TSTP Solution File: SCT162+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SCT162+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n003.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  : 600s
% DateTime : Mon Jul 18 22:04:15 EDT 2022

% Result   : Theorem 3.86s 4.12s
% Output   : Refutation 3.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SCT162+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.32  % Computer : n003.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Sat Jul  2 01:58:53 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 1.11/1.43  ============================== Prover9 ===============================
% 1.11/1.43  Prover9 (32) version 2009-11A, November 2009.
% 1.11/1.43  Process 16469 was started by sandbox on n003.cluster.edu,
% 1.11/1.43  Sat Jul  2 01:58:54 2022
% 1.11/1.43  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16315_n003.cluster.edu".
% 1.11/1.43  ============================== end of head ===========================
% 1.11/1.43  
% 1.11/1.43  ============================== INPUT =================================
% 1.11/1.43  
% 1.11/1.43  % Reading from file /tmp/Prover9_16315_n003.cluster.edu
% 1.11/1.43  
% 1.11/1.43  set(prolog_style_variables).
% 1.11/1.43  set(auto2).
% 1.11/1.43      % set(auto2) -> set(auto).
% 1.11/1.43      % set(auto) -> set(auto_inference).
% 1.11/1.43      % set(auto) -> set(auto_setup).
% 1.11/1.43      % set(auto_setup) -> set(predicate_elim).
% 1.11/1.43      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.11/1.43      % set(auto) -> set(auto_limits).
% 1.11/1.43      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.11/1.43      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.11/1.43      % set(auto) -> set(auto_denials).
% 1.11/1.43      % set(auto) -> set(auto_process).
% 1.11/1.43      % set(auto2) -> assign(new_constants, 1).
% 1.11/1.43      % set(auto2) -> assign(fold_denial_max, 3).
% 1.11/1.43      % set(auto2) -> assign(max_weight, "200.000").
% 1.11/1.43      % set(auto2) -> assign(max_hours, 1).
% 1.11/1.43      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.11/1.43      % set(auto2) -> assign(max_seconds, 0).
% 1.11/1.43      % set(auto2) -> assign(max_minutes, 5).
% 1.11/1.43      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.11/1.43      % set(auto2) -> set(sort_initial_sos).
% 1.11/1.43      % set(auto2) -> assign(sos_limit, -1).
% 1.11/1.43      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.11/1.43      % set(auto2) -> assign(max_megs, 400).
% 1.11/1.43      % set(auto2) -> assign(stats, some).
% 1.11/1.43      % set(auto2) -> clear(echo_input).
% 1.11/1.43      % set(auto2) -> set(quiet).
% 1.11/1.43      % set(auto2) -> clear(print_initial_clauses).
% 1.11/1.43      % set(auto2) -> clear(print_given).
% 1.11/1.43  assign(lrs_ticks,-1).
% 1.11/1.43  assign(sos_limit,10000).
% 1.11/1.43  assign(order,kbo).
% 1.11/1.43  set(lex_order_vars).
% 1.11/1.43  clear(print_given).
% 1.11/1.43  
% 1.11/1.43  % formulas(sos).  % not echoed (532 formulas)
% 1.11/1.43  
% 1.11/1.43  ============================== end of input ==========================
% 1.11/1.43  
% 1.11/1.43  % From the command line: assign(max_seconds, 300).
% 1.11/1.43  
% 1.11/1.43  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.11/1.43  
% 1.11/1.43  % Formulas that are not ordinary clauses:
% 1.11/1.43  1 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  2 (all V_ca_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> ((hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))) -> -(-hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)))))) # label(fact_equalityCE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  3 (all V_na_2 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),V_na_2))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf))) # label(fact_PiProf) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  4 (all V_i_2 all V_Fa_2 (c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2))))) # label(fact_dictator__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  5 (all V_S_2 all V_R_2 all T_a (hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) <-> V_R_2 = V_S_2)) # label(fact_pred__equals__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  6 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n))) # label(fact_less__not__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  7 (all V_na_2 all V_m_2 (V_m_2 != V_na_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  8 (all V_y all V_x (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x))))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  9 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n))) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  10 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  11 (all V_t all V_s (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  12 (all V_x_2 all T_a hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2))) # label(fact_top1I) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  13 (all V_x_2 all T_a hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_UNIV__I) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  14 (all V_A_2 all T_a all V_ba_2 all V_aa_2 (V_aa_2 = V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  15 (all V_A_2 all T_a all V_y_2 all V_x_2 (V_x_2 = V_y_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))))) # label(fact_eqelem__imp__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  16 (all V_x_2 all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  17 (all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) <-> V_x_2 = V_y_2)) # label(fact_eq__mem) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  18 (all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) <-> hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_mem__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  19 (all V_Pa_2 all V_na_2 all V_m_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) -> hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2))) -> ((V_m_2 = V_na_2 -> hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2))) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) -> hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  20 -(all B_e -c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_c____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_d____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,B_e,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt)))))) # label(fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  21 (all T_a c_List_Odistinct(T_a,c_List_Olist_ONil(T_a))) # label(fact_distinct_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  22 (all V_list_H all V_a_H all T_a c_List_Olist_ONil(T_a) != c_List_Olist_OCons(T_a,V_a_H,V_list_H)) # label(fact_list_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  23 (all V_list_H all V_a_H all T_a c_List_Olist_OCons(T_a,V_a_H,V_list_H) != c_List_Olist_ONil(T_a)) # label(fact_list_Osimps_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  24 (all V_x_2 all T_b all T_a (class_Orderings_Otop(T_a) -> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_top__apply) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  25 (all V_x_2 all T_a hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_iso__tuple__UNIV__I) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  26 (all V_b all V_a (V_a != V_b -> (exists B_c c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,V_a,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,V_b,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,B_c,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt)))))))) # label(fact_third__alt) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  27 (all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),V_L_2)),c_Arrow__Order__Mirabelle_OProf)))) # label(fact_const__Lin__Prof) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  28 (all V_x all T_a all V_xs V_xs != c_List_Olist_OCons(T_a,V_x,V_xs)) # label(fact_not__Cons__self) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  29 (all V_xs all V_x all T_a c_List_Olist_OCons(T_a,V_x,V_xs) != V_xs) # label(fact_not__Cons__self2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  30 (all V_y_2 all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (V_x_2 != V_y_2 -> (-hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2)))))) # label(fact_notin__Lin__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  31 (all V_ba_2 all V_aa_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2))))) # label(fact_Lin__irrefl) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  32 (all V_S_2 all V_R_2 all T_b all T_a (hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) <-> V_R_2 = V_S_2)) # label(fact_pred__equals__eq2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  33 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_aa_2),V_ba_2))) <-> V_x_2 != V_y_2 & (V_x_2 = V_ba_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2))) & (V_x_2 != V_ba_2 -> (V_y_2 = V_ba_2 -> V_x_2 = V_aa_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2))) & (V_y_2 != V_ba_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)))))))) # label(fact_in__above) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  34 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_z_2))) <-> V_y_2 != V_z_2 & (V_x_2 = V_z_2 -> V_x_2 != V_y_2) & (V_x_2 != V_z_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))))) # label(fact_in__mkbot) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  35 (all V_z_2 all V_L_2 all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_z_2))) <-> V_x_2 != V_z_2 & (V_y_2 = V_z_2 -> V_x_2 != V_y_2) & (V_y_2 != V_z_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))))) # label(fact_in__mktop) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  36 (all V_L_2 all V_y_2 all V_x_2 (V_x_2 != V_y_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin))))) # label(fact_above__Lin) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  37 (all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_mkbot__Lin) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  38 (all V_x_2 all V_L_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)))) # label(fact_mktop__Lin) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  39 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  40 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (V_x_2 != V_y_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  41 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) | V_x_2 = V_y_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  42 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) | V_x = V_y | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  43 (all V_x_2 all V_y_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  44 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  45 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  46 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  47 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.43  48 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_x != V_y))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  49 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_y != V_x))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  50 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  51 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  52 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  53 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  54 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  55 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  56 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  57 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  58 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__asym) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  59 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (V_x != V_y -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  60 (all V_list_H_2 all V_a_H_2 all V_list_2 all V_aa_2 all T_a (c_List_Olist_OCons(T_a,V_aa_2,V_list_2) = c_List_Olist_OCons(T_a,V_a_H_2,V_list_H_2) <-> V_aa_2 = V_a_H_2 & V_list_2 = V_list_H_2)) # label(fact_list_Oinject) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  61 (all V_y_2 all V_x_2 all V_L_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_aa_2,V_ba_2))) <-> V_x_2 != V_y_2 & (V_y_2 = V_aa_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2))) & (V_y_2 != V_aa_2 -> (V_x_2 = V_aa_2 -> V_y_2 = V_ba_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2))) & (V_x_2 != V_aa_2 -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)))))))) # label(fact_in__below) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  62 (all V_x_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2)) # label(fact_inv__f__f) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  63 (all V_y_2 all V_x_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (hAPP(V_f_2,V_x_2) = V_y_2 -> hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2))) # label(fact_inv__f__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  64 (all V_x_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2))) # label(fact_inv__into__f__f) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  65 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (hAPP(V_f_2,V_x_2) = V_y_2 -> hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2)))) # label(fact_inv__into__f__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  66 (all T_c all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a,c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_inj__fun) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  67 (all V_L_2 all V_y_2 all V_x_2 (V_x_2 != V_y_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin))))) # label(fact_below__Lin) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  68 (all V_y_2 all V_x_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) -> V_x_2 = V_y_2))) # label(fact_injD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  69 (all V_y_2 all V_x_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_inj__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  70 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (V_x_2 != V_y_2 -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) -> hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)))))) # label(fact_inj__on__contraD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  71 (all V_ca_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))))) # label(fact_psubsetD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  72 (all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) -> (hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) -> B_x = B_xa))))))) # label(fact_inj__on__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  73 (all V_A_2 all T_a c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2)) # label(fact_inj__on__id2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  74 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) -> V_x_2 = V_y_2))))) # label(fact_inj__onD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  75 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) <-> V_x_2 = V_y_2))))) # label(fact_inj__on__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  76 (all V_fs_2 all T_a all V_y_2 all V_x_2 all V_f_2 (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))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat),V_f_2,V_fs_2)))))) # label(fact_measures__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  77 (all V_fs_2 all V_f_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat),V_f_2,V_fs_2)))) <-> 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))) | hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))))) # label(fact_in__measures_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  78 (all V_y_2 all V_x_2 all V_R_2 all T_b all T_a (c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)))) # label(fact_in__rel__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  79 (all V_va all V_v all T_a c_List_Osplice(T_a,c_List_Olist_OCons(T_a,V_v,V_va),c_List_Olist_ONil(T_a)) = c_List_Olist_OCons(T_a,V_v,V_va)) # label(fact_splice_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  80 (all T_a all V_R_2 all V_y_2 all V_y_H_2 all T_b all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2)))))) # label(fact_same__fstI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  81 (all V_f2_2 all V_f1_2 all T_b all T_a c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,c_List_Olist_ONil(T_b)) = V_f1_2) # label(fact_list_Osimps_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  82 (all V_C_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))))) # label(fact_psubset__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  83 (all V_ys all V_y all V_xs all V_x all T_a c_List_Osplice(T_a,c_List_Olist_OCons(T_a,V_x,V_xs),c_List_Olist_OCons(T_a,V_y,V_ys)) = c_List_Olist_OCons(T_a,V_x,c_List_Olist_OCons(T_a,V_y,c_List_Osplice(T_a,V_xs,V_ys)))) # label(fact_splice_Osimps_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  84 (all V_xs all T_a c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs) # label(fact_splice__Nil2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  85 (all V_ys