TSTP Solution File: SCT104+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SCT104+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:12:30 EDT 2022
% Result : Unknown 6.80s 6.84s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SCT104+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:07:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.65/6.78 ----- Otter 3.3f, August 2004 -----
% 6.65/6.78 The process was started by sandbox2 on n019.cluster.edu,
% 6.65/6.78 Wed Jul 27 09:07:52 2022
% 6.65/6.78 The command was "./otter". The process ID is 11212.
% 6.65/6.78
% 6.65/6.78 set(prolog_style_variables).
% 6.65/6.78 set(auto).
% 6.65/6.78 dependent: set(auto1).
% 6.65/6.78 dependent: set(process_input).
% 6.65/6.78 dependent: clear(print_kept).
% 6.65/6.78 dependent: clear(print_new_demod).
% 6.65/6.78 dependent: clear(print_back_demod).
% 6.65/6.78 dependent: clear(print_back_sub).
% 6.65/6.78 dependent: set(control_memory).
% 6.65/6.78 dependent: assign(max_mem, 12000).
% 6.65/6.78 dependent: assign(pick_given_ratio, 4).
% 6.65/6.78 dependent: assign(stats_level, 1).
% 6.65/6.78 dependent: assign(max_seconds, 10800).
% 6.65/6.78 clear(print_given).
% 6.65/6.78
% 6.65/6.78 formula_list(usable).
% 6.65/6.78 all A (A=A).
% 6.65/6.78 all V_g_2 V_f_2 ((all B_x (hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x)))->V_f_2=V_g_2).
% 6.65/6.78 all V_c_2 T_a V_B_2 V_A_2 (V_A_2=V_B_2-> ((c_member(T_a,V_c_2,V_A_2)-> -c_member(T_a,V_c_2,V_B_2))-> -(-c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2)))).
% 6.65/6.78 all V_r_2 T_a T_b (c_Relation_Oconverse(T_b,T_a,c_Relation_Oconverse(T_a,T_b,V_r_2))=V_r_2).
% 6.65/6.78 all V_A_2 V_x_2 T_a (c_member(T_a,V_x_2,V_A_2)<->hBOOL(hAPP(V_A_2,V_x_2))).
% 6.65/6.78 all V_y_2 V_x_2 T_a (c_member(T_a,V_x_2,c_fe_qual(V_y_2))<->V_x_2=V_y_2).
% 6.65/6.78 all V_x_2 T_a V_B_2 V_A_2 (V_A_2=V_B_2-> (c_member(T_a,V_x_2,V_A_2)<->c_member(T_a,V_x_2,V_B_2))).
% 6.65/6.78 all V_A_2 T_a V_y_2 V_x_2 (V_x_2=V_y_2-> (c_member(T_a,V_x_2,V_A_2)<->c_member(T_a,V_y_2,V_A_2))).
% 6.65/6.78 all V_A_2 T_a V_b_2 V_a_2 (V_a_2=V_b_2-> (c_member(T_a,V_b_2,V_A_2)->c_member(T_a,V_a_2,V_A_2))).
% 6.65/6.78 all V_y_2 V_x_2 V_La_2 (c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_La_2,c_Arrow__Order__Mirabelle_OLin)-> (V_x_2!=V_y_2-> (-c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_La_2)<->c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_y_2,V_x_2),V_La_2)))).
% 6.65/6.78 all V_r_2 V_A_2 T_a (c_Relation_Ototal__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2))<->c_Relation_Ototal__on(T_a,V_A_2,V_r_2)).
% 6.65/6.78 all V_f_2 V_R_2 T_b T_a (c_Relation_Oconverse(T_a,T_a,hAPP(c_Relation_Oinv__image(T_b,T_a,V_R_2),V_f_2))=hAPP(c_Relation_Oinv__image(T_b,T_a,c_Relation_Oconverse(T_b,T_b,V_R_2)),V_f_2)).
% 6.65/6.78 all V_r_2 T_a (c_Relation_Oantisym(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))<->c_Relation_Oantisym(T_a,V_r_2)).
% 6.65/6.78 all V_A_2 T_a (c_Relation_Oconverse(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))=c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.78 all V_u_2 V_l_2 V_less_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2))).
% 6.65/6.78 all V_u_2 V_l_2 V_less_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))).
% 6.65/6.78 all V_u_2 V_l_2 V_less_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))).
% 6.65/6.78 all V_u_2 V_l_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2))).
% 6.65/6.78 all V_k_2 V_less_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))).
% 6.65/6.78 all V_k_2 V_less_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))).
% 6.65/6.78 all V_A_2 T_a c_Relation_Oantisym(T_a,c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.78 all V_f_2 V_r_2 T_b V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),hAPP(c_Relation_Oinv__image(T_b,T_a,V_r_2),V_f_2))<->c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)),V_r_2)).
% 6.65/6.78 all V_r_2 T_a (c_Relation_Oantisym(T_a,V_r_2)<-> (all B_x B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2)->B_x=B_y)))).
% 6.65/6.78 all V_b_2 V_a_2 V_r_2 T_a (c_Relation_Oantisym(T_a,V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),V_r_2)->V_a_2=V_b_2))).
% 6.65/6.78 all V_r_2 V_A_2 T_a (c_Relation_Ototal__on(T_a,V_A_2,V_r_2)<-> (all B_x (c_member(T_a,B_x,V_A_2)-> (all B_xa (c_member(T_a,B_xa,V_A_2)-> (B_x!=B_xa->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2))))))).
% 6.65/6.78 all V_A_2 T_a V_b_2 V_a_2 (V_a_2=V_b_2-> (c_member(T_a,V_a_2,V_A_2)->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId__on(T_a,V_A_2)))).
% 6.65/6.78 all V_A_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_OId__on(T_a,V_A_2))<->V_x_2=V_y_2&c_member(T_a,V_x_2,V_A_2)).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Relation_Oconverse(T_b,T_a,V_r_2))->c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_b_2,V_a_2),V_r_2)).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)->c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_b_2,V_a_2),c_Relation_Oconverse(T_a,T_b,V_r_2))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Relation_Oconverse(T_b,T_a,V_r_2))<->c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_b_2,V_a_2),V_r_2)).
% 6.65/6.78 all V_k_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__e_q_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_k_2))).
% 6.65/6.78 all V_k_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__e_q_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_k_2),V_i_2))).
% 6.65/6.78 all V_r_2 T_a (c_Relation_Oirrefl(T_a,V_r_2)<-> (all B_x (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2)))).
% 6.65/6.78 all V_A_2 V_c_2 T_a (c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2))-> -(all B_x (c_member(T_a,B_x,V_A_2)->V_c_2!=c_Product__Type_OPair(T_a,T_a,B_x,B_x)))).
% 6.65/6.78 all V_y_2 V_x_2 V_R_2 T_b T_a (hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))<->c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2)).
% 6.65/6.78 all V_r_2 V_yx_2 T_b T_a (c_member(tc_prod(T_a,T_b),V_yx_2,c_Relation_Oconverse(T_b,T_a,V_r_2))-> -(all B_x B_y (V_yx_2=c_Product__Type_OPair(T_a,T_b,B_y,B_x)-> -c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,B_y),V_r_2)))).
% 6.65/6.78 all T_a V_R_2 V_y_2 V_y_H_2 T_b V_x_2 V_P_2 (hBOOL(hAPP(V_P_2,V_x_2))-> (c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_y_H_2,V_y_2),hAPP(V_R_2,V_x_2))->c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_H_2),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2)),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)->c_member(T_b,V_b_2,c_Relation_ORange(T_a,T_b,V_r_2))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)->c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))).
% 6.65/6.78 all V_r_2 T_a (c_Nitpick_Orefl_H(T_a,V_r_2)<-> (all B_x c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2))).
% 6.65/6.78 all V_r_2 T_a ((all B_x B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2)->B_x=B_y)))->c_Relation_Oantisym(T_a,V_r_2)).
% 6.65/6.78 all V_r_2 T_a T_b (c_Relation_ORange(T_b,T_a,c_Relation_Oconverse(T_a,T_b,V_r_2))=c_Relation_ODomain(T_a,T_b,V_r_2)).
% 6.65/6.78 all V_r_2 T_b T_a (c_Relation_ODomain(T_a,T_b,c_Relation_Oconverse(T_b,T_a,V_r_2))=c_Relation_ORange(T_b,T_a,V_r_2)).
% 6.65/6.78 all V_r_2 T_a T_b (c_Relation_ORange(T_b,T_a,V_r_2)=c_Relation_ODomain(T_a,T_b,c_Relation_Oconverse(T_b,T_a,V_r_2))).
% 6.65/6.78 all V_A_2 T_a (c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))=V_A_2).
% 6.65/6.78 all V_A_2 T_a (c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))=V_A_2).
% 6.65/6.78 all V_r_2 T_b V_a_2 T_a (c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))<-> (exists B_y c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,B_y),V_r_2))).
% 6.65/6.78 all V_r_2 T_b V_a_2 T_a (c_member(T_a,V_a_2,c_Relation_ORange(T_b,T_a,V_r_2))<-> (exists B_y c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_y,V_a_2),V_r_2))).
% 6.65/6.78 all V_s_2 V_r_2 V_b_H_2 V_a_H_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),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))<->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_H_2),V_r_2)|V_a_2=V_a_H_2&c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_b_2,V_b_H_2),V_s_2)).
% 6.65/6.78 all V_r_2 T_b V_b_2 T_a (c_member(T_a,V_b_2,c_Relation_ORange(T_b,T_a,V_r_2))-> -(all B_x (-c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_x,V_b_2),V_r_2)))).
% 6.65/6.78 all V_r_2 T_b V_a_2 T_a (c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))-> -(all B_y (-c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,B_y),V_r_2)))).
% 6.65/6.78 all V_a_2 V_r_2 V_A_2 T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2)-> (c_member(T_a,V_a_2,V_A_2)->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2))).
% 6.65/6.78 all V_y_2 V_x_2 V_r_2 V_A_2 T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)->c_member(T_a,V_x_2,V_A_2))).
% 6.65/6.78 all V_y_2 V_x_2 V_r_2 V_A_2 T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)->c_member(T_a,V_y_2,V_A_2))).
% 6.65/6.78 all V_a2_2 V_a1_2 V_F_2 V_R_2 T_b T_a (c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,hAPP(hAPP(V_F_2,V_a2_2),V_a1_2))<-> (exists B_g (hAPP(hAPP(V_F_2,V_a2_2),V_a1_2)=hAPP(hAPP(V_F_2,B_g),V_a1_2)& (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2)->c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,B_z,hAPP(B_g,B_z))))))).
% 6.65/6.78 all V_z_2 V_y_2 V_x_2 V_r_2 T_b T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2)-> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_r_2)-> (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_z_2),V_r_2)->V_y_2=V_z_2))).
% 6.65/6.78 all V_r_2 T_b T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2)<-> (all B_x B_y (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_y),V_r_2)-> (all B_z (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_z),V_r_2)->B_y=B_z))))).
% 6.65/6.78 all V_f_2 T_b V_r_2 V_a_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2)->hAPP(c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_a_2),V_x_2)=hAPP(V_f_2,V_x_2)).
% 6.65/6.78 all V_r_2 V_A_2 T_a (c_Relation_Orefl__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2))<->c_Relation_Orefl__on(T_a,V_A_2,V_r_2)).
% 6.65/6.78 all V_A_2 T_a c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.78 all V_A_2 T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.78 all T_b V_a_2 V_x_2 T_a B_f B_R (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),B_R)->hAPP(c_Recdef_Ocut(T_a,T_b,B_f,B_R,V_a_2),V_x_2)=hAPP(B_f,V_x_2)).
% 6.65/6.78 all V_g_2 V_x_2 V_r_2 V_f_2 T_b T_a (c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_x_2)=c_Recdef_Ocut(T_a,T_b,V_g_2,V_r_2,V_x_2)<-> (all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_x_2),V_r_2)->hAPP(V_f_2,B_y)=hAPP(V_g_2,B_y)))).
% 6.65/6.78 all V_a2_2 V_a1_2 V_F_2 V_R_2 T_b T_a (c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,V_a2_2)<-> (exists B_g (V_a2_2=hAPP(hAPP(V_F_2,B_g),V_a1_2)& (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2)->c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,B_z,hAPP(B_g,B_z))))))).
% 6.65/6.78 all V_g_2 V_F_2 T_b V_R_2 V_x_2 T_a ((all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_x_2),V_R_2)->c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,B_z,hAPP(V_g_2,B_z))))->c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_x_2,hAPP(hAPP(V_F_2,V_g_2),V_x_2))).
% 6.65/6.78 all V_r_2 T_b T_a ((all B_x B_y (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_y),V_r_2)-> (all B_z (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_z),V_r_2)->B_y=B_z))))->c_Relation_Osingle__valued(T_a,T_b,V_r_2)).
% 6.65/6.78 all V_r_2 V_a_2 T_a (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))<-> (all B_x (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)->c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2))))).
% 6.65/6.78 all V_a_2 V_r_2 V_b_2 T_a (c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)->c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2)))).
% 6.65/6.78 all V_x_2 V_F_2 V_R_2 T_a T_b (c_Nitpick_Owf__wfrec_H(T_b,T_a,V_R_2,V_F_2,V_x_2)=hAPP(hAPP(V_F_2,c_Recdef_Ocut(T_b,T_a,c_Nitpick_Owf__wfrec(T_b,T_a,V_R_2,V_F_2),V_R_2,V_x_2)),V_x_2)).
% 6.65/6.78 all V_a_2 T_a c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),c_Relation_OId(T_a)).
% 6.65/6.78 all V_b_H V_a_H V_b V_a T_b T_a (c_Product__Type_OPair(T_a,T_b,V_a,V_b)=c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H)-> -(V_a=V_a_H->V_b!=V_b_H)).
% 6.65/6.78 all V_b_H_2 V_a_H_2 V_b_2 V_a_2 T_b T_a (c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)=c_Product__Type_OPair(T_a,T_b,V_a_H_2,V_b_H_2)<->V_a_2=V_a_H_2&V_b_2=V_b_H_2).
% 6.65/6.78 all T_a (c_Relation_Oconverse(T_a,T_a,c_Relation_OId(T_a))=c_Relation_OId(T_a)).
% 6.65/6.78 all T_a c_Relation_Oantisym(T_a,c_Relation_OId(T_a)).
% 6.65/6.78 all T_a c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)).
% 6.65/6.78 all V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId(T_a))<->V_a_2=V_b_2).
% 6.65/6.78 all T_b T_a V_P_2 ((all B_x1 hBOOL(hAPP(V_P_2,B_x1)))<-> (all B_a B_b hBOOL(hAPP(V_P_2,c_Product__Type_OPair(T_a,T_b,B_a,B_b))))).
% 6.65/6.78 all V_b_2 V_a_2 V_f1_2 T_a T_c T_b (c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2))=hAPP(hAPP(V_f1_2,V_a_2),V_b_2)).
% 6.65/6.78 all V_R_2 V_x_2 T_a (-c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_R_2))-> -(all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_x_2),V_R_2)->c_member(T_a,B_z,c_Wellfounded_Oacc(T_a,V_R_2))))).
% 6.65/6.78 all V_r_2 V_x_2 T_a ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_x_2),V_r_2)->c_member(T_a,B_y,c_Wellfounded_Oacc(T_a,V_r_2))))->c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2))).
% 6.65/6.78 all V_p_2 T_a (c_member(tc_prod(T_a,T_a),V_p_2,c_Relation_OId(T_a))-> -(all B_x (V_p_2!=c_Product__Type_OPair(T_a,T_a,B_x,B_x)))).
% 6.65/6.78 all V_b_2 V_a_2 V_c_2 T_a T_c T_b (c_Product__Type_Ointernal__split(T_b,T_c,T_a,V_c_2,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2))=hAPP(hAPP(V_c_2,V_a_2),V_b_2)).
% 6.65/6.78 all V_r_2 V_a_2 V_b_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))->c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2)))).
% 6.65/6.78 all V_b_2 V_r_2 V_a_2 T_a (c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))->c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2)))).
% 6.65/6.78 all V_b_2 V_a_2 T_b T_a V_f_2 (hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)))->hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_a_2,V_b_2))).
% 6.65/6.78 all V_b_2 V_a_2 V_f_2 T_b T_a (hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_a_2,V_b_2))->hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)))).
% 6.65/6.78 all V_b_2 V_a_2 V_f_2 T_b T_a (hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_a_2,V_b_2))->hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)))).
% 6.65/6.78 all V_b_2 V_a_2 V_f_2 T_a T_c T_b (c_Product__Type_Ocurry(T_b,T_c,T_a,V_f_2,V_a_2,V_b_2)=hAPP(V_f_2,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2))).
% 6.65/6.78 all V_r_2 V_a_2 T_a c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.78 all V_r_2 V_p_2 T_a (c_member(tc_prod(T_a,T_a),V_p_2,V_r_2)->c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.78 all V_y_2 V_R_2 V_x_2 T_a (-c_member(T_a,V_x_2,c_Relation_ODomain(T_a,T_a,V_R_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))<->V_x_2=V_y_2)).
% 6.65/6.78 all V_z_2 V_y_2 V_x_2 V_r_2 T_a (c_Relation_Osingle__valued(T_a,T_a,V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_z_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))).
% 6.65/6.78 all V_r_2 V_x_2 V_y_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))).
% 6.65/6.78 all V_r_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2)->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_r_2 T_a (c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))=c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.78 all V_r_2 T_a (c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))=c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_P_2 V_r_2 V_by_2 V_bx_2 V_ay_2 V_ax_2 T_b T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))-> (hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))-> ((all B_a B_b (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,B_a,B_b)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))-> (all B_aa B_ba (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba)),V_r_2)-> (hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))->hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)))))))->hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))))).
% 6.65/6.78 all V_P_2 V_r_2 V_by_2 V_bx_2 V_ay_2 V_ax_2 T_b T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))-> (hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))-> ((all B_a B_b B_aa B_ba (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba)),V_r_2)-> (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_aa,B_ba),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))-> (hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))->hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))))))->hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))))).
% 6.65/6.78 all V_r_2 V_zb_2 V_za_2 V_xb_2 V_xa_2 T_b T_a (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))-> (c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2)!=c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)-> -(all B_a B_b (c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,B_a,B_b)),V_r_2)-> -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_a,B_b),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)))))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (V_a_2!=V_b_2-> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,B_y),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_b_2),V_r_2))))).
% 6.65/6.78 all V_r_2 V_z_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (V_x_2!=V_z_2-> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_y),V_r_2)-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))).
% 6.65/6.78 all V_P_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (hBOOL(hAPP(V_P_2,V_b_2))-> ((all B_y B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (hBOOL(hAPP(V_P_2,B_z))->hBOOL(hAPP(V_P_2,B_y))))))->hBOOL(hAPP(V_P_2,V_a_2))))).
% 6.65/6.78 all V_P_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (hBOOL(hAPP(V_P_2,V_a_2))-> ((all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,B_y),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (all B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_z),V_r_2)-> (hBOOL(hAPP(V_P_2,B_y))->hBOOL(hAPP(V_P_2,B_z)))))))->hBOOL(hAPP(V_P_2,V_b_2))))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Oacyclic(T_a,V_r_2)->c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Oacyclic(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))<->c_Wellfounded_Oacyclic(T_a,V_r_2)).
% 6.65/6.78 all V_r_2 V_x_2 V_y_2 T_a (c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))<->c_Wellfounded_Oacyclic(T_a,V_r_2)& -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Oacyclic(T_a,V_r_2)<-> (all B_x (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))))).
% 6.65/6.78 all V_r_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))).
% 6.65/6.78 all V_r_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_B_2 V_b_2 T_b V_A_2 V_a_2 T_a (c_member(T_a,V_a_2,V_A_2)-> (c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2))->c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2)))).
% 6.65/6.78 all V_z_2 V_r_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_b_2 V_B_2 V_a_2 T_a ((-c_member(T_a,V_a_2,V_B_2)->V_a_2=V_b_2)->c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2))).
% 6.65/6.78 all V_A_2 V_b_2 V_a_2 T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))-> (V_a_2!=V_b_2->c_member(T_a,V_a_2,V_A_2))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))).
% 6.65/6.78 all V_x_2 V_A_2 V_y_2 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))).
% 6.65/6.78 all V_A_2 V_y_2 V_x_2 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))).
% 6.65/6.78 all V_A_2 V_x_2 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)).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_b T_a (c_Relation_ODomain(T_a,T_b,c_Set_Oinsert(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2))=c_Set_Oinsert(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_a T_b (c_Relation_ORange(T_b,T_a,c_Set_Oinsert(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_a_2,V_b_2),V_r_2))=c_Set_Oinsert(T_a,V_b_2,c_Relation_ORange(T_b,T_a,V_r_2))).
% 6.65/6.78 all V_A_2 V_a_2 T_a (c_member(T_a,V_a_2,V_A_2)->c_Set_Oinsert(T_a,V_a_2,V_A_2)=V_A_2).
% 6.65/6.78 all V_b_2 V_B_2 V_a_2 T_a (c_member(T_a,V_a_2,V_B_2)->c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2))).
% 6.65/6.78 all V_B_2 V_A_2 V_x_2 T_a (-c_member(T_a,V_x_2,V_A_2)-> (-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))).
% 6.65/6.78 all V_A_2 V_b_2 V_a_2 T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))<->V_a_2=V_b_2|c_member(T_a,V_a_2,V_A_2)).
% 6.65/6.78 all V_B_2 V_a_2 T_a c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 6.65/6.78 all V_r_2 V_p_2 T_a (c_member(tc_prod(T_a,T_a),V_p_2,V_r_2)->c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2))).
% 6.65/6.78 all V_R_2 T_a (c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2))=c_Transitive__Closure_Ortrancl(T_a,V_R_2)).
% 6.65/6.78 all V_R_2 T_a (c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2))=c_Transitive__Closure_Ortrancl(T_a,V_R_2)).
% 6.65/6.78 all V_r_2 T_a (c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))=c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 T_a (c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))=c_Relation_ODomain(T_a,T_a,V_r_2)).
% 6.65/6.78 all V_r_2 T_a (c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))=c_Relation_ORange(T_a,T_a,V_r_2)).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2)->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_c_2 V_R_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_R_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_R_2)->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))).
% 6.65/6.78 all V_B_2 V_A_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))-> -(c_member(T_a,V_a_2,V_A_2)-> -c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2)))).
% 6.65/6.78 all V_B_2 V_A_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))->c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2))).
% 6.65/6.78 all V_B_2 V_A_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))->c_member(T_a,V_a_2,V_A_2)).
% 6.65/6.78 all V_B_2 V_A_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))<->c_member(T_a,V_a_2,V_A_2)&c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2))).
% 6.65/6.78 all V_R_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))<->V_x_2=V_y_2|V_x_2!=V_y_2&c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_R_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))->V_a_2=V_b_2|V_a_2!=V_b_2&c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2)->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_c_2 V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))->c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_B_2 V_A_2 V_c_2 T_b T_a (c_member(tc_prod(T_a,T_b),V_c_2,c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))-> -(all B_x (c_member(T_a,B_x,V_A_2)-> (all B_y (c_member(T_b,B_y,hAPP(V_B_2,B_x))->V_c_2!=c_Product__Type_OPair(T_a,T_b,B_x,B_y)))))).
% 6.65/6.78 all V_r_2 T_a ((all B_x (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))))->c_Wellfounded_Oacyclic(T_a,V_r_2)).
% 6.65/6.78 all V_R_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))-> (exists B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_z),c_Transitive__Closure_Ortrancl(T_a,V_R_2))&c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_y_2),V_R_2)))).
% 6.65/6.78 all V_R_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))-> (exists B_z (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_z),V_R_2)&c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))))).
