x90354),x90355)))+~P1(f324(f324(f326(f845(x90353,a832)),x90351),f324(f324(f63(x90353),x90354),x90355)))+~P1(f324(f324(f326(f844(x90353,x90353)),f324(f324(f247(x90353,x90353),x90357),x90356)),x90355))
% 18.77/18.51 [9987]~P12(x99879,x99878,x99877)+~P12(x99871,x998711,x998710)+~P17(x99871,x99879,f845(x99876,a832),x998710,x99877,x99875)+P1(f324(f324(f326(x99871),f545(x99872,x99873,x99874,x99875,x99876,x99877,x99878,x99879,x998710,x998711,x99871)),x998711))+~P1(f324(f324(f326(f845(x99879,a832)),x99873),f324(f324(f63(x99879),x99878),x99877)))+~P1(f324(f324(f326(f845(x99871,a832)),x99874),f324(f324(f63(x99871),x998711),x998710)))+P1(f324(f324(f326(f845(x99876,a832)),f324(f324(f45(x99871,f845(x99876,a832)),x99874),f324(f324(f10(f845(x99879,f845(x99876,a832)),f845(x99876,a832),x99871),f324(f45(x99879,f845(x99876,a832)),x99873)),x99875))),x99872))
% 18.77/18.51 [9988]~P12(x998811,x998810,x99889)+~P12(x99881,x99888,x99887)+~P17(x998811,x99881,f845(x99886,a832),x99889,x99887,x99885)+P1(f324(f324(f326(x99881),f546(x99882,x99883,x99884,x99885,x99886,x99887,x99888,x99881,x99889,x998810,x998811)),x99888))+~P1(f324(f324(f326(f845(x998811,a832)),x99884),f324(f324(f63(x998811),x998810),x99889)))+~P1(f324(f324(f326(f845(x99881,a832)),x99883),f324(f324(f63(x99881),x99888),x99887)))+P1(f324(f324(f326(f845(x99886,a832)),f324(f324(f45(x998811,f845(x99886,a832)),x99884),f324(f324(f10(f845(x99881,f845(x99886,a832)),f845(x99886,a832),x998811),f324(f45(x99881,f845(x99886,a832)),x99883)),x99885))),x99882))
% 18.77/18.51 [9991]~P12(x99912,x99918,x99919)+~P12(x99914,x999110,x999111)+~P17(x99912,x99914,f845(x99911,a832),x99919,x999111,x99916)+~P1(f324(f324(f326(f845(x99912,a832)),x99913),f324(f324(f63(x99912),x99918),x99919)))+~P1(f324(f324(f326(f845(x99914,a832)),x99915),f324(f324(f63(x99914),x999110),x999111)))+~P1(f324(f324(f326(f845(x99911,a832)),f324(f324(x99916,f545(x99917,x99915,x99913,x99916,x99911,x999111,x999110,x99914,x99919,x99918,x99912)),f546(x99917,x99915,x99913,x99916,x99911,x999111,x999110,x99914,x99919,x99918,x99912))),x99917))+P1(f324(f324(f326(f845(x99911,a832)),f324(f324(f45(x99912,f845(x99911,a832)),x99913),f324(f324(f10(f845(x99914,f845(x99911,a832)),f845(x99911,a832),x99912),f324(f45(x99914,f845(x99911,a832)),x99915)),x99916))),x99917))
% 18.77/18.51 [8947]E(x89471,x89472)+~P86(x89474)+~P29(x89473,x89474,x89475,f324(f324(f103(f845(x89473,a832)),f324(f157(x89473),x89471)),f324(f157(x89473),x89472)))+~E(f324(f157(x89473),x89471),f324(f157(x89473),x89472))+~P18(x89474,f324(f324(f141(x89473,x89474),x89475),x89472))+~P18(x89474,f324(f324(f141(x89473,x89474),x89475),x89471))+~P1(f324(f127(x89474),f324(f324(f141(x89473,x89474),x89475),x89472)))+~P1(f324(f127(x89474),f324(f324(f141(x89473,x89474),x89475),x89471)))
% 18.77/18.51 %EqnAxiom
% 18.77/18.51 [1]E(x11,x11)
% 18.77/18.51 [2]E(x22,x21)+~E(x21,x22)
% 18.77/18.51 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 18.77/18.51 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 18.77/18.51 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 18.77/18.51 [6]~E(x61,x62)+E(f102(x61),f102(x62))
% 18.77/18.51 [7]~E(x71,x72)+E(f34(x71),f34(x72))
% 18.77/18.51 [8]~E(x81,x82)+E(f324(x81,x83),f324(x82,x83))
% 18.77/18.51 [9]~E(x91,x92)+E(f324(x93,x91),f324(x93,x92))
% 18.77/18.51 [10]~E(x101,x102)+E(f86(x101),f86(x102))
% 18.77/18.51 [11]~E(x111,x112)+E(f163(x111,x113),f163(x112,x113))
% 18.77/18.51 [12]~E(x121,x122)+E(f163(x123,x121),f163(x123,x122))
% 18.77/18.51 [13]~E(x131,x132)+E(f83(x131),f83(x132))
% 18.77/18.51 [14]~E(x141,x142)+E(f139(x141),f139(x142))
% 18.77/18.51 [15]~E(x151,x152)+E(f178(x151),f178(x152))
% 18.77/18.51 [16]~E(x161,x162)+E(f103(x161),f103(x162))
% 18.77/18.51 [17]~E(x171,x172)+E(f179(x171),f179(x172))
% 18.77/18.51 [18]~E(x181,x182)+E(f546(x181,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812),f546(x182,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812))
% 18.77/18.51 [19]~E(x191,x192)+E(f546(x193,x191,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912),f546(x193,x192,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912))
% 18.77/18.51 [20]~E(x201,x202)+E(f546(x203,x204,x201,x205,x206,x207,x208,x209,x2010,x2011,x2012),f546(x203,x204,x202,x205,x206,x207,x208,x209,x2010,x2011,x2012))
% 18.77/18.51 [21]~E(x211,x212)+E(f546(x213,x214,x215,x211,x216,x217,x218,x219,x2110,x2111,x2112),f546(x213,x214,x215,x212,x216,x217,x218,x219,x2110,x2111,x2112))
% 18.77/18.51 [22]~E(x221,x222)+E(f546(x223,x224,x225,x226,x221,x227,x228,x229,x2210,x2211,x2212),f546(x223,x224,x225,x226,x222,x227,x228,x229,x2210,x2211,x2212))
% 18.77/18.51 [23]~E(x231,x232)+E(f546(x233,x234,x235,x236,x237,x231,x238,x239,x2310,x2311,x2312),f546(x233,x234,x235,x236,x237,x232,x238,x239,x2310,x2311,x2312))
% 18.77/18.51 [24]~E(x241,x242)+E(f546(x243,x244,x245,x246,x247,x248,x241,x249,x2410,x2411,x2412),f546(x243,x244,x245,x246,x247,x248,x242,x249,x2410,x2411,x2412))
% 18.77/18.51 [25]~E(x251,x252)+E(f546(x253,x254,x255,x256,x257,x258,x259,x251,x2510,x2511,x2512),f546(x253,x254,x255,x256,x257,x258,x259,x252,x2510,x2511,x2512))
% 18.77/18.51 [26]~E(x261,x262)+E(f546(x263,x264,x265,x266,x267,x268,x269,x2610,x261,x2611,x2612),f546(x263,x264,x265,x266,x267,x268,x269,x2610,x262,x2611,x2612))
% 18.77/18.51 [27]~E(x271,x272)+E(f546(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x271,x2712),f546(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x272,x2712))
% 18.77/18.51 [28]~E(x281,x282)+E(f546(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x281),f546(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x282))
% 18.77/18.51 [29]~E(x291,x292)+E(f235(x291),f235(x292))
% 18.77/18.51 [30]~E(x301,x302)+E(f104(x301),f104(x302))
% 18.77/18.51 [31]~E(x311,x312)+E(f105(x311),f105(x312))
% 18.77/18.51 [32]~E(x321,x322)+E(f37(x321),f37(x322))
% 18.77/18.51 [33]~E(x331,x332)+E(f258(x331),f258(x332))
% 18.77/18.51 [34]~E(x341,x342)+E(f80(x341),f80(x342))
% 18.77/18.51 [35]~E(x351,x352)+E(f545(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f545(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512))
% 18.77/18.51 [36]~E(x361,x362)+E(f545(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f545(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612))
% 18.77/18.51 [37]~E(x371,x372)+E(f545(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f545(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 18.77/18.51 [38]~E(x381,x382)+E(f545(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f545(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812))
% 18.77/18.51 [39]~E(x391,x392)+E(f545(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f545(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912))
% 18.77/18.51 [40]~E(x401,x402)+E(f545(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f545(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012))
% 18.77/18.51 [41]~E(x411,x412)+E(f545(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f545(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112))
% 18.77/18.51 [42]~E(x421,x422)+E(f545(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f545(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212))
% 18.77/18.51 [43]~E(x431,x432)+E(f545(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f545(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312))
% 18.77/18.51 [44]~E(x441,x442)+E(f545(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f545(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412))
% 18.77/18.51 [45]~E(x451,x452)+E(f545(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f545(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452))
% 18.77/18.51 [46]~E(x461,x462)+E(f113(x461),f113(x462))
% 18.77/18.51 [47]~E(x471,x472)+E(f326(x471),f326(x472))
% 18.77/18.51 [48]~E(x481,x482)+E(f845(x481,x483),f845(x482,x483))
% 18.77/18.51 [49]~E(x491,x492)+E(f845(x493,x491),f845(x493,x492))
% 18.77/18.51 [50]~E(x501,x502)+E(f6(x501),f6(x502))
% 18.77/18.51 [51]~E(x511,x512)+E(f839(x511),f839(x512))
% 18.77/18.51 [52]~E(x521,x522)+E(f81(x521),f81(x522))
% 18.77/18.51 [53]~E(x531,x532)+E(f66(x531,x533),f66(x532,x533))
% 18.77/18.51 [54]~E(x541,x542)+E(f66(x543,x541),f66(x543,x542))
% 18.77/18.51 [55]~E(x551,x552)+E(f180(x551),f180(x552))
% 18.77/18.51 [56]~E(x561,x562)+E(f143(x561,x563,x564,x565),f143(x562,x563,x564,x565))
% 18.77/18.51 [57]~E(x571,x572)+E(f143(x573,x571,x574,x575),f143(x573,x572,x574,x575))
% 18.77/18.51 [58]~E(x581,x582)+E(f143(x583,x584,x581,x585),f143(x583,x584,x582,x585))
% 18.77/18.51 [59]~E(x591,x592)+E(f143(x593,x594,x595,x591),f143(x593,x594,x595,x592))
% 18.77/18.51 [60]~E(x601,x602)+E(f106(x601),f106(x602))
% 18.77/18.51 [61]~E(x611,x612)+E(f115(x611),f115(x612))
% 18.77/18.51 [62]~E(x621,x622)+E(f46(x621,x623),f46(x622,x623))
% 18.77/18.51 [63]~E(x631,x632)+E(f46(x633,x631),f46(x633,x632))
% 18.77/18.51 [64]~E(x641,x642)+E(f42(x641),f42(x642))
% 18.77/18.51 [65]~E(x651,x652)+E(f232(x651),f232(x652))
% 18.77/18.51 [66]~E(x661,x662)+E(f63(x661),f63(x662))
% 18.77/18.51 [67]~E(x671,x672)+E(f9(x671,x673,x674),f9(x672,x673,x674))
% 18.77/18.51 [68]~E(x681,x682)+E(f9(x683,x681,x684),f9(x683,x682,x684))
% 18.77/18.51 [69]~E(x691,x692)+E(f9(x693,x694,x691),f9(x693,x694,x692))
% 18.77/18.51 [70]~E(x701,x702)+E(f279(x701,x703),f279(x702,x703))
% 18.77/18.51 [71]~E(x711,x712)+E(f279(x713,x711),f279(x713,x712))
% 18.77/18.51 [72]~E(x721,x722)+E(f304(x721,x723,x724),f304(x722,x723,x724))
% 18.77/18.51 [73]~E(x731,x732)+E(f304(x733,x731,x734),f304(x733,x732,x734))
% 18.77/18.51 [74]~E(x741,x742)+E(f304(x743,x744,x741),f304(x743,x744,x742))
% 18.77/18.51 [75]~E(x751,x752)+E(f11(x751,x753),f11(x752,x753))
% 18.77/18.52 [76]~E(x761,x762)+E(f11(x763,x761),f11(x763,x762))
% 18.77/18.52 [77]~E(x771,x772)+E(f231(x771),f231(x772))
% 18.77/18.52 [78]~E(x781,x782)+E(f64(x781),f64(x782))
% 18.77/18.52 [79]~E(x791,x792)+E(f238(x791),f238(x792))
% 18.77/18.52 [80]~E(x801,x802)+E(f303(x801),f303(x802))
% 18.77/18.52 [81]~E(x811,x812)+E(f251(x811,x813),f251(x812,x813))
% 18.77/18.52 [82]~E(x821,x822)+E(f251(x823,x821),f251(x823,x822))
% 18.77/18.52 [83]~E(x831,x832)+E(f278(x831,x833,x834),f278(x832,x833,x834))
% 18.77/18.52 [84]~E(x841,x842)+E(f278(x843,x841,x844),f278(x843,x842,x844))
% 18.77/18.52 [85]~E(x851,x852)+E(f278(x853,x854,x851),f278(x853,x854,x852))
% 18.77/18.52 [86]~E(x861,x862)+E(f314(x861,x863),f314(x862,x863))
% 18.77/18.52 [87]~E(x871,x872)+E(f314(x873,x871),f314(x873,x872))
% 18.77/18.52 [88]~E(x881,x882)+E(f145(x881,x883),f145(x882,x883))
% 18.77/18.52 [89]~E(x891,x892)+E(f145(x893,x891),f145(x893,x892))
% 18.77/18.52 [90]~E(x901,x902)+E(f41(x901),f41(x902))
% 18.77/18.52 [91]~E(x911,x912)+E(f157(x911),f157(x912))
% 18.77/18.52 [92]~E(x921,x922)+E(f842(x921),f842(x922))
% 18.77/18.52 [93]~E(x931,x932)+E(f18(x931,x933),f18(x932,x933))
% 18.77/18.52 [94]~E(x941,x942)+E(f18(x943,x941),f18(x943,x942))
% 18.77/18.52 [95]~E(x951,x952)+E(f82(x951),f82(x952))
% 18.77/18.52 [96]~E(x961,x962)+E(f470(x961,x963),f470(x962,x963))
% 18.77/18.52 [97]~E(x971,x972)+E(f470(x973,x971),f470(x973,x972))
% 18.77/18.52 [98]~E(x981,x982)+E(f182(x981),f182(x982))
% 18.77/18.52 [99]~E(x991,x992)+E(f125(x991),f125(x992))
% 18.77/18.52 [100]~E(x1001,x1002)+E(f67(x1001,x1003,x1004),f67(x1002,x1003,x1004))
% 18.77/18.52 [101]~E(x1011,x1012)+E(f67(x1013,x1011,x1014),f67(x1013,x1012,x1014))
% 18.77/18.52 [102]~E(x1021,x1022)+E(f67(x1023,x1024,x1021),f67(x1023,x1024,x1022))
% 18.77/18.52 [103]~E(x1031,x1032)+E(f133(x1031,x1033),f133(x1032,x1033))
% 18.77/18.52 [104]~E(x1041,x1042)+E(f133(x1043,x1041),f133(x1043,x1042))
% 18.77/18.52 [105]~E(x1051,x1052)+E(f301(x1051,x1053),f301(x1052,x1053))
% 18.77/18.52 [106]~E(x1061,x1062)+E(f301(x1063,x1061),f301(x1063,x1062))
% 18.77/18.52 [107]~E(x1071,x1072)+E(f844(x1071,x1073),f844(x1072,x1073))
% 18.77/18.52 [108]~E(x1081,x1082)+E(f844(x1083,x1081),f844(x1083,x1082))
% 18.77/18.52 [109]~E(x1091,x1092)+E(f43(x1091,x1093),f43(x1092,x1093))
% 18.77/18.52 [110]~E(x1101,x1102)+E(f43(x1103,x1101),f43(x1103,x1102))
% 18.77/18.52 [111]~E(x1111,x1112)+E(f563(x1111,x1113,x1114,x1115),f563(x1112,x1113,x1114,x1115))
% 18.77/18.52 [112]~E(x1121,x1122)+E(f563(x1123,x1121,x1124,x1125),f563(x1123,x1122,x1124,x1125))
% 18.77/18.52 [113]~E(x1131,x1132)+E(f563(x1133,x1134,x1131,x1135),f563(x1133,x1134,x1132,x1135))
% 18.77/18.52 [114]~E(x1141,x1142)+E(f563(x1143,x1144,x1145,x1141),f563(x1143,x1144,x1145,x1142))
% 18.77/18.52 [115]~E(x1151,x1152)+E(f257(x1151),f257(x1152))
% 18.77/18.52 [116]~E(x1161,x1162)+E(f465(x1161,x1163),f465(x1162,x1163))
% 18.77/18.52 [117]~E(x1171,x1172)+E(f465(x1173,x1171),f465(x1173,x1172))
% 18.77/18.52 [118]~E(x1181,x1182)+E(f10(x1181,x1183,x1184),f10(x1182,x1183,x1184))
% 18.77/18.52 [119]~E(x1191,x1192)+E(f10(x1193,x1191,x1194),f10(x1193,x1192,x1194))
% 18.77/18.52 [120]~E(x1201,x1202)+E(f10(x1203,x1204,x1201),f10(x1203,x1204,x1202))
% 18.77/18.52 [121]~E(x1211,x1212)+E(f108(x1211),f108(x1212))
% 18.77/18.52 [122]~E(x1221,x1222)+E(f109(x1221),f109(x1222))
% 18.77/18.52 [123]~E(x1231,x1232)+E(f325(x1231),f325(x1232))
% 18.77/18.52 [124]~E(x1241,x1242)+E(f141(x1241,x1243),f141(x1242,x1243))
% 18.77/18.52 [125]~E(x1251,x1252)+E(f141(x1253,x1251),f141(x1253,x1252))
% 18.77/18.52 [126]~E(x1261,x1262)+E(f51(x1261,x1263,x1264),f51(x1262,x1263,x1264))
% 18.77/18.52 [127]~E(x1271,x1272)+E(f51(x1273,x1271,x1274),f51(x1273,x1272,x1274))
% 18.77/18.52 [128]~E(x1281,x1282)+E(f51(x1283,x1284,x1281),f51(x1283,x1284,x1282))
% 18.77/18.52 [129]~E(x1291,x1292)+E(f237(x1291,x1293),f237(x1292,x1293))
% 18.77/18.52 [130]~E(x1301,x1302)+E(f237(x1303,x1301),f237(x1303,x1302))
% 18.77/18.52 [131]~E(x1311,x1312)+E(f240(x1311),f240(x1312))
% 18.77/18.52 [132]~E(x1321,x1322)+E(f169(x1321,x1323,x1324,x1325),f169(x1322,x1323,x1324,x1325))
% 18.77/18.52 [133]~E(x1331,x1332)+E(f169(x1333,x1331,x1334,x1335),f169(x1333,x1332,x1334,x1335))
% 18.77/18.52 [134]~E(x1341,x1342)+E(f169(x1343,x1344,x1341,x1345),f169(x1343,x1344,x1342,x1345))
% 18.77/18.52 [135]~E(x1351,x1352)+E(f169(x1353,x1354,x1355,x1351),f169(x1353,x1354,x1355,x1352))
% 18.77/18.52 [136]~E(x1361,x1362)+E(f811(x1361,x1363,x1364),f811(x1362,x1363,x1364))
% 18.77/18.52 [137]~E(x1371,x1372)+E(f811(x1373,x1371,x1374),f811(x1373,x1372,x1374))
% 18.77/18.52 [138]~E(x1381,x1382)+E(f811(x1383,x1384,x1381),f811(x1383,x1384,x1382))
% 18.77/18.52 [139]~E(x1391,x1392)+E(f247(x1391,x1393),f247(x1392,x1393))
% 18.77/18.52 [140]~E(x1401,x1402)+E(f247(x1403,x1401),f247(x1403,x1402))
% 18.77/18.52 [141]~E(x1411,x1412)+E(f284(x1411),f284(x1412))
% 18.77/18.52 [142]~E(x1421,x1422)+E(f7(x1421),f7(x1422))
% 18.77/18.52 [143]~E(x1431,x1432)+E(f168(x1431,x1433,x1434),f168(x1432,x1433,x1434))
% 18.77/18.52 [144]~E(x1441,x1442)+E(f168(x1443,x1441,x1444),f168(x1443,x1442,x1444))
% 18.77/18.52 [145]~E(x1451,x1452)+E(f168(x1453,x1454,x1451),f168(x1453,x1454,x1452))
% 18.77/18.52 [146]~E(x1461,x1462)+E(f579(x1461),f579(x1462))
% 18.77/18.52 [147]~E(x1471,x1472)+E(f130(x1471),f130(x1472))
% 18.77/18.52 [148]~E(x1481,x1482)+E(f296(x1481,x1483,x1484),f296(x1482,x1483,x1484))
% 18.77/18.52 [149]~E(x1491,x1492)+E(f296(x1493,x1491,x1494),f296(x1493,x1492,x1494))
% 18.77/18.52 [150]~E(x1501,x1502)+E(f296(x1503,x1504,x1501),f296(x1503,x1504,x1502))
% 18.77/18.52 [151]~E(x1511,x1512)+E(f131(x1511,x1513,x1514,x1515),f131(x1512,x1513,x1514,x1515))
% 18.77/18.52 [152]~E(x1521,x1522)+E(f131(x1523,x1521,x1524,x1525),f131(x1523,x1522,x1524,x1525))
% 18.77/18.52 [153]~E(x1531,x1532)+E(f131(x1533,x1534,x1531,x1535),f131(x1533,x1534,x1532,x1535))
% 18.77/18.52 [154]~E(x1541,x1542)+E(f131(x1543,x1544,x1545,x1541),f131(x1543,x1544,x1545,x1542))
% 18.77/18.52 [155]~E(x1551,x1552)+E(f771(x1551,x1553,x1554),f771(x1552,x1553,x1554))
% 18.77/18.52 [156]~E(x1561,x1562)+E(f771(x1563,x1561,x1564),f771(x1563,x1562,x1564))
% 18.77/18.52 [157]~E(x1571,x1572)+E(f771(x1573,x1574,x1571),f771(x1573,x1574,x1572))
% 18.77/18.52 [158]~E(x1581,x1582)+E(f45(x1581,x1583),f45(x1582,x1583))
% 18.77/18.52 [159]~E(x1591,x1592)+E(f45(x1593,x1591),f45(x1593,x1592))
% 18.77/18.52 [160]~E(x1601,x1602)+E(f673(x1601,x1603,x1604),f673(x1602,x1603,x1604))
% 18.77/18.52 [161]~E(x1611,x1612)+E(f673(x1613,x1611,x1614),f673(x1613,x1612,x1614))
% 18.77/18.52 [162]~E(x1621,x1622)+E(f673(x1623,x1624,x1621),f673(x1623,x1624,x1622))
% 18.77/18.52 [163]~E(x1631,x1632)+E(f127(x1631),f127(x1632))
% 18.77/18.52 [164]~E(x1641,x1642)+E(f20(x1641,x1643,x1644),f20(x1642,x1643,x1644))
% 18.77/18.52 [165]~E(x1651,x1652)+E(f20(x1653,x1651,x1654),f20(x1653,x1652,x1654))
% 18.77/18.52 [166]~E(x1661,x1662)+E(f20(x1663,x1664,x1661),f20(x1663,x1664,x1662))
% 18.77/18.52 [167]~E(x1671,x1672)+E(f155(x1671,x1673,x1674),f155(x1672,x1673,x1674))
% 18.77/18.52 [168]~E(x1681,x1682)+E(f155(x1683,x1681,x1684),f155(x1683,x1682,x1684))
% 18.77/18.52 [169]~E(x1691,x1692)+E(f155(x1693,x1694,x1691),f155(x1693,x1694,x1692))
% 18.77/18.52 [170]~E(x1701,x1702)+E(f154(x1701),f154(x1702))
% 18.77/18.52 [171]~E(x1711,x1712)+E(f94(x1711,x1713,x1714),f94(x1712,x1713,x1714))
% 18.77/18.52 [172]~E(x1721,x1722)+E(f94(x1723,x1721,x1724),f94(x1723,x1722,x1724))
% 18.77/18.52 [173]~E(x1731,x1732)+E(f94(x1733,x1734,x1731),f94(x1733,x1734,x1732))
% 18.77/18.52 [174]~E(x1741,x1742)+E(f282(x1741,x1743,x1744),f282(x1742,x1743,x1744))
% 18.77/18.52 [175]~E(x1751,x1752)+E(f282(x1753,x1751,x1754),f282(x1753,x1752,x1754))
% 18.77/18.52 [176]~E(x1761,x1762)+E(f282(x1763,x1764,x1761),f282(x1763,x1764,x1762))
% 18.77/18.52 [177]~E(x1771,x1772)+E(f15(x1771,x1773),f15(x1772,x1773))
% 18.77/18.52 [178]~E(x1781,x1782)+E(f15(x1783,x1781),f15(x1783,x1782))
% 18.77/18.52 [179]~E(x1791,x1792)+E(f467(x1791,x1793,x1794,x1795),f467(x1792,x1793,x1794,x1795))
% 18.77/18.52 [180]~E(x1801,x1802)+E(f467(x1803,x1801,x1804,x1805),f467(x1803,x1802,x1804,x1805))
% 18.77/18.52 [181]~E(x1811,x1812)+E(f467(x1813,x1814,x1811,x1815),f467(x1813,x1814,x1812,x1815))
% 18.77/18.52 [182]~E(x1821,x1822)+E(f467(x1823,x1824,x1825,x1821),f467(x1823,x1824,x1825,x1822))
% 18.77/18.52 [183]~E(x1831,x1832)+E(f672(x1831,x1833,x1834),f672(x1832,x1833,x1834))
% 18.77/18.52 [184]~E(x1841,x1842)+E(f672(x1843,x1841,x1844),f672(x1843,x1842,x1844))
% 18.77/18.52 [185]~E(x1851,x1852)+E(f672(x1853,x1854,x1851),f672(x1853,x1854,x1852))
% 18.77/18.52 [186]~E(x1861,x1862)+E(f136(x1861,x1863),f136(x1862,x1863))
% 18.77/18.52 [187]~E(x1871,x1872)+E(f136(x1873,x1871),f136(x1873,x1872))
% 18.77/18.52 [188]~E(x1881,x1882)+E(f135(x1881,x1883),f135(x1882,x1883))
% 18.77/18.52 [189]~E(x1891,x1892)+E(f135(x1893,x1891),f135(x1893,x1892))
% 18.77/18.52 [190]~E(x1901,x1902)+E(f149(x1901),f149(x1902))
% 18.77/18.52 [191]~E(x1911,x1912)+E(f280(x1911),f280(x1912))
% 18.77/18.52 [192]~E(x1921,x1922)+E(f821(x1921,x1923,x1924,x1925),f821(x1922,x1923,x1924,x1925))
% 18.77/18.52 [193]~E(x1931,x1932)+E(f821(x1933,x1931,x1934,x1935),f821(x1933,x1932,x1934,x1935))
% 18.77/18.52 [194]~E(x1941,x1942)+E(f821(x1943,x1944,x1941,x1945),f821(x1943,x1944,x1942,x1945))
% 18.77/18.52 [195]~E(x1951,x1952)+E(f821(x1953,x1954,x1955,x1951),f821(x1953,x1954,x1955,x1952))
% 18.77/18.52 [196]~E(x1961,x1962)+E(f490(x1961,x1963,x1964,x1965),f490(x1962,x1963,x1964,x1965))
% 18.77/18.52 [197]~E(x1971,x1972)+E(f490(x1973,x1971,x1974,x1975),f490(x1973,x1972,x1974,x1975))
% 18.77/18.52 [198]~E(x1981,x1982)+E(f490(x1983,x1984,x1981,x1985),f490(x1983,x1984,x1982,x1985))
% 18.77/18.52 [199]~E(x1991,x1992)+E(f490(x1993,x1994,x1995,x1991),f490(x1993,x1994,x1995,x1992))
% 18.77/18.52 [200]~E(x2001,x2002)+E(f765(x2001,x2003,x2004,x2005,x2006),f765(x2002,x2003,x2004,x2005,x2006))
% 18.77/18.52 [201]~E(x2011,x2012)+E(f765(x2013,x2011,x2014,x2015,x2016),f765(x2013,x2012,x2014,x2015,x2016))
% 18.77/18.52 [202]~E(x2021,x2022)+E(f765(x2023,x2024,x2021,x2025,x2026),f765(x2023,x2024,x2022,x2025,x2026))
% 18.77/18.52 [203]~E(x2031,x2032)+E(f765(x2033,x2034,x2035,x2031,x2036),f765(x2033,x2034,x2035,x2032,x2036))
% 18.77/18.52 [204]~E(x2041,x2042)+E(f765(x2043,x2044,x2045,x2046,x2041),f765(x2043,x2044,x2045,x2046,x2042))
% 18.77/18.52 [205]~E(x2051,x2052)+E(f609(x2051,x2053,x2054),f609(x2052,x2053,x2054))
% 18.77/18.52 [206]~E(x2061,x2062)+E(f609(x2063,x2061,x2064),f609(x2063,x2062,x2064))
% 18.77/18.52 [207]~E(x2071,x2072)+E(f609(x2073,x2074,x2071),f609(x2073,x2074,x2072))
% 18.77/18.52 [208]~E(x2081,x2082)+E(f837(x2081),f837(x2082))
% 18.77/18.52 [209]~E(x2091,x2092)+E(f74(x2091,x2093),f74(x2092,x2093))
% 18.77/18.52 [210]~E(x2101,x2102)+E(f74(x2103,x2101),f74(x2103,x2102))
% 18.77/18.52 [211]~E(x2111,x2112)+E(f8(x2111,x2113),f8(x2112,x2113))
% 18.77/18.52 [212]~E(x2121,x2122)+E(f8(x2123,x2121),f8(x2123,x2122))
% 18.77/18.52 [213]~E(x2131,x2132)+E(f68(x2131,x2133,x2134),f68(x2132,x2133,x2134))
% 18.77/18.52 [214]~E(x2141,x2142)+E(f68(x2143,x2141,x2144),f68(x2143,x2142,x2144))
% 18.77/18.52 [215]~E(x2151,x2152)+E(f68(x2153,x2154,x2151),f68(x2153,x2154,x2152))
% 18.77/18.52 [216]~E(x2161,x2162)+E(f77(x2161),f77(x2162))
% 18.77/18.52 [217]~E(x2171,x2172)+E(f159(x2171,x2173,x2174),f159(x2172,x2173,x2174))
% 18.77/18.52 [218]~E(x2181,x2182)+E(f159(x2183,x2181,x2184),f159(x2183,x2182,x2184))
% 18.77/18.52 [219]~E(x2191,x2192)+E(f159(x2193,x2194,x2191),f159(x2193,x2194,x2192))
% 18.77/18.52 [220]~E(x2201,x2202)+E(f313(x2201,x2203),f313(x2202,x2203))
% 18.77/18.52 [221]~E(x2211,x2212)+E(f313(x2213,x2211),f313(x2213,x2212))
% 18.77/18.52 [222]~E(x2221,x2222)+E(f767(x2221,x2223,x2224),f767(x2222,x2223,x2224))
% 18.77/18.52 [223]~E(x2231,x2232)+E(f767(x2233,x2231,x2234),f767(x2233,x2232,x2234))
% 18.77/18.52 [224]~E(x2241,x2242)+E(f767(x2243,x2244,x2241),f767(x2243,x2244,x2242))
% 18.77/18.52 [225]~E(x2251,x2252)+E(f363(x2251,x2253,x2254,x2255),f363(x2252,x2253,x2254,x2255))
% 18.77/18.52 [226]~E(x2261,x2262)+E(f363(x2263,x2261,x2264,x2265),f363(x2263,x2262,x2264,x2265))
% 18.77/18.52 [227]~E(x2271,x2272)+E(f363(x2273,x2274,x2271,x2275),f363(x2273,x2274,x2272,x2275))
% 18.77/18.52 [228]~E(x2281,x2282)+E(f363(x2283,x2284,x2285,x2281),f363(x2283,x2284,x2285,x2282))
% 18.77/18.52 [229]~E(x2291,x2292)+E(f128(x2291),f128(x2292))
% 18.77/18.52 [230]~E(x2301,x2302)+E(f809(x2301,x2303,x2304),f809(x2302,x2303,x2304))
% 18.77/18.52 [231]~E(x2311,x2312)+E(f809(x2313,x2311,x2314),f809(x2313,x2312,x2314))
% 18.77/18.52 [232]~E(x2321,x2322)+E(f809(x2323,x2324,x2321),f809(x2323,x2324,x2322))
% 18.77/18.52 [233]~E(x2331,x2332)+E(f116(x2331,x2333),f116(x2332,x2333))
% 18.77/18.52 [234]~E(x2341,x2342)+E(f116(x2343,x2341),f116(x2343,x2342))
% 18.77/18.52 [235]~E(x2351,x2352)+E(f493(x2351,x2353,x2354),f493(x2352,x2353,x2354))
% 18.77/18.52 [236]~E(x2361,x2362)+E(f493(x2363,x2361,x2364),f493(x2363,x2362,x2364))
% 18.77/18.52 [237]~E(x2371,x2372)+E(f493(x2373,x2374,x2371),f493(x2373,x2374,x2372))
% 18.77/18.52 [238]~E(x2381,x2382)+E(f489(x2381,x2383,x2384),f489(x2382,x2383,x2384))
% 18.77/18.52 [239]~E(x2391,x2392)+E(f489(x2393,x2391,x2394),f489(x2393,x2392,x2394))
% 18.77/18.52 [240]~E(x2401,x2402)+E(f489(x2403,x2404,x2401),f489(x2403,x2404,x2402))
% 18.77/18.52 [241]~E(x2411,x2412)+E(f140(x2411,x2413),f140(x2412,x2413))
% 18.77/18.52 [242]~E(x2421,x2422)+E(f140(x2423,x2421),f140(x2423,x2422))
% 18.77/18.52 [243]~E(x2431,x2432)+E(f299(x2431,x2433,x2434),f299(x2432,x2433,x2434))
% 18.77/18.52 [244]~E(x2441,x2442)+E(f299(x2443,x2441,x2444),f299(x2443,x2442,x2444))
% 18.77/18.52 [245]~E(x2451,x2452)+E(f299(x2453,x2454,x2451),f299(x2453,x2454,x2452))
% 18.77/18.52 [246]~E(x2461,x2462)+E(f183(x2461),f183(x2462))
% 18.77/18.52 [247]~E(x2471,x2472)+E(f226(x2471),f226(x2472))
% 18.77/18.52 [248]~E(x2481,x2482)+E(f117(x2481),f117(x2482))
% 18.77/18.52 [249]~E(x2491,x2492)+E(f17(x2491,x2493),f17(x2492,x2493))
% 18.77/18.52 [250]~E(x2501,x2502)+E(f17(x2503,x2501),f17(x2503,x2502))
% 18.77/18.52 [251]~E(x2511,x2512)+E(f61(x2511,x2513,x2514),f61(x2512,x2513,x2514))
% 18.77/18.52 [252]~E(x2521,x2522)+E(f61(x2523,x2521,x2524),f61(x2523,x2522,x2524))
% 18.77/18.52 [253]~E(x2531,x2532)+E(f61(x2533,x2534,x2531),f61(x2533,x2534,x2532))
% 18.77/18.52 [254]~E(x2541,x2542)+E(f734(x2541,x2543,x2544,x2545),f734(x2542,x2543,x2544,x2545))
% 18.77/18.52 [255]~E(x2551,x2552)+E(f734(x2553,x2551,x2554,x2555),f734(x2553,x2552,x2554,x2555))
% 18.77/18.52 [256]~E(x2561,x2562)+E(f734(x2563,x2564,x2561,x2565),f734(x2563,x2564,x2562,x2565))
% 18.77/18.52 [257]~E(x2571,x2572)+E(f734(x2573,x2574,x2575,x2571),f734(x2573,x2574,x2575,x2572))
% 18.77/18.52 [258]~E(x2581,x2582)+E(f252(x2581,x2583,x2584),f252(x2582,x2583,x2584))
% 18.77/18.52 [259]~E(x2591,x2592)+E(f252(x2593,x2591,x2594),f252(x2593,x2592,x2594))
% 18.77/18.52 [260]~E(x2601,x2602)+E(f252(x2603,x2604,x2601),f252(x2603,x2604,x2602))
% 18.77/18.52 [261]~E(x2611,x2612)+E(f55(x2611,x2613),f55(x2612,x2613))
% 18.77/18.52 [262]~E(x2621,x2622)+E(f55(x2623,x2621),f55(x2623,x2622))
% 18.77/18.52 [263]~E(x2631,x2632)+E(f153(x2631),f153(x2632))
% 18.77/18.52 [264]~E(x2641,x2642)+E(f230(x2641),f230(x2642))
% 18.77/18.52 [265]~E(x2651,x2652)+E(f44(x2651,x2653),f44(x2652,x2653))
% 18.77/18.52 [266]~E(x2661,x2662)+E(f44(x2663,x2661),f44(x2663,x2662))
% 18.77/18.52 [267]~E(x2671,x2672)+E(f302(x2671),f302(x2672))
% 18.77/18.52 [268]~E(x2681,x2682)+E(f156(x2681),f156(x2682))
% 18.77/18.52 [269]~E(x2691,x2692)+E(f21(x2691,x2693,x2694,x2695),f21(x2692,x2693,x2694,x2695))
% 18.77/18.52 [270]~E(x2701,x2702)+E(f21(x2703,x2701,x2704,x2705),f21(x2703,x2702,x2704,x2705))
% 18.77/18.52 [271]~E(x2711,x2712)+E(f21(x2713,x2714,x2711,x2715),f21(x2713,x2714,x2712,x2715))
% 18.77/18.52 [272]~E(x2721,x2722)+E(f21(x2723,x2724,x2725,x2721),f21(x2723,x2724,x2725,x2722))
% 18.77/18.52 [273]~E(x2731,x2732)+E(f126(x2731,x2733),f126(x2732,x2733))
% 18.77/18.52 [274]~E(x2741,x2742)+E(f126(x2743,x2741),f126(x2743,x2742))
% 18.77/18.52 [275]~E(x2751,x2752)+E(f735(x2751,x2753,x2754),f735(x2752,x2753,x2754))
% 18.77/18.52 [276]~E(x2761,x2762)+E(f735(x2763,x2761,x2764),f735(x2763,x2762,x2764))
% 18.77/18.52 [277]~E(x2771,x2772)+E(f735(x2773,x2774,x2771),f735(x2773,x2774,x2772))
% 18.77/18.52 [278]~E(x2781,x2782)+E(f52(x2781,x2783),f52(x2782,x2783))
% 18.77/18.52 [279]~E(x2791,x2792)+E(f52(x2793,x2791),f52(x2793,x2792))
% 18.77/18.52 [280]~E(x2801,x2802)+E(f689(x2801,x2803,x2804,x2805,x2806),f689(x2802,x2803,x2804,x2805,x2806))
% 18.77/18.52 [281]~E(x2811,x2812)+E(f689(x2813,x2811,x2814,x2815,x2816),f689(x2813,x2812,x2814,x2815,x2816))
% 18.77/18.52 [282]~E(x2821,x2822)+E(f689(x2823,x2824,x2821,x2825,x2826),f689(x2823,x2824,x2822,x2825,x2826))
% 18.77/18.52 [283]~E(x2831,x2832)+E(f689(x2833,x2834,x2835,x2831,x2836),f689(x2833,x2834,x2835,x2832,x2836))
% 18.77/18.52 [284]~E(x2841,x2842)+E(f689(x2843,x2844,x2845,x2846,x2841),f689(x2843,x2844,x2845,x2846,x2842))
% 18.77/18.52 [285]~E(x2851,x2852)+E(f212(x2851,x2853),f212(x2852,x2853))
% 18.77/18.52 [286]~E(x2861,x2862)+E(f212(x2863,x2861),f212(x2863,x2862))
% 18.77/18.52 [287]~E(x2871,x2872)+E(f772(x2871,x2873,x2874),f772(x2872,x2873,x2874))
% 18.77/18.52 [288]~E(x2881,x2882)+E(f772(x2883,x2881,x2884),f772(x2883,x2882,x2884))
% 18.77/18.52 [289]~E(x2891,x2892)+E(f772(x2893,x2894,x2891),f772(x2893,x2894,x2892))
% 18.77/18.52 [290]~E(x2901,x2902)+E(f268(x2901,x2903),f268(x2902,x2903))
% 18.77/18.52 [291]~E(x2911,x2912)+E(f268(x2913,x2911),f268(x2913,x2912))
% 18.77/18.52 [292]~E(x2921,x2922)+E(f439(x2921,x2923,x2924,x2925),f439(x2922,x2923,x2924,x2925))
% 18.77/18.52 [293]~E(x2931,x2932)+E(f439(x2933,x2931,x2934,x2935),f439(x2933,x2932,x2934,x2935))
% 18.77/18.52 [294]~E(x2941,x2942)+E(f439(x2943,x2944,x2941,x2945),f439(x2943,x2944,x2942,x2945))
% 18.77/18.52 [295]~E(x2951,x2952)+E(f439(x2953,x2954,x2955,x2951),f439(x2953,x2954,x2955,x2952))
% 18.77/18.52 [296]~E(x2961,x2962)+E(f59(x2961,x2963),f59(x2962,x2963))
% 18.77/18.52 [297]~E(x2971,x2972)+E(f59(x2973,x2971),f59(x2973,x2972))
% 18.77/18.52 [298]~E(x2981,x2982)+E(f87(x2981,x2983),f87(x2982,x2983))
% 18.77/18.52 [299]~E(x2991,x2992)+E(f87(x2993,x2991),f87(x2993,x2992))
% 18.77/18.52 [300]~E(x3001,x3002)+E(f28(x3001,x3003),f28(x3002,x3003))
% 18.77/18.52 [301]~E(x3011,x3012)+E(f28(x3013,x3011),f28(x3013,x3012))
% 18.77/18.52 [302]~E(x3021,x3022)+E(f419(x3021),f419(x3022))
% 18.77/18.52 [303]~E(x3031,x3032)+E(f98(x3031),f98(x3032))
% 18.77/18.52 [304]~E(x3041,x3042)+E(f13(x3041,x3043,x3044),f13(x3042,x3043,x3044))
% 18.77/18.52 [305]~E(x3051,x3052)+E(f13(x3053,x3051,x3054),f13(x3053,x3052,x3054))
% 18.77/18.52 [306]~E(x3061,x3062)+E(f13(x3063,x3064,x3061),f13(x3063,x3064,x3062))
% 18.77/18.52 [307]~E(x3071,x3072)+E(f316(x3071,x3073),f316(x3072,x3073))
% 18.77/18.52 [308]~E(x3081,x3082)+E(f316(x3083,x3081),f316(x3083,x3082))
% 18.77/18.52 [309]~E(x3091,x3092)+E(f295(x3091,x3093),f295(x3092,x3093))
% 18.77/18.52 [310]~E(x3101,x3102)+E(f295(x3103,x3101),f295(x3103,x3102))
% 18.77/18.52 [311]~E(x3111,x3112)+E(f317(x3111,x3113),f317(x3112,x3113))
% 18.77/18.52 [312]~E(x3121,x3122)+E(f317(x3123,x3121),f317(x3123,x3122))
% 18.77/18.52 [313]~E(x3131,x3132)+E(f246(x3131,x3133),f246(x3132,x3133))
% 18.77/18.52 [314]~E(x3141,x3142)+E(f246(x3143,x3141),f246(x3143,x3142))
% 18.77/18.52 [315]~E(x3151,x3152)+E(f54(x3151,x3153),f54(x3152,x3153))
% 18.77/18.52 [316]~E(x3161,x3162)+E(f54(x3163,x3161),f54(x3163,x3162))
% 18.77/18.52 [317]~E(x3171,x3172)+E(f249(x3171,x3173),f249(x3172,x3173))
% 18.77/18.52 [318]~E(x3181,x3182)+E(f249(x3183,x3181),f249(x3183,x3182))
% 18.77/18.52 [319]~E(x3191,x3192)+E(f137(x3191,x3193,x3194),f137(x3192,x3193,x3194))
% 18.77/18.52 [320]~E(x3201,x3202)+E(f137(x3203,x3201,x3204),f137(x3203,x3202,x3204))
% 18.77/18.52 [321]~E(x3211,x3212)+E(f137(x3213,x3214,x3211),f137(x3213,x3214,x3212))
% 18.77/18.52 [322]~E(x3221,x3222)+E(f620(x3221,x3223),f620(x3222,x3223))
% 18.77/18.52 [323]~E(x3231,x3232)+E(f620(x3233,x3231),f620(x3233,x3232))
% 18.77/18.52 [324]~E(x3241,x3242)+E(f158(x3241),f158(x3242))
% 18.77/18.52 [325]~E(x3251,x3252)+E(f298(x3251,x3253,x3254),f298(x3252,x3253,x3254))
% 18.77/18.52 [326]~E(x3261,x3262)+E(f298(x3263,x3261,x3264),f298(x3263,x3262,x3264))
% 18.77/18.52 [327]~E(x3271,x3272)+E(f298(x3273,x3274,x3271),f298(x3273,x3274,x3272))
% 18.77/18.52 [328]~E(x3281,x3282)+E(f172(x3281,x3283),f172(x3282,x3283))
% 18.77/18.52 [329]~E(x3291,x3292)+E(f172(x3293,x3291),f172(x3293,x3292))
% 18.77/18.52 [330]~E(x3301,x3302)+E(f312(x3301,x3303,x3304,x3305),f312(x3302,x3303,x3304,x3305))
% 18.77/18.52 [331]~E(x3311,x3312)+E(f312(x3313,x3311,x3314,x3315),f312(x3313,x3312,x3314,x3315))
% 18.77/18.52 [332]~E(x3321,x3322)+E(f312(x3323,x3324,x3321,x3325),f312(x3323,x3324,x3322,x3325))
% 18.77/18.52 [333]~E(x3331,x3332)+E(f312(x3333,x3334,x3335,x3331),f312(x3333,x3334,x3335,x3332))
% 18.77/18.52 [334]~E(x3341,x3342)+E(f329(x3341),f329(x3342))
% 18.77/18.52 [335]~E(x3351,x3352)+E(f112(x3351),f112(x3352))
% 18.77/18.52 [336]~E(x3361,x3362)+E(f394(x3361,x3363,x3364),f394(x3362,x3363,x3364))
% 18.77/18.52 [337]~E(x3371,x3372)+E(f394(x3373,x3371,x3374),f394(x3373,x3372,x3374))
% 18.77/18.52 [338]~E(x3381,x3382)+E(f394(x3383,x3384,x3381),f394(x3383,x3384,x3382))
% 18.77/18.52 [339]~E(x3391,x3392)+E(f452(x3391,x3393),f452(x3392,x3393))
% 18.77/18.52 [340]~E(x3401,x3402)+E(f452(x3403,x3401),f452(x3403,x3402))
% 18.77/18.52 [341]~E(x3411,x3412)+E(f506(x3411,x3413,x3414,x3415,x3416,x3417),f506(x3412,x3413,x3414,x3415,x3416,x3417))
% 18.77/18.52 [342]~E(x3421,x3422)+E(f506(x3423,x3421,x3424,x3425,x3426,x3427),f506(x3423,x3422,x3424,x3425,x3426,x3427))
% 18.77/18.52 [343]~E(x3431,x3432)+E(f506(x3433,x3434,x3431,x3435,x3436,x3437),f506(x3433,x3434,x3432,x3435,x3436,x3437))
% 18.77/18.52 [344]~E(x3441,x3442)+E(f506(x3443,x3444,x3445,x3441,x3446,x3447),f506(x3443,x3444,x3445,x3442,x3446,x3447))
% 18.77/18.52 [345]~E(x3451,x3452)+E(f506(x3453,x3454,x3455,x3456,x3451,x3457),f506(x3453,x3454,x3455,x3456,x3452,x3457))
% 18.77/18.52 [346]~E(x3461,x3462)+E(f506(x3463,x3464,x3465,x3466,x3467,x3461),f506(x3463,x3464,x3465,x3466,x3467,x3462))
% 18.77/18.52 [347]~E(x3471,x3472)+E(f75(x3471,x3473,x3474,x3475),f75(x3472,x3473,x3474,x3475))
% 18.77/18.52 [348]~E(x3481,x3482)+E(f75(x3483,x3481,x3484,x3485),f75(x3483,x3482,x3484,x3485))
% 18.77/18.52 [349]~E(x3491,x3492)+E(f75(x3493,x3494,x3491,x3495),f75(x3493,x3494,x3492,x3495))
% 18.77/18.52 [350]~E(x3501,x3502)+E(f75(x3503,x3504,x3505,x3501),f75(x3503,x3504,x3505,x3502))
% 18.77/18.52 [351]~E(x3511,x3512)+E(f773(x3511,x3513,x3514),f773(x3512,x3513,x3514))
% 18.77/18.52 [352]~E(x3521,x3522)+E(f773(x3523,x3521,x3524),f773(x3523,x3522,x3524))
% 18.77/18.52 [353]~E(x3531,x3532)+E(f773(x3533,x3534,x3531),f773(x3533,x3534,x3532))
% 18.77/18.52 [354]~E(x3541,x3542)+E(f359(x3541,x3543,x3544,x3545),f359(x3542,x3543,x3544,x3545))
% 18.77/18.52 [355]~E(x3551,x3552)+E(f359(x3553,x3551,x3554,x3555),f359(x3553,x3552,x3554,x3555))
% 18.77/18.52 [356]~E(x3561,x3562)+E(f359(x3563,x3564,x3561,x3565),f359(x3563,x3564,x3562,x3565))
% 18.77/18.52 [357]~E(x3571,x3572)+E(f359(x3573,x3574,x3575,x3571),f359(x3573,x3574,x3575,x3572))
% 18.77/18.52 [358]~E(x3581,x3582)+E(f65(x3581,x3583,x3584),f65(x3582,x3583,x3584))
% 18.77/18.52 [359]~E(x3591,x3592)+E(f65(x3593,x3591,x3594),f65(x3593,x3592,x3594))
% 18.77/18.52 [360]~E(x3601,x3602)+E(f65(x3603,x3604,x3601),f65(x3603,x3604,x3602))
% 18.77/18.52 [361]~E(x3611,x3612)+E(f92(x3611,x3613),f92(x3612,x3613))
% 18.77/18.52 [362]~E(x3621,x3622)+E(f92(x3623,x3621),f92(x3623,x3622))
% 18.77/18.52 [363]~E(x3631,x3632)+E(f162(x3631,x3633),f162(x3632,x3633))
% 18.77/18.52 [364]~E(x3641,x3642)+E(f162(x3643,x3641),f162(x3643,x3642))
% 18.77/18.52 [365]~E(x3651,x3652)+E(f660(x3651,x3653,x3654,x3655,x3656,x3657,x3658,x3659),f660(x3652,x3653,x3654,x3655,x3656,x3657,x3658,x3659))
% 18.77/18.52 [366]~E(x3661,x3662)+E(f660(x3663,x3661,x3664,x3665,x3666,x3667,x3668,x3669),f660(x3663,x3662,x3664,x3665,x3666,x3667,x3668,x3669))
% 18.77/18.52 [367]~E(x3671,x3672)+E(f660(x3673,x3674,x3671,x3675,x3676,x3677,x3678,x3679),f660(x3673,x3674,x3672,x3675,x3676,x3677,x3678,x3679))
% 18.77/18.52 [368]~E(x3681,x3682)+E(f660(x3683,x3684,x3685,x3681,x3686,x3687,x3688,x3689),f660(x3683,x3684,x3685,x3682,x3686,x3687,x3688,x3689))
% 18.77/18.52 [369]~E(x3691,x3692)+E(f660(x3693,x3694,x3695,x3696,x3691,x3697,x3698,x3699),f660(x3693,x3694,x3695,x3696,x3692,x3697,x3698,x3699))
% 18.77/18.52 [370]~E(x3701,x3702)+E(f660(x3703,x3704,x3705,x3706,x3707,x3701,x3708,x3709),f660(x3703,x3704,x3705,x3706,x3707,x3702,x3708,x3709))
% 18.77/18.52 [371]~E(x3711,x3712)+E(f660(x3713,x3714,x3715,x3716,x3717,x3718,x3711,x3719),f660(x3713,x3714,x3715,x3716,x3717,x3718,x3712,x3719))
% 18.77/18.52 [372]~E(x3721,x3722)+E(f660(x3723,x3724,x3725,x3726,x3727,x3728,x3729,x3721),f660(x3723,x3724,x3725,x3726,x3727,x3728,x3729,x3722))
% 18.77/18.52 [373]~E(x3731,x3732)+E(f616(x3731,x3733),f616(x3732,x3733))
% 18.77/18.52 [374]~E(x3741,x3742)+E(f616(x3743,x3741),f616(x3743,x3742))
% 18.77/18.52 [375]~E(x3751,x3752)+E(f253(x3751,x3753,x3754,x3755,x3756,x3757),f253(x3752,x3753,x3754,x3755,x3756,x3757))
% 18.77/18.52 [376]~E(x3761,x3762)+E(f253(x3763,x3761,x3764,x3765,x3766,x3767),f253(x3763,x3762,x3764,x3765,x3766,x3767))
% 18.77/18.52 [377]~E(x3771,x3772)+E(f253(x3773,x3774,x3771,x3775,x3776,x3777),f253(x3773,x3774,x3772,x3775,x3776,x3777))
% 18.77/18.52 [378]~E(x3781,x3782)+E(f253(x3783,x3784,x3785,x3781,x3786,x3787),f253(x3783,x3784,x3785,x3782,x3786,x3787))
% 18.77/18.52 [379]~E(x3791,x3792)+E(f253(x3793,x3794,x3795,x3796,x3791,x3797),f253(x3793,x3794,x3795,x3796,x3792,x3797))
% 18.77/18.52 [380]~E(x3801,x3802)+E(f253(x3803,x3804,x3805,x3806,x3807,x3801),f253(x3803,x3804,x3805,x3806,x3807,x3802))
% 18.77/18.52 [381]~E(x3811,x3812)+E(f206(x3811),f206(x3812))
% 18.77/18.52 [382]~E(x3821,x3822)+E(f166(x3821,x3823),f166(x3822,x3823))
% 18.77/18.52 [383]~E(x3831,x3832)+E(f166(x3833,x3831),f166(x3833,x3832))
% 18.77/18.52 [384]~E(x3841,x3842)+E(f534(x3841,x3843,x3844,x3845,x3846),f534(x3842,x3843,x3844,x3845,x3846))
% 18.77/18.52 [385]~E(x3851,x3852)+E(f534(x3853,x3851,x3854,x3855,x3856),f534(x3853,x3852,x3854,x3855,x3856))
% 18.77/18.52 [386]~E(x3861,x3862)+E(f534(x3863,x3864,x3861,x3865,x3866),f534(x3863,x3864,x3862,x3865,x3866))
% 18.77/18.52 [387]~E(x3871,x3872)+E(f534(x3873,x3874,x3875,x3871,x3876),f534(x3873,x3874,x3875,x3872,x3876))
% 18.77/18.52 [388]~E(x3881,x3882)+E(f534(x3883,x3884,x3885,x3886,x3881),f534(x3883,x3884,x3885,x3886,x3882))
% 18.77/18.52 [389]~E(x3891,x3892)+E(f553(x3891),f553(x3892))
% 18.77/18.52 [390]~E(x3901,x3902)+E(f539(x3901),f539(x3902))
% 18.77/18.52 [391]~E(x3911,x3912)+E(f93(x3911),f93(x3912))
% 18.77/18.52 [392]~E(x3921,x3922)+E(f35(x3921,x3923),f35(x3922,x3923))
% 18.77/18.52 [393]~E(x3931,x3932)+E(f35(x3933,x3931),f35(x3933,x3932))
% 18.77/18.52 [394]~E(x3941,x3942)+E(f768(x3941,x3943,x3944),f768(x3942,x3943,x3944))
% 18.77/18.52 [395]~E(x3951,x3952)+E(f768(x3953,x3951,x3954),f768(x3953,x3952,x3954))
% 18.77/18.52 [396]~E(x3961,x3962)+E(f768(x3963,x3964,x3961),f768(x3963,x3964,x3962))
% 18.77/18.52 [397]~E(x3971,x3972)+E(f348(x3971,x3973),f348(x3972,x3973))
% 18.77/18.52 [398]~E(x3981,x3982)+E(f348(x3983,x3981),f348(x3983,x3982))
% 18.77/18.52 [399]~E(x3991,x3992)+E(f262(x3991,x3993),f262(x3992,x3993))
% 18.77/18.52 [400]~E(x4001,x4002)+E(f262(x4003,x4001),f262(x4003,x4002))
% 18.77/18.52 [401]~E(x4011,x4012)+E(f305(x4011,x4013,x4014),f305(x4012,x4013,x4014))
% 18.77/18.52 [402]~E(x4021,x4022)+E(f305(x4023,x4021,x4024),f305(x4023,x4022,x4024))
% 18.77/18.52 [403]~E(x4031,x4032)+E(f305(x4033,x4034,x4031),f305(x4033,x4034,x4032))
% 18.77/18.52 [404]~E(x4041,x4042)+E(f146(x4041,x4043),f146(x4042,x4043))
% 18.77/18.52 [405]~E(x4051,x4052)+E(f146(x4053,x4051),f146(x4053,x4052))
% 18.77/18.52 [406]~E(x4061,x4062)+E(f283(x4061,x4063,x4064,x4065),f283(x4062,x4063,x4064,x4065))
% 18.77/18.52 [407]~E(x4071,x4072)+E(f283(x4073,x4071,x4074,x4075),f283(x4073,x4072,x4074,x4075))
% 18.77/18.52 [408]~E(x4081,x4082)+E(f283(x4083,x4084,x4081,x4085),f283(x4083,x4084,x4082,x4085))
% 18.77/18.52 [409]~E(x4091,x4092)+E(f283(x4093,x4094,x4095,x4091),f283(x4093,x4094,x4095,x4092))
% 18.77/18.52 [410]~E(x4101,x4102)+E(f611(x4101,x4103,x4104,x4105),f611(x4102,x4103,x4104,x4105))