all T_a c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys) # label(fact_splice_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  86 (all V_y_2 all V_x_2 all T_a -hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat)))))) # label(fact_in__measures_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  87 (all V_list_2 all V_aa_2 all V_f2_2 all V_f1_2 all T_b all T_a c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,c_List_Olist_OCons(T_b,V_aa_2,V_list_2)) = hAPP(hAPP(V_f2_2,V_aa_2),V_list_2)) # label(fact_list_Osimps_I5_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  88 -(all B_Lab (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),B_Lab)) -> -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lab),c_Arrow__Order__Mirabelle_OLin)))) # label(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  89 -(all B_Lba (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),B_Lba)) -> -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lba),c_Arrow__Order__Mirabelle_OLin)))) # label(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  90 (all B_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),v_n____)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))))) # label(fact_n_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  91 (all V_s_2 all V_r_2 all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_2)) | V_aa_2 = V_a_H_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_H_2)),V_s_2)))) # label(fact_in__lex__prod) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  92 (all V_fs_2 all T_a all V_y_2 all V_x_2 all V_f_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat),V_f_2,V_fs_2))))))) # label(fact_measures__lesseq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  93 (all V_f_2 all V_y_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omeasure(T_a,V_f_2))) <-> 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))))) # label(fact_in__measure) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  94 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)))) # label(fact_order__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  95 (all V_y all V_z all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) -> hBOOL(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))))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  96 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) -> hBOOL(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))))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  97 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  98 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))))) # label(fact_le__funE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  99 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  100 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  101 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)))))) # label(fact_order__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  102 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  103 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  104 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  105 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  106 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  107 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  108 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))))) # label(fact_le__funD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  109 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  110 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_x_2 = V_y_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  111 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)))) # label(fact_linorder__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  112 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) <-> (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  113 (all V_n all V_k all V_m (hBOOL(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)) -> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))))) # label(fact_add__leE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  114 (all V_n all V_k all V_m (hBOOL(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)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_add__leD1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  115 (all V_n all V_k all V_m (hBOOL(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)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)))) # label(fact_add__leD2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  116 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) -> hBOOL(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)))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  117 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> V_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  118 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k))))) # label(fact_le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  119 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(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))))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  120 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(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))))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  121 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(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))))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  122 (all V_n all V_m (V_m = V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  123 (all V_na_2 all V_m_2 all V_k_2 (hBOOL(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_na_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  124 (all V_na_2 all V_k_2 all V_m_2 (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_na_2),V_k_2) <-> V_m_2 = V_na_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  125 (all V_na_2 all V_m_2 all V_k_2 (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_na_2) <-> V_m_2 = V_na_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  126 (all V_k all V_n all 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))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  127 (all V_z all V_y all 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))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  128 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  129 (all V_n all 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)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  130 (all V_na_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) <-> (exists B_k V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  131 (all V_m all V_n hBOOL(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)))) # label(fact_le__add1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  132 (all V_m all V_n hBOOL(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)))) # label(fact_le__add2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  133 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n))) # label(fact_le__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  134 (all V_N_2 all 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)) # label(fact_inj__on__add__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  135 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  136 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  137 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  138 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  139 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_a != V_b -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  140 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_a != V_b -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  141 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) | V_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  142 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  143 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  144 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))))) # label(fact_leD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  145 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  146 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  147 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  148 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))))) # label(fact_not__leE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  149 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_leI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  150 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) | V_x_2 = V_y_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  151 (all V_y_2 all V_x_2 all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  152 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  153 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  154 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  155 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  156 (all V_k all V_j all 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_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)))) # label(fact_add__lessD1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.44  157 (all V_n all V_m all V_l all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) -> (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) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  158 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) -> 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)))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  159 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),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_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  160 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> 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))))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  161 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> 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))))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  162 (all V_na_2 all V_m_2 all V_k_2 (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_na_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  163 (all V_i all 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))) # label(fact_not__add__less2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  164 (all V_j all 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))) # label(fact_not__add__less1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  165 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> 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))))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  166 (all V_y all V_z all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) -> 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))))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  167 (all V_x all T_a (class_Orderings_Otop(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),c_Orderings_Otop__class_Otop(T_a))))) # label(fact_top__greatest) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  168 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) | V_m = V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  169 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (V_m != V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  170 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  171 (all V_na_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) | V_m_2 = V_na_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  172 (all V_na_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) & V_m_2 != V_na_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  173 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  174 (exists B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) & (all B_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))))) & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))))) # label(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  175 (all V_P_H_2 all V_Pa_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(V_P_H_2,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(v_F,V_P_H_2))))))))) # label(fact__C3_C) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  176 (all V_P_H_2 all V_Pa_2 all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (V_a_H_2 != V_b_H_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2)))))))))) # label(fact_pairwise__neutrality) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  177 (all V_P_H_2 all V_Pa_2 all V_ca_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (V_ba_2 != V_ca_2 -> (V_aa_2 != V_ca_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(V_P_H_2,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(v_F,V_P_H_2))))))))))) # label(fact__C4_C) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  178 (all V_P_H_2 all V_Pa_2 all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (V_a_H_2 != V_b_H_2 -> (V_aa_2 != V_b_H_2 -> (V_ba_2 != V_a_H_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2)))))))))))) # label(fact__C1_C) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  179 (all V_P_H_2 all V_Pa_2 all V_b_H_2 all V_a_H_2 all V_ba_2 all V_aa_2 (V_aa_2 != V_ba_2 -> (V_a_H_2 != V_b_H_2 -> (V_aa_2 != V_b_H_2 -> (V_ba_2 != V_a_H_2 -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2)))))))))))) # label(fact__C2_C) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  180 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (-hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) -> -hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))))) # label(fact_PiE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  181 (all V_ca_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))))) # label(fact_subsetD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  182 (all V_B_2 all T_b all V_A_2 all V_A_H_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2),V_A_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2))))) # label(fact_Pi__anti__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  183 (all V_S_2 all V_R_2 all T_b all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2),V_S_2)))) # label(fact_pred__subset__eq2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  184 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_in__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  185 (all V_B_2 all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_set__rev__mp) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  186 (all V_x_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))))) # label(fact_set__mp) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  187 (all V_A_2 all T_a hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_subset__UNIV) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  188 (all V_A_2 all V_B_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)))) # label(fact_subset__inj__on) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  189 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) & -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2),V_f_2))))) # label(fact_less__fun__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  190 (all V_C_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))))) # label(fact_subset__psubset__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  191 (all V_C_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))))) # label(fact_psubset__subset__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  192 (all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)))) # label(fact_psubset__imp__subset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  193 (all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) | V_A_2 = V_B_2)) # label(fact_subset__iff__psubset__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  194 (all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) & V_A_2 != V_B_2)) # label(fact_psubset__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  195 (all V_S_2 all V_R_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2),V_S_2)))) # label(fact_pred__subset__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  196 (all V_A_2 all T_a hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2))))) # label(fact_funcset__id) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  197 (all V_A_2 all T_b all T_a c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) # label(fact_Pi__UNIV) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  198 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))))) # label(fact_Pi__mem) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  199 (all V_x_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2))))) # label(fact_funcset__mem) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  200 -(all B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) -> ((all B_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))))) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____))))))) # label(fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  201 (all V_i_2 all V_Fa_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b (B_a != B_b -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))))))) -> c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)))) # label(fact_dictatorI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  