% 6.65/6.78 all V_r_2 V_x_2 V_y_2 T_a (c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))<->c_Wellfounded_Owf(T_a,V_r_2)& -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 V_b_2 V_a_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))-> (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)-> -(all B_c (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,B_c),c_Transitive__Closure_Otrancl(T_a,V_r_2))-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_c,V_b_2),V_r_2))))).
% 6.65/6.78 all V_r_2 V_z_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))-> (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),V_r_2)-> -(all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,B_y),V_r_2)-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))))).
% 6.65/6.78 all V_f_2 T_b V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)->c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oinv__image(T_a,T_b,V_r_2),V_f_2))).
% 6.65/6.78 all V_rb_2 T_b V_ra_2 T_a (c_Wellfounded_Owf(T_a,V_ra_2)-> (c_Wellfounded_Owf(T_b,V_rb_2)->c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)->c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)->c_Wellfounded_Oacyclic(T_a,V_r_2)).
% 6.65/6.78 all V_a_2 V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2)).
% 6.65/6.78 all V_x_2 V_a_2 V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_x_2),V_r_2)-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2))).
% 6.65/6.78 all V_x_2 V_a_2 V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_x_2),V_r_2)-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2))).
% 6.65/6.78 all V_a_2 V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2)).
% 6.65/6.78 all V_x_2 V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)->c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)<-> (all B_x c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))->c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)))).
% 6.65/6.78 all V_f_2 T_a c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)).
% 6.65/6.78 all T_b T_a B_M B_R (c_Wellfounded_Owf(T_a,B_R)-> (all B_x (hAPP(c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_x)=hAPP(hAPP(B_M,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_R,B_x)),B_x)))).
% 6.65/6.78 all V_a_2 V_H_2 T_b V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)->hAPP(c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_a_2)=hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_r_2,V_a_2)),V_a_2)).
% 6.65/6.78 all V_a_2 V_H_2 V_r_2 T_b T_a V_f_2 (V_f_2=c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2)-> (c_Wellfounded_Owf(T_a,V_r_2)->hAPP(V_f_2,V_a_2)=hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_a_2)),V_a_2))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)<-> (all B_Q ((exists B_x c_member(T_a,B_x,B_Q))-> (exists B_x (c_member(T_a,B_x,B_Q)& (all B_y (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2)-> -c_member(T_a,B_y,B_Q)))))))).
% 6.65/6.78 all V_R_2 T_a (c_Wellfounded_Owf(T_a,V_R_2)->c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2))).
% 6.65/6.78 all T_a V_R_2 T_b V_P_2 ((all B_x (hBOOL(hAPP(V_P_2,B_x))->c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x))))->c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))).
% 6.65/6.78 all V_r_2 T_a ((all B_x c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)))->c_Wellfounded_Owf(T_a,V_r_2)).
% 6.65/6.78 all V_f_2 V_y_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))).
% 6.65/6.78 all V_y_2 V_x_2 V_r_2 T_a ((all B_x (-c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2))))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)->V_x_2!=V_y_2)).
% 6.65/6.78 all T_a (c_Wellfounded_Omeasure(T_a)=c_Relation_Oinv__image(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than)).
% 6.65/6.78 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than).
% 6.65/6.78 all V_y_2 V_x_2 (c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_x_2,V_y_2),c_Wellfounded_Oless__than)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)).
% 6.65/6.78 all V_R_2 T_a V_y_2 V_x_2 V_f_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))->c_member(tc_prod(T_a,T_a),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))).
% 6.65/6.78 c_Wellfounded_Oless__than=c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat).
% 6.65/6.78 all V_r_2 T_a (c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)-> (c_Wellfounded_Oacyclic(T_a,V_r_2)->c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))).
% 6.65/6.78 all V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)->c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2))).
% 6.65/6.78 all V_P_2 V_n_2 V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))).
% 6.65/6.78 all V_r_2 T_b T_a (c_Finite__Set_Ofinite(tc_prod(T_a,T_b),V_r_2)->c_Finite__Set_Ofinite(T_b,c_Relation_ORange(T_a,T_b,V_r_2))).
% 6.65/6.78 all V_r_2 T_b T_a (c_Finite__Set_Ofinite(tc_prod(T_a,T_b),V_r_2)->c_Finite__Set_Ofinite(T_a,c_Relation_ODomain(T_a,T_b,V_r_2))).
% 6.65/6.78 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat).
% 6.65/6.78 all V_r_2 T_a (c_Finite__Set_Ofinite(tc_prod(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))<->c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)).
% 6.65/6.78 all V_r_2 T_b T_a (c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Relation_Oconverse(T_b,T_a,V_r_2))<->c_Finite__Set_Ofinite(tc_prod(T_b,T_a),V_r_2)).
% 6.65/6.78 all V_r_2 T_a (c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)-> (c_Wellfounded_Owf(T_a,V_r_2)<->c_Wellfounded_Oacyclic(T_a,V_r_2))).
% 6.65/6.78 all V_r_2 T_a (c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)-> (c_Wellfounded_Oacyclic(T_a,V_r_2)->c_Wellfounded_Owf(T_a,V_r_2))).
% 6.65/6.78 all V_n_2 V_m_2 (c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_m_2,V_n_2),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 6.65/6.78 all V_f_2 V_R_2 T_a (c_Wellfounded_Owf(T_a,V_R_2)->c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))).
% 6.65/6.78 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 6.65/6.78 all V_n_2 V_m_2 (V_m_2!=V_n_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)).
% 6.65/6.78 all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))).
% 6.65/6.78 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 6.65/6.78 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 6.65/6.78 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 6.65/6.78 all V_a_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)->c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))).
% 6.65/6.78 all V_r_2 T_a (c_Nitpick_Owf_H(T_a,V_r_2)<->c_Wellfounded_Oacyclic(T_a,V_r_2)& (c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)|c_Nitpick_Ounknown(tc_HOL_Obool))).
% 6.65/6.79 all V_A_2 V_a_2 T_a (c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))<->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 6.65/6.79 all T_a c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)).
% 6.65/6.79 all V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)->c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2))).
% 6.65/6.79 all V_N_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)<-> (exists B_m all B_x (c_member(tc_Nat_Onat,B_x,V_N_2)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_x,B_m)))).
% 6.65/6.79 all V_A_2 T_a (class_Finite__Set_Ofinite(T_a)->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 6.65/6.79 all V_A_2 T_a (class_Finite__Set_Ofinite(T_a)->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 6.65/6.79 all V_x_2 V_A_2 V_F_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)-> (-c_member(T_b,V_x_2,V_A_2)->hAPP(V_F_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_F_2,V_A_2))))).
% 6.65/6.79 all V_t_2 V_s_2 V_b_2 V_a_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)->c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__le_q)).
% 6.65/6.79 all V_x_2 V_A_2 V_F_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)->hAPP(V_F_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_F_2,V_A_2)))).
% 6.65/6.79 all V_x_2 V_A_2 V_F_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)-> (c_member(T_b,V_x_2,V_A_2)->hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))=hAPP(V_F_2,V_A_2)))).
% 6.65/6.79 all V_t_2 V_s_2 V_b_2 V_a_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)->c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__less)).
% 6.65/6.79 all V_x_2 V_F_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)->hAPP(hAPP(V_f_2,V_x_2),V_x_2)=V_x_2).
% 6.65/6.79 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less).
% 6.65/6.79 c_FunDef_Opair__less=c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than).
% 6.65/6.79 all V_XS_2 V_x_2 V_YS_2 V_y_2 (c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_YS_2)-> (c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__le_q)-> (c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,V_YS_2),c_FunDef_Omax__weak)->c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_XS_2),V_YS_2),c_FunDef_Omax__weak)))).
% 6.65/6.79 all V_YS_2 V_y_2 V_XS_2 V_x_2 (c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_XS_2)-> (c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__le_q)-> (c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,V_YS_2),c_FunDef_Omin__weak)->c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_YS_2)),c_FunDef_Omin__weak)))).
% 6.65/6.79 all V_X_2 V_x_2 V_Y_2 V_y_2 (c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_Y_2)-> (c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__less)-> (c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_X_2,V_Y_2),c_FunDef_Omax__strict)->c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_X_2),V_Y_2),c_FunDef_Omax__strict)))).
% 6.65/6.79 all V_YS_2 V_y_2 V_XS_2 V_x_2 (c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_XS_2)-> (c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__less)-> (c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,V_YS_2),c_FunDef_Omin__strict)->c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_YS_2)),c_FunDef_Omin__strict)))).
% 6.65/6.79 all V_t_2 V_s_2 V_b_2 V_a_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,V_b_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s_2,V_t_2)->c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__less))).
% 6.65/6.79 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 6.65/6.79 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)).
% 6.65/6.79 all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 6.65/6.79 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k))).
% 6.65/6.79 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->V_m=V_n)).
% 6.65/6.79 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 6.65/6.79 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (V_m!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 6.65/6.79 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 6.65/6.79 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 6.65/6.79 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)&V_m_2!=V_n_2).
% 6.65/6.79 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)).
% 6.65/6.79 all V_N_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)<-> (exists B_m all B_x (c_member(tc_Nat_Onat,B_x,V_N_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_x,B_m)))).
% 6.65/6.79 all V_R_2 T_a V_y_2 V_x_2 V_f_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))-> (c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_R_2)->c_member(tc_prod(T_a,T_a),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)))).
% 6.65/6.79 c_FunDef_Omin__strict=c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less).
% 6.65/6.79 c_FunDef_Omax__strict=c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less).
% 6.65/6.79 all V_n_2 V_m_2 (c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_m_2,V_n_2),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 6.65/6.79 all V_t_2 V_s_2 V_b_2 V_a_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,V_b_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_s_2,V_t_2)->c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__le_q))).
% 6.65/6.79 all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 6.65/6.79 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omin__strict,c_FunDef_Omin__weak)).
% 6.65/6.79 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omax__strict,c_FunDef_Omax__weak)).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 6.65/6.79 all V_c_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2))).
% 6.65/6.79 all V_A_2 V_B_2 T_a (c_Finite__Set_Ofinite(T_a,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Finite__Set_Ofinite(T_a,V_A_2))).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(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))).
% 6.65/6.79 all V_x_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_x_2,V_A_2)->c_member(T_a,V_x_2,V_B_2))).
% 6.65/6.79 all V_B_2 V_A_2 V_x_2 T_a (c_member(T_a,V_x_2,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_member(T_a,V_x_2,V_B_2))).
% 6.65/6.79 all V_x_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_x_2,V_A_2)->c_member(T_a,V_x_2,V_B_2))).
% 6.65/6.79 all V_c_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2))).
% 6.65/6.79 all V_s_2 V_r_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2))->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))).
% 6.65/6.79 all V_S_2 V_R_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2))->c_Transitive__Closure_Ortrancl(T_a,V_S_2)=c_Transitive__Closure_Ortrancl(T_a,V_R_2))).
% 6.65/6.79 all V_s_2 V_r_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))).
% 6.65/6.79 all V_p_2 V_r_2 T_a (c_Wellfounded_Owf(T_a,V_r_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_p_2,V_r_2)->c_Wellfounded_Owf(T_a,V_p_2))).
% 6.65/6.79 all V_R2_2 V_R1_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2))).
% 6.65/6.79 all V_s_2 V_r_2 T_b T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_r_2),c_Relation_ODomain(T_a,T_b,V_s_2))).
% 6.65/6.79 all V_a_2 V_D_2 V_C_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_C_2),c_Set_Oinsert(T_a,V_a_2,V_D_2))).
% 6.65/6.79 all V_b_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_b_2,V_B_2))).
% 6.65/6.79 all V_a_2 V_B_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 6.65/6.79 all V_p_2 V_r_2 T_a (c_Wellfounded_OwfP(T_a,V_r_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_p_2,V_r_2)->c_Wellfounded_OwfP(T_a,V_p_2))).
% 6.65/6.79 all V_s_2 V_r_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)-> (c_Relation_Oantisym(T_a,V_s_2)->c_Relation_Oantisym(T_a,V_r_2))).
% 6.65/6.79 all V_r_2 V_s_2 T_a (c_Wellfounded_Oacyclic(T_a,V_s_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)->c_Wellfounded_Oacyclic(T_a,V_r_2))).
% 6.65/6.79 all V_s_2 V_r_2 T_b T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2)-> (c_Relation_Osingle__valued(T_a,T_b,V_s_2)->c_Relation_Osingle__valued(T_a,T_b,V_r_2))).
% 6.65/6.79 all V_B_2 V_A_2 V_x_2 T_a (-c_member(T_a,V_x_2,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 6.65/6.79 all V_B_2 V_A_2 V_x_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)<->c_member(T_a,V_x_2,V_B_2)&c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.79 all V_s_2 V_r_2 V_p_2 T_a (c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2))-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)->c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_s_2)))).
% 6.65/6.79 all V_B_2 V_A_2 V_F_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),V_B_2,V_A_2)->hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2))=hAPP(V_F_2,V_A_2)))).
% 6.65/6.79 all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (V_x_2=V_y_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 6.65/6.79 all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 6.65/6.79 all V_x_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 6.65/6.79 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 6.65/6.79 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 6.65/6.79 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 6.65/6.79 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->V_x=V_y))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)))).
% 6.65/6.79 all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->V_x=V_y))).
% 6.65/6.79 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)))).
% 6.65/6.79 all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 6.65/6.79 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2)).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 6.65/6.79 all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)).
% 6.65/6.79 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))).
% 6.65/6.79 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 6.65/6.79 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 6.65/6.79 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 6.65/6.79 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 6.65/6.79 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 6.65/6.79 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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))<->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)).
% 6.65/6.79 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 6.65/6.79 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 6.65/6.79 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 6.65/6.79 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 6.65/6.79 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 6.65/6.79 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 6.65/6.79 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 6.65/6.79 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2)).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&V_x_2!=V_y_2)).
% 6.65/6.79 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 6.65/6.79 all V_f_2 T_b V_P_2 T_a (c_FunDef_Oreduction__pair(T_a,V_P_2)->c_FunDef_Oreduction__pair(T_b,c_FunDef_Orp__inv__image(T_a,T_b,V_P_2,V_f_2))).
% 6.65/6.79 all V_S_2 V_R_2 T_a (c_Wellfounded_Owf(T_a,V_R_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)->c_FunDef_Oreduction__pair(T_a,c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)))).
% 6.65/6.79 all V_X_2 (V_X_2!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))->c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_X_2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__strict)).
% 6.65/6.79 all V_X_2 c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_X_2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__weak).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->V_A_2=V_B_2)).
% 6.65/6.79 all V_a_2 T_a (-c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 6.65/6.79 all T_a c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2).
% 6.65/6.79 all T_a c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.79 all V_s_2 V_c_2 T_c V_r_2 V_b_2 V_a_2 T_b T_a (c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)-> (c_member(tc_prod(T_b,T_c),c_Product__Type_OPair(T_b,T_c,V_b_2,V_c_2),V_s_2)->c_member(tc_prod(T_a,T_c),c_Product__Type_OPair(T_a,T_c,V_a_2,V_c_2),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)))).
% 6.65/6.79 all V_B_2 T_a V_A_2 (V_A_2=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.79 all V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2).
% 6.65/6.79 all V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all T_a V_B_2 V_A_2 (V_A_2=V_B_2<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)&c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 6.65/6.79 all V_Q_2 T_a V_x_2 V_P_2 (hBOOL(hAPP(V_P_2,V_x_2))-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)->hBOOL(hAPP(V_Q_2,V_x_2)))).
% 6.65/6.79 all T_a V_B_2 V_A_2 (V_A_2=V_B_2->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.79 all T_a V_B_2 V_A_2 (V_A_2=V_B_2->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 6.65/6.79 all V_x_2 V_Q_2 V_P_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)-> (hBOOL(hAPP(V_P_2,V_x_2))->hBOOL(hAPP(V_Q_2,V_x_2)))).
% 6.65/6.79 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 6.65/6.79 all V_s_2 V_s_H_2 T_c V_r_2 V_r_H_2 T_b T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_H_2,V_r_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_s_H_2,V_s_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_H_2,V_s_H_2),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)))).
% 6.65/6.79 all V_y_2 V_x_2 V_Q_2 V_P_2 T_b T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_P_2,V_Q_2)-> (hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))->hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)))).
% 6.65/6.79 all T_a V_B_2 V_A_2 (V_A_2=V_B_2-> -(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))).
% 6.65/6.79 all V_Q_2 T_b T_a V_y_2 V_x_2 V_P_2 (hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_P_2,V_Q_2)->hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)))).
% 6.65/6.79 all V_x_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2=c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 6.65/6.79 all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2))).
% 6.65/6.79 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 6.65/6.79 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)<->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2=V_B_2).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)&V_A_2!=V_B_2).
% 6.65/6.79 all V_A_2 T_a (-c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 6.65/6.79 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 6.65/6.79 all V_x_2 T_b T_a (class_Orderings_Obot(T_a)->hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2)=c_Orderings_Obot__class_Obot(T_a)).
% 6.65/6.79 all V_r_2 T_a (c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2))=c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2)).
% 6.65/6.79 all V_R_2 T_a (c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))=c_Transitive__Closure_Ortrancl(T_a,V_R_2)).
% 6.65/6.79 all T_a (c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.79 all V_R_2 T_b T_a (c_Relation_Orel__comp(T_a,T_b,T_b,V_R_2,c_Relation_OId(T_b))=V_R_2).
% 6.65/6.79 all V_R_2 T_b T_a (c_Relation_Orel__comp(T_a,T_a,T_b,c_Relation_OId(T_a),V_R_2)=V_R_2).
% 6.65/6.79 all T_a c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all V_B_2 T_b T_a (c_Product__Type_OSigma(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))).
% 6.65/6.79 all V_r_2 T_b T_a (c_Relation_ODomain(T_a,T_b,V_r_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<->V_r_2=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))).
% 6.65/6.79 all T_b T_a (c_Relation_ODomain(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all V_r_2 T_a T_b (c_Relation_ORange(T_b,T_a,V_r_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<->V_r_2=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))).
% 6.65/6.79 all T_a T_b (c_Relation_ORange(T_b,T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all T_a c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.79 all V_R_2 T_b T_c T_a (c_Relation_Orel__comp(T_a,T_c,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_R_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))).
% 6.65/6.79 all V_R_2 T_b T_c T_a (c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))).
% 6.65/6.79 all V_T_2 V_S_2 V_R_2 T_d T_b T_c T_a (c_Relation_Orel__comp(T_a,T_c,T_b,c_Relation_Orel__comp(T_a,T_d,T_c,V_R_2,V_S_2),V_T_2)=c_Relation_Orel__comp(T_a,T_d,T_b,V_R_2,c_Relation_Orel__comp(T_d,T_c,T_b,V_S_2,V_T_2))).
% 6.65/6.79 all T_a (c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.79 all V_s_2 V_r_2 T_c T_a T_b (c_Relation_Oconverse(T_b,T_a,c_Relation_Orel__comp(T_b,T_c,T_a,V_r_2,V_s_2))=c_Relation_Orel__comp(T_a,T_c,T_b,c_Relation_Oconverse(T_c,T_a,V_s_2),c_Relation_Oconverse(T_b,T_c,V_r_2))).
% 6.65/6.79 all V_A_2 V_a_2 T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_Oinsert(T_a,V_a_2,V_A_2)).
% 6.65/6.79 all V_A_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))<->V_a_2=V_c_2&V_b_2=V_d_2|V_a_2=V_d_2&V_b_2=V_c_2).
% 6.65/6.79 all V_b_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))->V_a_2=V_b_2).
% 6.65/6.79 all V_R_2 T_a (c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))->c_Wellfounded_Owf(T_a,V_R_2)).
% 6.65/6.79 all V_R_2 T_a (c_Wellfounded_Owf(T_a,V_R_2)<->c_Wellfounded_Owf(T_a,c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2))).
% 6.65/6.79 all V_a_2 T_a V_A_2 (V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))-> -c_member(T_a,V_a_2,V_A_2)).
% 6.65/6.79 all V_c_2 T_a (-c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 6.65/6.79 all V_A_2 T_a ((exists B_x c_member(T_a,B_x,V_A_2))<->V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all V_A_2 T_a ((all B_x (-c_member(T_a,B_x,V_A_2)))<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all V_s_2 T_c V_r_2 T_b T_a (c_Relation_Osingle__valued(T_a,T_b,V_r_2)-> (c_Relation_Osingle__valued(T_b,T_c,V_s_2)->c_Relation_Osingle__valued(T_a,T_c,c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)))).
% 6.65/6.79 all T_a c_Relation_Oantisym(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.79 all V_r_2 T_a c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2).
% 6.65/6.79 all V_x T_a (class_Orderings_Obot(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)).
% 6.65/6.79 all V_F_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)->hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=V_z_2).
% 6.65/6.79 all V_a_2 V_b_2 T_a (c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))<->V_b_2=V_a_2).
% 6.65/6.79 all V_a_2 V_b_2 T_a (c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))->V_b_2=V_a_2).
% 6.65/6.79 all V_r_2 T_a (c_Transitive__Closure_Otrancl(T_a,V_r_2)=c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2))).
% 6.65/6.79 all V_r_2 T_a (c_Transitive__Closure_Otrancl(T_a,V_r_2)=c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2)).
% 6.65/6.79 all T_a (c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))=c_Relation_OId(T_a)).
% 6.65/6.79 all V_Y_2 (c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_Y_2)-> (V_Y_2!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))->c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_Y_2),c_FunDef_Omax__strict))).
% 6.65/6.79 all V_X_2 (c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_X_2)->c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_FunDef_Omax__weak)).
% 6.65/6.79 all V_r_2 V_A_2 T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_Orel__comp(T_a,T_a,T_a,c_Relation_Oconverse(T_a,T_a,V_r_2),V_r_2))).
% 6.65/6.79 all V_x_2 T_a (c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_x_2).
% 6.65/6.79 all V_x_2 V_A_2 V_F_2 V_f_2 T_a (c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (-c_member(T_a,V_x_2,V_A_2)-> (V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))->hAPP(V_F_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)))))).
% 6.65/6.79 all V_x_2 V_F_2 V_f_2 T_a (c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)->hAPP(V_F_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_x_2).
% 6.65/6.79 c_FunDef_Omin__weak=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__le_q),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))).
% 6.65/6.79 c_FunDef_Omax__weak=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__le_q),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))).
% 6.65/6.79 all V_x_2 V_B_2 V_A_2 T_a (hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))-> (-hBOOL(hAPP(V_A_2,V_x_2))->hBOOL(hAPP(V_B_2,V_x_2)))).
% 6.65/6.79 all T_a V_A_2 V_x_2 V_B_2 ((-hBOOL(hAPP(V_B_2,V_x_2))->hBOOL(hAPP(V_A_2,V_x_2)))->hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))).
% 6.65/6.79 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))-> (-c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2))).
% 6.65/6.79 all V_A_2 V_B_2 V_c_2 T_a ((-c_member(T_a,V_c_2,V_B_2)->c_member(T_a,V_c_2,V_A_2))->c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 6.65/6.79 all V_B_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=V_B_2).
% 6.65/6.79 all V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=V_A_2).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))&V_B_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.79 all V_G_2 V_F_2 T_a (c_Finite__Set_Ofinite(T_a,V_F_2)-> (c_Finite__Set_Ofinite(T_a,V_G_2)->c_Finite__Set_Ofinite(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_F_2,V_G_2)))).
% 6.65/6.79 all V_G_2 V_F_2 T_a (c_Finite__Set_Ofinite(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_F_2,V_G_2))<->c_Finite__Set_Ofinite(T_a,V_F_2)&c_Finite__Set_Ofinite(T_a,V_G_2)).