% 18.77/18.52 [411]~E(x4111,x4112)+E(f611(x4113,x4111,x4114,x4115),f611(x4113,x4112,x4114,x4115))
% 18.77/18.52 [412]~E(x4121,x4122)+E(f611(x4123,x4124,x4121,x4125),f611(x4123,x4124,x4122,x4125))
% 18.77/18.52 [413]~E(x4131,x4132)+E(f611(x4133,x4134,x4135,x4131),f611(x4133,x4134,x4135,x4132))
% 18.77/18.52 [414]~E(x4141,x4142)+E(f722(x4141,x4143,x4144,x4145),f722(x4142,x4143,x4144,x4145))
% 18.77/18.52 [415]~E(x4151,x4152)+E(f722(x4153,x4151,x4154,x4155),f722(x4153,x4152,x4154,x4155))
% 18.77/18.52 [416]~E(x4161,x4162)+E(f722(x4163,x4164,x4161,x4165),f722(x4163,x4164,x4162,x4165))
% 18.77/18.52 [417]~E(x4171,x4172)+E(f722(x4173,x4174,x4175,x4171),f722(x4173,x4174,x4175,x4172))
% 18.77/18.52 [418]~E(x4181,x4182)+E(f69(x4181,x4183,x4184,x4185,x4186),f69(x4182,x4183,x4184,x4185,x4186))
% 18.77/18.52 [419]~E(x4191,x4192)+E(f69(x4193,x4191,x4194,x4195,x4196),f69(x4193,x4192,x4194,x4195,x4196))
% 18.77/18.52 [420]~E(x4201,x4202)+E(f69(x4203,x4204,x4201,x4205,x4206),f69(x4203,x4204,x4202,x4205,x4206))
% 18.77/18.52 [421]~E(x4211,x4212)+E(f69(x4213,x4214,x4215,x4211,x4216),f69(x4213,x4214,x4215,x4212,x4216))
% 18.77/18.52 [422]~E(x4221,x4222)+E(f69(x4223,x4224,x4225,x4226,x4221),f69(x4223,x4224,x4225,x4226,x4222))
% 18.77/18.52 [423]~E(x4231,x4232)+E(f387(x4231,x4233,x4234,x4235),f387(x4232,x4233,x4234,x4235))
% 18.77/18.52 [424]~E(x4241,x4242)+E(f387(x4243,x4241,x4244,x4245),f387(x4243,x4242,x4244,x4245))
% 18.77/18.52 [425]~E(x4251,x4252)+E(f387(x4253,x4254,x4251,x4255),f387(x4253,x4254,x4252,x4255))
% 18.77/18.52 [426]~E(x4261,x4262)+E(f387(x4263,x4264,x4265,x4261),f387(x4263,x4264,x4265,x4262))
% 18.77/18.52 [427]~E(x4271,x4272)+E(f56(x4271,x4273),f56(x4272,x4273))
% 18.77/18.52 [428]~E(x4281,x4282)+E(f56(x4283,x4281),f56(x4283,x4282))
% 18.77/18.52 [429]~E(x4291,x4292)+E(f848(x4291,x4293),f848(x4292,x4293))
% 18.77/18.52 [430]~E(x4301,x4302)+E(f848(x4303,x4301),f848(x4303,x4302))
% 18.77/18.52 [431]~E(x4311,x4312)+E(f225(x4311,x4313),f225(x4312,x4313))
% 18.77/18.52 [432]~E(x4321,x4322)+E(f225(x4323,x4321),f225(x4323,x4322))
% 18.77/18.52 [433]~E(x4331,x4332)+E(f824(x4331,x4333,x4334),f824(x4332,x4333,x4334))
% 18.77/18.52 [434]~E(x4341,x4342)+E(f824(x4343,x4341,x4344),f824(x4343,x4342,x4344))
% 18.77/18.52 [435]~E(x4351,x4352)+E(f824(x4353,x4354,x4351),f824(x4353,x4354,x4352))
% 18.77/18.52 [436]~E(x4361,x4362)+E(f16(x4361,x4363),f16(x4362,x4363))
% 18.77/18.52 [437]~E(x4371,x4372)+E(f16(x4373,x4371),f16(x4373,x4372))
% 18.77/18.52 [438]~E(x4381,x4382)+E(f161(x4381,x4383,x4384),f161(x4382,x4383,x4384))
% 18.77/18.52 [439]~E(x4391,x4392)+E(f161(x4393,x4391,x4394),f161(x4393,x4392,x4394))
% 18.77/18.52 [440]~E(x4401,x4402)+E(f161(x4403,x4404,x4401),f161(x4403,x4404,x4402))
% 18.77/18.52 [441]~E(x4411,x4412)+E(f781(x4411,x4413,x4414),f781(x4412,x4413,x4414))
% 18.77/18.52 [442]~E(x4421,x4422)+E(f781(x4423,x4421,x4424),f781(x4423,x4422,x4424))
% 18.77/18.52 [443]~E(x4431,x4432)+E(f781(x4433,x4434,x4431),f781(x4433,x4434,x4432))
% 18.77/18.52 [444]~E(x4441,x4442)+E(f341(x4441,x4443,x4444,x4445),f341(x4442,x4443,x4444,x4445))
% 18.77/18.52 [445]~E(x4451,x4452)+E(f341(x4453,x4451,x4454,x4455),f341(x4453,x4452,x4454,x4455))
% 18.77/18.52 [446]~E(x4461,x4462)+E(f341(x4463,x4464,x4461,x4465),f341(x4463,x4464,x4462,x4465))
% 18.77/18.52 [447]~E(x4471,x4472)+E(f341(x4473,x4474,x4475,x4471),f341(x4473,x4474,x4475,x4472))
% 18.77/18.52 [448]~E(x4481,x4482)+E(f129(x4481,x4483),f129(x4482,x4483))
% 18.77/18.52 [449]~E(x4491,x4492)+E(f129(x4493,x4491),f129(x4493,x4492))
% 18.77/18.52 [450]~E(x4501,x4502)+E(f300(x4501),f300(x4502))
% 18.77/18.52 [451]~E(x4511,x4512)+E(f662(x4511,x4513,x4514,x4515),f662(x4512,x4513,x4514,x4515))
% 18.77/18.52 [452]~E(x4521,x4522)+E(f662(x4523,x4521,x4524,x4525),f662(x4523,x4522,x4524,x4525))
% 18.77/18.52 [453]~E(x4531,x4532)+E(f662(x4533,x4534,x4531,x4535),f662(x4533,x4534,x4532,x4535))
% 18.77/18.52 [454]~E(x4541,x4542)+E(f662(x4543,x4544,x4545,x4541),f662(x4543,x4544,x4545,x4542))
% 18.77/18.52 [455]~E(x4551,x4552)+E(f88(x4551,x4553),f88(x4552,x4553))
% 18.77/18.52 [456]~E(x4561,x4562)+E(f88(x4563,x4561),f88(x4563,x4562))
% 18.77/18.52 [457]~E(x4571,x4572)+E(f786(x4571,x4573,x4574),f786(x4572,x4573,x4574))
% 18.77/18.52 [458]~E(x4581,x4582)+E(f786(x4583,x4581,x4584),f786(x4583,x4582,x4584))
% 18.77/18.52 [459]~E(x4591,x4592)+E(f786(x4593,x4594,x4591),f786(x4593,x4594,x4592))
% 18.77/18.52 [460]~E(x4601,x4602)+E(f171(x4601,x4603,x4604,x4605),f171(x4602,x4603,x4604,x4605))
% 18.77/18.52 [461]~E(x4611,x4612)+E(f171(x4613,x4611,x4614,x4615),f171(x4613,x4612,x4614,x4615))
% 18.77/18.52 [462]~E(x4621,x4622)+E(f171(x4623,x4624,x4621,x4625),f171(x4623,x4624,x4622,x4625))
% 18.77/18.52 [463]~E(x4631,x4632)+E(f171(x4633,x4634,x4635,x4631),f171(x4633,x4634,x4635,x4632))
% 18.77/18.52 [464]~E(x4641,x4642)+E(f852(x4641),f852(x4642))
% 18.77/18.52 [465]~E(x4651,x4652)+E(f297(x4651),f297(x4652))
% 18.77/18.52 [466]~E(x4661,x4662)+E(f589(x4661,x4663,x4664),f589(x4662,x4663,x4664))
% 18.77/18.52 [467]~E(x4671,x4672)+E(f589(x4673,x4671,x4674),f589(x4673,x4672,x4674))
% 18.77/18.52 [468]~E(x4681,x4682)+E(f589(x4683,x4684,x4681),f589(x4683,x4684,x4682))
% 18.77/18.52 [469]~E(x4691,x4692)+E(f654(x4691,x4693,x4694),f654(x4692,x4693,x4694))
% 18.77/18.52 [470]~E(x4701,x4702)+E(f654(x4703,x4701,x4704),f654(x4703,x4702,x4704))
% 18.77/18.52 [471]~E(x4711,x4712)+E(f654(x4713,x4714,x4711),f654(x4713,x4714,x4712))
% 18.77/18.52 [472]~E(x4721,x4722)+E(f33(x4721,x4723,x4724),f33(x4722,x4723,x4724))
% 18.77/18.52 [473]~E(x4731,x4732)+E(f33(x4733,x4731,x4734),f33(x4733,x4732,x4734))
% 18.77/18.52 [474]~E(x4741,x4742)+E(f33(x4743,x4744,x4741),f33(x4743,x4744,x4742))
% 18.77/18.52 [475]~E(x4751,x4752)+E(f681(x4751,x4753,x4754,x4755),f681(x4752,x4753,x4754,x4755))
% 18.77/18.52 [476]~E(x4761,x4762)+E(f681(x4763,x4761,x4764,x4765),f681(x4763,x4762,x4764,x4765))
% 18.77/18.52 [477]~E(x4771,x4772)+E(f681(x4773,x4774,x4771,x4775),f681(x4773,x4774,x4772,x4775))
% 18.77/18.52 [478]~E(x4781,x4782)+E(f681(x4783,x4784,x4785,x4781),f681(x4783,x4784,x4785,x4782))
% 18.77/18.52 [479]~E(x4791,x4792)+E(f294(x4791),f294(x4792))
% 18.77/18.52 [480]~E(x4801,x4802)+E(f259(x4801),f259(x4802))
% 18.77/18.52 [481]~E(x4811,x4812)+E(f816(x4811,x4813,x4814),f816(x4812,x4813,x4814))
% 18.77/18.52 [482]~E(x4821,x4822)+E(f816(x4823,x4821,x4824),f816(x4823,x4822,x4824))
% 18.77/18.52 [483]~E(x4831,x4832)+E(f816(x4833,x4834,x4831),f816(x4833,x4834,x4832))
% 18.77/18.52 [484]~E(x4841,x4842)+E(f708(x4841,x4843,x4844,x4845,x4846),f708(x4842,x4843,x4844,x4845,x4846))
% 18.77/18.52 [485]~E(x4851,x4852)+E(f708(x4853,x4851,x4854,x4855,x4856),f708(x4853,x4852,x4854,x4855,x4856))
% 18.77/18.52 [486]~E(x4861,x4862)+E(f708(x4863,x4864,x4861,x4865,x4866),f708(x4863,x4864,x4862,x4865,x4866))
% 18.77/18.52 [487]~E(x4871,x4872)+E(f708(x4873,x4874,x4875,x4871,x4876),f708(x4873,x4874,x4875,x4872,x4876))
% 18.77/18.52 [488]~E(x4881,x4882)+E(f708(x4883,x4884,x4885,x4886,x4881),f708(x4883,x4884,x4885,x4886,x4882))
% 18.77/18.52 [489]~E(x4891,x4892)+E(f740(x4891,x4893,x4894,x4895,x4896),f740(x4892,x4893,x4894,x4895,x4896))
% 18.77/18.52 [490]~E(x4901,x4902)+E(f740(x4903,x4901,x4904,x4905,x4906),f740(x4903,x4902,x4904,x4905,x4906))
% 18.77/18.52 [491]~E(x4911,x4912)+E(f740(x4913,x4914,x4911,x4915,x4916),f740(x4913,x4914,x4912,x4915,x4916))
% 18.77/18.52 [492]~E(x4921,x4922)+E(f740(x4923,x4924,x4925,x4921,x4926),f740(x4923,x4924,x4925,x4922,x4926))
% 18.77/18.52 [493]~E(x4931,x4932)+E(f740(x4933,x4934,x4935,x4936,x4931),f740(x4933,x4934,x4935,x4936,x4932))
% 18.77/18.52 [494]~E(x4941,x4942)+E(f621(x4941,x4943,x4944,x4945),f621(x4942,x4943,x4944,x4945))
% 18.77/18.52 [495]~E(x4951,x4952)+E(f621(x4953,x4951,x4954,x4955),f621(x4953,x4952,x4954,x4955))
% 18.77/18.52 [496]~E(x4961,x4962)+E(f621(x4963,x4964,x4961,x4965),f621(x4963,x4964,x4962,x4965))
% 18.77/18.52 [497]~E(x4971,x4972)+E(f621(x4973,x4974,x4975,x4971),f621(x4973,x4974,x4975,x4972))
% 18.77/18.52 [498]~E(x4981,x4982)+E(f529(x4981,x4983,x4984,x4985),f529(x4982,x4983,x4984,x4985))
% 18.77/18.52 [499]~E(x4991,x4992)+E(f529(x4993,x4991,x4994,x4995),f529(x4993,x4992,x4994,x4995))
% 18.77/18.52 [500]~E(x5001,x5002)+E(f529(x5003,x5004,x5001,x5005),f529(x5003,x5004,x5002,x5005))
% 18.77/18.52 [501]~E(x5011,x5012)+E(f529(x5013,x5014,x5015,x5011),f529(x5013,x5014,x5015,x5012))
% 18.77/18.52 [502]~E(x5021,x5022)+E(f260(x5021,x5023),f260(x5022,x5023))
% 18.77/18.52 [503]~E(x5031,x5032)+E(f260(x5033,x5031),f260(x5033,x5032))
% 18.77/18.52 [504]~E(x5041,x5042)+E(f186(x5041),f186(x5042))
% 18.77/18.52 [505]~E(x5051,x5052)+E(f361(x5051,x5053,x5054,x5055),f361(x5052,x5053,x5054,x5055))
% 18.77/18.52 [506]~E(x5061,x5062)+E(f361(x5063,x5061,x5064,x5065),f361(x5063,x5062,x5064,x5065))
% 18.77/18.52 [507]~E(x5071,x5072)+E(f361(x5073,x5074,x5071,x5075),f361(x5073,x5074,x5072,x5075))
% 18.77/18.52 [508]~E(x5081,x5082)+E(f361(x5083,x5084,x5085,x5081),f361(x5083,x5084,x5085,x5082))
% 18.77/18.52 [509]~E(x5091,x5092)+E(f174(x5091,x5093,x5094,x5095),f174(x5092,x5093,x5094,x5095))
% 18.77/18.52 [510]~E(x5101,x5102)+E(f174(x5103,x5101,x5104,x5105),f174(x5103,x5102,x5104,x5105))
% 18.77/18.52 [511]~E(x5111,x5112)+E(f174(x5113,x5114,x5111,x5115),f174(x5113,x5114,x5112,x5115))
% 18.77/18.52 [512]~E(x5121,x5122)+E(f174(x5123,x5124,x5125,x5121),f174(x5123,x5124,x5125,x5122))
% 18.77/18.52 [513]~E(x5131,x5132)+E(f549(x5131,x5133,x5134,x5135),f549(x5132,x5133,x5134,x5135))
% 18.77/18.52 [514]~E(x5141,x5142)+E(f549(x5143,x5141,x5144,x5145),f549(x5143,x5142,x5144,x5145))
% 18.77/18.52 [515]~E(x5151,x5152)+E(f549(x5153,x5154,x5151,x5155),f549(x5153,x5154,x5152,x5155))
% 18.77/18.52 [516]~E(x5161,x5162)+E(f549(x5163,x5164,x5165,x5161),f549(x5163,x5164,x5165,x5162))
% 18.77/18.52 [517]~E(x5171,x5172)+E(f550(x5171,x5173,x5174,x5175),f550(x5172,x5173,x5174,x5175))
% 18.77/18.52 [518]~E(x5181,x5182)+E(f550(x5183,x5181,x5184,x5185),f550(x5183,x5182,x5184,x5185))
% 18.77/18.52 [519]~E(x5191,x5192)+E(f550(x5193,x5194,x5191,x5195),f550(x5193,x5194,x5192,x5195))
% 18.77/18.52 [520]~E(x5201,x5202)+E(f550(x5203,x5204,x5205,x5201),f550(x5203,x5204,x5205,x5202))
% 18.77/18.52 [521]~E(x5211,x5212)+E(f53(x5211,x5213),f53(x5212,x5213))
% 18.77/18.52 [522]~E(x5221,x5222)+E(f53(x5223,x5221),f53(x5223,x5222))
% 18.77/18.52 [523]~E(x5231,x5232)+E(f265(x5231),f265(x5232))
% 18.77/18.52 [524]~E(x5241,x5242)+E(f150(x5241,x5243,x5244,x5245),f150(x5242,x5243,x5244,x5245))
% 18.77/18.52 [525]~E(x5251,x5252)+E(f150(x5253,x5251,x5254,x5255),f150(x5253,x5252,x5254,x5255))
% 18.77/18.52 [526]~E(x5261,x5262)+E(f150(x5263,x5264,x5261,x5265),f150(x5263,x5264,x5262,x5265))
% 18.77/18.52 [527]~E(x5271,x5272)+E(f150(x5273,x5274,x5275,x5271),f150(x5273,x5274,x5275,x5272))
% 18.77/18.52 [528]~E(x5281,x5282)+E(f151(x5281),f151(x5282))
% 18.77/18.52 [529]~E(x5291,x5292)+E(f788(x5291,x5293,x5294,x5295),f788(x5292,x5293,x5294,x5295))
% 18.77/18.52 [530]~E(x5301,x5302)+E(f788(x5303,x5301,x5304,x5305),f788(x5303,x5302,x5304,x5305))
% 18.77/18.52 [531]~E(x5311,x5312)+E(f788(x5313,x5314,x5311,x5315),f788(x5313,x5314,x5312,x5315))
% 18.77/18.52 [532]~E(x5321,x5322)+E(f788(x5323,x5324,x5325,x5321),f788(x5323,x5324,x5325,x5322))
% 18.77/18.52 [533]~E(x5331,x5332)+E(f598(x5331,x5333,x5334),f598(x5332,x5333,x5334))
% 18.77/18.52 [534]~E(x5341,x5342)+E(f598(x5343,x5341,x5344),f598(x5343,x5342,x5344))
% 18.77/18.52 [535]~E(x5351,x5352)+E(f598(x5353,x5354,x5351),f598(x5353,x5354,x5352))
% 18.77/18.52 [536]~E(x5361,x5362)+E(f724(x5361,x5363,x5364,x5365,x5366),f724(x5362,x5363,x5364,x5365,x5366))
% 18.77/18.52 [537]~E(x5371,x5372)+E(f724(x5373,x5371,x5374,x5375,x5376),f724(x5373,x5372,x5374,x5375,x5376))
% 18.77/18.52 [538]~E(x5381,x5382)+E(f724(x5383,x5384,x5381,x5385,x5386),f724(x5383,x5384,x5382,x5385,x5386))
% 18.77/18.52 [539]~E(x5391,x5392)+E(f724(x5393,x5394,x5395,x5391,x5396),f724(x5393,x5394,x5395,x5392,x5396))
% 18.77/18.52 [540]~E(x5401,x5402)+E(f724(x5403,x5404,x5405,x5406,x5401),f724(x5403,x5404,x5405,x5406,x5402))
% 18.77/18.52 [541]~E(x5411,x5412)+E(f411(x5411,x5413,x5414),f411(x5412,x5413,x5414))
% 18.77/18.52 [542]~E(x5421,x5422)+E(f411(x5423,x5421,x5424),f411(x5423,x5422,x5424))
% 18.77/18.52 [543]~E(x5431,x5432)+E(f411(x5433,x5434,x5431),f411(x5433,x5434,x5432))
% 18.77/18.52 [544]~E(x5441,x5442)+E(f239(x5441,x5443,x5444),f239(x5442,x5443,x5444))
% 18.77/18.52 [545]~E(x5451,x5452)+E(f239(x5453,x5451,x5454),f239(x5453,x5452,x5454))
% 18.77/18.52 [546]~E(x5461,x5462)+E(f239(x5463,x5464,x5461),f239(x5463,x5464,x5462))
% 18.77/18.52 [547]~E(x5471,x5472)+E(f245(x5471,x5473,x5474),f245(x5472,x5473,x5474))
% 18.77/18.52 [548]~E(x5481,x5482)+E(f245(x5483,x5481,x5484),f245(x5483,x5482,x5484))
% 18.77/18.52 [549]~E(x5491,x5492)+E(f245(x5493,x5494,x5491),f245(x5493,x5494,x5492))
% 18.77/18.52 [550]~E(x5501,x5502)+E(f713(x5501,x5503,x5504),f713(x5502,x5503,x5504))
% 18.77/18.52 [551]~E(x5511,x5512)+E(f713(x5513,x5511,x5514),f713(x5513,x5512,x5514))
% 18.77/18.52 [552]~E(x5521,x5522)+E(f713(x5523,x5524,x5521),f713(x5523,x5524,x5522))
% 18.77/18.52 [553]~E(x5531,x5532)+E(f777(x5531,x5533,x5534),f777(x5532,x5533,x5534))
% 18.77/18.52 [554]~E(x5541,x5542)+E(f777(x5543,x5541,x5544),f777(x5543,x5542,x5544))
% 18.77/18.52 [555]~E(x5551,x5552)+E(f777(x5553,x5554,x5551),f777(x5553,x5554,x5552))
% 18.77/18.52 [556]~E(x5561,x5562)+E(f195(x5561,x5563),f195(x5562,x5563))
% 18.77/18.52 [557]~E(x5571,x5572)+E(f195(x5573,x5571),f195(x5573,x5572))
% 18.77/18.52 [558]~E(x5581,x5582)+E(f709(x5581,x5583),f709(x5582,x5583))
% 18.77/18.52 [559]~E(x5591,x5592)+E(f709(x5593,x5591),f709(x5593,x5592))
% 18.77/18.52 [560]~E(x5601,x5602)+E(f138(x5601,x5603,x5604,x5605,x5606),f138(x5602,x5603,x5604,x5605,x5606))
% 18.77/18.52 [561]~E(x5611,x5612)+E(f138(x5613,x5611,x5614,x5615,x5616),f138(x5613,x5612,x5614,x5615,x5616))
% 18.77/18.52 [562]~E(x5621,x5622)+E(f138(x5623,x5624,x5621,x5625,x5626),f138(x5623,x5624,x5622,x5625,x5626))
% 18.77/18.52 [563]~E(x5631,x5632)+E(f138(x5633,x5634,x5635,x5631,x5636),f138(x5633,x5634,x5635,x5632,x5636))
% 18.77/18.52 [564]~E(x5641,x5642)+E(f138(x5643,x5644,x5645,x5646,x5641),f138(x5643,x5644,x5645,x5646,x5642))
% 18.77/18.52 [565]~E(x5651,x5652)+E(f362(x5651,x5653,x5654,x5655),f362(x5652,x5653,x5654,x5655))
% 18.77/18.52 [566]~E(x5661,x5662)+E(f362(x5663,x5661,x5664,x5665),f362(x5663,x5662,x5664,x5665))
% 18.77/18.52 [567]~E(x5671,x5672)+E(f362(x5673,x5674,x5671,x5675),f362(x5673,x5674,x5672,x5675))
% 18.77/18.52 [568]~E(x5681,x5682)+E(f362(x5683,x5684,x5685,x5681),f362(x5683,x5684,x5685,x5682))
% 18.77/18.52 [569]~E(x5691,x5692)+E(f450(x5691,x5693,x5694,x5695),f450(x5692,x5693,x5694,x5695))
% 18.77/18.52 [570]~E(x5701,x5702)+E(f450(x5703,x5701,x5704,x5705),f450(x5703,x5702,x5704,x5705))
% 18.77/18.52 [571]~E(x5711,x5712)+E(f450(x5713,x5714,x5711,x5715),f450(x5713,x5714,x5712,x5715))
% 18.77/18.52 [572]~E(x5721,x5722)+E(f450(x5723,x5724,x5725,x5721),f450(x5723,x5724,x5725,x5722))
% 18.77/18.52 [573]~E(x5731,x5732)+E(f266(x5731,x5733),f266(x5732,x5733))
% 18.77/18.52 [574]~E(x5741,x5742)+E(f266(x5743,x5741),f266(x5743,x5742))
% 18.77/18.52 [575]~E(x5751,x5752)+E(f840(x5751),f840(x5752))
% 18.77/18.52 [576]~E(x5761,x5762)+E(f165(x5761,x5763,x5764),f165(x5762,x5763,x5764))
% 18.77/18.52 [577]~E(x5771,x5772)+E(f165(x5773,x5771,x5774),f165(x5773,x5772,x5774))
% 18.77/18.52 [578]~E(x5781,x5782)+E(f165(x5783,x5784,x5781),f165(x5783,x5784,x5782))
% 18.77/18.52 [579]~E(x5791,x5792)+E(f696(x5791,x5793,x5794,x5795,x5796),f696(x5792,x5793,x5794,x5795,x5796))
% 18.77/18.52 [580]~E(x5801,x5802)+E(f696(x5803,x5801,x5804,x5805,x5806),f696(x5803,x5802,x5804,x5805,x5806))
% 18.77/18.52 [581]~E(x5811,x5812)+E(f696(x5813,x5814,x5811,x5815,x5816),f696(x5813,x5814,x5812,x5815,x5816))
% 18.77/18.52 [582]~E(x5821,x5822)+E(f696(x5823,x5824,x5825,x5821,x5826),f696(x5823,x5824,x5825,x5822,x5826))
% 18.77/18.52 [583]~E(x5831,x5832)+E(f696(x5833,x5834,x5835,x5836,x5831),f696(x5833,x5834,x5835,x5836,x5832))
% 18.77/18.52 [584]~E(x5841,x5842)+E(f641(x5841,x5843,x5844,x5845,x5846),f641(x5842,x5843,x5844,x5845,x5846))
% 18.77/18.52 [585]~E(x5851,x5852)+E(f641(x5853,x5851,x5854,x5855,x5856),f641(x5853,x5852,x5854,x5855,x5856))
% 18.77/18.52 [586]~E(x5861,x5862)+E(f641(x5863,x5864,x5861,x5865,x5866),f641(x5863,x5864,x5862,x5865,x5866))
% 18.77/18.52 [587]~E(x5871,x5872)+E(f641(x5873,x5874,x5875,x5871,x5876),f641(x5873,x5874,x5875,x5872,x5876))
% 18.77/18.52 [588]~E(x5881,x5882)+E(f641(x5883,x5884,x5885,x5886,x5881),f641(x5883,x5884,x5885,x5886,x5882))
% 18.77/18.52 [589]~E(x5891,x5892)+E(f761(x5891,x5893,x5894,x5895),f761(x5892,x5893,x5894,x5895))
% 18.77/18.52 [590]~E(x5901,x5902)+E(f761(x5903,x5901,x5904,x5905),f761(x5903,x5902,x5904,x5905))
% 18.77/18.52 [591]~E(x5911,x5912)+E(f761(x5913,x5914,x5911,x5915),f761(x5913,x5914,x5912,x5915))
% 18.77/18.52 [592]~E(x5921,x5922)+E(f761(x5923,x5924,x5925,x5921),f761(x5923,x5924,x5925,x5922))
% 18.77/18.52 [593]~E(x5931,x5932)+E(f370(x5931,x5933,x5934),f370(x5932,x5933,x5934))
% 18.77/18.52 [594]~E(x5941,x5942)+E(f370(x5943,x5941,x5944),f370(x5943,x5942,x5944))
% 18.77/18.52 [595]~E(x5951,x5952)+E(f370(x5953,x5954,x5951),f370(x5953,x5954,x5952))
% 18.77/18.52 [596]~E(x5961,x5962)+E(f736(x5961,x5963,x5964),f736(x5962,x5963,x5964))
% 18.77/18.52 [597]~E(x5971,x5972)+E(f736(x5973,x5971,x5974),f736(x5973,x5972,x5974))
% 18.77/18.52 [598]~E(x5981,x5982)+E(f736(x5983,x5984,x5981),f736(x5983,x5984,x5982))
% 18.77/18.52 [599]~E(x5991,x5992)+E(f89(x5991),f89(x5992))
% 18.77/18.52 [600]~E(x6001,x6002)+E(f164(x6001),f164(x6002))
% 18.77/18.52 [601]~E(x6011,x6012)+E(f84(x6011,x6013),f84(x6012,x6013))
% 18.77/18.52 [602]~E(x6021,x6022)+E(f84(x6023,x6021),f84(x6023,x6022))
% 18.77/18.52 [603]~E(x6031,x6032)+E(f794(x6031,x6033,x6034),f794(x6032,x6033,x6034))
% 18.77/18.52 [604]~E(x6041,x6042)+E(f794(x6043,x6041,x6044),f794(x6043,x6042,x6044))
% 18.77/18.52 [605]~E(x6051,x6052)+E(f794(x6053,x6054,x6051),f794(x6053,x6054,x6052))
% 18.77/18.52 [606]~E(x6061,x6062)+E(f613(x6061),f613(x6062))
% 18.77/18.52 [607]~E(x6071,x6072)+E(f444(x6071,x6073,x6074),f444(x6072,x6073,x6074))
% 18.77/18.52 [608]~E(x6081,x6082)+E(f444(x6083,x6081,x6084),f444(x6083,x6082,x6084))
% 18.77/18.52 [609]~E(x6091,x6092)+E(f444(x6093,x6094,x6091),f444(x6093,x6094,x6092))
% 18.77/18.52 [610]~E(x6101,x6102)+E(f261(x6101,x6103),f261(x6102,x6103))
% 18.77/18.52 [611]~E(x6111,x6112)+E(f261(x6113,x6111),f261(x6113,x6112))
% 18.77/18.52 [612]~E(x6121,x6122)+E(f31(x6121,x6123,x6124),f31(x6122,x6123,x6124))
% 18.77/18.52 [613]~E(x6131,x6132)+E(f31(x6133,x6131,x6134),f31(x6133,x6132,x6134))
% 18.77/18.52 [614]~E(x6141,x6142)+E(f31(x6143,x6144,x6141),f31(x6143,x6144,x6142))
% 18.77/18.52 [615]~E(x6151,x6152)+E(f495(x6151,x6153,x6154,x6155,x6156,x6157),f495(x6152,x6153,x6154,x6155,x6156,x6157))
% 18.77/18.52 [616]~E(x6161,x6162)+E(f495(x6163,x6161,x6164,x6165,x6166,x6167),f495(x6163,x6162,x6164,x6165,x6166,x6167))
% 18.77/18.52 [617]~E(x6171,x6172)+E(f495(x6173,x6174,x6171,x6175,x6176,x6177),f495(x6173,x6174,x6172,x6175,x6176,x6177))
% 18.77/18.52 [618]~E(x6181,x6182)+E(f495(x6183,x6184,x6185,x6181,x6186,x6187),f495(x6183,x6184,x6185,x6182,x6186,x6187))
% 18.77/18.52 [619]~E(x6191,x6192)+E(f495(x6193,x6194,x6195,x6196,x6191,x6197),f495(x6193,x6194,x6195,x6196,x6192,x6197))
% 18.77/18.52 [620]~E(x6201,x6202)+E(f495(x6203,x6204,x6205,x6206,x6207,x6201),f495(x6203,x6204,x6205,x6206,x6207,x6202))
% 18.77/18.52 [621]~E(x6211,x6212)+E(f14(x6211,x6213,x6214),f14(x6212,x6213,x6214))
% 18.77/18.52 [622]~E(x6221,x6222)+E(f14(x6223,x6221,x6224),f14(x6223,x6222,x6224))
% 18.77/18.52 [623]~E(x6231,x6232)+E(f14(x6233,x6234,x6231),f14(x6233,x6234,x6232))
% 18.77/18.52 [624]~E(x6241,x6242)+E(f693(x6241,x6243,x6244,x6245),f693(x6242,x6243,x6244,x6245))
% 18.77/18.52 [625]~E(x6251,x6252)+E(f693(x6253,x6251,x6254,x6255),f693(x6253,x6252,x6254,x6255))
% 18.77/18.52 [626]~E(x6261,x6262)+E(f693(x6263,x6264,x6261,x6265),f693(x6263,x6264,x6262,x6265))
% 18.77/18.52 [627]~E(x6271,x6272)+E(f693(x6273,x6274,x6275,x6271),f693(x6273,x6274,x6275,x6272))
% 18.77/18.52 [628]~E(x6281,x6282)+E(f818(x6281,x6283,x6284,x6285),f818(x6282,x6283,x6284,x6285))
% 18.77/18.52 [629]~E(x6291,x6292)+E(f818(x6293,x6291,x6294,x6295),f818(x6293,x6292,x6294,x6295))
% 18.77/18.52 [630]~E(x6301,x6302)+E(f818(x6303,x6304,x6301,x6305),f818(x6303,x6304,x6302,x6305))
% 18.77/18.52 [631]~E(x6311,x6312)+E(f818(x6313,x6314,x6315,x6311),f818(x6313,x6314,x6315,x6312))
% 18.77/18.52 [632]~E(x6321,x6322)+E(f209(x6321,x6323),f209(x6322,x6323))
% 18.77/18.52 [633]~E(x6331,x6332)+E(f209(x6333,x6331),f209(x6333,x6332))
% 18.77/18.52 [634]~E(x6341,x6342)+E(f695(x6341,x6343,x6344,x6345),f695(x6342,x6343,x6344,x6345))
% 18.77/18.52 [635]~E(x6351,x6352)+E(f695(x6353,x6351,x6354,x6355),f695(x6353,x6352,x6354,x6355))
% 18.77/18.52 [636]~E(x6361,x6362)+E(f695(x6363,x6364,x6361,x6365),f695(x6363,x6364,x6362,x6365))
% 18.77/18.52 [637]~E(x6371,x6372)+E(f695(x6373,x6374,x6375,x6371),f695(x6373,x6374,x6375,x6372))
% 18.77/18.52 [638]~E(x6381,x6382)+E(f473(x6381,x6383,x6384,x6385),f473(x6382,x6383,x6384,x6385))
% 18.77/18.52 [639]~E(x6391,x6392)+E(f473(x6393,x6391,x6394,x6395),f473(x6393,x6392,x6394,x6395))
% 18.77/18.52 [640]~E(x6401,x6402)+E(f473(x6403,x6404,x6401,x6405),f473(x6403,x6404,x6402,x6405))
% 18.77/18.52 [641]~E(x6411,x6412)+E(f473(x6413,x6414,x6415,x6411),f473(x6413,x6414,x6415,x6412))
% 18.77/18.52 [642]~E(x6421,x6422)+E(f32(x6421,x6423,x6424),f32(x6422,x6423,x6424))
% 18.77/18.52 [643]~E(x6431,x6432)+E(f32(x6433,x6431,x6434),f32(x6433,x6432,x6434))
% 18.77/18.52 [644]~E(x6441,x6442)+E(f32(x6443,x6444,x6441),f32(x6443,x6444,x6442))
% 18.77/18.52 [645]~E(x6451,x6452)+E(f787(x6451,x6453,x6454),f787(x6452,x6453,x6454))
% 18.77/18.52 [646]~E(x6461,x6462)+E(f787(x6463,x6461,x6464),f787(x6463,x6462,x6464))
% 18.77/18.52 [647]~E(x6471,x6472)+E(f787(x6473,x6474,x6471),f787(x6473,x6474,x6472))
% 18.77/18.52 [648]~E(x6481,x6482)+E(f254(x6481,x6483,x6484,x6485),f254(x6482,x6483,x6484,x6485))
% 18.77/18.52 [649]~E(x6491,x6492)+E(f254(x6493,x6491,x6494,x6495),f254(x6493,x6492,x6494,x6495))
% 18.77/18.52 [650]~E(x6501,x6502)+E(f254(x6503,x6504,x6501,x6505),f254(x6503,x6504,x6502,x6505))
% 18.77/18.52 [651]~E(x6511,x6512)+E(f254(x6513,x6514,x6515,x6511),f254(x6513,x6514,x6515,x6512))
% 18.77/18.52 [652]~E(x6521,x6522)+E(f552(x6521,x6523,x6524),f552(x6522,x6523,x6524))
% 18.77/18.52 [653]~E(x6531,x6532)+E(f552(x6533,x6531,x6534),f552(x6533,x6532,x6534))
% 18.77/18.52 [654]~E(x6541,x6542)+E(f552(x6543,x6544,x6541),f552(x6543,x6544,x6542))
% 18.77/18.52 [655]~E(x6551,x6552)+E(f187(x6551,x6553),f187(x6552,x6553))
% 18.77/18.52 [656]~E(x6561,x6562)+E(f187(x6563,x6561),f187(x6563,x6562))
% 18.77/18.52 [657]~E(x6571,x6572)+E(f578(x6571,x6573,x6574),f578(x6572,x6573,x6574))
% 18.77/18.52 [658]~E(x6581,x6582)+E(f578(x6583,x6581,x6584),f578(x6583,x6582,x6584))
% 18.77/18.52 [659]~E(x6591,x6592)+E(f578(x6593,x6594,x6591),f578(x6593,x6594,x6592))
% 18.77/18.52 [660]~E(x6601,x6602)+E(f469(x6601,x6603),f469(x6602,x6603))
% 18.77/18.52 [661]~E(x6611,x6612)+E(f469(x6613,x6611),f469(x6613,x6612))
% 18.77/18.52 [662]~E(x6621,x6622)+E(f264(x6621,x6623),f264(x6622,x6623))
% 18.77/18.52 [663]~E(x6631,x6632)+E(f264(x6633,x6631),f264(x6633,x6632))
% 18.77/18.52 [664]~E(x6641,x6642)+E(f200(x6641,x6643,x6644,x6645),f200(x6642,x6643,x6644,x6645))
% 18.77/18.52 [665]~E(x6651,x6652)+E(f200(x6653,x6651,x6654,x6655),f200(x6653,x6652,x6654,x6655))
% 18.77/18.52 [666]~E(x6661,x6662)+E(f200(x6663,x6664,x6661,x6665),f200(x6663,x6664,x6662,x6665))
% 18.77/18.52 [667]~E(x6671,x6672)+E(f200(x6673,x6674,x6675,x6671),f200(x6673,x6674,x6675,x6672))
% 18.77/18.52 [668]~E(x6681,x6682)+E(f668(x6681,x6683,x6684,x6685,x6686),f668(x6682,x6683,x6684,x6685,x6686))
% 18.77/18.52 [669]~E(x6691,x6692)+E(f668(x6693,x6691,x6694,x6695,x6696),f668(x6693,x6692,x6694,x6695,x6696))
% 18.77/18.52 [670]~E(x6701,x6702)+E(f668(x6703,x6704,x6701,x6705,x6706),f668(x6703,x6704,x6702,x6705,x6706))
% 18.77/18.52 [671]~E(x6711,x6712)+E(f668(x6713,x6714,x6715,x6711,x6716),f668(x6713,x6714,x6715,x6712,x6716))
% 18.77/18.52 [672]~E(x6721,x6722)+E(f668(x6723,x6724,x6725,x6726,x6721),f668(x6723,x6724,x6725,x6726,x6722))
% 18.77/18.52 [673]~E(x6731,x6732)+E(f646(x6731,x6733,x6734),f646(x6732,x6733,x6734))
% 18.77/18.52 [674]~E(x6741,x6742)+E(f646(x6743,x6741,x6744),f646(x6743,x6742,x6744))
% 18.77/18.52 [675]~E(x6751,x6752)+E(f646(x6753,x6754,x6751),f646(x6753,x6754,x6752))
% 18.77/18.52 [676]~E(x6761,x6762)+E(f228(x6761,x6763,x6764,x6765),f228(x6762,x6763,x6764,x6765))
% 18.77/18.52 [677]~E(x6771,x6772)+E(f228(x6773,x6771,x6774,x6775),f228(x6773,x6772,x6774,x6775))
% 18.77/18.52 [678]~E(x6781,x6782)+E(f228(x6783,x6784,x6781,x6785),f228(x6783,x6784,x6782,x6785))
% 18.77/18.52 [679]~E(x6791,x6792)+E(f228(x6793,x6794,x6795,x6791),f228(x6793,x6794,x6795,x6792))
% 18.77/18.52 [680]~E(x6801,x6802)+E(f344(x6801,x6803),f344(x6802,x6803))
% 18.77/18.52 [681]~E(x6811,x6812)+E(f344(x6813,x6811),f344(x6813,x6812))
% 18.77/18.52 [682]~E(x6821,x6822)+E(f134(x6821,x6823),f134(x6822,x6823))
% 18.77/18.52 [683]~E(x6831,x6832)+E(f134(x6833,x6831),f134(x6833,x6832))
% 18.77/18.52 [684]~E(x6841,x6842)+E(f345(x6841,x6843),f345(x6842,x6843))
% 18.77/18.52 [685]~E(x6851,x6852)+E(f345(x6853,x6851),f345(x6853,x6852))
% 18.77/18.52 [686]~E(x6861,x6862)+E(f340(x6861,x6863,x6864,x6865),f340(x6862,x6863,x6864,x6865))
% 18.77/18.52 [687]~E(x6871,x6872)+E(f340(x6873,x6871,x6874,x6875),f340(x6873,x6872,x6874,x6875))
% 18.77/18.52 [688]~E(x6881,x6882)+E(f340(x6883,x6884,x6881,x6885),f340(x6883,x6884,x6882,x6885))
% 18.77/18.52 [689]~E(x6891,x6892)+E(f340(x6893,x6894,x6895,x6891),f340(x6893,x6894,x6895,x6892))
% 18.77/18.52 [690]~E(x6901,x6902)+E(f152(x6901,x6903,x6904),f152(x6902,x6903,x6904))
% 18.77/18.52 [691]~E(x6911,x6912)+E(f152(x6913,x6911,x6914),f152(x6913,x6912,x6914))
% 18.77/18.52 [692]~E(x6921,x6922)+E(f152(x6923,x6924,x6921),f152(x6923,x6924,x6922))
% 18.77/18.52 [693]~E(x6931,x6932)+E(f336(x6931,x6933),f336(x6932,x6933))
% 18.77/18.52 [694]~E(x6941,x6942)+E(f336(x6943,x6941),f336(x6943,x6942))
% 18.77/18.52 [695]~E(x6951,x6952)+E(f277(x6951),f277(x6952))
% 18.77/18.52 [696]~E(x6961,x6962)+E(f719(x6961,x6963,x6964),f719(x6962,x6963,x6964))
% 18.77/18.52 [697]~E(x6971,x6972)+E(f719(x6973,x6971,x6974),f719(x6973,x6972,x6974))
% 18.77/18.52 [698]~E(x6981,x6982)+E(f719(x6983,x6984,x6981),f719(x6983,x6984,x6982))
% 18.77/18.52 [699]~E(x6991,x6992)+E(f147(x6991,x6993),f147(x6992,x6993))
% 18.77/18.52 [700]~E(x7001,x7002)+E(f147(x7003,x7001),f147(x7003,x7002))
% 18.77/18.52 [701]~E(x7011,x7012)+E(f192(x7011,x7013,x7014,x7015),f192(x7012,x7013,x7014,x7015))
% 18.77/18.52 [702]~E(x7021,x7022)+E(f192(x7023,x7021,x7024,x7025),f192(x7023,x7022,x7024,x7025))
% 18.77/18.52 [703]~E(x7031,x7032)+E(f192(x7033,x7034,x7031,x7035),f192(x7033,x7034,x7032,x7035))
% 18.77/18.52 [704]~E(x7041,x7042)+E(f192(x7043,x7044,x7045,x7041),f192(x7043,x7044,x7045,x7042))
% 18.77/18.52 [705]~E(x7051,x7052)+E(f742(x7051,x7053,x7054,x7055),f742(x7052,x7053,x7054,x7055))
% 18.77/18.52 [706]~E(x7061,x7062)+E(f742(x7063,x7061,x7064,x7065),f742(x7063,x7062,x7064,x7065))
% 18.77/18.52 [707]~E(x7071,x7072)+E(f742(x7073,x7074,x7071,x7075),f742(x7073,x7074,x7072,x7075))
% 18.77/18.52 [708]~E(x7081,x7082)+E(f742(x7083,x7084,x7085,x7081),f742(x7083,x7084,x7085,x7082))
% 18.77/18.52 [709]~E(x7091,x7092)+E(f822(x7091,x7093,x7094,x7095,x7096),f822(x7092,x7093,x7094,x7095,x7096))
% 18.77/18.52 [710]~E(x7101,x7102)+E(f822(x7103,x7101,x7104,x7105,x7106),f822(x7103,x7102,x7104,x7105,x7106))
% 18.77/18.52 [711]~E(x7111,x7112)+E(f822(x7113,x7114,x7111,x7115,x7116),f822(x7113,x7114,x7112,x7115,x7116))
% 18.77/18.52 [712]~E(x7121,x7122)+E(f822(x7123,x7124,x7125,x7121,x7126),f822(x7123,x7124,x7125,x7122,x7126))
% 18.77/18.52 [713]~E(x7131,x7132)+E(f822(x7133,x7134,x7135,x7136,x7131),f822(x7133,x7134,x7135,x7136,x7132))
% 18.77/18.52 [714]~E(x7141,x7142)+E(f700(x7141,x7143,x7144),f700(x7142,x7143,x7144))
% 18.77/18.52 [715]~E(x7151,x7152)+E(f700(x7153,x7151,x7154),f700(x7153,x7152,x7154))
% 18.77/18.52 [716]~E(x7161,x7162)+E(f700(x7163,x7164,x7161),f700(x7163,x7164,x7162))
% 18.77/18.52 [717]~E(x7171,x7172)+E(f223(x7171,x7173,x7174),f223(x7172,x7173,x7174))
% 18.77/18.52 [718]~E(x7181,x7182)+E(f223(x7183,x7181,x7184),f223(x7183,x7182,x7184))
% 18.77/18.52 [719]~E(x7191,x7192)+E(f223(x7193,x7194,x7191),f223(x7193,x7194,x7192))
% 18.77/18.52 [720]~E(x7201,x7202)+E(f468(x7201,x7203),f468(x7202,x7203))
% 18.77/18.52 [721]~E(x7211,x7212)+E(f468(x7213,x7211),f468(x7213,x7212))
% 18.77/18.52 [722]~E(x7221,x7222)+E(f683(x7221,x7223,x7224,x7225,x7226,x7227,x7228),f683(x7222,x7223,x7224,x7225,x7226,x7227,x7228))
% 18.77/18.52 [723]~E(x7231,x7232)+E(f683(x7233,x7231,x7234,x7235,x7236,x7237,x7238),f683(x7233,x7232,x7234,x7235,x7236,x7237,x7238))
% 18.77/18.52 [724]~E(x7241,x7242)+E(f683(x7243,x7244,x7241,x7245,x7246,x7247,x7248),f683(x7243,x7244,x7242,x7245,x7246,x7247,x7248))
% 18.77/18.52 [725]~E(x7251,x7252)+E(f683(x7253,x7254,x7255,x7251,x7256,x7257,x7258),f683(x7253,x7254,x7255,x7252,x7256,x7257,x7258))
% 18.77/18.52 [726]~E(x7261,x7262)+E(f683(x7263,x7264,x7265,x7266,x7261,x7267,x7268),f683(x7263,x7264,x7265,x7266,x7262,x7267,x7268))
% 18.77/18.52 [727]~E(x7271,x7272)+E(f683(x7273,x7274,x7275,x7276,x7277,x7271,x7278),f683(x7273,x7274,x7275,x7276,x7277,x7272,x7278))
% 18.77/18.52 [728]~E(x7281,x7282)+E(f683(x7283,x7284,x7285,x7286,x7287,x7288,x7281),f683(x7283,x7284,x7285,x7286,x7287,x7288,x7282))
% 18.77/18.52 [729]~E(x7291,x7292)+E(f603(x7291,x7293,x7294,x7295,x7296,x7297,x7298),f603(x7292,x7293,x7294,x7295,x7296,x7297,x7298))
% 18.77/18.52 [730]~E(x7301,x7302)+E(f603(x7303,x7301,x7304,x7305,x7306,x7307,x7308),f603(x7303,x7302,x7304,x7305,x7306,x7307,x7308))
% 18.77/18.52 [731]~E(x7311,x7312)+E(f603(x7313,x7314,x7311,x7315,x7316,x7317,x7318),f603(x7313,x7314,x7312,x7315,x7316,x7317,x7318))
% 18.77/18.52 [732]~E(x7321,x7322)+E(f603(x7323,x7324,x7325,x7321,x7326,x7327,x7328),f603(x7323,x7324,x7325,x7322,x7326,x7327,x7328))
% 18.77/18.52 [733]~E(x7331,x7332)+E(f603(x7333,x7334,x7335,x7336,x7331,x7337,x7338),f603(x7333,x7334,x7335,x7336,x7332,x7337,x7338))
% 18.77/18.52 [734]~E(x7341,x7342)+E(f603(x7343,x7344,x7345,x7346,x7347,x7341,x7348),f603(x7343,x7344,x7345,x7346,x7347,x7342,x7348))
% 18.77/18.52 [735]~E(x7351,x7352)+E(f603(x7353,x7354,x7355,x7356,x7357,x7358,x7351),f603(x7353,x7354,x7355,x7356,x7357,x7358,x7352))
% 18.77/18.52 [736]~E(x7361,x7362)+E(f739(x7361,x7363,x7364),f739(x7362,x7363,x7364))
% 18.77/18.52 [737]~E(x7371,x7372)+E(f739(x7373,x7371,x7374),f739(x7373,x7372,x7374))
% 18.77/18.52 [738]~E(x7381,x7382)+E(f739(x7383,x7384,x7381),f739(x7383,x7384,x7382))
% 18.77/18.52 [739]~E(x7391,x7392)+E(f569(x7391,x7393,x7394,x7395,x7396,x7397),f569(x7392,x7393,x7394,x7395,x7396,x7397))
% 18.77/18.52 [740]~E(x7401,x7402)+E(f569(x7403,x7401,x7404,x7405,x7406,x7407),f569(x7403,x7402,x7404,x7405,x7406,x7407))
% 18.77/18.52 [741]~E(x7411,x7412)+E(f569(x7413,x7414,x7411,x7415,x7416,x7417),f569(x7413,x7414,x7412,x7415,x7416,x7417))
% 18.77/18.52 [742]~E(x7421,x7422)+E(f569(x7423,x7424,x7425,x7421,x7426,x7427),f569(x7423,x7424,x7425,x7422,x7426,x7427))
% 18.77/18.52 [743]~E(x7431,x7432)+E(f569(x7433,x7434,x7435,x7436,x7431,x7437),f569(x7433,x7434,x7435,x7436,x7432,x7437))
% 18.77/18.52 [744]~E(x7441,x7442)+E(f569(x7443,x7444,x7445,x7446,x7447,x7441),f569(x7443,x7444,x7445,x7446,x7447,x7442))
% 18.77/18.52 [745]~E(x7451,x7452)+E(f441(x7451,x7453),f441(x7452,x7453))
% 18.77/18.52 [746]~E(x7461,x7462)+E(f441(x7463,x7461),f441(x7463,x7462))
% 18.77/18.52 [747]~E(x7471,x7472)+E(f287(x7471,x7473,x7474),f287(x7472,x7473,x7474))
% 18.77/18.52 [748]~E(x7481,x7482)+E(f287(x7483,x7481,x7484),f287(x7483,x7482,x7484))
% 18.77/18.52 [749]~E(x7491,x7492)+E(f287(x7493,x7494,x7491),f287(x7493,x7494,x7492))
% 18.77/18.52 [750]~E(x7501,x7502)+E(f608(x7501,x7503,x7504),f608(x7502,x7503,x7504))
% 18.77/18.52 [751]~E(x7511,x7512)+E(f608(x7513,x7511,x7514),f608(x7513,x7512,x7514))
% 18.77/18.52 [752]~E(x7521,x7522)+E(f608(x7523,x7524,x7521),f608(x7523,x7524,x7522))
% 18.77/18.52 [753]~E(x7531,x7532)+E(f78(x7531,x7533,x7534,x7535,x7536),f78(x7532,x7533,x7534,x7535,x7536))
% 18.77/18.52 [754]~E(x7541,x7542)+E(f78(x7543,x7541,x7544,x7545,x7546),f78(x7543,x7542,x7544,x7545,x7546))
% 18.77/18.52 [755]~E(x7551,x7552)+E(f78(x7553,x7554,x7551,x7555,x7556),f78(x7553,x7554,x7552,x7555,x7556))
% 18.77/18.52 [756]~E(x7561,x7562)+E(f78(x7563,x7564,x7565,x7561,x7566),f78(x7563,x7564,x7565,x7562,x7566))
% 18.77/18.52 [757]~E(x7571,x7572)+E(f78(x7573,x7574,x7575,x7576,x7571),f78(x7573,x7574,x7575,x7576,x7572))
% 18.77/18.52 [758]~E(x7581,x7582)+E(f745(x7581,x7583,x7584,x7585),f745(x7582,x7583,x7584,x7585))
% 18.77/18.52 [759]~E(x7591,x7592)+E(f745(x7593,x7591,x7594,x7595),f745(x7593,x7592,x7594,x7595))
% 18.77/18.52 [760]~E(x7601,x7602)+E(f745(x7603,x7604,x7601,x7605),f745(x7603,x7604,x7602,x7605))
% 18.77/18.52 [761]~E(x7611,x7612)+E(f745(x7613,x7614,x7615,x7611),f745(x7613,x7614,x7615,x7612))
% 18.77/18.52 [762]~E(x7621,x7622)+E(f365(x7621,x7623),f365(x7622,x7623))
% 18.77/18.52 [763]~E(x7631,x7632)+E(f365(x7633,x7631),f365(x7633,x7632))
% 18.77/18.52 [764]~E(x7641,x7642)+E(f769(x7641,x7643,x7644),f769(x7642,x7643,x7644))
% 18.77/18.52 [765]~E(x7651,x7652)+E(f769(x7653,x7651,x7654),f769(x7653,x7652,x7654))
% 18.77/18.52 [766]~E(x7661,x7662)+E(f769(x7663,x7664,x7661),f769(x7663,x7664,x7662))
% 18.77/18.52 [767]~E(x7671,x7672)+E(f471(x7671,x7673,x7674,x7675),f471(x7672,x7673,x7674,x7675))
% 18.77/18.52 [768]~E(x7681,x7682)+E(f471(x7683,x7681,x7684,x7685),f471(x7683,x7682,x7684,x7685))
% 18.77/18.52 [769]~E(x7691,x7692)+E(f471(x7693,x7694,x7691,x7695),f471(x7693,x7694,x7692,x7695))
% 18.77/18.52 [770]~E(x7701,x7702)+E(f471(x7703,x7704,x7705,x7701),f471(x7703,x7704,x7705,x7702))
% 18.77/18.52 [771]~E(x7711,x7712)+E(f281(x7711,x7713),f281(x7712,x7713))
% 18.77/18.52 [772]~E(x7721,x7722)+E(f281(x7723,x7721),f281(x7723,x7722))
% 18.77/18.52 [773]~E(x7731,x7732)+E(f572(x7731,x7733,x7734,x7735,x7736),f572(x7732,x7733,x7734,x7735,x7736))
% 18.77/18.52 [774]~E(x7741,x7742)+E(f572(x7743,x7741,x7744,x7745,x7746),f572(x7743,x7742,x7744,x7745,x7746))
% 18.77/18.52 [775]~E(x7751,x7752)+E(f572(x7753,x7754,x7751,x7755,x7756),f572(x7753,x7754,x7752,x7755,x7756))
% 18.77/18.52 [776]~E(x7761,x7762)+E(f572(x7763,x7764,x7765,x7761,x7766),f572(x7763,x7764,x7765,x7762,x7766))
% 18.77/18.52 [777]~E(x7771,x7772)+E(f572(x7773,x7774,x7775,x7776,x7771),f572(x7773,x7774,x7775,x7776,x7772))
% 18.77/18.52 [778]~E(x7781,x7782)+E(f617(x7781,x7783,x7784),f617(x7782,x7783,x7784))
% 18.77/18.52 [779]~E(x7791,x7792)+E(f617(x7793,x7791,x7794),f617(x7793,x7792,x7794))
% 18.77/18.52 [780]~E(x7801,x7802)+E(f617(x7803,x7804,x7801),f617(x7803,x7804,x7802))
% 18.77/18.52 [781]~E(x7811,x7812)+E(f421(x7811,x7813,x7814,x7815,x7816),f421(x7812,x7813,x7814,x7815,x7816))
% 18.77/18.52 [782]~E(x7821,x7822)+E(f421(x7823,x7821,x7824,x7825,x7826),f421(x7823,x7822,x7824,x7825,x7826))
% 18.77/18.52 [783]~E(x7831,x7832)+E(f421(x7833,x7834,x7831,x7835,x7836),f421(x7833,x7834,x7832,x7835,x7836))
% 18.77/18.52 [784]~E(x7841,x7842)+E(f421(x7843,x7844,x7845,x7841,x7846),f421(x7843,x7844,x7845,x7842,x7846))
% 18.77/18.52 [785]~E(x7851,x7852)+E(f421(x7853,x7854,x7855,x7856,x7851),f421(x7853,x7854,x7855,x7856,x7852))
% 18.77/18.52 [786]~E(x7861,x7862)+E(f250(x7861,x7863,x7864,x7865),f250(x7862,x7863,x7864,x7865))
% 18.77/18.52 [787]~E(x7871,x7872)+E(f250(x7873,x7871,x7874,x7875),f250(x7873,x7872,x7874,x7875))
% 18.77/18.52 [788]~E(x7881,x7882)+E(f250(x7883,x7884,x7881,x7885),f250(x7883,x7884,x7882,x7885))
% 18.77/18.52 [789]~E(x7891,x7892)+E(f250(x7893,x7894,x7895,x7891),f250(x7893,x7894,x7895,x7892))
% 18.77/18.52 [790]~E(x7901,x7902)+E(f210(x7901,x7903),f210(x7902,x7903))
% 18.77/18.52 [791]~E(x7911,x7912)+E(f210(x7913,x7911),f210(x7913,x7912))
% 18.77/18.52 [792]~E(x7921,x7922)+E(f751(x7921,x7923,x7924),f751(x7922,x7923,x7924))
% 18.77/18.52 [793]~E(x7931,x7932)+E(f751(x7933,x7931,x7934),f751(x7933,x7932,x7934))
% 18.77/18.52 [794]~E(x7941,x7942)+E(f751(x7943,x7944,x7941),f751(x7943,x7944,x7942))
% 18.77/18.52 [795]~E(x7951,x7952)+E(f484(x7951,x7953,x7954,x7955,x7956),f484(x7952,x7953,x7954,x7955,x7956))
% 18.77/18.52 [796]~E(x7961,x7962)+E(f484(x7963,x7961,x7964,x7965,x7966),f484(x7963,x7962,x7964,x7965,x7966))
% 18.77/18.52 [797]~E(x7971,x7972)+E(f484(x7973,x7974,x7971,x7975,x7976),f484(x7973,x7974,x7972,x7975,x7976))
% 18.77/18.52 [798]~E(x7981,x7982)+E(f484(x7983,x7984,x7985,x7981,x7986),f484(x7983,x7984,x7985,x7982,x7986))
% 18.77/18.52 [799]~E(x7991,x7992)+E(f484(x7993,x7994,x7995,x7996,x7991),f484(x7993,x7994,x7995,x7996,x7992))
% 18.77/18.52 [800]~E(x8001,x8002)+E(f70(x8001,x8003,x8004),f70(x8002,x8003,x8004))
% 18.77/18.52 [801]~E(x8011,x8012)+E(f70(x8013,x8011,x8014),f70(x8013,x8012,x8014))
% 18.77/18.52 [802]~E(x8021,x8022)+E(f70(x8023,x8024,x8021),f70(x8023,x8024,x8022))
% 18.77/18.52 [803]~E(x8031,x8032)+E(f12(x8031,x8033),f12(x8032,x8033))
% 18.77/18.52 [804]~E(x8041,x8042)+E(f12(x8043,x8041),f12(x8043,x8042))
% 18.77/18.52 [805]~E(x8051,x8052)+E(f318(x8051,x8053,x8054,x8055),f318(x8052,x8053,x8054,x8055))
% 18.77/18.52 [806]~E(x8061,x8062)+E(f318(x8063,x8061,x8064,x8065),f318(x8063,x8062,x8064,x8065))
% 18.77/18.52 [807]~E(x8071,x8072)+E(f318(x8073,x8074,x8071,x8075),f318(x8073,x8074,x8072,x8075))
% 18.77/18.52 [808]~E(x8081,x8082)+E(f318(x8083,x8084,x8085,x8081),f318(x8083,x8084,x8085,x8082))
% 18.77/18.52 [809]~E(x8091,x8092)+E(f561(x8091,x8093,x8094,x8095,x8096),f561(x8092,x8093,x8094,x8095,x8096))
% 18.77/18.52 [810]~E(x8101,x8102)+E(f561(x8103,x8101,x8104,x8105,x8106),f561(x8103,x8102,x8104,x8105,x8106))
% 18.77/18.52 [811]~E(x8111,x8112)+E(f561(x8113,x8114,x8111,x8115,x8116),f561(x8113,x8114,x8112,x8115,x8116))
% 18.77/18.52 [812]~E(x8121,x8122)+E(f561(x8123,x8124,x8125,x8121,x8126),f561(x8123,x8124,x8125,x8122,x8126))
% 18.77/18.52 [813]~E(x8131,x8132)+E(f561(x8133,x8134,x8135,x8136,x8131),f561(x8133,x8134,x8135,x8136,x8132))