202 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> 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)))))) # label(fact_less__add__one) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  203 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> 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))))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  204 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> 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))))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  205 (all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) -> V_A_2 = V_B_2))) # label(fact_equalityI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  206 (all V_Q_2 all T_b all T_a all V_y_2 all V_x_2 all V_Pa_2 (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) -> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))))) # label(fact_rev__predicate2D) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  207 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2))))) # label(fact_equalityE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  208 (all V_y_2 all V_x_2 all V_Q_2 all V_Pa_2 all T_b all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))))) # label(fact_predicate2D) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  209 (all V_C_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))))) # label(fact_subset__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  210 (all V_x_2 all V_Q_2 all V_Pa_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) -> (hBOOL(hAPP(V_Pa_2,V_x_2)) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_predicate1D) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  211 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)))) # label(fact_equalityD2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  212 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)))) # label(fact_equalityD1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  213 (all V_Q_2 all T_a all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) -> hBOOL(hAPP(V_Q_2,V_x_2))))) # label(fact_rev__predicate1D) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  214 (all T_a all V_B_2 all V_A_2 (V_A_2 = V_B_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)))) # label(fact_set__eq__subset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  215 (all V_A_2 all T_a hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_A_2))) # label(fact_subset__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  216 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  217 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> 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)))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  218 (all V_ca_2 all V_ba_2 all V_aa_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2) <-> V_ba_2 = V_ca_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  219 (all V_ca_2 all V_aa_2 all V_ba_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2) <-> V_ba_2 = V_ca_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  220 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(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_a),V_c) -> V_b = V_c))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  221 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(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_a),V_c) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  222 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (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) -> V_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  223 (all V_x_2 all T_a (class_Groups_Oone(T_a) -> (c_Groups_Oone__class_Oone(T_a) = V_x_2 <-> V_x_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_one__reorient) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  224 (all V_ba_2 all V_ca_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2))))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  225 (all V_ba_2 all V_aa_2 all V_ca_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2))))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  226 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(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)))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  227 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(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)))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  228 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> hBOOL(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))))))) # label(fact_add__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  229 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(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))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  230 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(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))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  231 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (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))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  232 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (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))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.45  233 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> 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))))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  234 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> 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)))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  235 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> 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)))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  236 (all V_ba_2 all V_aa_2 all V_ca_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  237 (all V_ba_2 all V_ca_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  238 (all V_R_2 all T_a all V_y_2 all V_x_2 all V_f_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)))))) # label(fact_mlex__leq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  239 (all V_R_2 all T_a all V_y_2 all V_x_2 all V_f_2 (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))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))))) # label(fact_mlex__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  240 (all V_Fa_2 (c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b ((all B_i hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))))))))) # label(fact_unanimity__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  241 (all V_Fa_2 (c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf)) -> (all B_a all B_b ((all B_i (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa)))))))))))) # label(fact_IIA__def) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  242 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) -> (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (c_Finite__Set_Ofinite(T_b,V_B_2) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))))))) # label(fact_card__inj) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  243 (all V_C_2 all V_B_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),hAPP(V_B_2,B_x)),hAPP(V_C_2,B_x))))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_C_2))))) # label(fact_Pi__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  244 (all V_B_2 all V_f_2 all T_b all V_A_2 all T_a ((all B_x (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))))) # label(fact_Pi__I) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  245 (all V_g_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) -> (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_g_2),c_FuncSet_OPi(T_b,T_a,V_B_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_A_2)))) -> (c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) -> (c_Finite__Set_Ofinite(T_a,V_A_2) -> (c_Finite__Set_Ofinite(T_b,V_B_2) -> c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2)))))))) # label(fact_card__bij) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  246 (all V_A_2 all V_B_2 all T_a (c_Finite__Set_Ofinite(T_a,V_B_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_card__psubset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  247 (all V_A_2 all V_B_2 all T_a (c_Finite__Set_Ofinite(T_a,V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2)))))) # label(fact_psubset__card__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  248 (all V_A_2 all V_B_2 all T_a (c_Finite__Set_Ofinite(T_a,V_B_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2)))))) # label(fact_card__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  249 (all V_A_2 all V_B_2 all T_a (c_Finite__Set_Ofinite(T_a,V_B_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_B_2)),c_Finite__Set_Ocard(T_a,V_A_2))) -> V_A_2 = V_B_2)))) # label(fact_card__seteq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  250 (all V_A_2 all T_a (class_Finite__Set_Ofinite(T_a) -> c_Finite__Set_Ofinite(T_a,V_A_2))) # label(fact_finite__code) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  251 (all V_A_2 all T_a (class_Finite__Set_Ofinite(T_a) -> c_Finite__Set_Ofinite(T_a,V_A_2))) # label(fact_finite) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  252 (all V_A_2 all V_B_2 all T_a (c_Finite__Set_Ofinite(T_a,V_B_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> c_Finite__Set_Ofinite(T_a,V_A_2)))) # label(fact_rev__finite__subset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  253 (all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> (c_Finite__Set_Ofinite(T_a,V_B_2) -> c_Finite__Set_Ofinite(T_a,V_A_2)))) # label(fact_finite__subset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  254 (all T_a (c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))) <-> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_finite__option__UNIV) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  255 (all T_b all T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))) <-> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_finite__Plus__UNIV__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  256 (all T_b all T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))))) # label(fact_finite__Prod__UNIV) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  257 (all T_a (class_Finite__Set_Ofinite(T_a) -> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_finite__UNIV) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  258 (all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_card__eq__UNIV__imp__eq__UNIV) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  259 (all T_b all T_a (c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) -> c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_finite__fun__UNIVD2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  260 (all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) & c_Finite__Set_Ofinite(T_a,V_B_2))) # label(fact_in__finite__psubset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  261 (all V_B_2 all T_b all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (c_Finite__Set_Ofinite(T_b,V_B_2) -> c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))))) # label(fact_card__Plus) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  262 (all V_x_2 all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,V_A_2))))) # label(fact_card_Oinsert) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  263 (all V_B_2 all V_A_2 all V_Fa_2 all V_g_2 all V_z_2 all V_f_2 all T_b all T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) -> (c_Finite__Set_Ofinite(T_b,V_A_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) -> hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2))))) # label(fact_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  264 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) -> (V_aa_2 != V_ba_2 -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_insertE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  265 (all V_ba_2 all V_B_2 all V_aa_2 all T_a ((-hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) -> V_aa_2 = V_ba_2) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))))) # label(fact_insertCI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  266 (all V_aa_2 all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)))) # label(fact_finite_OinsertI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  267 (all V_A_2 all V_aa_2 all T_a (c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) <-> c_Finite__Set_Ofinite(T_a,V_A_2))) # label(fact_finite__insert) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  268 (all V_x_2 all V_A_2 all V_Fa_2 all V_g_2 all V_z_2 all V_f_2 all T_b all T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) -> (c_Finite__Set_Ofinite(T_b,V_A_2) -> hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2))))) # label(fact_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  269 (all V_x_2 all V_Fa_2 all V_g_2 all V_z_2 all V_f_2 all T_b all T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) -> hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2)) # label(fact_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  270 (all V_B_2 all V_aa_2 all T_a hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)))) # label(fact_insertI1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  271 (all V_A_2 all V_ba_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) <-> V_aa_2 = V_ba_2 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)))) # label(fact_insert__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  272 (all V_B_2 all V_A_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) -> (c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2) <-> V_A_2 = V_B_2)))) # label(fact_insert__ident) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  273 (all V_ba_2 all V_B_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))))) # label(fact_insertI2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  274 (all V_A_2 all V_aa_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) -> c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2)) # label(fact_insert__absorb) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  275 (all V_x_2 all V_A_2 all V_y_2 all T_a (hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) <-> V_y_2 = V_x_2 | hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_insert__code) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  276 (all V_A_2 all V_y_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))) # label(fact_insert__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  277 (all V_A_2 all V_x_2 all T_a c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2)) # label(fact_insert__absorb2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  278 (all V_aa_2 all V_B_2 all T_a hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2)))) # label(fact_subset__insertI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  279 (all V_ba_2 all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))))) # label(fact_subset__insertI2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  280 (all V_aa_2 all V_D_2 all V_C_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_D_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2)),c_Set_Oinsert(T_a,V_aa_2,V_D_2))))) # label(fact_insert__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  281 (all V_B_2 all V_A_2 all T_b all T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) -> c_Finite__Set_Ofinite(T_b,V_B_2))) # label(fact_finite__PlusD_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  282 (all V_B_2 all V_A_2 all T_b all T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) -> c_Finite__Set_Ofinite(T_a,V_A_2))) # label(fact_finite__PlusD_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  283 (all V_B_2 all T_b all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (c_Finite__Set_Ofinite(T_b,V_B_2) -> c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))))) # label(fact_finite__Plus) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  284 (all V_B_2 all V_A_2 all T_b all T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) <-> c_Finite__Set_Ofinite(T_a,V_A_2) & c_Finite__Set_Ofinite(T_b,V_B_2))) # label(fact_finite__Plus__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  285 (all V_B_2 all V_A_2 all V_x_2 all T_a (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_x_2,V_B_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))))) # label(fact_subset__insert) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  286 (all V_B_2 all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2)),V_B_2)) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)))) # label(fact_insert__subset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  287 (all V_x_2 all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)))))) # label(fact_card__insert__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  288 (all V_x_2 all V_A_2 all V_Fa_2 all V_g_2 all V_z_2 all V_f_2 all T_b all T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) -> (c_Finite__Set_Ofinite(T_b,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2))))) # label(fact_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  