% 6.65/6.79 all V_A_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)).
% 6.65/6.79 all V_S_2 V_R_2 V_x_2 T_a (c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2))|c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_S_2))->c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)))).
% 6.65/6.79 all V_S_2 V_R_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))).
% 6.65/6.79 all V_S_2 V_R_2 T_a (c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))<->c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2),c_Relation_Orel__comp(T_a,T_a,T_a,V_S_2,V_R_2)),V_S_2))).
% 6.65/6.79 all V_r_2 T_a (c_Transitive__Closure_Otrancl(T_a,V_r_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2),V_r_2))).
% 6.65/6.79 all V_B_2 V_C_2 V_A_2 T_a (c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,V_C_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))-> (c_Relation_Orel__comp(T_a,T_a,T_a,V_B_2,V_C_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))->c_Relation_Orel__comp(T_a,T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))).
% 6.65/6.79 all V_C_2 V_B_2 V_A_2 T_a (c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))-> (c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,V_C_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))->c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_B_2,V_C_2))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))).
% 6.65/6.79 all V_R_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Relation_OId(T_a))=c_Transitive__Closure_Ortrancl(T_a,V_R_2)).
% 6.65/6.79 all V_R_2 T_a (c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,c_Relation_OId(T_a)))=c_Transitive__Closure_Ortrancl(T_a,V_R_2)).
% 6.65/6.79 all V_r_2 T_a (c_Relation_Oantisym(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))<->c_Relation_Oantisym(T_a,V_r_2)).
% 6.65/6.79 all V_S_2 V_R_2 T_a (c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)))=c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))).
% 6.65/6.79 all V_s_2 V_r_2 T_a T_b (c_Relation_Oconverse(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_r_2,V_s_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Oconverse(T_b,T_a,V_r_2),c_Relation_Oconverse(T_b,T_a,V_s_2))).
% 6.65/6.79 all V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.79 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 6.65/6.79 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 6.65/6.79 all V_P_2 V_B_2 V_A_2 T_a ((exists B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))&hBOOL(hAPP(V_P_2,B_x))))<-> (exists B_x (c_member(T_a,B_x,V_A_2)&hBOOL(hAPP(V_P_2,B_x))))| (exists B_x (c_member(T_a,B_x,V_B_2)&hBOOL(hAPP(V_P_2,B_x))))).
% 6.65/6.79 all V_P_2 V_B_2 V_A_2 T_a ((all B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))->hBOOL(hAPP(V_P_2,B_x))))<-> (all B_x (c_member(T_a,B_x,V_A_2)->hBOOL(hAPP(V_P_2,B_x))))& (all B_x (c_member(T_a,B_x,V_B_2)->hBOOL(hAPP(V_P_2,B_x))))).
% 6.65/6.79 all V_B_2 T_a V_x_2 V_A_2 (hBOOL(hAPP(V_A_2,V_x_2))->hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))).
% 6.65/6.79 all V_A_2 T_a V_x_2 V_B_2 (hBOOL(hAPP(V_B_2,V_x_2))->hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))).
% 6.65/6.79 all V_B_2 V_A_2 T_a T_b (c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2))).
% 6.65/6.79 all V_B_2 V_A_2 T_b T_a (c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2))).
% 6.65/6.79 all V_s_2 V_B_2 V_r_2 V_A_2 T_a (c_Relation_Orefl__on(T_a,V_A_2,V_r_2)-> (c_Relation_Orefl__on(T_a,V_B_2,V_s_2)->c_Relation_Orefl__on(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)))).
% 6.65/6.79 all V_B_2 V_a_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 6.65/6.79 all V_C_2 V_B_2 V_a_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 6.65/6.79 all V_A_2 V_B_2 V_c_2 T_a (c_member(T_a,V_c_2,V_B_2)->c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 6.65/6.79 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 6.65/6.79 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))<->c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2)).
% 6.65/6.79 all V_R_2 V_T_2 V_S_2 T_b T_c T_a (c_Relation_Orel__comp(T_a,T_c,T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),V_S_2,V_T_2),V_R_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_c,T_b,V_S_2,V_R_2),c_Relation_Orel__comp(T_a,T_c,T_b,V_T_2,V_R_2))).
% 6.65/6.79 all V_T_2 V_S_2 V_R_2 T_b T_c T_a (c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2,V_T_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,V_S_2),c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,V_T_2))).
% 6.65/6.79 all V_D_2 V_B_2 V_C_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)))).
% 6.65/6.79 all V_B_2 V_C_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2))).
% 6.65/6.79 all V_A_2 V_B_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2).
% 6.65/6.79 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)<->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2).
% 6.65/6.79 all V_A_2 V_B_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.79 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.79 all V_B_2 V_A_2 V_F_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)-> (c_Finite__Set_Ofinite(T_b,V_B_2)->hAPP(V_F_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2))=hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))))).
% 6.65/6.79 all V_S_2 V_R_2 T_a (c_Wellfounded_Owf(T_a,V_R_2)-> (c_Wellfounded_Owf(T_a,V_S_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)->c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))))).
% 6.65/6.79 all V_r_2 T_a (c_Transitive__Closure_Otrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))=c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.79 all V_r_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Otrancl(T_a,V_r_2),c_Relation_OId(T_a))=c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.79 all V_r_2 T_a (c_Transitive__Closure_Ortrancl(T_a,V_r_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_OId(T_a),c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2))).
% 6.65/6.79 all V_D_2 V_C_2 V_R_2 V_B_2 V_A_2 T_a (c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Wellfounded_Omax__ext(T_a,V_R_2))-> (c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2),c_Wellfounded_Omax__ext(T_a,V_R_2))->c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))).
% 6.65/6.79 all V_S_2 V_R_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_R_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_S_2),c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool))))),c_Wellfounded_Omax__ext(T_a,V_R_2))).
% 6.65/6.79 all V_S_2 V_R_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_R_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_S_2),c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool))))),c_Wellfounded_Omin__ext(T_a,V_R_2))).
% 6.65/6.79 all V_x_2 V_g_2 V_f_2 T_b T_a (class_Lattices_Olattice(T_a)->hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2)=c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))).
% 6.65/6.79 all V_y_2 V_x_2 T_a (class_Lattices_Obounded__lattice__bot(T_a)-> (c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)=c_Orderings_Obot__class_Obot(T_a)<->V_x_2=c_Orderings_Obot__class_Obot(T_a)&V_y_2=c_Orderings_Obot__class_Obot(T_a))).
% 6.65/6.79 c_FunDef_Opair__le_q=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))).
% 6.65/6.79 all V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a)=V_a).
% 6.65/6.79 all V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x)=V_x).
% 6.65/6.79 all V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_a)).
% 6.65/6.79 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x)).
% 6.65/6.79 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x)).
% 6.65/6.79 all V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 6.65/6.79 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 6.65/6.79 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 6.65/6.79 all V_c V_a V_b T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_c))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))).
% 6.65/6.79 all V_c V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_c)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))).
% 6.65/6.79 all V_z V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))).
% 6.65/6.79 all V_x V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)-> -(c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)-> -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)))).
% 6.65/6.79 all V_d V_b V_c V_a T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_c,V_d))))).
% 6.65/6.79 all V_z V_x V_y T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x)))).
% 6.65/6.80 all V_b V_x V_a T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)))).
% 6.65/6.80 all V_x V_y T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_x)).
% 6.65/6.80 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_y)).
% 6.65/6.80 all V_a V_b V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 6.65/6.80 all V_b V_a V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 6.65/6.80 all V_z_2 V_y_2 V_x_2 T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2),V_z_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_z_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_z_2))).
% 6.65/6.80 all V_y_2 V_x_2 T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)=V_y_2)).
% 6.65/6.80 all V_x V_y T_a (class_Lattices_Osemilattice__sup(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 6.65/6.80 all V_x V_y T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 6.65/6.80 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 6.65/6.80 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 6.65/6.80 all V_b V_a V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)->c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 6.65/6.80 all V_a V_b V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_b)->c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 6.65/6.80 all V_x T_a (class_Lattices_Obounded__lattice__bot(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)=V_x).
% 6.65/6.80 all V_x T_a (class_Lattices_Obounded__lattice__bot(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Obot__class_Obot(T_a))=V_x).
% 6.65/6.80 all V_A_2 V_F_2 V_f_2 T_a (c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))-> ((all B_x B_y c_member(T_a,hAPP(hAPP(V_f_2,B_x),B_y),c_Set_Oinsert(T_a,B_x,c_Set_Oinsert(T_a,B_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))->c_member(T_a,hAPP(V_F_2,V_A_2),V_A_2))))).
% 6.65/6.80 all V_x_2 V_r_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Oconverse(T_a,T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))-> -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_x_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))).
% 6.65/6.80 all T_a V_B_2 V_x_2 V_A_2 (hBOOL(hAPP(V_A_2,V_x_2))-> (hBOOL(hAPP(V_B_2,V_x_2))->hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)))).
% 6.65/6.80 all V_x_2 V_B_2 V_A_2 T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))-> -(hBOOL(hAPP(V_A_2,V_x_2))-> -hBOOL(hAPP(V_B_2,V_x_2)))).
% 6.65/6.80 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,V_A_2)-> (c_member(T_a,V_c_2,V_B_2)->c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))).
% 6.65/6.80 class_Lattices_Obounded__lattice(tc_HOL_Obool).
% 6.65/6.80 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_1 T_2 (class_Finite__Set_Ofinite(T_2)&class_Finite__Set_Ofinite(T_1)->class_Finite__Set_Ofinite(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Olattice(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 6.65/6.80 all T_2 T_1 (class_Orderings_Obot(T_1)->class_Orderings_Obot(tc_fun(T_2,T_1))).
% 6.65/6.80 class_Lattices_Osemilattice__sup(tc_Nat_Onat).
% 6.65/6.80 class_Orderings_Opreorder(tc_Nat_Onat).
% 6.65/6.80 class_Orderings_Olinorder(tc_Nat_Onat).
% 6.65/6.80 class_Lattices_Olattice(tc_Nat_Onat).
% 6.65/6.80 class_Orderings_Oorder(tc_Nat_Onat).
% 6.65/6.80 class_Orderings_Oord(tc_Nat_Onat).
% 6.65/6.80 class_Orderings_Obot(tc_Nat_Onat).
% 6.65/6.80 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool).
% 6.65/6.80 class_Lattices_Osemilattice__sup(tc_HOL_Obool).
% 6.65/6.80 class_Orderings_Opreorder(tc_HOL_Obool).
% 6.65/6.80 class_Finite__Set_Ofinite(tc_HOL_Obool).
% 6.65/6.80 class_Lattices_Olattice(tc_HOL_Obool).
% 6.65/6.80 class_Orderings_Oorder(tc_HOL_Obool).
% 6.65/6.80 class_Orderings_Oord(tc_HOL_Obool).
% 6.65/6.80 class_Orderings_Obot(tc_HOL_Obool).
% 6.65/6.80 all T_1 T_2 (class_Finite__Set_Ofinite(T_2)&class_Finite__Set_Ofinite(T_1)->class_Finite__Set_Ofinite(tc_prod(T_2,T_1))).
% 6.65/6.80 all V_y_2 V_x_2 (-hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2).
% 6.65/6.80 all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))).
% 6.65/6.80 -(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),c_Arrow__Order__Mirabelle_OLin)<->c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),v_L,c_Arrow__Order__Mirabelle_OLin)).
% 6.65/6.80 end_of_list.
% 6.65/6.80
% 6.65/6.80 -------> usable clausifies to:
% 6.65/6.80
% 6.65/6.80 list(usable).
% 6.65/6.80 0 [] A=A.
% 6.65/6.80 0 [] hAPP(V_f_2,$f1(V_g_2,V_f_2))!=hAPP(V_g_2,$f1(V_g_2,V_f_2))|V_f_2=V_g_2.
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_member(T_a,V_c_2,V_A_2)| -c_member(T_a,V_c_2,V_B_2).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_member(T_a,V_c_2,V_B_2)| -c_member(T_a,V_c_2,V_A_2).
% 6.65/6.80 0 [] c_Relation_Oconverse(T_b,T_a,c_Relation_Oconverse(T_a,T_b,V_r_2))=V_r_2.
% 6.65/6.80 0 [] -c_member(T_a,V_x_2,V_A_2)|hBOOL(hAPP(V_A_2,V_x_2)).
% 6.65/6.80 0 [] c_member(T_a,V_x_2,V_A_2)| -hBOOL(hAPP(V_A_2,V_x_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_x_2,c_fe_qual(V_y_2))|V_x_2=V_y_2.
% 6.65/6.80 0 [] c_member(T_a,V_x_2,c_fe_qual(V_y_2))|V_x_2!=V_y_2.
% 6.65/6.80 0 [] V_A_2!=V_B_2| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_x_2,V_B_2).
% 6.65/6.80 0 [] V_x_2!=V_y_2| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_y_2,V_A_2).
% 6.65/6.80 0 [] V_x_2!=V_y_2|c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_y_2,V_A_2).
% 6.65/6.80 0 [] V_a_2!=V_b_2| -c_member(T_a,V_b_2,V_A_2)|c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] -c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_La_2,c_Arrow__Order__Mirabelle_OLin)|V_x_2=V_y_2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_La_2)|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_y_2,V_x_2),V_La_2).
% 6.65/6.80 0 [] -c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),V_La_2,c_Arrow__Order__Mirabelle_OLin)|V_x_2=V_y_2| -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_x_2,V_y_2),V_La_2)| -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,V_y_2,V_x_2),V_La_2).
% 6.65/6.80 0 [] -c_Relation_Ototal__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2))|c_Relation_Ototal__on(T_a,V_A_2,V_r_2).
% 6.65/6.80 0 [] c_Relation_Ototal__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2))| -c_Relation_Ototal__on(T_a,V_A_2,V_r_2).
% 6.65/6.80 0 [] c_Relation_Oconverse(T_a,T_a,hAPP(c_Relation_Oinv__image(T_b,T_a,V_R_2),V_f_2))=hAPP(c_Relation_Oinv__image(T_b,T_a,c_Relation_Oconverse(T_b,T_b,V_R_2)),V_f_2).
% 6.65/6.80 0 [] -c_Relation_Oantisym(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))|c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.80 0 [] c_Relation_Oantisym(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))| -c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.80 0 [] c_Relation_Oconverse(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))=c_Relation_OId__on(T_a,V_A_2).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))|hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)).
% 6.65/6.80 0 [] c_Relation_Oantisym(T_a,c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),hAPP(c_Relation_Oinv__image(T_b,T_a,V_r_2),V_f_2))|c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)),V_r_2).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),hAPP(c_Relation_Oinv__image(T_b,T_a,V_r_2),V_f_2))| -c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)),V_r_2).
% 6.65/6.80 0 [] -c_Relation_Oantisym(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_y),V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,B_x),V_r_2)|B_x=B_y.
% 6.65/6.80 0 [] c_Relation_Oantisym(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f3(V_r_2,T_a),$f2(V_r_2,T_a)),V_r_2).
% 6.65/6.80 0 [] c_Relation_Oantisym(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f2(V_r_2,T_a),$f3(V_r_2,T_a)),V_r_2).
% 6.65/6.80 0 [] c_Relation_Oantisym(T_a,V_r_2)|$f3(V_r_2,T_a)!=$f2(V_r_2,T_a).
% 6.65/6.80 0 [] -c_Relation_Oantisym(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),V_r_2)|V_a_2=V_b_2.
% 6.65/6.80 0 [] -c_Relation_Ototal__on(T_a,V_A_2,V_r_2)| -c_member(T_a,B_x,V_A_2)| -c_member(T_a,B_xa,V_A_2)|B_x=B_xa|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_xa),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_xa,B_x),V_r_2).
% 6.65/6.80 0 [] c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|c_member(T_a,$f5(V_r_2,V_A_2,T_a),V_A_2).
% 6.65/6.80 0 [] c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|c_member(T_a,$f4(V_r_2,V_A_2,T_a),V_A_2).
% 6.65/6.80 0 [] c_Relation_Ototal__on(T_a,V_A_2,V_r_2)|$f5(V_r_2,V_A_2,T_a)!=$f4(V_r_2,V_A_2,T_a).
% 6.65/6.80 0 [] c_Relation_Ototal__on(T_a,V_A_2,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f5(V_r_2,V_A_2,T_a),$f4(V_r_2,V_A_2,T_a)),V_r_2).
% 6.65/6.80 0 [] c_Relation_Ototal__on(T_a,V_A_2,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f4(V_r_2,V_A_2,T_a),$f5(V_r_2,V_A_2,T_a)),V_r_2).
% 6.65/6.80 0 [] V_a_2!=V_b_2| -c_member(T_a,V_a_2,V_A_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_OId__on(T_a,V_A_2))|V_x_2=V_y_2.
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_OId__on(T_a,V_A_2))|c_member(T_a,V_x_2,V_A_2).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_OId__on(T_a,V_A_2))|V_x_2!=V_y_2| -c_member(T_a,V_x_2,V_A_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Relation_Oconverse(T_b,T_a,V_r_2))|c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_b_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)|c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_b_2,V_a_2),c_Relation_Oconverse(T_a,T_b,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Relation_Oconverse(T_b,T_a,V_r_2))|c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_b_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Relation_Oconverse(T_b,T_a,V_r_2))| -c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_b_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__e_q_2,V_k_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_k_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__e_q_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_k_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__e_q_2,V_k_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_k_2),V_i_2)).
% 6.65/6.80 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__e_q_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_k_2),V_i_2)).
% 6.65/6.80 0 [] -c_Relation_Oirrefl(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2).
% 6.65/6.80 0 [] c_Relation_Oirrefl(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f6(V_r_2,T_a),$f6(V_r_2,T_a)),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2))|c_member(T_a,$f7(V_A_2,V_c_2,T_a),V_A_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),V_c_2,c_Relation_OId__on(T_a,V_A_2))|V_c_2=c_Product__Type_OPair(T_a,T_a,$f7(V_A_2,V_c_2,T_a),$f7(V_A_2,V_c_2,T_a)).
% 6.65/6.80 0 [] -hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2).
% 6.65/6.80 0 [] hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))| -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_R_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),V_yx_2,c_Relation_Oconverse(T_b,T_a,V_r_2))|V_yx_2=c_Product__Type_OPair(T_a,T_b,$f8(V_r_2,V_yx_2,T_b,T_a),$f9(V_r_2,V_yx_2,T_b,T_a)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),V_yx_2,c_Relation_Oconverse(T_b,T_a,V_r_2))|c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,$f9(V_r_2,V_yx_2,T_b,T_a),$f8(V_r_2,V_yx_2,T_b,T_a)),V_r_2).
% 6.65/6.80 0 [] -hBOOL(hAPP(V_P_2,V_x_2))| -c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_y_H_2,V_y_2),hAPP(V_R_2,V_x_2))|c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_H_2),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2)),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)|c_member(T_b,V_b_2,c_Relation_ORange(T_a,T_b,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)|c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)).
% 6.65/6.80 0 [] -c_Nitpick_Orefl_H(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),V_r_2).
% 6.65/6.80 0 [] c_Nitpick_Orefl_H(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f10(V_r_2,T_a),$f10(V_r_2,T_a)),V_r_2).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f12(V_r_2,T_a),$f11(V_r_2,T_a)),V_r_2)|c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f11(V_r_2,T_a),$f12(V_r_2,T_a)),V_r_2)|c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.80 0 [] $f12(V_r_2,T_a)!=$f11(V_r_2,T_a)|c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.80 0 [] c_Relation_ORange(T_b,T_a,c_Relation_Oconverse(T_a,T_b,V_r_2))=c_Relation_ODomain(T_a,T_b,V_r_2).
% 6.65/6.80 0 [] c_Relation_ODomain(T_a,T_b,c_Relation_Oconverse(T_b,T_a,V_r_2))=c_Relation_ORange(T_b,T_a,V_r_2).
% 6.65/6.80 0 [] c_Relation_ORange(T_b,T_a,V_r_2)=c_Relation_ODomain(T_a,T_b,c_Relation_Oconverse(T_b,T_a,V_r_2)).
% 6.65/6.80 0 [] c_Relation_ODomain(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))=V_A_2.
% 6.65/6.80 0 [] c_Relation_ORange(T_a,T_a,c_Relation_OId__on(T_a,V_A_2))=V_A_2.
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,$f13(V_r_2,T_b,V_a_2,T_a)),V_r_2).
% 6.65/6.80 0 [] c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))| -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,B_y),V_r_2).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Relation_ORange(T_b,T_a,V_r_2))|c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,$f14(V_r_2,T_b,V_a_2,T_a),V_a_2),V_r_2).
% 6.65/6.80 0 [] c_member(T_a,V_a_2,c_Relation_ORange(T_b,T_a,V_r_2))| -c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,B_y,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),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))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_H_2),V_r_2)|V_a_2=V_a_H_2.
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),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))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_H_2),V_r_2)|c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_b_2,V_b_H_2),V_s_2).
% 6.65/6.80 0 [] c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),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))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_H_2),V_r_2).
% 6.65/6.80 0 [] c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),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))|V_a_2!=V_a_H_2| -c_member(tc_prod(T_b,T_b),c_Product__Type_OPair(T_b,T_b,V_b_2,V_b_H_2),V_s_2).
% 6.65/6.80 0 [] -c_member(T_a,V_b_2,c_Relation_ORange(T_b,T_a,V_r_2))|c_member(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,$f15(V_r_2,T_b,V_b_2,T_a),V_b_2),V_r_2).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2))|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,$f16(V_r_2,T_b,V_a_2,T_a)),V_r_2).
% 6.65/6.80 0 [] -c_Relation_Orefl__on(T_a,V_A_2,V_r_2)| -c_member(T_a,V_a_2,V_A_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_Relation_Orefl__on(T_a,V_A_2,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)|c_member(T_a,V_x_2,V_A_2).
% 6.65/6.80 0 [] -c_Relation_Orefl__on(T_a,V_A_2,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)|c_member(T_a,V_y_2,V_A_2).
% 6.65/6.80 0 [] -c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,hAPP(hAPP(V_F_2,V_a2_2),V_a1_2))|hAPP(hAPP(V_F_2,V_a2_2),V_a1_2)=hAPP(hAPP(V_F_2,$f17(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a)),V_a1_2).
% 6.65/6.80 0 [] -c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,hAPP(hAPP(V_F_2,V_a2_2),V_a1_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2)|c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,B_z,hAPP($f17(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a),B_z)).
% 6.65/6.80 0 [] c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,hAPP(hAPP(V_F_2,V_a2_2),V_a1_2))|hAPP(hAPP(V_F_2,V_a2_2),V_a1_2)!=hAPP(hAPP(V_F_2,B_g),V_a1_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f18(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a,B_g),V_a1_2),V_R_2).
% 6.65/6.80 0 [] c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,hAPP(hAPP(V_F_2,V_a2_2),V_a1_2))|hAPP(hAPP(V_F_2,V_a2_2),V_a1_2)!=hAPP(hAPP(V_F_2,B_g),V_a1_2)| -c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,$f18(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a,B_g),hAPP(B_g,$f18(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a,B_g))).
% 6.65/6.80 0 [] -c_Relation_Osingle__valued(T_a,T_b,V_r_2)| -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_y_2),V_r_2)| -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_x_2,V_z_2),V_r_2)|V_y_2=V_z_2.
% 6.65/6.80 0 [] -c_Relation_Osingle__valued(T_a,T_b,V_r_2)| -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_y),V_r_2)| -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,B_x,B_z),V_r_2)|B_y=B_z.
% 6.65/6.80 0 [] c_Relation_Osingle__valued(T_a,T_b,V_r_2)|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f21(V_r_2,T_b,T_a),$f20(V_r_2,T_b,T_a)),V_r_2).