% 18.77/18.52 [814]~E(x8141,x8142)+E(f682(x8141,x8143,x8144,x8145,x8146,x8147),f682(x8142,x8143,x8144,x8145,x8146,x8147))
% 18.77/18.52 [815]~E(x8151,x8152)+E(f682(x8153,x8151,x8154,x8155,x8156,x8157),f682(x8153,x8152,x8154,x8155,x8156,x8157))
% 18.77/18.52 [816]~E(x8161,x8162)+E(f682(x8163,x8164,x8161,x8165,x8166,x8167),f682(x8163,x8164,x8162,x8165,x8166,x8167))
% 18.77/18.52 [817]~E(x8171,x8172)+E(f682(x8173,x8174,x8175,x8171,x8176,x8177),f682(x8173,x8174,x8175,x8172,x8176,x8177))
% 18.77/18.52 [818]~E(x8181,x8182)+E(f682(x8183,x8184,x8185,x8186,x8181,x8187),f682(x8183,x8184,x8185,x8186,x8182,x8187))
% 18.77/18.52 [819]~E(x8191,x8192)+E(f682(x8193,x8194,x8195,x8196,x8197,x8191),f682(x8193,x8194,x8195,x8196,x8197,x8192))
% 18.77/18.52 [820]~E(x8201,x8202)+E(f203(x8201,x8203,x8204,x8205),f203(x8202,x8203,x8204,x8205))
% 18.77/18.52 [821]~E(x8211,x8212)+E(f203(x8213,x8211,x8214,x8215),f203(x8213,x8212,x8214,x8215))
% 18.77/18.52 [822]~E(x8221,x8222)+E(f203(x8223,x8224,x8221,x8225),f203(x8223,x8224,x8222,x8225))
% 18.77/18.52 [823]~E(x8231,x8232)+E(f203(x8233,x8234,x8235,x8231),f203(x8233,x8234,x8235,x8232))
% 18.77/18.52 [824]~E(x8241,x8242)+E(f604(x8241,x8243,x8244),f604(x8242,x8243,x8244))
% 18.77/18.52 [825]~E(x8251,x8252)+E(f604(x8253,x8251,x8254),f604(x8253,x8252,x8254))
% 18.77/18.52 [826]~E(x8261,x8262)+E(f604(x8263,x8264,x8261),f604(x8263,x8264,x8262))
% 18.77/18.52 [827]~E(x8271,x8272)+E(f749(x8271,x8273),f749(x8272,x8273))
% 18.77/18.52 [828]~E(x8281,x8282)+E(f749(x8283,x8281),f749(x8283,x8282))
% 18.77/18.52 [829]~E(x8291,x8292)+E(f197(x8291,x8293),f197(x8292,x8293))
% 18.77/18.52 [830]~E(x8301,x8302)+E(f197(x8303,x8301),f197(x8303,x8302))
% 18.77/18.52 [831]~E(x8311,x8312)+E(f269(x8311,x8313,x8314,x8315),f269(x8312,x8313,x8314,x8315))
% 18.77/18.52 [832]~E(x8321,x8322)+E(f269(x8323,x8321,x8324,x8325),f269(x8323,x8322,x8324,x8325))
% 18.77/18.52 [833]~E(x8331,x8332)+E(f269(x8333,x8334,x8331,x8335),f269(x8333,x8334,x8332,x8335))
% 18.77/18.52 [834]~E(x8341,x8342)+E(f269(x8343,x8344,x8345,x8341),f269(x8343,x8344,x8345,x8342))
% 18.77/18.52 [835]~E(x8351,x8352)+E(f658(x8351,x8353,x8354,x8355,x8356),f658(x8352,x8353,x8354,x8355,x8356))
% 18.77/18.52 [836]~E(x8361,x8362)+E(f658(x8363,x8361,x8364,x8365,x8366),f658(x8363,x8362,x8364,x8365,x8366))
% 18.77/18.52 [837]~E(x8371,x8372)+E(f658(x8373,x8374,x8371,x8375,x8376),f658(x8373,x8374,x8372,x8375,x8376))
% 18.77/18.52 [838]~E(x8381,x8382)+E(f658(x8383,x8384,x8385,x8381,x8386),f658(x8383,x8384,x8385,x8382,x8386))
% 18.77/18.52 [839]~E(x8391,x8392)+E(f658(x8393,x8394,x8395,x8396,x8391),f658(x8393,x8394,x8395,x8396,x8392))
% 18.77/18.52 [840]~E(x8401,x8402)+E(f759(x8401,x8403,x8404),f759(x8402,x8403,x8404))
% 18.77/18.52 [841]~E(x8411,x8412)+E(f759(x8413,x8411,x8414),f759(x8413,x8412,x8414))
% 18.77/18.52 [842]~E(x8421,x8422)+E(f759(x8423,x8424,x8421),f759(x8423,x8424,x8422))
% 18.77/18.52 [843]~E(x8431,x8432)+E(f386(x8431,x8433,x8434,x8435),f386(x8432,x8433,x8434,x8435))
% 18.77/18.52 [844]~E(x8441,x8442)+E(f386(x8443,x8441,x8444,x8445),f386(x8443,x8442,x8444,x8445))
% 18.77/18.52 [845]~E(x8451,x8452)+E(f386(x8453,x8454,x8451,x8455),f386(x8453,x8454,x8452,x8455))
% 18.77/18.52 [846]~E(x8461,x8462)+E(f386(x8463,x8464,x8465,x8461),f386(x8463,x8464,x8465,x8462))
% 18.77/18.52 [847]~E(x8471,x8472)+E(f537(x8471,x8473,x8474,x8475,x8476),f537(x8472,x8473,x8474,x8475,x8476))
% 18.77/18.52 [848]~E(x8481,x8482)+E(f537(x8483,x8481,x8484,x8485,x8486),f537(x8483,x8482,x8484,x8485,x8486))
% 18.77/18.52 [849]~E(x8491,x8492)+E(f537(x8493,x8494,x8491,x8495,x8496),f537(x8493,x8494,x8492,x8495,x8496))
% 18.77/18.52 [850]~E(x8501,x8502)+E(f537(x8503,x8504,x8505,x8501,x8506),f537(x8503,x8504,x8505,x8502,x8506))
% 18.77/18.52 [851]~E(x8511,x8512)+E(f537(x8513,x8514,x8515,x8516,x8511),f537(x8513,x8514,x8515,x8516,x8512))
% 18.77/18.52 [852]~E(x8521,x8522)+E(f144(x8521,x8523),f144(x8522,x8523))
% 18.77/18.52 [853]~E(x8531,x8532)+E(f144(x8533,x8531),f144(x8533,x8532))
% 18.77/18.52 [854]~E(x8541,x8542)+E(f802(x8541,x8543,x8544),f802(x8542,x8543,x8544))
% 18.77/18.52 [855]~E(x8551,x8552)+E(f802(x8553,x8551,x8554),f802(x8553,x8552,x8554))
% 18.77/18.52 [856]~E(x8561,x8562)+E(f802(x8563,x8564,x8561),f802(x8563,x8564,x8562))
% 18.77/18.52 [857]~E(x8571,x8572)+E(f575(x8571,x8573,x8574),f575(x8572,x8573,x8574))
% 18.77/18.52 [858]~E(x8581,x8582)+E(f575(x8583,x8581,x8584),f575(x8583,x8582,x8584))
% 18.77/18.52 [859]~E(x8591,x8592)+E(f575(x8593,x8594,x8591),f575(x8593,x8594,x8592))
% 18.77/18.52 [860]~E(x8601,x8602)+E(f701(x8601,x8603,x8604),f701(x8602,x8603,x8604))
% 18.77/18.52 [861]~E(x8611,x8612)+E(f701(x8613,x8611,x8614),f701(x8613,x8612,x8614))
% 18.77/18.52 [862]~E(x8621,x8622)+E(f701(x8623,x8624,x8621),f701(x8623,x8624,x8622))
% 18.77/18.52 [863]~E(x8631,x8632)+E(f193(x8631,x8633),f193(x8632,x8633))
% 18.77/18.52 [864]~E(x8641,x8642)+E(f193(x8643,x8641),f193(x8643,x8642))
% 18.77/18.52 [865]~E(x8651,x8652)+E(f416(x8651,x8653,x8654),f416(x8652,x8653,x8654))
% 18.77/18.52 [866]~E(x8661,x8662)+E(f416(x8663,x8661,x8664),f416(x8663,x8662,x8664))
% 18.77/18.52 [867]~E(x8671,x8672)+E(f416(x8673,x8674,x8671),f416(x8673,x8674,x8672))
% 18.77/18.52 [868]~E(x8681,x8682)+E(f120(x8681,x8683),f120(x8682,x8683))
% 18.77/18.52 [869]~E(x8691,x8692)+E(f120(x8693,x8691),f120(x8693,x8692))
% 18.77/18.52 [870]~E(x8701,x8702)+E(f184(x8701,x8703),f184(x8702,x8703))
% 18.77/18.52 [871]~E(x8711,x8712)+E(f184(x8713,x8711),f184(x8713,x8712))
% 18.77/18.52 [872]~E(x8721,x8722)+E(f358(x8721,x8723,x8724,x8725),f358(x8722,x8723,x8724,x8725))
% 18.77/18.52 [873]~E(x8731,x8732)+E(f358(x8733,x8731,x8734,x8735),f358(x8733,x8732,x8734,x8735))
% 18.77/18.52 [874]~E(x8741,x8742)+E(f358(x8743,x8744,x8741,x8745),f358(x8743,x8744,x8742,x8745))
% 18.77/18.52 [875]~E(x8751,x8752)+E(f358(x8753,x8754,x8755,x8751),f358(x8753,x8754,x8755,x8752))
% 18.77/18.52 [876]~E(x8761,x8762)+E(f121(x8761,x8763),f121(x8762,x8763))
% 18.77/18.52 [877]~E(x8771,x8772)+E(f121(x8773,x8771),f121(x8773,x8772))
% 18.77/18.52 [878]~E(x8781,x8782)+E(f533(x8781,x8783,x8784,x8785,x8786),f533(x8782,x8783,x8784,x8785,x8786))
% 18.77/18.52 [879]~E(x8791,x8792)+E(f533(x8793,x8791,x8794,x8795,x8796),f533(x8793,x8792,x8794,x8795,x8796))
% 18.77/18.52 [880]~E(x8801,x8802)+E(f533(x8803,x8804,x8801,x8805,x8806),f533(x8803,x8804,x8802,x8805,x8806))
% 18.77/18.52 [881]~E(x8811,x8812)+E(f533(x8813,x8814,x8815,x8811,x8816),f533(x8813,x8814,x8815,x8812,x8816))
% 18.77/18.52 [882]~E(x8821,x8822)+E(f533(x8823,x8824,x8825,x8826,x8821),f533(x8823,x8824,x8825,x8826,x8822))
% 18.77/18.52 [883]~E(x8831,x8832)+E(f368(x8831,x8833),f368(x8832,x8833))
% 18.77/18.52 [884]~E(x8841,x8842)+E(f368(x8843,x8841),f368(x8843,x8842))
% 18.77/18.52 [885]~E(x8851,x8852)+E(f560(x8851,x8853,x8854,x8855,x8856),f560(x8852,x8853,x8854,x8855,x8856))
% 18.77/18.52 [886]~E(x8861,x8862)+E(f560(x8863,x8861,x8864,x8865,x8866),f560(x8863,x8862,x8864,x8865,x8866))
% 18.77/18.52 [887]~E(x8871,x8872)+E(f560(x8873,x8874,x8871,x8875,x8876),f560(x8873,x8874,x8872,x8875,x8876))
% 18.77/18.52 [888]~E(x8881,x8882)+E(f560(x8883,x8884,x8885,x8881,x8886),f560(x8883,x8884,x8885,x8882,x8886))
% 18.77/18.52 [889]~E(x8891,x8892)+E(f560(x8893,x8894,x8895,x8896,x8891),f560(x8893,x8894,x8895,x8896,x8892))
% 18.77/18.52 [890]~E(x8901,x8902)+E(f208(x8901,x8903),f208(x8902,x8903))
% 18.77/18.52 [891]~E(x8911,x8912)+E(f208(x8913,x8911),f208(x8913,x8912))
% 18.77/18.52 [892]~E(x8921,x8922)+E(f379(x8921,x8923,x8924),f379(x8922,x8923,x8924))
% 18.77/18.52 [893]~E(x8931,x8932)+E(f379(x8933,x8931,x8934),f379(x8933,x8932,x8934))
% 18.77/18.52 [894]~E(x8941,x8942)+E(f379(x8943,x8944,x8941),f379(x8943,x8944,x8942))
% 18.77/18.52 [895]~E(x8951,x8952)+E(f657(x8951,x8953,x8954,x8955),f657(x8952,x8953,x8954,x8955))
% 18.77/18.52 [896]~E(x8961,x8962)+E(f657(x8963,x8961,x8964,x8965),f657(x8963,x8962,x8964,x8965))
% 18.77/18.52 [897]~E(x8971,x8972)+E(f657(x8973,x8974,x8971,x8975),f657(x8973,x8974,x8972,x8975))
% 18.77/18.52 [898]~E(x8981,x8982)+E(f657(x8983,x8984,x8985,x8981),f657(x8983,x8984,x8985,x8982))
% 18.77/18.52 [899]~E(x8991,x8992)+E(f762(x8991,x8993,x8994),f762(x8992,x8993,x8994))
% 18.77/18.52 [900]~E(x9001,x9002)+E(f762(x9003,x9001,x9004),f762(x9003,x9002,x9004))
% 18.77/18.52 [901]~E(x9011,x9012)+E(f762(x9013,x9014,x9011),f762(x9013,x9014,x9012))
% 18.77/18.52 [902]~E(x9021,x9022)+E(f610(x9021,x9023,x9024),f610(x9022,x9023,x9024))
% 18.77/18.52 [903]~E(x9031,x9032)+E(f610(x9033,x9031,x9034),f610(x9033,x9032,x9034))
% 18.77/18.52 [904]~E(x9041,x9042)+E(f610(x9043,x9044,x9041),f610(x9043,x9044,x9042))
% 18.77/18.52 [905]~E(x9051,x9052)+E(f634(x9051,x9053),f634(x9052,x9053))
% 18.77/18.52 [906]~E(x9061,x9062)+E(f634(x9063,x9061),f634(x9063,x9062))
% 18.77/18.52 [907]~E(x9071,x9072)+E(f36(x9071,x9073),f36(x9072,x9073))
% 18.77/18.52 [908]~E(x9081,x9082)+E(f36(x9083,x9081),f36(x9083,x9082))
% 18.77/18.52 [909]~E(x9091,x9092)+E(f243(x9091,x9093),f243(x9092,x9093))
% 18.77/18.52 [910]~E(x9101,x9102)+E(f243(x9103,x9101),f243(x9103,x9102))
% 18.77/18.52 [911]~E(x9111,x9112)+E(f328(x9111,x9113,x9114,x9115),f328(x9112,x9113,x9114,x9115))
% 18.77/18.52 [912]~E(x9121,x9122)+E(f328(x9123,x9121,x9124,x9125),f328(x9123,x9122,x9124,x9125))
% 18.77/18.52 [913]~E(x9131,x9132)+E(f328(x9133,x9134,x9131,x9135),f328(x9133,x9134,x9132,x9135))
% 18.77/18.52 [914]~E(x9141,x9142)+E(f328(x9143,x9144,x9145,x9141),f328(x9143,x9144,x9145,x9142))
% 18.77/18.52 [915]~E(x9151,x9152)+E(f371(x9151,x9153),f371(x9152,x9153))
% 18.77/18.52 [916]~E(x9161,x9162)+E(f371(x9163,x9161),f371(x9163,x9162))
% 18.77/18.52 [917]~E(x9171,x9172)+E(f694(x9171,x9173,x9174,x9175),f694(x9172,x9173,x9174,x9175))
% 18.77/18.52 [918]~E(x9181,x9182)+E(f694(x9183,x9181,x9184,x9185),f694(x9183,x9182,x9184,x9185))
% 18.77/18.52 [919]~E(x9191,x9192)+E(f694(x9193,x9194,x9191,x9195),f694(x9193,x9194,x9192,x9195))
% 18.77/18.52 [920]~E(x9201,x9202)+E(f694(x9203,x9204,x9205,x9201),f694(x9203,x9204,x9205,x9202))
% 18.77/18.52 [921]~E(x9211,x9212)+E(f551(x9211,x9213,x9214,x9215),f551(x9212,x9213,x9214,x9215))
% 18.77/18.52 [922]~E(x9221,x9222)+E(f551(x9223,x9221,x9224,x9225),f551(x9223,x9222,x9224,x9225))
% 18.77/18.52 [923]~E(x9231,x9232)+E(f551(x9233,x9234,x9231,x9235),f551(x9233,x9234,x9232,x9235))
% 18.77/18.52 [924]~E(x9241,x9242)+E(f551(x9243,x9244,x9245,x9241),f551(x9243,x9244,x9245,x9242))
% 18.77/18.52 [925]~E(x9251,x9252)+E(f442(x9251,x9253),f442(x9252,x9253))
% 18.77/18.52 [926]~E(x9261,x9262)+E(f442(x9263,x9261),f442(x9263,x9262))
% 18.77/18.52 [927]~E(x9271,x9272)+E(f813(x9271,x9273,x9274,x9275,x9276,x9277),f813(x9272,x9273,x9274,x9275,x9276,x9277))
% 18.77/18.52 [928]~E(x9281,x9282)+E(f813(x9283,x9281,x9284,x9285,x9286,x9287),f813(x9283,x9282,x9284,x9285,x9286,x9287))
% 18.77/18.52 [929]~E(x9291,x9292)+E(f813(x9293,x9294,x9291,x9295,x9296,x9297),f813(x9293,x9294,x9292,x9295,x9296,x9297))
% 18.77/18.52 [930]~E(x9301,x9302)+E(f813(x9303,x9304,x9305,x9301,x9306,x9307),f813(x9303,x9304,x9305,x9302,x9306,x9307))
% 18.77/18.52 [931]~E(x9311,x9312)+E(f813(x9313,x9314,x9315,x9316,x9311,x9317),f813(x9313,x9314,x9315,x9316,x9312,x9317))
% 18.77/18.52 [932]~E(x9321,x9322)+E(f813(x9323,x9324,x9325,x9326,x9327,x9321),f813(x9323,x9324,x9325,x9326,x9327,x9322))
% 18.77/18.52 [933]~E(x9331,x9332)+E(f521(x9331,x9333,x9334,x9335),f521(x9332,x9333,x9334,x9335))
% 18.77/18.52 [934]~E(x9341,x9342)+E(f521(x9343,x9341,x9344,x9345),f521(x9343,x9342,x9344,x9345))
% 18.77/18.52 [935]~E(x9351,x9352)+E(f521(x9353,x9354,x9351,x9355),f521(x9353,x9354,x9352,x9355))
% 18.77/18.52 [936]~E(x9361,x9362)+E(f521(x9363,x9364,x9365,x9361),f521(x9363,x9364,x9365,x9362))
% 18.77/18.52 [937]~E(x9371,x9372)+E(f718(x9371,x9373,x9374),f718(x9372,x9373,x9374))
% 18.77/18.52 [938]~E(x9381,x9382)+E(f718(x9383,x9381,x9384),f718(x9383,x9382,x9384))
% 18.77/18.52 [939]~E(x9391,x9392)+E(f718(x9393,x9394,x9391),f718(x9393,x9394,x9392))
% 18.77/18.52 [940]~E(x9401,x9402)+E(f335(x9401,x9403),f335(x9402,x9403))
% 18.77/18.52 [941]~E(x9411,x9412)+E(f335(x9413,x9411),f335(x9413,x9412))
% 18.77/18.52 [942]~E(x9421,x9422)+E(f389(x9421,x9423),f389(x9422,x9423))
% 18.77/18.52 [943]~E(x9431,x9432)+E(f389(x9433,x9431),f389(x9433,x9432))
% 18.77/18.52 [944]~E(x9441,x9442)+E(f574(x9441,x9443,x9444),f574(x9442,x9443,x9444))
% 18.77/18.52 [945]~E(x9451,x9452)+E(f574(x9453,x9451,x9454),f574(x9453,x9452,x9454))
% 18.77/18.52 [946]~E(x9461,x9462)+E(f574(x9463,x9464,x9461),f574(x9463,x9464,x9462))
% 18.77/18.52 [947]~E(x9471,x9472)+E(f532(x9471,x9473,x9474,x9475,x9476),f532(x9472,x9473,x9474,x9475,x9476))
% 18.77/18.52 [948]~E(x9481,x9482)+E(f532(x9483,x9481,x9484,x9485,x9486),f532(x9483,x9482,x9484,x9485,x9486))
% 18.77/18.52 [949]~E(x9491,x9492)+E(f532(x9493,x9494,x9491,x9495,x9496),f532(x9493,x9494,x9492,x9495,x9496))
% 18.77/18.52 [950]~E(x9501,x9502)+E(f532(x9503,x9504,x9505,x9501,x9506),f532(x9503,x9504,x9505,x9502,x9506))
% 18.77/18.52 [951]~E(x9511,x9512)+E(f532(x9513,x9514,x9515,x9516,x9511),f532(x9513,x9514,x9515,x9516,x9512))
% 18.77/18.52 [952]~E(x9521,x9522)+E(f405(x9521,x9523,x9524,x9525,x9526,x9527,x9528),f405(x9522,x9523,x9524,x9525,x9526,x9527,x9528))
% 18.77/18.52 [953]~E(x9531,x9532)+E(f405(x9533,x9531,x9534,x9535,x9536,x9537,x9538),f405(x9533,x9532,x9534,x9535,x9536,x9537,x9538))
% 18.77/18.52 [954]~E(x9541,x9542)+E(f405(x9543,x9544,x9541,x9545,x9546,x9547,x9548),f405(x9543,x9544,x9542,x9545,x9546,x9547,x9548))
% 18.77/18.52 [955]~E(x9551,x9552)+E(f405(x9553,x9554,x9555,x9551,x9556,x9557,x9558),f405(x9553,x9554,x9555,x9552,x9556,x9557,x9558))
% 18.77/18.52 [956]~E(x9561,x9562)+E(f405(x9563,x9564,x9565,x9566,x9561,x9567,x9568),f405(x9563,x9564,x9565,x9566,x9562,x9567,x9568))
% 18.77/18.52 [957]~E(x9571,x9572)+E(f405(x9573,x9574,x9575,x9576,x9577,x9571,x9578),f405(x9573,x9574,x9575,x9576,x9577,x9572,x9578))
% 18.77/18.52 [958]~E(x9581,x9582)+E(f405(x9583,x9584,x9585,x9586,x9587,x9588,x9581),f405(x9583,x9584,x9585,x9586,x9587,x9588,x9582))
% 18.77/18.52 [959]~E(x9591,x9592)+E(f776(x9591,x9593,x9594),f776(x9592,x9593,x9594))
% 18.77/18.52 [960]~E(x9601,x9602)+E(f776(x9603,x9601,x9604),f776(x9603,x9602,x9604))
% 18.77/18.52 [961]~E(x9611,x9612)+E(f776(x9613,x9614,x9611),f776(x9613,x9614,x9612))
% 18.77/18.52 [962]~E(x9621,x9622)+E(f571(x9621,x9623,x9624,x9625,x9626),f571(x9622,x9623,x9624,x9625,x9626))
% 18.77/18.52 [963]~E(x9631,x9632)+E(f571(x9633,x9631,x9634,x9635,x9636),f571(x9633,x9632,x9634,x9635,x9636))
% 18.77/18.52 [964]~E(x9641,x9642)+E(f571(x9643,x9644,x9641,x9645,x9646),f571(x9643,x9644,x9642,x9645,x9646))
% 18.77/18.52 [965]~E(x9651,x9652)+E(f571(x9653,x9654,x9655,x9651,x9656),f571(x9653,x9654,x9655,x9652,x9656))
% 18.77/18.52 [966]~E(x9661,x9662)+E(f571(x9663,x9664,x9665,x9666,x9661),f571(x9663,x9664,x9665,x9666,x9662))
% 18.77/18.52 [967]~E(x9671,x9672)+E(f170(x9671,x9673,x9674),f170(x9672,x9673,x9674))
% 18.77/18.52 [968]~E(x9681,x9682)+E(f170(x9683,x9681,x9684),f170(x9683,x9682,x9684))
% 18.77/18.52 [969]~E(x9691,x9692)+E(f170(x9693,x9694,x9691),f170(x9693,x9694,x9692))
% 18.77/18.52 [970]~E(x9701,x9702)+E(f356(x9701,x9703,x9704,x9705),f356(x9702,x9703,x9704,x9705))
% 18.77/18.52 [971]~E(x9711,x9712)+E(f356(x9713,x9711,x9714,x9715),f356(x9713,x9712,x9714,x9715))
% 18.77/18.52 [972]~E(x9721,x9722)+E(f356(x9723,x9724,x9721,x9725),f356(x9723,x9724,x9722,x9725))
% 18.77/18.52 [973]~E(x9731,x9732)+E(f356(x9733,x9734,x9735,x9731),f356(x9733,x9734,x9735,x9732))
% 18.77/18.52 [974]~E(x9741,x9742)+E(f504(x9741,x9743,x9744,x9745,x9746),f504(x9742,x9743,x9744,x9745,x9746))
% 18.77/18.52 [975]~E(x9751,x9752)+E(f504(x9753,x9751,x9754,x9755,x9756),f504(x9753,x9752,x9754,x9755,x9756))
% 18.77/18.52 [976]~E(x9761,x9762)+E(f504(x9763,x9764,x9761,x9765,x9766),f504(x9763,x9764,x9762,x9765,x9766))
% 18.77/18.52 [977]~E(x9771,x9772)+E(f504(x9773,x9774,x9775,x9771,x9776),f504(x9773,x9774,x9775,x9772,x9776))
% 18.77/18.52 [978]~E(x9781,x9782)+E(f504(x9783,x9784,x9785,x9786,x9781),f504(x9783,x9784,x9785,x9786,x9782))
% 18.77/18.52 [979]~E(x9791,x9792)+E(f764(x9791,x9793,x9794),f764(x9792,x9793,x9794))
% 18.77/18.52 [980]~E(x9801,x9802)+E(f764(x9803,x9801,x9804),f764(x9803,x9802,x9804))
% 18.77/18.52 [981]~E(x9811,x9812)+E(f764(x9813,x9814,x9811),f764(x9813,x9814,x9812))
% 18.77/18.52 [982]~E(x9821,x9822)+E(f97(x9821,x9823,x9824,x9825),f97(x9822,x9823,x9824,x9825))
% 18.77/18.52 [983]~E(x9831,x9832)+E(f97(x9833,x9831,x9834,x9835),f97(x9833,x9832,x9834,x9835))
% 18.77/18.52 [984]~E(x9841,x9842)+E(f97(x9843,x9844,x9841,x9845),f97(x9843,x9844,x9842,x9845))
% 18.77/18.52 [985]~E(x9851,x9852)+E(f97(x9853,x9854,x9855,x9851),f97(x9853,x9854,x9855,x9852))
% 18.77/18.52 [986]~E(x9861,x9862)+E(f770(x9861,x9863,x9864),f770(x9862,x9863,x9864))
% 18.77/18.52 [987]~E(x9871,x9872)+E(f770(x9873,x9871,x9874),f770(x9873,x9872,x9874))
% 18.77/18.52 [988]~E(x9881,x9882)+E(f770(x9883,x9884,x9881),f770(x9883,x9884,x9882))
% 18.77/18.52 [989]~E(x9891,x9892)+E(f656(x9891,x9893,x9894),f656(x9892,x9893,x9894))
% 18.77/18.52 [990]~E(x9901,x9902)+E(f656(x9903,x9901,x9904),f656(x9903,x9902,x9904))
% 18.77/18.52 [991]~E(x9911,x9912)+E(f656(x9913,x9914,x9911),f656(x9913,x9914,x9912))
% 18.77/18.52 [992]~E(x9921,x9922)+E(f491(x9921,x9923,x9924,x9925),f491(x9922,x9923,x9924,x9925))
% 18.77/18.52 [993]~E(x9931,x9932)+E(f491(x9933,x9931,x9934,x9935),f491(x9933,x9932,x9934,x9935))
% 18.77/18.52 [994]~E(x9941,x9942)+E(f491(x9943,x9944,x9941,x9945),f491(x9943,x9944,x9942,x9945))
% 18.77/18.52 [995]~E(x9951,x9952)+E(f491(x9953,x9954,x9955,x9951),f491(x9953,x9954,x9955,x9952))
% 18.77/18.52 [996]~E(x9961,x9962)+E(f256(x9961,x9963,x9964,x9965,x9966),f256(x9962,x9963,x9964,x9965,x9966))
% 18.77/18.52 [997]~E(x9971,x9972)+E(f256(x9973,x9971,x9974,x9975,x9976),f256(x9973,x9972,x9974,x9975,x9976))
% 18.77/18.52 [998]~E(x9981,x9982)+E(f256(x9983,x9984,x9981,x9985,x9986),f256(x9983,x9984,x9982,x9985,x9986))
% 18.77/18.52 [999]~E(x9991,x9992)+E(f256(x9993,x9994,x9995,x9991,x9996),f256(x9993,x9994,x9995,x9992,x9996))
% 18.77/18.52 [1000]~E(x10001,x10002)+E(f256(x10003,x10004,x10005,x10006,x10001),f256(x10003,x10004,x10005,x10006,x10002))
% 18.77/18.52 [1001]~E(x10011,x10012)+E(f498(x10011,x10013,x10014,x10015,x10016),f498(x10012,x10013,x10014,x10015,x10016))
% 18.77/18.52 [1002]~E(x10021,x10022)+E(f498(x10023,x10021,x10024,x10025,x10026),f498(x10023,x10022,x10024,x10025,x10026))
% 18.77/18.52 [1003]~E(x10031,x10032)+E(f498(x10033,x10034,x10031,x10035,x10036),f498(x10033,x10034,x10032,x10035,x10036))
% 18.77/18.52 [1004]~E(x10041,x10042)+E(f498(x10043,x10044,x10045,x10041,x10046),f498(x10043,x10044,x10045,x10042,x10046))
% 18.77/18.52 [1005]~E(x10051,x10052)+E(f498(x10053,x10054,x10055,x10056,x10051),f498(x10053,x10054,x10055,x10056,x10052))
% 18.77/18.52 [1006]~E(x10061,x10062)+E(f711(x10061,x10063,x10064),f711(x10062,x10063,x10064))
% 18.77/18.52 [1007]~E(x10071,x10072)+E(f711(x10073,x10071,x10074),f711(x10073,x10072,x10074))
% 18.77/18.52 [1008]~E(x10081,x10082)+E(f711(x10083,x10084,x10081),f711(x10083,x10084,x10082))
% 18.77/18.52 [1009]~E(x10091,x10092)+E(f531(x10091,x10093,x10094,x10095,x10096),f531(x10092,x10093,x10094,x10095,x10096))
% 18.77/18.52 [1010]~E(x10101,x10102)+E(f531(x10103,x10101,x10104,x10105,x10106),f531(x10103,x10102,x10104,x10105,x10106))
% 18.77/18.52 [1011]~E(x10111,x10112)+E(f531(x10113,x10114,x10111,x10115,x10116),f531(x10113,x10114,x10112,x10115,x10116))
% 18.77/18.52 [1012]~E(x10121,x10122)+E(f531(x10123,x10124,x10125,x10121,x10126),f531(x10123,x10124,x10125,x10122,x10126))
% 18.77/18.52 [1013]~E(x10131,x10132)+E(f531(x10133,x10134,x10135,x10136,x10131),f531(x10133,x10134,x10135,x10136,x10132))
% 18.77/18.52 [1014]~E(x10141,x10142)+E(f423(x10141,x10143,x10144),f423(x10142,x10143,x10144))
% 18.77/18.52 [1015]~E(x10151,x10152)+E(f423(x10153,x10151,x10154),f423(x10153,x10152,x10154))
% 18.77/18.52 [1016]~E(x10161,x10162)+E(f423(x10163,x10164,x10161),f423(x10163,x10164,x10162))
% 18.77/18.52 [1017]~E(x10171,x10172)+E(f485(x10171,x10173,x10174),f485(x10172,x10173,x10174))
% 18.77/18.52 [1018]~E(x10181,x10182)+E(f485(x10183,x10181,x10184),f485(x10183,x10182,x10184))
% 18.77/18.52 [1019]~E(x10191,x10192)+E(f485(x10193,x10194,x10191),f485(x10193,x10194,x10192))
% 18.77/18.52 [1020]~E(x10201,x10202)+E(f827(x10201,x10203,x10204),f827(x10202,x10203,x10204))
% 18.77/18.52 [1021]~E(x10211,x10212)+E(f827(x10213,x10211,x10214),f827(x10213,x10212,x10214))
% 18.77/18.52 [1022]~E(x10221,x10222)+E(f827(x10223,x10224,x10221),f827(x10223,x10224,x10222))
% 18.77/18.52 [1023]~E(x10231,x10232)+E(f594(x10231,x10233,x10234,x10235,x10236,x10237,x10238,x10239),f594(x10232,x10233,x10234,x10235,x10236,x10237,x10238,x10239))
% 18.77/18.52 [1024]~E(x10241,x10242)+E(f594(x10243,x10241,x10244,x10245,x10246,x10247,x10248,x10249),f594(x10243,x10242,x10244,x10245,x10246,x10247,x10248,x10249))
% 18.77/18.52 [1025]~E(x10251,x10252)+E(f594(x10253,x10254,x10251,x10255,x10256,x10257,x10258,x10259),f594(x10253,x10254,x10252,x10255,x10256,x10257,x10258,x10259))
% 18.77/18.52 [1026]~E(x10261,x10262)+E(f594(x10263,x10264,x10265,x10261,x10266,x10267,x10268,x10269),f594(x10263,x10264,x10265,x10262,x10266,x10267,x10268,x10269))
% 18.77/18.52 [1027]~E(x10271,x10272)+E(f594(x10273,x10274,x10275,x10276,x10271,x10277,x10278,x10279),f594(x10273,x10274,x10275,x10276,x10272,x10277,x10278,x10279))
% 18.77/18.52 [1028]~E(x10281,x10282)+E(f594(x10283,x10284,x10285,x10286,x10287,x10281,x10288,x10289),f594(x10283,x10284,x10285,x10286,x10287,x10282,x10288,x10289))
% 18.77/18.52 [1029]~E(x10291,x10292)+E(f594(x10293,x10294,x10295,x10296,x10297,x10298,x10291,x10299),f594(x10293,x10294,x10295,x10296,x10297,x10298,x10292,x10299))
% 18.77/18.52 [1030]~E(x10301,x10302)+E(f594(x10303,x10304,x10305,x10306,x10307,x10308,x10309,x10301),f594(x10303,x10304,x10305,x10306,x10307,x10308,x10309,x10302))
% 18.77/18.52 [1031]~E(x10311,x10312)+E(f352(x10311,x10313),f352(x10312,x10313))
% 18.77/18.52 [1032]~E(x10321,x10322)+E(f352(x10323,x10321),f352(x10323,x10322))
% 18.77/18.52 [1033]~E(x10331,x10332)+E(f632(x10331,x10333),f632(x10332,x10333))
% 18.77/18.52 [1034]~E(x10341,x10342)+E(f632(x10343,x10341),f632(x10343,x10342))
% 18.77/18.52 [1035]~E(x10351,x10352)+E(f509(x10351,x10353,x10354,x10355,x10356),f509(x10352,x10353,x10354,x10355,x10356))
% 18.77/18.52 [1036]~E(x10361,x10362)+E(f509(x10363,x10361,x10364,x10365,x10366),f509(x10363,x10362,x10364,x10365,x10366))
% 18.77/18.52 [1037]~E(x10371,x10372)+E(f509(x10373,x10374,x10371,x10375,x10376),f509(x10373,x10374,x10372,x10375,x10376))
% 18.77/18.52 [1038]~E(x10381,x10382)+E(f509(x10383,x10384,x10385,x10381,x10386),f509(x10383,x10384,x10385,x10382,x10386))
% 18.77/18.52 [1039]~E(x10391,x10392)+E(f509(x10393,x10394,x10395,x10396,x10391),f509(x10393,x10394,x10395,x10396,x10392))
% 18.77/18.52 [1040]~E(x10401,x10402)+E(f198(x10401),f198(x10402))
% 18.77/18.52 [1041]~E(x10411,x10412)+E(f507(x10411,x10413,x10414,x10415,x10416),f507(x10412,x10413,x10414,x10415,x10416))
% 18.77/18.52 [1042]~E(x10421,x10422)+E(f507(x10423,x10421,x10424,x10425,x10426),f507(x10423,x10422,x10424,x10425,x10426))
% 18.77/18.52 [1043]~E(x10431,x10432)+E(f507(x10433,x10434,x10431,x10435,x10436),f507(x10433,x10434,x10432,x10435,x10436))
% 18.77/18.52 [1044]~E(x10441,x10442)+E(f507(x10443,x10444,x10445,x10441,x10446),f507(x10443,x10444,x10445,x10442,x10446))
% 18.77/18.52 [1045]~E(x10451,x10452)+E(f507(x10453,x10454,x10455,x10456,x10451),f507(x10453,x10454,x10455,x10456,x10452))
% 18.77/18.52 [1046]~E(x10461,x10462)+E(f763(x10461,x10463,x10464),f763(x10462,x10463,x10464))
% 18.77/18.52 [1047]~E(x10471,x10472)+E(f763(x10473,x10471,x10474),f763(x10473,x10472,x10474))
% 18.77/18.52 [1048]~E(x10481,x10482)+E(f763(x10483,x10484,x10481),f763(x10483,x10484,x10482))
% 18.77/18.52 [1049]~E(x10491,x10492)+E(f808(x10491,x10493,x10494),f808(x10492,x10493,x10494))
% 18.77/18.52 [1050]~E(x10501,x10502)+E(f808(x10503,x10501,x10504),f808(x10503,x10502,x10504))
% 18.77/18.52 [1051]~E(x10511,x10512)+E(f808(x10513,x10514,x10511),f808(x10513,x10514,x10512))
% 18.77/18.52 [1052]~E(x10521,x10522)+E(f319(x10521,x10523,x10524),f319(x10522,x10523,x10524))
% 18.77/18.52 [1053]~E(x10531,x10532)+E(f319(x10533,x10531,x10534),f319(x10533,x10532,x10534))
% 18.77/18.52 [1054]~E(x10541,x10542)+E(f319(x10543,x10544,x10541),f319(x10543,x10544,x10542))
% 18.77/18.52 [1055]~E(x10551,x10552)+E(f497(x10551,x10553,x10554,x10555),f497(x10552,x10553,x10554,x10555))
% 18.77/18.52 [1056]~E(x10561,x10562)+E(f497(x10563,x10561,x10564,x10565),f497(x10563,x10562,x10564,x10565))
% 18.77/18.52 [1057]~E(x10571,x10572)+E(f497(x10573,x10574,x10571,x10575),f497(x10573,x10574,x10572,x10575))
% 18.77/18.52 [1058]~E(x10581,x10582)+E(f497(x10583,x10584,x10585,x10581),f497(x10583,x10584,x10585,x10582))
% 18.77/18.52 [1059]~E(x10591,x10592)+E(f547(x10591,x10593,x10594,x10595,x10596,x10597,x10598),f547(x10592,x10593,x10594,x10595,x10596,x10597,x10598))
% 18.77/18.52 [1060]~E(x10601,x10602)+E(f547(x10603,x10601,x10604,x10605,x10606,x10607,x10608),f547(x10603,x10602,x10604,x10605,x10606,x10607,x10608))
% 18.77/18.52 [1061]~E(x10611,x10612)+E(f547(x10613,x10614,x10611,x10615,x10616,x10617,x10618),f547(x10613,x10614,x10612,x10615,x10616,x10617,x10618))
% 18.77/18.52 [1062]~E(x10621,x10622)+E(f547(x10623,x10624,x10625,x10621,x10626,x10627,x10628),f547(x10623,x10624,x10625,x10622,x10626,x10627,x10628))
% 18.77/18.52 [1063]~E(x10631,x10632)+E(f547(x10633,x10634,x10635,x10636,x10631,x10637,x10638),f547(x10633,x10634,x10635,x10636,x10632,x10637,x10638))
% 18.77/18.52 [1064]~E(x10641,x10642)+E(f547(x10643,x10644,x10645,x10646,x10647,x10641,x10648),f547(x10643,x10644,x10645,x10646,x10647,x10642,x10648))
% 18.77/18.52 [1065]~E(x10651,x10652)+E(f547(x10653,x10654,x10655,x10656,x10657,x10658,x10651),f547(x10653,x10654,x10655,x10656,x10657,x10658,x10652))
% 18.77/18.52 [1066]~E(x10661,x10662)+E(f510(x10661,x10663,x10664,x10665,x10666),f510(x10662,x10663,x10664,x10665,x10666))
% 18.77/18.52 [1067]~E(x10671,x10672)+E(f510(x10673,x10671,x10674,x10675,x10676),f510(x10673,x10672,x10674,x10675,x10676))
% 18.77/18.52 [1068]~E(x10681,x10682)+E(f510(x10683,x10684,x10681,x10685,x10686),f510(x10683,x10684,x10682,x10685,x10686))
% 18.77/18.52 [1069]~E(x10691,x10692)+E(f510(x10693,x10694,x10695,x10691,x10696),f510(x10693,x10694,x10695,x10692,x10696))
% 18.77/18.52 [1070]~E(x10701,x10702)+E(f510(x10703,x10704,x10705,x10706,x10701),f510(x10703,x10704,x10705,x10706,x10702))
% 18.77/18.52 [1071]~E(x10711,x10712)+E(f564(x10711,x10713,x10714,x10715,x10716),f564(x10712,x10713,x10714,x10715,x10716))
% 18.77/18.52 [1072]~E(x10721,x10722)+E(f564(x10723,x10721,x10724,x10725,x10726),f564(x10723,x10722,x10724,x10725,x10726))
% 18.77/18.52 [1073]~E(x10731,x10732)+E(f564(x10733,x10734,x10731,x10735,x10736),f564(x10733,x10734,x10732,x10735,x10736))
% 18.77/18.52 [1074]~E(x10741,x10742)+E(f564(x10743,x10744,x10745,x10741,x10746),f564(x10743,x10744,x10745,x10742,x10746))
% 18.77/18.52 [1075]~E(x10751,x10752)+E(f564(x10753,x10754,x10755,x10756,x10751),f564(x10753,x10754,x10755,x10756,x10752))
% 18.77/18.52 [1076]~E(x10761,x10762)+E(f499(x10761,x10763,x10764,x10765,x10766),f499(x10762,x10763,x10764,x10765,x10766))
% 18.77/18.52 [1077]~E(x10771,x10772)+E(f499(x10773,x10771,x10774,x10775,x10776),f499(x10773,x10772,x10774,x10775,x10776))
% 18.77/18.52 [1078]~E(x10781,x10782)+E(f499(x10783,x10784,x10781,x10785,x10786),f499(x10783,x10784,x10782,x10785,x10786))
% 18.77/18.52 [1079]~E(x10791,x10792)+E(f499(x10793,x10794,x10795,x10791,x10796),f499(x10793,x10794,x10795,x10792,x10796))
% 18.77/18.52 [1080]~E(x10801,x10802)+E(f499(x10803,x10804,x10805,x10806,x10801),f499(x10803,x10804,x10805,x10806,x10802))
% 18.77/18.52 [1081]~E(x10811,x10812)+E(f803(x10811,x10813,x10814),f803(x10812,x10813,x10814))
% 18.77/18.52 [1082]~E(x10821,x10822)+E(f803(x10823,x10821,x10824),f803(x10823,x10822,x10824))
% 18.77/18.52 [1083]~E(x10831,x10832)+E(f803(x10833,x10834,x10831),f803(x10833,x10834,x10832))
% 18.77/18.52 [1084]~E(x10841,x10842)+E(f727(x10841,x10843,x10844,x10845,x10846),f727(x10842,x10843,x10844,x10845,x10846))
% 18.77/18.52 [1085]~E(x10851,x10852)+E(f727(x10853,x10851,x10854,x10855,x10856),f727(x10853,x10852,x10854,x10855,x10856))
% 18.77/18.52 [1086]~E(x10861,x10862)+E(f727(x10863,x10864,x10861,x10865,x10866),f727(x10863,x10864,x10862,x10865,x10866))
% 18.77/18.52 [1087]~E(x10871,x10872)+E(f727(x10873,x10874,x10875,x10871,x10876),f727(x10873,x10874,x10875,x10872,x10876))
% 18.77/18.52 [1088]~E(x10881,x10882)+E(f727(x10883,x10884,x10885,x10886,x10881),f727(x10883,x10884,x10885,x10886,x10882))
% 18.77/18.52 [1089]~E(x10891,x10892)+E(f702(x10891,x10893,x10894,x10895,x10896),f702(x10892,x10893,x10894,x10895,x10896))
% 18.77/18.52 [1090]~E(x10901,x10902)+E(f702(x10903,x10901,x10904,x10905,x10906),f702(x10903,x10902,x10904,x10905,x10906))
% 18.77/18.52 [1091]~E(x10911,x10912)+E(f702(x10913,x10914,x10911,x10915,x10916),f702(x10913,x10914,x10912,x10915,x10916))
% 18.77/18.52 [1092]~E(x10921,x10922)+E(f702(x10923,x10924,x10925,x10921,x10926),f702(x10923,x10924,x10925,x10922,x10926))
% 18.77/18.52 [1093]~E(x10931,x10932)+E(f702(x10933,x10934,x10935,x10936,x10931),f702(x10933,x10934,x10935,x10936,x10932))
% 18.77/18.52 [1094]~E(x10941,x10942)+E(f79(x10941,x10943,x10944,x10945),f79(x10942,x10943,x10944,x10945))
% 18.77/18.52 [1095]~E(x10951,x10952)+E(f79(x10953,x10951,x10954,x10955),f79(x10953,x10952,x10954,x10955))
% 18.77/18.52 [1096]~E(x10961,x10962)+E(f79(x10963,x10964,x10961,x10965),f79(x10963,x10964,x10962,x10965))
% 18.77/18.52 [1097]~E(x10971,x10972)+E(f79(x10973,x10974,x10975,x10971),f79(x10973,x10974,x10975,x10972))
% 18.77/18.52 [1098]~E(x10981,x10982)+E(f337(x10981,x10983),f337(x10982,x10983))
% 18.77/18.52 [1099]~E(x10991,x10992)+E(f337(x10993,x10991),f337(x10993,x10992))
% 18.77/18.52 [1100]~E(x11001,x11002)+E(f393(x11001,x11003),f393(x11002,x11003))
% 18.77/18.52 [1101]~E(x11011,x11012)+E(f393(x11013,x11011),f393(x11013,x11012))
% 18.77/18.52 [1102]~E(x11021,x11022)+E(f24(x11021,x11023),f24(x11022,x11023))
% 18.77/18.52 [1103]~E(x11031,x11032)+E(f24(x11033,x11031),f24(x11033,x11032))
% 18.77/18.52 [1104]~E(x11041,x11042)+E(f663(x11041,x11043,x11044,x11045),f663(x11042,x11043,x11044,x11045))
% 18.77/18.52 [1105]~E(x11051,x11052)+E(f663(x11053,x11051,x11054,x11055),f663(x11053,x11052,x11054,x11055))
% 18.77/18.52 [1106]~E(x11061,x11062)+E(f663(x11063,x11064,x11061,x11065),f663(x11063,x11064,x11062,x11065))
% 18.77/18.52 [1107]~E(x11071,x11072)+E(f663(x11073,x11074,x11075,x11071),f663(x11073,x11074,x11075,x11072))
% 18.77/18.52 [1108]~E(x11081,x11082)+E(f699(x11081,x11083,x11084,x11085,x11086,x11087,x11088),f699(x11082,x11083,x11084,x11085,x11086,x11087,x11088))
% 18.77/18.52 [1109]~E(x11091,x11092)+E(f699(x11093,x11091,x11094,x11095,x11096,x11097,x11098),f699(x11093,x11092,x11094,x11095,x11096,x11097,x11098))
% 18.77/18.52 [1110]~E(x11101,x11102)+E(f699(x11103,x11104,x11101,x11105,x11106,x11107,x11108),f699(x11103,x11104,x11102,x11105,x11106,x11107,x11108))
% 18.77/18.52 [1111]~E(x11111,x11112)+E(f699(x11113,x11114,x11115,x11111,x11116,x11117,x11118),f699(x11113,x11114,x11115,x11112,x11116,x11117,x11118))
% 18.77/18.52 [1112]~E(x11121,x11122)+E(f699(x11123,x11124,x11125,x11126,x11121,x11127,x11128),f699(x11123,x11124,x11125,x11126,x11122,x11127,x11128))
% 18.77/18.52 [1113]~E(x11131,x11132)+E(f699(x11133,x11134,x11135,x11136,x11137,x11131,x11138),f699(x11133,x11134,x11135,x11136,x11137,x11132,x11138))
% 18.77/18.52 [1114]~E(x11141,x11142)+E(f699(x11143,x11144,x11145,x11146,x11147,x11148,x11141),f699(x11143,x11144,x11145,x11146,x11147,x11148,x11142))
% 18.77/18.52 [1115]~E(x11151,x11152)+E(f647(x11151,x11153,x11154,x11155),f647(x11152,x11153,x11154,x11155))
% 18.77/18.52 [1116]~E(x11161,x11162)+E(f647(x11163,x11161,x11164,x11165),f647(x11163,x11162,x11164,x11165))
% 18.77/18.52 [1117]~E(x11171,x11172)+E(f647(x11173,x11174,x11171,x11175),f647(x11173,x11174,x11172,x11175))
% 18.77/18.52 [1118]~E(x11181,x11182)+E(f647(x11183,x11184,x11185,x11181),f647(x11183,x11184,x11185,x11182))
% 18.77/18.52 [1119]~E(x11191,x11192)+E(f512(x11191),f512(x11192))
% 18.77/18.52 [1120]~E(x11201,x11202)+E(f810(x11201,x11203,x11204),f810(x11202,x11203,x11204))
% 18.77/18.52 [1121]~E(x11211,x11212)+E(f810(x11213,x11211,x11214),f810(x11213,x11212,x11214))
% 18.77/18.52 [1122]~E(x11221,x11222)+E(f810(x11223,x11224,x11221),f810(x11223,x11224,x11222))
% 18.77/18.52 [1123]~E(x11231,x11232)+E(f543(x11231,x11233,x11234,x11235,x11236,x11237,x11238),f543(x11232,x11233,x11234,x11235,x11236,x11237,x11238))
% 18.77/18.52 [1124]~E(x11241,x11242)+E(f543(x11243,x11241,x11244,x11245,x11246,x11247,x11248),f543(x11243,x11242,x11244,x11245,x11246,x11247,x11248))
% 18.77/18.52 [1125]~E(x11251,x11252)+E(f543(x11253,x11254,x11251,x11255,x11256,x11257,x11258),f543(x11253,x11254,x11252,x11255,x11256,x11257,x11258))
% 18.77/18.52 [1126]~E(x11261,x11262)+E(f543(x11263,x11264,x11265,x11261,x11266,x11267,x11268),f543(x11263,x11264,x11265,x11262,x11266,x11267,x11268))
% 18.77/18.52 [1127]~E(x11271,x11272)+E(f543(x11273,x11274,x11275,x11276,x11271,x11277,x11278),f543(x11273,x11274,x11275,x11276,x11272,x11277,x11278))
% 18.77/18.52 [1128]~E(x11281,x11282)+E(f543(x11283,x11284,x11285,x11286,x11287,x11281,x11288),f543(x11283,x11284,x11285,x11286,x11287,x11282,x11288))
% 18.77/18.52 [1129]~E(x11291,x11292)+E(f543(x11293,x11294,x11295,x11296,x11297,x11298,x11291),f543(x11293,x11294,x11295,x11296,x11297,x11298,x11292))
% 18.77/18.52 [1130]~E(x11301,x11302)+E(f680(x11301,x11303,x11304,x11305),f680(x11302,x11303,x11304,x11305))
% 18.77/18.52 [1131]~E(x11311,x11312)+E(f680(x11313,x11311,x11314,x11315),f680(x11313,x11312,x11314,x11315))
% 18.77/18.52 [1132]~E(x11321,x11322)+E(f680(x11323,x11324,x11321,x11325),f680(x11323,x11324,x11322,x11325))
% 18.77/18.52 [1133]~E(x11331,x11332)+E(f680(x11333,x11334,x11335,x11331),f680(x11333,x11334,x11335,x11332))
% 18.77/18.52 [1134]~E(x11341,x11342)+E(f723(x11341,x11343,x11344),f723(x11342,x11343,x11344))
% 18.77/18.52 [1135]~E(x11351,x11352)+E(f723(x11353,x11351,x11354),f723(x11353,x11352,x11354))
% 18.77/18.52 [1136]~E(x11361,x11362)+E(f723(x11363,x11364,x11361),f723(x11363,x11364,x11362))
% 18.77/18.52 [1137]~E(x11371,x11372)+E(f415(x11371,x11373,x11374),f415(x11372,x11373,x11374))
% 18.77/18.52 [1138]~E(x11381,x11382)+E(f415(x11383,x11381,x11384),f415(x11383,x11382,x11384))
% 18.77/18.52 [1139]~E(x11391,x11392)+E(f415(x11393,x11394,x11391),f415(x11393,x11394,x11392))
% 18.77/18.52 [1140]~E(x11401,x11402)+E(f420(x11401,x11403,x11404),f420(x11402,x11403,x11404))
% 18.77/18.52 [1141]~E(x11411,x11412)+E(f420(x11413,x11411,x11414),f420(x11413,x11412,x11414))
% 18.77/18.52 [1142]~E(x11421,x11422)+E(f420(x11423,x11424,x11421),f420(x11423,x11424,x11422))
% 18.77/18.52 [1143]~E(x11431,x11432)+E(f293(x11431,x11433,x11434,x11435,x11436),f293(x11432,x11433,x11434,x11435,x11436))
% 18.77/18.52 [1144]~E(x11441,x11442)+E(f293(x11443,x11441,x11444,x11445,x11446),f293(x11443,x11442,x11444,x11445,x11446))
% 18.77/18.52 [1145]~E(x11451,x11452)+E(f293(x11453,x11454,x11451,x11455,x11456),f293(x11453,x11454,x11452,x11455,x11456))
% 18.77/18.52 [1146]~E(x11461,x11462)+E(f293(x11463,x11464,x11465,x11461,x11466),f293(x11463,x11464,x11465,x11462,x11466))
% 18.77/18.52 [1147]~E(x11471,x11472)+E(f293(x11473,x11474,x11475,x11476,x11471),f293(x11473,x11474,x11475,x11476,x11472))
% 18.77/18.52 [1148]~E(x11481,x11482)+E(f535(x11481,x11483,x11484,x11485,x11486),f535(x11482,x11483,x11484,x11485,x11486))
% 18.77/18.52 [1149]~E(x11491,x11492)+E(f535(x11493,x11491,x11494,x11495,x11496),f535(x11493,x11492,x11494,x11495,x11496))
% 18.77/18.52 [1150]~E(x11501,x11502)+E(f535(x11503,x11504,x11501,x11505,x11506),f535(x11503,x11504,x11502,x11505,x11506))
% 18.77/18.52 [1151]~E(x11511,x11512)+E(f535(x11513,x11514,x11515,x11511,x11516),f535(x11513,x11514,x11515,x11512,x11516))
% 18.77/18.52 [1152]~E(x11521,x11522)+E(f535(x11523,x11524,x11525,x11526,x11521),f535(x11523,x11524,x11525,x11526,x11522))
% 18.77/18.52 [1153]~E(x11531,x11532)+E(f412(x11531,x11533,x11534),f412(x11532,x11533,x11534))
% 18.77/18.52 [1154]~E(x11541,x11542)+E(f412(x11543,x11541,x11544),f412(x11543,x11542,x11544))
% 18.77/18.52 [1155]~E(x11551,x11552)+E(f412(x11553,x11554,x11551),f412(x11553,x11554,x11552))
% 18.77/18.52 [1156]~E(x11561,x11562)+E(f775(x11561,x11563,x11564,x11565),f775(x11562,x11563,x11564,x11565))
% 18.77/18.52 [1157]~E(x11571,x11572)+E(f775(x11573,x11571,x11574,x11575),f775(x11573,x11572,x11574,x11575))
% 18.77/18.52 [1158]~E(x11581,x11582)+E(f775(x11583,x11584,x11581,x11585),f775(x11583,x11584,x11582,x11585))
% 18.77/18.52 [1159]~E(x11591,x11592)+E(f775(x11593,x11594,x11595,x11591),f775(x11593,x11594,x11595,x11592))
% 18.77/18.52 [1160]~E(x11601,x11602)+E(f122(x11601,x11603,x11604,x11605),f122(x11602,x11603,x11604,x11605))
% 18.77/18.52 [1161]~E(x11611,x11612)+E(f122(x11613,x11611,x11614,x11615),f122(x11613,x11612,x11614,x11615))
% 18.77/18.52 [1162]~E(x11621,x11622)+E(f122(x11623,x11624,x11621,x11625),f122(x11623,x11624,x11622,x11625))
% 18.77/18.52 [1163]~E(x11631,x11632)+E(f122(x11633,x11634,x11635,x11631),f122(x11633,x11634,x11635,x11632))
% 18.77/18.52 [1164]~E(x11641,x11642)+E(f451(x11641,x11643,x11644,x11645),f451(x11642,x11643,x11644,x11645))
% 18.77/18.52 [1165]~E(x11651,x11652)+E(f451(x11653,x11651,x11654,x11655),f451(x11653,x11652,x11654,x11655))
% 18.77/18.52 [1166]~E(x11661,x11662)+E(f451(x11663,x11664,x11661,x11665),f451(x11663,x11664,x11662,x11665))
% 18.77/18.52 [1167]~E(x11671,x11672)+E(f451(x11673,x11674,x11675,x11671),f451(x11673,x11674,x11675,x11672))
% 18.77/18.52 [1168]~E(x11681,x11682)+E(f712(x11681,x11683,x11684),f712(x11682,x11683,x11684))
% 18.77/18.52 [1169]~E(x11691,x11692)+E(f712(x11693,x11691,x11694),f712(x11693,x11692,x11694))
% 18.77/18.52 [1170]~E(x11701,x11702)+E(f712(x11703,x11704,x11701),f712(x11703,x11704,x11702))
% 18.77/18.52 [1171]~E(x11711,x11712)+E(f754(x11711,x11713,x11714),f754(x11712,x11713,x11714))
% 18.77/18.52 [1172]~E(x11721,x11722)+E(f754(x11723,x11721,x11724),f754(x11723,x11722,x11724))
% 18.77/18.52 [1173]~E(x11731,x11732)+E(f754(x11733,x11734,x11731),f754(x11733,x11734,x11732))