289 (all T_b all T_a c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))) # label(fact_UNIV__Plus__UNIV) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  290 (all V_B_2 all T_b all V_A_2 all T_a ((c_Finite__Set_Ofinite(T_a,V_A_2) & c_Finite__Set_Ofinite(T_b,V_B_2) -> c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) & (-(c_Finite__Set_Ofinite(T_a,V_A_2) & c_Finite__Set_Ofinite(T_b,V_B_2)) -> c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_card__Plus__conv__if) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  291 (all V_x_2 all V_A_2 all V_Fa_2 all V_g_2 all V_z_2 all V_f_2 all T_b all T_a (c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) -> (c_Finite__Set_Ofinite(T_b,V_A_2) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)))))) # label(fact_folding__image__simple_Oinsert) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  292 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__zeroE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  293 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_le0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  294 (all V_x_2 all T_a (class_Groups_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_x_2 <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  295 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  296 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  297 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  298 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  299 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  300 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a))) # label(fact_zero__neq__one) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  301 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_one__neq__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  302 (all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)))) # label(fact_gr0I) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  303 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  304 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  305 (all V_na_2 (V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)))) # label(fact_neq0__conv) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  306 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_not__less0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  307 (all V_n all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  308 (all V_na_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  309 (all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  310 (all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  311 (all V_na_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_le__0__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  312 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  313 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(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))))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  314 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  315 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  316 (all V_y_2 all V_x_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  317 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(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))))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  318 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  319 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(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_aa_2),V_aa_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2))))) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  320 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> 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))))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  321 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> 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))))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  322 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> 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))))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  323 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  324 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (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_aa_2),V_aa_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_aa_2))))) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  325 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__le__one) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  326 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  327 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__less__one) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  328 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  329 (all V_na_2 all V_m_2 (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_na_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)))) # label(fact_add__gr__0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  330 (all V_A_2 all T_a (-c_Finite__Set_Ofinite(T_a,V_A_2) -> c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_card__infinite) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  331 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> 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))))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  332 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> 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))))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  333 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> 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))))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  334 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> 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))))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  335 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> 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))))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  336 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> 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))))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  337 (all T_a (class_Rings_Olinordered__semidom(T_a) -> 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)))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  338 (all V_A_2 all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,V_A_2))) -> c_Finite__Set_Ofinite(T_a,V_A_2))) # label(fact_card__ge__0__finite) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  339 (all T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))))) # label(fact_finite__UNIV__card__ge__0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  340 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  341 (all T_b all T_a (c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) -> (c_Finite__Set_Ocard(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) -> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_finite__fun__UNIVD1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  342 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  343 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n)))) # label(fact_lessI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  344 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))))) # label(fact_Suc__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  345 (all 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)))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  346 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  347 (all V_nat_H c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  348 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  349 (all V_nat_H_1 hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  350 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  351 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  352 (all V_y all V_x (hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) -> V_x = V_y)) # label(fact_Suc__inject) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  353 (all V_nat_H_2 all V_nat_2 (hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) <-> V_nat_2 = V_nat_H_2)) # label(fact_nat_Oinject) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  354 (all V_n hAPP(c_Nat_OSuc,V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  355 (all V_n V_n != hAPP(c_Nat_OSuc,V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  356 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_Suc__leD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  357 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> V_m = hAPP(c_Nat_OSuc,V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  358 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__SucI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  359 (all V_m_2 all V_na_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),V_m_2)))) # label(fact_Suc__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  360 (all V_na_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) | V_m_2 = hAPP(c_Nat_OSuc,V_na_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  361 (all V_na_2 all V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  362 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n))) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  363 (all V_n all 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))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  364 (all V_n all 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))) # label(fact_add__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  365 (all V_n all 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))) # label(fact_add__Suc__right) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  366 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__less__SucD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  367 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__lessD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  368 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> V_m = V_n))) # label(fact_less__SucE) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  369 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k))))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  370 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> (hAPP(c_Nat_OSuc,V_m) != V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.46  371 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_less__SucI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  372 (all V_m all V_n (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) -> V_m = V_n))) # label(fact_less__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  373 (all V_m_2 all V_na_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) <-> V_na_2 = V_m_2))) # label(fact_not__less__less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  374 (all V_na_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)))) # label(fact_Suc__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  375 (all V_na_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) | V_m_2 = V_na_2)) # label(fact_less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  376 (all V_na_2 all V_m_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))))) # label(fact_not__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  377 (all V_N_2 c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2)) # label(fact_inj__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  378 (all V_na_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | (exists B_j (V_m_2 = hAPP(c_Nat_OSuc,B_j) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)))))) # label(fact_less__Suc__eq__0__disj) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  379 (all V_na_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <-> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__Suc0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  380 (all V_na_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) <-> (exists B_m V_na_2 = hAPP(c_Nat_OSuc,B_m)))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  381 (all V_na_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  382 (all V_na_2 all V_m_2 (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_na_2) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_one__is__add) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  383 (all V_na_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) <-> (exists B_k V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))) # label(fact_less__iff__Suc__add) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  384 (all V_m all 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))))) # label(fact_less__add__Suc2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  385 (all V_m all 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))))) # label(fact_less__add__Suc1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  386 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__le__lessD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  387 (all V_na_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) <-> V_na_2 = V_m_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  388 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)))) # label(fact_Suc__leI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  389 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  390 (all V_na_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)))) # label(fact_Suc__le__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  391 (all V_na_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)))) # label(fact_less__Suc__eq__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  392 (all V_m_2 all V_na_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  393 (all V_na_2 hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2))) # label(fact_less__eq__Suc__le__raw) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  394 (all V_x_2 all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2)) & (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2))))) # label(fact_card__insert__if) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  395 (all V_x_2 all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (-hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2))))) # label(fact_card__insert__disjoint) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  396 (all 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))) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  397 (all 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)) # label(fact_Suc__eq__plus1__left) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  398 (all 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)))) # label(fact_nat_Osize_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  399 (all V_nat c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat_Osize_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  400 (all V_n c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n) # label(fact_nat__size) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  401 (all V_list_2 all V_aa_2 all V_fa_2 all T_a c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_OCons(T_a,V_aa_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_aa_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_list_Osize_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  402 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_aa_2)),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_Ints__odd__less__0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  403 (all T_a (class_Rings_Oring__1(T_a) -> hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))))) # label(fact_Ints__0) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  404 (all V_ba_2 all V_aa_2 all T_a (class_Rings_Oring__1(T_a) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Int_Oring__1__class_OInts(T_a))) -> hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_a))))))) # label(fact_Ints__add) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  405 (all T_a (class_Rings_Oring__1(T_a) -> hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))))) # label(fact_Ints__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  406 (all V_fa_2 all T_a c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_list_Osize_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  407 (all V_aa_2 all T_a (class_Int_Oring__char__0(T_a) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_Ints__double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  408 (all V_aa_2 all T_a (class_Int_Oring__char__0(T_a) -> (hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_aa_2)),V_aa_2) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_Ints__odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  409 (all V_aa_2 all V_ba_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  410 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  411 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(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_c),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  412 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  413 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  414 