% 6.65/6.80 0 [] c_Relation_Osingle__valued(T_a,T_b,V_r_2)|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f21(V_r_2,T_b,T_a),$f19(V_r_2,T_b,T_a)),V_r_2).
% 6.65/6.80 0 [] c_Relation_Osingle__valued(T_a,T_b,V_r_2)|$f20(V_r_2,T_b,T_a)!=$f19(V_r_2,T_b,T_a).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2)|hAPP(c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_a_2),V_x_2)=hAPP(V_f_2,V_x_2).
% 6.65/6.80 0 [] -c_Relation_Orefl__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2))|c_Relation_Orefl__on(T_a,V_A_2,V_r_2).
% 6.65/6.80 0 [] c_Relation_Orefl__on(T_a,V_A_2,c_Relation_Oconverse(T_a,T_a,V_r_2))| -c_Relation_Orefl__on(T_a,V_A_2,V_r_2).
% 6.65/6.80 0 [] c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.80 0 [] c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),B_R)|hAPP(c_Recdef_Ocut(T_a,T_b,B_f,B_R,V_a_2),V_x_2)=hAPP(B_f,V_x_2).
% 6.65/6.80 0 [] c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_x_2)!=c_Recdef_Ocut(T_a,T_b,V_g_2,V_r_2,V_x_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,V_x_2),V_r_2)|hAPP(V_f_2,B_y)=hAPP(V_g_2,B_y).
% 6.65/6.80 0 [] c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_x_2)=c_Recdef_Ocut(T_a,T_b,V_g_2,V_r_2,V_x_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f22(V_g_2,V_x_2,V_r_2,V_f_2,T_b,T_a),V_x_2),V_r_2).
% 6.65/6.80 0 [] c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_x_2)=c_Recdef_Ocut(T_a,T_b,V_g_2,V_r_2,V_x_2)|hAPP(V_f_2,$f22(V_g_2,V_x_2,V_r_2,V_f_2,T_b,T_a))!=hAPP(V_g_2,$f22(V_g_2,V_x_2,V_r_2,V_f_2,T_b,T_a)).
% 6.65/6.80 0 [] -c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,V_a2_2)|V_a2_2=hAPP(hAPP(V_F_2,$f23(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a)),V_a1_2).
% 6.65/6.80 0 [] -c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,V_a2_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_z,V_a1_2),V_R_2)|c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,B_z,hAPP($f23(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a),B_z)).
% 6.65/6.80 0 [] c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,V_a2_2)|V_a2_2!=hAPP(hAPP(V_F_2,B_g),V_a1_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f24(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a,B_g),V_a1_2),V_R_2).
% 6.65/6.80 0 [] c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_a1_2,V_a2_2)|V_a2_2!=hAPP(hAPP(V_F_2,B_g),V_a1_2)| -c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,$f24(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a,B_g),hAPP(B_g,$f24(V_a2_2,V_a1_2,V_F_2,V_R_2,T_b,T_a,B_g))).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f25(V_g_2,V_F_2,T_b,V_R_2,V_x_2,T_a),V_x_2),V_R_2)|c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_x_2,hAPP(hAPP(V_F_2,V_g_2),V_x_2)).
% 6.65/6.80 0 [] -c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,$f25(V_g_2,V_F_2,T_b,V_R_2,V_x_2,T_a),hAPP(V_g_2,$f25(V_g_2,V_F_2,T_b,V_R_2,V_x_2,T_a)))|c_Recdef_Owfrec__rel(T_a,T_b,V_R_2,V_F_2,V_x_2,hAPP(hAPP(V_F_2,V_g_2),V_x_2)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f28(V_r_2,T_b,T_a),$f27(V_r_2,T_b,T_a)),V_r_2)|c_Relation_Osingle__valued(T_a,T_b,V_r_2).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f28(V_r_2,T_b,T_a),$f26(V_r_2,T_b,T_a)),V_r_2)|c_Relation_Osingle__valued(T_a,T_b,V_r_2).
% 6.65/6.80 0 [] $f27(V_r_2,T_b,T_a)!=$f26(V_r_2,T_b,T_a)|c_Relation_Osingle__valued(T_a,T_b,V_r_2).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,V_a_2),V_r_2)|c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f29(V_r_2,V_a_2,T_a),V_a_2),V_r_2).
% 6.65/6.80 0 [] c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))| -c_member(T_a,$f29(V_r_2,V_a_2,T_a),c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)|c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Nitpick_Owf__wfrec_H(T_b,T_a,V_R_2,V_F_2,V_x_2)=hAPP(hAPP(V_F_2,c_Recdef_Ocut(T_b,T_a,c_Nitpick_Owf__wfrec(T_b,T_a,V_R_2,V_F_2),V_R_2,V_x_2)),V_x_2).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),c_Relation_OId(T_a)).
% 6.65/6.80 0 [] c_Product__Type_OPair(T_a,T_b,V_a,V_b)!=c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H)|V_a=V_a_H.
% 6.65/6.80 0 [] c_Product__Type_OPair(T_a,T_b,V_a,V_b)!=c_Product__Type_OPair(T_a,T_b,V_a_H,V_b_H)|V_b=V_b_H.
% 6.65/6.80 0 [] c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)!=c_Product__Type_OPair(T_a,T_b,V_a_H_2,V_b_H_2)|V_a_2=V_a_H_2.
% 6.65/6.80 0 [] c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)!=c_Product__Type_OPair(T_a,T_b,V_a_H_2,V_b_H_2)|V_b_2=V_b_H_2.
% 6.65/6.80 0 [] c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)=c_Product__Type_OPair(T_a,T_b,V_a_H_2,V_b_H_2)|V_a_2!=V_a_H_2|V_b_2!=V_b_H_2.
% 6.65/6.80 0 [] c_Relation_Oconverse(T_a,T_a,c_Relation_OId(T_a))=c_Relation_OId(T_a).
% 6.65/6.80 0 [] c_Relation_Oantisym(T_a,c_Relation_OId(T_a)).
% 6.65/6.80 0 [] c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId(T_a))|V_a_2=V_b_2.
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Relation_OId(T_a))|V_a_2!=V_b_2.
% 6.65/6.80 0 [] -hBOOL(hAPP(V_P_2,$f30(T_b,T_a,V_P_2)))|hBOOL(hAPP(V_P_2,c_Product__Type_OPair(T_a,T_b,B_a,B_b))).
% 6.65/6.80 0 [] hBOOL(hAPP(V_P_2,B_x1))| -hBOOL(hAPP(V_P_2,c_Product__Type_OPair(T_a,T_b,$f32(T_b,T_a,V_P_2),$f31(T_b,T_a,V_P_2)))).
% 6.65/6.80 0 [] c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2))=hAPP(hAPP(V_f1_2,V_a_2),V_b_2).
% 6.65/6.80 0 [] c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_R_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f33(V_R_2,V_x_2,T_a),V_x_2),V_R_2).
% 6.65/6.80 0 [] c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_R_2))| -c_member(T_a,$f33(V_R_2,V_x_2,T_a),c_Wellfounded_Oacc(T_a,V_R_2)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f34(V_r_2,V_x_2,T_a),V_x_2),V_r_2)|c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(T_a,$f34(V_r_2,V_x_2,T_a),c_Wellfounded_Oacc(T_a,V_r_2))|c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),V_p_2,c_Relation_OId(T_a))|V_p_2=c_Product__Type_OPair(T_a,T_a,$f35(V_p_2,T_a),$f35(V_p_2,T_a)).
% 6.65/6.80 0 [] c_Product__Type_Ointernal__split(T_b,T_c,T_a,V_c_2,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2))=hAPP(hAPP(V_c_2,V_a_2),V_b_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))|c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Wellfounded_Oacc(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(T_a,V_b_2,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] -hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2)))|hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_a_2,V_b_2)).
% 6.65/6.80 0 [] -hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_a_2,V_b_2))|hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2))).
% 6.65/6.80 0 [] -hBOOL(c_Product__Type_Ocurry(T_a,T_b,tc_HOL_Obool,V_f_2,V_a_2,V_b_2))|hBOOL(hAPP(V_f_2,c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2))).
% 6.65/6.80 0 [] c_Product__Type_Ocurry(T_b,T_c,T_a,V_f_2,V_a_2,V_b_2)=hAPP(V_f_2,c_Product__Type_OPair(T_b,T_c,V_a_2,V_b_2)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),V_p_2,V_r_2)|c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_member(T_a,V_x_2,c_Relation_ODomain(T_a,T_a,V_R_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))|V_x_2=V_y_2.
% 6.65/6.80 0 [] c_member(T_a,V_x_2,c_Relation_ODomain(T_a,T_a,V_R_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -c_Relation_Osingle__valued(T_a,T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_z_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))=c_Transitive__Closure_Ortrancl(T_a,V_r_2).
% 6.65/6.80 0 [] c_Transitive__Closure_Ortrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))=c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))|c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,$f39(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a),$f38(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a))),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))|hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))|c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f39(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a),$f38(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)),c_Product__Type_OPair(T_a,T_b,$f37(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a),$f36(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a))),V_r_2)|hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))|hBOOL(hAPP(hAPP(V_P_2,$f39(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)),$f38(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)))|hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))| -hBOOL(hAPP(hAPP(V_P_2,$f37(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)),$f36(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)))|hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))|c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f43(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a),$f42(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)),c_Product__Type_OPair(T_a,T_b,$f41(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a),$f40(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a))),V_r_2)|hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))|c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f41(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a),$f40(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))|hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))|hBOOL(hAPP(hAPP(V_P_2,$f41(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)),$f40(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)))|hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_ax_2,V_ay_2),c_Product__Type_OPair(T_a,T_b,V_bx_2,V_by_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))| -hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))| -hBOOL(hAPP(hAPP(V_P_2,$f43(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)),$f42(V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_b,T_a)))|hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))|c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2)=c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)|c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,$f45(V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_b,T_a),$f44(V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_b,T_a))),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2))|c_Product__Type_OPair(T_a,T_b,V_xa_2,V_xb_2)=c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)|c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,$f45(V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_b,T_a),$f44(V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_b,T_a)),c_Product__Type_OPair(T_a,T_b,V_za_2,V_zb_2)),c_Transitive__Closure_Ortrancl(tc_prod(T_a,T_b),V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|V_a_2=V_b_2|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,$f46(V_r_2,V_b_2,V_a_2,T_a)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|V_a_2=V_b_2|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f46(V_r_2,V_b_2,V_a_2,T_a),V_b_2),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|V_x_2=V_z_2|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,$f47(V_r_2,V_z_2,V_x_2,T_a)),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|V_x_2=V_z_2|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f47(V_r_2,V_z_2,V_x_2,T_a),V_z_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_b_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f49(V_P_2,V_r_2,V_b_2,V_a_2,T_a),$f48(V_P_2,V_r_2,V_b_2,V_a_2,T_a)),V_r_2)|hBOOL(hAPP(V_P_2,V_a_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_b_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f48(V_P_2,V_r_2,V_b_2,V_a_2,T_a),V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|hBOOL(hAPP(V_P_2,V_a_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_b_2))|hBOOL(hAPP(V_P_2,$f48(V_P_2,V_r_2,V_b_2,V_a_2,T_a)))|hBOOL(hAPP(V_P_2,V_a_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_b_2))| -hBOOL(hAPP(V_P_2,$f49(V_P_2,V_r_2,V_b_2,V_a_2,T_a)))|hBOOL(hAPP(V_P_2,V_a_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_a_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,$f51(V_P_2,V_r_2,V_b_2,V_a_2,T_a)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|hBOOL(hAPP(V_P_2,V_b_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_a_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f51(V_P_2,V_r_2,V_b_2,V_a_2,T_a),$f50(V_P_2,V_r_2,V_b_2,V_a_2,T_a)),V_r_2)|hBOOL(hAPP(V_P_2,V_b_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_a_2))|hBOOL(hAPP(V_P_2,$f51(V_P_2,V_r_2,V_b_2,V_a_2,T_a)))|hBOOL(hAPP(V_P_2,V_b_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -hBOOL(hAPP(V_P_2,V_a_2))| -hBOOL(hAPP(V_P_2,$f50(V_P_2,V_r_2,V_b_2,V_a_2,T_a)))|hBOOL(hAPP(V_P_2,V_b_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Oacyclic(T_a,V_r_2)|c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Oacyclic(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))|c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] c_Wellfounded_Oacyclic(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))| -c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))|c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Wellfounded_Oacyclic(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))| -c_Wellfounded_Oacyclic(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Oacyclic(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_x,B_x),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Wellfounded_Oacyclic(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f52(V_r_2,T_a),$f52(V_r_2,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,V_A_2)| -c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2))|c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,V_B_2)|c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 6.65/6.80 0 [] V_a_2!=V_b_2|c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))|V_a_2=V_b_2|c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -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)).
% 6.65/6.80 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))|V_y_2!=V_x_2.
% 6.65/6.80 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))| -hBOOL(hAPP(V_A_2,V_x_2)).
% 6.65/6.80 0 [] 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)).
% 6.65/6.80 0 [] 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).
% 6.65/6.80 0 [] c_Relation_ODomain(T_a,T_b,c_Set_Oinsert(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2))=c_Set_Oinsert(T_a,V_a_2,c_Relation_ODomain(T_a,T_b,V_r_2)).
% 6.65/6.80 0 [] c_Relation_ORange(T_b,T_a,c_Set_Oinsert(tc_prod(T_b,T_a),c_Product__Type_OPair(T_b,T_a,V_a_2,V_b_2),V_r_2))=c_Set_Oinsert(T_a,V_b_2,c_Relation_ORange(T_b,T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,V_A_2)|c_Set_Oinsert(T_a,V_a_2,V_A_2)=V_A_2.
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,V_B_2)|c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 6.65/6.80 0 [] c_member(T_a,V_x_2,V_A_2)|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.
% 6.65/6.80 0 [] c_member(T_a,V_x_2,V_A_2)|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.
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))|V_a_2=V_b_2|c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))|V_a_2!=V_b_2.
% 6.65/6.80 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))| -c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),V_p_2,V_r_2)|c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2))=c_Transitive__Closure_Ortrancl(T_a,V_R_2).
% 6.65/6.80 0 [] c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2))=c_Transitive__Closure_Ortrancl(T_a,V_R_2).
% 6.65/6.80 0 [] c_Transitive__Closure_Otrancl(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))=c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Relation_ODomain(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))=c_Relation_ODomain(T_a,T_a,V_r_2).
% 6.65/6.80 0 [] c_Relation_ORange(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))=c_Relation_ORange(T_a,T_a,V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_R_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_R_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))| -c_member(T_a,V_a_2,V_A_2)| -c_member(T_b,V_b_2,hAPP(V_B_2,V_a_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))|V_x_2=V_y_2|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))|V_x_2!=V_y_2.
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))|V_x_2=V_y_2| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))|V_a_2=V_b_2|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_b_2,V_c_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_c_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),V_c_2,c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_a,$f54(V_B_2,V_A_2,V_c_2,T_b,T_a),V_A_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),V_c_2,c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|c_member(T_b,$f53(V_B_2,V_A_2,V_c_2,T_b,T_a),hAPP(V_B_2,$f54(V_B_2,V_A_2,V_c_2,T_b,T_a))).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),V_c_2,c_Product__Type_OSigma(T_a,T_b,V_A_2,V_B_2))|V_c_2=c_Product__Type_OPair(T_a,T_b,$f54(V_B_2,V_A_2,V_c_2,T_b,T_a),$f53(V_B_2,V_A_2,V_c_2,T_b,T_a)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f55(V_r_2,T_a),$f55(V_r_2,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,$f56(V_R_2,V_y_2,V_x_2,T_a)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f56(V_R_2,V_y_2,V_x_2,T_a),V_y_2),V_R_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,$f57(V_R_2,V_y_2,V_x_2,T_a)),V_R_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f57(V_R_2,V_y_2,V_x_2,T_a),V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))|c_Wellfounded_Owf(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,c_Set_Oinsert(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_y_2,V_x_2),V_r_2))| -c_Wellfounded_Owf(T_a,V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,$f58(V_r_2,V_b_2,V_a_2,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_b_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f58(V_r_2,V_b_2,V_a_2,T_a),V_b_2),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,$f59(V_r_2,V_z_2,V_x_2,T_a)),V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_z_2),V_r_2)|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f59(V_r_2,V_z_2,V_x_2,T_a),V_z_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oinv__image(T_a,T_b,V_r_2),V_f_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_ra_2)| -c_Wellfounded_Owf(T_b,V_rb_2)|c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_x_2),V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_x_2),V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_a_2,V_a_2),V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|c_member(T_a,V_x_2,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|c_member(T_a,B_x,c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,V_r_2)| -c_member(T_a,$f60(V_r_2,T_a),c_Wellfounded_Oacc(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2))|c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2))).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,B_R)|hAPP(c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_x)=hAPP(hAPP(B_M,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,B_R,B_M),B_R,B_x)),B_x).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|hAPP(c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_a_2)=hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2),V_r_2,V_a_2)),V_a_2).
% 6.65/6.80 0 [] V_f_2!=c_Recdef_Owfrec(T_a,T_b,V_r_2,V_H_2)| -c_Wellfounded_Owf(T_a,V_r_2)|hAPP(V_f_2,V_a_2)=hAPP(hAPP(V_H_2,c_Recdef_Ocut(T_a,T_b,V_f_2,V_r_2,V_a_2)),V_a_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)| -c_member(T_a,B_x,B_Q)|c_member(T_a,$f61(V_r_2,T_a,B_Q),B_Q).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)| -c_member(T_a,B_x,B_Q)| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,B_y,$f61(V_r_2,T_a,B_Q)),V_r_2)| -c_member(T_a,B_y,B_Q).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,V_r_2)|c_member(T_a,$f62(V_r_2,T_a),$f64(V_r_2,T_a)).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,V_r_2)| -c_member(T_a,X1,$f64(V_r_2,T_a))|c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f63(V_r_2,T_a,X1),X1),V_r_2).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,V_r_2)| -c_member(T_a,X1,$f64(V_r_2,T_a))|c_member(T_a,$f63(V_r_2,T_a,X1),$f64(V_r_2,T_a)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_R_2)|c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)).
% 6.65/6.80 0 [] hBOOL(hAPP(V_P_2,$f65(T_a,V_R_2,T_b,V_P_2)))|c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_b,hAPP(V_R_2,$f65(T_a,V_R_2,T_b,V_P_2)))|c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)).
% 6.65/6.80 0 [] -c_member(T_a,$f66(V_r_2,T_a),c_Wellfounded_Oacc(T_a,V_r_2))|c_Wellfounded_Owf(T_a,V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)).
% 6.65/6.80 0 [] c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,$f67(V_y_2,V_x_2,V_r_2,T_a),$f67(V_y_2,V_x_2,V_r_2,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_r_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] c_Wellfounded_Omeasure(T_a)=c_Relation_Oinv__image(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than).
% 6.65/6.80 0 [] c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_x_2,V_y_2),c_Wellfounded_Oless__than)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 6.65/6.80 0 [] c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_x_2,V_y_2),c_Wellfounded_Oless__than)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))|c_member(tc_prod(T_a,T_a),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)).
% 6.65/6.80 0 [] c_Wellfounded_Oless__than=c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)| -c_Wellfounded_Oacyclic(T_a,V_r_2)|c_Wellfounded_Owf(T_a,c_Relation_Oconverse(T_a,T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_b),V_r_2)|c_Finite__Set_Ofinite(T_b,c_Relation_ORange(T_a,T_b,V_r_2)).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_b),V_r_2)|c_Finite__Set_Ofinite(T_a,c_Relation_ODomain(T_a,T_b,V_r_2)).
% 6.65/6.80 0 [] c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))|c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(tc_prod(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))| -c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Relation_Oconverse(T_b,T_a,V_r_2))|c_Finite__Set_Ofinite(tc_prod(T_b,T_a),V_r_2).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Relation_Oconverse(T_b,T_a,V_r_2))| -c_Finite__Set_Ofinite(tc_prod(T_b,T_a),V_r_2).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)| -c_Wellfounded_Owf(T_a,V_r_2)|c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)|c_Wellfounded_Owf(T_a,V_r_2)| -c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)| -c_Wellfounded_Oacyclic(T_a,V_r_2)|c_Wellfounded_Owf(T_a,V_r_2).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_m_2,V_n_2),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 6.65/6.80 0 [] c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_m_2,V_n_2),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_R_2)|c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 6.65/6.80 0 [] V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 6.65/6.80 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 6.65/6.80 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 6.65/6.80 0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2)).
% 6.65/6.80 0 [] -c_Nitpick_Owf_H(T_a,V_r_2)|c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Nitpick_Owf_H(T_a,V_r_2)|c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2)|c_Nitpick_Ounknown(tc_HOL_Obool).
% 6.65/6.80 0 [] c_Nitpick_Owf_H(T_a,V_r_2)| -c_Wellfounded_Oacyclic(T_a,V_r_2)| -c_Finite__Set_Ofinite(tc_prod(T_a,T_a),V_r_2).
% 6.65/6.80 0 [] c_Nitpick_Owf_H(T_a,V_r_2)| -c_Wellfounded_Oacyclic(T_a,V_r_2)| -c_Nitpick_Ounknown(tc_HOL_Obool).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))|c_Finite__Set_Ofinite(T_a,V_A_2).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))| -c_Finite__Set_Ofinite(T_a,V_A_2).
% 6.65/6.80 0 [] c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)|c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_member(tc_Nat_Onat,B_x,V_N_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_x,$f68(V_N_2)).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)|c_member(tc_Nat_Onat,$f69(V_N_2,B_m),V_N_2).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f69(V_N_2,B_m),B_m).
% 6.65/6.80 0 [] -class_Finite__Set_Ofinite(T_a)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 6.65/6.80 0 [] -class_Finite__Set_Ofinite(T_a)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)|c_member(T_b,V_x_2,V_A_2)|hAPP(V_F_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_F_2,V_A_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__le_q).
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)|hAPP(V_F_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_F_2,V_A_2)).
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)| -c_member(T_b,V_x_2,V_A_2)|hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))=hAPP(V_F_2,V_A_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__less).
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)|hAPP(hAPP(V_f_2,V_x_2),V_x_2)=V_x_2.
% 6.65/6.80 0 [] c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less).
% 6.65/6.80 0 [] c_FunDef_Opair__less=c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_YS_2)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__le_q)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,V_YS_2),c_FunDef_Omax__weak)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_XS_2),V_YS_2),c_FunDef_Omax__weak).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_XS_2)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__le_q)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,V_YS_2),c_FunDef_Omin__weak)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_YS_2)),c_FunDef_Omin__weak).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_Y_2)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__less)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_X_2,V_Y_2),c_FunDef_Omax__strict)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_X_2),V_Y_2),c_FunDef_Omax__strict).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_XS_2)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_x_2,V_y_2),c_FunDef_Opair__less)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,V_YS_2),c_FunDef_Omin__strict)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_XS_2,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_y_2,V_YS_2)),c_FunDef_Omin__strict).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s_2,V_t_2)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__less).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m).
% 6.65/6.80 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|V_m=V_n.
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 6.65/6.80 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_member(tc_Nat_Onat,B_x,V_N_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_x,$f70(V_N_2)).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)|c_member(tc_Nat_Onat,$f71(V_N_2,B_m),V_N_2).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f71(V_N_2,B_m),B_m).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_y_2),V_R_2)|c_member(tc_prod(T_a,T_a),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)).
% 6.65/6.80 0 [] c_FunDef_Omin__strict=c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less).