% 18.77/18.52 [1174]~E(x11741,x11742)+E(f554(x11741),f554(x11742))
% 18.77/18.52 [1175]~E(x11751,x11752)+E(f351(x11751,x11753,x11754,x11755),f351(x11752,x11753,x11754,x11755))
% 18.77/18.52 [1176]~E(x11761,x11762)+E(f351(x11763,x11761,x11764,x11765),f351(x11763,x11762,x11764,x11765))
% 18.77/18.52 [1177]~E(x11771,x11772)+E(f351(x11773,x11774,x11771,x11775),f351(x11773,x11774,x11772,x11775))
% 18.77/18.52 [1178]~E(x11781,x11782)+E(f351(x11783,x11784,x11785,x11781),f351(x11783,x11784,x11785,x11782))
% 18.77/18.52 [1179]~E(x11791,x11792)+E(f447(x11791,x11793),f447(x11792,x11793))
% 18.77/18.52 [1180]~E(x11801,x11802)+E(f447(x11803,x11801),f447(x11803,x11802))
% 18.77/18.52 [1181]~E(x11811,x11812)+E(f479(x11811,x11813,x11814,x11815,x11816),f479(x11812,x11813,x11814,x11815,x11816))
% 18.77/18.52 [1182]~E(x11821,x11822)+E(f479(x11823,x11821,x11824,x11825,x11826),f479(x11823,x11822,x11824,x11825,x11826))
% 18.77/18.52 [1183]~E(x11831,x11832)+E(f479(x11833,x11834,x11831,x11835,x11836),f479(x11833,x11834,x11832,x11835,x11836))
% 18.77/18.52 [1184]~E(x11841,x11842)+E(f479(x11843,x11844,x11845,x11841,x11846),f479(x11843,x11844,x11845,x11842,x11846))
% 18.77/18.52 [1185]~E(x11851,x11852)+E(f479(x11853,x11854,x11855,x11856,x11851),f479(x11853,x11854,x11855,x11856,x11852))
% 18.77/18.52 [1186]~E(x11861,x11862)+E(f426(x11861,x11863,x11864,x11865,x11866),f426(x11862,x11863,x11864,x11865,x11866))
% 18.77/18.52 [1187]~E(x11871,x11872)+E(f426(x11873,x11871,x11874,x11875,x11876),f426(x11873,x11872,x11874,x11875,x11876))
% 18.77/18.52 [1188]~E(x11881,x11882)+E(f426(x11883,x11884,x11881,x11885,x11886),f426(x11883,x11884,x11882,x11885,x11886))
% 18.77/18.52 [1189]~E(x11891,x11892)+E(f426(x11893,x11894,x11895,x11891,x11896),f426(x11893,x11894,x11895,x11892,x11896))
% 18.77/18.52 [1190]~E(x11901,x11902)+E(f426(x11903,x11904,x11905,x11906,x11901),f426(x11903,x11904,x11905,x11906,x11902))
% 18.77/18.52 [1191]~E(x11911,x11912)+E(f829(x11911,x11913),f829(x11912,x11913))
% 18.77/18.52 [1192]~E(x11921,x11922)+E(f829(x11923,x11921),f829(x11923,x11922))
% 18.77/18.52 [1193]~E(x11931,x11932)+E(f752(x11931,x11933,x11934),f752(x11932,x11933,x11934))
% 18.77/18.52 [1194]~E(x11941,x11942)+E(f752(x11943,x11941,x11944),f752(x11943,x11942,x11944))
% 18.77/18.52 [1195]~E(x11951,x11952)+E(f752(x11953,x11954,x11951),f752(x11953,x11954,x11952))
% 18.77/18.52 [1196]~E(x11961,x11962)+E(f597(x11961,x11963,x11964),f597(x11962,x11963,x11964))
% 18.77/18.52 [1197]~E(x11971,x11972)+E(f597(x11973,x11971,x11974),f597(x11973,x11972,x11974))
% 18.77/18.52 [1198]~E(x11981,x11982)+E(f597(x11983,x11984,x11981),f597(x11983,x11984,x11982))
% 18.77/18.52 [1199]~E(x11991,x11992)+E(f373(x11991,x11993,x11994,x11995),f373(x11992,x11993,x11994,x11995))
% 18.77/18.52 [1200]~E(x12001,x12002)+E(f373(x12003,x12001,x12004,x12005),f373(x12003,x12002,x12004,x12005))
% 18.77/18.52 [1201]~E(x12011,x12012)+E(f373(x12013,x12014,x12011,x12015),f373(x12013,x12014,x12012,x12015))
% 18.77/18.52 [1202]~E(x12021,x12022)+E(f373(x12023,x12024,x12025,x12021),f373(x12023,x12024,x12025,x12022))
% 18.77/18.52 [1203]~E(x12031,x12032)+E(f403(x12031,x12033,x12034,x12035),f403(x12032,x12033,x12034,x12035))
% 18.77/18.52 [1204]~E(x12041,x12042)+E(f403(x12043,x12041,x12044,x12045),f403(x12043,x12042,x12044,x12045))
% 18.77/18.52 [1205]~E(x12051,x12052)+E(f403(x12053,x12054,x12051,x12055),f403(x12053,x12054,x12052,x12055))
% 18.77/18.52 [1206]~E(x12061,x12062)+E(f403(x12063,x12064,x12065,x12061),f403(x12063,x12064,x12065,x12062))
% 18.77/18.52 [1207]~E(x12071,x12072)+E(f593(x12071,x12073,x12074,x12075,x12076,x12077,x12078,x12079),f593(x12072,x12073,x12074,x12075,x12076,x12077,x12078,x12079))
% 18.77/18.52 [1208]~E(x12081,x12082)+E(f593(x12083,x12081,x12084,x12085,x12086,x12087,x12088,x12089),f593(x12083,x12082,x12084,x12085,x12086,x12087,x12088,x12089))
% 18.77/18.52 [1209]~E(x12091,x12092)+E(f593(x12093,x12094,x12091,x12095,x12096,x12097,x12098,x12099),f593(x12093,x12094,x12092,x12095,x12096,x12097,x12098,x12099))
% 18.77/18.52 [1210]~E(x12101,x12102)+E(f593(x12103,x12104,x12105,x12101,x12106,x12107,x12108,x12109),f593(x12103,x12104,x12105,x12102,x12106,x12107,x12108,x12109))
% 18.77/18.52 [1211]~E(x12111,x12112)+E(f593(x12113,x12114,x12115,x12116,x12111,x12117,x12118,x12119),f593(x12113,x12114,x12115,x12116,x12112,x12117,x12118,x12119))
% 18.77/18.52 [1212]~E(x12121,x12122)+E(f593(x12123,x12124,x12125,x12126,x12127,x12121,x12128,x12129),f593(x12123,x12124,x12125,x12126,x12127,x12122,x12128,x12129))
% 18.77/18.52 [1213]~E(x12131,x12132)+E(f593(x12133,x12134,x12135,x12136,x12137,x12138,x12131,x12139),f593(x12133,x12134,x12135,x12136,x12137,x12138,x12132,x12139))
% 18.77/18.52 [1214]~E(x12141,x12142)+E(f593(x12143,x12144,x12145,x12146,x12147,x12148,x12149,x12141),f593(x12143,x12144,x12145,x12146,x12147,x12148,x12149,x12142))
% 18.77/18.52 [1215]~E(x12151,x12152)+E(f248(x12151,x12153,x12154,x12155,x12156),f248(x12152,x12153,x12154,x12155,x12156))
% 18.77/18.52 [1216]~E(x12161,x12162)+E(f248(x12163,x12161,x12164,x12165,x12166),f248(x12163,x12162,x12164,x12165,x12166))
% 18.77/18.52 [1217]~E(x12171,x12172)+E(f248(x12173,x12174,x12171,x12175,x12176),f248(x12173,x12174,x12172,x12175,x12176))
% 18.77/18.52 [1218]~E(x12181,x12182)+E(f248(x12183,x12184,x12185,x12181,x12186),f248(x12183,x12184,x12185,x12182,x12186))
% 18.77/18.52 [1219]~E(x12191,x12192)+E(f248(x12193,x12194,x12195,x12196,x12191),f248(x12193,x12194,x12195,x12196,x12192))
% 18.77/18.52 [1220]~E(x12201,x12202)+E(f705(x12201,x12203,x12204,x12205,x12206),f705(x12202,x12203,x12204,x12205,x12206))
% 18.77/18.52 [1221]~E(x12211,x12212)+E(f705(x12213,x12211,x12214,x12215,x12216),f705(x12213,x12212,x12214,x12215,x12216))
% 18.77/18.52 [1222]~E(x12221,x12222)+E(f705(x12223,x12224,x12221,x12225,x12226),f705(x12223,x12224,x12222,x12225,x12226))
% 18.77/18.52 [1223]~E(x12231,x12232)+E(f705(x12233,x12234,x12235,x12231,x12236),f705(x12233,x12234,x12235,x12232,x12236))
% 18.77/18.52 [1224]~E(x12241,x12242)+E(f705(x12243,x12244,x12245,x12246,x12241),f705(x12243,x12244,x12245,x12246,x12242))
% 18.77/18.52 [1225]~E(x12251,x12252)+E(f90(x12251),f90(x12252))
% 18.77/18.52 [1226]~E(x12261,x12262)+E(f746(x12261,x12263,x12264,x12265),f746(x12262,x12263,x12264,x12265))
% 18.77/18.52 [1227]~E(x12271,x12272)+E(f746(x12273,x12271,x12274,x12275),f746(x12273,x12272,x12274,x12275))
% 18.77/18.52 [1228]~E(x12281,x12282)+E(f746(x12283,x12284,x12281,x12285),f746(x12283,x12284,x12282,x12285))
% 18.77/18.52 [1229]~E(x12291,x12292)+E(f746(x12293,x12294,x12295,x12291),f746(x12293,x12294,x12295,x12292))
% 18.77/18.52 [1230]~E(x12301,x12302)+E(f417(x12301,x12303,x12304),f417(x12302,x12303,x12304))
% 18.77/18.52 [1231]~E(x12311,x12312)+E(f417(x12313,x12311,x12314),f417(x12313,x12312,x12314))
% 18.77/18.52 [1232]~E(x12321,x12322)+E(f417(x12323,x12324,x12321),f417(x12323,x12324,x12322))
% 18.77/18.52 [1233]~E(x12331,x12332)+E(f436(x12331,x12333,x12334,x12335,x12336),f436(x12332,x12333,x12334,x12335,x12336))
% 18.77/18.52 [1234]~E(x12341,x12342)+E(f436(x12343,x12341,x12344,x12345,x12346),f436(x12343,x12342,x12344,x12345,x12346))
% 18.77/18.52 [1235]~E(x12351,x12352)+E(f436(x12353,x12354,x12351,x12355,x12356),f436(x12353,x12354,x12352,x12355,x12356))
% 18.77/18.52 [1236]~E(x12361,x12362)+E(f436(x12363,x12364,x12365,x12361,x12366),f436(x12363,x12364,x12365,x12362,x12366))
% 18.77/18.52 [1237]~E(x12371,x12372)+E(f436(x12373,x12374,x12375,x12376,x12371),f436(x12373,x12374,x12375,x12376,x12372))
% 18.77/18.52 [1238]~E(x12381,x12382)+E(f477(x12381,x12383),f477(x12382,x12383))
% 18.77/18.52 [1239]~E(x12391,x12392)+E(f477(x12393,x12391),f477(x12393,x12392))
% 18.77/18.52 [1240]~E(x12401,x12402)+E(f523(x12401,x12403,x12404,x12405),f523(x12402,x12403,x12404,x12405))
% 18.77/18.52 [1241]~E(x12411,x12412)+E(f523(x12413,x12411,x12414,x12415),f523(x12413,x12412,x12414,x12415))
% 18.77/18.52 [1242]~E(x12421,x12422)+E(f523(x12423,x12424,x12421,x12425),f523(x12423,x12424,x12422,x12425))
% 18.77/18.52 [1243]~E(x12431,x12432)+E(f523(x12433,x12434,x12435,x12431),f523(x12433,x12434,x12435,x12432))
% 18.77/18.52 [1244]~E(x12441,x12442)+E(f629(x12441,x12443,x12444,x12445,x12446,x12447),f629(x12442,x12443,x12444,x12445,x12446,x12447))
% 18.77/18.52 [1245]~E(x12451,x12452)+E(f629(x12453,x12451,x12454,x12455,x12456,x12457),f629(x12453,x12452,x12454,x12455,x12456,x12457))
% 18.77/18.52 [1246]~E(x12461,x12462)+E(f629(x12463,x12464,x12461,x12465,x12466,x12467),f629(x12463,x12464,x12462,x12465,x12466,x12467))
% 18.77/18.52 [1247]~E(x12471,x12472)+E(f629(x12473,x12474,x12475,x12471,x12476,x12477),f629(x12473,x12474,x12475,x12472,x12476,x12477))
% 18.77/18.52 [1248]~E(x12481,x12482)+E(f629(x12483,x12484,x12485,x12486,x12481,x12487),f629(x12483,x12484,x12485,x12486,x12482,x12487))
% 18.77/18.52 [1249]~E(x12491,x12492)+E(f629(x12493,x12494,x12495,x12496,x12497,x12491),f629(x12493,x12494,x12495,x12496,x12497,x12492))
% 18.77/18.52 [1250]~E(x12501,x12502)+E(f422(x12501,x12503,x12504,x12505,x12506),f422(x12502,x12503,x12504,x12505,x12506))
% 18.77/18.52 [1251]~E(x12511,x12512)+E(f422(x12513,x12511,x12514,x12515,x12516),f422(x12513,x12512,x12514,x12515,x12516))
% 18.77/18.52 [1252]~E(x12521,x12522)+E(f422(x12523,x12524,x12521,x12525,x12526),f422(x12523,x12524,x12522,x12525,x12526))
% 18.77/18.52 [1253]~E(x12531,x12532)+E(f422(x12533,x12534,x12535,x12531,x12536),f422(x12533,x12534,x12535,x12532,x12536))
% 18.77/18.52 [1254]~E(x12541,x12542)+E(f422(x12543,x12544,x12545,x12546,x12541),f422(x12543,x12544,x12545,x12546,x12542))
% 18.77/18.52 [1255]~E(x12551,x12552)+E(f725(x12551,x12553,x12554,x12555,x12556),f725(x12552,x12553,x12554,x12555,x12556))
% 18.77/18.52 [1256]~E(x12561,x12562)+E(f725(x12563,x12561,x12564,x12565,x12566),f725(x12563,x12562,x12564,x12565,x12566))
% 18.77/18.52 [1257]~E(x12571,x12572)+E(f725(x12573,x12574,x12571,x12575,x12576),f725(x12573,x12574,x12572,x12575,x12576))
% 18.77/18.52 [1258]~E(x12581,x12582)+E(f725(x12583,x12584,x12585,x12581,x12586),f725(x12583,x12584,x12585,x12582,x12586))
% 18.77/18.52 [1259]~E(x12591,x12592)+E(f725(x12593,x12594,x12595,x12596,x12591),f725(x12593,x12594,x12595,x12596,x12592))
% 18.77/18.52 [1260]~E(x12601,x12602)+E(f778(x12601,x12603,x12604),f778(x12602,x12603,x12604))
% 18.77/18.52 [1261]~E(x12611,x12612)+E(f778(x12613,x12611,x12614),f778(x12613,x12612,x12614))
% 18.77/18.52 [1262]~E(x12621,x12622)+E(f778(x12623,x12624,x12621),f778(x12623,x12624,x12622))
% 18.77/18.52 [1263]~E(x12631,x12632)+E(f286(x12631,x12633),f286(x12632,x12633))
% 18.77/18.52 [1264]~E(x12641,x12642)+E(f286(x12643,x12641),f286(x12643,x12642))
% 18.77/18.52 [1265]~E(x12651,x12652)+E(f524(x12651,x12653,x12654,x12655),f524(x12652,x12653,x12654,x12655))
% 18.77/18.52 [1266]~E(x12661,x12662)+E(f524(x12663,x12661,x12664,x12665),f524(x12663,x12662,x12664,x12665))
% 18.77/18.52 [1267]~E(x12671,x12672)+E(f524(x12673,x12674,x12671,x12675),f524(x12673,x12674,x12672,x12675))
% 18.77/18.52 [1268]~E(x12681,x12682)+E(f524(x12683,x12684,x12685,x12681),f524(x12683,x12684,x12685,x12682))
% 18.77/18.52 [1269]~E(x12691,x12692)+E(f636(x12691,x12693,x12694,x12695,x12696),f636(x12692,x12693,x12694,x12695,x12696))
% 18.77/18.52 [1270]~E(x12701,x12702)+E(f636(x12703,x12701,x12704,x12705,x12706),f636(x12703,x12702,x12704,x12705,x12706))
% 18.77/18.52 [1271]~E(x12711,x12712)+E(f636(x12713,x12714,x12711,x12715,x12716),f636(x12713,x12714,x12712,x12715,x12716))
% 18.77/18.52 [1272]~E(x12721,x12722)+E(f636(x12723,x12724,x12725,x12721,x12726),f636(x12723,x12724,x12725,x12722,x12726))
% 18.77/18.52 [1273]~E(x12731,x12732)+E(f636(x12733,x12734,x12735,x12736,x12731),f636(x12733,x12734,x12735,x12736,x12732))
% 18.77/18.52 [1274]~E(x12741,x12742)+E(f242(x12741,x12743,x12744),f242(x12742,x12743,x12744))
% 18.77/18.52 [1275]~E(x12751,x12752)+E(f242(x12753,x12751,x12754),f242(x12753,x12752,x12754))
% 18.77/18.52 [1276]~E(x12761,x12762)+E(f242(x12763,x12764,x12761),f242(x12763,x12764,x12762))
% 18.77/18.52 [1277]~E(x12771,x12772)+E(f339(x12771,x12773,x12774,x12775),f339(x12772,x12773,x12774,x12775))
% 18.77/18.52 [1278]~E(x12781,x12782)+E(f339(x12783,x12781,x12784,x12785),f339(x12783,x12782,x12784,x12785))
% 18.77/18.52 [1279]~E(x12791,x12792)+E(f339(x12793,x12794,x12791,x12795),f339(x12793,x12794,x12792,x12795))
% 18.77/18.52 [1280]~E(x12801,x12802)+E(f339(x12803,x12804,x12805,x12801),f339(x12803,x12804,x12805,x12802))
% 18.77/18.52 [1281]~E(x12811,x12812)+E(f427(x12811,x12813),f427(x12812,x12813))
% 18.77/18.52 [1282]~E(x12821,x12822)+E(f427(x12823,x12821),f427(x12823,x12822))
% 18.77/18.52 [1283]~E(x12831,x12832)+E(f502(x12831,x12833,x12834),f502(x12832,x12833,x12834))
% 18.77/18.52 [1284]~E(x12841,x12842)+E(f502(x12843,x12841,x12844),f502(x12843,x12842,x12844))
% 18.77/18.52 [1285]~E(x12851,x12852)+E(f502(x12853,x12854,x12851),f502(x12853,x12854,x12852))
% 18.77/18.52 [1286]~E(x12861,x12862)+E(f628(x12861,x12863,x12864,x12865,x12866,x12867),f628(x12862,x12863,x12864,x12865,x12866,x12867))
% 18.77/18.52 [1287]~E(x12871,x12872)+E(f628(x12873,x12871,x12874,x12875,x12876,x12877),f628(x12873,x12872,x12874,x12875,x12876,x12877))
% 18.77/18.52 [1288]~E(x12881,x12882)+E(f628(x12883,x12884,x12881,x12885,x12886,x12887),f628(x12883,x12884,x12882,x12885,x12886,x12887))
% 18.77/18.52 [1289]~E(x12891,x12892)+E(f628(x12893,x12894,x12895,x12891,x12896,x12897),f628(x12893,x12894,x12895,x12892,x12896,x12897))
% 18.77/18.52 [1290]~E(x12901,x12902)+E(f628(x12903,x12904,x12905,x12906,x12901,x12907),f628(x12903,x12904,x12905,x12906,x12902,x12907))
% 18.77/18.52 [1291]~E(x12911,x12912)+E(f628(x12913,x12914,x12915,x12916,x12917,x12911),f628(x12913,x12914,x12915,x12916,x12917,x12912))
% 18.77/18.52 [1292]~E(x12921,x12922)+E(f690(x12921,x12923,x12924),f690(x12922,x12923,x12924))
% 18.77/18.52 [1293]~E(x12931,x12932)+E(f690(x12933,x12931,x12934),f690(x12933,x12932,x12934))
% 18.77/18.52 [1294]~E(x12941,x12942)+E(f690(x12943,x12944,x12941),f690(x12943,x12944,x12942))
% 18.77/18.52 [1295]~E(x12951,x12952)+E(f408(x12951,x12953,x12954),f408(x12952,x12953,x12954))
% 18.77/18.52 [1296]~E(x12961,x12962)+E(f408(x12963,x12961,x12964),f408(x12963,x12962,x12964))
% 18.77/18.52 [1297]~E(x12971,x12972)+E(f408(x12973,x12974,x12971),f408(x12973,x12974,x12972))
% 18.77/18.52 [1298]~E(x12981,x12982)+E(f430(x12981,x12983,x12984),f430(x12982,x12983,x12984))
% 18.77/18.52 [1299]~E(x12991,x12992)+E(f430(x12993,x12991,x12994),f430(x12993,x12992,x12994))
% 18.77/18.52 [1300]~E(x13001,x13002)+E(f430(x13003,x13004,x13001),f430(x13003,x13004,x13002))
% 18.77/18.52 [1301]~E(x13011,x13012)+E(f263(x13011,x13013,x13014),f263(x13012,x13013,x13014))
% 18.77/18.52 [1302]~E(x13021,x13022)+E(f263(x13023,x13021,x13024),f263(x13023,x13022,x13024))
% 18.77/18.52 [1303]~E(x13031,x13032)+E(f263(x13033,x13034,x13031),f263(x13033,x13034,x13032))
% 18.77/18.52 [1304]~E(x13041,x13042)+E(f425(x13041,x13043),f425(x13042,x13043))
% 18.77/18.52 [1305]~E(x13051,x13052)+E(f425(x13053,x13051),f425(x13053,x13052))
% 18.77/18.52 [1306]~E(x13061,x13062)+E(f445(x13061,x13063,x13064,x13065),f445(x13062,x13063,x13064,x13065))
% 18.77/18.52 [1307]~E(x13071,x13072)+E(f445(x13073,x13071,x13074,x13075),f445(x13073,x13072,x13074,x13075))
% 18.77/18.52 [1308]~E(x13081,x13082)+E(f445(x13083,x13084,x13081,x13085),f445(x13083,x13084,x13082,x13085))
% 18.77/18.52 [1309]~E(x13091,x13092)+E(f445(x13093,x13094,x13095,x13091),f445(x13093,x13094,x13095,x13092))
% 18.77/18.52 [1310]~E(x13101,x13102)+E(f95(x13101,x13103,x13104),f95(x13102,x13103,x13104))
% 18.77/18.52 [1311]~E(x13111,x13112)+E(f95(x13113,x13111,x13114),f95(x13113,x13112,x13114))
% 18.77/18.52 [1312]~E(x13121,x13122)+E(f95(x13123,x13124,x13121),f95(x13123,x13124,x13122))
% 18.77/18.52 [1313]~E(x13131,x13132)+E(f744(x13131,x13133,x13134),f744(x13132,x13133,x13134))
% 18.77/18.52 [1314]~E(x13141,x13142)+E(f744(x13143,x13141,x13144),f744(x13143,x13142,x13144))
% 18.77/18.52 [1315]~E(x13151,x13152)+E(f744(x13153,x13154,x13151),f744(x13153,x13154,x13152))
% 18.77/18.52 [1316]~E(x13161,x13162)+E(f375(x13161,x13163,x13164,x13165,x13166,x13167),f375(x13162,x13163,x13164,x13165,x13166,x13167))
% 18.77/18.52 [1317]~E(x13171,x13172)+E(f375(x13173,x13171,x13174,x13175,x13176,x13177),f375(x13173,x13172,x13174,x13175,x13176,x13177))
% 18.77/18.52 [1318]~E(x13181,x13182)+E(f375(x13183,x13184,x13181,x13185,x13186,x13187),f375(x13183,x13184,x13182,x13185,x13186,x13187))
% 18.77/18.52 [1319]~E(x13191,x13192)+E(f375(x13193,x13194,x13195,x13191,x13196,x13197),f375(x13193,x13194,x13195,x13192,x13196,x13197))
% 18.77/18.52 [1320]~E(x13201,x13202)+E(f375(x13203,x13204,x13205,x13206,x13201,x13207),f375(x13203,x13204,x13205,x13206,x13202,x13207))
% 18.77/18.52 [1321]~E(x13211,x13212)+E(f375(x13213,x13214,x13215,x13216,x13217,x13211),f375(x13213,x13214,x13215,x13216,x13217,x13212))
% 18.77/18.52 [1322]~E(x13221,x13222)+E(f376(x13221,x13223,x13224,x13225,x13226,x13227),f376(x13222,x13223,x13224,x13225,x13226,x13227))
% 18.77/18.52 [1323]~E(x13231,x13232)+E(f376(x13233,x13231,x13234,x13235,x13236,x13237),f376(x13233,x13232,x13234,x13235,x13236,x13237))
% 18.77/18.52 [1324]~E(x13241,x13242)+E(f376(x13243,x13244,x13241,x13245,x13246,x13247),f376(x13243,x13244,x13242,x13245,x13246,x13247))
% 18.77/18.52 [1325]~E(x13251,x13252)+E(f376(x13253,x13254,x13255,x13251,x13256,x13257),f376(x13253,x13254,x13255,x13252,x13256,x13257))
% 18.77/18.52 [1326]~E(x13261,x13262)+E(f376(x13263,x13264,x13265,x13266,x13261,x13267),f376(x13263,x13264,x13265,x13266,x13262,x13267))
% 18.77/18.52 [1327]~E(x13271,x13272)+E(f376(x13273,x13274,x13275,x13276,x13277,x13271),f376(x13273,x13274,x13275,x13276,x13277,x13272))
% 18.77/18.52 [1328]~E(x13281,x13282)+E(f173(x13281,x13283,x13284),f173(x13282,x13283,x13284))
% 18.77/18.52 [1329]~E(x13291,x13292)+E(f173(x13293,x13291,x13294),f173(x13293,x13292,x13294))
% 18.77/18.52 [1330]~E(x13301,x13302)+E(f173(x13303,x13304,x13301),f173(x13303,x13304,x13302))
% 18.77/18.52 [1331]~E(x13311,x13312)+E(f410(x13311,x13313,x13314),f410(x13312,x13313,x13314))
% 18.77/18.52 [1332]~E(x13321,x13322)+E(f410(x13323,x13321,x13324),f410(x13323,x13322,x13324))
% 18.77/18.52 [1333]~E(x13331,x13332)+E(f410(x13333,x13334,x13331),f410(x13333,x13334,x13332))
% 18.77/18.52 [1334]~E(x13341,x13342)+E(f798(x13341,x13343,x13344),f798(x13342,x13343,x13344))
% 18.77/18.52 [1335]~E(x13351,x13352)+E(f798(x13353,x13351,x13354),f798(x13353,x13352,x13354))
% 18.77/18.52 [1336]~E(x13361,x13362)+E(f798(x13363,x13364,x13361),f798(x13363,x13364,x13362))
% 18.77/18.52 [1337]~E(x13371,x13372)+E(f483(x13371,x13373,x13374,x13375,x13376),f483(x13372,x13373,x13374,x13375,x13376))
% 18.77/18.52 [1338]~E(x13381,x13382)+E(f483(x13383,x13381,x13384,x13385,x13386),f483(x13383,x13382,x13384,x13385,x13386))
% 18.77/18.52 [1339]~E(x13391,x13392)+E(f483(x13393,x13394,x13391,x13395,x13396),f483(x13393,x13394,x13392,x13395,x13396))
% 18.77/18.52 [1340]~E(x13401,x13402)+E(f483(x13403,x13404,x13405,x13401,x13406),f483(x13403,x13404,x13405,x13402,x13406))
% 18.77/18.52 [1341]~E(x13411,x13412)+E(f483(x13413,x13414,x13415,x13416,x13411),f483(x13413,x13414,x13415,x13416,x13412))
% 18.77/18.52 [1342]~E(x13421,x13422)+E(f488(x13421,x13423,x13424,x13425,x13426),f488(x13422,x13423,x13424,x13425,x13426))
% 18.77/18.52 [1343]~E(x13431,x13432)+E(f488(x13433,x13431,x13434,x13435,x13436),f488(x13433,x13432,x13434,x13435,x13436))
% 18.77/18.52 [1344]~E(x13441,x13442)+E(f488(x13443,x13444,x13441,x13445,x13446),f488(x13443,x13444,x13442,x13445,x13446))
% 18.77/18.52 [1345]~E(x13451,x13452)+E(f488(x13453,x13454,x13455,x13451,x13456),f488(x13453,x13454,x13455,x13452,x13456))
% 18.77/18.52 [1346]~E(x13461,x13462)+E(f488(x13463,x13464,x13465,x13466,x13461),f488(x13463,x13464,x13465,x13466,x13462))
% 18.77/18.52 [1347]~E(x13471,x13472)+E(f224(x13471,x13473,x13474,x13475),f224(x13472,x13473,x13474,x13475))
% 18.77/18.52 [1348]~E(x13481,x13482)+E(f224(x13483,x13481,x13484,x13485),f224(x13483,x13482,x13484,x13485))
% 18.77/18.52 [1349]~E(x13491,x13492)+E(f224(x13493,x13494,x13491,x13495),f224(x13493,x13494,x13492,x13495))
% 18.77/18.52 [1350]~E(x13501,x13502)+E(f224(x13503,x13504,x13505,x13501),f224(x13503,x13504,x13505,x13502))
% 18.77/18.52 [1351]~E(x13511,x13512)+E(f274(x13511),f274(x13512))
% 18.77/18.52 [1352]~E(x13521,x13522)+E(f649(x13521,x13523,x13524,x13525,x13526,x13527),f649(x13522,x13523,x13524,x13525,x13526,x13527))
% 18.77/18.52 [1353]~E(x13531,x13532)+E(f649(x13533,x13531,x13534,x13535,x13536,x13537),f649(x13533,x13532,x13534,x13535,x13536,x13537))
% 18.77/18.52 [1354]~E(x13541,x13542)+E(f649(x13543,x13544,x13541,x13545,x13546,x13547),f649(x13543,x13544,x13542,x13545,x13546,x13547))
% 18.77/18.52 [1355]~E(x13551,x13552)+E(f649(x13553,x13554,x13555,x13551,x13556,x13557),f649(x13553,x13554,x13555,x13552,x13556,x13557))
% 18.77/18.52 [1356]~E(x13561,x13562)+E(f649(x13563,x13564,x13565,x13566,x13561,x13567),f649(x13563,x13564,x13565,x13566,x13562,x13567))
% 18.77/18.52 [1357]~E(x13571,x13572)+E(f649(x13573,x13574,x13575,x13576,x13577,x13571),f649(x13573,x13574,x13575,x13576,x13577,x13572))
% 18.77/18.52 [1358]~E(x13581,x13582)+E(f791(x13581,x13583,x13584),f791(x13582,x13583,x13584))
% 18.77/18.52 [1359]~E(x13591,x13592)+E(f791(x13593,x13591,x13594),f791(x13593,x13592,x13594))
% 18.77/18.52 [1360]~E(x13601,x13602)+E(f791(x13603,x13604,x13601),f791(x13603,x13604,x13602))
% 18.77/18.52 [1361]~E(x13611,x13612)+E(f331(x13611),f331(x13612))
% 18.77/18.52 [1362]~E(x13621,x13622)+E(f399(x13621,x13623),f399(x13622,x13623))
% 18.77/18.52 [1363]~E(x13631,x13632)+E(f399(x13633,x13631),f399(x13633,x13632))
% 18.77/18.52 [1364]~E(x13641,x13642)+E(f518(x13641,x13643,x13644,x13645,x13646),f518(x13642,x13643,x13644,x13645,x13646))
% 18.77/18.52 [1365]~E(x13651,x13652)+E(f518(x13653,x13651,x13654,x13655,x13656),f518(x13653,x13652,x13654,x13655,x13656))
% 18.77/18.52 [1366]~E(x13661,x13662)+E(f518(x13663,x13664,x13661,x13665,x13666),f518(x13663,x13664,x13662,x13665,x13666))
% 18.77/18.52 [1367]~E(x13671,x13672)+E(f518(x13673,x13674,x13675,x13671,x13676),f518(x13673,x13674,x13675,x13672,x13676))
% 18.77/18.52 [1368]~E(x13681,x13682)+E(f518(x13683,x13684,x13685,x13686,x13681),f518(x13683,x13684,x13685,x13686,x13682))
% 18.77/18.52 [1369]~E(x13691,x13692)+E(f49(x13691),f49(x13692))
% 18.77/18.52 [1370]~E(x13701,x13702)+E(f446(x13701,x13703,x13704,x13705),f446(x13702,x13703,x13704,x13705))
% 18.77/18.52 [1371]~E(x13711,x13712)+E(f446(x13713,x13711,x13714,x13715),f446(x13713,x13712,x13714,x13715))
% 18.77/18.52 [1372]~E(x13721,x13722)+E(f446(x13723,x13724,x13721,x13725),f446(x13723,x13724,x13722,x13725))
% 18.77/18.52 [1373]~E(x13731,x13732)+E(f446(x13733,x13734,x13735,x13731),f446(x13733,x13734,x13735,x13732))
% 18.77/18.52 [1374]~E(x13741,x13742)+E(f374(x13741,x13743,x13744,x13745,x13746,x13747),f374(x13742,x13743,x13744,x13745,x13746,x13747))
% 18.77/18.52 [1375]~E(x13751,x13752)+E(f374(x13753,x13751,x13754,x13755,x13756,x13757),f374(x13753,x13752,x13754,x13755,x13756,x13757))
% 18.77/18.52 [1376]~E(x13761,x13762)+E(f374(x13763,x13764,x13761,x13765,x13766,x13767),f374(x13763,x13764,x13762,x13765,x13766,x13767))
% 18.77/18.52 [1377]~E(x13771,x13772)+E(f374(x13773,x13774,x13775,x13771,x13776,x13777),f374(x13773,x13774,x13775,x13772,x13776,x13777))
% 18.77/18.52 [1378]~E(x13781,x13782)+E(f374(x13783,x13784,x13785,x13786,x13781,x13787),f374(x13783,x13784,x13785,x13786,x13782,x13787))
% 18.77/18.52 [1379]~E(x13791,x13792)+E(f374(x13793,x13794,x13795,x13796,x13797,x13791),f374(x13793,x13794,x13795,x13796,x13797,x13792))
% 18.77/18.52 [1380]~E(x13801,x13802)+E(f726(x13801,x13803,x13804,x13805),f726(x13802,x13803,x13804,x13805))
% 18.77/18.52 [1381]~E(x13811,x13812)+E(f726(x13813,x13811,x13814,x13815),f726(x13813,x13812,x13814,x13815))
% 18.77/18.52 [1382]~E(x13821,x13822)+E(f726(x13823,x13824,x13821,x13825),f726(x13823,x13824,x13822,x13825))
% 18.77/18.52 [1383]~E(x13831,x13832)+E(f726(x13833,x13834,x13835,x13831),f726(x13833,x13834,x13835,x13832))
% 18.77/18.52 [1384]~E(x13841,x13842)+E(f142(x13841,x13843,x13844),f142(x13842,x13843,x13844))
% 18.77/18.52 [1385]~E(x13851,x13852)+E(f142(x13853,x13851,x13854),f142(x13853,x13852,x13854))
% 18.77/18.52 [1386]~E(x13861,x13862)+E(f142(x13863,x13864,x13861),f142(x13863,x13864,x13862))
% 18.77/18.52 [1387]~E(x13871,x13872)+E(f227(x13871,x13873,x13874),f227(x13872,x13873,x13874))
% 18.77/18.52 [1388]~E(x13881,x13882)+E(f227(x13883,x13881,x13884),f227(x13883,x13882,x13884))
% 18.77/18.52 [1389]~E(x13891,x13892)+E(f227(x13893,x13894,x13891),f227(x13893,x13894,x13892))
% 18.77/18.52 [1390]~E(x13901,x13902)+E(f388(x13901,x13903,x13904,x13905,x13906,x13907,x13908,x13909,x139010),f388(x13902,x13903,x13904,x13905,x13906,x13907,x13908,x13909,x139010))
% 18.77/18.52 [1391]~E(x13911,x13912)+E(f388(x13913,x13911,x13914,x13915,x13916,x13917,x13918,x13919,x139110),f388(x13913,x13912,x13914,x13915,x13916,x13917,x13918,x13919,x139110))
% 18.77/18.52 [1392]~E(x13921,x13922)+E(f388(x13923,x13924,x13921,x13925,x13926,x13927,x13928,x13929,x139210),f388(x13923,x13924,x13922,x13925,x13926,x13927,x13928,x13929,x139210))
% 18.77/18.52 [1393]~E(x13931,x13932)+E(f388(x13933,x13934,x13935,x13931,x13936,x13937,x13938,x13939,x139310),f388(x13933,x13934,x13935,x13932,x13936,x13937,x13938,x13939,x139310))
% 18.77/18.52 [1394]~E(x13941,x13942)+E(f388(x13943,x13944,x13945,x13946,x13941,x13947,x13948,x13949,x139410),f388(x13943,x13944,x13945,x13946,x13942,x13947,x13948,x13949,x139410))
% 18.77/18.52 [1395]~E(x13951,x13952)+E(f388(x13953,x13954,x13955,x13956,x13957,x13951,x13958,x13959,x139510),f388(x13953,x13954,x13955,x13956,x13957,x13952,x13958,x13959,x139510))
% 18.77/18.52 [1396]~E(x13961,x13962)+E(f388(x13963,x13964,x13965,x13966,x13967,x13968,x13961,x13969,x139610),f388(x13963,x13964,x13965,x13966,x13967,x13968,x13962,x13969,x139610))
% 18.77/18.52 [1397]~E(x13971,x13972)+E(f388(x13973,x13974,x13975,x13976,x13977,x13978,x13979,x13971,x139710),f388(x13973,x13974,x13975,x13976,x13977,x13978,x13979,x13972,x139710))
% 18.77/18.52 [1398]~E(x13981,x13982)+E(f388(x13983,x13984,x13985,x13986,x13987,x13988,x13989,x139810,x13981),f388(x13983,x13984,x13985,x13986,x13987,x13988,x13989,x139810,x13982))
% 18.77/18.52 [1399]~E(x13991,x13992)+E(f458(x13991,x13993,x13994,x13995),f458(x13992,x13993,x13994,x13995))
% 18.77/18.52 [1400]~E(x14001,x14002)+E(f458(x14003,x14001,x14004,x14005),f458(x14003,x14002,x14004,x14005))
% 18.77/18.52 [1401]~E(x14011,x14012)+E(f458(x14013,x14014,x14011,x14015),f458(x14013,x14014,x14012,x14015))
% 18.77/18.52 [1402]~E(x14021,x14022)+E(f458(x14023,x14024,x14025,x14021),f458(x14023,x14024,x14025,x14022))
% 18.77/18.52 [1403]~E(x14031,x14032)+E(f520(x14031,x14033,x14034,x14035),f520(x14032,x14033,x14034,x14035))
% 18.77/18.52 [1404]~E(x14041,x14042)+E(f520(x14043,x14041,x14044,x14045),f520(x14043,x14042,x14044,x14045))
% 18.77/18.52 [1405]~E(x14051,x14052)+E(f520(x14053,x14054,x14051,x14055),f520(x14053,x14054,x14052,x14055))
% 18.77/18.52 [1406]~E(x14061,x14062)+E(f520(x14063,x14064,x14065,x14061),f520(x14063,x14064,x14065,x14062))
% 18.77/18.52 [1407]~E(x14071,x14072)+E(f817(x14071,x14073,x14074,x14075),f817(x14072,x14073,x14074,x14075))
% 18.77/18.52 [1408]~E(x14081,x14082)+E(f817(x14083,x14081,x14084,x14085),f817(x14083,x14082,x14084,x14085))
% 18.77/18.52 [1409]~E(x14091,x14092)+E(f817(x14093,x14094,x14091,x14095),f817(x14093,x14094,x14092,x14095))
% 18.77/18.52 [1410]~E(x14101,x14102)+E(f817(x14103,x14104,x14105,x14101),f817(x14103,x14104,x14105,x14102))
% 18.77/18.52 [1411]~E(x14111,x14112)+E(f602(x14111,x14113,x14114,x14115),f602(x14112,x14113,x14114,x14115))
% 18.77/18.52 [1412]~E(x14121,x14122)+E(f602(x14123,x14121,x14124,x14125),f602(x14123,x14122,x14124,x14125))
% 18.77/18.52 [1413]~E(x14131,x14132)+E(f602(x14133,x14134,x14131,x14135),f602(x14133,x14134,x14132,x14135))
% 18.77/18.52 [1414]~E(x14141,x14142)+E(f602(x14143,x14144,x14145,x14141),f602(x14143,x14144,x14145,x14142))
% 18.77/18.52 [1415]~E(x14151,x14152)+E(f783(x14151,x14153,x14154),f783(x14152,x14153,x14154))
% 18.77/18.52 [1416]~E(x14161,x14162)+E(f783(x14163,x14161,x14164),f783(x14163,x14162,x14164))
% 18.77/18.52 [1417]~E(x14171,x14172)+E(f783(x14173,x14174,x14171),f783(x14173,x14174,x14172))
% 18.77/18.52 [1418]~E(x14181,x14182)+E(f606(x14181,x14183,x14184),f606(x14182,x14183,x14184))
% 18.77/18.52 [1419]~E(x14191,x14192)+E(f606(x14193,x14191,x14194),f606(x14193,x14192,x14194))
% 18.77/18.52 [1420]~E(x14201,x14202)+E(f606(x14203,x14204,x14201),f606(x14203,x14204,x14202))
% 18.77/18.52 [1421]~E(x14211,x14212)+E(f175(x14211),f175(x14212))
% 18.77/18.52 [1422]~E(x14221,x14222)+E(f244(x14221,x14223,x14224),f244(x14222,x14223,x14224))
% 18.77/18.52 [1423]~E(x14231,x14232)+E(f244(x14233,x14231,x14234),f244(x14233,x14232,x14234))
% 18.77/18.52 [1424]~E(x14241,x14242)+E(f244(x14243,x14244,x14241),f244(x14243,x14244,x14242))
% 18.77/18.52 [1425]~E(x14251,x14252)+E(f626(x14251,x14253,x14254),f626(x14252,x14253,x14254))
% 18.77/18.52 [1426]~E(x14261,x14262)+E(f626(x14263,x14261,x14264),f626(x14263,x14262,x14264))
% 18.77/18.52 [1427]~E(x14271,x14272)+E(f626(x14273,x14274,x14271),f626(x14273,x14274,x14272))
% 18.77/18.52 [1428]~E(x14281,x14282)+E(f478(x14281,x14283),f478(x14282,x14283))
% 18.77/18.52 [1429]~E(x14291,x14292)+E(f478(x14293,x14291),f478(x14293,x14292))
% 18.77/18.52 [1430]~E(x14301,x14302)+E(f96(x14301,x14303,x14304,x14305),f96(x14302,x14303,x14304,x14305))
% 18.77/18.52 [1431]~E(x14311,x14312)+E(f96(x14313,x14311,x14314,x14315),f96(x14313,x14312,x14314,x14315))
% 18.77/18.52 [1432]~E(x14321,x14322)+E(f96(x14323,x14324,x14321,x14325),f96(x14323,x14324,x14322,x14325))
% 18.77/18.52 [1433]~E(x14331,x14332)+E(f96(x14333,x14334,x14335,x14331),f96(x14333,x14334,x14335,x14332))
% 18.77/18.52 [1434]~E(x14341,x14342)+E(f800(x14341,x14343,x14344),f800(x14342,x14343,x14344))
% 18.77/18.52 [1435]~E(x14351,x14352)+E(f800(x14353,x14351,x14354),f800(x14353,x14352,x14354))
% 18.77/18.52 [1436]~E(x14361,x14362)+E(f800(x14363,x14364,x14361),f800(x14363,x14364,x14362))
% 18.77/18.52 [1437]~E(x14371,x14372)+E(f618(x14371,x14373,x14374,x14375),f618(x14372,x14373,x14374,x14375))
% 18.77/18.52 [1438]~E(x14381,x14382)+E(f618(x14383,x14381,x14384,x14385),f618(x14383,x14382,x14384,x14385))
% 18.77/18.52 [1439]~E(x14391,x14392)+E(f618(x14393,x14394,x14391,x14395),f618(x14393,x14394,x14392,x14395))
% 18.77/18.52 [1440]~E(x14401,x14402)+E(f618(x14403,x14404,x14405,x14401),f618(x14403,x14404,x14405,x14402))
% 18.77/18.52 [1441]~E(x14411,x14412)+E(f505(x14411,x14413,x14414,x14415,x14416,x14417),f505(x14412,x14413,x14414,x14415,x14416,x14417))
% 18.77/18.52 [1442]~E(x14421,x14422)+E(f505(x14423,x14421,x14424,x14425,x14426,x14427),f505(x14423,x14422,x14424,x14425,x14426,x14427))
% 18.77/18.52 [1443]~E(x14431,x14432)+E(f505(x14433,x14434,x14431,x14435,x14436,x14437),f505(x14433,x14434,x14432,x14435,x14436,x14437))
% 18.77/18.52 [1444]~E(x14441,x14442)+E(f505(x14443,x14444,x14445,x14441,x14446,x14447),f505(x14443,x14444,x14445,x14442,x14446,x14447))
% 18.77/18.52 [1445]~E(x14451,x14452)+E(f505(x14453,x14454,x14455,x14456,x14451,x14457),f505(x14453,x14454,x14455,x14456,x14452,x14457))
% 18.77/18.52 [1446]~E(x14461,x14462)+E(f505(x14463,x14464,x14465,x14466,x14467,x14461),f505(x14463,x14464,x14465,x14466,x14467,x14462))
% 18.77/18.52 [1447]~E(x14471,x14472)+E(f516(x14471,x14473),f516(x14472,x14473))
% 18.77/18.52 [1448]~E(x14481,x14482)+E(f516(x14483,x14481),f516(x14483,x14482))
% 18.77/18.52 [1449]~E(x14491,x14492)+E(f648(x14491,x14493,x14494,x14495,x14496),f648(x14492,x14493,x14494,x14495,x14496))
% 18.77/18.52 [1450]~E(x14501,x14502)+E(f648(x14503,x14501,x14504,x14505,x14506),f648(x14503,x14502,x14504,x14505,x14506))
% 18.77/18.52 [1451]~E(x14511,x14512)+E(f648(x14513,x14514,x14511,x14515,x14516),f648(x14513,x14514,x14512,x14515,x14516))
% 18.77/18.52 [1452]~E(x14521,x14522)+E(f648(x14523,x14524,x14525,x14521,x14526),f648(x14523,x14524,x14525,x14522,x14526))
% 18.77/18.52 [1453]~E(x14531,x14532)+E(f648(x14533,x14534,x14535,x14536,x14531),f648(x14533,x14534,x14535,x14536,x14532))
% 18.77/18.52 [1454]~E(x14541,x14542)+E(f220(x14541,x14543),f220(x14542,x14543))
% 18.77/18.52 [1455]~E(x14551,x14552)+E(f220(x14553,x14551),f220(x14553,x14552))
% 18.77/18.52 [1456]~E(x14561,x14562)+E(f513(x14561),f513(x14562))
% 18.77/18.52 [1457]~E(x14571,x14572)+E(f645(x14571,x14573,x14574,x14575,x14576,x14577),f645(x14572,x14573,x14574,x14575,x14576,x14577))
% 18.77/18.52 [1458]~E(x14581,x14582)+E(f645(x14583,x14581,x14584,x14585,x14586,x14587),f645(x14583,x14582,x14584,x14585,x14586,x14587))
% 18.77/18.52 [1459]~E(x14591,x14592)+E(f645(x14593,x14594,x14591,x14595,x14596,x14597),f645(x14593,x14594,x14592,x14595,x14596,x14597))
% 18.77/18.52 [1460]~E(x14601,x14602)+E(f645(x14603,x14604,x14605,x14601,x14606,x14607),f645(x14603,x14604,x14605,x14602,x14606,x14607))
% 18.77/18.52 [1461]~E(x14611,x14612)+E(f645(x14613,x14614,x14615,x14616,x14611,x14617),f645(x14613,x14614,x14615,x14616,x14612,x14617))
% 18.77/18.52 [1462]~E(x14621,x14622)+E(f645(x14623,x14624,x14625,x14626,x14627,x14621),f645(x14623,x14624,x14625,x14626,x14627,x14622))
% 18.77/18.52 [1463]~E(x14631,x14632)+E(f639(x14631,x14633,x14634,x14635,x14636),f639(x14632,x14633,x14634,x14635,x14636))
% 18.77/18.52 [1464]~E(x14641,x14642)+E(f639(x14643,x14641,x14644,x14645,x14646),f639(x14643,x14642,x14644,x14645,x14646))
% 18.77/18.52 [1465]~E(x14651,x14652)+E(f639(x14653,x14654,x14651,x14655,x14656),f639(x14653,x14654,x14652,x14655,x14656))
% 18.77/18.52 [1466]~E(x14661,x14662)+E(f639(x14663,x14664,x14665,x14661,x14666),f639(x14663,x14664,x14665,x14662,x14666))
% 18.77/18.52 [1467]~E(x14671,x14672)+E(f639(x14673,x14674,x14675,x14676,x14671),f639(x14673,x14674,x14675,x14676,x14672))
% 18.77/18.52 [1468]~E(x14681,x14682)+E(f418(x14681,x14683,x14684),f418(x14682,x14683,x14684))
% 18.77/18.52 [1469]~E(x14691,x14692)+E(f418(x14693,x14691,x14694),f418(x14693,x14692,x14694))
% 18.77/18.52 [1470]~E(x14701,x14702)+E(f418(x14703,x14704,x14701),f418(x14703,x14704,x14702))
% 18.77/18.52 [1471]~E(x14711,x14712)+E(f338(x14711,x14713,x14714),f338(x14712,x14713,x14714))
% 18.77/18.52 [1472]~E(x14721,x14722)+E(f338(x14723,x14721,x14724),f338(x14723,x14722,x14724))
% 18.77/18.52 [1473]~E(x14731,x14732)+E(f338(x14733,x14734,x14731),f338(x14733,x14734,x14732))
% 18.77/18.52 [1474]~E(x14741,x14742)+E(f181(x14741,x14743,x14744,x14745),f181(x14742,x14743,x14744,x14745))
% 18.77/18.52 [1475]~E(x14751,x14752)+E(f181(x14753,x14751,x14754,x14755),f181(x14753,x14752,x14754,x14755))
% 18.77/18.52 [1476]~E(x14761,x14762)+E(f181(x14763,x14764,x14761,x14765),f181(x14763,x14764,x14762,x14765))
% 18.77/18.52 [1477]~E(x14771,x14772)+E(f181(x14773,x14774,x14775,x14771),f181(x14773,x14774,x14775,x14772))
% 18.77/18.52 [1478]~E(x14781,x14782)+E(f592(x14781,x14783,x14784,x14785,x14786),f592(x14782,x14783,x14784,x14785,x14786))
% 18.77/18.52 [1479]~E(x14791,x14792)+E(f592(x14793,x14791,x14794,x14795,x14796),f592(x14793,x14792,x14794,x14795,x14796))
% 18.77/18.52 [1480]~E(x14801,x14802)+E(f592(x14803,x14804,x14801,x14805,x14806),f592(x14803,x14804,x14802,x14805,x14806))
% 18.77/18.52 [1481]~E(x14811,x14812)+E(f592(x14813,x14814,x14815,x14811,x14816),f592(x14813,x14814,x14815,x14812,x14816))
% 18.77/18.52 [1482]~E(x14821,x14822)+E(f592(x14823,x14824,x14825,x14826,x14821),f592(x14823,x14824,x14825,x14826,x14822))
% 18.77/18.52 [1483]~E(x14831,x14832)+E(f782(x14831,x14833,x14834),f782(x14832,x14833,x14834))
% 18.77/18.52 [1484]~E(x14841,x14842)+E(f782(x14843,x14841,x14844),f782(x14843,x14842,x14844))
% 18.77/18.52 [1485]~E(x14851,x14852)+E(f782(x14853,x14854,x14851),f782(x14853,x14854,x14852))
% 18.77/18.52 [1486]~E(x14861,x14862)+E(f756(x14861,x14863),f756(x14862,x14863))
% 18.77/18.52 [1487]~E(x14871,x14872)+E(f756(x14873,x14871),f756(x14873,x14872))
% 18.77/18.52 [1488]~E(x14881,x14882)+E(f697(x14881,x14883,x14884,x14885,x14886),f697(x14882,x14883,x14884,x14885,x14886))
% 18.77/18.52 [1489]~E(x14891,x14892)+E(f697(x14893,x14891,x14894,x14895,x14896),f697(x14893,x14892,x14894,x14895,x14896))
% 18.77/18.52 [1490]~E(x14901,x14902)+E(f697(x14903,x14904,x14901,x14905,x14906),f697(x14903,x14904,x14902,x14905,x14906))
% 18.77/18.52 [1491]~E(x14911,x14912)+E(f697(x14913,x14914,x14915,x14911,x14916),f697(x14913,x14914,x14915,x14912,x14916))
% 18.77/18.52 [1492]~E(x14921,x14922)+E(f697(x14923,x14924,x14925,x14926,x14921),f697(x14923,x14924,x14925,x14926,x14922))
% 18.77/18.52 [1493]~E(x14931,x14932)+E(f541(x14931,x14933,x14934,x14935),f541(x14932,x14933,x14934,x14935))
% 18.77/18.52 [1494]~E(x14941,x14942)+E(f541(x14943,x14941,x14944,x14945),f541(x14943,x14942,x14944,x14945))
% 18.77/18.52 [1495]~E(x14951,x14952)+E(f541(x14953,x14954,x14951,x14955),f541(x14953,x14954,x14952,x14955))
% 18.77/18.52 [1496]~E(x14961,x14962)+E(f541(x14963,x14964,x14965,x14961),f541(x14963,x14964,x14965,x14962))
% 18.77/18.52 [1497]~E(x14971,x14972)+E(f460(x14971,x14973,x14974,x14975),f460(x14972,x14973,x14974,x14975))
% 18.77/18.52 [1498]~E(x14981,x14982)+E(f460(x14983,x14981,x14984,x14985),f460(x14983,x14982,x14984,x14985))
% 18.77/18.52 [1499]~E(x14991,x14992)+E(f460(x14993,x14994,x14991,x14995),f460(x14993,x14994,x14992,x14995))
% 18.77/18.52 [1500]~E(x15001,x15002)+E(f460(x15003,x15004,x15005,x15001),f460(x15003,x15004,x15005,x15002))
% 18.77/18.52 [1501]~E(x15011,x15012)+E(f691(x15011,x15013,x15014,x15015),f691(x15012,x15013,x15014,x15015))
% 18.77/18.52 [1502]~E(x15021,x15022)+E(f691(x15023,x15021,x15024,x15025),f691(x15023,x15022,x15024,x15025))
% 18.77/18.52 [1503]~E(x15031,x15032)+E(f691(x15033,x15034,x15031,x15035),f691(x15033,x15034,x15032,x15035))
% 18.77/18.52 [1504]~E(x15041,x15042)+E(f691(x15043,x15044,x15045,x15041),f691(x15043,x15044,x15045,x15042))
% 18.77/18.52 [1505]~E(x15051,x15052)+E(f750(x15051,x15053),f750(x15052,x15053))
% 18.77/18.52 [1506]~E(x15061,x15062)+E(f750(x15063,x15061),f750(x15063,x15062))
% 18.77/18.52 [1507]~E(x15071,x15072)+E(f271(x15071,x15073),f271(x15072,x15073))
% 18.77/18.52 [1508]~E(x15081,x15082)+E(f271(x15083,x15081),f271(x15083,x15082))