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  415 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  416 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  417 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  418 (all V_na_2 all V_Pa_2 (-hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_Pa_2,V_na_2)) -> (exists B_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2)) & (all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) -> -hBOOL(hAPP(V_Pa_2,B_i)))) & 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))))))))) # label(fact_ex__least__nat__less) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  419 (all T_a all V_A_2 all T_b all V_x_2 all V_f_2 all V_ba_2 (V_ba_2 = hAPP(V_f_2,V_x_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))))) # label(fact_image__eqI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  420 (all V_ha_2 all T_b all V_Fa_2 all T_a (c_Finite__Set_Ofinite(T_a,V_Fa_2) -> c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_ha_2,V_Fa_2)))) # label(fact_finite__imageI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  421 (all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_b,V_A_2))) -> -c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2))) # label(fact_pigeonhole) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  422 (all V_ba_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) <-> (exists B_x (V_ba_2 = hAPP(V_f_2,B_x) & (all B_y (V_ba_2 = hAPP(V_f_2,B_y) -> B_y = B_x))))))) # label(fact_range__ex1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  423 (all V_A_2 all V_aa_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_aa_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) <-> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))))) # label(fact_inj__image__mem__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  424 (all V_f_2 all V_B_2 all T_b all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) -> c_Finite__Set_Ofinite(T_b,V_B_2)))) # label(fact_finite__surj) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  425 (all V_A_2 all V_f_2 all T_b all T_a (c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)) -> (c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) -> c_Finite__Set_Ofinite(T_b,V_A_2)))) # label(fact_finite__imageD) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  426 (all V_Pa_2 all V_na_2 ((exists B_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) & hBOOL(hAPP(V_Pa_2,B_m)))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2))) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ex__nat__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  427 (all V_Pa_2 all V_na_2 ((all B_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) -> hBOOL(hAPP(V_Pa_2,B_m)))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_all__nat__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  428 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) = c_Set_Oimage(T_a,T_b,V_f_2,V_B_2) <-> V_A_2 = V_B_2))) # label(fact_inj__image__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  429 (all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2))) # label(fact_card__image) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  430 (all V_y_2 all V_x_2 all V_f_2 all V_A_2 all T_b all T_a (hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) -> V_x_2 = V_y_2)))) # label(fact_inv__into__injective) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  431 (all V_A_2 all V_f_2 all T_b all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_x_2)),V_A_2)))) # label(fact_inv__into__into) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  432 (all V_A_2 all V_f_2 all T_b all V_y_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) -> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_y_2)) = V_y_2)) # label(fact_f__inv__into__f) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  433 (all V_B_H_2 all V_A_H_2 all V_A_2 all V_f_2 all T_a all T_b (c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = V_A_H_2 -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_H_2),V_A_H_2)) -> c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_H_2)) = V_B_H_2))) # label(fact_image__inv__into__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  434 (all V_A_2 all V_f_2 all T_a all T_b (c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) -> c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_A_2)) = V_A_2)) # label(fact_image__surj__f__inv__f) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  435 (all V_y_2 all V_f_2 all T_a all T_b (c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) -> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2)) # label(fact_surj__f__inv__f) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  436 (all V_f_2 all T_a all T_b (c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) <-> (all B_x hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_x)) = B_x))) # label(fact_surj__iff__all) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  437 (all V_A_2 all V_B_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)))))) # label(fact_inj__on__strict__subset) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  438 (all V_f_2 all T_c all V_g_2 all T_b all T_a (c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) -> c_Finite__Set_Ofinite(T_c,c_Set_Oimage(T_b,T_c,hAPP(c_COMBB(T_a,T_c,T_b,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_finite__range__imageI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  439 (all V_g_2 all V_f_2 all T_c all T_a all T_b c_Set_Oimage(T_b,T_a,hAPP(c_COMBB(T_c,T_a,T_b,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Set_Oimage(T_c,T_a,V_f_2,c_Set_Oimage(T_b,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_range__composition) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  440 (all V_A_2 all V_f_2 all T_b all V_z_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & V_z_2 = hAPP(V_f_2,B_x))))) # label(fact_image__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  441 (all V_f_2 all T_b all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))))) # label(fact_imageI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  442 (all T_b all V_f_2 all V_ba_2 all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> (V_ba_2 = hAPP(V_f_2,V_x_2) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))))) # label(fact_rev__image__eqI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  443 (all V_B_2 all V_aa_2 all V_f_2 all T_a all T_b c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oinsert(T_b,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,hAPP(V_f_2,V_aa_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2))) # label(fact_image__insert) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  444 (all V_f_2 all T_b all V_B_2 all V_A_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))))) # label(fact_image__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  445 (all V_A_2 all V_f_2 all T_b all V_B_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) <-> (exists B_AA (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA),V_A_2)) & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA))))) # label(fact_subset__image__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  446 (all V_A_2 all V_g_2 all T_c all V_f_2 all T_a all T_b c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_c,T_b,V_g_2,V_A_2)) = c_Set_Oimage(T_c,T_a,hAPP(c_COMBB(T_b,T_a,T_c,V_f_2),V_g_2),V_A_2)) # label(fact_image__image) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  447 (all V_Y_2 all T_a c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2) # label(fact_image__ident) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  448 (all T_b all V_x_2 all V_f_2 all T_a hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_rangeI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  449 (all T_b all T_a all V_x_2 all V_f_2 all V_ba_2 (V_ba_2 = hAPP(V_f_2,V_x_2) -> hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_range__eqI) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  450 (all V_f_2 all T_b all V_A_2 all V_x_2 all T_a (hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) -> c_Set_Oinsert(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) # label(fact_insert__image) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  451 (all V_f_2 all T_b all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) -> c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)))) # label(fact_eq__card__imp__inj__on) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  452 (all V_f_2 all T_b all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) <-> c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2)))) # label(fact_inj__on__iff__eq__card) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  453 (all V_f_2 all T_b all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_a,V_A_2))))) # label(fact_card__image__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  454 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))))) # label(fact_inj__image__subset__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  455 (all V_f_2 all T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_finite__UNIV__inj__surj) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  456 (all V_f_2 all T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> (c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) -> c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))))) # label(fact_finite__UNIV__surj__inj) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  457 (all V_f_2 all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)),V_A_2)) -> (c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) -> c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2)))) # label(fact_endo__inj__surj) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  458 (all V_f_2 all V_A_2 all T_a (c_Finite__Set_Ofinite(T_a,V_A_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2))) -> c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)))) # label(fact_finite__surj__inj) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  459 (all V_A_2 all V_f_2 all T_b all V_B_2 all T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) -> c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_2))) # label(fact_inj__on__inv__into) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  460 (all V_S_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_S_2),V_A_2)) -> c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_S_2)) = V_S_2))) # label(fact_inv__into__image__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  461 (all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) # label(fact_inj__imp__surj__inv) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  462 (all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = V_A_2)) # label(fact_image__inv__f__f) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  463 (all V_X_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) -> c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_X_2)) = V_X_2)) # label(fact_inv__image__comp) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  464 (all V_f_2 all T_a all T_b (c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) -> c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) # label(fact_surj__imp__inj__inv) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  465 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)))) # label(fact_funcset__image) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  466 (all V_g_2 all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)) -> (c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_g_2,V_B_2)),V_A_2)) -> (c_Finite__Set_Ofinite(T_a,V_A_2) -> (c_Finite__Set_Ofinite(T_b,V_B_2) -> c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2)))))))) # label(fact_card__bij__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  467 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)) -> (c_Finite__Set_Ofinite(T_b,V_B_2) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))))))) # label(fact_card__inj__on__le) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  468 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.47  469 (all T_1 all T_2 (class_Finite__Set_Ofinite(T_2) & class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_fun(T_2,T_1)))) # label(arity_fun__Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  470 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  471 (all T_2 all T_1 (class_Orderings_Otop(T_1) -> class_Orderings_Otop(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Otop) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  472 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  473 (all T_1 all T_2 (class_Finite__Set_Ofinite(T_2) & class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_sum(T_2,T_1)))) # label(arity_sum__Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  474 (all T_1 (class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)))) # label(arity_Option__Ooption__Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  475 (all T_1 all T_2 (class_Finite__Set_Ofinite(T_2) & class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_prod(T_2,T_1)))) # label(arity_prod__Finite__Set_Ofinite) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  476 (all V_P all T_a hAPP(c_COMBI(T_a),V_P) = V_P) # label(help_c__COMBI__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  477 (all V_Q all V_P all T_b all T_a hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P) # label(help_c__COMBK__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  478 (all V_R_2 all V_Q_2 all V_Pa_2 all T_c all T_a all T_b hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2))) # label(help_c__COMBB__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  479 (all V_R_2 all V_Q_2 all V_Pa_2 all T_a all T_c all T_b hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2)) # label(help_c__COMBC__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  480 (all V_R_2 all V_Q_2 all V_Pa_2 all T_a all T_c all T_b hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2))) # label(help_c__COMBS__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  481 (all V_y_2 all V_x_2 (-hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  482 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause).  [assumption].
% 1.11/1.48  
% 1.11/1.48  ============================== end of process non-clausal formulas ===
% 1.11/1.48  
% 1.11/1.48  ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.48  
% 1.11/1.48  ============================== PREDICATE ELIMINATION =================
% 1.11/1.48  483 c_Arrow__Order__Mirabelle_Odictator(A,B) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f2(B,A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_dictator__def) # label(axiom).  [clausify(4)].
% 1.11/1.48  484 -c_Arrow__Order__Mirabelle_Odictator(A,B) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B) # label(fact_dictator__def) # label(axiom).  [clausify(4)].
% 1.11/1.48  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f2(A,B)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(B,C) = hAPP(C,A).  [resolve(483,a,484,a)].
% 1.11/1.48  485 c_Arrow__Order__Mirabelle_Odictator(A,B) | hAPP(A,f2(B,A)) != hAPP(f2(B,A),B) # label(fact_dictator__def) # label(axiom).  [clausify(4)].
% 1.11/1.48  Derived: hAPP(A,f2(B,A)) != hAPP(f2(B,A),B) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B).  [resolve(485,a,484,a)].
% 1.11/1.48  486 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f13(B,A)),c_Arrow__Order__Mirabelle_OProf)) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom).  [clausify(201)].
% 1.11/1.48  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f13(B,A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B).  [resolve(486,c,484,a)].
% 1.11/1.48  487 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | f15(B,A) != f14(B,A) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom).  [clausify(201)].
% 1.11/1.48  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | f15(B,A) != f14(B,A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B).  [resolve(487,c,484,a)].
% 1.11/1.48  488 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f14(B,A)),f15(B,A))),hAPP(f13(B,A),B))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom).  [clausify(201)].
% 1.11/1.48  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f14(B,A)),f15(B,A))),hAPP(f13(B,A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B).  [resolve(488,c,484,a)].
% 1.11/1.48  489 -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f14(B,A)),f15(B,A))),hAPP(A,f13(B,A)))) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(fact_dictatorI) # label(axiom).  [clausify(201)].
% 1.11/1.56  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f14(B,A)),f15(B,A))),hAPP(A,f13(B,A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,C) = hAPP(C,B).  [resolve(489,c,484,a)].
% 1.11/1.56  490 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom).  [assumption].
% 1.11/1.56  491 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neq__iff) # label(axiom).  [clausify(40)].
% 1.11/1.56  492 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__neq__iff) # label(axiom).  [clausify(40)].
% 1.11/1.56  493 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neq__iff) # label(axiom).  [clausify(40)].