% 6.65/6.80 0 [] c_FunDef_Omax__strict=c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_m_2,V_n_2),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 6.65/6.80 0 [] c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_m_2,V_n_2),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_s_2,V_t_2)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_a_2,V_s_2),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,V_b_2,V_t_2)),c_FunDef_Opair__le_q).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 6.65/6.80 0 [] c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omin__strict,c_FunDef_Omin__weak)).
% 6.65/6.80 0 [] c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_FunDef_Omax__strict,c_FunDef_Omax__weak)).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(T_a,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(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).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2).
% 6.65/6.80 0 [] -c_member(T_a,V_x_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_member(T_a,V_x_2,V_B_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_s_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_S_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2))|c_Transitive__Closure_Ortrancl(T_a,V_S_2)=c_Transitive__Closure_Ortrancl(T_a,V_R_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_r_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_p_2,V_r_2)|c_Wellfounded_Owf(T_a,V_p_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R1_2,V_R2_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Oacc(T_a,V_R2_2),c_Wellfounded_Oacc(T_a,V_R1_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_r_2),c_Relation_ODomain(T_a,T_b,V_s_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_C_2),c_Set_Oinsert(T_a,V_a_2,V_D_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 6.65/6.80 0 [] -c_Wellfounded_OwfP(T_a,V_r_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),V_p_2,V_r_2)|c_Wellfounded_OwfP(T_a,V_p_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)| -c_Relation_Oantisym(T_a,V_s_2)|c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Wellfounded_Oacyclic(T_a,V_s_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)|c_Wellfounded_Oacyclic(T_a,V_r_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_2,V_s_2)| -c_Relation_Osingle__valued(T_a,T_b,V_s_2)|c_Relation_Osingle__valued(T_a,T_b,V_r_2).
% 6.65/6.80 0 [] c_member(T_a,V_x_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] c_member(T_a,V_x_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)|c_member(T_a,V_x_2,V_B_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)| -c_member(T_a,V_x_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_r_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)|c_member(tc_prod(T_a,T_a),V_p_2,c_Transitive__Closure_Otrancl(T_a,V_s_2)).
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),V_B_2,V_A_2)|hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2))=hAPP(V_F_2,V_A_2).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f72(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f72(V_g_2,V_f_2,T_a,T_b))).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|V_x_2=V_y_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|V_x=V_y.
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|V_x=V_y.
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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))|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] -c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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))|c_Finite__Set_Ofinite(T_a,V_B_2).
% 6.65/6.80 0 [] c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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))| -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).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 6.65/6.80 0 [] -c_FunDef_Oreduction__pair(T_a,V_P_2)|c_FunDef_Oreduction__pair(T_b,c_FunDef_Orp__inv__image(T_a,T_b,V_P_2,V_f_2)).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_R_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)|c_FunDef_Oreduction__pair(T_a,c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)).
% 6.65/6.80 0 [] V_X_2=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_X_2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__strict).
% 6.65/6.80 0 [] c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),V_X_2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_FunDef_Omin__weak).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|V_A_2=V_B_2.
% 6.65/6.80 0 [] -c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.80 0 [] -c_member(tc_prod(T_a,T_b),c_Product__Type_OPair(T_a,T_b,V_a_2,V_b_2),V_r_2)| -c_member(tc_prod(T_b,T_c),c_Product__Type_OPair(T_b,T_c,V_b_2,V_c_2),V_s_2)|c_member(tc_prod(T_a,T_c),c_Product__Type_OPair(T_a,T_c,V_a_2,V_c_2),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)).
% 6.65/6.80 0 [] V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 6.65/6.80 0 [] V_A_2=V_B_2| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 6.65/6.80 0 [] -hBOOL(hAPP(V_P_2,V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)|hBOOL(hAPP(V_Q_2,V_x_2)).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)| -hBOOL(hAPP(V_P_2,V_x_2))|hBOOL(hAPP(V_Q_2,V_x_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_r_H_2,V_r_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_s_H_2,V_s_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_H_2,V_s_H_2),c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_P_2,V_Q_2)| -hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))|hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 6.65/6.80 0 [] -hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_P_2,V_Q_2)|hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2=c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 6.65/6.80 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2=V_B_2.
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2!=V_B_2.
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2!=V_B_2.
% 6.65/6.80 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2=V_B_2.
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.80 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 6.65/6.80 0 [] -class_Orderings_Obot(T_a)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2)=c_Orderings_Obot__class_Obot(T_a).
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2))=c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2).
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))=c_Transitive__Closure_Ortrancl(T_a,V_R_2).
% 6.65/6.80 0 [] c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_b,T_b,V_R_2,c_Relation_OId(T_b))=V_R_2.
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_a,T_b,c_Relation_OId(T_a),V_R_2)=V_R_2.
% 6.65/6.80 0 [] c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.80 0 [] c_Product__Type_OSigma(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_ODomain(T_a,T_b,V_r_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_r_2=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_ODomain(T_a,T_b,V_r_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_r_2!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_ODomain(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_ORange(T_b,T_a,V_r_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_r_2=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_ORange(T_b,T_a,V_r_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_r_2!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_ORange(T_b,T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_c,T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_R_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_c,T_b,c_Relation_Orel__comp(T_a,T_d,T_c,V_R_2,V_S_2),V_T_2)=c_Relation_Orel__comp(T_a,T_d,T_b,V_R_2,c_Relation_Orel__comp(T_d,T_c,T_b,V_S_2,V_T_2)).
% 6.65/6.80 0 [] c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Relation_Oconverse(T_b,T_a,c_Relation_Orel__comp(T_b,T_c,T_a,V_r_2,V_s_2))=c_Relation_Orel__comp(T_a,T_c,T_b,c_Relation_Oconverse(T_c,T_a,V_s_2),c_Relation_Oconverse(T_b,T_c,V_r_2)).
% 6.65/6.80 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_Oinsert(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2=V_c_2|V_a_2=V_d_2.
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2=V_c_2|V_b_2=V_c_2.
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_d_2|V_a_2=V_d_2.
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_d_2|V_b_2=V_c_2.
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2!=V_c_2|V_b_2!=V_d_2.
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2!=V_d_2|V_b_2!=V_c_2.
% 6.65/6.80 0 [] c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))!=c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_a_2=V_b_2.
% 6.65/6.80 0 [] c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))|c_Wellfounded_Owf(T_a,V_R_2).
% 6.65/6.80 0 [] -c_Wellfounded_Owf(T_a,V_R_2)|c_Wellfounded_Owf(T_a,c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2)).
% 6.65/6.80 0 [] c_Wellfounded_Owf(T_a,V_R_2)| -c_Wellfounded_Owf(T_a,c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2)).
% 6.65/6.80 0 [] V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_member(T_a,V_a_2,V_A_2).
% 6.65/6.80 0 [] -c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 6.65/6.80 0 [] -c_member(T_a,B_x,V_A_2)|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] c_member(T_a,$f73(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] c_member(T_a,$f74(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] -c_member(T_a,B_x,V_A_2)|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.80 0 [] -c_Relation_Osingle__valued(T_a,T_b,V_r_2)| -c_Relation_Osingle__valued(T_b,T_c,V_s_2)|c_Relation_Osingle__valued(T_a,T_c,c_Relation_Orel__comp(T_a,T_b,T_c,V_r_2,V_s_2)).
% 6.65/6.80 0 [] c_Relation_Oantisym(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))).
% 6.65/6.80 0 [] c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2).
% 6.65/6.80 0 [] -class_Orderings_Obot(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Orderings_Obot__class_Obot(T_a),V_x).
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)|hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=V_z_2.
% 6.65/6.80 0 [] -c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_a_2.
% 6.65/6.80 0 [] c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2!=V_a_2.
% 6.65/6.80 0 [] -c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_a_2.
% 6.65/6.80 0 [] c_Transitive__Closure_Otrancl(T_a,V_r_2)=c_Relation_Orel__comp(T_a,T_a,T_a,V_r_2,c_Transitive__Closure_Ortrancl(T_a,V_r_2)).
% 6.65/6.80 0 [] c_Transitive__Closure_Otrancl(T_a,V_r_2)=c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2).
% 6.65/6.80 0 [] c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))=c_Relation_OId(T_a).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_Y_2)|V_Y_2=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_Y_2),c_FunDef_Omax__strict).
% 6.65/6.80 0 [] -c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat),V_X_2)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_FunDef_Omax__weak).
% 6.65/6.80 0 [] -c_Relation_Orefl__on(T_a,V_A_2,V_r_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_Orel__comp(T_a,T_a,T_a,c_Relation_Oconverse(T_a,T_a,V_r_2),V_r_2)).
% 6.65/6.80 0 [] c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_x_2.
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)| -c_Finite__Set_Ofinite(T_a,V_A_2)|c_member(T_a,V_x_2,V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|hAPP(V_F_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)).
% 6.65/6.80 0 [] -c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)|hAPP(V_F_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_x_2.
% 6.65/6.80 0 [] c_FunDef_Omin__weak=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__le_q),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))).
% 6.65/6.81 0 [] c_FunDef_Omax__weak=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__le_q),c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))).
% 6.65/6.81 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))|hBOOL(hAPP(V_A_2,V_x_2))|hBOOL(hAPP(V_B_2,V_x_2)).
% 6.65/6.81 0 [] -hBOOL(hAPP(V_B_2,V_x_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)).
% 6.65/6.81 0 [] -hBOOL(hAPP(V_A_2,V_x_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)).
% 6.65/6.81 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 6.65/6.81 0 [] -c_member(T_a,V_c_2,V_B_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=V_B_2.
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=V_A_2.
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_B_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_B_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 6.65/6.81 0 [] -c_Finite__Set_Ofinite(T_a,V_F_2)| -c_Finite__Set_Ofinite(T_a,V_G_2)|c_Finite__Set_Ofinite(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_F_2,V_G_2)).
% 6.65/6.81 0 [] -c_Finite__Set_Ofinite(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_F_2,V_G_2))|c_Finite__Set_Ofinite(T_a,V_F_2).
% 6.65/6.81 0 [] -c_Finite__Set_Ofinite(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_F_2,V_G_2))|c_Finite__Set_Ofinite(T_a,V_G_2).
% 6.65/6.81 0 [] c_Finite__Set_Ofinite(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_F_2,V_G_2))| -c_Finite__Set_Ofinite(T_a,V_F_2)| -c_Finite__Set_Ofinite(T_a,V_G_2).
% 6.65/6.81 0 [] c_Set_Oinsert(T_a,V_a_2,V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2).
% 6.65/6.81 0 [] -c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_R_2))|c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))).
% 6.65/6.81 0 [] -c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,V_S_2))|c_member(tc_prod(T_a,T_a),V_x_2,c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))).
% 6.65/6.81 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)),c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))).
% 6.65/6.81 0 [] -c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))|c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2),c_Relation_Orel__comp(T_a,T_a,T_a,V_S_2,V_R_2)),V_S_2)).
% 6.65/6.81 0 [] c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2))| -c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_R_2),c_Relation_Orel__comp(T_a,T_a,T_a,V_S_2,V_R_2)),V_S_2)).
% 6.65/6.81 0 [] c_Transitive__Closure_Otrancl(T_a,V_r_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2),V_r_2)).
% 6.65/6.81 0 [] c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,V_C_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))|c_Relation_Orel__comp(T_a,T_a,T_a,V_B_2,V_C_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))|c_Relation_Orel__comp(T_a,T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)).
% 6.65/6.81 0 [] c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))|c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,V_C_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))|c_Relation_Orel__comp(T_a,T_a,T_a,V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_B_2,V_C_2))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Relation_OId(T_a))=c_Transitive__Closure_Ortrancl(T_a,V_R_2).
% 6.65/6.81 0 [] c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,c_Relation_OId(T_a)))=c_Transitive__Closure_Ortrancl(T_a,V_R_2).
% 6.65/6.81 0 [] -c_Relation_Oantisym(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))|c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.81 0 [] c_Relation_Oantisym(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))| -c_Relation_Oantisym(T_a,V_r_2).
% 6.65/6.81 0 [] c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(T_a,V_R_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2)))=c_Transitive__Closure_Ortrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)).
% 6.65/6.81 0 [] c_Relation_Oconverse(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_r_2,V_s_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Oconverse(T_b,T_a,V_r_2),c_Relation_Oconverse(T_b,T_a,V_s_2)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2.
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 6.65/6.81 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_P_2,B_x))|c_member(T_a,$f75(V_P_2,V_B_2,V_A_2,T_a),V_A_2)|c_member(T_a,$f76(V_P_2,V_B_2,V_A_2,T_a),V_B_2).
% 6.65/6.81 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_P_2,B_x))|c_member(T_a,$f75(V_P_2,V_B_2,V_A_2,T_a),V_A_2)|hBOOL(hAPP(V_P_2,$f76(V_P_2,V_B_2,V_A_2,T_a))).
% 6.65/6.81 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,$f75(V_P_2,V_B_2,V_A_2,T_a)))|c_member(T_a,$f76(V_P_2,V_B_2,V_A_2,T_a),V_B_2).
% 6.65/6.81 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,$f75(V_P_2,V_B_2,V_A_2,T_a)))|hBOOL(hAPP(V_P_2,$f76(V_P_2,V_B_2,V_A_2,T_a))).
% 6.65/6.81 0 [] c_member(T_a,$f77(V_P_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X2,V_A_2)| -hBOOL(hAPP(V_P_2,X2)).
% 6.65/6.81 0 [] c_member(T_a,$f77(V_P_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X3,V_B_2)| -hBOOL(hAPP(V_P_2,X3)).
% 6.65/6.81 0 [] hBOOL(hAPP(V_P_2,$f77(V_P_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X2,V_A_2)| -hBOOL(hAPP(V_P_2,X2)).
% 6.65/6.81 0 [] hBOOL(hAPP(V_P_2,$f77(V_P_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X3,V_B_2)| -hBOOL(hAPP(V_P_2,X3)).
% 6.65/6.81 0 [] c_member(T_a,$f78(V_P_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,B_x,V_A_2)|hBOOL(hAPP(V_P_2,B_x)).
% 6.65/6.81 0 [] c_member(T_a,$f78(V_P_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X4,V_B_2)|hBOOL(hAPP(V_P_2,X4)).
% 6.65/6.81 0 [] -hBOOL(hAPP(V_P_2,$f78(V_P_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,B_x,V_A_2)|hBOOL(hAPP(V_P_2,B_x)).
% 6.65/6.81 0 [] -hBOOL(hAPP(V_P_2,$f78(V_P_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X4,V_B_2)|hBOOL(hAPP(V_P_2,X4)).
% 6.65/6.81 0 [] -c_member(T_a,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_P_2,X5))|c_member(T_a,$f79(V_P_2,V_B_2,V_A_2,T_a),V_A_2)|c_member(T_a,$f80(V_P_2,V_B_2,V_A_2,T_a),V_B_2).
% 6.65/6.81 0 [] -c_member(T_a,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_P_2,X5))|c_member(T_a,$f79(V_P_2,V_B_2,V_A_2,T_a),V_A_2)| -hBOOL(hAPP(V_P_2,$f80(V_P_2,V_B_2,V_A_2,T_a))).
% 6.65/6.81 0 [] -c_member(T_a,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_P_2,X5))| -hBOOL(hAPP(V_P_2,$f79(V_P_2,V_B_2,V_A_2,T_a)))|c_member(T_a,$f80(V_P_2,V_B_2,V_A_2,T_a),V_B_2).
% 6.65/6.81 0 [] -c_member(T_a,X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_P_2,X5))| -hBOOL(hAPP(V_P_2,$f79(V_P_2,V_B_2,V_A_2,T_a)))| -hBOOL(hAPP(V_P_2,$f80(V_P_2,V_B_2,V_A_2,T_a))).
% 6.65/6.81 0 [] -hBOOL(hAPP(V_A_2,V_x_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)).
% 6.65/6.81 0 [] -hBOOL(hAPP(V_B_2,V_x_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)).
% 6.65/6.81 0 [] c_Relation_ORange(T_b,T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ORange(T_b,T_a,V_A_2),c_Relation_ORange(T_b,T_a,V_B_2)).
% 6.65/6.81 0 [] c_Relation_ODomain(T_a,T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Relation_ODomain(T_a,T_b,V_A_2),c_Relation_ODomain(T_a,T_b,V_B_2)).
% 6.65/6.81 0 [] -c_Relation_Orefl__on(T_a,V_A_2,V_r_2)| -c_Relation_Orefl__on(T_a,V_B_2,V_s_2)|c_Relation_Orefl__on(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,V_s_2)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 6.65/6.81 0 [] -c_member(T_a,V_c_2,V_B_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 6.65/6.81 0 [] c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_A_2).
% 6.65/6.81 0 [] c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_B_2).
% 6.65/6.81 0 [] c_Relation_Orel__comp(T_a,T_c,T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),V_S_2,V_T_2),V_R_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_c,T_b,V_S_2,V_R_2),c_Relation_Orel__comp(T_a,T_c,T_b,V_T_2,V_R_2)).
% 6.65/6.81 0 [] c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2,V_T_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,V_S_2),c_Relation_Orel__comp(T_a,T_c,T_b,V_R_2,V_T_2)).
% 6.65/6.81 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)).
% 6.65/6.81 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2).
% 6.65/6.81 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2.
% 6.65/6.81 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2.
% 6.65/6.81 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2.
% 6.65/6.81 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=V_B_2.
% 6.65/6.81 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|hAPP(V_F_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool),V_A_2,V_B_2))=hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)).
% 6.65/6.81 0 [] -c_Wellfounded_Owf(T_a,V_R_2)| -c_Wellfounded_Owf(T_a,V_S_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)|c_Wellfounded_Owf(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2,V_S_2)).
% 6.65/6.81 0 [] c_Transitive__Closure_Otrancl(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_r_2,c_Relation_OId(T_a)))=c_Transitive__Closure_Ortrancl(T_a,V_r_2).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Transitive__Closure_Otrancl(T_a,V_r_2),c_Relation_OId(T_a))=c_Transitive__Closure_Ortrancl(T_a,V_r_2).
% 6.65/6.81 0 [] c_Transitive__Closure_Ortrancl(T_a,V_r_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_OId(T_a),c_Relation_Orel__comp(T_a,T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2),V_r_2)).
% 6.65/6.81 0 [] -c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Wellfounded_Omax__ext(T_a,V_R_2))| -c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2),c_Wellfounded_Omax__ext(T_a,V_R_2))|c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)).
% 6.65/6.81 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_R_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_S_2),c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool))))),c_Wellfounded_Omax__ext(T_a,V_R_2)).
% 6.65/6.81 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Orel__comp(T_a,T_a,T_a,V_R_2,V_S_2),V_R_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_R_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_S_2),c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool))))),c_Wellfounded_Omin__ext(T_a,V_R_2)).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_a)|hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_x_2)=c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 6.65/6.81 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)!=c_Orderings_Obot__class_Obot(T_a)|V_x_2=c_Orderings_Obot__class_Obot(T_a).
% 6.65/6.81 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)!=c_Orderings_Obot__class_Obot(T_a)|V_y_2=c_Orderings_Obot__class_Obot(T_a).
% 6.65/6.81 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)=c_Orderings_Obot__class_Obot(T_a)|V_x_2!=c_Orderings_Obot__class_Obot(T_a)|V_y_2!=c_Orderings_Obot__class_Obot(T_a).
% 6.65/6.81 0 [] c_FunDef_Opair__le_q=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool),c_FunDef_Opair__less,c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a)=V_a.
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x)=V_x.
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_a).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_c))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_c)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_c,V_d)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_x.
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_y.
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2),V_z_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_z_2).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2),V_z_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_z_2).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_z_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_z_2).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)=V_y_2.
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x_2,V_y_2)!=V_y_2.
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)|c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 6.65/6.81 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_b)|c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 6.65/6.81 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)=V_x.
% 6.65/6.81 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Obot__class_Obot(T_a))=V_x.
% 6.65/6.81 0 [] -c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)| -c_Finite__Set_Ofinite(T_a,V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_member(T_a,hAPP(hAPP(V_f_2,$f82(V_A_2,V_F_2,V_f_2,T_a)),$f81(V_A_2,V_F_2,V_f_2,T_a)),c_Set_Oinsert(T_a,$f82(V_A_2,V_F_2,V_f_2,T_a),c_Set_Oinsert(T_a,$f81(V_A_2,V_F_2,V_f_2,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))|c_member(T_a,hAPP(V_F_2,V_A_2),V_A_2).
% 6.65/6.81 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),c_Relation_Oconverse(T_a,T_a,V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))| -c_member(tc_prod(T_a,T_a),c_Product__Type_OPair(T_a,T_a,V_x_2,V_x_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)).
% 6.65/6.81 0 [] -hBOOL(hAPP(V_A_2,V_x_2))| -hBOOL(hAPP(V_B_2,V_x_2))|hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2)).
% 6.65/6.81 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))|hBOOL(hAPP(V_A_2,V_x_2)).
% 6.65/6.81 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_x_2))|hBOOL(hAPP(V_B_2,V_x_2)).
% 6.65/6.81 0 [] -c_member(T_a,V_c_2,V_A_2)| -c_member(T_a,V_c_2,V_B_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 6.65/6.81 0 [] class_Lattices_Obounded__lattice(tc_HOL_Obool).
% 6.65/6.81 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Finite__Set_Ofinite(T_2)| -class_Finite__Set_Ofinite(T_1)|class_Finite__Set_Ofinite(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Olattice(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] -class_Orderings_Obot(T_1)|class_Orderings_Obot(tc_fun(T_2,T_1)).
% 6.65/6.81 0 [] class_Lattices_Osemilattice__sup(tc_Nat_Onat).
% 6.65/6.81 0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 6.65/6.81 0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 6.65/6.81 0 [] class_Lattices_Olattice(tc_Nat_Onat).
% 6.65/6.81 0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 6.65/6.81 0 [] class_Orderings_Oord(tc_Nat_Onat).
% 6.65/6.81 0 [] class_Orderings_Obot(tc_Nat_Onat).
% 6.65/6.81 0 [] class_Lattices_Obounded__lattice__bot(tc_HOL_Obool).
% 6.65/6.81 0 [] class_Lattices_Osemilattice__sup(tc_HOL_Obool).
% 6.65/6.81 0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 6.65/6.81 0 [] class_Finite__Set_Ofinite(tc_HOL_Obool).
% 6.65/6.81 0 [] class_Lattices_Olattice(tc_HOL_Obool).
% 6.65/6.81 0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 6.65/6.81 0 [] class_Orderings_Oord(tc_HOL_Obool).
% 6.65/6.81 0 [] class_Orderings_Obot(tc_HOL_Obool).
% 6.65/6.81 0 [] -class_Finite__Set_Ofinite(T_2)| -class_Finite__Set_Ofinite(T_1)|class_Finite__Set_Ofinite(tc_prod(T_2,T_1)).
% 6.65/6.81 0 [] -hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2.
% 6.65/6.81 0 [] V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2)).
% 6.65/6.81 0 [] c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),c_Arrow__Order__Mirabelle_OLin)|c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),v_L,c_Arrow__Order__Mirabelle_OLin).
% 6.65/6.81 0 [] -c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),c_Arrow__Order__Mirabelle_OLin)| -c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),v_L,c_Arrow__Order__Mirabelle_OLin).
% 6.65/6.81 end_of_list.
% 6.65/6.81
% 6.65/6.81 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 6.65/6.81
% 6.65/6.81 This ia a non-Horn set with equality. The strategy will be
% 6.65/6.81 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 6.65/6.81 deletion, with positive clauses in sos and nonpositive
% 6.65/6.81 clauses in usable.
% 6.65/6.81
% 6.65/6.81 dependent: set(knuth_bendix).
% 6.65/6.81 dependent: set(anl_eq).
% 6.65/6.81 dependent: set(para_from).
% 6.65/6.81 dependent: set(para_into).