% 18.77/18.52 [1509]~E(x15091,x15092)+E(f792(x15091,x15093,x15094),f792(x15092,x15093,x15094))
% 18.77/18.52 [1510]~E(x15101,x15102)+E(f792(x15103,x15101,x15104),f792(x15103,x15102,x15104))
% 18.77/18.52 [1511]~E(x15111,x15112)+E(f792(x15113,x15114,x15111),f792(x15113,x15114,x15112))
% 18.77/18.52 [1512]~E(x15121,x15122)+E(f576(x15121,x15123,x15124,x15125,x15126),f576(x15122,x15123,x15124,x15125,x15126))
% 18.77/18.52 [1513]~E(x15131,x15132)+E(f576(x15133,x15131,x15134,x15135,x15136),f576(x15133,x15132,x15134,x15135,x15136))
% 18.77/18.52 [1514]~E(x15141,x15142)+E(f576(x15143,x15144,x15141,x15145,x15146),f576(x15143,x15144,x15142,x15145,x15146))
% 18.77/18.52 [1515]~E(x15151,x15152)+E(f576(x15153,x15154,x15155,x15151,x15156),f576(x15153,x15154,x15155,x15152,x15156))
% 18.77/18.52 [1516]~E(x15161,x15162)+E(f576(x15163,x15164,x15165,x15166,x15161),f576(x15163,x15164,x15165,x15166,x15162))
% 18.77/18.52 [1517]~E(x15171,x15172)+E(f568(x15171,x15173,x15174,x15175,x15176,x15177),f568(x15172,x15173,x15174,x15175,x15176,x15177))
% 18.77/18.52 [1518]~E(x15181,x15182)+E(f568(x15183,x15181,x15184,x15185,x15186,x15187),f568(x15183,x15182,x15184,x15185,x15186,x15187))
% 18.77/18.52 [1519]~E(x15191,x15192)+E(f568(x15193,x15194,x15191,x15195,x15196,x15197),f568(x15193,x15194,x15192,x15195,x15196,x15197))
% 18.77/18.52 [1520]~E(x15201,x15202)+E(f568(x15203,x15204,x15205,x15201,x15206,x15207),f568(x15203,x15204,x15205,x15202,x15206,x15207))
% 18.77/18.52 [1521]~E(x15211,x15212)+E(f568(x15213,x15214,x15215,x15216,x15211,x15217),f568(x15213,x15214,x15215,x15216,x15212,x15217))
% 18.77/18.52 [1522]~E(x15221,x15222)+E(f568(x15223,x15224,x15225,x15226,x15227,x15221),f568(x15223,x15224,x15225,x15226,x15227,x15222))
% 18.77/18.52 [1523]~E(x15231,x15232)+E(f716(x15231,x15233,x15234),f716(x15232,x15233,x15234))
% 18.77/18.52 [1524]~E(x15241,x15242)+E(f716(x15243,x15241,x15244),f716(x15243,x15242,x15244))
% 18.77/18.52 [1525]~E(x15251,x15252)+E(f716(x15253,x15254,x15251),f716(x15253,x15254,x15252))
% 18.77/18.52 [1526]~E(x15261,x15262)+E(f360(x15261,x15263),f360(x15262,x15263))
% 18.77/18.52 [1527]~E(x15271,x15272)+E(f360(x15273,x15271),f360(x15273,x15272))
% 18.77/18.52 [1528]~E(x15281,x15282)+E(f661(x15281,x15283,x15284,x15285,x15286,x15287,x15288,x15289),f661(x15282,x15283,x15284,x15285,x15286,x15287,x15288,x15289))
% 18.77/18.52 [1529]~E(x15291,x15292)+E(f661(x15293,x15291,x15294,x15295,x15296,x15297,x15298,x15299),f661(x15293,x15292,x15294,x15295,x15296,x15297,x15298,x15299))
% 18.77/18.52 [1530]~E(x15301,x15302)+E(f661(x15303,x15304,x15301,x15305,x15306,x15307,x15308,x15309),f661(x15303,x15304,x15302,x15305,x15306,x15307,x15308,x15309))
% 18.77/18.52 [1531]~E(x15311,x15312)+E(f661(x15313,x15314,x15315,x15311,x15316,x15317,x15318,x15319),f661(x15313,x15314,x15315,x15312,x15316,x15317,x15318,x15319))
% 18.77/18.52 [1532]~E(x15321,x15322)+E(f661(x15323,x15324,x15325,x15326,x15321,x15327,x15328,x15329),f661(x15323,x15324,x15325,x15326,x15322,x15327,x15328,x15329))
% 18.77/18.52 [1533]~E(x15331,x15332)+E(f661(x15333,x15334,x15335,x15336,x15337,x15331,x15338,x15339),f661(x15333,x15334,x15335,x15336,x15337,x15332,x15338,x15339))
% 18.77/18.52 [1534]~E(x15341,x15342)+E(f661(x15343,x15344,x15345,x15346,x15347,x15348,x15341,x15349),f661(x15343,x15344,x15345,x15346,x15347,x15348,x15342,x15349))
% 18.77/18.52 [1535]~E(x15351,x15352)+E(f661(x15353,x15354,x15355,x15356,x15357,x15358,x15359,x15351),f661(x15353,x15354,x15355,x15356,x15357,x15358,x15359,x15352))
% 18.77/18.52 [1536]~E(x15361,x15362)+E(f797(x15361,x15363,x15364),f797(x15362,x15363,x15364))
% 18.77/18.52 [1537]~E(x15371,x15372)+E(f797(x15373,x15371,x15374),f797(x15373,x15372,x15374))
% 18.77/18.52 [1538]~E(x15381,x15382)+E(f797(x15383,x15384,x15381),f797(x15383,x15384,x15382))
% 18.77/18.52 [1539]~E(x15391,x15392)+E(f433(x15391,x15393,x15394,x15395,x15396),f433(x15392,x15393,x15394,x15395,x15396))
% 18.77/18.52 [1540]~E(x15401,x15402)+E(f433(x15403,x15401,x15404,x15405,x15406),f433(x15403,x15402,x15404,x15405,x15406))
% 18.77/18.52 [1541]~E(x15411,x15412)+E(f433(x15413,x15414,x15411,x15415,x15416),f433(x15413,x15414,x15412,x15415,x15416))
% 18.77/18.52 [1542]~E(x15421,x15422)+E(f433(x15423,x15424,x15425,x15421,x15426),f433(x15423,x15424,x15425,x15422,x15426))
% 18.77/18.52 [1543]~E(x15431,x15432)+E(f433(x15433,x15434,x15435,x15436,x15431),f433(x15433,x15434,x15435,x15436,x15432))
% 18.77/18.52 [1544]~E(x15441,x15442)+E(f196(x15441),f196(x15442))
% 18.77/18.52 [1545]~E(x15451,x15452)+E(f622(x15451,x15453,x15454),f622(x15452,x15453,x15454))
% 18.77/18.52 [1546]~E(x15461,x15462)+E(f622(x15463,x15461,x15464),f622(x15463,x15462,x15464))
% 18.77/18.52 [1547]~E(x15471,x15472)+E(f622(x15473,x15474,x15471),f622(x15473,x15474,x15472))
% 18.77/18.52 [1548]~E(x15481,x15482)+E(f476(x15481,x15483),f476(x15482,x15483))
% 18.77/18.52 [1549]~E(x15491,x15492)+E(f476(x15493,x15491),f476(x15493,x15492))
% 18.77/18.52 [1550]~E(x15501,x15502)+E(f241(x15501,x15503,x15504),f241(x15502,x15503,x15504))
% 18.77/18.52 [1551]~E(x15511,x15512)+E(f241(x15513,x15511,x15514),f241(x15513,x15512,x15514))
% 18.77/18.52 [1552]~E(x15521,x15522)+E(f241(x15523,x15524,x15521),f241(x15523,x15524,x15522))
% 18.77/18.52 [1553]~E(x15531,x15532)+E(f624(x15531,x15533,x15534),f624(x15532,x15533,x15534))
% 18.77/18.52 [1554]~E(x15541,x15542)+E(f624(x15543,x15541,x15544),f624(x15543,x15542,x15544))
% 18.77/18.52 [1555]~E(x15551,x15552)+E(f624(x15553,x15554,x15551),f624(x15553,x15554,x15552))
% 18.77/18.52 [1556]~E(x15561,x15562)+E(f343(x15561),f343(x15562))
% 18.77/18.52 [1557]~E(x15571,x15572)+E(f202(x15571,x15573,x15574,x15575,x15576,x15577,x15578),f202(x15572,x15573,x15574,x15575,x15576,x15577,x15578))
% 18.77/18.52 [1558]~E(x15581,x15582)+E(f202(x15583,x15581,x15584,x15585,x15586,x15587,x15588),f202(x15583,x15582,x15584,x15585,x15586,x15587,x15588))
% 18.77/18.52 [1559]~E(x15591,x15592)+E(f202(x15593,x15594,x15591,x15595,x15596,x15597,x15598),f202(x15593,x15594,x15592,x15595,x15596,x15597,x15598))
% 18.77/18.52 [1560]~E(x15601,x15602)+E(f202(x15603,x15604,x15605,x15601,x15606,x15607,x15608),f202(x15603,x15604,x15605,x15602,x15606,x15607,x15608))
% 18.77/18.52 [1561]~E(x15611,x15612)+E(f202(x15613,x15614,x15615,x15616,x15611,x15617,x15618),f202(x15613,x15614,x15615,x15616,x15612,x15617,x15618))
% 18.77/18.52 [1562]~E(x15621,x15622)+E(f202(x15623,x15624,x15625,x15626,x15627,x15621,x15628),f202(x15623,x15624,x15625,x15626,x15627,x15622,x15628))
% 18.77/18.52 [1563]~E(x15631,x15632)+E(f202(x15633,x15634,x15635,x15636,x15637,x15638,x15631),f202(x15633,x15634,x15635,x15636,x15637,x15638,x15632))
% 18.77/18.52 [1564]~E(x15641,x15642)+E(f562(x15641,x15643,x15644,x15645,x15646),f562(x15642,x15643,x15644,x15645,x15646))
% 18.77/18.52 [1565]~E(x15651,x15652)+E(f562(x15653,x15651,x15654,x15655,x15656),f562(x15653,x15652,x15654,x15655,x15656))
% 18.77/18.52 [1566]~E(x15661,x15662)+E(f562(x15663,x15664,x15661,x15665,x15666),f562(x15663,x15664,x15662,x15665,x15666))
% 18.77/18.52 [1567]~E(x15671,x15672)+E(f562(x15673,x15674,x15675,x15671,x15676),f562(x15673,x15674,x15675,x15672,x15676))
% 18.77/18.52 [1568]~E(x15681,x15682)+E(f562(x15683,x15684,x15685,x15686,x15681),f562(x15683,x15684,x15685,x15686,x15682))
% 18.77/18.52 [1569]~E(x15691,x15692)+E(f692(x15691,x15693,x15694,x15695),f692(x15692,x15693,x15694,x15695))
% 18.77/18.52 [1570]~E(x15701,x15702)+E(f692(x15703,x15701,x15704,x15705),f692(x15703,x15702,x15704,x15705))
% 18.77/18.52 [1571]~E(x15711,x15712)+E(f692(x15713,x15714,x15711,x15715),f692(x15713,x15714,x15712,x15715))
% 18.77/18.52 [1572]~E(x15721,x15722)+E(f692(x15723,x15724,x15725,x15721),f692(x15723,x15724,x15725,x15722))
% 18.77/18.52 [1573]~E(x15731,x15732)+E(f273(x15731,x15733,x15734,x15735),f273(x15732,x15733,x15734,x15735))
% 18.77/18.52 [1574]~E(x15741,x15742)+E(f273(x15743,x15741,x15744,x15745),f273(x15743,x15742,x15744,x15745))
% 18.77/18.52 [1575]~E(x15751,x15752)+E(f273(x15753,x15754,x15751,x15755),f273(x15753,x15754,x15752,x15755))
% 18.77/18.52 [1576]~E(x15761,x15762)+E(f273(x15763,x15764,x15765,x15761),f273(x15763,x15764,x15765,x15762))
% 18.77/18.52 [1577]~E(x15771,x15772)+E(f438(x15771,x15773,x15774,x15775),f438(x15772,x15773,x15774,x15775))
% 18.77/18.52 [1578]~E(x15781,x15782)+E(f438(x15783,x15781,x15784,x15785),f438(x15783,x15782,x15784,x15785))
% 18.77/18.52 [1579]~E(x15791,x15792)+E(f438(x15793,x15794,x15791,x15795),f438(x15793,x15794,x15792,x15795))
% 18.77/18.52 [1580]~E(x15801,x15802)+E(f438(x15803,x15804,x15805,x15801),f438(x15803,x15804,x15805,x15802))
% 18.77/18.52 [1581]~E(x15811,x15812)+E(f519(x15811,x15813,x15814,x15815),f519(x15812,x15813,x15814,x15815))
% 18.77/18.52 [1582]~E(x15821,x15822)+E(f519(x15823,x15821,x15824,x15825),f519(x15823,x15822,x15824,x15825))
% 18.77/18.52 [1583]~E(x15831,x15832)+E(f519(x15833,x15834,x15831,x15835),f519(x15833,x15834,x15832,x15835))
% 18.77/18.52 [1584]~E(x15841,x15842)+E(f519(x15843,x15844,x15845,x15841),f519(x15843,x15844,x15845,x15842))
% 18.77/18.52 [1585]~E(x15851,x15852)+E(f596(x15851,x15853,x15854),f596(x15852,x15853,x15854))
% 18.77/18.52 [1586]~E(x15861,x15862)+E(f596(x15863,x15861,x15864),f596(x15863,x15862,x15864))
% 18.77/18.52 [1587]~E(x15871,x15872)+E(f596(x15873,x15874,x15871),f596(x15873,x15874,x15872))
% 18.77/18.52 [1588]~E(x15881,x15882)+E(f486(x15881,x15883,x15884),f486(x15882,x15883,x15884))
% 18.77/18.52 [1589]~E(x15891,x15892)+E(f486(x15893,x15891,x15894),f486(x15893,x15892,x15894))
% 18.77/18.52 [1590]~E(x15901,x15902)+E(f486(x15903,x15904,x15901),f486(x15903,x15904,x15902))
% 18.77/18.52 [1591]~E(x15911,x15912)+E(f801(x15911,x15913,x15914),f801(x15912,x15913,x15914))
% 18.77/18.52 [1592]~E(x15921,x15922)+E(f801(x15923,x15921,x15924),f801(x15923,x15922,x15924))
% 18.77/18.52 [1593]~E(x15931,x15932)+E(f801(x15933,x15934,x15931),f801(x15933,x15934,x15932))
% 18.77/18.52 [1594]~E(x15941,x15942)+E(f805(x15941,x15943,x15944),f805(x15942,x15943,x15944))
% 18.77/18.52 [1595]~E(x15951,x15952)+E(f805(x15953,x15951,x15954),f805(x15953,x15952,x15954))
% 18.77/18.52 [1596]~E(x15961,x15962)+E(f805(x15963,x15964,x15961),f805(x15963,x15964,x15962))
% 18.77/18.52 [1597]~E(x15971,x15972)+E(f675(x15971,x15973,x15974,x15975),f675(x15972,x15973,x15974,x15975))
% 18.77/18.52 [1598]~E(x15981,x15982)+E(f675(x15983,x15981,x15984,x15985),f675(x15983,x15982,x15984,x15985))
% 18.77/18.52 [1599]~E(x15991,x15992)+E(f675(x15993,x15994,x15991,x15995),f675(x15993,x15994,x15992,x15995))
% 18.77/18.52 [1600]~E(x16001,x16002)+E(f675(x16003,x16004,x16005,x16001),f675(x16003,x16004,x16005,x16002))
% 18.77/18.52 [1601]~E(x16011,x16012)+E(f631(x16011,x16013),f631(x16012,x16013))
% 18.77/18.52 [1602]~E(x16021,x16022)+E(f631(x16023,x16021),f631(x16023,x16022))
% 18.77/18.52 [1603]~E(x16031,x16032)+E(f828(x16031,x16033),f828(x16032,x16033))
% 18.77/18.52 [1604]~E(x16041,x16042)+E(f828(x16043,x16041),f828(x16043,x16042))
% 18.77/18.52 [1605]~E(x16051,x16052)+E(f466(x16051,x16053,x16054,x16055),f466(x16052,x16053,x16054,x16055))
% 18.77/18.52 [1606]~E(x16061,x16062)+E(f466(x16063,x16061,x16064,x16065),f466(x16063,x16062,x16064,x16065))
% 18.77/18.52 [1607]~E(x16071,x16072)+E(f466(x16073,x16074,x16071,x16075),f466(x16073,x16074,x16072,x16075))
% 18.77/18.52 [1608]~E(x16081,x16082)+E(f466(x16083,x16084,x16085,x16081),f466(x16083,x16084,x16085,x16082))
% 18.77/18.52 [1609]~E(x16091,x16092)+E(f659(x16091,x16093,x16094,x16095,x16096,x16097,x16098),f659(x16092,x16093,x16094,x16095,x16096,x16097,x16098))
% 18.77/18.52 [1610]~E(x16101,x16102)+E(f659(x16103,x16101,x16104,x16105,x16106,x16107,x16108),f659(x16103,x16102,x16104,x16105,x16106,x16107,x16108))
% 18.77/18.52 [1611]~E(x16111,x16112)+E(f659(x16113,x16114,x16111,x16115,x16116,x16117,x16118),f659(x16113,x16114,x16112,x16115,x16116,x16117,x16118))
% 18.77/18.52 [1612]~E(x16121,x16122)+E(f659(x16123,x16124,x16125,x16121,x16126,x16127,x16128),f659(x16123,x16124,x16125,x16122,x16126,x16127,x16128))
% 18.77/18.52 [1613]~E(x16131,x16132)+E(f659(x16133,x16134,x16135,x16136,x16131,x16137,x16138),f659(x16133,x16134,x16135,x16136,x16132,x16137,x16138))
% 18.77/18.52 [1614]~E(x16141,x16142)+E(f659(x16143,x16144,x16145,x16146,x16147,x16141,x16148),f659(x16143,x16144,x16145,x16146,x16147,x16142,x16148))
% 18.77/18.52 [1615]~E(x16151,x16152)+E(f659(x16153,x16154,x16155,x16156,x16157,x16158,x16151),f659(x16153,x16154,x16155,x16156,x16157,x16158,x16152))
% 18.77/18.52 [1616]~E(x16161,x16162)+E(f527(x16161,x16163,x16164,x16165),f527(x16162,x16163,x16164,x16165))
% 18.77/18.52 [1617]~E(x16171,x16172)+E(f527(x16173,x16171,x16174,x16175),f527(x16173,x16172,x16174,x16175))
% 18.77/18.52 [1618]~E(x16181,x16182)+E(f527(x16183,x16184,x16181,x16185),f527(x16183,x16184,x16182,x16185))
% 18.77/18.52 [1619]~E(x16191,x16192)+E(f527(x16193,x16194,x16195,x16191),f527(x16193,x16194,x16195,x16192))
% 18.77/18.52 [1620]~E(x16201,x16202)+E(f201(x16201,x16203,x16204,x16205),f201(x16202,x16203,x16204,x16205))
% 18.77/18.52 [1621]~E(x16211,x16212)+E(f201(x16213,x16211,x16214,x16215),f201(x16213,x16212,x16214,x16215))
% 18.77/18.52 [1622]~E(x16221,x16222)+E(f201(x16223,x16224,x16221,x16225),f201(x16223,x16224,x16222,x16225))
% 18.77/18.52 [1623]~E(x16231,x16232)+E(f201(x16233,x16234,x16235,x16231),f201(x16233,x16234,x16235,x16232))
% 18.77/18.52 [1624]~E(x16241,x16242)+E(f582(x16241,x16243,x16244,x16245,x16246,x16247),f582(x16242,x16243,x16244,x16245,x16246,x16247))
% 18.77/18.52 [1625]~E(x16251,x16252)+E(f582(x16253,x16251,x16254,x16255,x16256,x16257),f582(x16253,x16252,x16254,x16255,x16256,x16257))
% 18.77/18.52 [1626]~E(x16261,x16262)+E(f582(x16263,x16264,x16261,x16265,x16266,x16267),f582(x16263,x16264,x16262,x16265,x16266,x16267))
% 18.77/18.52 [1627]~E(x16271,x16272)+E(f582(x16273,x16274,x16275,x16271,x16276,x16277),f582(x16273,x16274,x16275,x16272,x16276,x16277))
% 18.77/18.52 [1628]~E(x16281,x16282)+E(f582(x16283,x16284,x16285,x16286,x16281,x16287),f582(x16283,x16284,x16285,x16286,x16282,x16287))
% 18.77/18.52 [1629]~E(x16291,x16292)+E(f582(x16293,x16294,x16295,x16296,x16297,x16291),f582(x16293,x16294,x16295,x16296,x16297,x16292))
% 18.77/18.52 [1630]~E(x16301,x16302)+E(f214(x16301,x16303,x16304,x16305),f214(x16302,x16303,x16304,x16305))
% 18.77/18.52 [1631]~E(x16311,x16312)+E(f214(x16313,x16311,x16314,x16315),f214(x16313,x16312,x16314,x16315))
% 18.77/18.52 [1632]~E(x16321,x16322)+E(f214(x16323,x16324,x16321,x16325),f214(x16323,x16324,x16322,x16325))
% 18.77/18.52 [1633]~E(x16331,x16332)+E(f214(x16333,x16334,x16335,x16331),f214(x16333,x16334,x16335,x16332))
% 18.77/18.52 [1634]~E(x16341,x16342)+E(f276(x16341,x16343,x16344,x16345),f276(x16342,x16343,x16344,x16345))
% 18.77/18.52 [1635]~E(x16351,x16352)+E(f276(x16353,x16351,x16354,x16355),f276(x16353,x16352,x16354,x16355))
% 18.77/18.52 [1636]~E(x16361,x16362)+E(f276(x16363,x16364,x16361,x16365),f276(x16363,x16364,x16362,x16365))
% 18.77/18.52 [1637]~E(x16371,x16372)+E(f276(x16373,x16374,x16375,x16371),f276(x16373,x16374,x16375,x16372))
% 18.77/18.52 [1638]~E(x16381,x16382)+E(f496(x16381,x16383,x16384,x16385),f496(x16382,x16383,x16384,x16385))
% 18.77/18.52 [1639]~E(x16391,x16392)+E(f496(x16393,x16391,x16394,x16395),f496(x16393,x16392,x16394,x16395))
% 18.77/18.52 [1640]~E(x16401,x16402)+E(f496(x16403,x16404,x16401,x16405),f496(x16403,x16404,x16402,x16405))
% 18.77/18.52 [1641]~E(x16411,x16412)+E(f496(x16413,x16414,x16415,x16411),f496(x16413,x16414,x16415,x16412))
% 18.77/18.52 [1642]~E(x16421,x16422)+E(f640(x16421,x16423,x16424,x16425,x16426),f640(x16422,x16423,x16424,x16425,x16426))
% 18.77/18.52 [1643]~E(x16431,x16432)+E(f640(x16433,x16431,x16434,x16435,x16436),f640(x16433,x16432,x16434,x16435,x16436))
% 18.77/18.52 [1644]~E(x16441,x16442)+E(f640(x16443,x16444,x16441,x16445,x16446),f640(x16443,x16444,x16442,x16445,x16446))
% 18.77/18.52 [1645]~E(x16451,x16452)+E(f640(x16453,x16454,x16455,x16451,x16456),f640(x16453,x16454,x16455,x16452,x16456))
% 18.77/18.52 [1646]~E(x16461,x16462)+E(f640(x16463,x16464,x16465,x16466,x16461),f640(x16463,x16464,x16465,x16466,x16462))
% 18.77/18.52 [1647]~E(x16471,x16472)+E(f779(x16471,x16473,x16474),f779(x16472,x16473,x16474))
% 18.77/18.52 [1648]~E(x16481,x16482)+E(f779(x16483,x16481,x16484),f779(x16483,x16482,x16484))
% 18.77/18.52 [1649]~E(x16491,x16492)+E(f779(x16493,x16494,x16491),f779(x16493,x16494,x16492))
% 18.77/18.52 [1650]~E(x16501,x16502)+E(f526(x16501,x16503,x16504,x16505),f526(x16502,x16503,x16504,x16505))
% 18.77/18.52 [1651]~E(x16511,x16512)+E(f526(x16513,x16511,x16514,x16515),f526(x16513,x16512,x16514,x16515))
% 18.77/18.52 [1652]~E(x16521,x16522)+E(f526(x16523,x16524,x16521,x16525),f526(x16523,x16524,x16522,x16525))
% 18.77/18.52 [1653]~E(x16531,x16532)+E(f526(x16533,x16534,x16535,x16531),f526(x16533,x16534,x16535,x16532))
% 18.77/18.52 [1654]~E(x16541,x16542)+E(f334(x16541,x16543,x16544),f334(x16542,x16543,x16544))
% 18.77/18.52 [1655]~E(x16551,x16552)+E(f334(x16553,x16551,x16554),f334(x16553,x16552,x16554))
% 18.77/18.52 [1656]~E(x16561,x16562)+E(f334(x16563,x16564,x16561),f334(x16563,x16564,x16562))
% 18.77/18.52 [1657]~E(x16571,x16572)+E(f270(x16571,x16573,x16574),f270(x16572,x16573,x16574))
% 18.77/18.52 [1658]~E(x16581,x16582)+E(f270(x16583,x16581,x16584),f270(x16583,x16582,x16584))
% 18.77/18.52 [1659]~E(x16591,x16592)+E(f270(x16593,x16594,x16591),f270(x16593,x16594,x16592))
% 18.77/18.52 [1660]~E(x16601,x16602)+E(f738(x16601,x16603,x16604),f738(x16602,x16603,x16604))
% 18.77/18.52 [1661]~E(x16611,x16612)+E(f738(x16613,x16611,x16614),f738(x16613,x16612,x16614))
% 18.77/18.52 [1662]~E(x16621,x16622)+E(f738(x16623,x16624,x16621),f738(x16623,x16624,x16622))
% 18.77/18.52 [1663]~E(x16631,x16632)+E(f605(x16631,x16633,x16634),f605(x16632,x16633,x16634))
% 18.77/18.52 [1664]~E(x16641,x16642)+E(f605(x16643,x16641,x16644),f605(x16643,x16642,x16644))
% 18.77/18.52 [1665]~E(x16651,x16652)+E(f605(x16653,x16654,x16651),f605(x16653,x16654,x16652))
% 18.77/18.52 [1666]~E(x16661,x16662)+E(f357(x16661,x16663,x16664,x16665),f357(x16662,x16663,x16664,x16665))
% 18.77/18.52 [1667]~E(x16671,x16672)+E(f357(x16673,x16671,x16674,x16675),f357(x16673,x16672,x16674,x16675))
% 18.77/18.52 [1668]~E(x16681,x16682)+E(f357(x16683,x16684,x16681,x16685),f357(x16683,x16684,x16682,x16685))
% 18.77/18.52 [1669]~E(x16691,x16692)+E(f357(x16693,x16694,x16695,x16691),f357(x16693,x16694,x16695,x16692))
% 18.77/18.52 [1670]~E(x16701,x16702)+E(f674(x16701,x16703,x16704,x16705,x16706,x16707,x16708,x16709),f674(x16702,x16703,x16704,x16705,x16706,x16707,x16708,x16709))
% 18.77/18.52 [1671]~E(x16711,x16712)+E(f674(x16713,x16711,x16714,x16715,x16716,x16717,x16718,x16719),f674(x16713,x16712,x16714,x16715,x16716,x16717,x16718,x16719))
% 18.77/18.52 [1672]~E(x16721,x16722)+E(f674(x16723,x16724,x16721,x16725,x16726,x16727,x16728,x16729),f674(x16723,x16724,x16722,x16725,x16726,x16727,x16728,x16729))
% 18.77/18.52 [1673]~E(x16731,x16732)+E(f674(x16733,x16734,x16735,x16731,x16736,x16737,x16738,x16739),f674(x16733,x16734,x16735,x16732,x16736,x16737,x16738,x16739))
% 18.77/18.52 [1674]~E(x16741,x16742)+E(f674(x16743,x16744,x16745,x16746,x16741,x16747,x16748,x16749),f674(x16743,x16744,x16745,x16746,x16742,x16747,x16748,x16749))
% 18.77/18.52 [1675]~E(x16751,x16752)+E(f674(x16753,x16754,x16755,x16756,x16757,x16751,x16758,x16759),f674(x16753,x16754,x16755,x16756,x16757,x16752,x16758,x16759))
% 18.77/18.52 [1676]~E(x16761,x16762)+E(f674(x16763,x16764,x16765,x16766,x16767,x16768,x16761,x16769),f674(x16763,x16764,x16765,x16766,x16767,x16768,x16762,x16769))
% 18.77/18.52 [1677]~E(x16771,x16772)+E(f674(x16773,x16774,x16775,x16776,x16777,x16778,x16779,x16771),f674(x16773,x16774,x16775,x16776,x16777,x16778,x16779,x16772))
% 18.77/18.52 [1678]~E(x16781,x16782)+E(f118(x16781,x16783,x16784,x16785),f118(x16782,x16783,x16784,x16785))
% 18.77/18.52 [1679]~E(x16791,x16792)+E(f118(x16793,x16791,x16794,x16795),f118(x16793,x16792,x16794,x16795))
% 18.77/18.52 [1680]~E(x16801,x16802)+E(f118(x16803,x16804,x16801,x16805),f118(x16803,x16804,x16802,x16805))
% 18.77/18.52 [1681]~E(x16811,x16812)+E(f118(x16813,x16814,x16815,x16811),f118(x16813,x16814,x16815,x16812))
% 18.77/18.52 [1682]~E(x16821,x16822)+E(f414(x16821,x16823,x16824),f414(x16822,x16823,x16824))
% 18.77/18.52 [1683]~E(x16831,x16832)+E(f414(x16833,x16831,x16834),f414(x16833,x16832,x16834))
% 18.77/18.52 [1684]~E(x16841,x16842)+E(f414(x16843,x16844,x16841),f414(x16843,x16844,x16842))
% 18.77/18.52 [1685]~E(x16851,x16852)+E(f216(x16851,x16853,x16854),f216(x16852,x16853,x16854))
% 18.77/18.52 [1686]~E(x16861,x16862)+E(f216(x16863,x16861,x16864),f216(x16863,x16862,x16864))
% 18.77/18.52 [1687]~E(x16871,x16872)+E(f216(x16873,x16874,x16871),f216(x16873,x16874,x16872))
% 18.77/18.52 [1688]~E(x16881,x16882)+E(f806(x16881,x16883,x16884),f806(x16882,x16883,x16884))
% 18.77/18.52 [1689]~E(x16891,x16892)+E(f806(x16893,x16891,x16894),f806(x16893,x16892,x16894))
% 18.77/18.52 [1690]~E(x16901,x16902)+E(f806(x16903,x16904,x16901),f806(x16903,x16904,x16902))
% 18.77/18.52 [1691]~E(x16911,x16912)+E(f766(x16911,x16913),f766(x16912,x16913))
% 18.77/18.52 [1692]~E(x16921,x16922)+E(f766(x16923,x16921),f766(x16923,x16922))
% 18.77/18.52 [1693]~E(x16931,x16932)+E(f528(x16931,x16933,x16934,x16935,x16936),f528(x16932,x16933,x16934,x16935,x16936))
% 18.77/18.52 [1694]~E(x16941,x16942)+E(f528(x16943,x16941,x16944,x16945,x16946),f528(x16943,x16942,x16944,x16945,x16946))
% 18.77/18.52 [1695]~E(x16951,x16952)+E(f528(x16953,x16954,x16951,x16955,x16956),f528(x16953,x16954,x16952,x16955,x16956))
% 18.77/18.52 [1696]~E(x16961,x16962)+E(f528(x16963,x16964,x16965,x16961,x16966),f528(x16963,x16964,x16965,x16962,x16966))
% 18.77/18.52 [1697]~E(x16971,x16972)+E(f528(x16973,x16974,x16975,x16976,x16971),f528(x16973,x16974,x16975,x16976,x16972))
% 18.77/18.52 [1698]~E(x16981,x16982)+E(f677(x16981,x16983,x16984),f677(x16982,x16983,x16984))
% 18.77/18.52 [1699]~E(x16991,x16992)+E(f677(x16993,x16991,x16994),f677(x16993,x16992,x16994))
% 18.77/18.52 [1700]~E(x17001,x17002)+E(f677(x17003,x17004,x17001),f677(x17003,x17004,x17002))
% 18.77/18.52 [1701]~E(x17011,x17012)+E(f119(x17011,x17013,x17014,x17015),f119(x17012,x17013,x17014,x17015))
% 18.77/18.52 [1702]~E(x17021,x17022)+E(f119(x17023,x17021,x17024,x17025),f119(x17023,x17022,x17024,x17025))
% 18.77/18.52 [1703]~E(x17031,x17032)+E(f119(x17033,x17034,x17031,x17035),f119(x17033,x17034,x17032,x17035))
% 18.77/18.52 [1704]~E(x17041,x17042)+E(f119(x17043,x17044,x17045,x17041),f119(x17043,x17044,x17045,x17042))
% 18.77/18.52 [1705]~E(x17051,x17052)+E(f729(x17051,x17053,x17054,x17055,x17056),f729(x17052,x17053,x17054,x17055,x17056))
% 18.77/18.52 [1706]~E(x17061,x17062)+E(f729(x17063,x17061,x17064,x17065,x17066),f729(x17063,x17062,x17064,x17065,x17066))
% 18.77/18.52 [1707]~E(x17071,x17072)+E(f729(x17073,x17074,x17071,x17075,x17076),f729(x17073,x17074,x17072,x17075,x17076))
% 18.77/18.52 [1708]~E(x17081,x17082)+E(f729(x17083,x17084,x17085,x17081,x17086),f729(x17083,x17084,x17085,x17082,x17086))
% 18.77/18.52 [1709]~E(x17091,x17092)+E(f729(x17093,x17094,x17095,x17096,x17091),f729(x17093,x17094,x17095,x17096,x17092))
% 18.77/18.52 [1710]~E(x17101,x17102)+E(f291(x17101,x17103,x17104),f291(x17102,x17103,x17104))
% 18.77/18.52 [1711]~E(x17111,x17112)+E(f291(x17113,x17111,x17114),f291(x17113,x17112,x17114))
% 18.77/18.52 [1712]~E(x17121,x17122)+E(f291(x17123,x17124,x17121),f291(x17123,x17124,x17122))
% 18.77/18.52 [1713]~E(x17131,x17132)+E(f233(x17131,x17133),f233(x17132,x17133))
% 18.77/18.52 [1714]~E(x17141,x17142)+E(f233(x17143,x17141),f233(x17143,x17142))
% 18.77/18.52 [1715]~E(x17151,x17152)+E(f643(x17151,x17153,x17154,x17155),f643(x17152,x17153,x17154,x17155))
% 18.77/18.52 [1716]~E(x17161,x17162)+E(f643(x17163,x17161,x17164,x17165),f643(x17163,x17162,x17164,x17165))
% 18.77/18.52 [1717]~E(x17171,x17172)+E(f643(x17173,x17174,x17171,x17175),f643(x17173,x17174,x17172,x17175))
% 18.77/18.52 [1718]~E(x17181,x17182)+E(f643(x17183,x17184,x17185,x17181),f643(x17183,x17184,x17185,x17182))
% 18.77/18.52 [1719]~E(x17191,x17192)+E(f443(x17191,x17193,x17194),f443(x17192,x17193,x17194))
% 18.77/18.52 [1720]~E(x17201,x17202)+E(f443(x17203,x17201,x17204),f443(x17203,x17202,x17204))
% 18.77/18.52 [1721]~E(x17211,x17212)+E(f443(x17213,x17214,x17211),f443(x17213,x17214,x17212))
% 18.77/18.52 [1722]~E(x17221,x17222)+E(f623(x17221,x17223,x17224),f623(x17222,x17223,x17224))
% 18.77/18.52 [1723]~E(x17231,x17232)+E(f623(x17233,x17231,x17234),f623(x17233,x17232,x17234))
% 18.77/18.52 [1724]~E(x17241,x17242)+E(f623(x17243,x17244,x17241),f623(x17243,x17244,x17242))
% 18.77/18.52 [1725]~E(x17251,x17252)+E(f385(x17251,x17253),f385(x17252,x17253))
% 18.77/18.52 [1726]~E(x17261,x17262)+E(f385(x17263,x17261),f385(x17263,x17262))
% 18.77/18.52 [1727]~E(x17271,x17272)+E(f267(x17271,x17273),f267(x17272,x17273))
% 18.77/18.52 [1728]~E(x17281,x17282)+E(f267(x17283,x17281),f267(x17283,x17282))
% 18.77/18.52 [1729]~E(x17291,x17292)+E(f784(x17291,x17293,x17294),f784(x17292,x17293,x17294))
% 18.77/18.52 [1730]~E(x17301,x17302)+E(f784(x17303,x17301,x17304),f784(x17303,x17302,x17304))
% 18.77/18.52 [1731]~E(x17311,x17312)+E(f784(x17313,x17314,x17311),f784(x17313,x17314,x17312))
% 18.77/18.52 [1732]~E(x17321,x17322)+E(f292(x17321,x17323,x17324,x17325),f292(x17322,x17323,x17324,x17325))
% 18.77/18.52 [1733]~E(x17331,x17332)+E(f292(x17333,x17331,x17334,x17335),f292(x17333,x17332,x17334,x17335))
% 18.77/18.52 [1734]~E(x17341,x17342)+E(f292(x17343,x17344,x17341,x17345),f292(x17343,x17344,x17342,x17345))
% 18.77/18.52 [1735]~E(x17351,x17352)+E(f292(x17353,x17354,x17355,x17351),f292(x17353,x17354,x17355,x17352))
% 18.77/18.52 [1736]~E(x17361,x17362)+E(f290(x17361,x17363,x17364,x17365,x17366),f290(x17362,x17363,x17364,x17365,x17366))
% 18.77/18.52 [1737]~E(x17371,x17372)+E(f290(x17373,x17371,x17374,x17375,x17376),f290(x17373,x17372,x17374,x17375,x17376))
% 18.77/18.52 [1738]~E(x17381,x17382)+E(f290(x17383,x17384,x17381,x17385,x17386),f290(x17383,x17384,x17382,x17385,x17386))
% 18.77/18.52 [1739]~E(x17391,x17392)+E(f290(x17393,x17394,x17395,x17391,x17396),f290(x17393,x17394,x17395,x17392,x17396))
% 18.77/18.52 [1740]~E(x17401,x17402)+E(f290(x17403,x17404,x17405,x17406,x17401),f290(x17403,x17404,x17405,x17406,x17402))
% 18.77/18.52 [1741]~E(x17411,x17412)+E(f377(x17411,x17413),f377(x17412,x17413))
% 18.77/18.52 [1742]~E(x17421,x17422)+E(f377(x17423,x17421),f377(x17423,x17422))
% 18.77/18.52 [1743]~E(x17431,x17432)+E(f542(x17431,x17433,x17434,x17435,x17436),f542(x17432,x17433,x17434,x17435,x17436))
% 18.77/18.52 [1744]~E(x17441,x17442)+E(f542(x17443,x17441,x17444,x17445,x17446),f542(x17443,x17442,x17444,x17445,x17446))
% 18.77/18.52 [1745]~E(x17451,x17452)+E(f542(x17453,x17454,x17451,x17455,x17456),f542(x17453,x17454,x17452,x17455,x17456))
% 18.77/18.52 [1746]~E(x17461,x17462)+E(f542(x17463,x17464,x17465,x17461,x17466),f542(x17463,x17464,x17465,x17462,x17466))
% 18.77/18.52 [1747]~E(x17471,x17472)+E(f542(x17473,x17474,x17475,x17476,x17471),f542(x17473,x17474,x17475,x17476,x17472))
% 18.77/18.52 [1748]~E(x17481,x17482)+E(f148(x17481,x17483),f148(x17482,x17483))
% 18.77/18.52 [1749]~E(x17491,x17492)+E(f148(x17493,x17491),f148(x17493,x17492))
% 18.77/18.52 [1750]~E(x17501,x17502)+E(f577(x17501,x17503,x17504),f577(x17502,x17503,x17504))
% 18.77/18.52 [1751]~E(x17511,x17512)+E(f577(x17513,x17511,x17514),f577(x17513,x17512,x17514))
% 18.77/18.52 [1752]~E(x17521,x17522)+E(f577(x17523,x17524,x17521),f577(x17523,x17524,x17522))
% 18.77/18.52 [1753]~E(x17531,x17532)+E(f457(x17531,x17533,x17534,x17535),f457(x17532,x17533,x17534,x17535))
% 18.77/18.52 [1754]~E(x17541,x17542)+E(f457(x17543,x17541,x17544,x17545),f457(x17543,x17542,x17544,x17545))
% 18.77/18.52 [1755]~E(x17551,x17552)+E(f457(x17553,x17554,x17551,x17555),f457(x17553,x17554,x17552,x17555))
% 18.77/18.52 [1756]~E(x17561,x17562)+E(f457(x17563,x17564,x17565,x17561),f457(x17563,x17564,x17565,x17562))
% 18.77/18.52 [1757]~E(x17571,x17572)+E(f741(x17571,x17573,x17574,x17575),f741(x17572,x17573,x17574,x17575))
% 18.77/18.52 [1758]~E(x17581,x17582)+E(f741(x17583,x17581,x17584,x17585),f741(x17583,x17582,x17584,x17585))
% 18.77/18.52 [1759]~E(x17591,x17592)+E(f741(x17593,x17594,x17591,x17595),f741(x17593,x17594,x17592,x17595))
% 18.77/18.52 [1760]~E(x17601,x17602)+E(f741(x17603,x17604,x17605,x17601),f741(x17603,x17604,x17605,x17602))
% 18.77/18.52 [1761]~E(x17611,x17612)+E(f392(x17611),f392(x17612))
% 18.77/18.52 [1762]~E(x17621,x17622)+E(f428(x17621,x17623,x17624,x17625,x17626),f428(x17622,x17623,x17624,x17625,x17626))
% 18.77/18.52 [1763]~E(x17631,x17632)+E(f428(x17633,x17631,x17634,x17635,x17636),f428(x17633,x17632,x17634,x17635,x17636))
% 18.77/18.52 [1764]~E(x17641,x17642)+E(f428(x17643,x17644,x17641,x17645,x17646),f428(x17643,x17644,x17642,x17645,x17646))
% 18.77/18.52 [1765]~E(x17651,x17652)+E(f428(x17653,x17654,x17655,x17651,x17656),f428(x17653,x17654,x17655,x17652,x17656))
% 18.77/18.52 [1766]~E(x17661,x17662)+E(f428(x17663,x17664,x17665,x17666,x17661),f428(x17663,x17664,x17665,x17666,x17662))
% 18.77/18.52 [1767]~E(x17671,x17672)+E(f666(x17671,x17673,x17674,x17675,x17676),f666(x17672,x17673,x17674,x17675,x17676))
% 18.77/18.52 [1768]~E(x17681,x17682)+E(f666(x17683,x17681,x17684,x17685,x17686),f666(x17683,x17682,x17684,x17685,x17686))
% 18.77/18.52 [1769]~E(x17691,x17692)+E(f666(x17693,x17694,x17691,x17695,x17696),f666(x17693,x17694,x17692,x17695,x17696))
% 18.77/18.52 [1770]~E(x17701,x17702)+E(f666(x17703,x17704,x17705,x17701,x17706),f666(x17703,x17704,x17705,x17702,x17706))
% 18.77/18.52 [1771]~E(x17711,x17712)+E(f666(x17713,x17714,x17715,x17716,x17711),f666(x17713,x17714,x17715,x17716,x17712))
% 18.77/18.52 [1772]~E(x17721,x17722)+E(f354(x17721,x17723,x17724),f354(x17722,x17723,x17724))
% 18.77/18.52 [1773]~E(x17731,x17732)+E(f354(x17733,x17731,x17734),f354(x17733,x17732,x17734))
% 18.77/18.52 [1774]~E(x17741,x17742)+E(f354(x17743,x17744,x17741),f354(x17743,x17744,x17742))
% 18.77/18.52 [1775]~E(x17751,x17752)+E(f825(x17751,x17753,x17754,x17755,x17756,x17757,x17758),f825(x17752,x17753,x17754,x17755,x17756,x17757,x17758))
% 18.77/18.52 [1776]~E(x17761,x17762)+E(f825(x17763,x17761,x17764,x17765,x17766,x17767,x17768),f825(x17763,x17762,x17764,x17765,x17766,x17767,x17768))
% 18.77/18.52 [1777]~E(x17771,x17772)+E(f825(x17773,x17774,x17771,x17775,x17776,x17777,x17778),f825(x17773,x17774,x17772,x17775,x17776,x17777,x17778))
% 18.77/18.52 [1778]~E(x17781,x17782)+E(f825(x17783,x17784,x17785,x17781,x17786,x17787,x17788),f825(x17783,x17784,x17785,x17782,x17786,x17787,x17788))
% 18.77/18.52 [1779]~E(x17791,x17792)+E(f825(x17793,x17794,x17795,x17796,x17791,x17797,x17798),f825(x17793,x17794,x17795,x17796,x17792,x17797,x17798))
% 18.77/18.52 [1780]~E(x17801,x17802)+E(f825(x17803,x17804,x17805,x17806,x17807,x17801,x17808),f825(x17803,x17804,x17805,x17806,x17807,x17802,x17808))
% 18.77/18.52 [1781]~E(x17811,x17812)+E(f825(x17813,x17814,x17815,x17816,x17817,x17818,x17811),f825(x17813,x17814,x17815,x17816,x17817,x17818,x17812))
% 18.77/18.52 [1782]~E(x17821,x17822)+E(f678(x17821,x17823,x17824),f678(x17822,x17823,x17824))
% 18.77/18.52 [1783]~E(x17831,x17832)+E(f678(x17833,x17831,x17834),f678(x17833,x17832,x17834))
% 18.77/18.52 [1784]~E(x17841,x17842)+E(f678(x17843,x17844,x17841),f678(x17843,x17844,x17842))
% 18.77/18.52 [1785]~E(x17851,x17852)+E(f435(x17851,x17853,x17854,x17855,x17856),f435(x17852,x17853,x17854,x17855,x17856))
% 18.77/18.52 [1786]~E(x17861,x17862)+E(f435(x17863,x17861,x17864,x17865,x17866),f435(x17863,x17862,x17864,x17865,x17866))
% 18.77/18.52 [1787]~E(x17871,x17872)+E(f435(x17873,x17874,x17871,x17875,x17876),f435(x17873,x17874,x17872,x17875,x17876))
% 18.77/18.52 [1788]~E(x17881,x17882)+E(f435(x17883,x17884,x17885,x17881,x17886),f435(x17883,x17884,x17885,x17882,x17886))
% 18.77/18.52 [1789]~E(x17891,x17892)+E(f435(x17893,x17894,x17895,x17896,x17891),f435(x17893,x17894,x17895,x17896,x17892))
% 18.77/18.52 [1790]~E(x17901,x17902)+E(f714(x17901,x17903),f714(x17902,x17903))
% 18.77/18.52 [1791]~E(x17911,x17912)+E(f714(x17913,x17911),f714(x17913,x17912))
% 18.77/18.52 [1792]~E(x17921,x17922)+E(f559(x17921,x17923,x17924,x17925,x17926),f559(x17922,x17923,x17924,x17925,x17926))
% 18.77/18.52 [1793]~E(x17931,x17932)+E(f559(x17933,x17931,x17934,x17935,x17936),f559(x17933,x17932,x17934,x17935,x17936))
% 18.77/18.52 [1794]~E(x17941,x17942)+E(f559(x17943,x17944,x17941,x17945,x17946),f559(x17943,x17944,x17942,x17945,x17946))
% 18.77/18.52 [1795]~E(x17951,x17952)+E(f559(x17953,x17954,x17955,x17951,x17956),f559(x17953,x17954,x17955,x17952,x17956))
% 18.77/18.52 [1796]~E(x17961,x17962)+E(f559(x17963,x17964,x17965,x17966,x17961),f559(x17963,x17964,x17965,x17966,x17962))
% 18.77/18.52 [1797]~E(x17971,x17972)+E(f785(x17971,x17973,x17974),f785(x17972,x17973,x17974))
% 18.77/18.52 [1798]~E(x17981,x17982)+E(f785(x17983,x17981,x17984),f785(x17983,x17982,x17984))
% 18.77/18.52 [1799]~E(x17991,x17992)+E(f785(x17993,x17994,x17991),f785(x17993,x17994,x17992))
% 18.77/18.52 [1800]~E(x18001,x18002)+E(f289(x18001,x18003,x18004),f289(x18002,x18003,x18004))
% 18.77/18.52 [1801]~E(x18011,x18012)+E(f289(x18013,x18011,x18014),f289(x18013,x18012,x18014))
% 18.77/18.52 [1802]~E(x18021,x18022)+E(f289(x18023,x18024,x18021),f289(x18023,x18024,x18022))
% 18.77/18.52 [1803]~E(x18031,x18032)+E(f669(x18031,x18033,x18034,x18035,x18036,x18037,x18038),f669(x18032,x18033,x18034,x18035,x18036,x18037,x18038))
% 18.77/18.52 [1804]~E(x18041,x18042)+E(f669(x18043,x18041,x18044,x18045,x18046,x18047,x18048),f669(x18043,x18042,x18044,x18045,x18046,x18047,x18048))
% 18.77/18.52 [1805]~E(x18051,x18052)+E(f669(x18053,x18054,x18051,x18055,x18056,x18057,x18058),f669(x18053,x18054,x18052,x18055,x18056,x18057,x18058))
% 18.77/18.52 [1806]~E(x18061,x18062)+E(f669(x18063,x18064,x18065,x18061,x18066,x18067,x18068),f669(x18063,x18064,x18065,x18062,x18066,x18067,x18068))
% 18.77/18.52 [1807]~E(x18071,x18072)+E(f669(x18073,x18074,x18075,x18076,x18071,x18077,x18078),f669(x18073,x18074,x18075,x18076,x18072,x18077,x18078))
% 18.77/18.52 [1808]~E(x18081,x18082)+E(f669(x18083,x18084,x18085,x18086,x18087,x18081,x18088),f669(x18083,x18084,x18085,x18086,x18087,x18082,x18088))
% 18.77/18.52 [1809]~E(x18091,x18092)+E(f669(x18093,x18094,x18095,x18096,x18097,x18098,x18091),f669(x18093,x18094,x18095,x18096,x18097,x18098,x18092))
% 18.77/18.52 [1810]~E(x18101,x18102)+E(f285(x18101,x18103),f285(x18102,x18103))
% 18.77/18.52 [1811]~E(x18111,x18112)+E(f285(x18113,x18111),f285(x18113,x18112))
% 18.77/18.52 [1812]~E(x18121,x18122)+E(f191(x18121,x18123,x18124,x18125),f191(x18122,x18123,x18124,x18125))
% 18.77/18.52 [1813]~E(x18131,x18132)+E(f191(x18133,x18131,x18134,x18135),f191(x18133,x18132,x18134,x18135))
% 18.77/18.52 [1814]~E(x18141,x18142)+E(f191(x18143,x18144,x18141,x18145),f191(x18143,x18144,x18142,x18145))
% 18.77/18.52 [1815]~E(x18151,x18152)+E(f191(x18153,x18154,x18155,x18151),f191(x18153,x18154,x18155,x18152))
% 18.77/18.52 [1816]~E(x18161,x18162)+E(f557(x18161,x18163,x18164),f557(x18162,x18163,x18164))
% 18.77/18.52 [1817]~E(x18171,x18172)+E(f557(x18173,x18171,x18174),f557(x18173,x18172,x18174))
% 18.77/18.52 [1818]~E(x18181,x18182)+E(f557(x18183,x18184,x18181),f557(x18183,x18184,x18182))
% 18.77/18.52 [1819]~E(x18191,x18192)+E(f461(x18191,x18193,x18194,x18195),f461(x18192,x18193,x18194,x18195))
% 18.77/18.52 [1820]~E(x18201,x18202)+E(f461(x18203,x18201,x18204,x18205),f461(x18203,x18202,x18204,x18205))
% 18.77/18.52 [1821]~E(x18211,x18212)+E(f461(x18213,x18214,x18211,x18215),f461(x18213,x18214,x18212,x18215))
% 18.77/18.52 [1822]~E(x18221,x18222)+E(f461(x18223,x18224,x18225,x18221),f461(x18223,x18224,x18225,x18222))
% 18.77/18.52 [1823]~E(x18231,x18232)+E(f189(x18231,x18233,x18234,x18235),f189(x18232,x18233,x18234,x18235))
% 18.77/18.52 [1824]~E(x18241,x18242)+E(f189(x18243,x18241,x18244,x18245),f189(x18243,x18242,x18244,x18245))
% 18.77/18.52 [1825]~E(x18251,x18252)+E(f189(x18253,x18254,x18251,x18255),f189(x18253,x18254,x18252,x18255))
% 18.77/18.52 [1826]~E(x18261,x18262)+E(f189(x18263,x18264,x18265,x18261),f189(x18263,x18264,x18265,x18262))
% 18.77/18.52 [1827]~E(x18271,x18272)+E(f333(x18271,x18273,x18274),f333(x18272,x18273,x18274))
% 18.77/18.52 [1828]~E(x18281,x18282)+E(f333(x18283,x18281,x18284),f333(x18283,x18282,x18284))
% 18.77/18.52 [1829]~E(x18291,x18292)+E(f333(x18293,x18294,x18291),f333(x18293,x18294,x18292))
% 18.77/18.52 [1830]~E(x18301,x18302)+E(f454(x18301,x18303,x18304),f454(x18302,x18303,x18304))
% 18.77/18.52 [1831]~E(x18311,x18312)+E(f454(x18313,x18311,x18314),f454(x18313,x18312,x18314))
% 18.77/18.52 [1832]~E(x18321,x18322)+E(f454(x18323,x18324,x18321),f454(x18323,x18324,x18322))
% 18.77/18.52 [1833]~E(x18331,x18332)+E(f349(x18331,x18333,x18334,x18335),f349(x18332,x18333,x18334,x18335))
% 18.77/18.52 [1834]~E(x18341,x18342)+E(f349(x18343,x18341,x18344,x18345),f349(x18343,x18342,x18344,x18345))
% 18.77/18.52 [1835]~E(x18351,x18352)+E(f349(x18353,x18354,x18351,x18355),f349(x18353,x18354,x18352,x18355))
% 18.77/18.52 [1836]~E(x18361,x18362)+E(f349(x18363,x18364,x18365,x18361),f349(x18363,x18364,x18365,x18362))
% 18.77/18.52 [1837]~E(x18371,x18372)+E(f229(x18371,x18373,x18374,x18375,x18376),f229(x18372,x18373,x18374,x18375,x18376))
% 18.77/18.52 [1838]~E(x18381,x18382)+E(f229(x18383,x18381,x18384,x18385,x18386),f229(x18383,x18382,x18384,x18385,x18386))
% 18.77/18.52 [1839]~E(x18391,x18392)+E(f229(x18393,x18394,x18391,x18395,x18396),f229(x18393,x18394,x18392,x18395,x18396))
% 18.77/18.52 [1840]~E(x18401,x18402)+E(f229(x18403,x18404,x18405,x18401,x18406),f229(x18403,x18404,x18405,x18402,x18406))
% 18.77/18.52 [1841]~E(x18411,x18412)+E(f229(x18413,x18414,x18415,x18416,x18411),f229(x18413,x18414,x18415,x18416,x18412))
% 18.77/18.52 [1842]~E(x18421,x18422)+E(f698(x18421,x18423,x18424,x18425,x18426,x18427),f698(x18422,x18423,x18424,x18425,x18426,x18427))
% 18.77/18.52 [1843]~E(x18431,x18432)+E(f698(x18433,x18431,x18434,x18435,x18436,x18437),f698(x18433,x18432,x18434,x18435,x18436,x18437))
% 18.77/18.52 [1844]~E(x18441,x18442)+E(f698(x18443,x18444,x18441,x18445,x18446,x18447),f698(x18443,x18444,x18442,x18445,x18446,x18447))