% 1.11/1.56  494 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | C = B # label(fact_not__less__iff__gr__or__eq) # label(axiom).  [clausify(41)].
% 1.11/1.56  495 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_not__less__iff__gr__or__eq) # label(axiom).  [clausify(41)].
% 1.11/1.56  496 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C != B # label(fact_not__less__iff__gr__or__eq) # label(axiom).  [clausify(41)].
% 1.11/1.56  497 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__less__linear) # label(axiom).  [clausify(42)].
% 1.11/1.56  498 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | B = C # label(fact_linorder__antisym__conv3) # label(axiom).  [clausify(43)].
% 1.11/1.56  499 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | B != C # label(fact_linorder__antisym__conv3) # label(axiom).  [clausify(43)].
% 1.11/1.56  500 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__neqE) # label(axiom).  [clausify(44)].
% 1.11/1.56  501 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__cases) # label(axiom).  [clausify(59)].
% 1.11/1.56  502 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__le__cases) # label(axiom).  [clausify(97)].
% 1.11/1.56  503 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__linear) # label(axiom).  [clausify(111)].
% 1.11/1.56  504 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C = B # label(fact_linorder__antisym__conv2) # label(axiom).  [clausify(142)].
% 1.11/1.56  505 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C != B # label(fact_linorder__antisym__conv2) # label(axiom).  [clausify(142)].
% 1.11/1.56  506 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_leD) # label(axiom).  [clausify(144)].
% 1.11/1.56  507 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | C = B # label(fact_linorder__antisym__conv1) # label(axiom).  [clausify(147)].
% 1.11/1.56  508 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | C != B # label(fact_linorder__antisym__conv1) # label(axiom).  [clausify(147)].
% 1.11/1.56  509 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_not__leE) # label(axiom).  [clausify(148)].
% 1.11/1.56  510 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_leI) # label(axiom).  [clausify(149)].
% 1.11/1.56  511 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__le__less__linear) # label(axiom).  [clausify(153)].
% 1.11/1.56  512 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__not__le) # label(axiom).  [clausify(154)].
% 1.11/1.56  513 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__not__le) # label(axiom).  [clausify(154)].
% 1.11/1.56  514 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__not__less) # label(axiom).  [clausify(155)].
% 1.11/1.56  515 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__not__less) # label(axiom).  [clausify(155)].
% 1.11/1.56  Derived: A = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)).  [resolve(490,a,491,a)].
% 1.11/1.56  Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)).  [resolve(490,a,492,a)].
% 1.11/1.56  Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)).  [resolve(490,a,493,a)].
% 1.11/1.56  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)).  [resolve(490,a,495,a)].
% 1.11/1.56  Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),A)).  [resolve(490,a,502,a)].
% 1.11/1.56  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | B = A.  [resolve(490,a,504,a)].
% 1.11/1.56  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)).  [resolve(490,a,506,a)].
% 1.11/1.56  Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | B != A.  [resolve(490,a,508,a)].
% 1.11/1.61  Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)).  [resolve(490,a,509,a)].
% 1.11/1.61  516 c_FunDef_Oin__rel(A,B,C,D,E) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,B)),hAPP(hAPP(c_Product__Type_OPair(A,B),D),E)),C)) # label(fact_in__rel__def) # label(axiom).  [clausify(78)].
% 1.11/1.61  517 -c_FunDef_Oin__rel(A,B,C,D,E) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,B)),hAPP(hAPP(c_Product__Type_OPair(A,B),D),E)),C)) # label(fact_in__rel__def) # label(axiom).  [clausify(78)].
% 1.11/1.61  518 -c_Arrow__Order__Mirabelle_Ounanimity(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f16(A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,B))) # label(fact_unanimity__def) # label(axiom).  [clausify(240)].
% 1.11/1.61  519 c_Arrow__Order__Mirabelle_Ounanimity(v_F) # label(fact_u) # label(axiom).  [assumption].
% 1.11/1.61  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B),C)),hAPP(A,f16(v_F,A,B,C)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B),C)),hAPP(v_F,A))).  [resolve(518,a,519,a)].
% 1.11/1.61  520 c_Arrow__Order__Mirabelle_Ounanimity(A) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f17(A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_unanimity__def) # label(axiom).  [clausify(240)].
% 1.11/1.61  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f17(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f16(A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,B))).  [resolve(520,a,518,a)].
% 1.11/1.61  521 c_Arrow__Order__Mirabelle_Ounanimity(A) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f18(A)),f19(A))),hAPP(f17(A),B))) # label(fact_unanimity__def) # label(axiom).  [clausify(240)].
% 1.11/1.61  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f18(A)),f19(A))),hAPP(f17(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f16(A,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(521,a,518,a)].
% 1.11/1.63  522 c_Arrow__Order__Mirabelle_Ounanimity(A) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f18(A)),f19(A))),hAPP(A,f17(A)))) # label(fact_unanimity__def) # label(axiom).  [clausify(240)].
% 1.11/1.63  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f18(A)),f19(A))),hAPP(A,f17(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f16(A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,B))).  [resolve(522,a,518,a)].
% 1.11/1.63  523 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.63  524 c_Arrow__Order__Mirabelle_OIIA(v_F) # label(fact_assms_I3_J) # label(axiom).  [assumption].
% 1.11/1.63  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f20(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f20(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))).  [resolve(523,a,524,a)].
% 1.11/1.63  525 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.63  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f20(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f20(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))).  [resolve(525,a,524,a)].
% 1.11/1.64  526 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f20(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f20(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))).  [resolve(526,a,524,a)].
% 1.11/1.64  527 -c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),A),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(A,f20(v_F,A,B,C,D)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(B,f20(v_F,A,B,C,D)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,A))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C),D)),hAPP(v_F,B))).  [resolve(527,a,524,a)].
% 1.11/1.64  528 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f21(A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f21(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(528,a,523,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f21(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(528,a,525,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f21(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(528,a,526,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f21(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(528,a,527,a)].
% 1.11/1.64  529 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f22(A)),c_Arrow__Order__Mirabelle_OProf)) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f22(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(529,a,523,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f22(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(529,a,525,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f22(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(529,a,526,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),f22(A)),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(529,a,527,a)].
% 1.11/1.64  530 c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(530,a,523,a)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(530,a,525,a)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(530,a,526,a)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(530,a,527,a)].
% 1.11/1.64  531 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(531,a,523,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(531,a,525,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(531,a,526,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f21(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(f22(A),B))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(C,f20(A,C,D,E,F)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(D,f20(A,C,D,E,F)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,C))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),E),F)),hAPP(A,D))).  [resolve(531,a,527,a)].
% 1.11/1.64  532 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(532,a,523,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(532,a,525,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(532,a,526,a)].
% 1.11/1.64  Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(532,a,527,a)].
% 1.11/1.64  533 c_Arrow__Order__Mirabelle_OIIA(A) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) # label(fact_IIA__def) # label(axiom).  [clausify(241)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(533,a,523,a)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(533,a,525,a)].
% 1.11/1.64  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(533,a,526,a)].
% 1.11/1.69  Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f21(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),f23(A)),f24(A))),hAPP(A,f22(A)))) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),C),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(B,f20(A,B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(C,f20(A,B,C,D,E)))) | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,B))) | -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),D),E)),hAPP(A,C))).  [resolve(533,a,527,a)].
% 1.11/1.69  534 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom).  [assumption].
% 1.11/1.69  535 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A)))) # label(fact_less__add__one) # label(axiom).  [clausify(202)].
% 1.11/1.69  536 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_pos__add__strict) # label(axiom).  [clausify(321)].
% 1.11/1.73  537 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))) # label(fact_zero__le__one) # label(axiom).  [clausify(325)].
% 1.11/1.73  538 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__one__le__zero) # label(axiom).  [clausify(326)].
% 1.11/1.73  539 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))) # label(fact_zero__less__one) # label(axiom).  [clausify(327)].
% 1.11/1.73  540 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__one__less__zero) # label(axiom).  [clausify(328)].
% 1.11/1.73  541 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A)))) # label(fact_zero__less__two) # label(axiom).  [clausify(337)].
% 1.11/1.73  Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).  [resolve(534,a,535,a)].
% 1.11/1.73  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))).  [resolve(534,a,536,a)].
% 1.11/1.73  Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))).  [resolve(534,a,537,a)].
% 1.11/1.73  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).  [resolve(534,a,538,a)].
% 1.11/1.73  Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))).  [resolve(534,a,539,a)].
% 1.11/1.73  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).  [resolve(534,a,540,a)].
% 1.11/1.73  Derived: 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),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).  [resolve(534,a,541,a)].
% 1.11/1.73  542 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 1.11/1.73  543 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__le__less__mono) # label(axiom).  [clausify(203)].
% 1.11/1.73  544 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__less__le__mono) # label(axiom).  [clausify(204)].
% 1.11/1.73  545 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__strict__mono) # label(axiom).  [clausify(233)].
% 1.57/1.83  546 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) # label(fact_add__strict__left__mono) # label(axiom).  [clausify(234)].
% 1.57/1.83  547 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))) # label(fact_add__strict__right__mono) # label(axiom).  [clausify(235)].
% 1.57/1.83  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).  [resolve(542,a,543,a)].
% 1.57/1.83  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).  [resolve(542,a,544,a)].
% 1.57/1.83  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).  [resolve(542,a,545,a)].
% 1.57/1.83  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).  [resolve(542,a,546,a)].
% 1.57/1.83  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).  [resolve(542,a,547,a)].