% 6.65/6.81 dependent: clear(para_from_right).
% 6.65/6.81 dependent: clear(para_into_right).
% 6.65/6.81 dependent: set(para_from_vars).
% 6.65/6.81 dependent: set(eq_units_both_ways).
% 6.65/6.81 dependent: set(dynamic_demod_all).
% 6.65/6.81 dependent: set(dynamic_demod).
% 6.65/6.81 dependent: set(order_eq).
% 6.65/6.81 dependent: set(back_demod).
% 6.65/6.81 dependent: set(lrpo).
% 6.65/6.81 dependent: set(hyper_res).
% 6.65/6.81 dependent: set(unit_deletion).
% 6.65/6.81 dependent: set(factor).
% 6.65/6.81
% 6.65/6.81 ------------> process usable:
% 6.65/6.81 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 6.65/6.81 ** KEPT (pick-wt=11): 2 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 6.65/6.81 ** KEPT (pick-wt=11): 3 [] A!=B|c_member(C,D,B)| -c_member(C,D,A).
% 6.65/6.81 ** KEPT (pick-wt=8): 4 [] -c_member(A,B,C)|hBOOL(hAPP(C,B)).
% 6.65/6.81 ** KEPT (pick-wt=8): 5 [] c_member(A,B,C)| -hBOOL(hAPP(C,B)).
% 6.65/6.81 ** KEPT (pick-wt=8): 6 [] -c_member(A,B,c_fe_qual(C))|B=C.
% 6.65/6.81 ** KEPT (pick-wt=8): 7 [] c_member(A,B,c_fe_qual(C))|B!=C.
% 6.65/6.81 Following clause subsumed by 3 during input processing: 0 [] A!=B| -c_member(C,D,A)|c_member(C,D,B).
% 6.65/6.81 Following clause subsumed by 2 during input processing: 0 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 6.65/6.81 ** KEPT (pick-wt=11): 8 [] A!=B| -c_member(C,A,D)|c_member(C,B,D).
% 6.65/6.81 ** KEPT (pick-wt=11): 9 [] A!=B|c_member(C,A,D)| -c_member(C,B,D).
% 6.65/6.81 Following clause subsumed by 9 during input processing: 0 [] A!=B| -c_member(C,B,D)|c_member(C,A,D).
% 6.65/6.81 ** KEPT (pick-wt=31): 10 [] -c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),A,c_Arrow__Order__Mirabelle_OLin)|B=C|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),A)|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,B),A).
% 6.65/6.81 ** KEPT (pick-wt=31): 11 [] -c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),A,c_Arrow__Order__Mirabelle_OLin)|B=C| -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,B,C),A)| -c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,C,B),A).
% 6.65/6.81 ** KEPT (pick-wt=11): 12 [] -c_Relation_Ototal__on(A,B,c_Relation_Oconverse(A,A,C))|c_Relation_Ototal__on(A,B,C).
% 6.65/6.81 ** KEPT (pick-wt=11): 13 [] c_Relation_Ototal__on(A,B,c_Relation_Oconverse(A,A,C))| -c_Relation_Ototal__on(A,B,C).
% 6.65/6.81 ** KEPT (pick-wt=9): 14 [] -c_Relation_Oantisym(A,c_Relation_Oconverse(A,A,B))|c_Relation_Oantisym(A,B).
% 6.65/6.81 ** KEPT (pick-wt=9): 15 [] c_Relation_Oantisym(A,c_Relation_Oconverse(A,A,B))| -c_Relation_Oantisym(A,B).
% 6.65/6.81 ** KEPT (pick-wt=15): 16 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))|hBOOL(hAPP(hAPP(D,E),B)).
% 6.65/6.81 ** KEPT (pick-wt=15): 17 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))|hBOOL(hAPP(hAPP(C,B),F)).
% 6.65/6.81 ** KEPT (pick-wt=21): 18 [] c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))| -hBOOL(hAPP(hAPP(D,E),B))| -hBOOL(hAPP(hAPP(C,B),F)).
% 6.65/6.81 ** KEPT (pick-wt=15): 19 [] -c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))|hBOOL(hAPP(hAPP(C,E),B)).
% 6.65/6.81 ** KEPT (pick-wt=15): 20 [] -c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))|hBOOL(hAPP(hAPP(D,B),F)).
% 6.65/6.81 ** KEPT (pick-wt=21): 21 [] c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))| -hBOOL(hAPP(hAPP(C,E),B))| -hBOOL(hAPP(hAPP(D,B),F)).
% 6.65/6.81 ** KEPT (pick-wt=14): 22 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))|hBOOL(hAPP(hAPP(C,D),B)).
% 6.65/6.81 ** KEPT (pick-wt=14): 23 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))|hBOOL(hAPP(hAPP(C,B),E)).
% 6.65/6.81 ** KEPT (pick-wt=20): 24 [] c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))| -hBOOL(hAPP(hAPP(C,D),B))| -hBOOL(hAPP(hAPP(C,B),E)).
% 6.65/6.81 ** KEPT (pick-wt=14): 25 [] -c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))|hBOOL(hAPP(hAPP(C,D),B)).
% 6.65/6.81 ** KEPT (pick-wt=14): 26 [] -c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))|hBOOL(hAPP(hAPP(C,B),E)).
% 6.65/6.81 ** KEPT (pick-wt=20): 27 [] c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))| -hBOOL(hAPP(hAPP(C,D),B))| -hBOOL(hAPP(hAPP(C,B),E)).
% 6.65/6.81 ** KEPT (pick-wt=13): 28 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThan(A,C,D))|hBOOL(hAPP(hAPP(C,D),B)).
% 6.65/6.81 ** KEPT (pick-wt=13): 29 [] c_member(A,B,c_SetInterval_Oord_OgreaterThan(A,C,D))| -hBOOL(hAPP(hAPP(C,D),B)).
% 6.65/6.81 ** KEPT (pick-wt=13): 30 [] -c_member(A,B,c_SetInterval_Oord_OlessThan(A,C,D))|hBOOL(hAPP(hAPP(C,B),D)).
% 6.65/6.81 ** KEPT (pick-wt=13): 31 [] c_member(A,B,c_SetInterval_Oord_OlessThan(A,C,D))| -hBOOL(hAPP(hAPP(C,B),D)).
% 6.65/6.81 ** KEPT (pick-wt=29): 32 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),hAPP(c_Relation_Oinv__image(D,A,E),F))|c_member(tc_prod(D,D),c_Product__Type_OPair(D,D,hAPP(F,B),hAPP(F,C)),E).
% 6.65/6.81 ** KEPT (pick-wt=29): 33 [] c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),hAPP(c_Relation_Oinv__image(D,A,E),F))| -c_member(tc_prod(D,D),c_Product__Type_OPair(D,D,hAPP(F,B),hAPP(F,C)),E).
% 6.65/6.81 ** KEPT (pick-wt=26): 34 [] -c_Relation_Oantisym(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,D),B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,C),B)|C=D.
% 6.65/6.81 ** KEPT (pick-wt=10): 35 [] c_Relation_Oantisym(A,B)|$f3(B,A)!=$f2(B,A).
% 6.65/6.81 Following clause subsumed by 34 during input processing: 0 [] -c_Relation_Oantisym(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,D),B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,C),B)|C=D.
% 6.65/6.81 ** KEPT (pick-wt=35): 36 [] -c_Relation_Ototal__on(A,B,C)| -c_member(A,D,B)| -c_member(A,E,B)|D=E|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,E),C)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,E,D),C).
% 6.65/6.81 ** KEPT (pick-wt=13): 37 [] c_Relation_Ototal__on(A,B,C)|$f5(C,B,A)!=$f4(C,B,A).
% 6.65/6.81 ** KEPT (pick-wt=20): 38 [] c_Relation_Ototal__on(A,B,C)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f5(C,B,A),$f4(C,B,A)),C).
% 6.65/6.81 ** KEPT (pick-wt=20): 39 [] c_Relation_Ototal__on(A,B,C)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f4(C,B,A),$f5(C,B,A)),C).
% 6.65/6.81 ** KEPT (pick-wt=19): 40 [] A!=B| -c_member(C,A,D)|c_member(tc_prod(C,C),c_Product__Type_OPair(C,C,A,B),c_Relation_OId__on(C,D)).
% 6.65/6.81 ** KEPT (pick-wt=15): 41 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Relation_OId__on(A,D))|B=C.
% 6.65/6.81 ** KEPT (pick-wt=16): 42 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Relation_OId__on(A,D))|c_member(A,B,D).
% 6.65/6.81 Following clause subsumed by 40 during input processing: 0 [] c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Relation_OId__on(A,D))|B!=C| -c_member(A,B,D).
% 6.65/6.81 ** KEPT (pick-wt=23): 43 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Relation_Oconverse(B,A,E))|c_member(tc_prod(B,A),c_Product__Type_OPair(B,A,D,C),E).
% 6.65/6.81 ** KEPT (pick-wt=23): 44 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),E)|c_member(tc_prod(B,A),c_Product__Type_OPair(B,A,D,C),c_Relation_Oconverse(A,B,E)).
% 6.65/6.81 Following clause subsumed by 43 during input processing: 0 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Relation_Oconverse(B,A,E))|c_member(tc_prod(B,A),c_Product__Type_OPair(B,A,D,C),E).
% 6.65/6.81 Following clause subsumed by 44 during input processing: 0 [] c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Relation_Oconverse(B,A,E))| -c_member(tc_prod(B,A),c_Product__Type_OPair(B,A,D,C),E).
% 6.65/6.81 ** KEPT (pick-wt=13): 45 [] -c_member(A,B,c_SetInterval_Oord_OatMost(A,C,D))|hBOOL(hAPP(hAPP(C,B),D)).
% 6.65/6.81 ** KEPT (pick-wt=13): 46 [] c_member(A,B,c_SetInterval_Oord_OatMost(A,C,D))| -hBOOL(hAPP(hAPP(C,B),D)).
% 6.65/6.81 ** KEPT (pick-wt=13): 47 [] -c_member(A,B,c_SetInterval_Oord_OatLeast(A,C,D))|hBOOL(hAPP(hAPP(C,D),B)).
% 6.65/6.81 ** KEPT (pick-wt=13): 48 [] c_member(A,B,c_SetInterval_Oord_OatLeast(A,C,D))| -hBOOL(hAPP(hAPP(C,D),B)).
% 6.65/6.81 ** KEPT (pick-wt=13): 49 [] -c_Relation_Oirrefl(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,C),B).
% 6.65/6.81 ** KEPT (pick-wt=15): 50 [] -c_member(tc_prod(A,A),B,c_Relation_OId__on(A,C))|c_member(A,$f7(C,B,A),C).
% 6.65/6.81 ** KEPT (pick-wt=21): 52 [copy,51,flip.2] -c_member(tc_prod(A,A),B,c_Relation_OId__on(A,C))|c_Product__Type_OPair(A,A,$f7(C,B,A),$f7(C,B,A))=B.
% 6.65/6.81 ** KEPT (pick-wt=19): 53 [] -hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(A,B,C),D),E))|c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,D,E),C).
% 6.65/6.81 ** KEPT (pick-wt=19): 54 [] hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(A,B,C),D),E))| -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,D,E),C).
% 6.65/6.81 ** KEPT (pick-wt=24): 56 [copy,55,flip.2] -c_member(tc_prod(A,B),C,c_Relation_Oconverse(B,A,D))|c_Product__Type_OPair(A,B,$f8(D,C,B,A),$f9(D,C,B,A))=C.
% 6.65/6.82 ** KEPT (pick-wt=27): 57 [] -c_member(tc_prod(A,B),C,c_Relation_Oconverse(B,A,D))|c_member(tc_prod(B,A),c_Product__Type_OPair(B,A,$f9(D,C,B,A),$f8(D,C,B,A)),D).
% 6.65/6.82 ** KEPT (pick-wt=46): 58 [] -hBOOL(hAPP(A,B))| -c_member(tc_prod(C,C),c_Product__Type_OPair(C,C,D,E),hAPP(F,B))|c_member(tc_prod(tc_prod(G,C),tc_prod(G,C)),c_Product__Type_OPair(tc_prod(G,C),tc_prod(G,C),c_Product__Type_OPair(G,C,B,D),c_Product__Type_OPair(G,C,B,E)),c_Recdef_Osame__fst(G,C,A,F)).
% 6.65/6.82 ** KEPT (pick-wt=17): 59 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),E)|c_member(B,D,c_Relation_ORange(A,B,E)).
% 6.65/6.82 ** KEPT (pick-wt=17): 60 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),E)|c_member(A,C,c_Relation_ODomain(A,B,E)).
% 6.65/6.82 ** KEPT (pick-wt=13): 61 [] -c_Nitpick_Orefl_H(A,B)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,C),B).
% 6.65/6.82 ** KEPT (pick-wt=17): 62 [] c_Nitpick_Orefl_H(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f10(B,A),$f10(B,A)),B).
% 6.65/6.82 ** KEPT (pick-wt=10): 63 [] $f12(A,B)!=$f11(A,B)|c_Relation_Oantisym(B,A).
% 6.65/6.82 ** KEPT (pick-wt=21): 64 [] -c_member(A,B,c_Relation_ODomain(A,C,D))|c_member(tc_prod(A,C),c_Product__Type_OPair(A,C,B,$f13(D,C,B,A)),D).
% 6.65/6.82 Following clause subsumed by 60 during input processing: 0 [] c_member(A,B,c_Relation_ODomain(A,C,D))| -c_member(tc_prod(A,C),c_Product__Type_OPair(A,C,B,E),D).
% 6.65/6.82 ** KEPT (pick-wt=21): 65 [] -c_member(A,B,c_Relation_ORange(C,A,D))|c_member(tc_prod(C,A),c_Product__Type_OPair(C,A,$f14(D,C,B,A),B),D).
% 6.65/6.82 Following clause subsumed by 59 during input processing: 0 [] c_member(A,B,c_Relation_ORange(C,A,D))| -c_member(tc_prod(C,A),c_Product__Type_OPair(C,A,E,B),D).
% 6.65/6.82 ** KEPT (pick-wt=43): 66 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Wellfounded_Olex__prod(A,B,G,H))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),G)|C=E.
% 6.65/6.82 ** KEPT (pick-wt=50): 67 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Wellfounded_Olex__prod(A,B,G,H))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),G)|c_member(tc_prod(B,B),c_Product__Type_OPair(B,B,D,F),H).
% 6.65/6.82 ** KEPT (pick-wt=40): 68 [] c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Wellfounded_Olex__prod(A,B,G,H))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),G).
% 6.65/6.82 ** KEPT (pick-wt=43): 69 [] c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Wellfounded_Olex__prod(A,B,G,H))|C!=E| -c_member(tc_prod(B,B),c_Product__Type_OPair(B,B,D,F),H).
% 6.65/6.82 ** KEPT (pick-wt=21): 70 [] -c_member(A,B,c_Relation_ORange(C,A,D))|c_member(tc_prod(C,A),c_Product__Type_OPair(C,A,$f15(D,C,B,A),B),D).
% 6.65/6.82 ** KEPT (pick-wt=21): 71 [] -c_member(A,B,c_Relation_ODomain(A,C,D))|c_member(tc_prod(A,C),c_Product__Type_OPair(A,C,B,$f16(D,C,B,A)),D).
% 6.65/6.82 ** KEPT (pick-wt=18): 72 [] -c_Relation_Orefl__on(A,B,C)| -c_member(A,D,B)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,D),C).
% 6.65/6.82 ** KEPT (pick-wt=18): 73 [] -c_Relation_Orefl__on(A,B,C)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,E),C)|c_member(A,D,B).
% 6.65/6.82 ** KEPT (pick-wt=18): 74 [] -c_Relation_Orefl__on(A,B,C)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,E),C)|c_member(A,E,B).
% 6.65/6.82 ** KEPT (pick-wt=28): 76 [copy,75,flip.2] -c_Recdef_Owfrec__rel(A,B,C,D,E,hAPP(hAPP(D,F),E))|hAPP(hAPP(D,$f17(F,E,D,C,B,A)),E)=hAPP(hAPP(D,F),E).
% 6.65/6.82 ** KEPT (pick-wt=36): 77 [] -c_Recdef_Owfrec__rel(A,B,C,D,E,hAPP(hAPP(D,F),E))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,G,E),C)|c_Recdef_Owfrec__rel(A,B,C,D,G,hAPP($f17(F,E,D,C,B,A),G)).
% 6.65/6.82 ** KEPT (pick-wt=39): 78 [] c_Recdef_Owfrec__rel(A,B,C,D,E,hAPP(hAPP(D,F),E))|hAPP(hAPP(D,F),E)!=hAPP(hAPP(D,G),E)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f18(F,E,D,C,B,A,G),E),C).
% 6.65/6.82 ** KEPT (pick-wt=45): 79 [] c_Recdef_Owfrec__rel(A,B,C,D,E,hAPP(hAPP(D,F),E))|hAPP(hAPP(D,F),E)!=hAPP(hAPP(D,G),E)| -c_Recdef_Owfrec__rel(A,B,C,D,$f18(F,E,D,C,B,A,G),hAPP(G,$f18(F,E,D,C,B,A,G))).
% 6.65/6.82 ** KEPT (pick-wt=27): 80 [] -c_Relation_Osingle__valued(A,B,C)| -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,D,E),C)| -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,D,F),C)|E=F.
% 6.65/6.82 Following clause subsumed by 80 during input processing: 0 [] -c_Relation_Osingle__valued(A,B,C)| -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,D,E),C)| -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,D,F),C)|E=F.
% 6.65/6.82 ** KEPT (pick-wt=13): 81 [] c_Relation_Osingle__valued(A,B,C)|$f20(C,B,A)!=$f19(C,B,A).
% 6.65/6.82 ** KEPT (pick-wt=22): 82 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)|hAPP(c_Recdef_Ocut(A,E,F,D,C),B)=hAPP(F,B).
% 6.65/6.82 ** KEPT (pick-wt=11): 83 [] -c_Relation_Orefl__on(A,B,c_Relation_Oconverse(A,A,C))|c_Relation_Orefl__on(A,B,C).
% 6.65/6.82 ** KEPT (pick-wt=11): 84 [] c_Relation_Orefl__on(A,B,c_Relation_Oconverse(A,A,C))| -c_Relation_Orefl__on(A,B,C).
% 6.65/6.82 Following clause subsumed by 82 during input processing: 0 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)|hAPP(c_Recdef_Ocut(A,E,F,D,C),B)=hAPP(F,B).
% 6.65/6.82 ** KEPT (pick-wt=30): 85 [] c_Recdef_Ocut(A,B,C,D,E)!=c_Recdef_Ocut(A,B,F,D,E)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,G,E),D)|hAPP(C,G)=hAPP(F,G).
% 6.65/6.82 ** KEPT (pick-wt=32): 86 [] c_Recdef_Ocut(A,B,C,D,E)=c_Recdef_Ocut(A,B,F,D,E)|hAPP(C,$f22(F,E,D,C,B,A))!=hAPP(F,$f22(F,E,D,C,B,A)).
% 6.65/6.82 ** KEPT (pick-wt=20): 88 [copy,87,flip.2] -c_Recdef_Owfrec__rel(A,B,C,D,E,F)|hAPP(hAPP(D,$f23(F,E,D,C,B,A)),E)=F.
% 6.65/6.82 ** KEPT (pick-wt=32): 89 [] -c_Recdef_Owfrec__rel(A,B,C,D,E,F)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,G,E),C)|c_Recdef_Owfrec__rel(A,B,C,D,G,hAPP($f23(F,E,D,C,B,A),G)).
% 6.65/6.82 ** KEPT (pick-wt=31): 90 [] c_Recdef_Owfrec__rel(A,B,C,D,E,F)|F!=hAPP(hAPP(D,G),E)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f24(F,E,D,C,B,A,G),E),C).
% 6.65/6.82 ** KEPT (pick-wt=37): 91 [] c_Recdef_Owfrec__rel(A,B,C,D,E,F)|F!=hAPP(hAPP(D,G),E)| -c_Recdef_Owfrec__rel(A,B,C,D,$f24(F,E,D,C,B,A,G),hAPP(G,$f24(F,E,D,C,B,A,G))).
% 6.65/6.82 ** KEPT (pick-wt=32): 92 [] -c_Recdef_Owfrec__rel(A,B,C,D,$f25(E,D,B,C,F,A),hAPP(E,$f25(E,D,B,C,F,A)))|c_Recdef_Owfrec__rel(A,B,C,D,F,hAPP(hAPP(D,E),F)).
% 6.65/6.82 ** KEPT (pick-wt=13): 93 [] $f27(A,B,C)!=$f26(A,B,C)|c_Relation_Osingle__valued(C,B,A).
% 6.65/6.82 ** KEPT (pick-wt=22): 94 [] -c_member(A,B,c_Wellfounded_Oacc(A,C))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,B),C)|c_member(A,D,c_Wellfounded_Oacc(A,C)).
% 6.65/6.82 ** KEPT (pick-wt=15): 95 [] c_member(A,B,c_Wellfounded_Oacc(A,C))| -c_member(A,$f29(C,B,A),c_Wellfounded_Oacc(A,C)).
% 6.65/6.82 Following clause subsumed by 94 during input processing: 0 [] -c_member(A,B,c_Wellfounded_Oacc(A,C))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,B),C)|c_member(A,D,c_Wellfounded_Oacc(A,C)).
% 6.65/6.82 ** KEPT (pick-wt=14): 96 [] c_Product__Type_OPair(A,B,C,D)!=c_Product__Type_OPair(A,B,E,F)|C=E.
% 6.65/6.82 ** KEPT (pick-wt=14): 97 [] c_Product__Type_OPair(A,B,C,D)!=c_Product__Type_OPair(A,B,E,F)|D=F.
% 6.65/6.82 Following clause subsumed by 96 during input processing: 0 [] c_Product__Type_OPair(A,B,C,D)!=c_Product__Type_OPair(A,B,E,F)|C=E.
% 6.65/6.82 Following clause subsumed by 97 during input processing: 0 [] c_Product__Type_OPair(A,B,C,D)!=c_Product__Type_OPair(A,B,E,F)|D=F.
% 6.65/6.82 ** KEPT (pick-wt=17): 98 [] c_Product__Type_OPair(A,B,C,D)=c_Product__Type_OPair(A,B,E,F)|C!=E|D!=F.
% 6.65/6.82 ** KEPT (pick-wt=14): 99 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Relation_OId(A))|B=C.
% 6.65/6.82 ** KEPT (pick-wt=14): 100 [] c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Relation_OId(A))|B!=C.
% 6.65/6.82 ** KEPT (pick-wt=15): 101 [] -hBOOL(hAPP(A,$f30(B,C,A)))|hBOOL(hAPP(A,c_Product__Type_OPair(C,B,D,E))).
% 6.65/6.82 ** KEPT (pick-wt=18): 102 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Product__Type_OPair(C,D,$f32(D,C,A),$f31(D,C,A)))).
% 6.65/6.82 ** KEPT (pick-wt=15): 103 [] c_member(A,B,c_Wellfounded_Oacc(A,C))| -c_member(A,$f33(C,B,A),c_Wellfounded_Oacc(A,C)).
% 6.65/6.82 ** KEPT (pick-wt=15): 104 [] -c_member(A,$f34(B,C,A),c_Wellfounded_Oacc(A,B))|c_member(A,C,c_Wellfounded_Oacc(A,B)).
% 6.80/6.82 ** KEPT (pick-wt=18): 106 [copy,105,flip.2] -c_member(tc_prod(A,A),B,c_Relation_OId(A))|c_Product__Type_OPair(A,A,$f35(B,A),$f35(B,A))=B.