% 18.77/18.52 [1845]~E(x18451,x18452)+E(f698(x18453,x18454,x18455,x18451,x18456,x18457),f698(x18453,x18454,x18455,x18452,x18456,x18457))
% 18.77/18.52 [1846]~E(x18461,x18462)+E(f698(x18463,x18464,x18465,x18466,x18461,x18467),f698(x18463,x18464,x18465,x18466,x18462,x18467))
% 18.77/18.52 [1847]~E(x18471,x18472)+E(f698(x18473,x18474,x18475,x18476,x18477,x18471),f698(x18473,x18474,x18475,x18476,x18477,x18472))
% 18.77/18.52 [1848]~E(x18481,x18482)+E(f653(x18481,x18483,x18484),f653(x18482,x18483,x18484))
% 18.77/18.52 [1849]~E(x18491,x18492)+E(f653(x18493,x18491,x18494),f653(x18493,x18492,x18494))
% 18.77/18.52 [1850]~E(x18501,x18502)+E(f653(x18503,x18504,x18501),f653(x18503,x18504,x18502))
% 18.77/18.52 [1851]~E(x18511,x18512)+E(f671(x18511,x18513,x18514),f671(x18512,x18513,x18514))
% 18.77/18.52 [1852]~E(x18521,x18522)+E(f671(x18523,x18521,x18524),f671(x18523,x18522,x18524))
% 18.77/18.52 [1853]~E(x18531,x18532)+E(f671(x18533,x18534,x18531),f671(x18533,x18534,x18532))
% 18.77/18.52 [1854]~E(x18541,x18542)+E(f288(x18541,x18543,x18544),f288(x18542,x18543,x18544))
% 18.77/18.52 [1855]~E(x18551,x18552)+E(f288(x18553,x18551,x18554),f288(x18553,x18552,x18554))
% 18.77/18.52 [1856]~E(x18561,x18562)+E(f288(x18563,x18564,x18561),f288(x18563,x18564,x18562))
% 18.77/18.52 [1857]~E(x18571,x18572)+E(f687(x18571,x18573,x18574,x18575),f687(x18572,x18573,x18574,x18575))
% 18.77/18.52 [1858]~E(x18581,x18582)+E(f687(x18583,x18581,x18584,x18585),f687(x18583,x18582,x18584,x18585))
% 18.77/18.52 [1859]~E(x18591,x18592)+E(f687(x18593,x18594,x18591,x18595),f687(x18593,x18594,x18592,x18595))
% 18.77/18.52 [1860]~E(x18601,x18602)+E(f687(x18603,x18604,x18605,x18601),f687(x18603,x18604,x18605,x18602))
% 18.77/18.52 [1861]~E(x18611,x18612)+E(f404(x18611,x18613,x18614,x18615,x18616,x18617,x18618),f404(x18612,x18613,x18614,x18615,x18616,x18617,x18618))
% 18.77/18.52 [1862]~E(x18621,x18622)+E(f404(x18623,x18621,x18624,x18625,x18626,x18627,x18628),f404(x18623,x18622,x18624,x18625,x18626,x18627,x18628))
% 18.77/18.52 [1863]~E(x18631,x18632)+E(f404(x18633,x18634,x18631,x18635,x18636,x18637,x18638),f404(x18633,x18634,x18632,x18635,x18636,x18637,x18638))
% 18.77/18.52 [1864]~E(x18641,x18642)+E(f404(x18643,x18644,x18645,x18641,x18646,x18647,x18648),f404(x18643,x18644,x18645,x18642,x18646,x18647,x18648))
% 18.77/18.52 [1865]~E(x18651,x18652)+E(f404(x18653,x18654,x18655,x18656,x18651,x18657,x18658),f404(x18653,x18654,x18655,x18656,x18652,x18657,x18658))
% 18.77/18.52 [1866]~E(x18661,x18662)+E(f404(x18663,x18664,x18665,x18666,x18667,x18661,x18668),f404(x18663,x18664,x18665,x18666,x18667,x18662,x18668))
% 18.77/18.52 [1867]~E(x18671,x18672)+E(f404(x18673,x18674,x18675,x18676,x18677,x18678,x18671),f404(x18673,x18674,x18675,x18676,x18677,x18678,x18672))
% 18.77/18.52 [1868]~E(x18681,x18682)+E(f558(x18681,x18683,x18684,x18685,x18686),f558(x18682,x18683,x18684,x18685,x18686))
% 18.77/18.52 [1869]~E(x18691,x18692)+E(f558(x18693,x18691,x18694,x18695,x18696),f558(x18693,x18692,x18694,x18695,x18696))
% 18.77/18.52 [1870]~E(x18701,x18702)+E(f558(x18703,x18704,x18701,x18705,x18706),f558(x18703,x18704,x18702,x18705,x18706))
% 18.77/18.52 [1871]~E(x18711,x18712)+E(f558(x18713,x18714,x18715,x18711,x18716),f558(x18713,x18714,x18715,x18712,x18716))
% 18.77/18.52 [1872]~E(x18721,x18722)+E(f558(x18723,x18724,x18725,x18726,x18721),f558(x18723,x18724,x18725,x18726,x18722))
% 18.77/18.52 [1873]~E(x18731,x18732)+E(f601(x18731,x18733,x18734,x18735,x18736),f601(x18732,x18733,x18734,x18735,x18736))
% 18.77/18.52 [1874]~E(x18741,x18742)+E(f601(x18743,x18741,x18744,x18745,x18746),f601(x18743,x18742,x18744,x18745,x18746))
% 18.77/18.52 [1875]~E(x18751,x18752)+E(f601(x18753,x18754,x18751,x18755,x18756),f601(x18753,x18754,x18752,x18755,x18756))
% 18.77/18.52 [1876]~E(x18761,x18762)+E(f601(x18763,x18764,x18765,x18761,x18766),f601(x18763,x18764,x18765,x18762,x18766))
% 18.77/18.52 [1877]~E(x18771,x18772)+E(f601(x18773,x18774,x18775,x18776,x18771),f601(x18773,x18774,x18775,x18776,x18772))
% 18.77/18.52 [1878]~E(x18781,x18782)+E(f655(x18781,x18783,x18784),f655(x18782,x18783,x18784))
% 18.77/18.52 [1879]~E(x18791,x18792)+E(f655(x18793,x18791,x18794),f655(x18793,x18792,x18794))
% 18.77/18.52 [1880]~E(x18801,x18802)+E(f655(x18803,x18804,x18801),f655(x18803,x18804,x18802))
% 18.77/18.52 [1881]~E(x18811,x18812)+E(f730(x18811,x18813,x18814,x18815),f730(x18812,x18813,x18814,x18815))
% 18.77/18.52 [1882]~E(x18821,x18822)+E(f730(x18823,x18821,x18824,x18825),f730(x18823,x18822,x18824,x18825))
% 18.77/18.52 [1883]~E(x18831,x18832)+E(f730(x18833,x18834,x18831,x18835),f730(x18833,x18834,x18832,x18835))
% 18.77/18.52 [1884]~E(x18841,x18842)+E(f730(x18843,x18844,x18845,x18841),f730(x18843,x18844,x18845,x18842))
% 18.77/18.52 [1885]~E(x18851,x18852)+E(f472(x18851,x18853,x18854,x18855),f472(x18852,x18853,x18854,x18855))
% 18.77/18.52 [1886]~E(x18861,x18862)+E(f472(x18863,x18861,x18864,x18865),f472(x18863,x18862,x18864,x18865))
% 18.77/18.52 [1887]~E(x18871,x18872)+E(f472(x18873,x18874,x18871,x18875),f472(x18873,x18874,x18872,x18875))
% 18.77/18.52 [1888]~E(x18881,x18882)+E(f472(x18883,x18884,x18885,x18881),f472(x18883,x18884,x18885,x18882))
% 18.77/18.52 [1889]~E(x18891,x18892)+E(f823(x18891,x18893),f823(x18892,x18893))
% 18.77/18.52 [1890]~E(x18901,x18902)+E(f823(x18903,x18901),f823(x18903,x18902))
% 18.77/18.52 [1891]~E(x18911,x18912)+E(f755(x18911,x18913,x18914),f755(x18912,x18913,x18914))
% 18.77/18.52 [1892]~E(x18921,x18922)+E(f755(x18923,x18921,x18924),f755(x18923,x18922,x18924))
% 18.77/18.52 [1893]~E(x18931,x18932)+E(f755(x18933,x18934,x18931),f755(x18933,x18934,x18932))
% 18.77/18.52 [1894]~E(x18941,x18942)+E(f635(x18941,x18943,x18944,x18945,x18946),f635(x18942,x18943,x18944,x18945,x18946))
% 18.77/18.52 [1895]~E(x18951,x18952)+E(f635(x18953,x18951,x18954,x18955,x18956),f635(x18953,x18952,x18954,x18955,x18956))
% 18.77/18.52 [1896]~E(x18961,x18962)+E(f635(x18963,x18964,x18961,x18965,x18966),f635(x18963,x18964,x18962,x18965,x18966))
% 18.77/18.52 [1897]~E(x18971,x18972)+E(f635(x18973,x18974,x18975,x18971,x18976),f635(x18973,x18974,x18975,x18972,x18976))
% 18.77/18.52 [1898]~E(x18981,x18982)+E(f635(x18983,x18984,x18985,x18986,x18981),f635(x18983,x18984,x18985,x18986,x18982))
% 18.77/18.52 [1899]~E(x18991,x18992)+E(f585(x18991,x18993,x18994,x18995),f585(x18992,x18993,x18994,x18995))
% 18.77/18.52 [1900]~E(x19001,x19002)+E(f585(x19003,x19001,x19004,x19005),f585(x19003,x19002,x19004,x19005))
% 18.77/18.52 [1901]~E(x19011,x19012)+E(f585(x19013,x19014,x19011,x19015),f585(x19013,x19014,x19012,x19015))
% 18.77/18.52 [1902]~E(x19021,x19022)+E(f585(x19023,x19024,x19025,x19021),f585(x19023,x19024,x19025,x19022))
% 18.77/18.52 [1903]~E(x19031,x19032)+E(f600(x19031,x19033,x19034,x19035,x19036),f600(x19032,x19033,x19034,x19035,x19036))
% 18.77/18.52 [1904]~E(x19041,x19042)+E(f600(x19043,x19041,x19044,x19045,x19046),f600(x19043,x19042,x19044,x19045,x19046))
% 18.77/18.52 [1905]~E(x19051,x19052)+E(f600(x19053,x19054,x19051,x19055,x19056),f600(x19053,x19054,x19052,x19055,x19056))
% 18.77/18.52 [1906]~E(x19061,x19062)+E(f600(x19063,x19064,x19065,x19061,x19066),f600(x19063,x19064,x19065,x19062,x19066))
% 18.77/18.52 [1907]~E(x19071,x19072)+E(f600(x19073,x19074,x19075,x19076,x19071),f600(x19073,x19074,x19075,x19076,x19072))
% 18.77/18.52 [1908]~E(x19081,x19082)+E(f492(x19081,x19083,x19084,x19085),f492(x19082,x19083,x19084,x19085))
% 18.77/18.52 [1909]~E(x19091,x19092)+E(f492(x19093,x19091,x19094,x19095),f492(x19093,x19092,x19094,x19095))
% 18.77/18.52 [1910]~E(x19101,x19102)+E(f492(x19103,x19104,x19101,x19105),f492(x19103,x19104,x19102,x19105))
% 18.77/18.52 [1911]~E(x19111,x19112)+E(f492(x19113,x19114,x19115,x19111),f492(x19113,x19114,x19115,x19112))
% 18.77/18.52 [1912]~E(x19121,x19122)+E(f307(x19121,x19123,x19124),f307(x19122,x19123,x19124))
% 18.77/18.52 [1913]~E(x19131,x19132)+E(f307(x19133,x19131,x19134),f307(x19133,x19132,x19134))
% 18.77/18.52 [1914]~E(x19141,x19142)+E(f307(x19143,x19144,x19141),f307(x19143,x19144,x19142))
% 18.77/18.52 [1915]~E(x19151,x19152)+E(f487(x19151,x19153,x19154,x19155,x19156),f487(x19152,x19153,x19154,x19155,x19156))
% 18.77/18.52 [1916]~E(x19161,x19162)+E(f487(x19163,x19161,x19164,x19165,x19166),f487(x19163,x19162,x19164,x19165,x19166))
% 18.77/18.52 [1917]~E(x19171,x19172)+E(f487(x19173,x19174,x19171,x19175,x19176),f487(x19173,x19174,x19172,x19175,x19176))
% 18.77/18.52 [1918]~E(x19181,x19182)+E(f487(x19183,x19184,x19185,x19181,x19186),f487(x19183,x19184,x19185,x19182,x19186))
% 18.77/18.52 [1919]~E(x19191,x19192)+E(f487(x19193,x19194,x19195,x19196,x19191),f487(x19193,x19194,x19195,x19196,x19192))
% 18.77/18.52 [1920]~E(x19201,x19202)+E(f637(x19201,x19203,x19204,x19205,x19206),f637(x19202,x19203,x19204,x19205,x19206))
% 18.77/18.52 [1921]~E(x19211,x19212)+E(f637(x19213,x19211,x19214,x19215,x19216),f637(x19213,x19212,x19214,x19215,x19216))
% 18.77/18.52 [1922]~E(x19221,x19222)+E(f637(x19223,x19224,x19221,x19225,x19226),f637(x19223,x19224,x19222,x19225,x19226))
% 18.77/18.52 [1923]~E(x19231,x19232)+E(f637(x19233,x19234,x19235,x19231,x19236),f637(x19233,x19234,x19235,x19232,x19236))
% 18.77/18.52 [1924]~E(x19241,x19242)+E(f637(x19243,x19244,x19245,x19246,x19241),f637(x19243,x19244,x19245,x19246,x19242))
% 18.77/18.52 [1925]~E(x19251,x19252)+E(f60(x19251,x19253),f60(x19252,x19253))
% 18.77/18.52 [1926]~E(x19261,x19262)+E(f60(x19263,x19261),f60(x19263,x19262))
% 18.77/18.52 [1927]~E(x19271,x19272)+E(f221(x19271,x19273,x19274),f221(x19272,x19273,x19274))
% 18.77/18.52 [1928]~E(x19281,x19282)+E(f221(x19283,x19281,x19284),f221(x19283,x19282,x19284))
% 18.77/18.52 [1929]~E(x19291,x19292)+E(f221(x19293,x19294,x19291),f221(x19293,x19294,x19292))
% 18.77/18.52 [1930]~E(x19301,x19302)+E(f406(x19301,x19303,x19304,x19305),f406(x19302,x19303,x19304,x19305))
% 18.77/18.52 [1931]~E(x19311,x19312)+E(f406(x19313,x19311,x19314,x19315),f406(x19313,x19312,x19314,x19315))
% 18.77/18.52 [1932]~E(x19321,x19322)+E(f406(x19323,x19324,x19321,x19325),f406(x19323,x19324,x19322,x19325))
% 18.77/18.52 [1933]~E(x19331,x19332)+E(f406(x19333,x19334,x19335,x19331),f406(x19333,x19334,x19335,x19332))
% 18.77/18.52 [1934]~E(x19341,x19342)+E(f19(x19341,x19343,x19344,x19345),f19(x19342,x19343,x19344,x19345))
% 18.77/18.52 [1935]~E(x19351,x19352)+E(f19(x19353,x19351,x19354,x19355),f19(x19353,x19352,x19354,x19355))
% 18.77/18.52 [1936]~E(x19361,x19362)+E(f19(x19363,x19364,x19361,x19365),f19(x19363,x19364,x19362,x19365))
% 18.77/18.52 [1937]~E(x19371,x19372)+E(f19(x19373,x19374,x19375,x19371),f19(x19373,x19374,x19375,x19372))
% 18.77/18.52 [1938]~E(x19381,x19382)+E(f432(x19381,x19383,x19384),f432(x19382,x19383,x19384))
% 18.77/18.52 [1939]~E(x19391,x19392)+E(f432(x19393,x19391,x19394),f432(x19393,x19392,x19394))
% 18.77/18.52 [1940]~E(x19401,x19402)+E(f432(x19403,x19404,x19401),f432(x19403,x19404,x19402))
% 18.77/18.52 [1941]~E(x19411,x19412)+E(f501(x19411,x19413,x19414,x19415,x19416),f501(x19412,x19413,x19414,x19415,x19416))
% 18.77/18.52 [1942]~E(x19421,x19422)+E(f501(x19423,x19421,x19424,x19425,x19426),f501(x19423,x19422,x19424,x19425,x19426))
% 18.77/18.52 [1943]~E(x19431,x19432)+E(f501(x19433,x19434,x19431,x19435,x19436),f501(x19433,x19434,x19432,x19435,x19436))
% 18.77/18.52 [1944]~E(x19441,x19442)+E(f501(x19443,x19444,x19445,x19441,x19446),f501(x19443,x19444,x19445,x19442,x19446))
% 18.77/18.52 [1945]~E(x19451,x19452)+E(f501(x19453,x19454,x19455,x19456,x19451),f501(x19453,x19454,x19455,x19456,x19452))
% 18.77/18.52 [1946]~E(x19461,x19462)+E(f160(x19461,x19463,x19464),f160(x19462,x19463,x19464))
% 18.77/18.52 [1947]~E(x19471,x19472)+E(f160(x19473,x19471,x19474),f160(x19473,x19472,x19474))
% 18.77/18.52 [1948]~E(x19481,x19482)+E(f160(x19483,x19484,x19481),f160(x19483,x19484,x19482))
% 18.77/18.52 [1949]~E(x19491,x19492)+E(f310(x19491),f310(x19492))
% 18.77/18.52 [1950]~E(x19501,x19502)+E(f480(x19501,x19503,x19504,x19505,x19506),f480(x19502,x19503,x19504,x19505,x19506))
% 18.77/18.52 [1951]~E(x19511,x19512)+E(f480(x19513,x19511,x19514,x19515,x19516),f480(x19513,x19512,x19514,x19515,x19516))
% 18.77/18.52 [1952]~E(x19521,x19522)+E(f480(x19523,x19524,x19521,x19525,x19526),f480(x19523,x19524,x19522,x19525,x19526))
% 18.77/18.52 [1953]~E(x19531,x19532)+E(f480(x19533,x19534,x19535,x19531,x19536),f480(x19533,x19534,x19535,x19532,x19536))
% 18.77/18.52 [1954]~E(x19541,x19542)+E(f480(x19543,x19544,x19545,x19546,x19541),f480(x19543,x19544,x19545,x19546,x19542))
% 18.77/18.52 [1955]~E(x19551,x19552)+E(f456(x19551,x19553,x19554,x19555),f456(x19552,x19553,x19554,x19555))
% 18.77/18.52 [1956]~E(x19561,x19562)+E(f456(x19563,x19561,x19564,x19565),f456(x19563,x19562,x19564,x19565))
% 18.77/18.52 [1957]~E(x19571,x19572)+E(f456(x19573,x19574,x19571,x19575),f456(x19573,x19574,x19572,x19575))
% 18.77/18.52 [1958]~E(x19581,x19582)+E(f456(x19583,x19584,x19585,x19581),f456(x19583,x19584,x19585,x19582))
% 18.77/18.52 [1959]~E(x19591,x19592)+E(f588(x19591,x19593),f588(x19592,x19593))
% 18.77/18.52 [1960]~E(x19601,x19602)+E(f588(x19603,x19601),f588(x19603,x19602))
% 18.77/18.52 [1961]~E(x19611,x19612)+E(f638(x19611,x19613,x19614,x19615,x19616),f638(x19612,x19613,x19614,x19615,x19616))
% 18.77/18.52 [1962]~E(x19621,x19622)+E(f638(x19623,x19621,x19624,x19625,x19626),f638(x19623,x19622,x19624,x19625,x19626))
% 18.77/18.52 [1963]~E(x19631,x19632)+E(f638(x19633,x19634,x19631,x19635,x19636),f638(x19633,x19634,x19632,x19635,x19636))
% 18.77/18.52 [1964]~E(x19641,x19642)+E(f638(x19643,x19644,x19645,x19641,x19646),f638(x19643,x19644,x19645,x19642,x19646))
% 18.77/18.52 [1965]~E(x19651,x19652)+E(f638(x19653,x19654,x19655,x19656,x19651),f638(x19653,x19654,x19655,x19656,x19652))
% 18.77/18.52 [1966]~E(x19661,x19662)+E(f455(x19661,x19663,x19664),f455(x19662,x19663,x19664))
% 18.77/18.52 [1967]~E(x19671,x19672)+E(f455(x19673,x19671,x19674),f455(x19673,x19672,x19674))
% 18.77/18.52 [1968]~E(x19681,x19682)+E(f455(x19683,x19684,x19681),f455(x19683,x19684,x19682))
% 18.77/18.52 [1969]~E(x19691,x19692)+E(f396(x19691,x19693,x19694),f396(x19692,x19693,x19694))
% 18.77/18.52 [1970]~E(x19701,x19702)+E(f396(x19703,x19701,x19704),f396(x19703,x19702,x19704))
% 18.77/18.52 [1971]~E(x19711,x19712)+E(f396(x19713,x19714,x19711),f396(x19713,x19714,x19712))
% 18.77/18.52 [1972]~E(x19721,x19722)+E(f760(x19721,x19723),f760(x19722,x19723))
% 18.77/18.52 [1973]~E(x19731,x19732)+E(f760(x19733,x19731),f760(x19733,x19732))
% 18.77/18.52 [1974]~E(x19741,x19742)+E(f774(x19741,x19743,x19744),f774(x19742,x19743,x19744))
% 18.77/18.52 [1975]~E(x19751,x19752)+E(f774(x19753,x19751,x19754),f774(x19753,x19752,x19754))
% 18.77/18.52 [1976]~E(x19761,x19762)+E(f774(x19763,x19764,x19761),f774(x19763,x19764,x19762))
% 18.77/18.52 [1977]~E(x19771,x19772)+E(f369(x19771,x19773,x19774),f369(x19772,x19773,x19774))
% 18.77/18.52 [1978]~E(x19781,x19782)+E(f369(x19783,x19781,x19784),f369(x19783,x19782,x19784))
% 18.77/18.52 [1979]~E(x19791,x19792)+E(f369(x19793,x19794,x19791),f369(x19793,x19794,x19792))
% 18.77/18.52 [1980]~E(x19801,x19802)+E(f581(x19801,x19803,x19804,x19805,x19806,x19807),f581(x19802,x19803,x19804,x19805,x19806,x19807))
% 18.77/18.52 [1981]~E(x19811,x19812)+E(f581(x19813,x19811,x19814,x19815,x19816,x19817),f581(x19813,x19812,x19814,x19815,x19816,x19817))
% 18.77/18.52 [1982]~E(x19821,x19822)+E(f581(x19823,x19824,x19821,x19825,x19826,x19827),f581(x19823,x19824,x19822,x19825,x19826,x19827))
% 18.77/18.52 [1983]~E(x19831,x19832)+E(f581(x19833,x19834,x19835,x19831,x19836,x19837),f581(x19833,x19834,x19835,x19832,x19836,x19837))
% 18.77/18.52 [1984]~E(x19841,x19842)+E(f581(x19843,x19844,x19845,x19846,x19841,x19847),f581(x19843,x19844,x19845,x19846,x19842,x19847))
% 18.77/18.52 [1985]~E(x19851,x19852)+E(f581(x19853,x19854,x19855,x19856,x19857,x19851),f581(x19853,x19854,x19855,x19856,x19857,x19852))
% 18.77/18.52 [1986]~E(x19861,x19862)+E(f651(x19861,x19863),f651(x19862,x19863))
% 18.77/18.52 [1987]~E(x19871,x19872)+E(f651(x19873,x19871),f651(x19873,x19872))
% 18.77/18.52 [1988]~E(x19881,x19882)+E(f204(x19881,x19883,x19884,x19885),f204(x19882,x19883,x19884,x19885))
% 18.77/18.52 [1989]~E(x19891,x19892)+E(f204(x19893,x19891,x19894,x19895),f204(x19893,x19892,x19894,x19895))
% 18.77/18.52 [1990]~E(x19901,x19902)+E(f204(x19903,x19904,x19901,x19905),f204(x19903,x19904,x19902,x19905))
% 18.77/18.52 [1991]~E(x19911,x19912)+E(f204(x19913,x19914,x19915,x19911),f204(x19913,x19914,x19915,x19912))
% 18.77/18.52 [1992]~E(x19921,x19922)+E(f707(x19921,x19923,x19924,x19925,x19926),f707(x19922,x19923,x19924,x19925,x19926))
% 18.77/18.52 [1993]~E(x19931,x19932)+E(f707(x19933,x19931,x19934,x19935,x19936),f707(x19933,x19932,x19934,x19935,x19936))
% 18.77/18.52 [1994]~E(x19941,x19942)+E(f707(x19943,x19944,x19941,x19945,x19946),f707(x19943,x19944,x19942,x19945,x19946))
% 18.77/18.52 [1995]~E(x19951,x19952)+E(f707(x19953,x19954,x19955,x19951,x19956),f707(x19953,x19954,x19955,x19952,x19956))
% 18.77/18.52 [1996]~E(x19961,x19962)+E(f707(x19963,x19964,x19965,x19966,x19961),f707(x19963,x19964,x19965,x19966,x19962))
% 18.77/18.52 [1997]~E(x19971,x19972)+E(f255(x19971,x19973,x19974,x19975,x19976),f255(x19972,x19973,x19974,x19975,x19976))
% 18.77/18.52 [1998]~E(x19981,x19982)+E(f255(x19983,x19981,x19984,x19985,x19986),f255(x19983,x19982,x19984,x19985,x19986))
% 18.77/18.52 [1999]~E(x19991,x19992)+E(f255(x19993,x19994,x19991,x19995,x19996),f255(x19993,x19994,x19992,x19995,x19996))
% 18.77/18.52 [2000]~E(x20001,x20002)+E(f255(x20003,x20004,x20005,x20001,x20006),f255(x20003,x20004,x20005,x20002,x20006))
% 18.77/18.52 [2001]~E(x20011,x20012)+E(f255(x20013,x20014,x20015,x20016,x20011),f255(x20013,x20014,x20015,x20016,x20012))
% 18.77/18.52 [2002]~E(x20021,x20022)+E(f665(x20021,x20023,x20024,x20025,x20026),f665(x20022,x20023,x20024,x20025,x20026))
% 18.77/18.52 [2003]~E(x20031,x20032)+E(f665(x20033,x20031,x20034,x20035,x20036),f665(x20033,x20032,x20034,x20035,x20036))
% 18.77/18.52 [2004]~E(x20041,x20042)+E(f665(x20043,x20044,x20041,x20045,x20046),f665(x20043,x20044,x20042,x20045,x20046))
% 18.77/18.52 [2005]~E(x20051,x20052)+E(f665(x20053,x20054,x20055,x20051,x20056),f665(x20053,x20054,x20055,x20052,x20056))
% 18.77/18.52 [2006]~E(x20061,x20062)+E(f665(x20063,x20064,x20065,x20066,x20061),f665(x20063,x20064,x20065,x20066,x20062))
% 18.77/18.52 [2007]~E(x20071,x20072)+E(f625(x20071,x20073,x20074),f625(x20072,x20073,x20074))
% 18.77/18.52 [2008]~E(x20081,x20082)+E(f625(x20083,x20081,x20084),f625(x20083,x20082,x20084))
% 18.77/18.52 [2009]~E(x20091,x20092)+E(f625(x20093,x20094,x20091),f625(x20093,x20094,x20092))
% 18.77/18.52 [2010]~E(x20101,x20102)+E(f704(x20101,x20103,x20104,x20105),f704(x20102,x20103,x20104,x20105))
% 18.77/18.52 [2011]~E(x20111,x20112)+E(f704(x20113,x20111,x20114,x20115),f704(x20113,x20112,x20114,x20115))
% 18.77/18.52 [2012]~E(x20121,x20122)+E(f704(x20123,x20124,x20121,x20125),f704(x20123,x20124,x20122,x20125))
% 18.77/18.52 [2013]~E(x20131,x20132)+E(f704(x20133,x20134,x20135,x20131),f704(x20133,x20134,x20135,x20132))
% 18.77/18.52 [2014]~E(x20141,x20142)+E(f633(x20141,x20143),f633(x20142,x20143))
% 18.77/18.52 [2015]~E(x20151,x20152)+E(f633(x20153,x20151),f633(x20153,x20152))
% 18.77/18.52 [2016]~E(x20161,x20162)+E(f565(x20161,x20163,x20164,x20165),f565(x20162,x20163,x20164,x20165))
% 18.77/18.52 [2017]~E(x20171,x20172)+E(f565(x20173,x20171,x20174,x20175),f565(x20173,x20172,x20174,x20175))
% 18.77/18.52 [2018]~E(x20181,x20182)+E(f565(x20183,x20184,x20181,x20185),f565(x20183,x20184,x20182,x20185))
% 18.77/18.52 [2019]~E(x20191,x20192)+E(f565(x20193,x20194,x20195,x20191),f565(x20193,x20194,x20195,x20192))
% 18.77/18.52 [2020]~E(x20201,x20202)+E(f437(x20201,x20203,x20204,x20205,x20206),f437(x20202,x20203,x20204,x20205,x20206))
% 18.77/18.52 [2021]~E(x20211,x20212)+E(f437(x20213,x20211,x20214,x20215,x20216),f437(x20213,x20212,x20214,x20215,x20216))
% 18.77/18.52 [2022]~E(x20221,x20222)+E(f437(x20223,x20224,x20221,x20225,x20226),f437(x20223,x20224,x20222,x20225,x20226))
% 18.77/18.52 [2023]~E(x20231,x20232)+E(f437(x20233,x20234,x20235,x20231,x20236),f437(x20233,x20234,x20235,x20232,x20236))
% 18.77/18.52 [2024]~E(x20241,x20242)+E(f437(x20243,x20244,x20245,x20246,x20241),f437(x20243,x20244,x20245,x20246,x20242))
% 18.77/18.52 [2025]~E(x20251,x20252)+E(f728(x20251,x20253,x20254,x20255,x20256),f728(x20252,x20253,x20254,x20255,x20256))
% 18.77/18.52 [2026]~E(x20261,x20262)+E(f728(x20263,x20261,x20264,x20265,x20266),f728(x20263,x20262,x20264,x20265,x20266))
% 18.77/18.52 [2027]~E(x20271,x20272)+E(f728(x20273,x20274,x20271,x20275,x20276),f728(x20273,x20274,x20272,x20275,x20276))
% 18.77/18.52 [2028]~E(x20281,x20282)+E(f728(x20283,x20284,x20285,x20281,x20286),f728(x20283,x20284,x20285,x20282,x20286))
% 18.77/18.52 [2029]~E(x20291,x20292)+E(f728(x20293,x20294,x20295,x20296,x20291),f728(x20293,x20294,x20295,x20296,x20292))
% 18.77/18.52 [2030]~E(x20301,x20302)+E(f76(x20301,x20303),f76(x20302,x20303))
% 18.77/18.52 [2031]~E(x20311,x20312)+E(f76(x20313,x20311),f76(x20313,x20312))
% 18.77/18.52 [2032]~E(x20321,x20322)+E(f650(x20321,x20323,x20324,x20325,x20326,x20327),f650(x20322,x20323,x20324,x20325,x20326,x20327))
% 18.77/18.52 [2033]~E(x20331,x20332)+E(f650(x20333,x20331,x20334,x20335,x20336,x20337),f650(x20333,x20332,x20334,x20335,x20336,x20337))
% 18.77/18.52 [2034]~E(x20341,x20342)+E(f650(x20343,x20344,x20341,x20345,x20346,x20347),f650(x20343,x20344,x20342,x20345,x20346,x20347))
% 18.77/18.52 [2035]~E(x20351,x20352)+E(f650(x20353,x20354,x20355,x20351,x20356,x20357),f650(x20353,x20354,x20355,x20352,x20356,x20357))
% 18.77/18.52 [2036]~E(x20361,x20362)+E(f650(x20363,x20364,x20365,x20366,x20361,x20367),f650(x20363,x20364,x20365,x20366,x20362,x20367))
% 18.77/18.52 [2037]~E(x20371,x20372)+E(f650(x20373,x20374,x20375,x20376,x20377,x20371),f650(x20373,x20374,x20375,x20376,x20377,x20372))
% 18.77/18.52 [2038]~E(x20381,x20382)+E(f366(x20381,x20383),f366(x20382,x20383))
% 18.77/18.52 [2039]~E(x20391,x20392)+E(f366(x20393,x20391),f366(x20393,x20392))
% 18.77/18.52 [2040]~E(x20401,x20402)+E(f567(x20401,x20403,x20404,x20405,x20406,x20407),f567(x20402,x20403,x20404,x20405,x20406,x20407))
% 18.77/18.52 [2041]~E(x20411,x20412)+E(f567(x20413,x20411,x20414,x20415,x20416,x20417),f567(x20413,x20412,x20414,x20415,x20416,x20417))
% 18.77/18.52 [2042]~E(x20421,x20422)+E(f567(x20423,x20424,x20421,x20425,x20426,x20427),f567(x20423,x20424,x20422,x20425,x20426,x20427))
% 18.77/18.52 [2043]~E(x20431,x20432)+E(f567(x20433,x20434,x20435,x20431,x20436,x20437),f567(x20433,x20434,x20435,x20432,x20436,x20437))
% 18.77/18.52 [2044]~E(x20441,x20442)+E(f567(x20443,x20444,x20445,x20446,x20441,x20447),f567(x20443,x20444,x20445,x20446,x20442,x20447))
% 18.77/18.52 [2045]~E(x20451,x20452)+E(f567(x20453,x20454,x20455,x20456,x20457,x20451),f567(x20453,x20454,x20455,x20456,x20457,x20452))
% 18.77/18.52 [2046]~E(x20461,x20462)+E(f503(x20461,x20463,x20464,x20465,x20466),f503(x20462,x20463,x20464,x20465,x20466))
% 18.77/18.52 [2047]~E(x20471,x20472)+E(f503(x20473,x20471,x20474,x20475,x20476),f503(x20473,x20472,x20474,x20475,x20476))
% 18.77/18.52 [2048]~E(x20481,x20482)+E(f503(x20483,x20484,x20481,x20485,x20486),f503(x20483,x20484,x20482,x20485,x20486))
% 18.77/18.52 [2049]~E(x20491,x20492)+E(f503(x20493,x20494,x20495,x20491,x20496),f503(x20493,x20494,x20495,x20492,x20496))
% 18.77/18.52 [2050]~E(x20501,x20502)+E(f503(x20503,x20504,x20505,x20506,x20501),f503(x20503,x20504,x20505,x20506,x20502))
% 18.77/18.52 [2051]~E(x20511,x20512)+E(f475(x20511,x20513),f475(x20512,x20513))
% 18.77/18.52 [2052]~E(x20521,x20522)+E(f475(x20523,x20521),f475(x20523,x20522))
% 18.77/18.52 [2053]~E(x20531,x20532)+E(f703(x20531,x20533,x20534,x20535,x20536),f703(x20532,x20533,x20534,x20535,x20536))
% 18.77/18.52 [2054]~E(x20541,x20542)+E(f703(x20543,x20541,x20544,x20545,x20546),f703(x20543,x20542,x20544,x20545,x20546))
% 18.77/18.52 [2055]~E(x20551,x20552)+E(f703(x20553,x20554,x20551,x20555,x20556),f703(x20553,x20554,x20552,x20555,x20556))
% 18.77/18.52 [2056]~E(x20561,x20562)+E(f703(x20563,x20564,x20565,x20561,x20566),f703(x20563,x20564,x20565,x20562,x20566))
% 18.77/18.52 [2057]~E(x20571,x20572)+E(f703(x20573,x20574,x20575,x20576,x20571),f703(x20573,x20574,x20575,x20576,x20572))
% 18.77/18.52 [2058]~E(x20581,x20582)+E(f453(x20581),f453(x20582))
% 18.77/18.52 [2059]~E(x20591,x20592)+E(f400(x20591,x20593),f400(x20592,x20593))
% 18.77/18.52 [2060]~E(x20601,x20602)+E(f400(x20603,x20601),f400(x20603,x20602))
% 18.77/18.52 [2061]~E(x20611,x20612)+E(f753(x20611,x20613,x20614,x20615,x20616),f753(x20612,x20613,x20614,x20615,x20616))
% 18.77/18.52 [2062]~E(x20621,x20622)+E(f753(x20623,x20621,x20624,x20625,x20626),f753(x20623,x20622,x20624,x20625,x20626))
% 18.77/18.52 [2063]~E(x20631,x20632)+E(f753(x20633,x20634,x20631,x20635,x20636),f753(x20633,x20634,x20632,x20635,x20636))
% 18.77/18.52 [2064]~E(x20641,x20642)+E(f753(x20643,x20644,x20645,x20641,x20646),f753(x20643,x20644,x20645,x20642,x20646))
% 18.77/18.52 [2065]~E(x20651,x20652)+E(f753(x20653,x20654,x20655,x20656,x20651),f753(x20653,x20654,x20655,x20656,x20652))
% 18.77/18.52 [2066]~E(x20661,x20662)+E(f346(x20661,x20663),f346(x20662,x20663))
% 18.77/18.52 [2067]~E(x20671,x20672)+E(f346(x20673,x20671),f346(x20673,x20672))
% 18.77/18.52 [2068]~E(x20681,x20682)+E(f494(x20681,x20683,x20684,x20685,x20686),f494(x20682,x20683,x20684,x20685,x20686))
% 18.77/18.52 [2069]~E(x20691,x20692)+E(f494(x20693,x20691,x20694,x20695,x20696),f494(x20693,x20692,x20694,x20695,x20696))
% 18.77/18.52 [2070]~E(x20701,x20702)+E(f494(x20703,x20704,x20701,x20705,x20706),f494(x20703,x20704,x20702,x20705,x20706))
% 18.77/18.52 [2071]~E(x20711,x20712)+E(f494(x20713,x20714,x20715,x20711,x20716),f494(x20713,x20714,x20715,x20712,x20716))
% 18.77/18.52 [2072]~E(x20721,x20722)+E(f494(x20723,x20724,x20725,x20726,x20721),f494(x20723,x20724,x20725,x20726,x20722))
% 18.77/18.52 [2073]~E(x20731,x20732)+E(f737(x20731,x20733,x20734,x20735),f737(x20732,x20733,x20734,x20735))
% 18.77/18.52 [2074]~E(x20741,x20742)+E(f737(x20743,x20741,x20744,x20745),f737(x20743,x20742,x20744,x20745))
% 18.77/18.52 [2075]~E(x20751,x20752)+E(f737(x20753,x20754,x20751,x20755),f737(x20753,x20754,x20752,x20755))
% 18.77/18.52 [2076]~E(x20761,x20762)+E(f737(x20763,x20764,x20765,x20761),f737(x20763,x20764,x20765,x20762))
% 18.77/18.52 [2077]~E(x20771,x20772)+E(f849(x20771),f849(x20772))
% 18.77/18.52 [2078]~E(x20781,x20782)+E(f642(x20781,x20783,x20784,x20785),f642(x20782,x20783,x20784,x20785))
% 18.77/18.52 [2079]~E(x20791,x20792)+E(f642(x20793,x20791,x20794,x20795),f642(x20793,x20792,x20794,x20795))
% 18.77/18.52 [2080]~E(x20801,x20802)+E(f642(x20803,x20804,x20801,x20805),f642(x20803,x20804,x20802,x20805))
% 18.77/18.52 [2081]~E(x20811,x20812)+E(f642(x20813,x20814,x20815,x20811),f642(x20813,x20814,x20815,x20812))
% 18.77/18.52 [2082]~E(x20821,x20822)+E(f807(x20821,x20823),f807(x20822,x20823))
% 18.77/18.52 [2083]~E(x20831,x20832)+E(f807(x20833,x20831),f807(x20833,x20832))
% 18.77/18.52 [2084]~E(x20841,x20842)+E(f685(x20841,x20843,x20844),f685(x20842,x20843,x20844))
% 18.77/18.52 [2085]~E(x20851,x20852)+E(f685(x20853,x20851,x20854),f685(x20853,x20852,x20854))
% 18.77/18.52 [2086]~E(x20861,x20862)+E(f685(x20863,x20864,x20861),f685(x20863,x20864,x20862))
% 18.77/18.52 [2087]~E(x20871,x20872)+E(f474(x20871,x20873,x20874,x20875),f474(x20872,x20873,x20874,x20875))
% 18.77/18.52 [2088]~E(x20881,x20882)+E(f474(x20883,x20881,x20884,x20885),f474(x20883,x20882,x20884,x20885))
% 18.77/18.52 [2089]~E(x20891,x20892)+E(f474(x20893,x20894,x20891,x20895),f474(x20893,x20894,x20892,x20895))
% 18.77/18.52 [2090]~E(x20901,x20902)+E(f474(x20903,x20904,x20905,x20901),f474(x20903,x20904,x20905,x20902))
% 18.77/18.52 [2091]~E(x20911,x20912)+E(f732(x20911,x20913,x20914,x20915),f732(x20912,x20913,x20914,x20915))
% 18.77/18.52 [2092]~E(x20921,x20922)+E(f732(x20923,x20921,x20924,x20925),f732(x20923,x20922,x20924,x20925))
% 18.77/18.52 [2093]~E(x20931,x20932)+E(f732(x20933,x20934,x20931,x20935),f732(x20933,x20934,x20932,x20935))
% 18.77/18.52 [2094]~E(x20941,x20942)+E(f732(x20943,x20944,x20945,x20941),f732(x20943,x20944,x20945,x20942))
% 18.77/18.52 [2095]~E(x20951,x20952)+E(f424(x20951,x20953,x20954),f424(x20952,x20953,x20954))
% 18.77/18.52 [2096]~E(x20961,x20962)+E(f424(x20963,x20961,x20964),f424(x20963,x20962,x20964))
% 18.77/18.52 [2097]~E(x20971,x20972)+E(f424(x20973,x20974,x20971),f424(x20973,x20974,x20972))
% 18.77/18.52 [2098]~E(x20981,x20982)+E(f482(x20981,x20983,x20984,x20985,x20986),f482(x20982,x20983,x20984,x20985,x20986))
% 18.77/18.52 [2099]~E(x20991,x20992)+E(f482(x20993,x20991,x20994,x20995,x20996),f482(x20993,x20992,x20994,x20995,x20996))
% 18.77/18.52 [2100]~E(x21001,x21002)+E(f482(x21003,x21004,x21001,x21005,x21006),f482(x21003,x21004,x21002,x21005,x21006))
% 18.77/18.52 [2101]~E(x21011,x21012)+E(f482(x21013,x21014,x21015,x21011,x21016),f482(x21013,x21014,x21015,x21012,x21016))
% 18.77/18.52 [2102]~E(x21021,x21022)+E(f482(x21023,x21024,x21025,x21026,x21021),f482(x21023,x21024,x21025,x21026,x21022))
% 18.77/18.52 [2103]~E(x21031,x21032)+E(f395(x21031,x21033,x21034,x21035),f395(x21032,x21033,x21034,x21035))
% 18.77/18.52 [2104]~E(x21041,x21042)+E(f395(x21043,x21041,x21044,x21045),f395(x21043,x21042,x21044,x21045))
% 18.77/18.52 [2105]~E(x21051,x21052)+E(f395(x21053,x21054,x21051,x21055),f395(x21053,x21054,x21052,x21055))
% 18.77/18.52 [2106]~E(x21061,x21062)+E(f395(x21063,x21064,x21065,x21061),f395(x21063,x21064,x21065,x21062))
% 18.77/18.52 [2107]~E(x21071,x21072)+E(f397(x21071,x21073),f397(x21072,x21073))
% 18.77/18.52 [2108]~E(x21081,x21082)+E(f397(x21083,x21081),f397(x21083,x21082))
% 18.77/18.52 [2109]~E(x21091,x21092)+E(f382(x21091,x21093),f382(x21092,x21093))
% 18.77/18.52 [2110]~E(x21101,x21102)+E(f382(x21103,x21101),f382(x21103,x21102))
% 18.77/18.52 [2111]~E(x21111,x21112)+E(f670(x21111,x21113,x21114),f670(x21112,x21113,x21114))
% 18.77/18.52 [2112]~E(x21121,x21122)+E(f670(x21123,x21121,x21124),f670(x21123,x21122,x21124))
% 18.77/18.52 [2113]~E(x21131,x21132)+E(f670(x21133,x21134,x21131),f670(x21133,x21134,x21132))
% 18.77/18.52 [2114]~E(x21141,x21142)+E(f748(x21141,x21143),f748(x21142,x21143))
% 18.77/18.52 [2115]~E(x21151,x21152)+E(f748(x21153,x21151),f748(x21153,x21152))
% 18.77/18.52 [2116]~E(x21161,x21162)+E(f627(x21161,x21163,x21164,x21165),f627(x21162,x21163,x21164,x21165))
% 18.77/18.52 [2117]~E(x21171,x21172)+E(f627(x21173,x21171,x21174,x21175),f627(x21173,x21172,x21174,x21175))
% 18.77/18.52 [2118]~E(x21181,x21182)+E(f627(x21183,x21184,x21181,x21185),f627(x21183,x21184,x21182,x21185))
% 18.77/18.52 [2119]~E(x21191,x21192)+E(f627(x21193,x21194,x21195,x21191),f627(x21193,x21194,x21195,x21192))
% 18.77/18.52 [2120]~E(x21201,x21202)+E(f380(x21201,x21203),f380(x21202,x21203))
% 18.77/18.52 [2121]~E(x21211,x21212)+E(f380(x21213,x21211),f380(x21213,x21212))
% 18.77/18.52 [2122]~E(x21221,x21222)+E(f795(x21221,x21223,x21224),f795(x21222,x21223,x21224))
% 18.77/18.52 [2123]~E(x21231,x21232)+E(f795(x21233,x21231,x21234),f795(x21233,x21232,x21234))
% 18.77/18.52 [2124]~E(x21241,x21242)+E(f795(x21243,x21244,x21241),f795(x21243,x21244,x21242))
% 18.77/18.52 [2125]~E(x21251,x21252)+E(f132(x21251,x21253),f132(x21252,x21253))
% 18.77/18.52 [2126]~E(x21261,x21262)+E(f132(x21263,x21261),f132(x21263,x21262))
% 18.77/18.52 [2127]~E(x21271,x21272)+E(f804(x21271,x21273,x21274),f804(x21272,x21273,x21274))
% 18.77/18.52 [2128]~E(x21281,x21282)+E(f804(x21283,x21281,x21284),f804(x21283,x21282,x21284))
% 18.77/18.52 [2129]~E(x21291,x21292)+E(f804(x21293,x21294,x21291),f804(x21293,x21294,x21292))
% 18.77/18.52 [2130]~E(x21301,x21302)+E(f391(x21301,x21303),f391(x21302,x21303))
% 18.77/18.52 [2131]~E(x21311,x21312)+E(f391(x21313,x21311),f391(x21313,x21312))
% 18.77/18.52 [2132]~E(x21321,x21322)+E(f500(x21321,x21323,x21324,x21325,x21326),f500(x21322,x21323,x21324,x21325,x21326))
% 18.77/18.52 [2133]~E(x21331,x21332)+E(f500(x21333,x21331,x21334,x21335,x21336),f500(x21333,x21332,x21334,x21335,x21336))
% 18.77/18.52 [2134]~E(x21341,x21342)+E(f500(x21343,x21344,x21341,x21345,x21346),f500(x21343,x21344,x21342,x21345,x21346))
% 18.77/18.52 [2135]~E(x21351,x21352)+E(f500(x21353,x21354,x21355,x21351,x21356),f500(x21353,x21354,x21355,x21352,x21356))
% 18.77/18.52 [2136]~E(x21361,x21362)+E(f500(x21363,x21364,x21365,x21366,x21361),f500(x21363,x21364,x21365,x21366,x21362))
% 18.77/18.52 [2137]~E(x21371,x21372)+E(f409(x21371,x21373,x21374),f409(x21372,x21373,x21374))
% 18.77/18.52 [2138]~E(x21381,x21382)+E(f409(x21383,x21381,x21384),f409(x21383,x21382,x21384))
% 18.77/18.52 [2139]~E(x21391,x21392)+E(f409(x21393,x21394,x21391),f409(x21393,x21394,x21392))
% 18.77/18.52 [2140]~E(x21401,x21402)+E(f342(x21401,x21403,x21404,x21405),f342(x21402,x21403,x21404,x21405))
% 18.77/18.52 [2141]~E(x21411,x21412)+E(f342(x21413,x21411,x21414,x21415),f342(x21413,x21412,x21414,x21415))
% 18.77/18.52 [2142]~E(x21421,x21422)+E(f342(x21423,x21424,x21421,x21425),f342(x21423,x21424,x21422,x21425))
% 18.77/18.52 [2143]~E(x21431,x21432)+E(f342(x21433,x21434,x21435,x21431),f342(x21433,x21434,x21435,x21432))
% 18.77/18.52 [2144]~E(x21441,x21442)+E(f570(x21441,x21443,x21444,x21445,x21446,x21447),f570(x21442,x21443,x21444,x21445,x21446,x21447))
% 18.77/18.52 [2145]~E(x21451,x21452)+E(f570(x21453,x21451,x21454,x21455,x21456,x21457),f570(x21453,x21452,x21454,x21455,x21456,x21457))
% 18.77/18.52 [2146]~E(x21461,x21462)+E(f570(x21463,x21464,x21461,x21465,x21466,x21467),f570(x21463,x21464,x21462,x21465,x21466,x21467))
% 18.77/18.52 [2147]~E(x21471,x21472)+E(f570(x21473,x21474,x21475,x21471,x21476,x21477),f570(x21473,x21474,x21475,x21472,x21476,x21477))
% 18.77/18.52 [2148]~E(x21481,x21482)+E(f570(x21483,x21484,x21485,x21486,x21481,x21487),f570(x21483,x21484,x21485,x21486,x21482,x21487))
% 18.77/18.52 [2149]~E(x21491,x21492)+E(f570(x21493,x21494,x21495,x21496,x21497,x21491),f570(x21493,x21494,x21495,x21496,x21497,x21492))
% 18.77/18.52 [2150]~E(x21501,x21502)+E(f590(x21501,x21503,x21504),f590(x21502,x21503,x21504))
% 18.77/18.52 [2151]~E(x21511,x21512)+E(f590(x21513,x21511,x21514),f590(x21513,x21512,x21514))
% 18.77/18.52 [2152]~E(x21521,x21522)+E(f590(x21523,x21524,x21521),f590(x21523,x21524,x21522))
% 18.77/18.52 [2153]~E(x21531,x21532)+E(f390(x21531,x21533),f390(x21532,x21533))
% 18.77/18.52 [2154]~E(x21541,x21542)+E(f390(x21543,x21541),f390(x21543,x21542))
% 18.77/18.52 [2155]~E(x21551,x21552)+E(f688(x21551,x21553,x21554,x21555),f688(x21552,x21553,x21554,x21555))
% 18.77/18.52 [2156]~E(x21561,x21562)+E(f688(x21563,x21561,x21564,x21565),f688(x21563,x21562,x21564,x21565))
% 18.77/18.52 [2157]~E(x21571,x21572)+E(f688(x21573,x21574,x21571,x21575),f688(x21573,x21574,x21572,x21575))
% 18.77/18.52 [2158]~E(x21581,x21582)+E(f688(x21583,x21584,x21585,x21581),f688(x21583,x21584,x21585,x21582))
% 18.77/18.52 [2159]~E(x21591,x21592)+E(f644(x21591,x21593,x21594,x21595),f644(x21592,x21593,x21594,x21595))
% 18.77/18.52 [2160]~E(x21601,x21602)+E(f644(x21603,x21601,x21604,x21605),f644(x21603,x21602,x21604,x21605))
% 18.77/18.52 [2161]~E(x21611,x21612)+E(f644(x21613,x21614,x21611,x21615),f644(x21613,x21614,x21612,x21615))
% 18.77/18.52 [2162]~E(x21621,x21622)+E(f644(x21623,x21624,x21625,x21621),f644(x21623,x21624,x21625,x21622))
% 18.77/18.52 [2163]~E(x21631,x21632)+E(f720(x21631,x21633,x21634),f720(x21632,x21633,x21634))
% 18.77/18.52 [2164]~E(x21641,x21642)+E(f720(x21643,x21641,x21644),f720(x21643,x21642,x21644))
% 18.77/18.52 [2165]~E(x21651,x21652)+E(f720(x21653,x21654,x21651),f720(x21653,x21654,x21652))
% 18.77/18.52 [2166]~E(x21661,x21662)+E(f721(x21661,x21663,x21664,x21665),f721(x21662,x21663,x21664,x21665))
% 18.77/18.52 [2167]~E(x21671,x21672)+E(f721(x21673,x21671,x21674,x21675),f721(x21673,x21672,x21674,x21675))
% 18.77/18.52 [2168]~E(x21681,x21682)+E(f721(x21683,x21684,x21681,x21685),f721(x21683,x21684,x21682,x21685))
% 18.77/18.52 [2169]~E(x21691,x21692)+E(f721(x21693,x21694,x21695,x21691),f721(x21693,x21694,x21695,x21692))
% 18.77/18.52 [2170]~E(x21701,x21702)+E(f793(x21701,x21703,x21704),f793(x21702,x21703,x21704))
% 18.77/18.52 [2171]~E(x21711,x21712)+E(f793(x21713,x21711,x21714),f793(x21713,x21712,x21714))
% 18.77/18.52 [2172]~E(x21721,x21722)+E(f793(x21723,x21724,x21721),f793(x21723,x21724,x21722))
% 18.77/18.52 [2173]~E(x21731,x21732)+E(f306(x21731,x21733),f306(x21732,x21733))
% 18.77/18.52 [2174]~E(x21741,x21742)+E(f306(x21743,x21741),f306(x21743,x21742))
% 18.77/18.52 [2175]~E(x21751,x21752)+E(f731(x21751,x21753,x21754,x21755),f731(x21752,x21753,x21754,x21755))
% 18.77/18.52 [2176]~E(x21761,x21762)+E(f731(x21763,x21761,x21764,x21765),f731(x21763,x21762,x21764,x21765))
% 18.77/18.52 [2177]~E(x21771,x21772)+E(f731(x21773,x21774,x21771,x21775),f731(x21773,x21774,x21772,x21775))
% 18.77/18.52 [2178]~E(x21781,x21782)+E(f731(x21783,x21784,x21785,x21781),f731(x21783,x21784,x21785,x21782))
% 18.77/18.52 [2179]~E(x21791,x21792)+E(f381(x21791),f381(x21792))
% 18.77/18.52 [2180]~E(x21801,x21802)+E(f710(x21801,x21803),f710(x21802,x21803))
% 18.77/18.52 [2181]~E(x21811,x21812)+E(f710(x21813,x21811),f710(x21813,x21812))
% 18.77/18.52 [2182]~E(x21821,x21822)+E(f508(x21821,x21823,x21824,x21825),f508(x21822,x21823,x21824,x21825))
% 18.77/18.52 [2183]~E(x21831,x21832)+E(f508(x21833,x21831,x21834,x21835),f508(x21833,x21832,x21834,x21835))
% 18.77/18.52 [2184]~E(x21841,x21842)+E(f508(x21843,x21844,x21841,x21845),f508(x21843,x21844,x21842,x21845))
% 18.77/18.52 [2185]~E(x21851,x21852)+E(f508(x21853,x21854,x21855,x21851),f508(x21853,x21854,x21855,x21852))
% 18.77/18.52 [2186]~E(x21861,x21862)+E(f464(x21861),f464(x21862))
% 18.77/18.52 [2187]~E(x21871,x21872)+E(f715(x21871,x21873,x21874),f715(x21872,x21873,x21874))
% 18.77/18.52 [2188]~E(x21881,x21882)+E(f715(x21883,x21881,x21884),f715(x21883,x21882,x21884))
% 18.77/18.52 [2189]~E(x21891,x21892)+E(f715(x21893,x21894,x21891),f715(x21893,x21894,x21892))
% 18.77/18.52 [2190]~E(x21901,x21902)+E(f355(x21901,x21903,x21904,x21905),f355(x21902,x21903,x21904,x21905))
% 18.77/18.52 [2191]~E(x21911,x21912)+E(f355(x21913,x21911,x21914,x21915),f355(x21913,x21912,x21914,x21915))
% 18.77/18.52 [2192]~E(x21921,x21922)+E(f355(x21923,x21924,x21921,x21925),f355(x21923,x21924,x21922,x21925))