% 1.57/1.83  548 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom).  [assumption].
% 1.57/1.83  549 -class_Groups_Oab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom).  [clausify(217)].
% 1.57/1.83  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)).  [resolve(548,a,549,a)].
% 1.57/1.83  550 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 1.57/1.83  551 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__cancel) # label(axiom).  [clausify(218)].
% 1.57/1.83  552 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C != D # label(fact_add__left__cancel) # label(axiom).  [clausify(218)].
% 1.57/1.83  553 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__cancel) # label(axiom).  [clausify(219)].
% 1.57/1.83  554 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B != D # label(fact_add__right__cancel) # label(axiom).  [clausify(219)].
% 1.57/1.83  555 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__imp__eq) # label(axiom).  [clausify(220)].
% 1.59/1.87  556 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__imp__eq) # label(axiom).  [clausify(222)].
% 1.59/1.87  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B = C.  [resolve(550,a,551,a)].
% 1.59/1.87  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B != C.  [resolve(550,a,552,a)].
% 1.59/1.87  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A = C.  [resolve(550,a,553,a)].
% 1.59/1.87  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A != C.  [resolve(550,a,554,a)].
% 1.59/1.87  557 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 1.59/1.87  558 -class_Groups_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__imp__eq) # label(axiom).  [clausify(221)].
% 1.59/1.87  559 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
% 1.59/1.87  560 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__cancel__right) # label(axiom).  [clausify(224)].
% 1.59/1.87  561 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__cancel__right) # label(axiom).  [clausify(224)].
% 1.59/1.87  562 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__cancel__left) # label(axiom).  [clausify(225)].
% 1.59/1.87  563 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__cancel__left) # label(axiom).  [clausify(225)].
% 1.59/1.87  564 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__imp__le__right) # label(axiom).  [clausify(229)].
% 1.59/1.87  565 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__imp__le__left) # label(axiom).  [clausify(230)].
% 1.59/1.87  566 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__imp__less__left) # label(axiom).  [clausify(231)].
% 1.59/1.87  567 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__imp__less__right) # label(axiom).  [clausify(232)].
% 1.59/1.89  568 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__cancel__left) # label(axiom).  [clausify(236)].
% 1.59/1.89  569 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__cancel__left) # label(axiom).  [clausify(236)].
% 1.59/1.89  570 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__cancel__right) # label(axiom).  [clausify(237)].
% 1.59/1.89  571 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__cancel__right) # label(axiom).  [clausify(237)].
% 1.59/1.89  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)).  [resolve(559,a,560,a)].
% 1.59/1.89  Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)).  [resolve(559,a,561,a)].
% 1.59/1.89  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)).  [resolve(559,a,562,a)].
% 1.59/1.89  Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)).  [resolve(559,a,563,a)].
% 1.59/1.89  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)).  [resolve(559,a,566,a)].
% 1.59/1.89  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)).  [resolve(559,a,567,a)].
% 1.59/1.89  572 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
% 1.59/1.89  573 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))) # label(fact_add__right__mono) # label(axiom).  [clausify(226)].
% 1.59/1.89  574 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) # label(fact_add__left__mono) # label(axiom).  [clausify(227)].
% 1.59/1.89  575 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))) # label(fact_add__mono) # label(axiom).  [clausify(228)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).  [resolve(572,a,575,a)].
% 1.73/2.02  576 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__add) # label(axiom).  [assumption].
% 1.73/2.02  577 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add_Ocomm__neutral) # label(axiom).  [clausify(295)].
% 1.73/2.02  578 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_add__0) # label(axiom).  [clausify(298)].
% 1.73/2.02  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A.  [resolve(576,a,577,a)].
% 1.73/2.02  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A.  [resolve(576,a,578,a)].
% 1.73/2.02  579 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom).  [assumption].
% 1.73/2.02  580 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom).  [clausify(296)].
% 1.73/2.02  581 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_add__0__left) # label(axiom).  [clausify(299)].
% 1.73/2.02  582 class_Rings_Ozero__neq__one(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ozero__neq__one) # label(axiom).  [assumption].
% 1.73/2.02  583 -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oone__class_Oone(A) # label(fact_zero__neq__one) # label(axiom).  [clausify(300)].
% 1.73/2.02  584 -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oone__class_Oone(A) # label(fact_one__neq__zero) # label(axiom).  [clausify(301)].
% 1.73/2.02  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat).  [resolve(582,a,583,a)].
% 1.73/2.02  585 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
% 1.73/2.02  586 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__nonpos__nonpos) # label(axiom).  [clausify(313)].
% 1.73/2.02  587 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B))) # label(fact_add__increasing2) # label(axiom).  [clausify(314)].
% 1.73/2.02  588 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__increasing) # label(axiom).  [clausify(315)].
% 1.73/2.02  589 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom).  [clausify(316)].
% 1.73/2.02  590 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom).  [clausify(316)].
% 1.73/2.02  591 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__nonneg__eq__0__iff) # label(axiom).  [clausify(316)].
% 1.73/2.02  592 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__nonneg__nonneg) # label(axiom).  [clausify(317)].
% 1.73/2.02  593 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__neg__neg) # label(axiom).  [clausify(320)].
% 1.73/2.02  594 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__pos__pos) # label(axiom).  [clausify(322)].
% 1.73/2.02  595 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__nonpos__neg) # label(axiom).  [clausify(331)].
% 1.73/2.02  596 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__neg__nonpos) # label(axiom).  [clausify(332)].
% 1.73/2.02  597 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__strict__increasing2) # label(axiom).  [clausify(333)].
% 1.73/2.02  598 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__strict__increasing) # label(axiom).  [clausify(334)].
% 1.73/2.02  599 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__nonneg__pos) # label(axiom).  [clausify(335)].
% 1.73/2.02  600 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__pos__nonneg) # label(axiom).  [clausify(336)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).  [resolve(585,a,586,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A))).  [resolve(585,a,587,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))).  [resolve(585,a,588,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A.  [resolve(585,a,589,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(585,a,590,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B.  [resolve(585,a,591,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).  [resolve(585,a,593,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).  [resolve(585,a,595,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).  [resolve(585,a,596,a)].
% 1.73/2.02  Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))).  [resolve(585,a,597,a)].
% 1.83/2.10  Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))).  [resolve(585,a,598,a)].
% 1.83/2.10  601 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) # label(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom).  [assumption].
% 1.83/2.10  602 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom).  [clausify(409)].
% 1.83/2.10  603 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom).  [clausify(409)].
% 1.83/2.10  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(601,a,602,a)].
% 1.83/2.10  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B.  [resolve(601,a,603,a)].
% 1.83/2.10  604 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring__1) # label(axiom).  [assumption].
% 1.83/2.10  605 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom).  [clausify(410)].
% 1.83/2.10  606 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom).  [clausify(411)].
% 1.83/2.10  607 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom).  [clausify(412)].
% 1.83/2.10  608 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom).  [clausify(413)].
% 1.83/2.10  609 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom).  [clausify(414)].
% 1.83/2.10  610 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom).  [clausify(415)].
% 1.83/2.10  611 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom).  [clausify(416)].
% 1.83/2.10  612 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom).  [clausify(417)].
% 1.83/2.10  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),A).  [resolve(604,a,606,a)].
% 3.47/3.75  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)).  [resolve(604,a,607,a)].
% 3.47/3.75  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),B).  [resolve(604,a,610,a)].
% 3.47/3.75  Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)).  [resolve(604,a,611,a)].
% 3.47/3.75  
% 3.47/3.75  ============================== end predicate elimination =============
% 3.47/3.75  
% 3.47/3.75  Auto_denials:  (non-Horn, no changes).
% 3.47/3.75  
% 3.47/3.75  Term ordering decisions:
% 3.47/3.75  Function symbol KB weights:  tc_Arrow__Order__Mirabelle_Oalt=1. tc_Nat_Onat=1. tc_HOL_Obool=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. c_Nat_OSuc=1. v_F=1. c_Arrow__Order__Mirabelle_OLin=1. c_Arrow__Order__Mirabelle_Oabove=1. v_a____=1. v_b____=1. v_h____=1. v_Lab____=1. v_Lba____=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_fequal=1. v_n____=1. tc_Product__Type_Ounit=1. v_P____=1. v_c____=1. v_d____=1. v_e____=1. c2=1. c3=1. c4=1. c5=1. hAPP=1. tc_fun=1. tc_prod=1. c_Product__Type_OPair=1. c_Orderings_Oord__class_Oless__eq=1. c_Finite__Set_Ocard=1. tc_sum=1. c_COMBK=1. c_List_Omeasures=1. c_Nat_Osize__class_Osize=1. c_Wellfounded_Omeasure=1. f1=1. f2=1. f7=1. f13=1. f14=1. f15=1. f27=1. f29=1. f30=1. f33=1. f34=1. f35=1. f36=1. c_member=1. c_Orderings_Oord__class_Oless=1. c_Groups_Oplus__class_Oplus=1. c_Groups_Ozero__class_Ozero=1. c_Orderings_Otop__class_Otop=1. c_Groups_Oone__class_Oone=1. c_If=1. c_List_Olist_ONil=1. tc_Option_Ooption=1. c_COMBI=1. c_Nat_Onat_Onat__size=1. c_Wellfounded_Ofinite__psubset=1. f17=1. f18=1. f19=1. f21=1. f22=1. f23=1. f24=1. f28=1. c_COMBC=1. c_Set_Oinsert=1. c_List_Olist_OCons=1. c_Arrow__Order__Mirabelle_Obelow=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_List_Osplice=1. c_List_Olist_Olist__size=1. c_Wellfounded_Omlex__prod=1. f37=1. c_Set_Oimage=1. c_COMBB=1. c_FuncSet_OPi=1. c_Hilbert__Choice_Oinv__into=1. c_Sum__Type_OPlus=1. c_Wellfounded_Olex__prod=1. c_Recdef_Osame__fst=1. f4=1. f5=1. f6=1. f8=1. f16=1. f31=1. c_List_Olist_Olist__case=1. c_COMBS=1. f10=1. f20=1. f25=1. f26=1. f32=1. f38=1. f39=1. f9=1. f11=1. f12=1.