% 6.80/6.82 ** KEPT (pick-wt=24): 107 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -c_member(A,C,c_Wellfounded_Oacc(A,D))|c_member(A,B,c_Wellfounded_Oacc(A,D)).
% 6.80/6.82 Following clause subsumed by 107 during input processing: 0 [] -c_member(A,B,c_Wellfounded_Oacc(A,C))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,B),c_Transitive__Closure_Ortrancl(A,C))|c_member(A,D,c_Wellfounded_Oacc(A,C)).
% 6.80/6.82 ** KEPT (pick-wt=16): 108 [] -hBOOL(hAPP(A,c_Product__Type_OPair(B,C,D,E)))|hBOOL(c_Product__Type_Ocurry(B,C,tc_HOL_Obool,A,D,E)).
% 6.80/6.82 ** KEPT (pick-wt=16): 109 [] -hBOOL(c_Product__Type_Ocurry(A,B,tc_HOL_Obool,C,D,E))|hBOOL(hAPP(C,c_Product__Type_OPair(A,B,D,E))).
% 6.80/6.82 Following clause subsumed by 109 during input processing: 0 [] -hBOOL(c_Product__Type_Ocurry(A,B,tc_HOL_Obool,C,D,E))|hBOOL(hAPP(C,c_Product__Type_OPair(A,B,D,E))).
% 6.80/6.82 ** KEPT (pick-wt=14): 110 [] -c_member(tc_prod(A,A),B,C)|c_member(tc_prod(A,A),B,c_Transitive__Closure_Ortrancl(A,C)).
% 6.80/6.82 ** KEPT (pick-wt=22): 111 [] c_member(A,B,c_Relation_ODomain(A,A,C))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,D),c_Transitive__Closure_Ortrancl(A,C))|B=D.
% 6.80/6.82 ** KEPT (pick-wt=22): 112 [] c_member(A,B,c_Relation_ODomain(A,A,C))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,D),c_Transitive__Closure_Ortrancl(A,C))|B!=D.
% 6.80/6.82 ** KEPT (pick-wt=52): 113 [] -c_Relation_Osingle__valued(A,A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,D),c_Transitive__Closure_Ortrancl(A,B))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Ortrancl(A,B))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,E),c_Transitive__Closure_Ortrancl(A,B))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,E,D),c_Transitive__Closure_Ortrancl(A,B)).
% 6.80/6.82 ** KEPT (pick-wt=27): 114 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),c_Transitive__Closure_Ortrancl(A,c_Relation_Oconverse(A,A,D))).
% 6.80/6.82 ** KEPT (pick-wt=27): 115 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,c_Relation_Oconverse(A,A,D)))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=34): 116 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Ortrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=34): 117 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=36): 118 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Ortrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=88): 119 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,C),D))|c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,$f39(H,G,F,E,D,C,B,A),$f38(H,G,F,E,D,C,B,A))),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))|hBOOL(hAPP(hAPP(H,E),F)).
% 6.80/6.82 ** KEPT (pick-wt=100): 120 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,C),D))|c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,$f39(H,G,F,E,D,C,B,A),$f38(H,G,F,E,D,C,B,A)),c_Product__Type_OPair(A,B,$f37(H,G,F,E,D,C,B,A),$f36(H,G,F,E,D,C,B,A))),G)|hBOOL(hAPP(hAPP(H,E),F)).
% 6.80/6.82 ** KEPT (pick-wt=64): 121 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,C),D))|hBOOL(hAPP(hAPP(H,$f39(H,G,F,E,D,C,B,A)),$f38(H,G,F,E,D,C,B,A)))|hBOOL(hAPP(hAPP(H,E),F)).
% 6.80/6.82 ** KEPT (pick-wt=64): 122 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,C),D))| -hBOOL(hAPP(hAPP(H,$f37(H,G,F,E,D,C,B,A)),$f36(H,G,F,E,D,C,B,A)))|hBOOL(hAPP(hAPP(H,E),F)).
% 6.80/6.82 ** KEPT (pick-wt=100): 123 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,E),F))|c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,$f43(H,G,F,E,D,C,B,A),$f42(H,G,F,E,D,C,B,A)),c_Product__Type_OPair(A,B,$f41(H,G,F,E,D,C,B,A),$f40(H,G,F,E,D,C,B,A))),G)|hBOOL(hAPP(hAPP(H,C),D)).
% 6.80/6.82 ** KEPT (pick-wt=88): 124 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,E),F))|c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,$f41(H,G,F,E,D,C,B,A),$f40(H,G,F,E,D,C,B,A)),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))|hBOOL(hAPP(hAPP(H,C),D)).
% 6.80/6.82 ** KEPT (pick-wt=64): 125 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,E),F))|hBOOL(hAPP(hAPP(H,$f41(H,G,F,E,D,C,B,A)),$f40(H,G,F,E,D,C,B,A)))|hBOOL(hAPP(hAPP(H,C),D)).
% 6.80/6.82 ** KEPT (pick-wt=64): 126 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))| -hBOOL(hAPP(hAPP(H,E),F))| -hBOOL(hAPP(hAPP(H,$f43(H,G,F,E,D,C,B,A)),$f42(H,G,F,E,D,C,B,A)))|hBOOL(hAPP(hAPP(H,C),D)).
% 6.80/6.82 ** KEPT (pick-wt=81): 127 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))|c_Product__Type_OPair(A,B,C,D)=c_Product__Type_OPair(A,B,E,F)|c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,$f45(G,F,E,D,C,B,A),$f44(G,F,E,D,C,B,A))),G).
% 6.80/6.82 ** KEPT (pick-wt=85): 128 [] -c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G))|c_Product__Type_OPair(A,B,C,D)=c_Product__Type_OPair(A,B,E,F)|c_member(tc_prod(tc_prod(A,B),tc_prod(A,B)),c_Product__Type_OPair(tc_prod(A,B),tc_prod(A,B),c_Product__Type_OPair(A,B,$f45(G,F,E,D,C,B,A),$f44(G,F,E,D,C,B,A)),c_Product__Type_OPair(A,B,E,F)),c_Transitive__Closure_Ortrancl(tc_prod(A,B),G)).
% 6.80/6.82 ** KEPT (pick-wt=31): 129 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B=C|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,$f46(D,C,B,A)),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=29): 130 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B=C|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f46(D,C,B,A),C),D).
% 6.80/6.82 ** KEPT (pick-wt=29): 131 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B=C|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,$f47(D,C,B,A)),D).
% 6.80/6.82 ** KEPT (pick-wt=31): 132 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B=C|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f47(D,C,B,A),C),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=40): 133 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,C))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f49(E,D,C,B,A),$f48(E,D,C,B,A)),D)|hBOOL(hAPP(E,B)).
% 6.80/6.82 ** KEPT (pick-wt=37): 134 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,C))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f48(E,D,C,B,A),C),c_Transitive__Closure_Ortrancl(A,D))|hBOOL(hAPP(E,B)).
% 6.80/6.82 ** KEPT (pick-wt=29): 135 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,C))|hBOOL(hAPP(E,$f48(E,D,C,B,A)))|hBOOL(hAPP(E,B)).
% 6.80/6.82 ** KEPT (pick-wt=29): 136 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,C))| -hBOOL(hAPP(E,$f49(E,D,C,B,A)))|hBOOL(hAPP(E,B)).
% 6.80/6.82 ** KEPT (pick-wt=37): 137 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,B))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,$f51(E,D,C,B,A)),c_Transitive__Closure_Ortrancl(A,D))|hBOOL(hAPP(E,C)).
% 6.80/6.82 ** KEPT (pick-wt=40): 138 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,B))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f51(E,D,C,B,A),$f50(E,D,C,B,A)),D)|hBOOL(hAPP(E,C)).
% 6.80/6.82 ** KEPT (pick-wt=29): 139 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,B))|hBOOL(hAPP(E,$f51(E,D,C,B,A)))|hBOOL(hAPP(E,C)).
% 6.80/6.82 ** KEPT (pick-wt=29): 140 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -hBOOL(hAPP(E,B))| -hBOOL(hAPP(E,$f50(E,D,C,B,A)))|hBOOL(hAPP(E,C)).
% 6.80/6.82 ** KEPT (pick-wt=8): 141 [] -c_Wellfounded_Oacyclic(A,B)|c_Relation_Oantisym(A,c_Transitive__Closure_Ortrancl(A,B)).
% 6.80/6.82 ** KEPT (pick-wt=9): 142 [] -c_Wellfounded_Oacyclic(A,c_Relation_Oconverse(A,A,B))|c_Wellfounded_Oacyclic(A,B).
% 6.80/6.82 ** KEPT (pick-wt=9): 143 [] c_Wellfounded_Oacyclic(A,c_Relation_Oconverse(A,A,B))| -c_Wellfounded_Oacyclic(A,B).
% 6.80/6.82 ** KEPT (pick-wt=15): 144 [] -c_Wellfounded_Oacyclic(A,c_Set_Oinsert(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D))|c_Wellfounded_Oacyclic(A,D).
% 6.80/6.82 ** KEPT (pick-wt=24): 145 [] -c_Wellfounded_Oacyclic(A,c_Set_Oinsert(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=27): 146 [] c_Wellfounded_Oacyclic(A,c_Set_Oinsert(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D))| -c_Wellfounded_Oacyclic(A,D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=24): 147 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.82 ** KEPT (pick-wt=15): 148 [] -c_Wellfounded_Oacyclic(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,C),c_Transitive__Closure_Otrancl(A,B)).
% 6.80/6.82 ** KEPT (pick-wt=30): 149 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Relation_Oconverse(A,A,c_Transitive__Closure_Otrancl(A,D)))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,c_Relation_Oconverse(A,A,D))).
% 6.80/6.82 ** KEPT (pick-wt=30): 150 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,c_Relation_Oconverse(A,A,D)))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Relation_Oconverse(A,A,c_Transitive__Closure_Otrancl(A,D))).
% 6.80/6.82 ** KEPT (pick-wt=24): 151 [] -c_member(A,B,C)| -c_member(D,E,hAPP(F,B))|c_member(tc_prod(A,D),c_Product__Type_OPair(A,D,B,E),c_Product__Type_OSigma(A,D,C,F)).
% 6.80/6.83 ** KEPT (pick-wt=36): 152 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=11): 153 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 6.80/6.83 ** KEPT (pick-wt=10): 154 [] A!=B|c_member(C,A,c_Set_Oinsert(C,B,D)).
% 6.80/6.83 ** KEPT (pick-wt=14): 155 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 6.80/6.83 ** KEPT (pick-wt=22): 156 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=14): 157 [] -hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B=D|hBOOL(hAPP(C,D)).
% 6.80/6.83 ** KEPT (pick-wt=10): 158 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B!=D.
% 6.80/6.83 ** KEPT (pick-wt=11): 159 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))| -hBOOL(hAPP(C,D)).
% 6.80/6.83 ** KEPT (pick-wt=10): 160 [] -c_member(A,B,C)|c_Set_Oinsert(A,B,C)=C.
% 6.80/6.83 Following clause subsumed by 153 during input processing: 0 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 6.80/6.83 ** KEPT (pick-wt=20): 161 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)!=c_Set_Oinsert(A,B,D)|C=D.
% 6.80/6.83 ** KEPT (pick-wt=20): 162 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)=c_Set_Oinsert(A,B,D)|C!=D.
% 6.80/6.83 Following clause subsumed by 155 during input processing: 0 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 6.80/6.83 Following clause subsumed by 154 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))|B!=C.
% 6.80/6.83 Following clause subsumed by 153 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))| -c_member(A,B,D).
% 6.80/6.83 ** KEPT (pick-wt=14): 163 [] -c_member(tc_prod(A,A),B,C)|c_member(tc_prod(A,A),B,c_Transitive__Closure_Otrancl(A,C)).
% 6.80/6.83 ** KEPT (pick-wt=36): 164 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=34): 165 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=34): 166 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=32): 167 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=18): 168 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OSigma(A,B,E,F))|c_member(A,C,E).
% 6.80/6.83 ** KEPT (pick-wt=20): 169 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OSigma(A,B,E,F))|c_member(B,D,hAPP(F,C)).
% 6.80/6.83 Following clause subsumed by 169 during input processing: 0 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OSigma(A,B,E,F))|c_member(B,D,hAPP(F,C)).
% 6.80/6.83 Following clause subsumed by 168 during input processing: 0 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OSigma(A,B,E,F))|c_member(A,C,E).
% 6.80/6.83 Following clause subsumed by 168 during input processing: 0 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OSigma(A,B,E,F))|c_member(A,C,E).
% 6.80/6.83 Following clause subsumed by 169 during input processing: 0 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OSigma(A,B,E,F))|c_member(B,D,hAPP(F,C)).
% 6.80/6.83 Following clause subsumed by 151 during input processing: 0 [] c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),c_Product__Type_OSigma(A,B,E,F))| -c_member(A,C,E)| -c_member(B,D,hAPP(F,C)).
% 6.80/6.83 ** KEPT (pick-wt=27): 170 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B=C|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=15): 171 [] c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B!=C.
% 6.80/6.83 Following clause subsumed by 147 during input processing: 0 [] c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B=C| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=34): 172 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Ortrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 Following clause subsumed by 170 during input processing: 0 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))|B=C|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=34): 173 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Ortrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=36): 174 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,E),c_Transitive__Closure_Ortrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,E),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=19): 175 [] -c_member(tc_prod(A,B),C,c_Product__Type_OSigma(A,B,D,E))|c_member(A,$f54(E,D,C,B,A),D).
% 6.80/6.83 ** KEPT (pick-wt=26): 176 [] -c_member(tc_prod(A,B),C,c_Product__Type_OSigma(A,B,D,E))|c_member(B,$f53(E,D,C,B,A),hAPP(E,$f54(E,D,C,B,A))).
% 6.80/6.83 ** KEPT (pick-wt=27): 178 [copy,177,flip.2] -c_member(tc_prod(A,B),C,c_Product__Type_OSigma(A,B,D,E))|c_Product__Type_OPair(A,B,$f54(E,D,C,B,A),$f53(E,D,C,B,A))=C.
% 6.80/6.83 ** KEPT (pick-wt=28): 179 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,$f56(D,C,B,A)),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=26): 180 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f56(D,C,B,A),C),D).
% 6.80/6.83 ** KEPT (pick-wt=26): 181 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,$f57(D,C,B,A)),D).
% 6.80/6.83 ** KEPT (pick-wt=28): 182 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f57(D,C,B,A),C),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=15): 183 [] -c_Wellfounded_Owf(A,c_Set_Oinsert(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D))|c_Wellfounded_Owf(A,D).
% 6.80/6.83 ** KEPT (pick-wt=24): 184 [] -c_Wellfounded_Owf(A,c_Set_Oinsert(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=27): 185 [] c_Wellfounded_Owf(A,c_Set_Oinsert(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D))| -c_Wellfounded_Owf(A,D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),c_Transitive__Closure_Ortrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=38): 186 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,$f58(D,C,B,A)),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=36): 187 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f58(D,C,B,A),C),D).
% 6.80/6.83 ** KEPT (pick-wt=36): 188 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,$f59(D,C,B,A)),D).
% 6.80/6.83 ** KEPT (pick-wt=38): 189 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),c_Transitive__Closure_Otrancl(A,D))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),D)|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f59(D,C,B,A),C),c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=11): 190 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_Owf(C,hAPP(c_Relation_Oinv__image(A,C,B),D)).
% 6.80/6.83 ** KEPT (pick-wt=15): 191 [] -c_Wellfounded_Owf(A,B)| -c_Wellfounded_Owf(C,D)|c_Wellfounded_Owf(tc_prod(A,C),c_Wellfounded_Olex__prod(A,C,B,D)).
% 6.80/6.83 ** KEPT (pick-wt=8): 192 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_Owf(A,c_Transitive__Closure_Otrancl(A,B)).
% 6.80/6.83 ** KEPT (pick-wt=6): 193 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_Oacyclic(A,B).
% 6.80/6.83 ** KEPT (pick-wt=13): 194 [] -c_Wellfounded_Owf(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,C),B).
% 6.80/6.83 ** KEPT (pick-wt=23): 195 [] -c_Wellfounded_Owf(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,D),B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,C),B).
% 6.80/6.83 Following clause subsumed by 195 during input processing: 0 [] -c_Wellfounded_Owf(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,D),B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,D,C),B).
% 6.80/6.83 Following clause subsumed by 194 during input processing: 0 [] -c_Wellfounded_Owf(A,B)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,C),B).
% 6.80/6.83 ** KEPT (pick-wt=9): 196 [] -c_Wellfounded_Owf(A,B)|c_member(A,C,c_Wellfounded_Oacc(A,B)).
% 6.80/6.83 Following clause subsumed by 196 during input processing: 0 [] -c_Wellfounded_Owf(A,B)|c_member(A,C,c_Wellfounded_Oacc(A,B)).
% 6.80/6.83 ** KEPT (pick-wt=11): 197 [] c_Wellfounded_Owf(A,B)| -c_member(A,$f60(B,A),c_Wellfounded_Oacc(A,B)).
% 6.80/6.83 ** KEPT (pick-wt=14): 198 [] -c_Wellfounded_Owf(A,c_Relation_Oconverse(A,A,B))|c_Wellfounded_Owf(A,c_Relation_Oconverse(A,A,c_Transitive__Closure_Otrancl(A,B))).
% 6.80/6.83 ** KEPT (pick-wt=25): 200 [copy,199,flip.2] -c_Wellfounded_Owf(A,B)|hAPP(hAPP(C,c_Recdef_Ocut(A,D,c_Recdef_Owfrec(A,D,B,C),B,E)),E)=hAPP(c_Recdef_Owfrec(A,D,B,C),E).
% 6.80/6.83 Following clause subsumed by 200 during input processing: 0 [flip.2] -c_Wellfounded_Owf(A,B)|hAPP(hAPP(D,c_Recdef_Ocut(A,C,c_Recdef_Owfrec(A,C,B,D),B,E)),E)=hAPP(c_Recdef_Owfrec(A,C,B,D),E).
% 6.80/6.83 ** KEPT (pick-wt=24): 202 [copy,201,flip.3] A!=c_Recdef_Owfrec(B,C,D,E)| -c_Wellfounded_Owf(B,D)|hAPP(hAPP(E,c_Recdef_Ocut(B,C,A,D,F)),F)=hAPP(A,F).
% 6.80/6.83 ** KEPT (pick-wt=14): 203 [] -c_Wellfounded_Owf(A,B)| -c_member(A,C,D)|c_member(A,$f61(B,A,D),D).
% 6.80/6.83 ** KEPT (pick-wt=20): 205 [copy,204,factor_simp] -c_Wellfounded_Owf(A,B)| -c_member(A,C,D)| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,$f61(B,A,D)),B).
% 6.80/6.83 ** KEPT (pick-wt=22): 206 [] c_Wellfounded_Owf(A,B)| -c_member(A,C,$f64(B,A))|c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f63(B,A,C),C),B).
% 6.80/6.83 ** KEPT (pick-wt=18): 207 [] c_Wellfounded_Owf(A,B)| -c_member(A,C,$f64(B,A))|c_member(A,$f63(B,A,C),$f64(B,A)).
% 6.80/6.83 ** KEPT (pick-wt=9): 208 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_OwfP(A,c_FunDef_Oin__rel(A,A,B)).
% 6.80/6.83 ** KEPT (pick-wt=18): 209 [] -c_Wellfounded_Owf(A,hAPP(B,$f65(C,B,A,D)))|c_Wellfounded_Owf(tc_prod(C,A),c_Recdef_Osame__fst(C,A,D,B)).
% 6.80/6.83 ** KEPT (pick-wt=11): 210 [] -c_member(A,$f66(B,A),c_Wellfounded_Oacc(A,B))|c_Wellfounded_Owf(A,B).
% 6.80/6.83 ** KEPT (pick-wt=21): 211 [] -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),hAPP(c_Wellfounded_Omeasure(A),D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(D,B),hAPP(D,C)).
% 6.80/6.83 ** KEPT (pick-wt=21): 212 [] c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,B,C),hAPP(c_Wellfounded_Omeasure(A),D))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(D,B),hAPP(D,C)).
% 6.80/6.83 ** KEPT (pick-wt=33): 213 [] c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,$f67(B,C,D,A),$f67(B,C,D,A)),c_Transitive__Closure_Otrancl(A,D))| -c_member(tc_prod(A,A),c_Product__Type_OPair(A,A,C,B),D)|C!=B.
% 6.80/6.83 ** KEPT (pick-wt=14): 214 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,B),c_Wellfounded_Oless__than)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=14): 215 [] c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,B),c_Wellfounded_Oless__than)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=21): 216 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C))|c_member(tc_prod(D,D),c_Product__Type_OPair(D,D,B,C),c_Wellfounded_Omlex__prod(D,A,E)).
% 6.80/6.83 ** KEPT (pick-wt=14): 217 [] -c_Finite__Set_Ofinite(tc_prod(A,A),B)| -c_Wellfounded_Oacyclic(A,B)|c_Wellfounded_Owf(A,c_Relation_Oconverse(A,A,B)).
% 6.80/6.83 ** KEPT (pick-wt=10): 218 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_Owf(tc_fun(A,tc_HOL_Obool),c_Wellfounded_Omin__ext(A,B)).
% 6.80/6.83 ** KEPT (pick-wt=11): 219 [] -c_Finite__Set_Ofinite(tc_prod(A,B),C)|c_Finite__Set_Ofinite(B,c_Relation_ORange(A,B,C)).
% 6.80/6.83 ** KEPT (pick-wt=11): 220 [] -c_Finite__Set_Ofinite(tc_prod(A,B),C)|c_Finite__Set_Ofinite(A,c_Relation_ODomain(A,B,C)).
% 6.80/6.83 ** KEPT (pick-wt=12): 221 [] -c_Finite__Set_Ofinite(tc_prod(A,A),c_Transitive__Closure_Otrancl(A,B))|c_Finite__Set_Ofinite(tc_prod(A,A),B).
% 6.80/6.83 ** KEPT (pick-wt=12): 222 [] c_Finite__Set_Ofinite(tc_prod(A,A),c_Transitive__Closure_Otrancl(A,B))| -c_Finite__Set_Ofinite(tc_prod(A,A),B).
% 6.80/6.83 ** KEPT (pick-wt=13): 223 [] -c_Finite__Set_Ofinite(tc_prod(A,B),c_Relation_Oconverse(B,A,C))|c_Finite__Set_Ofinite(tc_prod(B,A),C).
% 6.80/6.83 ** KEPT (pick-wt=13): 224 [] c_Finite__Set_Ofinite(tc_prod(A,B),c_Relation_Oconverse(B,A,C))| -c_Finite__Set_Ofinite(tc_prod(B,A),C).
% 6.80/6.83 Following clause subsumed by 193 during input processing: 0 [] -c_Finite__Set_Ofinite(tc_prod(A,A),B)| -c_Wellfounded_Owf(A,B)|c_Wellfounded_Oacyclic(A,B).
% 6.80/6.83 ** KEPT (pick-wt=11): 225 [] -c_Finite__Set_Ofinite(tc_prod(A,A),B)|c_Wellfounded_Owf(A,B)| -c_Wellfounded_Oacyclic(A,B).
% 6.80/6.83 Following clause subsumed by 225 during input processing: 0 [] -c_Finite__Set_Ofinite(tc_prod(A,A),B)| -c_Wellfounded_Oacyclic(A,B)|c_Wellfounded_Owf(A,B).
% 6.80/6.83 ** KEPT (pick-wt=16): 226 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,B),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=16): 227 [] c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,B),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=9): 228 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_Owf(A,c_Wellfounded_Omlex__prod(A,C,B)).