% 18.77/18.52 [2193]~E(x21931,x21932)+E(f355(x21933,x21934,x21935,x21931),f355(x21933,x21934,x21935,x21932))
% 18.77/18.52 [2194]~E(x21941,x21942)+E(f652(x21941,x21943,x21944),f652(x21942,x21943,x21944))
% 18.77/18.52 [2195]~E(x21951,x21952)+E(f652(x21953,x21951,x21954),f652(x21953,x21952,x21954))
% 18.77/18.52 [2196]~E(x21961,x21962)+E(f652(x21963,x21964,x21961),f652(x21963,x21964,x21962))
% 18.77/18.52 [2197]~E(x21971,x21972)+E(f619(x21971,x21973,x21974),f619(x21972,x21973,x21974))
% 18.77/18.52 [2198]~E(x21981,x21982)+E(f619(x21983,x21981,x21984),f619(x21983,x21982,x21984))
% 18.77/18.52 [2199]~E(x21991,x21992)+E(f619(x21993,x21994,x21991),f619(x21993,x21994,x21992))
% 18.77/18.52 [2200]~E(x22001,x22002)+E(f234(x22001,x22003),f234(x22002,x22003))
% 18.77/18.52 [2201]~E(x22011,x22012)+E(f234(x22013,x22011),f234(x22013,x22012))
% 18.77/18.52 [2202]~E(x22021,x22022)+E(f686(x22021,x22023,x22024),f686(x22022,x22023,x22024))
% 18.77/18.52 [2203]~E(x22031,x22032)+E(f686(x22033,x22031,x22034),f686(x22033,x22032,x22034))
% 18.77/18.52 [2204]~E(x22041,x22042)+E(f686(x22043,x22044,x22041),f686(x22043,x22044,x22042))
% 18.77/18.52 [2205]~E(x22051,x22052)+E(f402(x22051,x22053),f402(x22052,x22053))
% 18.77/18.52 [2206]~E(x22061,x22062)+E(f402(x22063,x22061),f402(x22063,x22062))
% 18.77/18.52 [2207]~E(x22071,x22072)+E(f407(x22071,x22073,x22074),f407(x22072,x22073,x22074))
% 18.77/18.52 [2208]~E(x22081,x22082)+E(f407(x22083,x22081,x22084),f407(x22083,x22082,x22084))
% 18.77/18.52 [2209]~E(x22091,x22092)+E(f407(x22093,x22094,x22091),f407(x22093,x22094,x22092))
% 18.77/18.52 [2210]~E(x22101,x22102)+E(f799(x22101,x22103,x22104),f799(x22102,x22103,x22104))
% 18.77/18.52 [2211]~E(x22111,x22112)+E(f799(x22113,x22111,x22114),f799(x22113,x22112,x22114))
% 18.77/18.52 [2212]~E(x22121,x22122)+E(f799(x22123,x22124,x22121),f799(x22123,x22124,x22122))
% 18.77/18.52 [2213]~E(x22131,x22132)+E(f522(x22131,x22133,x22134,x22135),f522(x22132,x22133,x22134,x22135))
% 18.77/18.52 [2214]~E(x22141,x22142)+E(f522(x22143,x22141,x22144,x22145),f522(x22143,x22142,x22144,x22145))
% 18.77/18.52 [2215]~E(x22151,x22152)+E(f522(x22153,x22154,x22151,x22155),f522(x22153,x22154,x22152,x22155))
% 18.77/18.52 [2216]~E(x22161,x22162)+E(f522(x22163,x22164,x22165,x22161),f522(x22163,x22164,x22165,x22162))
% 18.77/18.52 [2217]~E(x22171,x22172)+E(f548(x22171,x22173,x22174,x22175,x22176),f548(x22172,x22173,x22174,x22175,x22176))
% 18.77/18.52 [2218]~E(x22181,x22182)+E(f548(x22183,x22181,x22184,x22185,x22186),f548(x22183,x22182,x22184,x22185,x22186))
% 18.77/18.52 [2219]~E(x22191,x22192)+E(f548(x22193,x22194,x22191,x22195,x22196),f548(x22193,x22194,x22192,x22195,x22196))
% 18.77/18.52 [2220]~E(x22201,x22202)+E(f548(x22203,x22204,x22205,x22201,x22206),f548(x22203,x22204,x22205,x22202,x22206))
% 18.77/18.52 [2221]~E(x22211,x22212)+E(f548(x22213,x22214,x22215,x22216,x22211),f548(x22213,x22214,x22215,x22216,x22212))
% 18.77/18.52 [2222]~E(x22221,x22222)+E(f820(x22221,x22223,x22224),f820(x22222,x22223,x22224))
% 18.77/18.52 [2223]~E(x22231,x22232)+E(f820(x22233,x22231,x22234),f820(x22233,x22232,x22234))
% 18.77/18.52 [2224]~E(x22241,x22242)+E(f820(x22243,x22244,x22241),f820(x22243,x22244,x22242))
% 18.77/18.52 [2225]~E(x22251,x22252)+E(f664(x22251,x22253,x22254,x22255,x22256),f664(x22252,x22253,x22254,x22255,x22256))
% 18.77/18.52 [2226]~E(x22261,x22262)+E(f664(x22263,x22261,x22264,x22265,x22266),f664(x22263,x22262,x22264,x22265,x22266))
% 18.77/18.52 [2227]~E(x22271,x22272)+E(f664(x22273,x22274,x22271,x22275,x22276),f664(x22273,x22274,x22272,x22275,x22276))
% 18.77/18.52 [2228]~E(x22281,x22282)+E(f664(x22283,x22284,x22285,x22281,x22286),f664(x22283,x22284,x22285,x22282,x22286))
% 18.77/18.52 [2229]~E(x22291,x22292)+E(f664(x22293,x22294,x22295,x22296,x22291),f664(x22293,x22294,x22295,x22296,x22292))
% 18.77/18.52 [2230]~E(x22301,x22302)+E(f384(x22301,x22303,x22304),f384(x22302,x22303,x22304))
% 18.77/18.52 [2231]~E(x22311,x22312)+E(f384(x22313,x22311,x22314),f384(x22313,x22312,x22314))
% 18.77/18.52 [2232]~E(x22321,x22322)+E(f384(x22323,x22324,x22321),f384(x22323,x22324,x22322))
% 18.77/18.52 [2233]~E(x22331,x22332)+E(f330(x22331,x22333),f330(x22332,x22333))
% 18.77/18.52 [2234]~E(x22341,x22342)+E(f330(x22343,x22341),f330(x22343,x22342))
% 18.77/18.52 [2235]~E(x22351,x22352)+E(f630(x22351,x22353,x22354,x22355,x22356,x22357,x22358,x22359),f630(x22352,x22353,x22354,x22355,x22356,x22357,x22358,x22359))
% 18.77/18.52 [2236]~E(x22361,x22362)+E(f630(x22363,x22361,x22364,x22365,x22366,x22367,x22368,x22369),f630(x22363,x22362,x22364,x22365,x22366,x22367,x22368,x22369))
% 18.77/18.52 [2237]~E(x22371,x22372)+E(f630(x22373,x22374,x22371,x22375,x22376,x22377,x22378,x22379),f630(x22373,x22374,x22372,x22375,x22376,x22377,x22378,x22379))
% 18.77/18.52 [2238]~E(x22381,x22382)+E(f630(x22383,x22384,x22385,x22381,x22386,x22387,x22388,x22389),f630(x22383,x22384,x22385,x22382,x22386,x22387,x22388,x22389))
% 18.77/18.52 [2239]~E(x22391,x22392)+E(f630(x22393,x22394,x22395,x22396,x22391,x22397,x22398,x22399),f630(x22393,x22394,x22395,x22396,x22392,x22397,x22398,x22399))
% 18.77/18.52 [2240]~E(x22401,x22402)+E(f630(x22403,x22404,x22405,x22406,x22407,x22401,x22408,x22409),f630(x22403,x22404,x22405,x22406,x22407,x22402,x22408,x22409))
% 18.77/18.52 [2241]~E(x22411,x22412)+E(f630(x22413,x22414,x22415,x22416,x22417,x22418,x22411,x22419),f630(x22413,x22414,x22415,x22416,x22417,x22418,x22412,x22419))
% 18.77/18.52 [2242]~E(x22421,x22422)+E(f630(x22423,x22424,x22425,x22426,x22427,x22428,x22429,x22421),f630(x22423,x22424,x22425,x22426,x22427,x22428,x22429,x22422))
% 18.77/18.52 [2243]~E(x22431,x22432)+E(f462(x22431,x22433,x22434,x22435),f462(x22432,x22433,x22434,x22435))
% 18.77/18.52 [2244]~E(x22441,x22442)+E(f462(x22443,x22441,x22444,x22445),f462(x22443,x22442,x22444,x22445))
% 18.77/18.52 [2245]~E(x22451,x22452)+E(f462(x22453,x22454,x22451,x22455),f462(x22453,x22454,x22452,x22455))
% 18.77/18.52 [2246]~E(x22461,x22462)+E(f462(x22463,x22464,x22465,x22461),f462(x22463,x22464,x22465,x22462))
% 18.77/18.52 [2247]~E(x22471,x22472)+E(f440(x22471,x22473),f440(x22472,x22473))
% 18.77/18.52 [2248]~E(x22481,x22482)+E(f440(x22483,x22481),f440(x22483,x22482))
% 18.77/18.52 [2249]~E(x22491,x22492)+E(f733(x22491,x22493,x22494,x22495),f733(x22492,x22493,x22494,x22495))
% 18.77/18.52 [2250]~E(x22501,x22502)+E(f733(x22503,x22501,x22504,x22505),f733(x22503,x22502,x22504,x22505))
% 18.77/18.52 [2251]~E(x22511,x22512)+E(f733(x22513,x22514,x22511,x22515),f733(x22513,x22514,x22512,x22515))
% 18.77/18.52 [2252]~E(x22521,x22522)+E(f733(x22523,x22524,x22525,x22521),f733(x22523,x22524,x22525,x22522))
% 18.77/18.52 [2253]~E(x22531,x22532)+E(f481(x22531,x22533,x22534,x22535,x22536),f481(x22532,x22533,x22534,x22535,x22536))
% 18.77/18.52 [2254]~E(x22541,x22542)+E(f481(x22543,x22541,x22544,x22545,x22546),f481(x22543,x22542,x22544,x22545,x22546))
% 18.77/18.52 [2255]~E(x22551,x22552)+E(f481(x22553,x22554,x22551,x22555,x22556),f481(x22553,x22554,x22552,x22555,x22556))
% 18.77/18.52 [2256]~E(x22561,x22562)+E(f481(x22563,x22564,x22565,x22561,x22566),f481(x22563,x22564,x22565,x22562,x22566))
% 18.77/18.52 [2257]~E(x22571,x22572)+E(f481(x22573,x22574,x22575,x22576,x22571),f481(x22573,x22574,x22575,x22576,x22572))
% 18.77/18.52 [2258]~E(x22581,x22582)+E(f679(x22581,x22583,x22584,x22585),f679(x22582,x22583,x22584,x22585))
% 18.77/18.52 [2259]~E(x22591,x22592)+E(f679(x22593,x22591,x22594,x22595),f679(x22593,x22592,x22594,x22595))
% 18.77/18.52 [2260]~E(x22601,x22602)+E(f679(x22603,x22604,x22601,x22605),f679(x22603,x22604,x22602,x22605))
% 18.77/18.52 [2261]~E(x22611,x22612)+E(f679(x22613,x22614,x22615,x22611),f679(x22613,x22614,x22615,x22612))
% 18.77/18.52 [2262]~E(x22621,x22622)+E(f309(x22621,x22623,x22624),f309(x22622,x22623,x22624))
% 18.77/18.52 [2263]~E(x22631,x22632)+E(f309(x22633,x22631,x22634),f309(x22633,x22632,x22634))
% 18.77/18.52 [2264]~E(x22641,x22642)+E(f309(x22643,x22644,x22641),f309(x22643,x22644,x22642))
% 18.77/18.52 [2265]~E(x22651,x22652)+E(f190(x22651,x22653,x22654,x22655),f190(x22652,x22653,x22654,x22655))
% 18.77/18.52 [2266]~E(x22661,x22662)+E(f190(x22663,x22661,x22664,x22665),f190(x22663,x22662,x22664,x22665))
% 18.77/18.52 [2267]~E(x22671,x22672)+E(f190(x22673,x22674,x22671,x22675),f190(x22673,x22674,x22672,x22675))
% 18.77/18.52 [2268]~E(x22681,x22682)+E(f190(x22683,x22684,x22685,x22681),f190(x22683,x22684,x22685,x22682))
% 18.77/18.52 [2269]~E(x22691,x22692)+E(f586(x22691,x22693,x22694,x22695),f586(x22692,x22693,x22694,x22695))
% 18.77/18.52 [2270]~E(x22701,x22702)+E(f586(x22703,x22701,x22704,x22705),f586(x22703,x22702,x22704,x22705))
% 18.77/18.52 [2271]~E(x22711,x22712)+E(f586(x22713,x22714,x22711,x22715),f586(x22713,x22714,x22712,x22715))
% 18.77/18.52 [2272]~E(x22721,x22722)+E(f586(x22723,x22724,x22725,x22721),f586(x22723,x22724,x22725,x22722))
% 18.77/18.52 [2273]~E(x22731,x22732)+E(f448(x22731,x22733),f448(x22732,x22733))
% 18.77/18.52 [2274]~E(x22741,x22742)+E(f448(x22743,x22741),f448(x22743,x22742))
% 18.77/18.52 [2275]~E(x22751,x22752)+E(f676(x22751,x22753,x22754),f676(x22752,x22753,x22754))
% 18.77/18.52 [2276]~E(x22761,x22762)+E(f676(x22763,x22761,x22764),f676(x22763,x22762,x22764))
% 18.77/18.52 [2277]~E(x22771,x22772)+E(f676(x22773,x22774,x22771),f676(x22773,x22774,x22772))
% 18.77/18.52 [2278]~E(x22781,x22782)+E(f219(x22781,x22783,x22784,x22785,x22786),f219(x22782,x22783,x22784,x22785,x22786))
% 18.77/18.52 [2279]~E(x22791,x22792)+E(f219(x22793,x22791,x22794,x22795,x22796),f219(x22793,x22792,x22794,x22795,x22796))
% 18.77/18.52 [2280]~E(x22801,x22802)+E(f219(x22803,x22804,x22801,x22805,x22806),f219(x22803,x22804,x22802,x22805,x22806))
% 18.77/18.52 [2281]~E(x22811,x22812)+E(f219(x22813,x22814,x22815,x22811,x22816),f219(x22813,x22814,x22815,x22812,x22816))
% 18.77/18.52 [2282]~E(x22821,x22822)+E(f219(x22823,x22824,x22825,x22826,x22821),f219(x22823,x22824,x22825,x22826,x22822))
% 18.77/18.52 [2283]~E(x22831,x22832)+E(f538(x22831,x22833,x22834,x22835,x22836,x22837,x22838),f538(x22832,x22833,x22834,x22835,x22836,x22837,x22838))
% 18.77/18.52 [2284]~E(x22841,x22842)+E(f538(x22843,x22841,x22844,x22845,x22846,x22847,x22848),f538(x22843,x22842,x22844,x22845,x22846,x22847,x22848))
% 18.77/18.52 [2285]~E(x22851,x22852)+E(f538(x22853,x22854,x22851,x22855,x22856,x22857,x22858),f538(x22853,x22854,x22852,x22855,x22856,x22857,x22858))
% 18.77/18.52 [2286]~E(x22861,x22862)+E(f538(x22863,x22864,x22865,x22861,x22866,x22867,x22868),f538(x22863,x22864,x22865,x22862,x22866,x22867,x22868))
% 18.77/18.52 [2287]~E(x22871,x22872)+E(f538(x22873,x22874,x22875,x22876,x22871,x22877,x22878),f538(x22873,x22874,x22875,x22876,x22872,x22877,x22878))
% 18.77/18.52 [2288]~E(x22881,x22882)+E(f538(x22883,x22884,x22885,x22886,x22887,x22881,x22888),f538(x22883,x22884,x22885,x22886,x22887,x22882,x22888))
% 18.77/18.52 [2289]~E(x22891,x22892)+E(f538(x22893,x22894,x22895,x22896,x22897,x22898,x22891),f538(x22893,x22894,x22895,x22896,x22897,x22898,x22892))
% 18.77/18.52 [2290]~E(x22901,x22902)+E(f401(x22901,x22903),f401(x22902,x22903))
% 18.77/18.52 [2291]~E(x22911,x22912)+E(f401(x22913,x22911),f401(x22913,x22912))
% 18.77/18.52 [2292]~E(x22921,x22922)+E(f194(x22921),f194(x22922))
% 18.77/18.52 [2293]~E(x22931,x22932)+E(f536(x22931,x22933,x22934,x22935,x22936),f536(x22932,x22933,x22934,x22935,x22936))
% 18.77/18.52 [2294]~E(x22941,x22942)+E(f536(x22943,x22941,x22944,x22945,x22946),f536(x22943,x22942,x22944,x22945,x22946))
% 18.77/18.52 [2295]~E(x22951,x22952)+E(f536(x22953,x22954,x22951,x22955,x22956),f536(x22953,x22954,x22952,x22955,x22956))
% 18.77/18.52 [2296]~E(x22961,x22962)+E(f536(x22963,x22964,x22965,x22961,x22966),f536(x22963,x22964,x22965,x22962,x22966))
% 18.77/18.52 [2297]~E(x22971,x22972)+E(f536(x22973,x22974,x22975,x22976,x22971),f536(x22973,x22974,x22975,x22976,x22972))
% 18.77/18.52 [2298]~E(x22981,x22982)+E(f667(x22981,x22983,x22984,x22985,x22986),f667(x22982,x22983,x22984,x22985,x22986))
% 18.77/18.52 [2299]~E(x22991,x22992)+E(f667(x22993,x22991,x22994,x22995,x22996),f667(x22993,x22992,x22994,x22995,x22996))
% 18.77/18.52 [2300]~E(x23001,x23002)+E(f667(x23003,x23004,x23001,x23005,x23006),f667(x23003,x23004,x23002,x23005,x23006))
% 18.77/18.52 [2301]~E(x23011,x23012)+E(f667(x23013,x23014,x23015,x23011,x23016),f667(x23013,x23014,x23015,x23012,x23016))
% 18.77/18.52 [2302]~E(x23021,x23022)+E(f667(x23023,x23024,x23025,x23026,x23021),f667(x23023,x23024,x23025,x23026,x23022))
% 18.77/18.52 [2303]~E(x23031,x23032)+E(f372(x23031,x23033),f372(x23032,x23033))
% 18.77/18.52 [2304]~E(x23041,x23042)+E(f372(x23043,x23041),f372(x23043,x23042))
% 18.77/18.52 [2305]~E(x23051,x23052)+E(f814(x23051,x23053,x23054,x23055,x23056,x23057),f814(x23052,x23053,x23054,x23055,x23056,x23057))
% 18.77/18.52 [2306]~E(x23061,x23062)+E(f814(x23063,x23061,x23064,x23065,x23066,x23067),f814(x23063,x23062,x23064,x23065,x23066,x23067))
% 18.77/18.52 [2307]~E(x23071,x23072)+E(f814(x23073,x23074,x23071,x23075,x23076,x23077),f814(x23073,x23074,x23072,x23075,x23076,x23077))
% 18.77/18.52 [2308]~E(x23081,x23082)+E(f814(x23083,x23084,x23085,x23081,x23086,x23087),f814(x23083,x23084,x23085,x23082,x23086,x23087))
% 18.77/18.52 [2309]~E(x23091,x23092)+E(f814(x23093,x23094,x23095,x23096,x23091,x23097),f814(x23093,x23094,x23095,x23096,x23092,x23097))
% 18.77/18.52 [2310]~E(x23101,x23102)+E(f814(x23103,x23104,x23105,x23106,x23107,x23101),f814(x23103,x23104,x23105,x23106,x23107,x23102))
% 18.77/18.52 [2311]~E(x23111,x23112)+E(f780(x23111,x23113,x23114),f780(x23112,x23113,x23114))
% 18.77/18.52 [2312]~E(x23121,x23122)+E(f780(x23123,x23121,x23124),f780(x23123,x23122,x23124))
% 18.77/18.52 [2313]~E(x23131,x23132)+E(f780(x23133,x23134,x23131),f780(x23133,x23134,x23132))
% 18.77/18.52 [2314]~E(x23141,x23142)+E(f612(x23141),f612(x23142))
% 18.77/18.52 [2315]~E(x23151,x23152)+E(f123(x23151),f123(x23152))
% 18.77/18.52 [2316]~E(x23161,x23162)+E(f789(x23161,x23163,x23164),f789(x23162,x23163,x23164))
% 18.77/18.52 [2317]~E(x23171,x23172)+E(f789(x23173,x23171,x23174),f789(x23173,x23172,x23174))
% 18.77/18.52 [2318]~E(x23181,x23182)+E(f789(x23183,x23184,x23181),f789(x23183,x23184,x23182))
% 18.77/18.52 [2319]~E(x23191,x23192)+E(f747(x23191,x23193,x23194),f747(x23192,x23193,x23194))
% 18.77/18.52 [2320]~E(x23201,x23202)+E(f747(x23203,x23201,x23204),f747(x23203,x23202,x23204))
% 18.77/18.52 [2321]~E(x23211,x23212)+E(f747(x23213,x23214,x23211),f747(x23213,x23214,x23212))
% 18.77/18.52 [2322]~E(x23221,x23222)+E(f308(x23221,x23223,x23224),f308(x23222,x23223,x23224))
% 18.77/18.52 [2323]~E(x23231,x23232)+E(f308(x23233,x23231,x23234),f308(x23233,x23232,x23234))
% 18.77/18.52 [2324]~E(x23241,x23242)+E(f308(x23243,x23244,x23241),f308(x23243,x23244,x23242))
% 18.77/18.52 [2325]~E(x23251,x23252)+E(f332(x23251),f332(x23252))
% 18.77/18.52 [2326]~E(x23261,x23262)+E(f843(x23261,x23263),f843(x23262,x23263))
% 18.77/18.52 [2327]~E(x23271,x23272)+E(f843(x23273,x23271),f843(x23273,x23272))
% 18.77/18.52 [2328]~E(x23281,x23282)+E(f511(x23281,x23283,x23284,x23285,x23286),f511(x23282,x23283,x23284,x23285,x23286))
% 18.77/18.52 [2329]~E(x23291,x23292)+E(f511(x23293,x23291,x23294,x23295,x23296),f511(x23293,x23292,x23294,x23295,x23296))
% 18.77/18.52 [2330]~E(x23301,x23302)+E(f511(x23303,x23304,x23301,x23305,x23306),f511(x23303,x23304,x23302,x23305,x23306))
% 18.77/18.52 [2331]~E(x23311,x23312)+E(f511(x23313,x23314,x23315,x23311,x23316),f511(x23313,x23314,x23315,x23312,x23316))
% 18.77/18.52 [2332]~E(x23321,x23322)+E(f511(x23323,x23324,x23325,x23326,x23321),f511(x23323,x23324,x23325,x23326,x23322))
% 18.77/18.52 [2333]~E(x23331,x23332)+E(f429(x23331,x23333,x23334,x23335,x23336),f429(x23332,x23333,x23334,x23335,x23336))
% 18.77/18.52 [2334]~E(x23341,x23342)+E(f429(x23343,x23341,x23344,x23345,x23346),f429(x23343,x23342,x23344,x23345,x23346))
% 18.77/18.52 [2335]~E(x23351,x23352)+E(f429(x23353,x23354,x23351,x23355,x23356),f429(x23353,x23354,x23352,x23355,x23356))
% 18.77/18.52 [2336]~E(x23361,x23362)+E(f429(x23363,x23364,x23365,x23361,x23366),f429(x23363,x23364,x23365,x23362,x23366))
% 18.77/18.52 [2337]~E(x23371,x23372)+E(f429(x23373,x23374,x23375,x23376,x23371),f429(x23373,x23374,x23375,x23376,x23372))
% 18.77/18.52 [2338]~E(x23381,x23382)+E(f350(x23381,x23383,x23384,x23385),f350(x23382,x23383,x23384,x23385))
% 18.77/18.52 [2339]~E(x23391,x23392)+E(f350(x23393,x23391,x23394,x23395),f350(x23393,x23392,x23394,x23395))
% 18.77/18.52 [2340]~E(x23401,x23402)+E(f350(x23403,x23404,x23401,x23405),f350(x23403,x23404,x23402,x23405))
% 18.77/18.52 [2341]~E(x23411,x23412)+E(f350(x23413,x23414,x23415,x23411),f350(x23413,x23414,x23415,x23412))
% 18.77/18.52 [2342]~E(x23421,x23422)+E(f367(x23421,x23423),f367(x23422,x23423))
% 18.77/18.52 [2343]~E(x23431,x23432)+E(f367(x23433,x23431),f367(x23433,x23432))
% 18.77/18.52 [2344]~E(x23441,x23442)+E(f514(x23441),f514(x23442))
% 18.77/18.52 [2345]~E(x23451,x23452)+E(f743(x23451,x23453,x23454),f743(x23452,x23453,x23454))
% 18.77/18.52 [2346]~E(x23461,x23462)+E(f743(x23463,x23461,x23464),f743(x23463,x23462,x23464))
% 18.77/18.52 [2347]~E(x23471,x23472)+E(f743(x23473,x23474,x23471),f743(x23473,x23474,x23472))
% 18.77/18.52 [2348]~E(x23481,x23482)+E(f591(x23481,x23483,x23484,x23485,x23486),f591(x23482,x23483,x23484,x23485,x23486))
% 18.77/18.52 [2349]~E(x23491,x23492)+E(f591(x23493,x23491,x23494,x23495,x23496),f591(x23493,x23492,x23494,x23495,x23496))
% 18.77/18.52 [2350]~E(x23501,x23502)+E(f591(x23503,x23504,x23501,x23505,x23506),f591(x23503,x23504,x23502,x23505,x23506))
% 18.77/18.52 [2351]~E(x23511,x23512)+E(f591(x23513,x23514,x23515,x23511,x23516),f591(x23513,x23514,x23515,x23512,x23516))
% 18.77/18.52 [2352]~E(x23521,x23522)+E(f591(x23523,x23524,x23525,x23526,x23521),f591(x23523,x23524,x23525,x23526,x23522))
% 18.77/18.52 [2353]~E(x23531,x23532)+E(f583(x23531,x23533),f583(x23532,x23533))
% 18.77/18.52 [2354]~E(x23541,x23542)+E(f583(x23543,x23541),f583(x23543,x23542))
% 18.77/18.52 [2355]~E(x23551,x23552)+E(f815(x23551,x23553,x23554,x23555,x23556,x23557),f815(x23552,x23553,x23554,x23555,x23556,x23557))
% 18.77/18.52 [2356]~E(x23561,x23562)+E(f815(x23563,x23561,x23564,x23565,x23566,x23567),f815(x23563,x23562,x23564,x23565,x23566,x23567))
% 18.77/18.52 [2357]~E(x23571,x23572)+E(f815(x23573,x23574,x23571,x23575,x23576,x23577),f815(x23573,x23574,x23572,x23575,x23576,x23577))
% 18.77/18.52 [2358]~E(x23581,x23582)+E(f815(x23583,x23584,x23585,x23581,x23586,x23587),f815(x23583,x23584,x23585,x23582,x23586,x23587))
% 18.77/18.52 [2359]~E(x23591,x23592)+E(f815(x23593,x23594,x23595,x23596,x23591,x23597),f815(x23593,x23594,x23595,x23596,x23592,x23597))
% 18.77/18.52 [2360]~E(x23601,x23602)+E(f815(x23603,x23604,x23605,x23606,x23607,x23601),f815(x23603,x23604,x23605,x23606,x23607,x23602))
% 18.77/18.52 [2361]~E(x23611,x23612)+E(f222(x23611,x23613,x23614,x23615),f222(x23612,x23613,x23614,x23615))
% 18.77/18.52 [2362]~E(x23621,x23622)+E(f222(x23623,x23621,x23624,x23625),f222(x23623,x23622,x23624,x23625))
% 18.77/18.52 [2363]~E(x23631,x23632)+E(f222(x23633,x23634,x23631,x23635),f222(x23633,x23634,x23632,x23635))
% 18.77/18.52 [2364]~E(x23641,x23642)+E(f222(x23643,x23644,x23645,x23641),f222(x23643,x23644,x23645,x23642))
% 18.77/18.52 [2365]~E(x23651,x23652)+E(f199(x23651),f199(x23652))
% 18.77/18.52 [2366]~E(x23661,x23662)+E(f614(x23661,x23663),f614(x23662,x23663))
% 18.77/18.52 [2367]~E(x23671,x23672)+E(f614(x23673,x23671),f614(x23673,x23672))
% 18.77/18.52 [2368]~E(x23681,x23682)+E(f758(x23681,x23683),f758(x23682,x23683))
% 18.77/18.52 [2369]~E(x23691,x23692)+E(f758(x23693,x23691),f758(x23693,x23692))
% 18.77/18.52 [2370]~E(x23701,x23702)+E(f717(x23701,x23703),f717(x23702,x23703))
% 18.77/18.52 [2371]~E(x23711,x23712)+E(f717(x23713,x23711),f717(x23713,x23712))
% 18.77/18.52 [2372]~E(x23721,x23722)+E(f413(x23721,x23723,x23724),f413(x23722,x23723,x23724))
% 18.77/18.52 [2373]~E(x23731,x23732)+E(f413(x23733,x23731,x23734),f413(x23733,x23732,x23734))
% 18.77/18.52 [2374]~E(x23741,x23742)+E(f413(x23743,x23744,x23741),f413(x23743,x23744,x23742))
% 18.77/18.52 [2375]~E(x23751,x23752)+E(f434(x23751,x23753,x23754),f434(x23752,x23753,x23754))
% 18.77/18.52 [2376]~E(x23761,x23762)+E(f434(x23763,x23761,x23764),f434(x23763,x23762,x23764))
% 18.77/18.52 [2377]~E(x23771,x23772)+E(f434(x23773,x23774,x23771),f434(x23773,x23774,x23772))
% 18.77/18.52 [2378]~E(x23781,x23782)+E(f218(x23781,x23783,x23784,x23785,x23786),f218(x23782,x23783,x23784,x23785,x23786))
% 18.77/18.52 [2379]~E(x23791,x23792)+E(f218(x23793,x23791,x23794,x23795,x23796),f218(x23793,x23792,x23794,x23795,x23796))
% 18.77/18.52 [2380]~E(x23801,x23802)+E(f218(x23803,x23804,x23801,x23805,x23806),f218(x23803,x23804,x23802,x23805,x23806))
% 18.77/18.52 [2381]~E(x23811,x23812)+E(f218(x23813,x23814,x23815,x23811,x23816),f218(x23813,x23814,x23815,x23812,x23816))
% 18.77/18.52 [2382]~E(x23821,x23822)+E(f218(x23823,x23824,x23825,x23826,x23821),f218(x23823,x23824,x23825,x23826,x23822))
% 18.77/18.52 [2383]~E(x23831,x23832)+E(f595(x23831),f595(x23832))
% 18.77/18.52 [2384]~E(x23841,x23842)+E(f47(x23841),f47(x23842))
% 18.77/18.52 [2385]~E(x23851,x23852)+E(f525(x23851,x23853,x23854,x23855),f525(x23852,x23853,x23854,x23855))
% 18.77/18.52 [2386]~E(x23861,x23862)+E(f525(x23863,x23861,x23864,x23865),f525(x23863,x23862,x23864,x23865))
% 18.77/18.52 [2387]~E(x23871,x23872)+E(f525(x23873,x23874,x23871,x23875),f525(x23873,x23874,x23872,x23875))
% 18.77/18.52 [2388]~E(x23881,x23882)+E(f525(x23883,x23884,x23885,x23881),f525(x23883,x23884,x23885,x23882))
% 18.77/18.52 [2389]~E(x23891,x23892)+E(f530(x23891,x23893,x23894,x23895),f530(x23892,x23893,x23894,x23895))
% 18.77/18.52 [2390]~E(x23901,x23902)+E(f530(x23903,x23901,x23904,x23905),f530(x23903,x23902,x23904,x23905))
% 18.77/18.52 [2391]~E(x23911,x23912)+E(f530(x23913,x23914,x23911,x23915),f530(x23913,x23914,x23912,x23915))
% 18.77/18.52 [2392]~E(x23921,x23922)+E(f530(x23923,x23924,x23925,x23921),f530(x23923,x23924,x23925,x23922))
% 18.77/18.52 [2393]~E(x23931,x23932)+E(f431(x23931,x23933,x23934),f431(x23932,x23933,x23934))
% 18.77/18.52 [2394]~E(x23941,x23942)+E(f431(x23943,x23941,x23944),f431(x23943,x23942,x23944))
% 18.77/18.52 [2395]~E(x23951,x23952)+E(f431(x23953,x23954,x23951),f431(x23953,x23954,x23952))
% 18.77/18.52 [2396]~E(x23961,x23962)+E(f217(x23961,x23963,x23964,x23965,x23966),f217(x23962,x23963,x23964,x23965,x23966))
% 18.77/18.52 [2397]~E(x23971,x23972)+E(f217(x23973,x23971,x23974,x23975,x23976),f217(x23973,x23972,x23974,x23975,x23976))
% 18.77/18.52 [2398]~E(x23981,x23982)+E(f217(x23983,x23984,x23981,x23985,x23986),f217(x23983,x23984,x23982,x23985,x23986))
% 18.77/18.52 [2399]~E(x23991,x23992)+E(f217(x23993,x23994,x23995,x23991,x23996),f217(x23993,x23994,x23995,x23992,x23996))
% 18.77/18.52 [2400]~E(x24001,x24002)+E(f217(x24003,x24004,x24005,x24006,x24001),f217(x24003,x24004,x24005,x24006,x24002))
% 18.77/18.52 [2401]~E(x24011,x24012)+E(f607(x24011,x24013),f607(x24012,x24013))
% 18.77/18.52 [2402]~E(x24021,x24022)+E(f607(x24023,x24021),f607(x24023,x24022))
% 18.77/18.52 [2403]~E(x24031,x24032)+E(f463(x24031,x24033,x24034,x24035),f463(x24032,x24033,x24034,x24035))
% 18.77/18.52 [2404]~E(x24041,x24042)+E(f463(x24043,x24041,x24044,x24045),f463(x24043,x24042,x24044,x24045))
% 18.77/18.52 [2405]~E(x24051,x24052)+E(f463(x24053,x24054,x24051,x24055),f463(x24053,x24054,x24052,x24055))
% 18.77/18.52 [2406]~E(x24061,x24062)+E(f463(x24063,x24064,x24065,x24061),f463(x24063,x24064,x24065,x24062))
% 18.77/18.52 [2407]~E(x24071,x24072)+E(f573(x24071,x24073,x24074),f573(x24072,x24073,x24074))
% 18.77/18.52 [2408]~E(x24081,x24082)+E(f573(x24083,x24081,x24084),f573(x24083,x24082,x24084))
% 18.77/18.52 [2409]~E(x24091,x24092)+E(f573(x24093,x24094,x24091),f573(x24093,x24094,x24092))
% 18.77/18.52 [2410]~E(x24101,x24102)+E(f459(x24101,x24103,x24104,x24105),f459(x24102,x24103,x24104,x24105))
% 18.77/18.52 [2411]~E(x24111,x24112)+E(f459(x24113,x24111,x24114,x24115),f459(x24113,x24112,x24114,x24115))
% 18.77/18.52 [2412]~E(x24121,x24122)+E(f459(x24123,x24124,x24121,x24125),f459(x24123,x24124,x24122,x24125))
% 18.77/18.52 [2413]~E(x24131,x24132)+E(f459(x24133,x24134,x24135,x24131),f459(x24133,x24134,x24135,x24132))
% 18.77/18.52 [2414]~E(x24141,x24142)+E(f826(x24141,x24143,x24144,x24145,x24146,x24147,x24148),f826(x24142,x24143,x24144,x24145,x24146,x24147,x24148))
% 18.77/18.52 [2415]~E(x24151,x24152)+E(f826(x24153,x24151,x24154,x24155,x24156,x24157,x24158),f826(x24153,x24152,x24154,x24155,x24156,x24157,x24158))
% 18.77/18.52 [2416]~E(x24161,x24162)+E(f826(x24163,x24164,x24161,x24165,x24166,x24167,x24168),f826(x24163,x24164,x24162,x24165,x24166,x24167,x24168))
% 18.77/18.52 [2417]~E(x24171,x24172)+E(f826(x24173,x24174,x24175,x24171,x24176,x24177,x24178),f826(x24173,x24174,x24175,x24172,x24176,x24177,x24178))
% 18.77/18.52 [2418]~E(x24181,x24182)+E(f826(x24183,x24184,x24185,x24186,x24181,x24187,x24188),f826(x24183,x24184,x24185,x24186,x24182,x24187,x24188))
% 18.77/18.52 [2419]~E(x24191,x24192)+E(f826(x24193,x24194,x24195,x24196,x24197,x24191,x24198),f826(x24193,x24194,x24195,x24196,x24197,x24192,x24198))
% 18.77/18.52 [2420]~E(x24201,x24202)+E(f826(x24203,x24204,x24205,x24206,x24207,x24208,x24201),f826(x24203,x24204,x24205,x24206,x24207,x24208,x24202))
% 18.77/18.52 [2421]~E(x24211,x24212)+E(f587(x24211,x24213),f587(x24212,x24213))
% 18.77/18.52 [2422]~E(x24221,x24222)+E(f587(x24223,x24221),f587(x24223,x24222))
% 18.77/18.52 [2423]~E(x24231,x24232)+E(f819(x24231),f819(x24232))
% 18.77/18.52 [2424]~E(x24241,x24242)+E(f364(x24241,x24243,x24244),f364(x24242,x24243,x24244))
% 18.77/18.52 [2425]~E(x24251,x24252)+E(f364(x24253,x24251,x24254),f364(x24253,x24252,x24254))
% 18.77/18.52 [2426]~E(x24261,x24262)+E(f364(x24263,x24264,x24261),f364(x24263,x24264,x24262))
% 18.77/18.52 [2427]~E(x24271,x24272)+E(f556(x24271,x24273,x24274),f556(x24272,x24273,x24274))
% 18.77/18.52 [2428]~E(x24281,x24282)+E(f556(x24283,x24281,x24284),f556(x24283,x24282,x24284))
% 18.77/18.52 [2429]~E(x24291,x24292)+E(f556(x24293,x24294,x24291),f556(x24293,x24294,x24292))
% 18.77/18.52 [2430]~E(x24301,x24302)+E(f615(x24301,x24303),f615(x24302,x24303))
% 18.77/18.52 [2431]~E(x24311,x24312)+E(f615(x24313,x24311),f615(x24313,x24312))
% 18.77/18.52 [2432]~E(x24321,x24322)+E(f757(x24321,x24323,x24324),f757(x24322,x24323,x24324))
% 18.77/18.52 [2433]~E(x24331,x24332)+E(f757(x24333,x24331,x24334),f757(x24333,x24332,x24334))
% 18.77/18.52 [2434]~E(x24341,x24342)+E(f757(x24343,x24344,x24341),f757(x24343,x24344,x24342))
% 18.77/18.52 [2435]~E(x24351,x24352)+E(f383(x24351),f383(x24352))
% 18.77/18.52 [2436]~E(x24361,x24362)+E(f566(x24361,x24363,x24364,x24365,x24366),f566(x24362,x24363,x24364,x24365,x24366))
% 18.77/18.52 [2437]~E(x24371,x24372)+E(f566(x24373,x24371,x24374,x24375,x24376),f566(x24373,x24372,x24374,x24375,x24376))
% 18.77/18.52 [2438]~E(x24381,x24382)+E(f566(x24383,x24384,x24381,x24385,x24386),f566(x24383,x24384,x24382,x24385,x24386))
% 18.77/18.52 [2439]~E(x24391,x24392)+E(f566(x24393,x24394,x24395,x24391,x24396),f566(x24393,x24394,x24395,x24392,x24396))
% 18.77/18.52 [2440]~E(x24401,x24402)+E(f566(x24403,x24404,x24405,x24406,x24401),f566(x24403,x24404,x24405,x24406,x24402))
% 18.77/18.52 [2441]~E(x24411,x24412)+E(f272(x24411,x24413,x24414,x24415),f272(x24412,x24413,x24414,x24415))
% 18.77/18.52 [2442]~E(x24421,x24422)+E(f272(x24423,x24421,x24424,x24425),f272(x24423,x24422,x24424,x24425))
% 18.77/18.52 [2443]~E(x24431,x24432)+E(f272(x24433,x24434,x24431,x24435),f272(x24433,x24434,x24432,x24435))
% 18.77/18.52 [2444]~E(x24441,x24442)+E(f272(x24443,x24444,x24445,x24441),f272(x24443,x24444,x24445,x24442))
% 18.77/18.52 [2445]~E(x24451,x24452)+E(f205(x24451,x24453,x24454,x24455,x24456,x24457,x24458),f205(x24452,x24453,x24454,x24455,x24456,x24457,x24458))
% 18.77/18.52 [2446]~E(x24461,x24462)+E(f205(x24463,x24461,x24464,x24465,x24466,x24467,x24468),f205(x24463,x24462,x24464,x24465,x24466,x24467,x24468))
% 18.77/18.52 [2447]~E(x24471,x24472)+E(f205(x24473,x24474,x24471,x24475,x24476,x24477,x24478),f205(x24473,x24474,x24472,x24475,x24476,x24477,x24478))
% 18.77/18.52 [2448]~E(x24481,x24482)+E(f205(x24483,x24484,x24485,x24481,x24486,x24487,x24488),f205(x24483,x24484,x24485,x24482,x24486,x24487,x24488))
% 18.77/18.52 [2449]~E(x24491,x24492)+E(f205(x24493,x24494,x24495,x24496,x24491,x24497,x24498),f205(x24493,x24494,x24495,x24496,x24492,x24497,x24498))
% 18.77/18.52 [2450]~E(x24501,x24502)+E(f205(x24503,x24504,x24505,x24506,x24507,x24501,x24508),f205(x24503,x24504,x24505,x24506,x24507,x24502,x24508))
% 18.77/18.52 [2451]~E(x24511,x24512)+E(f205(x24513,x24514,x24515,x24516,x24517,x24518,x24511),f205(x24513,x24514,x24515,x24516,x24517,x24518,x24512))
% 18.77/18.52 [2452]~E(x24521,x24522)+E(f544(x24521,x24523,x24524,x24525,x24526,x24527,x24528),f544(x24522,x24523,x24524,x24525,x24526,x24527,x24528))
% 18.77/18.52 [2453]~E(x24531,x24532)+E(f544(x24533,x24531,x24534,x24535,x24536,x24537,x24538),f544(x24533,x24532,x24534,x24535,x24536,x24537,x24538))
% 18.77/18.52 [2454]~E(x24541,x24542)+E(f544(x24543,x24544,x24541,x24545,x24546,x24547,x24548),f544(x24543,x24544,x24542,x24545,x24546,x24547,x24548))
% 18.77/18.52 [2455]~E(x24551,x24552)+E(f544(x24553,x24554,x24555,x24551,x24556,x24557,x24558),f544(x24553,x24554,x24555,x24552,x24556,x24557,x24558))
% 18.77/18.52 [2456]~E(x24561,x24562)+E(f544(x24563,x24564,x24565,x24566,x24561,x24567,x24568),f544(x24563,x24564,x24565,x24566,x24562,x24567,x24568))
% 18.77/18.52 [2457]~E(x24571,x24572)+E(f544(x24573,x24574,x24575,x24576,x24577,x24571,x24578),f544(x24573,x24574,x24575,x24576,x24577,x24572,x24578))
% 18.77/18.52 [2458]~E(x24581,x24582)+E(f544(x24583,x24584,x24585,x24586,x24587,x24588,x24581),f544(x24583,x24584,x24585,x24586,x24587,x24588,x24582))
% 18.77/18.52 [2459]~E(x24591,x24592)+E(f555(x24591),f555(x24592))
% 18.77/18.52 [2460]~E(x24601,x24602)+E(f706(x24601,x24603,x24604,x24605,x24606),f706(x24602,x24603,x24604,x24605,x24606))
% 18.77/18.52 [2461]~E(x24611,x24612)+E(f706(x24613,x24611,x24614,x24615,x24616),f706(x24613,x24612,x24614,x24615,x24616))
% 18.77/18.52 [2462]~E(x24621,x24622)+E(f706(x24623,x24624,x24621,x24625,x24626),f706(x24623,x24624,x24622,x24625,x24626))
% 18.77/18.52 [2463]~E(x24631,x24632)+E(f706(x24633,x24634,x24635,x24631,x24636),f706(x24633,x24634,x24635,x24632,x24636))
% 18.77/18.52 [2464]~E(x24641,x24642)+E(f706(x24643,x24644,x24645,x24646,x24641),f706(x24643,x24644,x24645,x24646,x24642))
% 18.77/18.52 [2465]~E(x24651,x24652)+E(f50(x24651),f50(x24652))
% 18.77/18.52 [2466]~E(x24661,x24662)+E(f580(x24661,x24663,x24664,x24665,x24666,x24667),f580(x24662,x24663,x24664,x24665,x24666,x24667))
% 18.77/18.52 [2467]~E(x24671,x24672)+E(f580(x24673,x24671,x24674,x24675,x24676,x24677),f580(x24673,x24672,x24674,x24675,x24676,x24677))
% 18.77/18.52 [2468]~E(x24681,x24682)+E(f580(x24683,x24684,x24681,x24685,x24686,x24687),f580(x24683,x24684,x24682,x24685,x24686,x24687))
% 18.77/18.52 [2469]~E(x24691,x24692)+E(f580(x24693,x24694,x24695,x24691,x24696,x24697),f580(x24693,x24694,x24695,x24692,x24696,x24697))
% 18.77/18.52 [2470]~E(x24701,x24702)+E(f580(x24703,x24704,x24705,x24706,x24701,x24707),f580(x24703,x24704,x24705,x24706,x24702,x24707))
% 18.77/18.52 [2471]~E(x24711,x24712)+E(f580(x24713,x24714,x24715,x24716,x24717,x24711),f580(x24713,x24714,x24715,x24716,x24717,x24712))
% 18.77/18.52 [2472]~E(x24721,x24722)+E(f347(x24721,x24723),f347(x24722,x24723))
% 18.77/18.52 [2473]~E(x24731,x24732)+E(f347(x24733,x24731),f347(x24733,x24732))
% 18.77/18.52 [2474]~E(x24741,x24742)+E(f812(x24741,x24743,x24744,x24745,x24746,x24747),f812(x24742,x24743,x24744,x24745,x24746,x24747))
% 18.77/18.52 [2475]~E(x24751,x24752)+E(f812(x24753,x24751,x24754,x24755,x24756,x24757),f812(x24753,x24752,x24754,x24755,x24756,x24757))
% 18.77/18.52 [2476]~E(x24761,x24762)+E(f812(x24763,x24764,x24761,x24765,x24766,x24767),f812(x24763,x24764,x24762,x24765,x24766,x24767))
% 18.77/18.52 [2477]~E(x24771,x24772)+E(f812(x24773,x24774,x24775,x24771,x24776,x24777),f812(x24773,x24774,x24775,x24772,x24776,x24777))
% 18.77/18.52 [2478]~E(x24781,x24782)+E(f812(x24783,x24784,x24785,x24786,x24781,x24787),f812(x24783,x24784,x24785,x24786,x24782,x24787))
% 18.77/18.52 [2479]~E(x24791,x24792)+E(f812(x24793,x24794,x24795,x24796,x24797,x24791),f812(x24793,x24794,x24795,x24796,x24797,x24792))
% 18.77/18.52 [2480]~E(x24801,x24802)+E(f275(x24801,x24803,x24804,x24805),f275(x24802,x24803,x24804,x24805))
% 18.77/18.52 [2481]~E(x24811,x24812)+E(f275(x24813,x24811,x24814,x24815),f275(x24813,x24812,x24814,x24815))
% 18.77/18.52 [2482]~E(x24821,x24822)+E(f275(x24823,x24824,x24821,x24825),f275(x24823,x24824,x24822,x24825))
% 18.77/18.52 [2483]~E(x24831,x24832)+E(f275(x24833,x24834,x24835,x24831),f275(x24833,x24834,x24835,x24832))
% 18.77/18.52 [2484]~E(x24841,x24842)+E(f353(x24841,x24843),f353(x24842,x24843))
% 18.77/18.52 [2485]~E(x24851,x24852)+E(f353(x24853,x24851),f353(x24853,x24852))
% 18.77/18.52 [2486]~E(x24861,x24862)+E(f515(x24861),f515(x24862))
% 18.77/18.52 [2487]~E(x24871,x24872)+E(f378(x24871),f378(x24872))
% 18.77/18.52 [2488]~E(x24881,x24882)+E(f48(x24881),f48(x24882))
% 18.77/18.52 [2489]~E(x24891,x24892)+E(f584(x24891),f584(x24892))
% 18.77/18.52 [2490]~E(x24901,x24902)+E(f790(x24901,x24903,x24904),f790(x24902,x24903,x24904))
% 18.77/18.52 [2491]~E(x24911,x24912)+E(f790(x24913,x24911,x24914),f790(x24913,x24912,x24914))
% 18.77/18.52 [2492]~E(x24921,x24922)+E(f790(x24923,x24924,x24921),f790(x24923,x24924,x24922))
% 18.77/18.52 [2493]~E(x24931,x24932)+E(f540(x24931),f540(x24932))
% 18.77/18.52 [2494]~E(x24941,x24942)+E(f398(x24941,x24943),f398(x24942,x24943))
% 18.77/18.52 [2495]~E(x24951,x24952)+E(f398(x24953,x24951),f398(x24953,x24952))
% 18.77/18.52 [2496]~E(x24961,x24962)+E(f517(x24961,x24963),f517(x24962,x24963))
% 18.77/18.52 [2497]~E(x24971,x24972)+E(f517(x24973,x24971),f517(x24973,x24972))
% 18.77/18.52 [2498]~E(x24981,x24982)+E(f599(x24981,x24983),f599(x24982,x24983))
% 18.77/18.52 [2499]~E(x24991,x24992)+E(f599(x24993,x24991),f599(x24993,x24992))
% 18.77/18.52 [2500]~E(x25001,x25002)+E(f124(x25001),f124(x25002))
% 18.77/18.52 [2501]~E(x25011,x25012)+E(f449(x25011,x25013),f449(x25012,x25013))
% 18.77/18.52 [2502]~E(x25021,x25022)+E(f449(x25023,x25021),f449(x25023,x25022))
% 18.77/18.52 [2503]~E(x25031,x25032)+E(f796(x25031,x25033,x25034),f796(x25032,x25033,x25034))
% 18.77/18.52 [2504]~E(x25041,x25042)+E(f796(x25043,x25041,x25044),f796(x25043,x25042,x25044))
% 18.77/18.52 [2505]~E(x25051,x25052)+E(f796(x25053,x25054,x25051),f796(x25053,x25054,x25052))
% 18.77/18.52 [2506]~P1(x25061)+P1(x25062)+~E(x25061,x25062)
% 18.77/18.52 [2507]~P2(x25071)+P2(x25072)+~E(x25071,x25072)
% 18.77/18.52 [2508]~P72(x25081)+P72(x25082)+~E(x25081,x25082)
% 18.77/18.52 [2509]~P94(x25091)+P94(x25092)+~E(x25091,x25092)
% 18.77/18.52 [2510]~P3(x25101)+P3(x25102)+~E(x25101,x25102)
% 18.77/18.52 [2511]P18(x25112,x25113)+~E(x25111,x25112)+~P18(x25111,x25113)
% 18.77/18.52 [2512]P18(x25123,x25122)+~E(x25121,x25122)+~P18(x25123,x25121)
% 18.77/18.52 [2513]~P84(x25131)+P84(x25132)+~E(x25131,x25132)
% 18.77/18.52 [2514]P140(x25142,x25143,x25144)+~E(x25141,x25142)+~P140(x25141,x25143,x25144)
% 18.77/18.52 [2515]P140(x25153,x25152,x25154)+~E(x25151,x25152)+~P140(x25153,x25151,x25154)
% 18.77/18.52 [2516]P140(x25163,x25164,x25162)+~E(x25161,x25162)+~P140(x25163,x25164,x25161)
% 18.77/18.52 [2517]P139(x25172,x25173,x25174)+~E(x25171,x25172)+~P139(x25171,x25173,x25174)
% 18.77/18.52 [2518]P139(x25183,x25182,x25184)+~E(x25181,x25182)+~P139(x25183,x25181,x25184)
% 18.77/18.52 [2519]P139(x25193,x25194,x25192)+~E(x25191,x25192)+~P139(x25193,x25194,x25191)
% 18.77/18.52 [2520]~P86(x25201)+P86(x25202)+~E(x25201,x25202)
% 18.77/18.52 [2521]~P85(x25211)+P85(x25212)+~E(x25211,x25212)
% 18.77/18.52 [2522]~P117(x25221)+P117(x25222)+~E(x25221,x25222)
% 18.77/18.52 [2523]P29(x25232,x25233,x25234,x25235)+~E(x25231,x25232)+~P29(x25231,x25233,x25234,x25235)
% 18.77/18.52 [2524]P29(x25243,x25242,x25244,x25245)+~E(x25241,x25242)+~P29(x25243,x25241,x25244,x25245)
% 18.77/18.52 [2525]P29(x25253,x25254,x25252,x25255)+~E(x25251,x25252)+~P29(x25253,x25254,x25251,x25255)
% 18.77/18.52 [2526]P29(x25263,x25264,x25265,x25262)+~E(x25261,x25262)+~P29(x25263,x25264,x25265,x25261)
% 18.77/18.52 [2527]~P97(x25271)+P97(x25272)+~E(x25271,x25272)
% 18.77/18.52 [2528]~P102(x25281)+P102(x25282)+~E(x25281,x25282)
% 18.77/18.52 [2529]~P104(x25291)+P104(x25292)+~E(x25291,x25292)
% 18.77/18.52 [2530]~P122(x25301)+P122(x25302)+~E(x25301,x25302)
% 18.77/18.52 [2531]P34(x25312,x25313,x25314,x25315)+~E(x25311,x25312)+~P34(x25311,x25313,x25314,x25315)
% 18.77/18.52 [2532]P34(x25323,x25322,x25324,x25325)+~E(x25321,x25322)+~P34(x25323,x25321,x25324,x25325)
% 18.77/18.52 [2533]P34(x25333,x25334,x25332,x25335)+~E(x25331,x25332)+~P34(x25333,x25334,x25331,x25335)
% 18.77/18.52 [2534]P34(x25343,x25344,x25345,x25342)+~E(x25341,x25342)+~P34(x25343,x25344,x25345,x25341)
% 18.77/18.52 [2535]~P75(x25351)+P75(x25352)+~E(x25351,x25352)
% 18.77/18.52 [2536]~P67(x25361)+P67(x25362)+~E(x25361,x25362)
% 18.77/18.52 [2537]~P92(x25371)+P92(x25372)+~E(x25371,x25372)
% 18.77/18.52 [2538]~P87(x25381)+P87(x25382)+~E(x25381,x25382)
% 18.77/18.52 [2539]P28(x25392,x25393,x25394)+~E(x25391,x25392)+~P28(x25391,x25393,x25394)
% 18.77/18.52 [2540]P28(x25403,x25402,x25404)+~E(x25401,x25402)+~P28(x25403,x25401,x25404)
% 18.77/18.52 [2541]P28(x25413,x25414,x25412)+~E(x25411,x25412)+~P28(x25413,x25414,x25411)
% 18.77/18.52 [2542]~P76(x25421)+P76(x25422)+~E(x25421,x25422)
% 18.77/18.52 [2543]~P101(x25431)+P101(x25432)+~E(x25431,x25432)
% 18.77/18.52 [2544]~P61(x25441)+P61(x25442)+~E(x25441,x25442)
% 18.77/18.52 [2545]~P62(x25451)+P62(x25452)+~E(x25451,x25452)
% 18.77/18.52 [2546]~P89(x25461)+P89(x25462)+~E(x25461,x25462)
% 18.77/18.52 [2547]~P103(x25471)+P103(x25472)+~E(x25471,x25472)
% 18.77/18.52 [2548]~P119(x25481)+P119(x25482)+~E(x25481,x25482)
% 18.77/18.52 [2549]~P88(x25491)+P88(x25492)+~E(x25491,x25492)
% 18.77/18.52 [2550]~P4(x25501)+P4(x25502)+~E(x25501,x25502)