% 3.47/3.75  
% 3.47/3.75  ============================== end of process initial clauses ========
% 3.47/3.75  
% 3.47/3.75  ============================== CLAUSES FOR SEARCH ====================
% 3.47/3.75  
% 3.47/3.75  ============================== end of clauses for search =============
% 3.47/3.75  
% 3.47/3.75  ============================== SEARCH ================================
% 3.47/3.75  
% 3.47/3.75  % Starting search at 0.90 seconds.
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=180.000, iters=3587
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=159.000, iters=3336
% 3.47/3.75  
% 3.47/3.75  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 1.93 sec).
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=149.000, iters=3400
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=146.000, iters=3375
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=128.000, iters=3436
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=116.000, iters=3334
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=104.000, iters=3341
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=103.000, iters=3335
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=101.000, iters=3333
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=74.000, iters=3450
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=71.000, iters=3548
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=68.000, iters=3615
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=45.000, iters=3375
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=42.000, iters=3403
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=41.000, iters=3342
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=40.000, iters=3382
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=38.000, iters=3368
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=37.000, iters=3388
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=36.000, iters=3353
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=35.000, iters=3391
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=32.000, iters=3380
% 3.47/3.75  
% 3.47/3.75  Low Water (keep): wt=30.000, iters=3345
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=28.000, iters=3498
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=27.000, iters=3358
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=26.000, iters=3487
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=25.000, iters=3336
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=24.000, iters=3353
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=23.000, iters=3352
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=22.000, iters=3335
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=21.000, iters=3381
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=20.000, iters=3593
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=19.000, iters=3391
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=18.000, iters=3459
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=17.000, iters=3376
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=14.000, iters=3462
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=12.000, iters=3346
% 3.86/4.12  
% 3.86/4.12  Low Water (keep): wt=10.000, iters=3333
% 3.86/4.12  
% 3.86/4.12  ============================== PROOF =================================
% 3.86/4.12  % SZS status Theorem
% 3.86/4.12  % SZS output start Refutation
% 3.86/4.12  
% 3.86/4.12  % Proof 1 at 2.74 (+ 0.03) seconds.
% 3.86/4.12  % Length of proof is 35.
% 3.86/4.12  % Level of proof is 9.
% 3.86/4.12  % Maximum clause weight is 32.000.
% 3.86/4.12  % Given clauses 1314.
% 3.86/4.12  
% 3.86/4.12  307 (all V_n all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  309 (all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  346 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  363 (all V_n all 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))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  364 (all V_n all 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))) # label(fact_add__Suc) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  396 (all 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))) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  401 (all V_list_2 all V_aa_2 all V_fa_2 all T_a c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_OCons(T_a,V_aa_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_aa_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_list_Osize_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  406 (all V_fa_2 all T_a c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_list_Osize_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  476 (all V_P all T_a hAPP(c_COMBI(T_a),V_P) = V_P) # label(help_c__COMBI__1) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  478 (all V_R_2 all V_Q_2 all V_Pa_2 all T_c all T_a all T_b hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2))) # label(help_c__COMBB__1) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  480 (all V_R_2 all V_Q_2 all V_Pa_2 all T_a all T_c all T_b hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2))) # label(help_c__COMBS__1) # label(axiom) # label(non_clause).  [assumption].
% 3.86/4.12  953 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B # label(fact_add__eq__self__zero) # label(axiom).  [clausify(307)].
% 3.86/4.12  960 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A # label(fact_Nat_Oadd__0__right) # label(axiom).  [clausify(309)].
% 3.86/4.12  973 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,A) # label(fact_Zero__not__Suc) # label(axiom).  [clausify(346)].
% 3.86/4.12  974 hAPP(c_Nat_OSuc,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [copy(973),flip(a)].
% 3.86/4.12  992 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) # label(fact_add__Suc__shift) # label(axiom).  [clausify(363)].
% 3.86/4.12  993 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)) # label(fact_add__Suc) # label(axiom).  [clausify(364)].
% 3.86/4.12  994 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)).  [copy(993),rewrite([992(6)])].
% 3.86/4.12  1031 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_One__nat__def) # label(axiom).  [assumption].
% 3.86/4.12  1032 hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat).  [copy(1031),flip(a)].
% 3.86/4.12  1036 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,A) # label(fact_Suc__eq__plus1) # label(axiom).  [clausify(396)].
% 3.86/4.12  1045 c_List_Olist_Olist__size(A,B,c_List_Olist_OCons(A,C,D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(B,C)),c_List_Olist_Olist__size(A,B,D))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_list_Osize_I2_J) # label(axiom).  [clausify(401)].
% 3.86/4.12  1046 c_List_Olist_Olist__size(A,B,c_List_Olist_OCons(A,C,D)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(B,C)),c_List_Olist_Olist__size(A,B,D))).  [copy(1045),rewrite([1032(15),1036(14)])].
% 3.86/4.12  1047 c_List_Olist_Olist__size(A,B,c_List_Olist_ONil(A)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) # label(fact_list_Osize_I1_J) # label(axiom).  [clausify(406)].
% 3.86/4.12  1134 hAPP(c_COMBI(A),B) = B # label(help_c__COMBI__1) # label(axiom).  [clausify(476)].
% 3.86/4.12  1136 hAPP(hAPP(c_COMBB(A,B,C,D),E),F) = hAPP(D,hAPP(E,F)) # label(help_c__COMBB__1) # label(axiom).  [clausify(478)].
% 3.86/4.12  1138 hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(D,F),hAPP(E,F)) # label(help_c__COMBS__1) # label(axiom).  [clausify(480)].
% 3.86/4.12  2706 hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)) != A.  [para(994(a,1),953(a,1)),flip(b),unit_del(b,974)].
% 3.86/4.12  2947 c_List_Olist_Olist__size(A,B,c_List_Olist_OCons(A,C,c_List_Olist_ONil(A))) = hAPP(c_Nat_OSuc,hAPP(B,C)).  [para(1047(a,1),1046(a,2,2,2)),rewrite([960(11)])].
% 3.86/4.12  5422 c_List_Olist_Olist__size(A,B,c_List_Olist_OCons(A,C,D)) != hAPP(B,C).  [para(1046(a,2),2706(a,1))].
% 3.86/4.12  5562 c_List_Olist_Olist__size(A,c_COMBS(B,C,D,E,F),c_List_Olist_OCons(A,V6,V7)) != hAPP(hAPP(E,V6),hAPP(F,V6)).  [para(1138(a,1),5422(a,2))].
% 3.86/4.12  11806 c_List_Olist_Olist__size(A,c_COMBS(B,C,D,c_COMBI(E),F),c_List_Olist_OCons(A,V6,V7)) != hAPP(V6,hAPP(F,V6)).  [para(1134(a,1),5562(a,2,1))].
% 3.86/4.12  11913 c_List_Olist_Olist__size(A,c_COMBS(B,C,D,c_COMBI(E),c_COMBI(F)),c_List_Olist_OCons(A,V6,V7)) != hAPP(V6,V6).  [para(1134(a,1),11806(a,2,2))].
% 3.86/4.12  11939 c_List_Olist_Olist__size(A,c_COMBS(B,C,D,c_COMBI(E),c_COMBI(F)),c_List_Olist_OCons(A,hAPP(c_COMBB(V6,V7,V8,V9),V10),V11)) != hAPP(V9,hAPP(V10,hAPP(c_COMBB(V6,V7,V8,V9),V10))).  [para(1136(a,1),11913(a,2))].
% 3.86/4.12  11940 $F.  [resolve(11939,a,2947,a)].
% 3.86/4.12  
% 3.86/4.12  % SZS output end Refutation
% 3.86/4.12  ============================== end of proof ==========================
% 3.86/4.12  
% 3.86/4.12  ============================== STATISTICS ============================
% 3.86/4.12  
% 3.86/4.12  Given=1314. Generated=27299. Kept=11225. proofs=1.
% 3.86/4.12  Usable=1297. Sos=9624. Demods=149. Limbo=5, Disabled=1156. Hints=0.
% 3.86/4.12  Megabytes=34.74.
% 3.86/4.12  User_CPU=2.74, System_CPU=0.03, Wall_clock=3.
% 3.86/4.12  
% 3.86/4.12  ============================== end of statistics =====================
% 3.86/4.12  
% 3.86/4.12  ============================== end of search =========================
% 3.86/4.12  
% 3.86/4.12  THEOREM PROVED
% 3.86/4.12  % SZS status Theorem
% 3.86/4.12  
% 3.86/4.12  Exiting with 1 proof.
% 3.86/4.12  
% 3.86/4.12  Process 16469 exit (max_proofs) Sat Jul  2 01:58:57 2022
% 3.86/4.12  Prover9 interrupted
%------------------------------------------------------------------------------