% 6.80/6.83 ** KEPT (pick-wt=4): 229 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 6.80/6.83 ** KEPT (pick-wt=7): 230 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=7): 231 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 6.80/6.83 Following clause subsumed by 229 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 6.80/6.83 Following clause subsumed by 231 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 6.80/6.83 Following clause subsumed by 230 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 6.80/6.83 ** KEPT (pick-wt=9): 232 [] -c_Finite__Set_Ofinite(A,B)|c_Finite__Set_Ofinite(A,c_Set_Oinsert(A,C,B)).
% 6.80/6.83 ** KEPT (pick-wt=6): 233 [] -c_Nitpick_Owf_H(A,B)|c_Wellfounded_Oacyclic(A,B).
% 6.80/6.83 ** KEPT (pick-wt=10): 234 [] -c_Nitpick_Owf_H(A,B)|c_Finite__Set_Ofinite(tc_prod(A,A),B)|c_Nitpick_Ounknown(tc_HOL_Obool).
% 6.80/6.83 ** KEPT (pick-wt=11): 235 [] c_Nitpick_Owf_H(A,B)| -c_Wellfounded_Oacyclic(A,B)| -c_Finite__Set_Ofinite(tc_prod(A,A),B).
% 6.80/6.83 ** KEPT (pick-wt=8): 236 [] c_Nitpick_Owf_H(A,B)| -c_Wellfounded_Oacyclic(A,B)| -c_Nitpick_Ounknown(tc_HOL_Obool).
% 6.80/6.83 ** KEPT (pick-wt=9): 237 [] -c_Finite__Set_Ofinite(A,c_Set_Oinsert(A,B,C))|c_Finite__Set_Ofinite(A,C).
% 6.80/6.83 Following clause subsumed by 232 during input processing: 0 [] c_Finite__Set_Ofinite(A,c_Set_Oinsert(A,B,C))| -c_Finite__Set_Ofinite(A,C).
% 6.80/6.83 ** KEPT (pick-wt=10): 238 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_Owf(tc_fun(A,tc_HOL_Obool),c_Wellfounded_Omax__ext(A,B)).
% 6.80/6.83 ** KEPT (pick-wt=12): 239 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_member(tc_Nat_Onat,B,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,$f68(A)).
% 6.80/6.83 ** KEPT (pick-wt=9): 240 [] c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f69(A,B),B).
% 6.80/6.83 ** KEPT (pick-wt=5): 241 [] -class_Finite__Set_Ofinite(A)|c_Finite__Set_Ofinite(A,B).
% 6.80/6.83 Following clause subsumed by 241 during input processing: 0 [] -class_Finite__Set_Ofinite(A)|c_Finite__Set_Ofinite(A,B).
% 6.80/6.83 ** KEPT (pick-wt=30): 242 [] -c_Finite__Set_Ofolding__image__simple(A,B,C,D,E,F)| -c_Finite__Set_Ofinite(B,G)|c_member(B,H,G)|hAPP(F,c_Set_Oinsert(B,H,G))=hAPP(hAPP(C,hAPP(E,H)),hAPP(F,G)).
% 6.80/6.83 ** KEPT (pick-wt=30): 243 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,C),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,B,D)),c_FunDef_Opair__le_q).
% 6.80/6.83 ** KEPT (pick-wt=26): 244 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)| -c_Finite__Set_Ofinite(B,G)|hAPP(F,c_Set_Oinsert(B,H,G))=hAPP(hAPP(C,hAPP(E,H)),hAPP(F,G)).
% 6.80/6.83 ** KEPT (pick-wt=27): 245 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)| -c_Finite__Set_Ofinite(B,G)| -c_member(B,H,G)|hAPP(hAPP(C,hAPP(E,H)),hAPP(F,G))=hAPP(F,G).
% 6.80/6.83 ** KEPT (pick-wt=30): 246 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,C),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,B,D)),c_FunDef_Opair__less).
% 6.80/6.83 ** KEPT (pick-wt=14): 247 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)|hAPP(hAPP(C,G),G)=G.
% 6.80/6.83 ** KEPT (pick-wt=81): 248 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),A,B)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),C,A),c_FunDef_Opair__le_q)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),D,B),c_FunDef_Omax__weak)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),C,D),B),c_FunDef_Omax__weak).
% 6.80/6.83 ** KEPT (pick-wt=81): 249 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),A,B)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),A,C),c_FunDef_Opair__le_q)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),B,D),c_FunDef_Omin__weak)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),B,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),C,D)),c_FunDef_Omin__weak).
% 6.80/6.83 ** KEPT (pick-wt=81): 250 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),A,B)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),C,A),c_FunDef_Opair__less)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),D,B),c_FunDef_Omax__strict)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),C,D),B),c_FunDef_Omax__strict).
% 6.80/6.83 ** KEPT (pick-wt=81): 251 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),A,B)| -c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),A,C),c_FunDef_Opair__less)| -c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),B,D),c_FunDef_Omin__strict)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),B,c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat),C,D)),c_FunDef_Omin__strict).
% 6.80/6.83 ** KEPT (pick-wt=34): 252 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,C),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,B,D)),c_FunDef_Opair__less).
% 6.80/6.83 ** KEPT (pick-wt=7): 253 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=12): 254 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 6.80/6.83 ** KEPT (pick-wt=11): 255 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B.
% 6.80/6.83 ** KEPT (pick-wt=8): 256 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 Following clause subsumed by 253 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=11): 257 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 6.80/6.83 Following clause subsumed by 256 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 Following clause subsumed by 257 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 6.80/6.83 Following clause subsumed by 256 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 6.80/6.83 Following clause subsumed by 253 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 6.80/6.83 Following clause subsumed by 256 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 Following clause subsumed by 230 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 6.80/6.83 Following clause subsumed by 257 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B.
% 6.80/6.83 Following clause subsumed by 256 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=12): 258 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_member(tc_Nat_Onat,B,A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,$f70(A)).
% 6.80/6.83 ** KEPT (pick-wt=9): 259 [] c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f71(A,B),B).
% 6.80/6.83 ** KEPT (pick-wt=31): 260 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(A,B),hAPP(A,C))| -c_member(tc_prod(D,D),c_Product__Type_OPair(D,D,B,C),E)|c_member(tc_prod(D,D),c_Product__Type_OPair(D,D,B,C),c_Wellfounded_Omlex__prod(D,A,E)).
% 6.80/6.83 ** KEPT (pick-wt=16): 261 [] -c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,B),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=16): 262 [] c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,B),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 6.80/6.83 ** KEPT (pick-wt=34): 263 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,A,C),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat,B,D)),c_FunDef_Opair__le_q).
% 6.80/6.83 ** KEPT (pick-wt=6): 264 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B).
% 6.80/6.83 ** KEPT (pick-wt=10): 265 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.83 ** KEPT (pick-wt=10): 266 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.83 ** KEPT (pick-wt=14): 267 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 6.80/6.83 ** KEPT (pick-wt=12): 268 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B)|c_Finite__Set_Ofinite(A,C).
% 6.80/6.83 Following clause subsumed by 268 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Finite__Set_Ofinite(A,C)|c_Finite__Set_Ofinite(A,B).
% 6.80/6.83 Following clause subsumed by 267 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 6.80/6.83 Following clause subsumed by 267 during input processing: 0 [] -c_member(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_member(A,B,D).
% 6.80/6.83 Following clause subsumed by 267 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 6.80/6.83 ** KEPT (pick-wt=14): 269 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 6.80/6.83 ** KEPT (pick-wt=22): 270 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,c_Transitive__Closure_Ortrancl(A,C))|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(A,B),c_Transitive__Closure_Ortrancl(A,C)).
% 6.80/6.83 ** KEPT (pick-wt=25): 271 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Transitive__Closure_Ortrancl(A,B))|c_Transitive__Closure_Ortrancl(A,C)=c_Transitive__Closure_Ortrancl(A,B).
% 6.80/6.83 ** KEPT (pick-wt=20): 272 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(A,B),c_Transitive__Closure_Ortrancl(A,C)).
% 6.80/6.83 ** KEPT (pick-wt=14): 273 [] -c_Wellfounded_Owf(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,B)|c_Wellfounded_Owf(A,C).
% 6.80/6.83 ** KEPT (pick-wt=18): 274 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Wellfounded_Oacc(A,C),c_Wellfounded_Oacc(A,B)).
% 6.80/6.83 ** KEPT (pick-wt=20): 275 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,B),tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Relation_ODomain(A,B,C),c_Relation_ODomain(A,B,D)).
% 6.80/6.83 ** KEPT (pick-wt=18): 276 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,D,B),c_Set_Oinsert(A,D,C)).
% 6.80/6.83 ** KEPT (pick-wt=15): 277 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,D,C)).
% 6.80/6.83 ** KEPT (pick-wt=14): 278 [] -c_Wellfounded_OwfP(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_fun(A,tc_HOL_Obool)),C,B)|c_Wellfounded_OwfP(A,C).
% 6.80/6.83 ** KEPT (pick-wt=14): 279 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),B,C)| -c_Relation_Oantisym(A,C)|c_Relation_Oantisym(A,B).
% 6.80/6.83 ** KEPT (pick-wt=14): 280 [] -c_Wellfounded_Oacyclic(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,B)|c_Wellfounded_Oacyclic(A,C).
% 6.80/6.83 ** KEPT (pick-wt=16): 281 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,B),tc_HOL_Obool),C,D)| -c_Relation_Osingle__valued(A,B,D)|c_Relation_Osingle__valued(A,B,C).
% 6.80/6.83 ** KEPT (pick-wt=19): 282 [] c_member(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,D))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 6.80/6.83 Following clause subsumed by 277 during input processing: 0 [] c_member(A,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 6.80/6.83 ** KEPT (pick-wt=13): 283 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,C),D)|c_member(A,B,D).
% 6.80/6.83 ** KEPT (pick-wt=15): 284 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,C),D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 6.80/6.83 ** KEPT (pick-wt=19): 285 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,C),D)| -c_member(A,B,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 6.80/6.83 ** KEPT (pick-wt=24): 286 [] -c_member(tc_prod(A,A),B,c_Transitive__Closure_Otrancl(A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,D)|c_member(tc_prod(A,A),B,c_Transitive__Closure_Otrancl(A,D)).
% 6.80/6.83 ** KEPT (pick-wt=29): 287 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)| -c_Finite__Set_Ofinite(B,G)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),H,G)|hAPP(hAPP(C,hAPP(F,H)),hAPP(F,G))=hAPP(F,G).
% 6.80/6.83 ** KEPT (pick-wt=16): 288 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 6.80/6.83 ** KEPT (pick-wt=24): 289 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f72(D,C,B,A)),hAPP(D,$f72(D,C,B,A))).
% 6.80/6.83 ** KEPT (pick-wt=10): 290 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.83 ** KEPT (pick-wt=9): 291 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 6.80/6.83 ** KEPT (pick-wt=9): 292 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.83 ** KEPT (pick-wt=13): 293 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.83 ** KEPT (pick-wt=9): 294 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 6.80/6.83 Following clause subsumed by 288 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 6.80/6.83 Following clause subsumed by 293 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 6.80/6.83 Following clause subsumed by 291 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B)|C!=B.
% 6.80/6.83 ** KEPT (pick-wt=13): 295 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 6.80/6.83 ** KEPT (pick-wt=13): 296 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 6.80/6.84 ** KEPT (pick-wt=13): 297 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C!=D|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 6.80/6.84 ** KEPT (pick-wt=13): 298 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=D|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 6.80/6.84 Following clause subsumed by 293 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|B=C.
% 6.80/6.84 ** KEPT (pick-wt=14): 299 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 6.80/6.84 Following clause subsumed by 293 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 6.80/6.84 ** KEPT (pick-wt=14): 300 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 6.80/6.84 Following clause subsumed by 288 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 6.80/6.84 Following clause subsumed by 290 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=6): 301 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 6.80/6.84 ** KEPT (pick-wt=13): 302 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=9): 303 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 6.80/6.84 ** KEPT (pick-wt=9): 304 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 302 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|B=C.
% 6.80/6.84 ** KEPT (pick-wt=10): 305 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 303 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 6.80/6.84 Following clause subsumed by 302 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 302 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|C=B.
% 6.80/6.84 Following clause subsumed by 303 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B.
% 6.80/6.84 Following clause subsumed by 302 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=9): 306 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 6.80/6.84 ** KEPT (pick-wt=10): 307 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 307 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 306 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 6.80/6.84 ** KEPT (pick-wt=9): 308 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 6.80/6.84 Following clause subsumed by 307 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=10): 309 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=13): 310 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 6.80/6.84 ** KEPT (pick-wt=13): 311 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 6.80/6.84 ** KEPT (pick-wt=13): 312 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 6.80/6.84 ** KEPT (pick-wt=13): 313 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 6.80/6.84 ** KEPT (pick-wt=14): 314 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 6.80/6.84 ** KEPT (pick-wt=14): 315 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 6.80/6.84 Following clause subsumed by 307 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 302 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=25): 316 [] -c_member(tc_prod(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),B,C),c_Wellfounded_Ofinite__psubset(A))|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C).
% 6.80/6.84 ** KEPT (pick-wt=22): 317 [] -c_member(tc_prod(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),B,C),c_Wellfounded_Ofinite__psubset(A))|c_Finite__Set_Ofinite(A,C).
% 6.80/6.84 ** KEPT (pick-wt=28): 318 [] c_member(tc_prod(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),B,C),c_Wellfounded_Ofinite__psubset(A))| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_Finite__Set_Ofinite(A,C).
% 6.80/6.84 ** KEPT (pick-wt=14): 319 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 6.80/6.84 ** KEPT (pick-wt=14): 320 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 6.80/6.84 ** KEPT (pick-wt=14): 321 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 6.80/6.84 ** KEPT (pick-wt=14): 322 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 6.80/6.84 ** KEPT (pick-wt=13): 323 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 6.80/6.84 ** KEPT (pick-wt=13): 324 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C).
% 6.80/6.84 Following clause subsumed by 324 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 6.80/6.84 ** KEPT (pick-wt=13): 325 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 6.80/6.84 Following clause subsumed by 303 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 6.80/6.84 ** KEPT (pick-wt=10): 326 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 6.80/6.84 Following clause subsumed by 266 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 323 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 324 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C).
% 6.80/6.84 Following clause subsumed by 325 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 6.80/6.84 ** KEPT (pick-wt=13): 327 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 6.80/6.84 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.84 Following clause subsumed by 324 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 6.80/6.84 ** KEPT (pick-wt=10): 328 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 6.80/6.84 Following clause subsumed by 291 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 6.80/6.84 Following clause subsumed by 326 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 6.80/6.84 ** KEPT (pick-wt=10): 329 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=14): 330 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 6.80/6.84 Following clause subsumed by 328 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 6.80/6.84 Following clause subsumed by 306 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 6.80/6.84 Following clause subsumed by 324 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 6.80/6.84 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 265 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 Following clause subsumed by 266 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 6.80/6.84 ** KEPT (pick-wt=10): 331 [] -c_FunDef_Oreduction__pair(A,B)|c_FunDef_Oreduction__pair(C,c_FunDef_Orp__inv__image(A,C,B,D)).
% 6.80/6.84 ** KEPT (pick-wt=31): 332 [] -c_Wellfounded_Owf(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),c_Relation_Orel__comp(A,A,A,B,C),B)|c_FunDef_Oreduction__pair(A,c_Product__Type_OPair(tc_fun(tc_prod(A,A),tc_HOL_Obool),tc_fun(tc_prod(A,A),tc_HOL_Obool),B,C)).
% 6.80/6.84 ** KEPT (pick-wt=15): 333 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B)|B=C.
% 6.80/6.84 ** KEPT (pick-wt=7): 334 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 6.80/6.84 ** KEPT (pick-wt=35): 335 [] -c_member(tc_prod(A,B),c_Product__Type_OPair(A,B,C,D),E)| -c_member(tc_prod(B,F),c_Product__Type_OPair(B,F,D,G),H)|c_member(tc_prod(A,F),c_Product__Type_OPair(A,F,C,G),c_Relation_Orel__comp(A,B,F,E,H)).
% 6.80/6.84 ** KEPT (pick-wt=16): 336 [] A!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(B,B),tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(B,B),tc_HOL_Obool),A,C).
% 6.80/6.84 ** KEPT (pick-wt=15): 337 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=15): 338 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=9): 339 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 6.80/6.84 ** KEPT (pick-wt=9): 340 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 6.80/6.84 Following clause subsumed by 333 during input processing: 0 [] A=B| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 6.80/6.84 ** KEPT (pick-wt=14): 341 [] -hBOOL(hAPP(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,D)|hBOOL(hAPP(D,B)).
% 6.80/6.84 Following clause subsumed by 339 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 6.80/6.84 Following clause subsumed by 340 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 6.80/6.84 Following clause subsumed by 341 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -hBOOL(hAPP(B,D))|hBOOL(hAPP(C,D)).
% 6.80/6.84 ** KEPT (pick-wt=18): 342 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 6.80/6.84 ** KEPT (pick-wt=34): 343 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,B),tc_HOL_Obool),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(B,E),tc_HOL_Obool),F,G)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,E),tc_HOL_Obool),c_Relation_Orel__comp(A,B,E,C,F),c_Relation_Orel__comp(A,B,E,D,G)).
% 6.80/6.84 ** KEPT (pick-wt=20): 344 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_fun(B,tc_HOL_Obool)),C,D)| -hBOOL(hAPP(hAPP(C,E),F))|hBOOL(hAPP(hAPP(D,E),F)).
% 6.80/6.84 Following clause subsumed by 339 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 6.80/6.84 Following clause subsumed by 340 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 6.80/6.84 Following clause subsumed by 344 during input processing: 0 [] -hBOOL(hAPP(hAPP(A,B),C))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(D,tc_fun(E,tc_HOL_Obool)),A,F)|hBOOL(hAPP(hAPP(F,B),C)).
% 6.80/6.84 ** KEPT (pick-wt=27): 345 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|B=c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 6.80/6.84 ** KEPT (pick-wt=14): 346 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D).
% 6.80/6.84 ** KEPT (pick-wt=14): 347 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 6.80/6.84 ** KEPT (pick-wt=20): 348 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 6.80/6.84 ** KEPT (pick-wt=18): 349 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 6.80/6.84 ** KEPT (pick-wt=18): 350 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 6.80/6.84 ** KEPT (pick-wt=12): 351 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C).
% 6.80/6.84 ** KEPT (pick-wt=15): 352 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|B=C.
% 6.80/6.84 Following clause subsumed by 351 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C).
% 6.80/6.84 Following clause subsumed by 339 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 6.80/6.84 Following clause subsumed by 351 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C).
% 6.80/6.84 ** KEPT (pick-wt=9): 353 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 6.80/6.84 Following clause subsumed by 352 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|B=C.
% 6.80/6.84 ** KEPT (pick-wt=9): 354 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 6.80/6.84 ** KEPT (pick-wt=18): 355 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 6.80/6.84 ** KEPT (pick-wt=11): 356 [] -class_Orderings_Obot(A)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(B,A)),C)=c_Orderings_Obot__class_Obot(A).
% 6.80/6.84 ** KEPT (pick-wt=17): 357 [] c_Relation_ODomain(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|C=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,B),tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=17): 358 [] c_Relation_ODomain(A,B,C)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|C!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,B),tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=17): 359 [] c_Relation_ORange(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))|C=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,B),tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=17): 360 [] c_Relation_ORange(A,B,C)=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))|C!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,B),tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=9): 361 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_Oinsert(A,B,C).
% 6.80/6.84 ** KEPT (pick-wt=9): 362 [] c_Set_Oinsert(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=27): 363 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=D|B=E.
% 6.80/6.84 ** KEPT (pick-wt=27): 364 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=D|C=D.
% 6.80/6.84 ** KEPT (pick-wt=27): 365 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|C=E|B=E.
% 6.80/6.84 ** KEPT (pick-wt=27): 366 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|C=E|C=D.
% 6.80/6.84 ** KEPT (pick-wt=27): 367 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B!=D|C!=E.
% 6.80/6.84 ** KEPT (pick-wt=27): 368 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B!=E|C!=D.
% 6.80/6.84 ** KEPT (pick-wt=18): 369 [] c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))!=c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B=C.
% 6.80/6.84 ** KEPT (pick-wt=16): 370 [] c_Relation_Orel__comp(A,A,A,B,B)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(A,A),tc_HOL_Obool))|c_Wellfounded_Owf(A,B).
% 6.80/6.84 ** KEPT (pick-wt=11): 371 [] -c_Wellfounded_Owf(A,B)|c_Wellfounded_Owf(A,c_Relation_Orel__comp(A,A,A,B,B)).
% 6.80/6.84 ** KEPT (pick-wt=11): 372 [] c_Wellfounded_Owf(A,B)| -c_Wellfounded_Owf(A,c_Relation_Orel__comp(A,A,A,B,B)).
% 6.80/6.84 ** KEPT (pick-wt=10): 373 [] A!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))| -c_member(B,C,A).
% 6.80/6.84 Following clause subsumed by 334 during input processing: 0 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 6.80/6.84 Following clause subsumed by 373 during input processing: 0 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 6.80/6.84 Following clause subsumed by 373 during input processing:
% 6.80/6.84 Search stopped in tp_alloc by max_mem option.
% 6.80/6.84 0 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 6.80/6.84 ** KEPT (pick-wt=17): 374 [] -c_Relation_Osingle__valued(A,B,C)| -c_Relation_Osingle__valued(B,D,E)|c_Relation_Osingle__valued(A,D,c_Relation_Orel__comp(A,B,D,C,E)).
% 6.80/6.84 ** KEPT (pick-wt=7): 375 [] -class_Orderings_Obot(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Orderings_Obot__class_Obot(A),B).
% 6.80/6.84 ** KEPT (pick-wt=15): 376 [] -c_Finite__Set_Ofolding__image__simple(A,B,C,D,E,F)|hAPP(F,c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)))=D.
% 6.80/6.84 ** KEPT (pick-wt=13): 377 [] -c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=C.
% 6.80/6.84 Following clause subsumed by 154 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B!=C.
% 6.80/6.84 Following clause subsumed by 377 during input processing: 0 [] -c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=C.
% 6.80/6.84 ** KEPT (pick-wt=44): 378 [] -c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat),A)|A=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),A),c_FunDef_Omax__strict).
% 6.80/6.84 ** KEPT (pick-wt=36): 379 [] -c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat),A)|c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),A),c_FunDef_Omax__weak).
% 6.80/6.84 ** KEPT (pick-wt=20): 380 [] -c_Relation_Orefl__on(A,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_prod(A,A),tc_HOL_Obool),C,c_Relation_Orel__comp(A,A,A,c_Relation_Oconverse(A,A,C),C)).
% 6.80/6.84
% 6.80/6.84 Search stopped in tp_alloc by max_mem option.
% 6.80/6.84
% 6.80/6.84 ============ end of search ============
% 6.80/6.84
% 6.80/6.84 -------------- statistics -------------
% 6.80/6.84 clauses given 0
% 6.80/6.84 clauses generated 0
% 6.80/6.84 clauses kept 371
% 6.80/6.84 clauses forward subsumed 103
% 6.80/6.84 clauses back subsumed 0
% 6.80/6.84 Kbytes malloced 11718
% 6.80/6.84
% 6.80/6.84 ----------- times (seconds) -----------
% 6.80/6.84 user CPU time 0.11 (0 hr, 0 min, 0 sec)
% 6.80/6.84 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 6.80/6.84 wall-clock time 6 (0 hr, 0 min, 6 sec)
% 6.80/6.84
% 6.80/6.84 Process 11212 finished Wed Jul 27 09:07:58 2022
% 6.80/6.84 Otter interrupted
% 6.80/6.84 PROOF NOT FOUND
%------------------------------------------------------------------------------