% 18.77/18.52 [2551]P54(x25512,x25513,x25514,x25515,x25516)+~E(x25511,x25512)+~P54(x25511,x25513,x25514,x25515,x25516)
% 18.77/18.52 [2552]P54(x25523,x25522,x25524,x25525,x25526)+~E(x25521,x25522)+~P54(x25523,x25521,x25524,x25525,x25526)
% 18.77/18.52 [2553]P54(x25533,x25534,x25532,x25535,x25536)+~E(x25531,x25532)+~P54(x25533,x25534,x25531,x25535,x25536)
% 18.77/18.52 [2554]P54(x25543,x25544,x25545,x25542,x25546)+~E(x25541,x25542)+~P54(x25543,x25544,x25545,x25541,x25546)
% 18.77/18.52 [2555]P54(x25553,x25554,x25555,x25556,x25552)+~E(x25551,x25552)+~P54(x25553,x25554,x25555,x25556,x25551)
% 18.77/18.52 [2556]~P90(x25561)+P90(x25562)+~E(x25561,x25562)
% 18.77/18.52 [2557]~P120(x25571)+P120(x25572)+~E(x25571,x25572)
% 18.77/18.52 [2558]~P68(x25581)+P68(x25582)+~E(x25581,x25582)
% 18.77/18.52 [2559]~P7(x25591)+P7(x25592)+~E(x25591,x25592)
% 18.77/18.52 [2560]~P132(x25601)+P132(x25602)+~E(x25601,x25602)
% 18.77/18.52 [2561]~P121(x25611)+P121(x25612)+~E(x25611,x25612)
% 18.77/18.52 [2562]~P70(x25621)+P70(x25622)+~E(x25621,x25622)
% 18.77/18.52 [2563]~P78(x25631)+P78(x25632)+~E(x25631,x25632)
% 18.77/18.52 [2564]~P69(x25641)+P69(x25642)+~E(x25641,x25642)
% 18.77/18.52 [2565]P57(x25652,x25653)+~E(x25651,x25652)+~P57(x25651,x25653)
% 18.77/18.52 [2566]P57(x25663,x25662)+~E(x25661,x25662)+~P57(x25663,x25661)
% 18.77/18.52 [2567]P44(x25672,x25673)+~E(x25671,x25672)+~P44(x25671,x25673)
% 18.77/18.52 [2568]P44(x25683,x25682)+~E(x25681,x25682)+~P44(x25683,x25681)
% 18.77/18.52 [2569]P20(x25692,x25693,x25694)+~E(x25691,x25692)+~P20(x25691,x25693,x25694)
% 18.77/18.52 [2570]P20(x25703,x25702,x25704)+~E(x25701,x25702)+~P20(x25703,x25701,x25704)
% 18.77/18.52 [2571]P20(x25713,x25714,x25712)+~E(x25711,x25712)+~P20(x25713,x25714,x25711)
% 18.77/18.52 [2572]~P91(x25721)+P91(x25722)+~E(x25721,x25722)
% 18.77/18.52 [2573]P36(x25732,x25733)+~E(x25731,x25732)+~P36(x25731,x25733)
% 18.77/18.52 [2574]P36(x25743,x25742)+~E(x25741,x25742)+~P36(x25743,x25741)
% 18.77/18.52 [2575]P16(x25752,x25753,x25754,x25755)+~E(x25751,x25752)+~P16(x25751,x25753,x25754,x25755)
% 18.77/18.52 [2576]P16(x25763,x25762,x25764,x25765)+~E(x25761,x25762)+~P16(x25763,x25761,x25764,x25765)
% 18.77/18.52 [2577]P16(x25773,x25774,x25772,x25775)+~E(x25771,x25772)+~P16(x25773,x25774,x25771,x25775)
% 18.77/18.52 [2578]P16(x25783,x25784,x25785,x25782)+~E(x25781,x25782)+~P16(x25783,x25784,x25785,x25781)
% 18.77/18.52 [2579]~P118(x25791)+P118(x25792)+~E(x25791,x25792)
% 18.77/18.52 [2580]~P105(x25801)+P105(x25802)+~E(x25801,x25802)
% 18.77/18.52 [2581]~P99(x25811)+P99(x25812)+~E(x25811,x25812)
% 18.77/18.52 [2582]P24(x25822,x25823,x25824,x25825)+~E(x25821,x25822)+~P24(x25821,x25823,x25824,x25825)
% 18.77/18.52 [2583]P24(x25833,x25832,x25834,x25835)+~E(x25831,x25832)+~P24(x25833,x25831,x25834,x25835)
% 18.77/18.52 [2584]P24(x25843,x25844,x25842,x25845)+~E(x25841,x25842)+~P24(x25843,x25844,x25841,x25845)
% 18.77/18.52 [2585]P24(x25853,x25854,x25855,x25852)+~E(x25851,x25852)+~P24(x25853,x25854,x25855,x25851)
% 18.77/18.52 [2586]~P63(x25861)+P63(x25862)+~E(x25861,x25862)
% 18.77/18.52 [2587]P39(x25872,x25873,x25874,x25875)+~E(x25871,x25872)+~P39(x25871,x25873,x25874,x25875)
% 18.77/18.52 [2588]P39(x25883,x25882,x25884,x25885)+~E(x25881,x25882)+~P39(x25883,x25881,x25884,x25885)
% 18.77/18.52 [2589]P39(x25893,x25894,x25892,x25895)+~E(x25891,x25892)+~P39(x25893,x25894,x25891,x25895)
% 18.77/18.52 [2590]P39(x25903,x25904,x25905,x25902)+~E(x25901,x25902)+~P39(x25903,x25904,x25905,x25901)
% 18.77/18.52 [2591]~P64(x25911)+P64(x25912)+~E(x25911,x25912)
% 18.77/18.52 [2592]~P112(x25921)+P112(x25922)+~E(x25921,x25922)
% 18.77/18.52 [2593]~P126(x25931)+P126(x25932)+~E(x25931,x25932)
% 18.77/18.52 [2594]~P127(x25941)+P127(x25942)+~E(x25941,x25942)
% 18.77/18.52 [2595]~P38(x25951)+P38(x25952)+~E(x25951,x25952)
% 18.77/18.52 [2596]P33(x25962,x25963)+~E(x25961,x25962)+~P33(x25961,x25963)
% 18.77/18.52 [2597]P33(x25973,x25972)+~E(x25971,x25972)+~P33(x25973,x25971)
% 18.77/18.52 [2598]~P128(x25981)+P128(x25982)+~E(x25981,x25982)
% 18.77/18.52 [2599]~P130(x25991)+P130(x25992)+~E(x25991,x25992)
% 18.77/18.52 [2600]P55(x26002,x26003)+~E(x26001,x26002)+~P55(x26001,x26003)
% 18.77/18.52 [2601]P55(x26013,x26012)+~E(x26011,x26012)+~P55(x26013,x26011)
% 18.77/18.52 [2602]~P107(x26021)+P107(x26022)+~E(x26021,x26022)
% 18.77/18.52 [2603]~P129(x26031)+P129(x26032)+~E(x26031,x26032)
% 18.77/18.52 [2604]~P77(x26041)+P77(x26042)+~E(x26041,x26042)
% 18.77/18.52 [2605]P15(x26052,x26053,x26054,x26055,x26056)+~E(x26051,x26052)+~P15(x26051,x26053,x26054,x26055,x26056)
% 18.77/18.52 [2606]P15(x26063,x26062,x26064,x26065,x26066)+~E(x26061,x26062)+~P15(x26063,x26061,x26064,x26065,x26066)
% 18.77/18.52 [2607]P15(x26073,x26074,x26072,x26075,x26076)+~E(x26071,x26072)+~P15(x26073,x26074,x26071,x26075,x26076)
% 18.77/18.52 [2608]P15(x26083,x26084,x26085,x26082,x26086)+~E(x26081,x26082)+~P15(x26083,x26084,x26085,x26081,x26086)
% 18.77/18.52 [2609]P15(x26093,x26094,x26095,x26096,x26092)+~E(x26091,x26092)+~P15(x26093,x26094,x26095,x26096,x26091)
% 18.77/18.52 [2610]~P123(x26101)+P123(x26102)+~E(x26101,x26102)
% 18.77/18.52 [2611]~P10(x26111)+P10(x26112)+~E(x26111,x26112)
% 18.77/18.52 [2612]~P58(x26121)+P58(x26122)+~E(x26121,x26122)
% 18.77/18.52 [2613]P23(x26132,x26133,x26134,x26135)+~E(x26131,x26132)+~P23(x26131,x26133,x26134,x26135)
% 18.77/18.52 [2614]P23(x26143,x26142,x26144,x26145)+~E(x26141,x26142)+~P23(x26143,x26141,x26144,x26145)
% 18.77/18.52 [2615]P23(x26153,x26154,x26152,x26155)+~E(x26151,x26152)+~P23(x26153,x26154,x26151,x26155)
% 18.77/18.52 [2616]P23(x26163,x26164,x26165,x26162)+~E(x26161,x26162)+~P23(x26163,x26164,x26165,x26161)
% 18.77/18.52 [2617]P56(x26172,x26173,x26174,x26175)+~E(x26171,x26172)+~P56(x26171,x26173,x26174,x26175)
% 18.77/18.52 [2618]P56(x26183,x26182,x26184,x26185)+~E(x26181,x26182)+~P56(x26183,x26181,x26184,x26185)
% 18.77/18.52 [2619]P56(x26193,x26194,x26192,x26195)+~E(x26191,x26192)+~P56(x26193,x26194,x26191,x26195)
% 18.77/18.52 [2620]P56(x26203,x26204,x26205,x26202)+~E(x26201,x26202)+~P56(x26203,x26204,x26205,x26201)
% 18.77/18.52 [2621]~P81(x26211)+P81(x26212)+~E(x26211,x26212)
% 18.77/18.52 [2622]P27(x26222,x26223,x26224,x26225,x26226,x26227)+~E(x26221,x26222)+~P27(x26221,x26223,x26224,x26225,x26226,x26227)
% 18.77/18.52 [2623]P27(x26233,x26232,x26234,x26235,x26236,x26237)+~E(x26231,x26232)+~P27(x26233,x26231,x26234,x26235,x26236,x26237)
% 18.77/18.52 [2624]P27(x26243,x26244,x26242,x26245,x26246,x26247)+~E(x26241,x26242)+~P27(x26243,x26244,x26241,x26245,x26246,x26247)
% 18.77/18.52 [2625]P27(x26253,x26254,x26255,x26252,x26256,x26257)+~E(x26251,x26252)+~P27(x26253,x26254,x26255,x26251,x26256,x26257)
% 18.77/18.52 [2626]P27(x26263,x26264,x26265,x26266,x26262,x26267)+~E(x26261,x26262)+~P27(x26263,x26264,x26265,x26266,x26261,x26267)
% 18.77/18.52 [2627]P27(x26273,x26274,x26275,x26276,x26277,x26272)+~E(x26271,x26272)+~P27(x26273,x26274,x26275,x26276,x26277,x26271)
% 18.77/18.52 [2628]~P65(x26281)+P65(x26282)+~E(x26281,x26282)
% 18.77/18.52 [2629]P47(x26292,x26293,x26294)+~E(x26291,x26292)+~P47(x26291,x26293,x26294)
% 18.77/18.52 [2630]P47(x26303,x26302,x26304)+~E(x26301,x26302)+~P47(x26303,x26301,x26304)
% 18.77/18.52 [2631]P47(x26313,x26314,x26312)+~E(x26311,x26312)+~P47(x26313,x26314,x26311)
% 18.77/18.52 [2632]~P93(x26321)+P93(x26322)+~E(x26321,x26322)
% 18.77/18.52 [2633]~P5(x26331)+P5(x26332)+~E(x26331,x26332)
% 18.77/18.52 [2634]~P59(x26341)+P59(x26342)+~E(x26341,x26342)
% 18.77/18.52 [2635]~P136(x26351)+P136(x26352)+~E(x26351,x26352)
% 18.77/18.52 [2636]~P71(x26361)+P71(x26362)+~E(x26361,x26362)
% 18.77/18.52 [2637]P19(x26372,x26373,x26374)+~E(x26371,x26372)+~P19(x26371,x26373,x26374)
% 18.77/18.52 [2638]P19(x26383,x26382,x26384)+~E(x26381,x26382)+~P19(x26383,x26381,x26384)
% 18.77/18.52 [2639]P19(x26393,x26394,x26392)+~E(x26391,x26392)+~P19(x26393,x26394,x26391)
% 18.77/18.52 [2640]~P35(x26401)+P35(x26402)+~E(x26401,x26402)
% 18.77/18.52 [2641]~P131(x26411)+P131(x26412)+~E(x26411,x26412)
% 18.77/18.52 [2642]~P6(x26421)+P6(x26422)+~E(x26421,x26422)
% 18.77/18.52 [2643]~P60(x26431)+P60(x26432)+~E(x26431,x26432)
% 18.77/18.52 [2644]P21(x26442,x26443,x26444)+~E(x26441,x26442)+~P21(x26441,x26443,x26444)
% 18.77/18.52 [2645]P21(x26453,x26452,x26454)+~E(x26451,x26452)+~P21(x26453,x26451,x26454)
% 18.77/18.52 [2646]P21(x26463,x26464,x26462)+~E(x26461,x26462)+~P21(x26463,x26464,x26461)
% 18.77/18.52 [2647]~P108(x26471)+P108(x26472)+~E(x26471,x26472)
% 18.77/18.52 [2648]~P137(x26481)+P137(x26482)+~E(x26481,x26482)
% 18.77/18.52 [2649]~P113(x26491)+P113(x26492)+~E(x26491,x26492)
% 18.77/18.52 [2650]P12(x26502,x26503,x26504)+~E(x26501,x26502)+~P12(x26501,x26503,x26504)
% 18.77/18.52 [2651]P12(x26513,x26512,x26514)+~E(x26511,x26512)+~P12(x26513,x26511,x26514)
% 18.77/18.52 [2652]P12(x26523,x26524,x26522)+~E(x26521,x26522)+~P12(x26523,x26524,x26521)
% 18.77/18.52 [2653]P31(x26532,x26533,x26534)+~E(x26531,x26532)+~P31(x26531,x26533,x26534)
% 18.77/18.52 [2654]P31(x26543,x26542,x26544)+~E(x26541,x26542)+~P31(x26543,x26541,x26544)
% 18.77/18.52 [2655]P31(x26553,x26554,x26552)+~E(x26551,x26552)+~P31(x26553,x26554,x26551)
% 18.77/18.52 [2656]~P9(x26561)+P9(x26562)+~E(x26561,x26562)
% 18.77/18.52 [2657]~P8(x26571)+P8(x26572)+~E(x26571,x26572)
% 18.77/18.52 [2658]~P80(x26581)+P80(x26582)+~E(x26581,x26582)
% 18.77/18.52 [2659]~P135(x26591)+P135(x26592)+~E(x26591,x26592)
% 18.77/18.52 [2660]P53(x26602,x26603,x26604)+~E(x26601,x26602)+~P53(x26601,x26603,x26604)
% 18.77/18.52 [2661]P53(x26613,x26612,x26614)+~E(x26611,x26612)+~P53(x26613,x26611,x26614)
% 18.77/18.52 [2662]P53(x26623,x26624,x26622)+~E(x26621,x26622)+~P53(x26623,x26624,x26621)
% 18.77/18.52 [2663]~P79(x26631)+P79(x26632)+~E(x26631,x26632)
% 18.77/18.52 [2664]~P133(x26641)+P133(x26642)+~E(x26641,x26642)
% 18.77/18.52 [2665]P45(x26652,x26653,x26654)+~E(x26651,x26652)+~P45(x26651,x26653,x26654)
% 18.77/18.52 [2666]P45(x26663,x26662,x26664)+~E(x26661,x26662)+~P45(x26663,x26661,x26664)
% 18.77/18.52 [2667]P45(x26673,x26674,x26672)+~E(x26671,x26672)+~P45(x26673,x26674,x26671)
% 18.77/18.52 [2668]~P134(x26681)+P134(x26682)+~E(x26681,x26682)
% 18.77/18.52 [2669]~P124(x26691)+P124(x26692)+~E(x26691,x26692)
% 18.77/18.52 [2670]~P43(x26701)+P43(x26702)+~E(x26701,x26702)
% 18.77/18.52 [2671]~P106(x26711)+P106(x26712)+~E(x26711,x26712)
% 18.77/18.52 [2672]P11(x26722,x26723)+~E(x26721,x26722)+~P11(x26721,x26723)
% 18.77/18.52 [2673]P11(x26733,x26732)+~E(x26731,x26732)+~P11(x26733,x26731)
% 18.77/18.52 [2674]P42(x26742,x26743)+~E(x26741,x26742)+~P42(x26741,x26743)
% 18.77/18.52 [2675]P42(x26753,x26752)+~E(x26751,x26752)+~P42(x26753,x26751)
% 18.77/18.52 [2676]P48(x26762,x26763)+~E(x26761,x26762)+~P48(x26761,x26763)
% 18.77/18.52 [2677]P48(x26773,x26772)+~E(x26771,x26772)+~P48(x26773,x26771)
% 18.77/18.52 [2678]~P98(x26781)+P98(x26782)+~E(x26781,x26782)
% 18.77/18.52 [2679]P22(x26792,x26793,x26794)+~E(x26791,x26792)+~P22(x26791,x26793,x26794)
% 18.77/18.52 [2680]P22(x26803,x26802,x26804)+~E(x26801,x26802)+~P22(x26803,x26801,x26804)
% 18.77/18.52 [2681]P22(x26813,x26814,x26812)+~E(x26811,x26812)+~P22(x26813,x26814,x26811)
% 18.77/18.52 [2682]P52(x26822,x26823,x26824)+~E(x26821,x26822)+~P52(x26821,x26823,x26824)
% 18.77/18.52 [2683]P52(x26833,x26832,x26834)+~E(x26831,x26832)+~P52(x26833,x26831,x26834)
% 18.77/18.52 [2684]P52(x26843,x26844,x26842)+~E(x26841,x26842)+~P52(x26843,x26844,x26841)
% 18.77/18.52 [2685]~P114(x26851)+P114(x26852)+~E(x26851,x26852)
% 18.77/18.52 [2686]~P138(x26861)+P138(x26862)+~E(x26861,x26862)
% 18.77/18.52 [2687]~P95(x26871)+P95(x26872)+~E(x26871,x26872)
% 18.77/18.52 [2688]P41(x26882,x26883,x26884,x26885,x26886,x26887)+~E(x26881,x26882)+~P41(x26881,x26883,x26884,x26885,x26886,x26887)
% 18.77/18.52 [2689]P41(x26893,x26892,x26894,x26895,x26896,x26897)+~E(x26891,x26892)+~P41(x26893,x26891,x26894,x26895,x26896,x26897)
% 18.77/18.52 [2690]P41(x26903,x26904,x26902,x26905,x26906,x26907)+~E(x26901,x26902)+~P41(x26903,x26904,x26901,x26905,x26906,x26907)
% 18.77/18.52 [2691]P41(x26913,x26914,x26915,x26912,x26916,x26917)+~E(x26911,x26912)+~P41(x26913,x26914,x26915,x26911,x26916,x26917)
% 18.77/18.52 [2692]P41(x26923,x26924,x26925,x26926,x26922,x26927)+~E(x26921,x26922)+~P41(x26923,x26924,x26925,x26926,x26921,x26927)
% 18.77/18.52 [2693]P41(x26933,x26934,x26935,x26936,x26937,x26932)+~E(x26931,x26932)+~P41(x26933,x26934,x26935,x26936,x26937,x26931)
% 18.77/18.52 [2694]~P82(x26941)+P82(x26942)+~E(x26941,x26942)
% 18.77/18.52 [2695]~P73(x26951)+P73(x26952)+~E(x26951,x26952)
% 18.77/18.52 [2696]~P115(x26961)+P115(x26962)+~E(x26961,x26962)
% 18.77/18.52 [2697]~P125(x26971)+P125(x26972)+~E(x26971,x26972)
% 18.77/18.52 [2698]~P66(x26981)+P66(x26982)+~E(x26981,x26982)
% 18.77/18.52 [2699]P30(x26992,x26993)+~E(x26991,x26992)+~P30(x26991,x26993)
% 18.77/18.52 [2700]P30(x27003,x27002)+~E(x27001,x27002)+~P30(x27003,x27001)
% 18.77/18.52 [2701]~P13(x27011)+P13(x27012)+~E(x27011,x27012)
% 18.77/18.52 [2702]~P111(x27021)+P111(x27022)+~E(x27021,x27022)
% 18.77/18.52 [2703]P25(x27032,x27033,x27034,x27035,x27036)+~E(x27031,x27032)+~P25(x27031,x27033,x27034,x27035,x27036)
% 18.77/18.52 [2704]P25(x27043,x27042,x27044,x27045,x27046)+~E(x27041,x27042)+~P25(x27043,x27041,x27044,x27045,x27046)
% 18.77/18.52 [2705]P25(x27053,x27054,x27052,x27055,x27056)+~E(x27051,x27052)+~P25(x27053,x27054,x27051,x27055,x27056)
% 18.77/18.52 [2706]P25(x27063,x27064,x27065,x27062,x27066)+~E(x27061,x27062)+~P25(x27063,x27064,x27065,x27061,x27066)
% 18.77/18.52 [2707]P25(x27073,x27074,x27075,x27076,x27072)+~E(x27071,x27072)+~P25(x27073,x27074,x27075,x27076,x27071)
% 18.77/18.52 [2708]P17(x27082,x27083,x27084,x27085,x27086,x27087)+~E(x27081,x27082)+~P17(x27081,x27083,x27084,x27085,x27086,x27087)
% 18.77/18.52 [2709]P17(x27093,x27092,x27094,x27095,x27096,x27097)+~E(x27091,x27092)+~P17(x27093,x27091,x27094,x27095,x27096,x27097)
% 18.77/18.52 [2710]P17(x27103,x27104,x27102,x27105,x27106,x27107)+~E(x27101,x27102)+~P17(x27103,x27104,x27101,x27105,x27106,x27107)
% 18.77/18.52 [2711]P17(x27113,x27114,x27115,x27112,x27116,x27117)+~E(x27111,x27112)+~P17(x27113,x27114,x27115,x27111,x27116,x27117)
% 18.77/18.52 [2712]P17(x27123,x27124,x27125,x27126,x27122,x27127)+~E(x27121,x27122)+~P17(x27123,x27124,x27125,x27126,x27121,x27127)
% 18.77/18.52 [2713]P17(x27133,x27134,x27135,x27136,x27137,x27132)+~E(x27131,x27132)+~P17(x27133,x27134,x27135,x27136,x27137,x27131)
% 18.77/18.52 [2714]P32(x27142,x27143,x27144)+~E(x27141,x27142)+~P32(x27141,x27143,x27144)
% 18.77/18.52 [2715]P32(x27153,x27152,x27154)+~E(x27151,x27152)+~P32(x27153,x27151,x27154)
% 18.77/18.52 [2716]P32(x27163,x27164,x27162)+~E(x27161,x27162)+~P32(x27163,x27164,x27161)
% 18.77/18.52 [2717]~P110(x27171)+P110(x27172)+~E(x27171,x27172)
% 18.77/18.52 [2718]P40(x27182,x27183,x27184,x27185)+~E(x27181,x27182)+~P40(x27181,x27183,x27184,x27185)
% 18.77/18.52 [2719]P40(x27193,x27192,x27194,x27195)+~E(x27191,x27192)+~P40(x27193,x27191,x27194,x27195)
% 18.77/18.52 [2720]P40(x27203,x27204,x27202,x27205)+~E(x27201,x27202)+~P40(x27203,x27204,x27201,x27205)
% 18.77/18.52 [2721]P40(x27213,x27214,x27215,x27212)+~E(x27211,x27212)+~P40(x27213,x27214,x27215,x27211)
% 18.77/18.52 [2722]~P100(x27221)+P100(x27222)+~E(x27221,x27222)
% 18.77/18.52 [2723]P50(x27232,x27233,x27234,x27235)+~E(x27231,x27232)+~P50(x27231,x27233,x27234,x27235)
% 18.77/18.52 [2724]P50(x27243,x27242,x27244,x27245)+~E(x27241,x27242)+~P50(x27243,x27241,x27244,x27245)
% 18.77/18.52 [2725]P50(x27253,x27254,x27252,x27255)+~E(x27251,x27252)+~P50(x27253,x27254,x27251,x27255)
% 18.77/18.52 [2726]P50(x27263,x27264,x27265,x27262)+~E(x27261,x27262)+~P50(x27263,x27264,x27265,x27261)
% 18.77/18.52 [2727]P51(x27272,x27273,x27274,x27275)+~E(x27271,x27272)+~P51(x27271,x27273,x27274,x27275)
% 18.77/18.52 [2728]P51(x27283,x27282,x27284,x27285)+~E(x27281,x27282)+~P51(x27283,x27281,x27284,x27285)
% 18.77/18.52 [2729]P51(x27293,x27294,x27292,x27295)+~E(x27291,x27292)+~P51(x27293,x27294,x27291,x27295)
% 18.77/18.52 [2730]P51(x27303,x27304,x27305,x27302)+~E(x27301,x27302)+~P51(x27303,x27304,x27305,x27301)
% 18.77/18.52 [2731]~P109(x27311)+P109(x27312)+~E(x27311,x27312)
% 18.77/18.52 [2732]P37(x27322,x27323)+~E(x27321,x27322)+~P37(x27321,x27323)
% 18.77/18.52 [2733]P37(x27333,x27332)+~E(x27331,x27332)+~P37(x27333,x27331)
% 18.77/18.52 [2734]P26(x27342,x27343,x27344,x27345,x27346,x27347)+~E(x27341,x27342)+~P26(x27341,x27343,x27344,x27345,x27346,x27347)
% 18.77/18.52 [2735]P26(x27353,x27352,x27354,x27355,x27356,x27357)+~E(x27351,x27352)+~P26(x27353,x27351,x27354,x27355,x27356,x27357)
% 18.77/18.52 [2736]P26(x27363,x27364,x27362,x27365,x27366,x27367)+~E(x27361,x27362)+~P26(x27363,x27364,x27361,x27365,x27366,x27367)
% 18.77/18.52 [2737]P26(x27373,x27374,x27375,x27372,x27376,x27377)+~E(x27371,x27372)+~P26(x27373,x27374,x27375,x27371,x27376,x27377)
% 18.77/18.52 [2738]P26(x27383,x27384,x27385,x27386,x27382,x27387)+~E(x27381,x27382)+~P26(x27383,x27384,x27385,x27386,x27381,x27387)
% 18.77/18.52 [2739]P26(x27393,x27394,x27395,x27396,x27397,x27392)+~E(x27391,x27392)+~P26(x27393,x27394,x27395,x27396,x27397,x27391)
% 18.77/18.52 [2740]~P74(x27401)+P74(x27402)+~E(x27401,x27402)
% 18.77/18.52 [2741]P49(x27412,x27413)+~E(x27411,x27412)+~P49(x27411,x27413)
% 18.77/18.52 [2742]P49(x27423,x27422)+~E(x27421,x27422)+~P49(x27423,x27421)
% 18.77/18.52 [2743]~P96(x27431)+P96(x27432)+~E(x27431,x27432)
% 18.77/18.52 [2744]~P83(x27441)+P83(x27442)+~E(x27441,x27442)
% 18.77/18.52 [2745]P14(x27452,x27453,x27454)+~E(x27451,x27452)+~P14(x27451,x27453,x27454)
% 18.77/18.52 [2746]P14(x27463,x27462,x27464)+~E(x27461,x27462)+~P14(x27463,x27461,x27464)
% 18.77/18.52 [2747]P14(x27473,x27474,x27472)+~E(x27471,x27472)+~P14(x27473,x27474,x27471)
% 18.77/18.52 [2748]P46(x27482,x27483,x27484)+~E(x27481,x27482)+~P46(x27481,x27483,x27484)
% 18.77/18.52 [2749]P46(x27493,x27492,x27494)+~E(x27491,x27492)+~P46(x27493,x27491,x27494)
% 18.77/18.52 [2750]P46(x27503,x27504,x27502)+~E(x27501,x27502)+~P46(x27503,x27504,x27501)
% 18.77/18.52 [2751]~P116(x27511)+P116(x27512)+~E(x27511,x27512)
% 18.77/18.52
% 18.77/18.52 %-------------------------------------------
% 18.77/18.53 cnf(9994,plain,
% 18.77/18.53 (~E(f324(f324(f139(x99941),x99942),x99943),x99943)),
% 18.77/18.53 inference(rename_variables,[],[4327])).
% 18.77/18.53 cnf(10001,plain,
% 18.77/18.53 (~E(f324(f324(f139(x100011),x100012),x100013),x100013)),
% 18.77/18.53 inference(rename_variables,[],[4327])).
% 18.77/18.53 cnf(10010,plain,
% 18.77/18.53 (~E(f324(a114,x100101),x100101)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10017,plain,
% 18.77/18.53 (~E(f324(a114,x100171),x100171)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10020,plain,
% 18.77/18.53 (E(f239(x100201,x100202,f239(x100202,x100201,x100203)),x100203)),
% 18.77/18.53 inference(rename_variables,[],[3225])).
% 18.77/18.53 cnf(10023,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),f51(a838,x100231,x100232)),x100231))),
% 18.77/18.53 inference(rename_variables,[],[3585])).
% 18.77/18.53 cnf(10026,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),f324(f324(f82(a838),x100261),x100262)),x100262))),
% 18.77/18.53 inference(rename_variables,[],[4403])).
% 18.77/18.53 cnf(10029,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),f324(f324(f82(a838),x100291),x100292)),x100292))),
% 18.77/18.53 inference(rename_variables,[],[4403])).
% 18.77/18.53 cnf(10032,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x100321),x100321))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10044,plain,
% 18.77/18.53 (P1(f324(f324(f326(x100441),x100442),f238(f845(x100441,a832))))),
% 18.77/18.53 inference(rename_variables,[],[3288])).
% 18.77/18.53 cnf(10047,plain,
% 18.77/18.53 (~E(f324(a114,x100471),x100471)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10050,plain,
% 18.77/18.53 (~E(f324(a27,x100501),a25)),
% 18.77/18.53 inference(rename_variables,[],[4291])).
% 18.77/18.53 cnf(10055,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x100551),x100551))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10072,plain,
% 18.77/18.53 (P1(f324(f324(f326(x100721),x100722),f238(f845(x100721,a832))))),
% 18.77/18.53 inference(rename_variables,[],[3288])).
% 18.77/18.53 cnf(10077,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x100771),f324(a114,x100771)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10101,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x101011),f324(a114,x101011)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10110,plain,
% 18.77/18.53 (P1(f324(f324(f186(a25),x101101),x101101))),
% 18.77/18.53 inference(rename_variables,[],[3131])).
% 18.77/18.53 cnf(10125,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x101251),x101251))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10140,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x101401),f324(a114,x101401)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10143,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x101431),f324(a114,x101431)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10170,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),f324(f324(f82(a838),x101701),x101702)),x101702))),
% 18.77/18.53 inference(rename_variables,[],[4403])).
% 18.77/18.53 cnf(10175,plain,
% 18.77/18.53 (~P1(f324(f324(f231(a838),f324(a114,x101751)),x101751))),
% 18.77/18.53 inference(rename_variables,[],[4387])).
% 18.77/18.53 cnf(10189,plain,
% 18.77/18.53 (E(f239(x101891,x101892,f239(x101892,x101891,x101893)),x101893)),
% 18.77/18.53 inference(rename_variables,[],[3225])).
% 18.77/18.53 cnf(10192,plain,
% 18.77/18.53 (E(f324(f7(x101921),x101922),x101922)),
% 18.77/18.53 inference(rename_variables,[],[2970])).
% 18.77/18.53 cnf(10201,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x102011),x102012),f179(f845(x102011,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(10204,plain,
% 18.77/18.53 (E(f239(x102041,x102042,f239(x102042,x102041,x102043)),x102043)),
% 18.77/18.53 inference(rename_variables,[],[3225])).
% 18.77/18.53 cnf(10216,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x102161,a832)),x102162),x102162))),
% 18.77/18.53 inference(rename_variables,[],[3430])).
% 18.77/18.53 cnf(10221,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x102211),f324(a114,x102211)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10240,plain,
% 18.77/18.53 (P1(f324(f324(f186(a25),x102401),x102401))),
% 18.77/18.53 inference(rename_variables,[],[3131])).
% 18.77/18.53 cnf(10243,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x102431),f324(a114,x102431)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10250,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x102501),f324(a114,x102501)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10253,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x102531),f324(a114,x102531)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10258,plain,
% 18.77/18.53 (P1(f324(f324(f186(a25),x102581),x102581))),
% 18.77/18.53 inference(rename_variables,[],[3131])).
% 18.77/18.53 cnf(10271,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x102711),x102711))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10278,plain,
% 18.77/18.53 (~E(f324(a27,x102781),a25)),
% 18.77/18.53 inference(rename_variables,[],[4291])).
% 18.77/18.53 cnf(10287,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x102871),x102871))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10296,plain,
% 18.77/18.53 (~E(f324(a114,x102961),x102961)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10299,plain,
% 18.77/18.53 (~E(f324(f324(f139(x102991),x102992),x102993),x102993)),
% 18.77/18.53 inference(rename_variables,[],[4327])).
% 18.77/18.53 cnf(10306,plain,
% 18.77/18.53 (~E(f324(f324(f139(x103061),x103062),x103063),x103063)),
% 18.77/18.53 inference(rename_variables,[],[4327])).
% 18.77/18.53 cnf(10332,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x103321),x103321))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10342,plain,
% 18.77/18.53 (E(f239(x103421,x103422,f239(x103422,x103421,x103423)),x103423)),
% 18.77/18.53 inference(rename_variables,[],[3225])).
% 18.77/18.53 cnf(10345,plain,
% 18.77/18.53 (E(f239(x103451,x103452,f239(x103452,x103451,x103453)),x103453)),
% 18.77/18.53 inference(rename_variables,[],[3225])).
% 18.77/18.53 cnf(10348,plain,
% 18.77/18.53 (~E(f324(a114,x103481),x103481)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10351,plain,
% 18.77/18.53 (~P1(f324(f65(x103511,x103512,f179(f845(x103511,a832))),x103513))),
% 18.77/18.53 inference(rename_variables,[],[4402])).
% 18.77/18.53 cnf(10356,plain,
% 18.77/18.53 (~P1(f324(f65(x103561,x103562,f179(f845(x103561,a832))),x103563))),
% 18.77/18.53 inference(rename_variables,[],[4402])).
% 18.77/18.53 cnf(10380,plain,
% 18.77/18.53 (~P1(f324(f324(f231(a838),f324(a114,x103801)),x103801))),
% 18.77/18.53 inference(rename_variables,[],[4387])).
% 18.77/18.53 cnf(10383,plain,
% 18.77/18.53 (~P1(f324(f324(f231(a838),f324(a114,x103831)),x103831))),
% 18.77/18.53 inference(rename_variables,[],[4387])).
% 18.77/18.53 cnf(10388,plain,
% 18.77/18.53 (~E(f324(f304(x103881,f845(x103881,a832),x103882),x103883),f324(f302(x103881),x103883))),
% 18.77/18.53 inference(rename_variables,[],[4388])).
% 18.77/18.53 cnf(10397,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),f2(a838)),x103971))),
% 18.77/18.53 inference(rename_variables,[],[3155])).
% 18.77/18.53 cnf(10400,plain,
% 18.77/18.53 (P1(f324(f324(f280(a838),x104001),x104001))),
% 18.77/18.53 inference(rename_variables,[],[3135])).
% 18.77/18.53 cnf(10403,plain,
% 18.77/18.53 (P1(f324(f324(f231(a1),x104031),x104031))),
% 18.77/18.53 inference(rename_variables,[],[3134])).
% 18.77/18.53 cnf(10408,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x104081),f324(f324(f83(a838),x104081),x104081)))),
% 18.77/18.53 inference(rename_variables,[],[3399])).
% 18.77/18.53 cnf(10411,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x104111),f324(f324(f83(a838),x104111),x104111)))),
% 18.77/18.53 inference(rename_variables,[],[3399])).
% 18.77/18.53 cnf(10414,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x104141),f324(f324(f82(a838),x104142),x104141)))),
% 18.77/18.53 inference(rename_variables,[],[3400])).
% 18.77/18.53 cnf(10417,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x104171),f324(f324(f82(a838),x104172),x104171)))),
% 18.77/18.53 inference(rename_variables,[],[3400])).
% 18.77/18.53 cnf(10420,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x104201),f324(a114,f324(f324(f82(a838),x104202),x104201))))),
% 18.77/18.53 inference(rename_variables,[],[3578])).
% 18.77/18.53 cnf(10427,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x104271,a832)),f324(f304(x104272,x104271,x104273),f324(f305(x104272,x104271,x104273),x104274))),x104274))),
% 18.77/18.53 inference(rename_variables,[],[4011])).
% 18.77/18.53 cnf(10430,plain,
% 18.77/18.53 (P1(f324(f324(f280(a838),x104301),x104301))),
% 18.77/18.53 inference(rename_variables,[],[3135])).
% 18.77/18.53 cnf(10435,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x104351),x104351))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10442,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x104421),x104421))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10451,plain,
% 18.77/18.53 (P1(f324(f324(f231(a1),x104511),x104511))),
% 18.77/18.53 inference(rename_variables,[],[3134])).
% 18.77/18.53 cnf(10468,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x104681),f324(f324(f83(a838),x104681),x104681)))),
% 18.77/18.53 inference(rename_variables,[],[3399])).
% 18.77/18.53 cnf(10471,plain,
% 18.77/18.53 (~P1(f324(f324(f231(a838),f324(a114,x104711)),x104711))),
% 18.77/18.53 inference(rename_variables,[],[4387])).
% 18.77/18.53 cnf(10476,plain,
% 18.77/18.53 (~P1(f324(f324(f231(a838),f324(a114,x104761)),x104761))),
% 18.77/18.53 inference(rename_variables,[],[4387])).
% 18.77/18.53 cnf(10481,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),f324(f324(f82(a838),x104811),x104812)),x104812))),
% 18.77/18.53 inference(rename_variables,[],[4403])).
% 18.77/18.53 cnf(10484,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),f324(f324(f82(a838),x104841),x104842)),x104841))),
% 18.77/18.53 inference(rename_variables,[],[4404])).
% 18.77/18.53 cnf(10487,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),f324(f324(f82(a838),x104871),x104872)),x104872))),
% 18.77/18.53 inference(rename_variables,[],[4403])).
% 18.77/18.53 cnf(10493,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x104931),x104931))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10496,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x104961),f324(f324(f83(a838),x104961),x104961)))),
% 18.77/18.53 inference(rename_variables,[],[3399])).
% 18.77/18.53 cnf(10505,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x105051),f324(a114,x105051)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10628,plain,
% 18.77/18.53 (~E(f324(a114,x106281),x106281)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10631,plain,
% 18.77/18.53 (~E(f324(a114,x106311),x106311)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10647,plain,
% 18.77/18.53 (P1(f324(f324(f326(x106471),x106472),f238(f845(x106471,a832))))),
% 18.77/18.53 inference(rename_variables,[],[3288])).
% 18.77/18.53 cnf(10653,plain,
% 18.77/18.53 (P1(f324(f324(f326(x106531),x106532),f238(f845(x106531,a832))))),
% 18.77/18.53 inference(rename_variables,[],[3288])).
% 18.77/18.53 cnf(10656,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x106561),x106562),f179(f845(x106561,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(10664,plain,
% 18.77/18.53 (~E(f324(a114,x106641),x106641)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10671,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x106711),x106712),f179(f845(x106711,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(10734,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x107341),x107341))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10737,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x107371),f324(a114,x107371)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10742,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x107421),x107421))),
% 18.77/18.53 inference(rename_variables,[],[4373])).
% 18.77/18.53 cnf(10745,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x107451),x107451))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10752,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x107521),x107521))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10773,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x107731),x107731))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10784,plain,
% 18.77/18.53 (~P1(f324(f324(f232(a838),x107841),f2(a838)))),
% 18.77/18.53 inference(rename_variables,[],[4376])).
% 18.77/18.53 cnf(10787,plain,
% 18.77/18.53 (~E(f324(a114,x107871),x107871)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10811,plain,
% 18.77/18.53 (E(f324(f324(f125(x108111),f115(x108111)),x108112),x108112)),
% 18.77/18.53 inference(rename_variables,[],[3085])).
% 18.77/18.53 cnf(10825,plain,
% 18.77/18.53 (E(f239(x108251,x108252,f239(x108252,x108251,x108253)),x108253)),
% 18.77/18.53 inference(rename_variables,[],[3225])).
% 18.77/18.53 cnf(10831,plain,
% 18.77/18.53 (~E(f324(a114,x108311),x108311)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10834,plain,
% 18.77/18.53 (~E(f324(a114,x108341),x108341)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10852,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x108521),x108522),f179(f845(x108521,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(10859,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x108591,a832)),f179(f845(x108591,a832))),x108592))),
% 18.77/18.53 inference(rename_variables,[],[3577])).
% 18.77/18.53 cnf(10864,plain,
% 18.77/18.53 (P1(f324(f324(f232(a838),x108641),f324(a114,x108641)))),
% 18.77/18.53 inference(rename_variables,[],[3202])).
% 18.77/18.53 cnf(10869,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x108691,a832)),x108692),f324(f324(f303(x108691),x108693),x108692)))),
% 18.77/18.53 inference(rename_variables,[],[3573])).
% 18.77/18.53 cnf(10874,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x108741,a832)),x108742),f324(f324(f303(x108741),x108743),x108742)))),
% 18.77/18.53 inference(rename_variables,[],[3573])).
% 18.77/18.53 cnf(10880,plain,
% 18.77/18.53 (P1(f324(f324(f326(x108801),x108802),f238(f845(x108801,a832))))),
% 18.77/18.53 inference(rename_variables,[],[3288])).
% 18.77/18.53 cnf(10889,plain,
% 18.77/18.53 (P1(f324(f324(f326(x108891),x108892),f238(f845(x108891,a832))))),
% 18.77/18.53 inference(rename_variables,[],[3288])).
% 18.77/18.53 cnf(10911,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x109111),x109111))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10917,plain,
% 18.77/18.53 (P1(f324(f324(f231(a838),x109171),x109171))),
% 18.77/18.53 inference(rename_variables,[],[3133])).
% 18.77/18.53 cnf(10924,plain,
% 18.77/18.53 (P1(f324(f238(f845(x109241,a832)),x109242))),
% 18.77/18.53 inference(rename_variables,[],[3196])).
% 18.77/18.53 cnf(10946,plain,
% 18.77/18.53 (~E(f324(a114,x109461),x109461)),
% 18.77/18.53 inference(rename_variables,[],[4293])).
% 18.77/18.53 cnf(10959,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x109591,a832)),f179(f845(x109591,a832))),x109592))),
% 18.77/18.53 inference(rename_variables,[],[3577])).
% 18.77/18.53 cnf(10976,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x109761,a832)),x109762),x109762))),
% 18.77/18.53 inference(rename_variables,[],[3430])).
% 18.77/18.53 cnf(10982,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x109821),x109822),f179(f845(x109821,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(11006,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x110061),x110062),f179(f845(x110061,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(11012,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x110121),x110122),f179(f845(x110121,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(11039,plain,
% 18.77/18.53 (~P1(f324(f324(f326(x110391),x110392),f179(f845(x110391,a832))))),
% 18.77/18.53 inference(rename_variables,[],[4389])).
% 18.77/18.53 cnf(11042,plain,
% 18.77/18.53 (P1(f324(f324(f231(f845(x110421,a832)),x110422),f238(f845(x110421,a832))))),
% 18.77/18.53 inference(rename_variables,[],[3508])).
% 18.77/18.53 cnf(11051,plain,
% 18.77/18.53 ($false),
% 18.77/18.53 inference(scs_inference,[],[4399,2752,2936,4322,4323,3330,4366,4367,4369,3109,3111,3113,4368,4370,3110,3112,2974,3136,4375,4386,4385,3014,3163,3161,3162,3643,3228,4135,4293,10010,10017,10047,10296,10348,10628,10631,10664,10787,10831,10834,10946,4291,10050,10278,4301,3225,10020,10189,10204,10342,10345,10825,2970,10192,2971,3588,4327,9994,10001,10299,10306,3048,3117,3341,3131,10110,10240,10258,3133,10055,10493,10734,10745,10752,10773,10911,10917,3134,10403,10451,3135,10400,10430,4373,10032,10125,10271,10287,10332,10435,10442,10742,3196,10924,2995,3065,3085,10811,3038,3027,3202,10077,10101,10140,10143,10221,10243,10250,10253,10505,10737,10864,4376,10784,3155,10397,3585,10023,4387,10175,10380,10383,10471,10476,4402,10351,10356,3430,10216,10976,4388,10388,3214,3453,3288,10044,10072,10647,10653,10880,10889,4389,10201,10656,10671,10852,10982,11006,11012,11039,3290,3493,4406,3331,4394,3508,11042,4400,3655,3443,3577,10859,10959,4391,3399,10408,10411,10468,10496,3400,10414,10417,3401,4403,10026,10029,10170,10481,10487,4404,10484,3580,3573,10869,10874,3578,10420,3579,3734,4011,10427,3434,3717,3861,4405,4398,3427,3647,4407,4408,3955,4113,2,9431,6105,5071,4878,4831,4789,4788,4620,4523,4522,4429,4421,5032,5022,4943,4880,4416,4908,4828,9,8,9675,9432,8493,7575,6953,6552,6265,6245,6098,6097,6090,6073,5944,5858,5726,5702,5636,5626,5625,5570,5555,5554,5550,5548,5496,5490,5489,5484,5471,5451,5440,5436,5419,5418,5409,5320,5228,5221,5212,5211,5168,5154,5146,5138,5137,5129,5063,5040,5006,5000,4999,4998,4997,4996,4995,4954,4946,4933,4932,4874,4857,4851,4614,4547,4495,4493,4492,4486,4485,9616,8580,8414,8413,8406,7375,7110,6811,6594,6407,6406,6404,6403,6291,6266,6199,6198,6099,6079,6067,5991,5949,5943,5942,5936,5916,5913,5912,5828,5827,5753,5710,5688,5644,5639,5633,5632,5605,5599,5574,5571,5506,5421,5420,5405,5391,5379,5367,5345,5298,5254,5225,5224,5223,5197,5158,5147,5057,5030,5019,5017,4924,4886,4885,4765,4727,4604,4728,9744,9701,9700,9699,9698,9686,9354,8933,8900,8728,8695,8649,8602,8562,8558,8264,7745,7553,7306,7287,7226,7208,7207,7206,7205,7204,7164,7092,6758,6755,6644,6631,6543,6542,6522,6506,6472,6471,6461,6191,6190,6188,6187,6186,6185,6145,6138,6052,6051,6050,6049,6048,6047,6046,6045,5922,5921,5920,5919,5918,5899,5897,5896,5895,5894,5893,5855,5744,5743,5742,5736,5665,5606,5561,5560,5559,5558,5557,5556,5509,5464,5380,5377,5376,5375,5374,5373,5372,5348,5347,5344,5294,5286,5220,5190,5189,5179,5173,5172,5171,5141,5121,5104,5066,5044,5043,5041,5008,4948,4814,4813,4812,4702,4701,4584,4583,4582,4548,4541,4540,4444,4443,4440,8443,8442,8441,8440,8335,8334,8333,7708,7615,7503,7297,7179,6837,6738,6647,6646,6486,6182,5879,5876,5875,5631,5585,5584,5545,5544,5543,5501,5390,5326,5271,5260,5145,9367,9366,9365,9364,8515,8423,8422,8421,8420,8348,7605,7604,7523,7370,7234,6895,6759,6732,6661,6660,6617,6616,6615,6614,6613,6612,6611,6593,6564,6563,6562,6561,6527,6453,6385,6384,6362,6347,6346,6345,6082,5947,5946,5771,5498,5497,5270,5210,5209,5163,5160,5159,5128,5127,4879,8935,8934,8761,8760,8738,8737,8732,8617,8616,8424,8415,8322,8286,8133,8071,7931,7902,7654,7529,7510,7509,7374,7232,7231,7100,7041,7040,6872,6871,6717,6716,6605,6604,6306,6295,6236,6131,6075,6062,6010,6001,5992,5774,5714,5564,5563,5426,5362,5114,5021,8464,8398,8397,8354,8353,8281,8090,8021,7870,7840,7835,7834,7719,7656,7623,7422,7421,7367,7194,6730,6701,6658,6587,6586,6307,5553,5452,5246,5124,5123,9042,8769,8754,8657,8358,8301,8258,8227,8157,8086]),
% 18.77/18.53 ['proof']).
% 18.77/18.53 % SZS output end Proof
% 18.77/18.53 % Total time :14.880000s
%------------------------------------------------------------------------------